TSTP Solution File: HAL001+2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : HAL001+2 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:53:29 EDT 2023
% Result : Theorem 41.33s 41.53s
% Output : Proof 41.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : HAL001+2 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 02:29:44 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 41.33/41.53 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.B2xOwvFZ7j/cvc5---1.0.5_11748.p...
% 41.33/41.53 ------- get file name : TPTP file name is HAL001+2
% 41.33/41.53 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_11748.smt2...
% 41.33/41.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 41.33/41.53 --- Run --no-e-matching --full-saturate-quant at 5...
% 41.33/41.53 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 41.33/41.53 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 41.33/41.53 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 41.33/41.53 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 41.33/41.53 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 41.33/41.53 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 41.33/41.53 % SZS status Theorem for HAL001+2
% 41.33/41.53 % SZS output start Proof for HAL001+2
% 41.33/41.53 (
% 41.33/41.53 (let ((_let_1 (tptp.injection tptp.g))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.injection tptp.h))) (let ((_let_4 (tptp.injection tptp.f))) (let ((_let_5 (tptp.commute tptp.beta tptp.h tptp.g tptp.delta))) (let ((_let_6 (tptp.commute tptp.alpha tptp.g tptp.f tptp.gamma))) (let ((_let_7 (tptp.exact tptp.alpha tptp.beta))) (let ((_let_8 (tptp.injection tptp.gamma))) (let ((_let_9 (tptp.morphism tptp.h tptp.c tptp.r))) (let ((_let_10 (tptp.morphism tptp.g tptp.b tptp.e))) (let ((_let_11 (tptp.morphism tptp.f tptp.a tptp.d))) (let ((_let_12 (tptp.morphism tptp.delta tptp.e tptp.r))) (let ((_let_13 (tptp.morphism tptp.gamma tptp.d tptp.e))) (let ((_let_14 (tptp.morphism tptp.beta tptp.b tptp.c))) (let ((_let_15 (tptp.morphism tptp.alpha tptp.a tptp.b))) (let ((_let_16 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (and (tptp.morphism Morphism Dom Cod) (forall ((El $$unsorted)) (=> (and (tptp.element El Dom) (= (tptp.apply Morphism El) (tptp.zero Cod))) (= El (tptp.zero Dom))))) (tptp.injection Morphism))))) (let ((_let_17 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (and (tptp.injection Morphism) (tptp.morphism Morphism Dom Cod)) (forall ((El $$unsorted)) (=> (and (tptp.element El Dom) (= (tptp.apply Morphism El) (tptp.zero Cod))) (= El (tptp.zero Dom)))))))) (let ((_let_18 (forall ((M1 $$unsorted) (M2 $$unsorted) (M3 $$unsorted) (M4 $$unsorted) (Dom $$unsorted) (DomCod1 $$unsorted) (DomCod2 $$unsorted) (Cod $$unsorted)) (=> (and (tptp.morphism M1 Dom DomCod1) (tptp.morphism M2 DomCod1 Cod) (tptp.morphism M3 Dom DomCod2) (tptp.morphism M4 DomCod2 Cod) (forall ((ElDom $$unsorted)) (=> (tptp.element ElDom Dom) (= (tptp.apply M2 (tptp.apply M1 ElDom)) (tptp.apply M4 (tptp.apply M3 ElDom)))))) (tptp.commute M1 M2 M3 M4))))) (let ((_let_19 (forall ((M1 $$unsorted) (M2 $$unsorted) (M3 $$unsorted) (M4 $$unsorted) (Dom $$unsorted) (DomCod1 $$unsorted) (DomCod2 $$unsorted) (Cod $$unsorted)) (=> (and (tptp.commute M1 M2 M3 M4) (tptp.morphism M1 Dom DomCod1) (tptp.morphism M2 DomCod1 Cod) (tptp.morphism M3 Dom DomCod2) (tptp.morphism M4 DomCod2 Cod)) (forall ((ElDom $$unsorted)) (=> (tptp.element ElDom Dom) (= (tptp.apply M2 (tptp.apply M1 ElDom)) (tptp.apply M4 (tptp.apply