%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU098+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n005.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 16:29:15 EDT 2023

% Result   : Theorem 7.60s 7.87s
% Output   : Proof 7.60s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU098+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n005.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 13:14:09 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 7.60/7.87  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.wccigD6FhC/cvc5---1.0.5_7935.p...
% 7.60/7.87  ------- get file name : TPTP file name is SEU098+1
% 7.60/7.87  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_7935.smt2...
% 7.60/7.87  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 7.60/7.87  % SZS status Theorem for SEU098+1
% 7.60/7.87  % SZS output start Proof for SEU098+1
% 7.60/7.87  (
% 7.60/7.87  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))))) (let ((_let_2 (not (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (= (tptp.finite (tptp.relation_dom A)) (tptp.finite A))))))) (let ((_let_3 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.finite (tptp.relation_dom A)) (tptp.finite (tptp.relation_rng A))))))) (let ((_let_4 (forall ((A $$unsorted)) (=> (tptp.relation A) (tptp.subset A (tptp.cartesian_product2 (tptp.relation_dom A) (tptp.relation_rng A))))))) (let ((_let_5 (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (let ((_let_2 (tptp.relation_rng A))) (=> (and (tptp.relation A) (tptp.function A)) (= (tptp.function_image (tptp.cartesian_product2 _let_1 _let_2) _let_1 (tptp.first_projection_as_func_of _let_1 _let_2) A) _let_1))))))) (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 $$unsorted)) (= (tptp.first_projection_as_func_of A B) (tptp.first_projection A B))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.function C) (tptp.quasi_total C A B) (tptp.relation_of2 C A B)) (= (tptp.function_image A B C D) (tptp.relation_image C D)))))) (let ((_let_9 (tptp.relation tptp.empty_set))) (let ((_let_10 (tptp.empty tptp.empty_set))) (let ((_let_11 (tptp.relation_empty_yielding tptp.empty_set))) (let ((_let_12 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B)) (tptp.finite (tptp.cartesian_product2 A B)))))) (let ((_let_13 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.function A) (tptp.finite B)) (tptp.finite (tptp.relation_image A B)))))) (let ((_let_14 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.cartesian_product2 A B))) (let ((_let_2 (tptp.first_projection_as_func_of A B))) (and (tptp.function _let_2) (tptp.quasi_total _let_2 _let_1 A) (tptp.relation_of2_as_subset _let_2 _let_1 A))))))) (let ((_let_15 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.first_projection A B))) (and (tptp.relation _let_1) (tptp.function _let_1)))))) (let ((_let_16 (forall ((A $$unsorted)) (=> (tptp.finite A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.finite B))))))) (let ((_let_17 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.finite A)) (not (tptp.finite B)) (tptp.finite (tptp.cartesian_product2 A B)))))) (let ((_let_18 (tptp.relation_rng SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_19 (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_20 (tptp.cartesian_product2 _let_19 _let_18))) (let ((_let_21 (tptp.finite _let_20))) (let ((_let_22 (tptp.finite _let_18))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.finite _let_19))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23 _let_21))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (not _let_26))) (let ((_let_29 (tptp.finite SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_30 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 (tptp.powerset _let_20)))) (let ((_let_31 (not _let_30))) (let ((_let_32 (not _let_21))) (let ((_let_33 (or _let_32 _let_31 _let_29))) (let ((_let_34 (forall ((A $$unsorted) (BOUND_VARIABLE_1382 $$unsorted)) (or (not (tptp.finite A)) (not (tptp.element BOUND_VARIABLE_1382 (tptp.powerset A))) (tptp.finite BOUND_VARIABLE_1382))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 _let_20))) (let ((_let_37 (= _let_36 _let_30))) (let ((_let_38 (_let_1))) (let ((_let_39 (ASSUME :args _let_38))) (let ((_let_40 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_36))) (let ((_let_43 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (tptp.subset A (tptp.cartesian_product2 (tptp.relation_dom A) (tptp.relation_rng A))))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (= _let_24 _let_29))) (let ((_let_46 (tptp.function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_41 _let_47 _let_45))) (let ((_let_49 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (not (tptp.function A)) (= (tptp.finite (tptp.relation_dom A)) (tptp.finite A)))))) (let ((_let_50 (not _let_48))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (or))) (let ((_let_53 (not _let_49))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_51) :args (_let_53))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_49))) (REFL :args (_let_50)) :args _let_52)) _let_51 :args (_let_50 true _let_49)))) (let ((_let_55 (REFL :args (_let_48)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 0)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_52)) :args ((or _let_40 _let_48))) _let_54 :args (_let_40 true _let_48)))) (let ((_let_57 (not _let_29))) (let ((_let_58 (tptp.first_projection_as_func_of _let_19 _let_18))) (let ((_let_59 (tptp.function _let_58))) (let ((_let_60 (tptp.relation _let_58))) (let ((_let_61 (tptp.relation_image _let_58 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_62 (tptp.finite _let_61))) (let ((_let_63 (not _let_59))) (let ((_let_64 (not _let_60))) (let ((_let_65 (or _let_64 _let_63 _let_57 _let_62))) (let ((_let_66 (tptp.function_image _let_20 _let_19 _let_58 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_67 (= _let_19 _let_66))) (let ((_let_68 (= _let_66 _let_61))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_48 2)) _let_54 :args ((not _let_45) true _let_48)))) (let ((_let_70 (_let_45))) (let ((_let_71 (forall ((BOUND_VARIABLE_1445 $$unsorted) (BOUND_VARIABLE_1447 $$unsorted)) (tptp.function (tptp.first_projection_as_func_of BOUND_VARIABLE_1445 BOUND_VARIABLE_1447))))) (let ((_let_72 (0))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (_let_71))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_74) :args (_let_19 _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.first_projection_as_func_of BOUND_VARIABLE_1445 BOUND_VARIABLE_1447)))) :args _let_74)) (AND_ELIM _let_73 :args _let_72) :args (_let_59 false _let_71)))) (let ((_let_76 (tptp.first_projection _let_19 _let_18))) (let ((_let_77 (tptp.relation _let_76))) (let ((_let_78 (= _let_58 _let_76))) (let ((_let_79 (forall ((BOUND_VARIABLE_1427 $$unsorted) (BOUND_VARIABLE_1429 $$unsorted)) (tptp.relation (tptp.first_projection BOUND_VARIABLE_1427 BOUND_VARIABLE_1429))))) (let ((_let_80 (_let_79))) (let ((_let_81 (_let_7))) (let ((_let_82 (ASSUME :args _let_81))) (let ((_let_83 (and _let_78 _let_77))) (let ((_let_84 (ASSUME :args (_let_77)))) (let ((_let_85 (ASSUME :args (_let_78)))) (let ((_let_86 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.relation A)) (not (tptp.function A)) (not (tptp.finite B)) (tptp.finite (tptp.relation_image A B)))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (or _let_41 _let_47 _let_67))) (let ((_let_89 (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_rng A))) (let ((_let_2 (tptp.relation_dom A))) (or (not (tptp.relation A)) (not (tptp.function A)) (= _let_2 (tptp.function_image (tptp.cartesian_product2 _let_2 _let_1) _let_2 (tptp.first_projection_as_func_of _let_2 _let_1) A)))))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 1)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_52)) :args ((or _let_46 _let_48))) _let_54 :args (_let_46 true _let_48)))) (let ((_let_92 (tptp.relation_of2 _let_58 _let_20 _let_19))) (let ((_let_93 (not _let_92))) (let ((_let_94 (tptp.quasi_total _let_58 _let_20 _let_19))) (let ((_let_95 (not _let_94))) (let ((_let_96 (or _let_63 _let_95 _let_93 _let_68))) (let ((_let_97 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (or (not (tptp.function C)) (not (tptp.quasi_total C A B)) (not (tptp.relation_of2 C A B)) (= (tptp.function_image A B C D) (tptp.relation_image C D)))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (tptp.relation_of2_as_subset _let_58 _let_20 _let_19))) (let ((_let_100 (= _let_92 _let_99))) (let ((_let_101 (_let_6))) (let ((_let_102 (ASSUME :args _let_101))) (let ((_let_103 (forall ((BOUND_VARIABLE_1462 $$unsorted) (BOUND_VARIABLE_1464 $$unsorted)) (tptp.relation_of2_as_subset (tptp.first_projection_as_func_of BOUND_VARIABLE_1462 BOUND_VARIABLE_1464) (tptp.cartesian_product2 BOUND_VARIABLE_1462 BOUND_VARIABLE_1464) BOUND_VARIABLE_1462)))) (let ((_let_104 (_let_103))) (let ((_let_105 (forall ((BOUND_VARIABLE_1453 $$unsorted) (BOUND_VARIABLE_1455 $$unsorted)) (tptp.quasi_total (tptp.first_projection_as_func_of BOUND_VARIABLE_1453 BOUND_VARIABLE_1455) (tptp.cartesian_product2 BOUND_VARIABLE_1453 BOUND_VARIABLE_1455) BOUND_VARIABLE_1453)))) (let ((_let_106 (_let_105))) (let ((_let_107 (and _let_25 _let_67 _let_68))) (let ((_let_108 (_let_25 _let_67 _let_68))) (let ((_let_109 (ASSUME :args (_let_25)))) (let ((_let_110 (ASSUME :args (_let_67)))) (let ((_let_111 (ASSUME :args (_let_68)))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_107)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_109 _let_110 _let_111) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS (SYMM _let_111) (SYMM _let_110)) :args (APPLY_UF