TSTP Solution File: SEU387+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU387+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 16:31:19 EDT 2023
% Result : Theorem 0.21s 0.64s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU387+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 15:54:00 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.64 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.bEM4PNpV6s/cvc5---1.0.5_27678.p...
% 0.21/0.64 ------- get file name : TPTP file name is SEU387+1
% 0.21/0.64 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_27678.smt2...
% 0.21/0.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.64 % SZS status Theorem for SEU387+1
% 0.21/0.64 % SZS output start Proof for SEU387+1
% 0.21/0.64 (
% 0.21/0.64 (let ((_let_1 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.lower_bounded_relstr A) (tptp.rel_str A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.the_carrier A)))) (=> (and (not (tptp.empty B)) (tptp.filtered_subset B A) (tptp.upper_relstr_subset B A) (tptp.element B _let_1)) (= (tptp.proper_element B _let_1) (not (tptp.in (tptp.bottom_of_relstr A) B)))))))))) (let ((_let_2 (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))))) (let ((_let_3 (not (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (let ((_let_2 (tptp.powerset (tptp.the_carrier _let_1)))) (=> (and (not (tptp.empty B)) (tptp.filtered_subset B _let_1) (tptp.upper_relstr_subset B _let_1) (tptp.proper_element B _let_2) (tptp.element B _let_2)) (forall ((C $$unsorted)) (not (and (tptp.in C B) (tptp.empty C))))))))))))) (let ((_let_4 (forall ((A $$unsorted)) (= (tptp.bottom_of_relstr (tptp.boole_POSet A)) tptp.empty_set)))) (let ((_let_5 (tptp.relation tptp.empty_set))) (let ((_let_6 (tptp.empty tptp.empty_set))) (let ((_let_7 (forall ((A $$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)))))) (let ((_let_8 (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (and (tptp.strict_rel_str _let_1) (tptp.rel_str _let_1)))))) (let ((_let_9 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_10 (tptp.boole_POSet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_11 (tptp.bottom_of_relstr _let_10))) (let ((_let_12 (= tptp.empty_set _let_11))) (let ((_let_13 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_14 (tptp.in _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_15 (tptp.empty SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_16 (not _let_15))) (let ((_let_17 (not _let_9))) (let ((_let_18 (tptp.powerset (tptp.the_carrier _let_10)))) (let ((_let_19 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_18))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.proper_element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_18))) (let ((_let_22 (not _let_21))) (let ((_let_23 (tptp.upper_relstr_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_10))) (let ((_let_24 (not _let_23))) (let ((_let_25 (tptp.filtered_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_10))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.empty SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_28 (or (tptp.empty SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) _let_27 _let_26 _let_24 _let_22 _let_20 _let_17 _let_16))) (let ((_let_29 (forall ((A $$unsorted) (BOUND_VARIABLE_2481 $$unsorted) (BOUND_VARIABLE_2479 $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (let ((_let_2 (tptp.powerset (tptp.the_carrier _let_1)))) (or (tptp.empty A) (tptp.empty BOUND_VARIABLE_2479) (not (tptp.filtered_subset BOUND_VARIABLE_2479 _let_1)) (not (tptp.upper_relstr_subset BOUND_VARIABLE_2479 _let_1)) (not (tptp.proper_element BOUND_VARIABLE_2479 _let_2)) (not (tptp.element BOUND_VARIABLE_2479 _let_2)) (not (tptp.in BOUND_VARIABLE_2481 BOUND_VARIABLE_2479)) (not (tptp.empty BOUND_VARIABLE_2481)))))))) (let ((_let_30 (not _let_28))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (or))) (let ((_let_33 (not _let_29))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_31) :args (_let_33))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_29))) (REFL :args (_let_30)) :args _let_32)) _let_31 :args (_let_30 true _let_29)))) (let ((_let_35 (REFL :args (_let_28)))) (let ((_let_36 (forall ((A $$unsorted)) (= tptp.empty_set (tptp.bottom_of_relstr (tptp.boole_POSet A)))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (or _let_16 _let_13))) (let ((_let_39 (forall ((A $$unsorted)) (or (not (tptp.empty A)) (= tptp.empty_set A))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (not _let_14))) (let ((_let_42 (= _let_21 _let_41))) (let ((_let_43 (tptp.rel_str _let_10))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.lower_bounded_relstr _let_10))) (let ((_let_46 (not _let_45))) (let ((_let_47 (tptp.antisymmetric_relstr _let_10))) (let ((_let_48 (not _let_47))) (let ((_let_49 (tptp.transitive_relstr _let_10))) (let ((_let_50 (not _let_49))) (let ((_let_51 (tptp.reflexive_relstr _let_10))) (let ((_let_52 (not _let_51))) (let ((_let_53 (tptp.empty_carrier _let_10))) (let ((_let_54 (or _let_53 _let_52 _let_50 _let_48 _let_46 _let_44 _let_27 _let_26 _let_24 _let_20 _let_42))) (let ((_let_55 (forall ((A $$unsorted) (BOUND_VARIABLE_2552 $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.the_carrier A)))) (or (tptp.empty_carrier A) (not (tptp.reflexive_relstr A)) (not (tptp.transitive_relstr A)) (not (tptp.antisymmetric_relstr A)) (not (tptp.lower_bounded_relstr A)) (not (tptp.rel_str A)) (tptp.empty BOUND_VARIABLE_2552) (not (tptp.filtered_subset BOUND_VARIABLE_2552 A)) (not (tptp.upper_relstr_subset BOUND_VARIABLE_2552 A)) (not (tptp.element BOUND_VARIABLE_2552 _let_1)) (= (tptp.proper_element BOUND_VARIABLE_2552 _let_1) (not (tptp.in (tptp.bottom_of_relstr A) BOUND_VARIABLE_2552)))))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (forall ((BOUND_VARIABLE_1818 $$unsorted)) (tptp.lower_bounded_relstr (tptp.boole_POSet BOUND_VARIABLE_1818))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (_let_57))) (let ((_let_60 (forall ((BOUND_VARIABLE_1811 $$unsorted)) (tptp.antisymmetric_relstr (tptp.boole_POSet BOUND_VARIABLE_1811))))) (let ((_let_61 (_let_60))) (let ((_let_62 (forall ((BOUND_VARIABLE_1804 $$unsorted)) (tptp.transitive_relstr (tptp.boole_POSet BOUND_VARIABLE_1804))))) (let ((_let_63 (_let_62))) (let ((_let_64 (forall ((BOUND_VARIABLE_1797 $$unsorted)) (tptp.reflexive_relstr (tptp.boole_POSet BOUND_VARIABLE_1797))))) (let ((_let_65 (_let_64))) (let ((_let_66 (forall ((BOUND_VARIABLE_1784 $$unsorted)) (not (tptp.empty_carrier (tptp.boole_POSet BOUND_VARIABLE_1784)))))) (let ((_let_67 (_let_66))) (let ((_let_68 (forall ((BOUND_VARIABLE_1728 $$unsorted)) (tptp.rel_str (tptp.boole_POSet BOUND_VARIABLE_1728))))) (let ((_let_69 (_let_68))) (let ((_let_70 (and _let_9 _let_12 _let_13))) (let ((_let_71 (ASSUME :args (_let_9)))) (let ((_let_72 (ASSUME :args (_let_13)))) (let ((_let_73 (ASSUME :args (_let_12)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_70)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_71 _let_72 _let_73) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS (SYMM _let_73) (SYMM (SYMM _let_72))) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19)) :args (APPLY_UF tptp.in)) (TRUE_INTRO _let_71))) :args (_let_9 _let_13 _let_12))) :args (_let_9 _let_12 _let_13))) :args (true _let_70)) :args ((or _let_17 _let_14 (not _let_12) (not _let_13)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_42)) :args ((or _let_22 _let_41 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 4)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_32)) :args ((or _let_21 _let_28))) _let_34 :args (_let_21 true _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_27 _let_26 _let_24 _let_20 _let_44 _let_53 _let_52 _let_50 _let_48 _let_46 _let_42 (not _let_54)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_28 1)) _let_34 :args ((not _let_27) true _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 2)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_32)) :args ((or _let_25 _let_28))) _let_34 :args (_let_25 true _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 3)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_32)) :args ((or _let_23 _let_28))) _let_34 :args (_let_23 true _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 5)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_32)) :args ((or _let_19 _let_28))) _let_34 :args (_let_19 true _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_69) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_POSet BOUND_VARIABLE_1728)))) :args _let_69)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) :args (1)) :args (_let_43 false _let_68)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_67) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_POSet BOUND_VARIABLE_1784)))) :args _let_67)) (AND_ELIM _let_58 :args (0)) :args ((not _let_53) false _let_66)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_65) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_POSet