TSTP Solution File: SEU388+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU388+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 16:31:19 EDT 2023
% Result : Theorem 0.23s 0.71s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU388+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.16/0.36 % Computer : n028.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu Aug 24 00:31:34 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.23/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.71 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.wcp6Feg75J/cvc5---1.0.5_20959.p...
% 0.23/0.71 ------- get file name : TPTP file name is SEU388+1
% 0.23/0.71 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_20959.smt2...
% 0.23/0.71 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.23/0.71 % SZS status Theorem for SEU388+1
% 0.23/0.71 % SZS output start Proof for SEU388+1
% 0.23/0.71 (
% 0.23/0.71 (let ((_let_1 (not (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (= (tptp.in C (tptp.neighborhood_system A B)) (tptp.point_neighbourhood C A B)))))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.topological_space B) (tptp.top_str B) (tptp.element C (tptp.the_carrier B))) (= (tptp.in A (tptp.a_2_0_yellow19 B C)) (exists ((D $$unsorted)) (and (tptp.point_neighbourhood D B C) (= A D)))))))) (let ((_let_3 (tptp.relation tptp.empty_set))) (let ((_let_4 (tptp.empty tptp.empty_set))) (let ((_let_5 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (= (tptp.neighborhood_system A B) (tptp.a_2_0_yellow19 A B)))))))) (let ((_let_6 (tptp.a_2_0_yellow19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_7 (tptp.neighborhood_system SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_8 (= _let_7 _let_6))) (let ((_let_9 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_7))) (let ((_let_10 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_6))) (let ((_let_11 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)))) (let ((_let_12 (not _let_11))) (let ((_let_13 (tptp.top_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_14 (not _let_13))) (let ((_let_15 (tptp.topological_space SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.empty_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_18 (or _let_17 _let_16 _let_14 _let_12 _let_8))) (let ((_let_19 (forall ((A $$unsorted) (BOUND_VARIABLE_2442 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.topological_space A)) (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_2442 (tptp.the_carrier A))) (= (tptp.neighborhood_system A BOUND_VARIABLE_2442) (tptp.a_2_0_yellow19 A BOUND_VARIABLE_2442)))))) (let ((_let_20 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_21 (tptp.point_neighbourhood SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_22 (= _let_9 _let_21))) (let ((_let_23 (or _let_17 _let_16 _let_14 _let_12 _let_22))) (let ((_let_24 (forall ((A $$unsorted) (BOUND_VARIABLE_3575 $$unsorted) (BOUND_VARIABLE_3573 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.topological_space A)) (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_3573 (tptp.the_carrier A))) (= (tptp.in BOUND_VARIABLE_3575 (tptp.neighborhood_system A BOUND_VARIABLE_3573)) (tptp.point_neighbourhood BOUND_VARIABLE_3575 A BOUND_VARIABLE_3573)))))) (let ((_let_25 (not _let_23))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (or))) (let ((_let_28 (not _let_24))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_26) :args (_let_28))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_24))) (REFL :args (_let_25)) :args _let_27)) _let_26 :args (_let_25 true _let_24)))) (let ((_let_30 (REFL :args (_let_23)))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 3)) (CONG _let_30 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_27)) :args ((or _let_11 _let_23))) _let_29 :args (_let_11 true _let_23)))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 2)) (CONG _let_30 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_27)) :args ((or _let_13 _let_23))) _let_29 :args (_let_13 true _let_23)))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 1)) (CONG _let_30 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_27)) :args ((or _let_15 _let_23))) _let_29 :args (_let_15 true _let_23)))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_23 0)) _let_29 :args ((not _let_17) true _let_23)))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_17 _let_16 _let_14 _let_12 _let_8 (not _let_18)))) _let_34 _let_33 _let_32 _let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element BOUND_VARIABLE_2442 (tptp.the_carrier A)) false))))) :args (_let_19))) _let_20 :args (_let_18 false _let_19)) :args (_let_8 true _let_17 false _let_15 false _let_13 false _let_11 false _let_18)))) (let ((_let_36 (= _let_21 _let_10))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_23 4)) _let_29 :args ((not _let_22) true _let_23)))) (let ((_let_38 (_let_22))) (let ((_let_39 (or _let_17 _let_16 _let_14 _let_12 _let_36))) (let ((_let_40 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (tptp.empty_carrier B) (not (tptp.topological_space B)) (not (tptp.top_str B)) (not (tptp.element C (tptp.the_carrier B))) (= (tptp.in A (tptp.a_2_0_yellow19 B C)) (tptp.point_neighbourhood A B C)))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_17 _let_16 _let_14 _let_12 _let_36 (not _let_39)))) _let_34 _let_33 _let_32 _let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.point_neighbourhood A B C)))) :args (_let_40)))) _let_41 :args (_let_39 false _let_40)) :args (_let_36 true _let_17 false _let_15 false _let_13 false _let_11 false _let_39)))) (let ((_let_43 (not _let_36))) (let ((_let_44 (not _let_21))) (let ((_let_45 (_let_36))) (let ((_let_46 (not _let_10))) (let ((_let_47 (not _let_8))) (let ((_let_48 (not _let_9))) (let ((_let_49 (and _let_48 _let_8))) (let ((_let_50 (_let_48 _let_8))) (let ((_let_51 (ASSUME :args (_let_48)))) (let ((_let_52 (ASSUME :args (_let_8)))) (let ((_let_53 (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19)) (SYMM _let_52) :args (APPLY_UF tptp.in)))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_49)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_51 _let_52) (SCOPE (FALSE_ELIM (TRANS _let_53 (FALSE_INTRO _let_51))) :args _let_50)) :args _let_50)) :args (true _let_49)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_9))) (REFL :args (_let_47)) (REFL :args (_let_46)) :args _let_27)) _let_35 (REORDERING (CNF_EQUIV_POS1 :args _let_45) :args ((or _let_44 _let_10 _let_43))) _let_42 (REORDERING (CNF_EQUIV_NEG1 :args _let_38) :args ((or _let_9 _let_21 _let_22))) _let_37 :args (_let_9 false _let_8 false _let_10 false _let_36 false _let_21 true _let_22)))) (let ((_let_55 (and _let_9 _let_8))) (let ((_let_56 (_let_9 _let_8))) (let ((_let_57 (ASSUME :args (_let_9)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_55)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_57 _let_52) (SCOPE (TRUE_ELIM (TRANS _let_53 (TRUE_INTRO _let_57))) :args _let_56)) :args _let_56)) :args (true _let_55)) :args ((or _let_48 _let_10 _let_47))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_45) :args ((or _let_21 _let_46 _let_43))) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_38) _let_37 _let_54 :args (_let_44 true _let_22 false _let_9)) _let_42 :args (_let_46 true _let_21 false _let_36)) _let_54 _let_35 :args (false true _let_10 false _let_9 false _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)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (tptp.empty B) (and (tptp.open_subset B A) (tptp.closed_subset B A))))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_1 (tptp.complete_relstr A)) (and _let_1 (tptp.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)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (tptp.empty B) (tptp.boundary_set B A)))))) (forall ((A $$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.trivial_carrier A)) (and _let_2 _let_1 (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.complete_relstr A))))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (tptp.empty B) (tptp.nowhere_dense B 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)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (tptp.nowhere_dense B A) (tptp.boundary_set B A)))))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (tptp.bounded_relstr A) (and (tptp.lower_bounded_relstr A) (tptp.upper_bounded_relstr A))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.boundary_set B A))) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (and (tptp.closed_subset B A) _let_1) (and _let_1 (tptp.nowhere_dense B A)))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.reflexive_relstr A))) (let ((_let_2 (not (tptp.empty_carrier A)))) (=> (tptp.rel_str A) (=> (and _let_2 _let_1 (tptp.trivial_carrier A)) (and _let_2 _let_1 (tptp.connected_relstr A))))))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (and (tptp.lower_bounded_relstr A) (tptp.upper_bounded_relstr A)) (tptp.bounded_relstr A)))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.nowhere_dense B A))) (let ((_let_2 (tptp.open_subset B A))) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (and _let_2 _let_1) (and (tptp.empty B) _let_2 (tptp.closed_subset B A) (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B) (tptp.boundary_set B A) _let_1)))))))) (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 $$unsorted)) (let ((_let_1 (tptp.rel_str_of A B))) (=> (tptp.relation_of2 B A A) (and (tptp.strict_rel_str _let_1) (tptp.rel_str _let_1))))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.the_carrier A))) (tptp.element (tptp.neighborhood_system A B) (tptp.powerset (tptp.the_carrier (tptp.boole_POSet (tptp.cast_as_carrier_subset A))))))) true (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (tptp.element (tptp.cast_as_carrier_subset A) (tptp.powerset (tptp.the_carrier 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))) (forall ((A $$unsorted)) (=> (tptp.top_str A) (tptp.one_sorted_str A))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.the_carrier A))) (forall ((C $$unsorted)) (=> (tptp.point_neighbourhood C A B) (tptp.element C (tptp.powerset (tptp.the_carrier A))))))) 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.top_str A)) (exists ((A $$unsorted)) (tptp.one_sorted_str A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.the_carrier A))) (exists ((C $$unsorted)) (tptp.point_neighbourhood C A B)))) (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 $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (tptp.closed_subset (tptp.cast_as_carrier_subset A) A))) (forall ((A $$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.cast_as_carrier_subset A))) (=> (and (tptp.topological_space A) (tptp.top_str A)) (and (tptp.open_subset _let_1 A) (tptp.closed_subset _let_1 A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.lower_bounded_relstr _let_1) (tptp.upper_bounded_relstr _let_1) (tptp.bounded_relstr _let_1) (tptp.with_suprema_relstr _let_1) (tptp.with_infima_relstr _let_1) (tptp.complete_relstr _let_1)))) (forall ((A $$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)))) (forall ((A $$unsorted)) (=> (tptp.top_str A) (tptp.dense (tptp.cast_as_carrier_subset A) A))) _let_2 (forall ((A $$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 $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.open_subset B A))))) (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 $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.open_subset B A) (tptp.closed_subset B A))))) (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)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)) (tptp.open_subset B A) (tptp.closed_subset B A))))) (forall ((A $$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 $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)) (tptp.finite B))))) (forall ((A $$unsorted)) (=> (tptp.top_str A) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.empty B) (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B) (tptp.boundary_set B A))))) (exists ((A $$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 $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.empty B) (tptp.open_subset B A) (tptp.closed_subset B A) (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B) (tptp.boundary_set B A) (tptp.nowhere_dense B A))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.closed_subset B A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)) (tptp.closed_subset B A))))) (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 $$unsorted)) (tptp.subset A A)) (forall ((A $$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))) _let_1 (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.23/0.71 )
% 0.23/0.71 % SZS output end Proof for SEU388+1
% 0.23/0.71 % cvc5---1.0.5 exiting
% 0.23/0.71 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------