tptp.finite)) (FALSE_INTRO _let_109))) :args _let_108)) :args _let_108)) :args (true _let_107)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) (REFL :args ((not _let_67))) (REFL :args ((not _let_68))) (REFL :args ((not _let_62))) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_63 _let_95 _let_93 _let_68 (not _let_96)))) _let_75 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_106) :args (_let_19 _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.first_projection_as_func_of BOUND_VARIABLE_1453 BOUND_VARIABLE_1455)))) :args _let_106)) (AND_ELIM _let_73 :args (1)) :args (_let_94 false _let_105)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_100)) :args ((or _let_92 (not _let_99) (not _let_100)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_104) :args (_let_19 _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.first_projection_as_func_of BOUND_VARIABLE_1462 BOUND_VARIABLE_1464)))) :args _let_104)) (AND_ELIM _let_73 :args (2)) :args (_let_99 false _let_103)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_102 :args (_let_20 _let_19 _let_58 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.relation_of2_as_subset C A B)))) :args _let_101))) _let_102 :args (_let_100 false _let_6)) :args (_let_92 false _let_99 false _let_100)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_98 :args (_let_20 _let_19 _let_58 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.function_image A B C D)))) :args (_let_97))) _let_98 :args (_let_96 false _let_97)) :args (_let_68 false _let_59 false _let_94 false _let_92 false _let_96)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_41 _let_47 _let_67 (not _let_88)))) _let_56 _let_91 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation A) false))))) :args (_let_89))) _let_90 :args (_let_88 false _let_89)) :args (_let_67 false _let_40 false _let_46 false _let_88)) (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_57 _let_63 _let_64 _let_62 (not _let_65)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (_let_58 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.relation_image A B)))) :args (_let_86))) _let_87 :args (_let_65 false _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_83)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_84 _let_85) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_85)) :args (APPLY_UF tptp.relation)) (TRUE_INTRO _let_84))) :args (_let_77 _let_78))) :args (_let_78 _let_77))) :args (true _let_83)) :args ((or (not _let_78) _let_60 (not _let_77)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (_let_19 _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.first_projection_as_func_of A B)))) :args _let_81)) _let_82 :args (_let_78 false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_80) :args (_let_19 _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.first_projection BOUND_VARIABLE_1427 BOUND_VARIABLE_1429)))) :args _let_80)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))) :args _let_72) :args (_let_77 false _let_79)) :args (_let_60 false _let_78 false _let_77)) _let_75 (REORDERING (CNF_EQUIV_NEG1 :args _let_70) :args ((or _let_24 _let_29 _let_45))) _let_69 :args (_let_24 false _let_68 false _let_67 false _let_62 false _let_65 false _let_60 false _let_59 false _let_29 true _let_45)))) (let ((_let_113 (or _let_41 _let_47 _let_25 _let_22))) (let ((_let_114 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (not (tptp.function A)) (not (tptp.finite (tptp.relation_dom A))) (tptp.finite (tptp.relation_rng A)))))) (let ((_let_115 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (_let_19 _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cartesian_product2 A B)))) :args (_let_17))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_23 _let_21 _let_28))) _let_112 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_113)) :args ((or _let_41 _let_47 _let_25 _let_22 (not _let_113)))) _let_56 _let_91 _let_112 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_115 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation A) false))))) :args (_let_114))) _let_115 :args (_let_113 false _let_114)) :args (_let_22 false _let_40 false _let_46 false _let_24 false _let_113)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_29 _let_31 _let_32 (not _let_33)))) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_70) _let_69 _let_112 :args (_let_57 true _let_45 false _let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_37)) :args ((or (not _let_36) _let_30 (not _let_37)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_41 _let_36 (not _let_42)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.relation_dom A)))) :args (_let_43))) _let_44 :args (_let_42 false _let_43)) :args (_let_36 false _let_40 false _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_39 