TSTP Solution File: SEU011+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU011+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.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 16:29:02 EDT 2023
% Result : Theorem 25.65s 25.99s
% Output : Proof 25.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU011+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : do_cvc5 %s %d
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 19:17:12 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.46 %----Proving TF0_NAR, FOF, or CNF
% 25.65/25.99 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.26OLxSrOBC/cvc5---1.0.5_3608.p...
% 25.65/25.99 ------- get file name : TPTP file name is SEU011+1
% 25.65/25.99 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_3608.smt2...
% 25.65/25.99 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.65/25.99 --- Run --no-e-matching --full-saturate-quant at 5...
% 25.65/25.99 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.65/25.99 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.65/25.99 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.65/25.99 % SZS status Theorem for SEU011+1
% 25.65/25.99 % SZS output start Proof for SEU011+1
% 25.65/25.99 (
% 25.65/25.99 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.relation_composition (tptp.identity_relation B) (tptp.identity_relation A)) (tptp.identity_relation (tptp.set_intersection2 A B)))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (= (tptp.relation_dom (tptp.relation_composition (tptp.identity_relation A) B)) (tptp.set_intersection2 (tptp.relation_dom B) A)))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (= (= B (tptp.identity_relation A)) (and (= (tptp.relation_dom B) A) (forall ((C $$unsorted)) (=> (tptp.in C A) (= (tptp.apply B C) C))))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.relation_composition C B))) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in A (tptp.relation_dom _let_1)) (= (tptp.apply _let_1 A) (tptp.apply B (tptp.apply C A))))))))))) (let ((_let_6 (tptp.relation tptp.empty_set))) (let ((_let_7 (tptp.empty tptp.empty_set))) (let ((_let_8 (forall ((A $$unsorted)) (let ((_let_1 (tptp.identity_relation A))) (and (tptp.relation _let_1) (tptp.function _let_1)))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition A B))) (=> (and (tptp.relation A) (tptp.function A) (tptp.relation B) (tptp.function B)) (and (tptp.relation _let_1) (tptp.function _let_1))))))) (let ((_let_10 (forall ((A $$unsorted)) (tptp.relation (tptp.identity_relation A))))) (let ((_let_11 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.relation_composition A B)))))) (let ((_let_12 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_intersection2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (tptp.in D B)))))))) (let ((_let_13 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))))) (let ((_let_14 (tptp.identity_relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_15 (tptp.identity_relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_16 (tptp.relation_composition _let_15 _let_14))) (let ((_let_17 (tptp.apply _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 _let_17))) (let ((_let_19 (tptp.apply _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26))) (let ((_let_20 (= _let_17 (tptp.apply _let_14 _let_19)))) (let ((_let_21 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 _let_19))) (let ((_let_22 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 (tptp.apply _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26)))) (let ((_let_23 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_24 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 _let_23))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_18))) (let ((_let_27 (not _let_18))) (let ((_let_28 (forall ((C $$unsorted)) (or (not (tptp.in C (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (= C (tptp.apply (tptp.relation_composition (tptp.identity_relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) (tptp.identity_relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) C)))))) (let ((_let_29 (not _let_26))) (let ((_let_30 (tptp.relation_dom _let_16))) (let ((_let_31 (= _let_23 _let_30))) (let ((_let_32 (and _let_31 _let_28))) (let ((_let_33 (not _let_28))) (let ((_let_34 (tptp.relation_dom _let_14))) (let ((_let_35 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_34))) (let ((_let_36 (= _let_30 (tptp.set_intersection2 _let_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (let ((_let_37 (forall ((C $$unsorted)) (or (not (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (= C (tptp.apply (tptp.identity_relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) C)))))) (let ((_let_38 (and _let_35 _let_37))) (let ((_let_39 (tptp.function _let_14))) (let ((_let_40 (not _let_39))) (let ((_let_41 (tptp.relation _let_14))) (let ((_let_42 (not _let_41))) (let ((_let_43 (or _let_42 _let_40 _let_38))) (let ((_let_44 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.relation B)) (not (tptp.function B)) (= (= B (tptp.identity_relation A)) (and (= A (tptp.relation_dom B)) (forall ((C $$unsorted)) (or (not (tptp.in C A)) (= C (tptp.apply B C)))))))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (_let_44))) (let ((_let_47 (forall ((BOUND_VARIABLE_1036 $$unsorted)) (tptp.function (tptp.identity_relation BOUND_VARIABLE_1036))))) (let ((_let_48 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) :args (1)))) (let ((_let_49 (_let_47))) (let ((_let_50 ((tptp.identity_relation BOUND_VARIABLE_1036)))) (let ((_let_51 (ASSUME :args _let_49))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_39 false _let_47)))) (let ((_let_53 (_let_10))) (let ((_let_54 (ASSUME :args _let_53))) (let ((_let_55 ((tptp.identity_relation A)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_55)) :args _let_53)) _let_54 :args (_let_41 false _let_10)))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_42 _let_40 _let_38 (not _let_43)))) _let_56 _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_14 QUANTIFIERS_INST_CBQI_PROP)) :args _let_46))) _let_45 :args (_let_43 false _let_44)) :args (_let_38 false _let_41 false _let_39 false _let_43)))) (let ((_let_58 (not _let_38))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_38 0)) :args ((or _let_35 _let_58))) _let_57 :args (_let_35 false _let_38)))) (let ((_let_60 (or _let_42 _let_40 _let_36))) (let ((_let_61 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.relation B)) (not (tptp.function B)) (= (tptp.relation_dom (tptp.relation_composition (tptp.identity_relation A) B)) (tptp.set_intersection2 (tptp.relation_dom B) A)))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_42 _let_40 _let_36 (not _let_60)))) _let_56 _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_14 QUANTIFIERS_INST_E_MATCHING ((tptp.relation_composition (tptp.identity_relation A) B)))) :args (_let_61))) _let_62 :args (_let_60 false _let_61)) :args (_let_36 false _let_41 false _let_39 false _let_60)))) (let ((_let_64 (and _let_36 _let_35))) (let ((_let_65 (_let_36 _let_35))) (let ((_let_66 (ASSUME :args (_let_36)))) (let ((_let_67 (SYMM _let_66))) (let ((_let_68 (APPLY_UF tptp.set_intersection2))) (let ((_let_69 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (let ((_let_70 (ASSUME :args (_let_35)))) (let ((_let_71 (SYMM (SYMM _let_70)))) (let ((_let_72 (= _let_16 (tptp.identity_relation _let_23)))) (let ((_let_73 (= _let_72 _let_32))) (let ((_let_74 (not _let_32))) (let ((_let_75 (tptp.function _let_16))) (let ((_let_76 (not _let_75))) (let ((_let_77 (tptp.relation _let_16))) (let ((_let_78 (not _let_77))) (let ((_let_79 (or _let_78 _let_76 _let_73))) (let ((_let_80 (and _let_77 _let_75))) (let ((_let_81 (tptp.function _let_15))) (let ((_let_82 (not _let_81))) (let ((_let_83 (tptp.relation _let_15))) (let ((_let_84 (not _let_83))) (let ((_let_85 (or _let_84 _let_82 _let_42 _let_40 _let_80))) (let ((_let_86 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition A B))) (or (not (tptp.relation A)) (not (tptp.function A)) (not (tptp.relation B)) (not (tptp.function B)) (and (tptp.relation _let_1) (tptp.function _let_1))))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_81 false _let_47)))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_55)) :args _let_53)) _let_54 :args (_let_83 false _let_10)))) (let ((_let_90 (or _let_84 _let_42 _let_77))) (let ((_let_91 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.relation A)) (not (tptp.relation B)) (tptp.relation (tptp.relation_composition A B)))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (not _let_72))) (let ((_let_94 (_let_2))) (let ((_let_95 (ASSUME :args _let_94))) (let ((_let_96 (or))) (let ((_let_97 (_let_33))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_97)) :args _let_97)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_28))) (REFL :args (_let_29)) :args _let_96)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_73)) :args ((or _let_72 _let_74 (not _let_73)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_95) :args _let_94)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_93)) :args _let_96)) _let_95 :args (_let_93 true _let_1)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_78 _let_76 _let_73 (not _let_79)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_84 _let_42 _let_77 (not _let_90)))) _let_89 _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_92 :args (_let_15 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.relation_composition A B)))) :args (_let_91))) _let_92 :args (_let_90 false _let_91)) :args (_let_77 false _let_83 false _let_41 false _let_90)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_80 1)) :args ((or _let_75 (not _let_80)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_84 _let_42 _let_82 _let_40 _let_80 (not _let_85)))) _let_89 _let_56 _let_88 _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (_let_15 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.relation_composition A B)))) :args (_let_86))) _let_87 :args (_let_85 false _let_86)) :args (_let_80 false _let_83 false _let_41 false _let_81 false _let_39 false _let_85)) :args (_let_75 false _let_80)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (_let_23 _let_16 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.relation B) false)) (tptp.identity_relation A)))) :args _let_46)) _let_45 :args (_let_79 false _let_44)) :args (_let_73 false _let_77 false _let_75 false _let_79)) :args (_let_74 true _let_72 false _let_73)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_64)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_66 _let_70) (SCOPE (TRANS (CONG _let_71 _let_69 :args _let_68) _let_67) :args _let_65)) :args _let_65)) :args (true _let_64)) _let_63 _let_59 :args (_let_31 false _let_36 false _let_35)) :args (_let_33 true _let_32 false _let_31)) :args (_let_29 true _let_28)))) (let ((_let_99 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 _let_30))) (let ((_let_100 (not _let_99))) (let ((_let_101 (or _let_42 _let_40 _let_84 _let_82 _let_100 _let_20))) (let ((_let_102 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1153 $$unsorted)) (let ((_let_1 (tptp.relation_composition BOUND_VARIABLE_1153 B))) (or (not (tptp.relation B)) (not (tptp.function B)) (not (tptp.relation BOUND_VARIABLE_1153)) (not (tptp.function BOUND_VARIABLE_1153)) (not (tptp.in A (tptp.relation_dom _let_1))) (= (tptp.apply _let_1 A) (tptp.apply B (tptp.apply BOUND_VARIABLE_1153 A)))))))) (let ((_let_103 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 0)) (CONG (REFL :args (_let_26)) (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_96)) :args ((or _let_24 _let_26))) _let_98 :args (_let_24 true _let_26)))) (let ((_let_105 (and _let_36 _let_35 _let_24))) (let ((_let_106 (ASSUME :args (_let_24)))) (let ((_let_107 (TRUE_INTRO _let_106))) (let ((_let_108 (APPLY_UF tptp.in))) (let ((_let_109 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26)))) (let ((_let_110 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_111 (not _let_110))) (let ((_let_112 (or _let_111 _let_21))) (let ((_let_113 (forall ((C $$unsorted)) (or (not (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)) (= C (tptp.apply (tptp.identity_relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) C)))))) (let ((_let_114 (and (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 (tptp.relation_dom _let_15)) _let_113))) (let ((_let_115 (or _let_84 _let_82 _let_114))) (let ((_let_116 (_let_113))) (let ((_let_117 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_118 (and _let_110 _let_117))) (let ((_let_119 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_120 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 _let_119))) (let ((_let_121 (= _let_120 _let_118))) (let ((_let_122 (forall ((D $$unsorted)) (= (tptp.in D (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (and (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))))) (let ((_let_123 (_let_12))) (let ((_let_124 (ASSUME :args _let_123))) (let ((_let_125 (_let_122))) (let ((_let_126 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_127 (= _let_23 _let_119))) (let ((_let_128 (_let_13))) (let ((_let_129 (ASSUME :args _let_128))) (let ((_let_130 (and _let_127 _let_24))) (let ((_let_131 (ASSUME :args (_let_127)))) (let ((_let_132 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_121)) :args ((or _let_118 (not _let_120) (not _let_121)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_130)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_106 _let_131) (SCOPE (TRUE_ELIM (TRANS (CONG _let_109 (SYMM _let_131) :args _let_108) _let_107)) :args (_let_24 _let_127))) :args (_let_127 _let_24))) :args (true _let_130)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_129 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_intersection2 A B)))) :args _let_128)) _let_129 :args (_let_127 false _let_13)) _let_104 :args (_let_120 false _let_127 false _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_125) :args _let_126) :args _let_125)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_124 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_119 QUANTIFIERS_INST_CBQI_PROP)) :args _let_123))) _let_124 :args (_let_122 false _let_12)) :args (_let_121 false _let_122)) :args (_let_118 false _let_120 false _let_121)))) (let ((_let_133 (not _let_118))) (let ((_let_134 (not _let_117))) (let ((_let_135 (or _let_134 _let_22))) (let ((_let_136 (_let_37))) (let ((_let_137 (not _let_22))) (let ((_let_138 (_let_137))) (let ((_let_139 (ASSUME :args (_let_22)))) (let ((_let_140 (ASSUME :args (_let_27)))) (let ((_let_141 (ASSUME :args (_let_20)))) (let ((_let_142 (ASSUME :args (_let_21)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_140 _let_141 _let_142) (SCOPE (FALSE_ELIM (TRANS (CONG _let_109 (TRANS (CONG (REFL :args (_let_14)) (SYMM (SYMM _let_142)) :args (APPLY_UF tptp.apply)) (SYMM _let_141)) :args (=)) (FALSE_INTRO _let_140))) :args (_let_27 _let_20 _let_21))) _let_139) :args (_let_27 _let_21 _let_20 _let_22)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args _let_138))) (TRUE_INTRO _let_139))) :args (_let_137 _let_22)) :args ((not (and _let_27 _let_21 _let_20 _let_22)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_18))) (REFL :args ((not _let_21))) (REFL :args ((not _let_20))) (REFL :args _let_138) :args _let_96)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_135)) :args ((or _let_134 _let_22 (not _let_135)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_118 1)) :args ((or _let_117 _let_133))) _let_132 :args (_let_117 false _let_118)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_136) :args _let_126) :args _let_136)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_38 1)) :args ((or _let_37 _let_58))) _let_57 :args (_let_37 false _let_38)) :args (_let_135 false _let_37)) :args (_let_22 false _let_117 false _let_135)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_112)) :args ((or _let_21 _let_111 (not _let_112)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_118 0)) :args ((or _let_110 _let_133))) _let_132 :args (_let_110 false _let_118)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_116) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) false))))) :args _let_116)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_114 1)) :args ((or _let_113 (not _let_114)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_115)) :args ((or _let_84 _let_82 _let_114 (not _let_115)))) _let_89 _let_88 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_15 QUANTIFIERS_INST_CBQI_PROP)) :args _let_46))) _let_45 :args (_let_115 false _let_44)) :args (_let_114 false _let_83 false _let_81 false _let_115)) :args (_let_113 false _let_114)) :args (_let_112 false _let_113)) :args (_let_21 false _let_110 false _let_112)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_101)) :args ((or _let_84 _let_42 _let_82 _let_40 _let_100 _let_20 (not _let_101)))) _let_89 _let_56 _let_88 _let_52 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_105)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_106 _let_70 _let_66) (SCOPE (TRUE_ELIM (TRANS (CONG _let_109 (TRANS (SYMM _let_67) (CONG (SYMM _let_71) _let_69 :args _let_68)) :args _let_108) _let_107)) :args (_let_24 _let_35 _let_36))) :args (_let_36 _let_35 _let_24))) :args (true _let_105)) _let_63 _let_59 _let_104 :args (_let_99 false _let_36 false _let_35 false _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_103 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 _let_14 _let_15 QUANTIFIERS_INST_E_MATCHING ((tptp.apply (tptp.relation_composition BOUND_VARIABLE_1153 B) A)))) :args (_let_102))) _let_103 :args (_let_101 false _let_102)) :args (_let_20 false _let_83 false _let_41 false _let_81 false _let_39 false _let_99 false _let_101)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 1)) _let_98 :args (_let_27 true _let_26)) :args (false false _let_22 false _let_21 false _let_20 true _let_18)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) _let_13 _let_12 _let_11 _let_10 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition B A))) (=> (and (tptp.empty A) (tptp.relation B)) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (and _let_7 _let_6 (tptp.relation_empty_yielding tptp.empty_set)) _let_9 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_intersection2 A B)))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_7 _let_8 (and _let_7 _let_6) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_dom A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition A B))) (=> (and (tptp.empty A) (tptp.relation B)) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (exists ((A $$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 (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.relation A) (tptp.relation_empty_yielding A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_5 (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) _let_4 _let_3 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) _let_2 (forall ((A $$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)))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (=> (and (= (tptp.relation_dom A) (tptp.relation_dom B)) (forall ((C $$unsorted)) (=> (tptp.in C (tptp.relation_dom A)) (= (tptp.apply A C) (tptp.apply B C))))) (= A B)))))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.65/25.99 )
% 25.65/25.99 % SZS output end Proof for SEU011+1
% 25.65/25.99 % cvc5---1.0.5 exiting
% 25.65/26.00 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------