TSTP Solution File: SEU390+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU390+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n013.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 282.96s 283.17s
% Output : Proof 283.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU390+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 19:37:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.44 %----Proving TF0_NAR, FOF, or CNF
% 282.96/283.17 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.vPUmU4YXyM/cvc5---1.0.5_24374.p...
% 282.96/283.17 ------- get file name : TPTP file name is SEU390+1
% 282.96/283.17 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_24374.smt2...
% 282.96/283.17 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 282.96/283.17 --- Run --no-e-matching --full-saturate-quant at 5...
% 282.96/283.17 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 282.96/283.17 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 282.96/283.17 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 282.96/283.17 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 282.96/283.17 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 282.96/283.17 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 282.96/283.17 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 282.96/283.17 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 282.96/283.17 --- Run --relevant-triggers --full-saturate-quant at 5...
% 282.96/283.17 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 282.96/283.17 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 282.96/283.17 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 282.96/283.17 --- Run --no-cbqi --full-saturate-quant at 10...
% 282.96/283.17 --- Run --macros-quant --macros-quant-mode=all --full-saturate-quant...
% 282.96/283.17 % SZS status Theorem for SEU390+1
% 282.96/283.17 % SZS output start Proof for SEU390+1
% 282.96/283.17 (
% 282.96/283.17 (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.transitive_relstr B) (tptp.directed_relstr B) (tptp.net_str B A)) (forall ((C $$unsorted)) (=> (tptp.netstr_induced_subset C A B) (tptp.is_eventually_in A B C)))))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.function D) (tptp.quasi_total D A B) (tptp.relation_of2_as_subset D A B)) (=> (tptp.in C A) (or (= B tptp.empty_set) (tptp.in (tptp.apply D C) (tptp.relation_rng D)))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))))) (let ((_let_5 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (forall ((B $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.directed_relstr B) (tptp.net_str B A)) (forall ((C $$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_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (= (tptp.relation_rng_as_subset A B C) (tptp.relation_rng C)))))) (let ((_let_8 (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_9 (tptp.relation tptp.empty_set))) (let ((_let_10 (tptp.empty tptp.empty_set))) (let ((_let_11 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.netstr_restr_to_element A B C))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.directed_relstr B) (tptp.net_str B A) (tptp.element C (tptp.the_carrier B))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_net_str _let_1 A))))))) (let ((_let_12 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))))) (let ((_let_13 (and _let_10 _let_9 (tptp.relation_empty_yielding tptp.empty_set)))) (let ((_let_14 (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_15 (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)) (forall ((C $$unsorted)) (=> (tptp.netstr_induced_subset C A B) (tptp.element C (tptp.powerset (tptp.the_carrier A))))))))) (let ((_let_16 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (forall ((B $$unsorted)) (=> (tptp.net_str B A) (tptp.rel_str B))))))) (let ((_let_17 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (tptp.one_sorted_str A))))) (let ((_let_18 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.netstr_restr_to_element A B C))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.net_str B A) (tptp.element C (tptp.the_carrier B))) (and (tptp.strict_net_str _let_1 A) (tptp.net_str _let_1 A))))))) (let ((_let_19 (forall ((A $$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_20 (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_21 (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 $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.the_carrier A))) (= (tptp.netstr_induced_subset C A B) (exists ((D $$unsorted)) (let ((_let_1 (tptp.netstr_restr_to_element A B D))) (and (tptp.element D (tptp.the_carrier B)) (= C (tptp.relation_rng_as_subset (tptp.the_carrier _let_1) (tptp.the_carrier A) (tptp.the_mapping A _let_1))))))))))))))) (let ((_let_22 (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 $$unsorted)) (= (tptp.is_eventually_in A B C) (exists ((D $$unsorted)) (and (tptp.element D (tptp.the_carrier B)) (forall ((E $$unsorted)) (=> (tptp.element E (tptp.the_carrier B)) (=> (tptp.related B D E) (tptp.in (tptp.apply_netmap A B E) C)))))))))))))) (let ((_let_23 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_24 (tptp.empty _let_23))) (let ((_let_25 (= tptp.empty_set _let_23))) (let ((_let_26 (not _let_24))) (let ((_let_27 (tptp.one_sorted_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_28 (not _let_27))) (let ((_let_29 (tptp.empty_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_30 (or _let_29 _let_28 _let_26))) (let ((_let_31 (forall ((A $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (tptp.is_eventually_in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_34 (tptp.netstr_induced_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.net_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.directed_relstr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.empty_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_41 (or _let_29 _let_28 _let_40 (not (tptp.transitive_relstr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)) _let_39 _let_37 _let_35 _let_33))) (let ((_let_42 (forall ((A $$unsorted) (BOUND_VARIABLE_2893 $$unsorted) (BOUND_VARIABLE_2891 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty_carrier BOUND_VARIABLE_2891) (not (tptp.transitive_relstr BOUND_VARIABLE_2891)) (not (tptp.directed_relstr BOUND_VARIABLE_2891)) (not (tptp.net_str BOUND_VARIABLE_2891 A)) (not (tptp.netstr_induced_subset BOUND_VARIABLE_2893 A BOUND_VARIABLE_2891)) (tptp.is_eventually_in A BOUND_VARIABLE_2891 BOUND_VARIABLE_2893))))) (let ((_let_43 (not _let_41))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (or))) (let ((_let_46 (not _let_42))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_44) :args (_let_46))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_42))) (REFL :args (_let_43)) :args _let_45)) _let_44 :args (_let_43 true _let_42)))) (let ((_let_48 (REFL :args (_let_41)))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_41 1)) (CONG _let_48 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_45)) :args ((or _let_27 _let_41))) _let_47 :args (_let_27 true _let_41)))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_41 0)) _let_47 :args ((not _let_29) true _let_41)))) (let ((_let_51 (tptp.netstr_restr_to_element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32))) (let ((_let_52 (tptp.the_mapping SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_51))) (let ((_let_53 (tptp.relation_rng _let_52))) (let ((_let_54 (tptp.apply _let_52 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67))) (let ((_let_55 (tptp.in _let_54 _let_53))) (let ((_let_56 (tptp.the_carrier _let_51))) (let ((_let_57 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67 _let_56))) (let ((_let_58 (not _let_57))) (let ((_let_59 (tptp.relation_of2 _let_52 _let_56 _let_23))) (let ((_let_60 (not _let_59))) (let ((_let_61 (tptp.quasi_total _let_52 _let_56 _let_23))) (let ((_let_62 (not _let_61))) (let ((_let_63 (tptp.function _let_52))) (let ((_let_64 (not _let_63))) (let ((_let_65 (or _let_64 _let_62 _let_60 _let_58 _let_25 _let_55))) (let ((_let_66 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (or (not (tptp.function D)) (not (tptp.quasi_total D A B)) (not (tptp.relation_of2 D A B)) (not (tptp.in C A)) (= tptp.empty_set B) (tptp.in (tptp.apply D C) (tptp.relation_rng D)))))) (let ((_let_67 (AND_INTRO (TRUST_SUBS_EQ (ASSUME :args (_let_3)) :args ((= tptp.subset (lambda ((BOUND_VARIABLE_2924 $$unsorted) (BOUND_VARIABLE_2925 $$unsorted)) (tptp.element BOUND_VARIABLE_2924 (tptp.powerset BOUND_VARIABLE_2925)))))) (TRUST_SUBS_EQ (ASSUME :args (_let_6)) :args ((= tptp.relation_of2_as_subset (lambda ((BOUND_VARIABLE_2912 $$unsorted) (BOUND_VARIABLE_2913 $$unsorted) (BOUND_VARIABLE_2914 $$unsorted)) (tptp.relation_of2 BOUND_VARIABLE_2912 BOUND_VARIABLE_2913 BOUND_VARIABLE_2914)))))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_67 :args ((forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (or (not (tptp.function D)) (not (tptp.quasi_total D A B)) (not (tptp.relation_of2_as_subset D A B)) (not (tptp.in C A)) (= tptp.empty_set B) (tptp.in (tptp.apply D C) (tptp.relation_rng D)))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_69 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67 _let_56))) (let ((_let_70 (not _let_55))) (let ((_let_71 (or _let_58 _let_69))) (let ((_let_72 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.in A B)) (tptp.element A B))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (tptp.related SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67))) (let ((_let_75 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_76 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67 _let_75))) (let ((_let_77 (and _let_76 _let_74))) (let ((_let_78 (= _let_77 _let_57))) (let ((_let_79 (forall ((E $$unsorted)) (= (and (tptp.element E (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)) (tptp.related SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 E)) (tptp.in E (tptp.the_carrier (tptp.netstr_restr_to_element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32))))))) (let ((_let_80 (and _let_79 (= (tptp.the_InternalRel _let_51) (tptp.relation_restriction_as_relation_of (tptp.the_InternalRel SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) _let_56)) (= _let_52 (tptp.partfun_dom_restriction _let_75 _let_23 (tptp.the_mapping SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) _let_56))))) (let ((_let_81 (tptp.net_str _let_51 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_82 (not _let_81))) (let ((_let_83 (tptp.strict_net_str _let_51 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_84 (not _let_83))) (let ((_let_85 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 _let_75))) (let ((_let_86 (not _let_85))) (let ((_let_87 (or _let_29 _let_28 _let_40 _let_37 _let_86 _let_84 _let_82 _let_80))) (let ((_let_88 (forall ((A $$unsorted) (BOUND_VARIABLE_2083 $$unsorted) (BOUND_VARIABLE_2081 $$unsorted) (BOUND_VARIABLE_2079 $$unsorted)) (let ((_let_1 (tptp.the_carrier BOUND_VARIABLE_2081))) (let ((_let_2 (tptp.the_carrier BOUND_VARIABLE_2079))) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty_carrier BOUND_VARIABLE_2079) (not (tptp.net_str BOUND_VARIABLE_2079 A)) (not (tptp.element BOUND_VARIABLE_2083 _let_2)) (not (tptp.strict_net_str BOUND_VARIABLE_2081 A)) (not (tptp.net_str BOUND_VARIABLE_2081 A)) (= (and (forall ((E $$unsorted)) (= (and (tptp.element E (tptp.the_carrier BOUND_VARIABLE_2079)) (tptp.related BOUND_VARIABLE_2079 BOUND_VARIABLE_2083 E)) (tptp.in E (tptp.the_carrier BOUND_VARIABLE_2081)))) (= (tptp.the_InternalRel BOUND_VARIABLE_2081) (tptp.relation_restriction_as_relation_of (tptp.the_InternalRel BOUND_VARIABLE_2079) _let_1)) (= (tptp.the_mapping A BOUND_VARIABLE_2081) (tptp.partfun_dom_restriction _let_2 (tptp.the_carrier A) (tptp.the_mapping A BOUND_VARIABLE_2079) _let_1))) (= BOUND_VARIABLE_2081 (tptp.netstr_restr_to_element A BOUND_VARIABLE_2079 BOUND_VARIABLE_2083))))))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (and _let_83 _let_81))) (let ((_let_91 (or _let_29 _let_28 _let_40 _let_37 _let_86 _let_90))) (let ((_let_92 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.netstr_restr_to_element A B C))) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty_carrier B) (not (tptp.net_str B A)) (not (tptp.element C (tptp.the_carrier B))) (and (tptp.strict_net_str _let_1 A) (tptp.net_str _let_1 A))))))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (tptp.relation_rng_as_subset _let_56 _let_23 _let_52))) (let ((_let_95 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_94))) (let ((_let_96 (not _let_95))) (let ((_let_97 (or _let_86 _let_96))) (let ((_let_98 (forall ((D $$unsorted)) (let ((_let_1 (tptp.netstr_restr_to_element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 D))) (or (not (tptp.element D (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 (tptp.relation_rng_as_subset (tptp.the_carrier _let_1) (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) (tptp.the_mapping SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_1))))))))) (let ((_let_99 (not _let_97))) (let ((_let_100 (not _let_98))) (let ((_let_101 (= _let_34 _let_100))) (let ((_let_102 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 (tptp.powerset _let_23)))) (let ((_let_103 (not _let_102))) (let ((_let_104 (or _let_29 _let_28 _let_40 _let_37 _let_103 _let_101))) (let ((_let_105 (forall ((A $$unsorted) (BOUND_VARIABLE_1922 $$unsorted) (BOUND_VARIABLE_1920 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty_carrier BOUND_VARIABLE_1920) (not (tptp.net_str BOUND_VARIABLE_1920 A)) (not (tptp.element BOUND_VARIABLE_1922 (tptp.powerset (tptp.the_carrier A)))) (= (tptp.netstr_induced_subset BOUND_VARIABLE_1922 A BOUND_VARIABLE_1920) (not (forall ((D $$unsorted)) (let ((_let_1 (tptp.netstr_restr_to_element A BOUND_VARIABLE_1920 D))) (or (not (tptp.element D (tptp.the_carrier BOUND_VARIABLE_1920))) (not (= BOUND_VARIABLE_1922 (tptp.relation_rng_as_subset (tptp.the_carrier _let_1) (tptp.the_carrier A) (tptp.the_mapping A _let_1))))))))))))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_107 (or _let_29 _let_28 _let_40 _let_37 _let_35 _let_102))) (let ((_let_108 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_2277 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty_carrier B) (not (tptp.net_str B A)) (not 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_let_113)) :args _let_113)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_100) _let_98))) (REFL :args (_let_99)) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_101)) :args ((or _let_35 _let_100 (not _let_101)))) _let_110 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_29 _let_28 _let_40 _let_37 _let_103 _let_101 (not _let_104)))) _let_50 _let_49 _let_112 _let_111 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_107)) :args ((or _let_29 _let_28 _let_40 _let_37 _let_35 _let_102 (not _let_107)))) _let_50 _let_49 _let_112 _let_111 _let_110 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_109 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.netstr_induced_subset BOUND_VARIABLE_2277 A B) false))))) :args (_let_108))) _let_109 :args (_let_107 false _let_108)) :args (_let_102 true _let_29 false _let_27 true _let_40 false _let_36 false _let_34 false _let_107)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.netstr_induced_subset BOUND_VARIABLE_1922 A BOUND_VARIABLE_1920)))) :args (_let_105))) _let_106 :args (_let_104 false _let_105)) :args (_let_101 true _let_29 false _let_27 true _let_40 false _let_36 false _let_102 false _let_104)) :args (_let_100 false _let_34 false _let_101)) :args (_let_99 true _let_98)))) (let ((_let_115 (REFL :args (_let_97)))) (let ((_let_116 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_97 0)) (CONG _let_115 (MACRO_SR_PRED_INTRO :args ((= (not _let_86) _let_85))) :args _let_45)) :args ((or _let_85 _let_97))) _let_114 :args (_let_85 true _let_97)))) (let ((_let_117 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_29 _let_28 _let_40 _let_37 _let_86 _let_90 (not _let_91)))) _let_50 _let_49 _let_112 _let_111 _let_116 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_93 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.netstr_restr_to_element A B C)))) :args (_let_92))) _let_93 :args (_let_91 false _let_92)) :args (_let_90 true _let_29 false _let_27 true _let_40 false _let_36 false _let_85 false _let_91)))) (let ((_let_118 (not _let_90))) (let ((_let_119 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_90 1)) :args ((or _let_81 _let_118))) _let_117 :args (_let_81 false _let_90)))) (let ((_let_120 (_let_79))) (let ((_let_121 (tptp.apply_netmap SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67))) (let ((_let_122 (tptp.in _let_121 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_123 (not _let_74))) (let ((_let_124 (not _let_76))) (let ((_let_125 (or _let_124 _let_123 _let_122))) (let ((_let_126 (forall ((E $$unsorted)) (or (not (tptp.element E (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (not (tptp.related SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 E)) (tptp.in (tptp.apply_netmap SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 E) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))))) (let ((_let_127 (not _let_125))) (let ((_let_128 (not _let_126))) (let ((_let_129 (or _let_86 _let_128))) (let ((_let_130 (forall ((D $$unsorted)) (or (not (tptp.element D (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (not (forall ((E $$unsorted)) (or (not (tptp.element E (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (not (tptp.related SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 D E)) (tptp.in (tptp.apply_netmap SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 E) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))))))) (let ((_let_131 (not _let_130))) (let ((_let_132 (= _let_33 _let_131))) (let ((_let_133 (or _let_29 _let_28 _let_40 _let_37 _let_132))) (let ((_let_134 (forall ((A $$unsorted) (BOUND_VARIABLE_1839 $$unsorted) (BOUND_VARIABLE_1837 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty_carrier BOUND_VARIABLE_1837) (not (tptp.net_str BOUND_VARIABLE_1837 A)) (= (tptp.is_eventually_in A BOUND_VARIABLE_1837 BOUND_VARIABLE_1839) (not (forall ((D $$unsorted)) (or (not (tptp.element D (tptp.the_carrier BOUND_VARIABLE_1837))) (not (forall ((E $$unsorted)) (or (not (tptp.element E (tptp.the_carrier BOUND_VARIABLE_1837))) (not (tptp.related BOUND_VARIABLE_1837 D E)) (tptp.in (tptp.apply_netmap A BOUND_VARIABLE_1837 E) BOUND_VARIABLE_1839)))))))))))) (let ((_let_135 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_136 (not _let_132))) (let ((_let_137 (_let_130))) (let ((_let_138 (_let_128))) (let ((_let_139 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_138)) :args _let_138)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_128) _let_126))) (REFL :args (_let_127)) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_129)) :args ((or _let_86 _let_128 (not _let_129)))) _let_116 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_137) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.element D _let_75) false))))) :args _let_137)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_132)) (CONG (REFL :args (_let_136)) (REFL :args (_let_33)) (MACRO_SR_PRED_INTRO :args ((= (not _let_131) _let_130))) :args _let_45)) :args ((or _let_33 _let_130 _let_136))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_41 7)) _let_47 :args ((not _let_33) true _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_133)) :args ((or _let_29 _let_28 _let_40 _let_37 _let_132 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(CNF_EQUIV_POS1 :args (_let_78)) :args ((or (not _let_77) _let_57 (not _let_78)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_77)) :args ((or _let_124 _let_123 _let_77))) _let_141 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_125 1)) (CONG _let_140 (MACRO_SR_PRED_INTRO :args ((= (not _let_123) _let_74))) :args _let_45)) :args ((or _let_74 _let_125))) _let_139 :args (_let_74 true _let_125)) :args (_let_77 false _let_76 false _let_74)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_120) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_120)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_80 0)) :args ((or _let_79 (not _let_80)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_29 _let_28 _let_40 _let_37 _let_86 _let_82 _let_84 _let_80 (not _let_87)))) _let_50 _let_49 _let_112 _let_111 _let_116 _let_119 (MACRO_RESOLUTION_TRUST 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(tptp.one_sorted_str _let_51))) (let ((_let_149 (tptp.apply_on_structs _let_51 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_52 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67))) (let ((_let_150 (= _let_149 _let_54))) (let ((_let_151 (not _let_148))) (let ((_let_152 (or _let_147 _let_151 _let_29 _let_28 _let_64 _let_62 _let_60 _let_145 _let_150))) (let ((_let_153 (= _let_143 _let_149))) (let ((_let_154 (or _let_29 _let_28 _let_147 _let_82 _let_145 _let_153))) (let ((_let_155 (= _let_94 _let_53))) (let ((_let_156 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_41 4)) (CONG _let_48 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_45)) :args ((or _let_38 _let_41))) _let_47 :args (_let_38 true _let_41)))) (let ((_let_157 (forall ((A $$unsorted) (BOUND_VARIABLE_2782 $$unsorted) (BOUND_VARIABLE_2780 $$unsorted) (BOUND_VARIABLE_2778 $$unsorted)) (let ((_let_1 (tptp.netstr_restr_to_element A BOUND_VARIABLE_2778 BOUND_VARIABLE_2782))) (let ((_let_2 (tptp.the_carrier BOUND_VARIABLE_2778))) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (tptp.empty_carrier BOUND_VARIABLE_2778) (not (tptp.directed_relstr BOUND_VARIABLE_2778)) (not (tptp.net_str BOUND_VARIABLE_2778 A)) (not (tptp.element BOUND_VARIABLE_2782 _let_2)) (not (tptp.element BOUND_VARIABLE_2780 _let_2)) (not (tptp.element BOUND_VARIABLE_2780 (tptp.the_carrier _let_1))) (= (tptp.apply_netmap A BOUND_VARIABLE_2778 BOUND_VARIABLE_2780) (tptp.apply_netmap A _let_1 BOUND_VARIABLE_2780)))))))) (let ((_let_158 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_159 (not _let_147))) (let ((_let_160 (and _let_159 _let_83))) (let ((_let_161 (or _let_29 _let_28 _let_40 _let_39 _let_37 _let_86 _let_160))) (let ((_let_162 (forall ((A $$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)) 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_let_114 :args (_let_95 true _let_97)) (REORDERING (CNF_OR_POS :args (_let_154)) :args ((or _let_29 _let_28 _let_82 _let_147 _let_145 _let_153 (not _let_154)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_186 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67 _let_51 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.apply_netmap A BOUND_VARIABLE_2151 BOUND_VARIABLE_2153)))) :args (_let_185))) _let_186 :args (_let_154 false _let_185)) _let_164 _let_119 _let_49 _let_50 (REORDERING (CNF_OR_POS :args (_let_152)) :args ((or _let_29 _let_28 _let_147 _let_151 _let_60 _let_64 _let_62 _let_145 _let_150 (not _let_152)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_183 :args (_let_51 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_52 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.quasi_total C _let_184 (tptp.the_carrier B)) false)) (not (= (tptp.element D _let_184) false))))) :args (_let_182))) _let_183 :args 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(IMPLIES_ELIM (SCOPE (INSTANTIATE _let_158 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element BOUND_VARIABLE_2780 (tptp.the_carrier (tptp.netstr_restr_to_element A BOUND_VARIABLE_2778 BOUND_VARIABLE_2782))) false))))) :args (_let_157))) _let_158 :args (_let_146 false _let_157)) _let_141 _let_116 _let_111 _let_156 _let_112 _let_49 _let_50 :args ((or _let_145 _let_70) true _let_122 false _let_155 false _let_95 false _let_153 false _let_154 true _let_147 false _let_81 false _let_27 true _let_29 false _let_150 false _let_152 false _let_148 false _let_59 false _let_61 false _let_63 true _let_147 false _let_27 true _let_29 false _let_144 false _let_146 false _let_76 false _let_85 false _let_36 false _let_38 true _let_40 false _let_27 true _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_69 _let_58 (not _let_71)))) _let_142 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67 _let_56 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_72))) _let_73 :args (_let_71 false _let_72)) :args (_let_69 false _let_57 false _let_71)) :args (_let_70 false _let_69)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (_let_56 _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67 _let_52 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_66))) _let_68 :args (_let_65 false _let_66)) :args (_let_25 false _let_59 false _let_63 false _let_61 false _let_57 true _let_55 false _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_29 _let_28 _let_26 (not _let_30)))) _let_50 _let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.empty_carrier A) true))))) :args (_let_31))) _let_32 :args (_let_30 false _let_31)) :args (_let_26 true _let_29 false _let_27 false _let_30)) (AND_ELIM (ASSUME :args (_let_13)) :args (0)) :args (false false _let_25 true _let_24 false _let_10)) :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.