M3 ElDom))))))))) (let ((_let_20 (forall ((Morphism1 $$unsorted) (Morphism2 $$unsorted) (Dom $$unsorted) (CodDom $$unsorted) (Cod $$unsorted)) (=> (and (tptp.exact Morphism1 Morphism2) (tptp.morphism Morphism1 Dom CodDom) (tptp.morphism Morphism2 CodDom Cod)) (forall ((ElCodDom $$unsorted)) (= (and (tptp.element ElCodDom CodDom) (= (tptp.apply Morphism2 ElCodDom) (tptp.zero Cod))) (exists ((ElDom $$unsorted)) (and (tptp.element ElDom Dom) (= (tptp.apply Morphism1 ElDom) ElCodDom))))))))) (let ((_let_21 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (tptp.morphism Morphism Dom Cod) (and (forall ((El $$unsorted)) (=> (tptp.element El Dom) (tptp.element (tptp.apply Morphism El) Cod))) (= (tptp.apply Morphism (tptp.zero Dom)) (tptp.zero Cod))))))) (let ((_let_22 (tptp.zero tptp.b))) (let ((_let_23 (= _let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_24 (tptp.zero tptp.a))) (let ((_let_25 (= _let_22 (tptp.apply tptp.alpha _let_24)))) (let ((_let_26 (tptp.apply tptp.alpha SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))) (let ((_let_27 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_26))) (let ((_let_28 (= _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))) (let ((_let_29 (tptp.apply tptp.g SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_30 (tptp.zero tptp.e))) (let ((_let_31 (= _let_30 _let_29))) (let ((_let_32 (not _let_31))) (let ((_let_33 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.b))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_32 _let_23))) (let ((_let_36 (forall ((El $$unsorted)) (or (not (tptp.element El tptp.b)) (not (= (tptp.zero tptp.e) (tptp.apply tptp.g El))) (= El (tptp.zero tptp.b)))))) (let ((_let_37 (not _let_35))) (let ((_let_38 (not _let_36))) (let ((_let_39 (not _let_10))) (let ((_let_40 (or _let_39 _let_38 _let_1))) (let ((_let_41 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (or (not (tptp.morphism Morphism Dom Cod)) (not (forall ((El $$unsorted)) (or (not (tptp.element El Dom)) (not (= (tptp.apply Morphism El) (tptp.zero Cod))) (= El (tptp.zero Dom))))) (tptp.injection Morphism))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (ASSUME :args (_let_10)))) (let ((_let_44 (or))) (let ((_let_45 (_let_38))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_45)) :args _let_45) (REWRITE :args ((=> _let_38 (not (or _let_34 _let_32 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_22)))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_36))) (REFL :args (_let_37)) :args _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_1 _let_39 _let_38 (not _let_40)))) (ASSUME :args (_let_2)) _let_43 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_42 :args (tptp.g tptp.b tptp.e QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.morphism Morphism Dom Cod) false))))) :args (_let_41)))) _let_42 :args (_let_40 false _let_41)) :args (_let_38 true _let_1 false _let_10 false _let_40)) :args (_let_37 true _let_36)))) (let ((_let_47 (tptp.apply tptp.alpha SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21))) (let ((_let_48 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 tptp.a))) (let ((_let_49 (not _let_48))) (let ((_let_50 (and (or _let_49 (tptp.element _let_47 tptp.b)) _let_25))) (let ((_let_51 (not _let_15))) (let ((_let_52 (or _let_51 _let_50))) (let ((_let_53 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted) (BOUND_VARIABLE_937 $$unsorted)) (or (not (tptp.morphism Morphism Dom Cod)) (and (or (not (tptp.element BOUND_VARIABLE_937 Dom)) (tptp.element (tptp.apply