TSTP Solution File: SEU385+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU385+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n006.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 16:31:18 EDT 2023
% Result : Theorem 3.02s 3.28s
% Output : Proof 3.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU385+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 17:19:23 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.43 %----Proving TF0_NAR, FOF, or CNF
% 3.02/3.28 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.dKqGVOzRFB/cvc5---1.0.5_1643.p...
% 3.02/3.28 ------- get file name : TPTP file name is SEU385+1
% 3.02/3.28 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1643.smt2...
% 3.02/3.28 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 3.02/3.28 % SZS status Theorem for SEU385+1
% 3.02/3.28 % SZS output start Proof for SEU385+1
% 3.02/3.28 (
% 3.02/3.28 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in B A) (= (tptp.apply (tptp.relation_dom_restriction C A) B) (tptp.apply C B))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))))) (let ((_let_3 (not (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (forall ((B $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.directed_relstr B) (tptp.net_str B A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier B)) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier B)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.netstr_restr_to_element A B C))) (=> (tptp.element E (tptp.the_carrier _let_1)) (=> (= D E) (= (tptp.apply_netmap A B D) (tptp.apply_netmap A _let_1 E))))))))))))))))) (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 $$unsorted)) (=> (and (tptp.function C) (tptp.relation_of2 C A B)) (= (tptp.partfun_dom_restriction A B C D) (tptp.relation_dom_restriction C D)))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.the_carrier B))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.one_sorted_str B) (tptp.function C) (tptp.quasi_total C _let_1 _let_2) (tptp.relation_of2 C _let_1 _let_2) (tptp.element D _let_1)) (= (tptp.apply_on_structs A B C D) (tptp.apply C D)))))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.netstr_restr_to_element A B C))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.directed_relstr B) (tptp.net_str B A) (tptp.element C (tptp.the_carrier B))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_net_str _let_1 A))))))) (let ((_let_8 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.the_mapping A B))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.net_str B A)) (and (not (tptp.empty _let_1)) (tptp.relation _let_1) (tptp.function _let_1) (tptp.quasi_total _let_1 (tptp.the_carrier B) (tptp.the_carrier A)))))))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.the_carrier B))) (let ((_let_3 (tptp.the_mapping A B))) (=> (and (tptp.one_sorted_str A) (tptp.net_str B A)) (and (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.relation_of2_as_subset _let_3 _let_2 _let_1))))))))) (let ((_let_11 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (forall ((B $$unsorted)) (=> (tptp.net_str B A) (tptp.rel_str B))))))) (let ((_let_12 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (tptp.one_sorted_str A))))) (let ((_let_13 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.netstr_restr_to_element A B C))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.net_str B A) (tptp.element C (tptp.the_carrier B))) (and (tptp.strict_net_str _let_1 A) (tptp.net_str _let_1 A))))))) (let ((_let_14 (forall ((A $$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.element C (tptp.the_carrier B)) (= (tptp.apply_netmap A B C) (tptp.apply_on_structs B A (tptp.the_mapping A B) C)))))))))) (let ((_let_15 (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 $$unsorted)) (=> (tptp.element C (tptp.the_carrier B)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.the_carrier D))) (=> (and (tptp.strict_net_str D A) (tptp.net_str D A)) (= (= D (tptp.netstr_restr_to_element A B C)) (and (forall ((E $$unsorted)) (= (tptp.in E (tptp.the_carrier D)) (exists ((F $$unsorted)) (and (tptp.element F (tptp.the_carrier B)) (= F E) (tptp.related B C F))))) (= (tptp.the_InternalRel D) (tptp.relation_restriction_as_relation_of (tptp.the_InternalRel B) _let_1)) (= (tptp.the_mapping A D) (tptp.partfun_dom_restriction (tptp.the_carrier B) (tptp.the_carrier A) (tptp.the_mapping A B) _let_1))))))))))))))) (let ((_let_16 (tptp.netstr_restr_to_element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_17 (tptp.apply_netmap SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_18 (tptp.apply_netmap SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_19 (= _let_18 _let_17))) (let ((_let_20 (tptp.the_mapping SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_21 (tptp.apply_on_structs SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_22 (= _let_18 _let_21))) (let ((_let_23 (tptp.the_mapping SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_16))) (let ((_let_24 (tptp.apply_on_structs _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_25 (= _let_17 _let_24))) (let ((_let_26 (tptp.the_carrier _let_16))) (let ((_let_27 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_28 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_29 (tptp.partfun_dom_restriction _let_28 _let_27 _let_20 _let_26))) (let ((_let_30 (= _let_23 _let_29))) (let ((_let_31 (tptp.apply _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_32 (= _let_21 _let_31))) (let ((_let_33 (tptp.relation_dom_restriction _let_20 _let_26))) (let ((_let_34 (= _let_29 _let_33))) (let ((_let_35 (= _let_24 (tptp.apply _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)))) (let ((_let_36 (= _let_31 (tptp.apply _let_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)))) (let ((_let_37 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_26))) (let ((_let_38 (not _let_37))) (let ((_let_39 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_28))) (let ((_let_40 (not _let_39))) (let ((_let_41 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_28))) (let ((_let_42 (not _let_41))) (let ((_let_43 (tptp.net_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.directed_relstr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_46 (not _let_45))) (let ((_let_47 (tptp.empty_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_48 (tptp.one_sorted_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_49 (not _let_48))) (let ((_let_50 (tptp.empty_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_51 (or _let_50 _let_49 _let_47 _let_46 _let_44 _let_42 _let_40 _let_38 _let_19))) (let ((_let_52 (not _let_19))) (let ((_let_53 (forall ((A $$unsorted) (BOUND_VARIABLE_2346 $$unsorted) (BOUND_VARIABLE_2344 $$unsorted) (BOUND_VARIABLE_2342 $$unsorted)) (let ((_let_1 (tptp.netstr_restr_to_element A BOUND_VARIABLE_2342 BOUND_VARIABLE_2346))) (let ((_let_2 (tptp.the_carrier BOUND_VARIABLE_2342))) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty_carrier BOUND_VARIABLE_2342) (not (tptp.directed_relstr BOUND_VARIABLE_2342)) (not (tptp.net_str BOUND_VARIABLE_2342 A)) (not (tptp.element BOUND_VARIABLE_2346 _let_2)) (not (tptp.element BOUND_VARIABLE_2344 _let_2)) (not (tptp.element BOUND_VARIABLE_2344 (tptp.the_carrier _let_1))) (= (tptp.apply_netmap A BOUND_VARIABLE_2342 BOUND_VARIABLE_2344) (tptp.apply_netmap A _let_1 BOUND_VARIABLE_2344)))))))) (let ((_let_54 (not _let_51))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (or))) (let ((_let_57 (not _let_53))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_55) :args (_let_57))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_53))) (REFL :args (_let_54)) :args _let_56)) _let_55 :args (_let_54 true _let_53)))) (let ((_let_59 (or _let_50 _let_49 _let_47 _let_44 _let_40 _let_22))) (let ((_let_60 (forall ((A $$unsorted) (BOUND_VARIABLE_1846 $$unsorted) (BOUND_VARIABLE_1844 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty_carrier BOUND_VARIABLE_1844) (not (tptp.net_str BOUND_VARIABLE_1844 A)) (not (tptp.element BOUND_VARIABLE_1846 (tptp.the_carrier BOUND_VARIABLE_1844))) (= (tptp.apply_netmap A BOUND_VARIABLE_1844 BOUND_VARIABLE_1846) (tptp.apply_on_structs BOUND_VARIABLE_1844 A (tptp.the_mapping A BOUND_VARIABLE_1844) BOUND_VARIABLE_1846)))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (_let_60))) (let ((_let_63 ((tptp.apply_netmap A BOUND_VARIABLE_1844 BOUND_VARIABLE_1846)))) (let ((_let_64 (REFL :args (_let_51)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 6)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_39))) :args _let_56)) :args ((or _let_39 _let_51))) _let_58 :args (_let_39 true _let_51)))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 4)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_56)) :args ((or _let_43 _let_51))) _let_58 :args (_let_43 true _let_51)))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_51 2)) _let_58 :args ((not _let_47) true _let_51)))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 1)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_56)) :args ((or _let_48 _let_51))) _let_58 :args (_let_48 true _let_51)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_51 0)) _let_58 :args ((not _let_50) true _let_51)))) (let ((_let_70 (tptp.net_str _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_71 (not _let_70))) (let ((_let_72 (tptp.empty_carrier _let_16))) (let ((_let_73 (or _let_50 _let_49 _let_72 _let_71 _let_38 _let_25))) (let ((_let_74 (tptp.strict_net_str _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_75 (and _let_74 _let_70))) (let ((_let_76 (or _let_50 _let_49 _let_47 _let_44 _let_42 _let_75))) (let ((_let_77 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.netstr_restr_to_element A B C))) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty_carrier B) (not (tptp.net_str B A)) (not (tptp.element C (tptp.the_carrier B))) (and (tptp.strict_net_str _let_1 A) (tptp.net_str _let_1 A))))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 5)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) :args _let_56)) :args ((or _let_41 _let_51))) _let_58 :args (_let_41 true _let_51)))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_50 _let_49 _let_47 _let_44 _let_42 _let_75 (not _let_76)))) _let_69 _let_68 _let_67 _let_66 _let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.netstr_restr_to_element A B C)))) :args (_let_77))) _let_78 :args (_let_76 false _let_77)) :args (_let_75 true _let_50 false _let_48 true _let_47 false _let_43 false _let_41 false _let_76)))) (let ((_let_81 (not _let_75))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_75 1)) :args ((or _let_70 _let_81))) _let_80 :args (_let_70 false _let_75)))) (let ((_let_83 (not _let_72))) (let ((_let_84 (and _let_83 _let_74))) (let ((_let_85 (or _let_50 _let_49 _let_47 _let_46 _let_44 _let_42 _let_84))) (let ((_let_86 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.netstr_restr_to_element A B C))) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty_carrier B) (not (tptp.directed_relstr B)) (not (tptp.net_str B A)) (not (tptp.element C (tptp.the_carrier B))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_net_str _let_1 A))))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_84 0)) :args ((or _let_83 (not _let_84)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_50 _let_49 _let_47 _let_46 _let_44 _let_42 _let_84 (not _let_85)))) _let_69 _let_68 _let_67 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 3)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_56)) :args ((or _let_45 _let_51))) _let_58 :args (_let_45 true _let_51)) _let_66 _let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.netstr_restr_to_element A B C)))) :args (_let_86))) _let_87 :args (_let_85 false _let_86)) :args (_let_84 true _let_50 false _let_48 true _let_47 false _let_45 false _let_43 false _let_41 false _let_85)) :args (_let_83 false _let_84)))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 7)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) :args _let_56)) :args ((or _let_37 _let_51))) _let_58 :args (_let_37 true _let_51)))) (let ((_let_90 (and (forall ((E $$unsorted)) (= (and (tptp.element E (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)) (tptp.related SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 E)) (tptp.in E (tptp.the_carrier (tptp.netstr_restr_to_element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))))) (= (tptp.the_InternalRel _let_16) (tptp.relation_restriction_as_relation_of (tptp.the_InternalRel SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) _let_26)) _let_30))) (let ((_let_91 (not _let_74))) (let ((_let_92 (or _let_50 _let_49 _let_47 _let_44 _let_42 _let_91 _let_71 _let_90))) (let ((_let_93 (forall ((A $$unsorted) (BOUND_VARIABLE_1776 $$unsorted) (BOUND_VARIABLE_1774 $$unsorted) (BOUND_VARIABLE_1772 $$unsorted)) (let ((_let_1 (tptp.the_carrier BOUND_VARIABLE_1774))) (let ((_let_2 (tptp.the_carrier BOUND_VARIABLE_1772))) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty_carrier BOUND_VARIABLE_1772) (not (tptp.net_str BOUND_VARIABLE_1772 A)) (not (tptp.element BOUND_VARIABLE_1776 _let_2)) (not (tptp.strict_net_str BOUND_VARIABLE_1774 A)) (not (tptp.net_str BOUND_VARIABLE_1774 A)) (= (and (forall ((E $$unsorted)) (= (and (tptp.element E (tptp.the_carrier BOUND_VARIABLE_1772)) (tptp.related BOUND_VARIABLE_1772 BOUND_VARIABLE_1776 E)) (tptp.in E (tptp.the_carrier BOUND_VARIABLE_1774)))) (= (tptp.the_InternalRel BOUND_VARIABLE_1774) (tptp.relation_restriction_as_relation_of (tptp.the_InternalRel BOUND_VARIABLE_1772) _let_1)) (= (tptp.the_mapping A BOUND_VARIABLE_1774) (tptp.partfun_dom_restriction _let_2 (tptp.the_carrier A) (tptp.the_mapping A BOUND_VARIABLE_1772) _let_1))) (= BOUND_VARIABLE_1774 (tptp.netstr_restr_to_element A 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_let_135)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_103)) :args ((or _let_50 _let_49 _let_47 _let_40 _let_102 _let_100 _let_98 _let_96 _let_32 (not _let_103)))) _let_69 _let_68 _let_67 _let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_125)) :args ((or _let_124 _let_101 (not _let_125)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_130)) :args ((or _let_49 _let_44 _let_123 (not _let_130)))) _let_68 _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_132 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_134)) :args _let_133)) _let_132 :args (_let_130 false _let_131)) :args (_let_123 false _let_48 false _let_43 false _let_130)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_127 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_129)) :args _let_128)) _let_127 :args (_let_125 false _let_126)) :args (_let_101 false _let_123 false _let_125)) _let_122 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_113 1)) :args ((or _let_97 _let_120))) _let_119 :args (_let_97 false _let_113)) _let_121 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_105 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_107)) :args _let_106)) _let_105 :args (_let_103 false _let_104)) :args (_let_32 true _let_50 false _let_48 true _let_47 false _let_39 false _let_101 false _let_99 false _let_97 false _let_95 false _let_103)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_90 2)) :args ((or _let_30 (not _let_90)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_50 _let_49 _let_47 _let_44 _let_42 _let_71 _let_91 _let_90 (not _let_92)))) _let_69 _let_68 _let_67 _let_66 _let_79 _let_82 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_75 0)) :args ((or _let_74 _let_81))) _let_80 :args (_let_74 false _let_75)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_94 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element BOUND_VARIABLE_1776 (tptp.the_carrier BOUND_VARIABLE_1772)) false)) (not (= (tptp.strict_net_str BOUND_VARIABLE_1774 A) false))))) :args (_let_93)))) _let_94 :args (_let_92 false _let_93)) :args (_let_90 true _let_50 false _let_48 true _let_47 false _let_43 false _let_41 false _let_70 false _let_74 false _let_92)) :args (_let_30 false _let_90)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_50 _let_49 _let_38 _let_72 _let_71 _let_25 (not _let_73)))) _let_69 _let_68 _let_89 _let_88 _let_82 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_63)) :args _let_62)) _let_61 :args (_let_73 false _let_60)) :args (_let_25 true _let_50 false _let_48 false _let_37 true _let_72 false _let_70 false _let_73)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_50 _let_49 _let_47 _let_44 _let_40 _let_22 (not _let_59)))) _let_69 _let_68 _let_67 _let_66 _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_63)) :args _let_62)) _let_61 :args (_let_59 false _let_60)) :args (_let_22 true _let_50 false _let_48 true _let_47 false _let_43 false _let_39 false _let_59)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_51 8)) _let_58 :args (_let_52 true _let_51)) :args (false false _let_36 false _let_35 false _let_34 false _let_32 false _let_30 false _let_25 false _let_22 true _let_19)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.one_sorted_str A) (tptp.net_str B A)) (=> (tptp.strict_net_str B A) (= B (tptp.net_str_of A (tptp.the_carrier B) (tptp.the_InternalRel B) (tptp.the_mapping A B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.finite A))) (forall ((A $$unsorted)) (=> (tptp.preboolean A) (and (tptp.cup_closed A) (tptp.diff_closed A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function 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) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))) (forall ((A $$unsorted)) (=> (tptp.finite A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.finite B))))) (forall ((A $$unsorted)) (=> (and (tptp.cup_closed A) (tptp.diff_closed A)) (tptp.preboolean A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.function A))) (let ((_let_2 (tptp.relation A))) (=> (and _let_2 (tptp.empty A) _let_1) (and _let_2 _let_1 (tptp.one_to_one A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (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_15 _let_14 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.net_str_of A B C D))) (let ((_let_2 (tptp.the_carrier A))) (=> (and (tptp.one_sorted_str A) (tptp.relation_of2 C B B) (tptp.function D) (tptp.quasi_total D B _let_2) (tptp.relation_of2 D B _let_2)) (and (tptp.strict_net_str _let_1 A) (tptp.net_str _let_1 A)))))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation A) (tptp.relation_of2_as_subset (tptp.relation_restriction_as_relation_of A B) B B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.the_carrier B))) (let ((_let_2 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.one_sorted_str B) (tptp.function C) (tptp.quasi_total C _let_2 _let_1) (tptp.relation_of2 C _let_2 _let_1) (tptp.element D _let_2)) (tptp.element (tptp.apply_on_structs A B C D) _let_1))))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.partfun_dom_restriction A B C D))) (=> (and (tptp.function C) (tptp.relation_of2 C A B)) (and (tptp.function _let_1) (tptp.relation_of2_as_subset _let_1 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_restriction A B)))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.net_str B A) (tptp.element C (tptp.the_carrier B))) (tptp.element (tptp.apply_netmap A B C) (tptp.the_carrier A)))) _let_13 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_dom_restriction A B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.the_carrier B))) (=> (and (not (tptp.empty A)) (not (tptp.empty_carrier B)) (tptp.one_sorted_str B) (tptp.function C) (tptp.quasi_total C A _let_1) (tptp.relation_of2 C A _let_1) (tptp.element D A)) (tptp.element (tptp.apply_on_set_and_struct2 A B C D) _let_1)))) _let_12 true _let_11 true true (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.rel_str A) (tptp.relation_of2_as_subset (tptp.the_InternalRel A) _let_1 _let_1)))) true _let_10 (exists ((A $$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 $$unsorted)) (tptp.relation_of2_as_subset C A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B)) (tptp.finite (tptp.cartesian_product2 A B)))) _let_9 (forall ((A $$unsorted)) (let ((_let_1 (tptp.powerset A))) (and (not (tptp.empty _let_1)) (tptp.cup_closed _let_1) (tptp.diff_closed _let_1) (tptp.preboolean _let_1)))) _let_8 (tptp.empty tptp.empty_set) _let_7 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_dom_restriction A B))) (=> (and (tptp.relation A) (tptp.function A)) (and (tptp.relation _let_1) (tptp.function _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.net_str_of A B C D))) (let ((_let_2 (tptp.the_carrier A))) (=> (and (tptp.one_sorted_str A) (not (tptp.empty B)) (tptp.relation_of2 C B B) (tptp.function D) (tptp.quasi_total D B _let_2) (tptp.relation_of2 D B _let_2)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_net_str _let_1 A)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (tptp.one_sorted_str A) (tptp.relation_of2 C B B) (tptp.function D) (tptp.quasi_total D B _let_1) (tptp.relation_of2 D B _let_1)) (forall ((E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (=> (= (tptp.net_str_of A B C D) (tptp.net_str_of E F G H)) (and (= A E) (= B F) (= C G) (= D H))))))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.finite A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (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)) (tptp.empty A)) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))) (exists ((A $$unsorted)) (not (tptp.empty 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 $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A))) (exists ((A $$unsorted)) (and (tptp.one_sorted_str A) (not (tptp.empty_carrier 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))))) (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (exists ((B $$unsorted)) (and (tptp.net_str B A) (tptp.strict_net_str B 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)) (=> (tptp.relation A) (= (tptp.relation_restriction_as_relation_of A B) (tptp.relation_restriction A B)))) _let_6 _let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.the_carrier B))) (=> (and (not (tptp.empty A)) (not (tptp.empty_carrier B)) (tptp.one_sorted_str B) (tptp.function C) (tptp.quasi_total C A _let_1) (tptp.relation_of2 C A _let_1) (tptp.element D A)) (= (tptp.apply_on_set_and_struct2 A B C D) (tptp.apply C D))))) _let_4 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _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 $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) _let_1 (forall ((A $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 3.12/3.29 )
% 3.12/3.29 % SZS output end Proof for SEU385+1
% 3.12/3.29 % cvc5---1.0.5 exiting
% 3.12/3.30 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------