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 _let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args _let_38))) _let_39 :args (_let_37 false _let_1)) :args (_let_30 false _let_36 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (_let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element BOUND_VARIABLE_1382 (tptp.powerset A)) false))))) :args (_let_34))) _let_35 :args (_let_33 false _let_34)) :args (_let_32 true _let_29 false _let_30 false _let_33)) :args (_let_28 false _let_24 false _let_22 true _let_21)) _let_27 :args (false true _let_26 false _let_17)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.epsilon_transitive B) (tptp.epsilon_connected B) (tptp.ordinal B)))))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.finite A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected 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 $$unsorted)) (let ((_let_1 (tptp.ordinal A))) (=> (and (tptp.empty A) _let_1) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) _let_1 (tptp.natural A))))) _let_16 (forall ((A $$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 $$unsorted)) (=> (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)) (tptp.ordinal A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.ordinal A))) (=> (tptp.element A tptp.positive_rationals) (=> _let_1 (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) _let_1 (tptp.natural A)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.function C) (tptp.quasi_total C A B) (tptp.relation_of2 C A B)) (tptp.element (tptp.function_image A B C D) (tptp.powerset B)))) _let_15 _let_14 (forall ((A $$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)) (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_10 _let_9 _let_11) _let_13 _let_12 (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_10 (and _let_9 _let_11 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) _let_10 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set)) (and _let_10 _let_9) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (=> (and (tptp.relation A) (tptp.function A) (tptp.transfinite_sequence A)) (and (tptp.epsilon_transitive _let_1) (tptp.epsilon_connected _let_1) (tptp.ordinal _let_1))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_dom A))))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.relation_non_empty A) (tptp.function A)) (tptp.with_non_empty_elements (tptp.relation_rng A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_rng A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (not (tptp.empty tptp.positive_rationals)) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_rng A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A) (tptp.natural A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.finite A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.function_yielding A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$unsorted)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A) (tptp.being_limit_ordinal A))) (exists ((A $$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 $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (and (tptp.element A tptp.positive_rationals) (not (tptp.empty A)) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B) (tptp.relation B) (tptp.function B) (tptp.one_to_one B) (tptp.epsilon_transitive B) (tptp.epsilon_connected B) (tptp.ordinal B) (tptp.natural B) (tptp.finite B)))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A) (tptp.empty A) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.transfinite_sequence A) (tptp.ordinal_yielding A))) (exists ((A $$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)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.element A tptp.positive_rationals) (tptp.empty A) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A) (tptp.natural 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 (not (tptp.empty A)) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))) (forall ((A $$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) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.transfinite_sequence A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_non_empty A) (tptp.function A))) _let_8 _let_7 _let_6 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.subset A B) (tptp.finite B)) (tptp.finite A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (=> (tptp.finite A) (tptp.finite (tptp.relation_image B A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B)) (tptp.finite (tptp.cartesian_product2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_4 _let_3 _let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) _let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 7.60/7.92  )
% 7.60/7.92  % SZS output end Proof for SEU098+1
% 7.60/7.92  % cvc5---1.0.5 exiting
% 7.60/7.92  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------