Morphism BOUND_VARIABLE_937) Cod)) (= (tptp.apply Morphism (tptp.zero Dom)) (tptp.zero Cod))))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (_let_53))) (let ((_let_56 ((not (= (tptp.morphism Morphism Dom Cod) false)) (tptp.element BOUND_VARIABLE_937 Dom)))) (let ((_let_57 (ASSUME :args (_let_15)))) (let ((_let_58 (not _let_27))) (let ((_let_59 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 tptp.a))) (let ((_let_60 (not _let_59))) (let ((_let_61 (or _let_60 _let_58))) (let ((_let_62 (forall ((ElDom $$unsorted)) (or (not (tptp.element ElDom tptp.a)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.apply tptp.alpha ElDom))))))) (let ((_let_63 (not _let_61))) (let ((_let_64 (forall ((ElDom $$unsorted)) (or (not (tptp.element ElDom tptp.a)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.apply tptp.alpha ElDom))))))) (let ((_let_65 (not _let_62))) (let ((_let_66 (not _let_64))) (let ((_let_67 (tptp.apply tptp.beta SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_68 (tptp.zero tptp.c))) (let ((_let_69 (= _let_68 _let_67))) (let ((_let_70 (and _let_33 _let_69))) (let ((_let_71 (= _let_70 _let_66))) (let ((_let_72 (not _let_14))) (let ((_let_73 (not _let_7))) (let ((_let_74 (or _let_73 _let_51 _let_72 _let_71))) (let ((_let_75 (forall ((Morphism1 $$unsorted) (Morphism2 $$unsorted) (Dom $$unsorted) (CodDom $$unsorted) (Cod $$unsorted) (BOUND_VARIABLE_1095 $$unsorted)) (or (not (tptp.exact Morphism1 Morphism2)) (not (tptp.morphism Morphism1 Dom CodDom)) (not (tptp.morphism Morphism2 CodDom Cod)) (= (and (tptp.element BOUND_VARIABLE_1095 CodDom) (= (tptp.zero Cod) (tptp.apply Morphism2 BOUND_VARIABLE_1095))) (not (forall ((ElDom $$unsorted)) (or (not (tptp.element ElDom Dom)) (not (= (tptp.apply Morphism1 ElDom) BOUND_VARIABLE_1095)))))))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (ASSUME :args (_let_14)))) (let ((_let_78 (tptp.apply tptp.h _let_67))) (let ((_let_79 (tptp.zero tptp.r))) (let ((_let_80 (= _let_79 _let_78))) (let ((_let_81 (not _let_80))) (let ((_let_82 (tptp.element _let_67 tptp.c))) (let ((_let_83 (not _let_82))) (let ((_let_84 (not _let_9))) (let ((_let_85 (not _let_3))) (let ((_let_86 (or _let_85 _let_84 _let_83 _let_81 _let_69))) (let ((_let_87 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted) (BOUND_VARIABLE_1258 $$unsorted)) (or (not (tptp.injection Morphism)) (not (tptp.morphism Morphism Dom Cod)) (not (tptp.element BOUND_VARIABLE_1258 Dom)) (not (= (tptp.zero Cod) (tptp.apply Morphism BOUND_VARIABLE_1258))) (= (tptp.zero Dom) BOUND_VARIABLE_1258))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (_let_87))) (let ((_let_90 (= _let_79 (tptp.apply tptp.delta _let_30)))) (let ((_let_91 (= (tptp.apply tptp.delta _let_29) _let_78))) (let ((_let_92 (and (or (not (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 tptp.e)) (tptp.element (tptp.apply tptp.delta SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24) tptp.r)) _let_90))) (let ((_let_93 (not _let_12))) (let ((_let_94 (or _let_93 _let_92))) (let ((_let_95 (ASSUME :args (_let_12)))) (let ((_let_96 (tptp.commute tptp.g tptp.delta tptp.beta tptp.h))) (let ((_let_97 (not _let_96))) (let ((_let_98 (or _let_97 _let_39 _let_93 _let_72 _let_84 _let_34 _let_91))) (let ((_let_99 (forall ((M1 $$unsorted) (M2 $$unsorted) (M3 $$unsorted) (M4 $$unsorted) (Dom $$unsorted) (DomCod1 $$unsorted) (DomCod2 $$unsorted) (Cod $$unsorted) (BOUND_VARIABLE_1159 $$unsorted)) (or (not (tptp.commute M1 M2 M3 M4)) (not (tptp.morphism M1 Dom DomCod1)) (not (tptp.morphism