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)) (=> (tptp.finite A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.finite B))))) _let_22 _let_21 _let_20 _let_19 (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.partfun_dom_restriction A B C D))) (=> (and (tptp.function C) (tptp.relation_of2 C A B)) (and (tptp.function _let_1) (tptp.relation_of2_as_subset _let_1 A B))))) true (forall ((A $$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)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (tptp.element (tptp.relation_rng_as_subset A B C) (tptp.powerset B)))) _let_18 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.subnetstr_of_element A B C))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.transitive_relstr B) (tptp.directed_relstr B) (tptp.net_str B A) (tptp.element C (tptp.the_carrier B))) (and (tptp.strict_net_str _let_1 A) (tptp.subnet _let_1 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_dom_restriction A B)))) _let_17 true _let_16 true true _let_15 (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) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.transitive_relstr B) (tptp.directed_relstr B) (tptp.net_str B A)) (forall ((C $$unsorted)) (=> (tptp.subnet C A B) (and (not (tptp.empty_carrier C)) (tptp.transitive_relstr C) (tptp.directed_relstr C) (tptp.net_str C A)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.rel_str A) (tptp.relation_of2_as_subset (tptp.the_InternalRel A) _let_1 _let_1)))) true _let_14 (exists ((A $$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)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.net_str B A)) (exists ((C $$unsorted)) (tptp.netstr_induced_subset C A B)))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2_as_subset C A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.transitive_relstr B) (tptp.directed_relstr B) (tptp.net_str B A)) (exists ((C $$unsorted)) (tptp.subnet C A B)))) _let_13 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_dom_restriction A B))) (=> (and (tptp.relation A) (tptp.relation_empty_yielding A)) (and (tptp.relation _let_1) (tptp.relation_empty_yielding _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B)) (tptp.finite (tptp.cartesian_product2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.the_mapping A B))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.net_str B A)) (and (not (tptp.empty _let_1)) (tptp.relation _let_1) (tptp.function _let_1) (tptp.quasi_total _let_1 (tptp.the_carrier B) (tptp.the_carrier A)))))) _let_12 (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_11 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.netstr_restr_to_element A B C))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.transitive_relstr B) (tptp.directed_relstr B) (tptp.net_str B A) (tptp.element C (tptp.the_carrier B))) (and (not (tptp.empty_carrier _let_1)) (tptp.transitive_relstr _let_1) (tptp.strict_net_str _let_1 A) (tptp.directed_relstr _let_1))))) (and _let_10 _let_9) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_rng A))))) (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 $$unsorted)) (let ((_let_1 (tptp.relation_rng A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (forall ((A $$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 $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.transitive_relstr B) (tptp.directed_relstr B) (tptp.net_str B A)) (exists ((C $$unsorted)) (and (tptp.subnet C A B) (not (tptp.empty_carrier C)) (tptp.transitive_relstr C) (tptp.strict_net_str C A) (tptp.directed_relstr C))))) (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 $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.powerset A))) (not (tptp.empty B)) (tptp.finite B)))) (forall ((A $$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)) (=> (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 $$unsorted)) (=> (tptp.relation A) (= (tptp.relation_restriction_as_relation_of A B) (tptp.relation_restriction A B)))) _let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.function C) (tptp.relation_of2 C A B)) (= (tptp.partfun_dom_restriction A B C D) (tptp.relation_dom_restriction C D)))) _let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.transitive_relstr B) (tptp.directed_relstr B) (tptp.net_str B A) (tptp.element C (tptp.the_carrier B))) (= (tptp.subnetstr_of_element A B C) (tptp.netstr_restr_to_element A B C)))) _let_6 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_5 _let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) _let_3 (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 $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) _let_2 (forall ((A $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 283.01/283.19 )
% 283.01/283.19 % SZS output end Proof for SEU390+1
% 283.01/283.19 % cvc5---1.0.5 exiting
% 283.01/283.20 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------