BOUND_VARIABLE_1797)))) :args _let_65)) (AND_ELIM _let_58 :args (2)) :args (_let_51 false _let_64)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_63) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_POSet BOUND_VARIABLE_1804)))) :args _let_63)) (AND_ELIM _let_58 :args (3)) :args (_let_49 false _let_62)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_61) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_POSet BOUND_VARIABLE_1811)))) :args _let_61)) (AND_ELIM _let_58 :args (4)) :args (_let_47 false _let_60)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_59) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_POSet BOUND_VARIABLE_1818)))) :args _let_59)) (AND_ELIM _let_58 :args (5)) :args (_let_45 false _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (_let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.filtered_subset BOUND_VARIABLE_2552 A) false))))) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_42 true _let_27 false _let_25 false _let_23 false _let_19 false _let_43 true _let_53 false _let_51 false _let_49 false _let_47 false _let_45 false _let_54)) :args (_let_41 false _let_21 false _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_16 _let_13 (not _let_38)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 7)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_32)) :args ((or _let_15 _let_28))) _let_34 :args (_let_15 true _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.empty A) false))))) :args (_let_39))) _let_40 :args (_let_38 false _let_39)) :args (_let_13 false _let_15 false _let_38)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_POSet A)))) :args (_let_36))) _let_37 :args (_let_12 false _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 6)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_9))) :args _let_32)) :args ((or _let_9 _let_28))) _let_34 :args (_let_9 true _let_28)) :args (false true _let_14 false _let_13 false _let_12 false _let_9)) :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))))))) (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 true (forall ((A $$unsorted)) (=> (tptp.rel_str A) (tptp.element (tptp.bottom_of_relstr A) (tptp.the_carrier A)))) _let_8 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (tptp.one_sorted_str A))) true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))) (forall ((A $$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 $$unsorted) (B $$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_6 _let_5 (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 $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_7 (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_POSet A))) (=> (not (tptp.empty A)) (and (not (tptp.empty_carrier _let_1)) (not (tptp.trivial_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.lower_bounded_relstr _let_1) (tptp.upper_bounded_relstr _let_1) (tptp.bounded_relstr _let_1) (tptp.up_complete_relstr _let_1) (tptp.join_complete_relstr _let_1) (not (tptp.v1_yellow_3 _let_1)) (tptp.distributive_relstr _let_1) (tptp.heyting_relstr _let_1) (tptp.complemented_relstr _let_1) (tptp.boolean_relstr _let_1) (tptp.with_suprema_relstr _let_1) (tptp.with_infima_relstr _let_1) (tptp.complete_relstr _let_1))))) (and _let_6 _let_5) (forall ((A $$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.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)))) (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))))) (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 $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$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)) (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))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (not (tptp.trivial_carrier A)) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.upper_bounded_relstr A) (tptp.rel_str A)) (exists ((B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.the_carrier A)))) (and (tptp.element B _let_1) (not (tptp.empty B)) (tptp.proper_element B _let_1) (tptp.filtered_subset B A) (tptp.upper_relstr_subset 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) (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_4 (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)))) _let_3 (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)))) _let_2 (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.64 )
% 0.21/0.64 % SZS output end Proof for SEU387+1
% 0.21/0.64 % cvc5---1.0.5 exiting
% 0.21/0.64 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------