M2 DomCod1 Cod)) (not (tptp.morphism M3 Dom DomCod2)) (not (tptp.morphism M4 DomCod2 Cod)) (not (tptp.element BOUND_VARIABLE_1159 Dom)) (= (tptp.apply M2 (tptp.apply M1 BOUND_VARIABLE_1159)) (tptp.apply M4 (tptp.apply M3 BOUND_VARIABLE_1159))))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (_let_99))) (let ((_let_102 ((not (= (tptp.commute M1 M2 M3 M4) false)) (not (= (tptp.morphism M2 DomCod1 Cod) false)) (not (= (tptp.morphism M3 Dom DomCod2) false)) (not (= (tptp.element BOUND_VARIABLE_1159 Dom) false))))) (let ((_let_103 (REFL :args (_let_35)))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 0)) (CONG _let_103 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_44)) :args ((or _let_33 _let_35))) _let_46 :args (_let_33 true _let_35)))) (let ((_let_105 (forall ((ElDom $$unsorted)) (or (not (tptp.element ElDom tptp.b)) (= (tptp.apply tptp.delta (tptp.apply tptp.g ElDom)) (tptp.apply tptp.h (tptp.apply tptp.beta ElDom))))))) (let ((_let_106 (not _let_105))) (let ((_let_107 (or _let_39 _let_93 _let_72 _let_84 _let_106 _let_96))) (let ((_let_108 (forall ((M1 $$unsorted) (M2 $$unsorted) (M3 $$unsorted) (M4 $$unsorted) (Dom $$unsorted) (DomCod1 $$unsorted) (DomCod2 $$unsorted) (Cod $$unsorted)) (or (not (tptp.morphism M1 Dom DomCod1)) (not (tptp.morphism M2 DomCod1 Cod)) (not (tptp.morphism M3 Dom DomCod2)) (not (tptp.morphism M4 DomCod2 Cod)) (not (forall ((ElDom $$unsorted)) (or (not (tptp.element ElDom Dom)) (= (tptp.apply M2 (tptp.apply M1 ElDom)) (tptp.apply M4 (tptp.apply M3 ElDom)))))) (tptp.commute M1 M2 M3 M4))))) (let ((_let_109 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_110 (_let_108))) (let ((_let_111 ((not (= (tptp.morphism M1 Dom DomCod1) false)) (not (= (tptp.morphism M2 DomCod1 Cod) false)) (not (= (tptp.morphism M3 Dom DomCod2) false)) (not (= (tptp.morphism M4 DomCod2 Cod) false))))) (let ((_let_112 (= (tptp.apply tptp.delta (tptp.apply tptp.g SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22)) (tptp.apply tptp.h (tptp.apply tptp.beta SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))))) (let ((_let_113 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 tptp.b))) (let ((_let_114 (not _let_113))) (let ((_let_115 (or _let_114 _let_112))) (let ((_let_116 (not _let_5))) (let ((_let_117 (or _let_116 _let_72 _let_84 _let_39 _let_93 _let_114 _let_112))) (let ((_let_118 (ASSUME :args (_let_9)))) (let ((_let_119 (_let_106))) (let ((_let_120 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 1)) (CONG _let_103 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_44)) :args ((or _let_31 _let_35))) _let_46 :args (_let_31 true _let_35)))) (let ((_let_121 (and _let_31 _let_91 _let_90))) (let ((_let_122 (ASSUME :args (_let_91)))) (let ((_let_123 (APPLY_UF tptp.apply))) (let ((_let_124 (ASSUME :args (_let_31)))) (let ((_let_125 (SYMM (SYMM _let_124)))) (let ((_let_126 (ASSUME :args (_let_90)))) (let ((_let_127 (or _let_34 _let_82))) (let ((_let_128 (and _let_127 (= _let_68 (tptp.apply tptp.beta _let_22))))) (let ((_let_129 (or _let_72 _let_128))) (let ((_let_130 (_let_65))) (let ((_let_131 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_130)) :args _let_130)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_62))) (REFL :args (_let_63)) :args _let_44)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_62 (= ElDom ElDom)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_71)) :args ((or _let_66 (not _let_70) (not _let_71)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_70)) :args ((or _let_34 (not _let_69) _let_70))) _let_104 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_84 _let_85 _let_69 _let_83 _let_81 (not _let_86)))) _let_118 (ASSUME :args (_let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_127)) :args ((or _let_34 _let_82 (not _let_127)))) _let_104 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_128 0)) :args ((or _let_127 (not _let_128)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_129)) :args ((or _let_72 _let_128 (not _let_129)))) _let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (tptp.beta tptp.b tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_MT _let_56)) :args _let_55))) _let_54 :args (_let_129 false _let_53)) :args (_let_128 false _let_14 false _let_129)) :args (_let_127 false _let_128)) :args (_let_82 false _let_33 false _let_127)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_121)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_122 _let_124 _let_126) (SCOPE (TRANS (SYMM (SYMM _let_126)) (CONG (REFL :args (tptp.delta)) _let_125 :args _let_123) (SYMM (SYMM _let_122))) :args (_let_91 _let_31 _let_90))) :args (_let_31 _let_91 _let_90))) :args (true _let_121)) _let_120 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_72 _let_93 _let_39 _let_84 _let_97 _let_34 _let_91 (not _let_98)))) _let_77 _let_95 _let_43 _let_118 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_107)) :args ((or _let_72 _let_93 _let_39 _let_84 _let_106 _let_96 (not _let_107)))) _let_77 _let_95 _let_43 _let_118 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_119)) :args _let_119)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_106) _let_105))) (REFL :args ((not _let_115))) :args _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_117)) :args ((or _let_72 _let_93 _let_39 _let_84 _let_116 _let_114 _let_112 (not _let_117)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_100 :args (tptp.beta tptp.h tptp.g tptp.delta tptp.b tptp.c tptp.e tptp.r SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_101))) _let_100 :args (_let_117 false _let_99)) (ASSUME :args (_let_5)) _let_118 _let_43 _let_95 _let_77 (CNF_OR_NEG :args (_let_115 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_115 0)) (CONG (REFL :args (_let_115)) (MACRO_SR_PRED_INTRO :args ((= (not _let_114) _let_113))) :args _let_44)) :args ((or _let_113 _let_115))) :args (_let_115 false _let_117 false _let_5 false _let_9 false _let_10 false _let_12 false _let_14 true _let_112 false _let_113)) :args (_let_105 false _let_115)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_109 :args (tptp.g tptp.delta tptp.beta tptp.h tptp.b tptp.e tptp.c tptp.r QUANTIFIERS_INST_E_MATCHING_MT _let_111)) :args _let_110)) _let_109 :args (_let_107 false _let_108)) :args (_let_96 false _let_14 false _let_12 false _let_10 false _let_9 false _let_105 false _let_107)) _let_104 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args (tptp.g tptp.delta tptp.beta tptp.h tptp.b tptp.e tptp.c tptp.r SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_MT _let_102)) :args _let_101)) _let_100 :args (_let_98 false _let_99)) :args (_let_91 false _let_14 false _let_12 false _let_10 false _let_9 false _let_96 false _let_33 false _let_98)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_92 1)) :args ((or _let_90 (not _let_92)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_93 _let_92 (not _let_94)))) _let_95 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (tptp.delta tptp.e tptp.r SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 QUANTIFIERS_INST_E_MATCHING_MT _let_56)) :args _let_55))) _let_54 :args (_let_94 false _let_53)) :args (_let_92 false _let_12 false _let_94)) :args (_let_90 false _let_92)) :args (_let_80 false _let_31 false _let_91 false _let_90)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (tptp.h tptp.c tptp.r _let_67 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_89)) _let_88 :args (_let_86 false _let_87)) :args (_let_69 false _let_9 false _let_3 false _let_82 false _let_80 false _let_86)) :args (_let_70 false _let_33 false _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_51 _let_72 _let_73 _let_71 (not _let_74)))) _let_57 _let_77 (ASSUME :args (_let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_76 :args (tptp.alpha tptp.beta tptp.a tptp.b tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_MT ((not (= (tptp.morphism Morphism1 Dom CodDom) false)) (not (= (tptp.morphism Morphism2 CodDom Cod) false)) (tptp.element BOUND_VARIABLE_1095 CodDom)))) :args (_let_75)))) _let_76 :args (_let_74 false _let_75)) :args (_let_71 false _let_15 false _let_14 false _let_7 false _let_74)) :args (_let_66 false _let_70 false _let_71)) :args (_let_65 true _let_64)) :args (_let_63 true _let_62)))) (let ((_let_132 (REFL :args (_let_61)))) (let ((_let_133 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 1)) (CONG _let_132 (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_27))) :args _let_44)) :args ((or _let_27 _let_61))) _let_131 :args (_let_27 true _let_61)))) (let ((_let_134 (tptp.apply tptp.f SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))) (let ((_let_135 (tptp.zero tptp.d))) (let ((_let_136 (= _let_135 _let_134))) (let ((_let_137 (not _let_136))) (let ((_let_138 (not _let_11))) (let ((_let_139 (not _let_4))) (let ((_let_140 (or _let_139 _let_138 _let_60 _let_137 _let_28))) (let ((_let_141 (tptp.apply tptp.gamma _let_134))) (let ((_let_142 (= _let_30 _let_141))) (let ((_let_143 (not _let_142))) (let ((_let_144 (tptp.element _let_134 tptp.d))) (let ((_let_145 (not _let_144))) (let ((_let_146 (not _let_13))) (let ((_let_147 (not _let_8))) (let ((_let_148 (or _let_147 _let_146 _let_145 _let_143 _let_136))) (let ((_let_149 (= _let_141 (tptp.apply tptp.g _let_26)))) (let ((_let_150 (tptp.commute tptp.f tptp.gamma tptp.alpha tptp.g))) (let ((_let_151 (not _let_150))) (let ((_let_152 (or _let_151 _let_138 _let_146 _let_51 _let_39 _let_60 _let_149))) (let ((_let_153 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 0)) (CONG _let_132 (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_59))) :args _let_44)) :args ((or _let_59 _let_61))) _let_131 :args (_let_59 true _let_61)))) (let ((_let_154 (forall ((ElDom $$unsorted)) (or (not (tptp.element ElDom tptp.a)) (= (tptp.apply tptp.gamma (tptp.apply tptp.f ElDom)) (tptp.apply tptp.g (tptp.apply tptp.alpha ElDom))))))) (let ((_let_155 (not _let_154))) (let ((_let_156 (or _let_138 _let_146 _let_51 _let_39 _let_155 _let_150))) (let ((_let_157 (= (tptp.apply tptp.gamma (tptp.apply tptp.f SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21)) (tptp.apply tptp.g _let_47)))) (let ((_let_158 (or _let_49 _let_157))) (let ((_let_159 (not _let_6))) (let ((_let_160 (or _let_159 _let_51 _let_39 _let_138 _let_146 _let_49 _let_157))) (let ((_let_161 (ASSUME :args (_let_13)))) (let ((_let_162 (ASSUME :args (_let_11)))) (let ((_let_163 (_let_155))) (let ((_let_164 (and _let_31 _let_27 _let_149))) (let ((_let_165 (ASSUME :args (_let_149)))) (let ((_let_166 (ASSUME :args (_let_27)))) (let ((_let_167 (SYMM _let_166))) (let ((_let_168 (or _let_60 _let_144))) (let ((_let_169 (and _let_168 (= _let_135 (tptp.apply tptp.f _let_24))))) (let ((_let_170 (or _let_138 _let_169))) (let ((_let_171 (and _let_25 _let_27 _let_28))) (let ((_let_172 (ASSUME :args (_let_28)))) (let ((_let_173 (ASSUME :args (_let_25)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_171)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_166 _let_172 _let_173) (SCOPE (TRANS (SYMM (SYMM _let_173)) (CONG (REFL :args (tptp.alpha)) (SYMM (SYMM _let_172)) :args _let_123) _let_167) :args (_let_27 _let_28 _let_25))) :args (_let_25 _let_27 _let_28))) :args (true _let_171)) :args ((or _let_23 (not _let_25) _let_58 (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_140)) :args ((or _let_138 _let_139 _let_60 _let_137 _let_28 (not _let_140)))) _let_162 (ASSUME :args (_let_4)) _let_153 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_148)) :args ((or _let_146 _let_147 _let_136 _let_145 _let_143 (not _let_148)))) _let_161 (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_168)) :args ((or _let_60 _let_144 (not _let_168)))) _let_153 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_169 0)) :args ((or _let_168 (not _let_169)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_170)) :args ((or _let_138 _let_169 (not _let_170)))) _let_162 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (tptp.f tptp.a tptp.d SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 QUANTIFIERS_INST_E_MATCHING_MT _let_56)) :args _let_55))) _let_54 :args (_let_170 false _let_53)) :args (_let_169 false _let_11 false _let_170)) :args (_let_168 false _let_169)) :args (_let_144 false _let_59 false _let_168)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_164)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_165 _let_166 _let_124) (SCOPE (TRANS _let_125 (CONG (REFL :args (tptp.g)) (SYMM _let_167) :args _let_123) (SYMM _let_165)) :args (_let_149 _let_27 _let_31))) :args (_let_31 _let_27 _let_149))) :args (true _let_164)) _let_120 _let_133 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_152)) :args ((or _let_51 _let_146 _let_138 _let_39 _let_151 _let_60 _let_149 (not _let_152)))) _let_57 _let_161 _let_162 _let_43 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_156)) :args ((or _let_51 _let_146 _let_138 _let_39 _let_155 _let_150 (not _let_156)))) _let_57 _let_161 _let_162 _let_43 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_163)) :args _let_163)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_155) _let_154))) (REFL :args ((not _let_158))) :args _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_160)) :args ((or _let_51 _let_146 _let_138 _let_39 _let_159 _let_49 _let_157 (not _let_160)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_100 :args (tptp.alpha tptp.g tptp.f tptp.gamma tptp.a tptp.b tptp.d tptp.e SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_101))) _let_100 :args (_let_160 false _let_99)) (ASSUME :args (_let_6)) _let_43 _let_162 _let_161 _let_57 (CNF_OR_NEG :args (_let_158 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_158 0)) (CONG (REFL :args (_let_158)) (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_44)) :args ((or _let_48 _let_158))) :args (_let_158 false _let_160 false _let_6 false _let_10 false _let_11 false _let_13 false _let_15 true _let_157 false _let_48)) :args (_let_154 false _let_158)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_109 :args (tptp.f tptp.gamma tptp.alpha tptp.g tptp.a tptp.d tptp.b tptp.e QUANTIFIERS_INST_E_MATCHING_MT _let_111)) :args _let_110)) _let_109 :args (_let_156 false _let_108)) :args (_let_150 false _let_15 false _let_13 false _let_11 false _let_10 false _let_154 false _let_156)) _let_153 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args (tptp.f tptp.gamma tptp.alpha tptp.g tptp.a tptp.d tptp.b tptp.e SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 QUANTIFIERS_INST_E_MATCHING_MT _let_102)) :args _let_101)) _let_100 :args (_let_152 false _let_99)) :args (_let_149 false _let_15 false _let_13 false _let_11 false _let_10 false _let_150 false _let_59 false _let_152)) :args (_let_142 false _let_31 false _let_27 false _let_149)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (tptp.gamma tptp.d tptp.e _let_134 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_89)) _let_88 :args (_let_148 false _let_87)) :args (_let_136 false _let_13 false _let_8 false _let_144 false _let_142 false _let_148)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (tptp.f tptp.a tptp.d SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 QUANTIFIERS_INST_E_MATCHING_MT ((not (= (tptp.morphism Morphism Dom Cod) false)) (not (= (tptp.element BOUND_VARIABLE_1258 Dom) false))))) :args _let_89)) _let_88 :args (_let_140 false _let_87)) :args (_let_28 false _let_11 false _let_4 false _let_59 false _let_136 false _let_140)) _let_133 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_50 1)) :args ((or _let_25 (not _let_50)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_51 _let_50 (not _let_52)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_54 :args (tptp.alpha tptp.a tptp.b SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 QUANTIFIERS_INST_E_MATCHING_MT _let_56)) :args _let_55))) _let_54 :args (_let_52 false _let_53)) :args (_let_50 false _let_15 false _let_52)) :args (_let_25 false _let_50)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_35 2)) _let_46 :args ((not _let_23) true _let_35)) :args (false false _let_28 false _let_27 false _let_25 true _let_23)) :args (_let_21 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (and (tptp.injection Morphism) (tptp.morphism Morphism Dom Cod)) (forall ((El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom) (= (tptp.apply Morphism El1) (tptp.apply Morphism El2))) (= El1 El2))))) (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (and (tptp.morphism Morphism Dom Cod) (forall ((El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom) (= (tptp.apply Morphism El1) (tptp.apply Morphism El2))) (= El1 El2)))) (tptp.injection Morphism))) (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (and (tptp.surjection Morphism) (tptp.morphism Morphism Dom Cod)) (forall ((ElCod $$unsorted)) (=> (tptp.element ElCod Cod) (exists ((ElDom $$unsorted)) (and (tptp.element ElDom Dom) (= (tptp.apply Morphism ElDom) ElCod))))))) (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (and (tptp.morphism Morphism Dom Cod) (forall ((ElCod $$unsorted)) (=> (tptp.element ElCod Cod) (exists ((ElDom $$unsorted)) (and (tptp.element ElDom Dom) (= (tptp.apply Morphism ElDom) ElCod)))))) (tptp.surjection Morphism))) _let_20 (forall ((Morphism1 $$unsorted) (Morphism2 $$unsorted) (Dom $$unsorted) (CodDom $$unsorted) (Cod $$unsorted)) (=> (and (tptp.morphism Morphism1 Dom CodDom) (tptp.morphism Morphism2 CodDom Cod) (forall ((ElCodDom $$unsorted)) (= (and (tptp.element ElCodDom CodDom) (= (tptp.apply Morphism2 ElCodDom) (tptp.zero Cod))) (exists ((ElDom $$unsorted)) (and (tptp.element ElDom Dom) (= (tptp.apply Morphism1 ElDom) ElCodDom)))))) (tptp.exact Morphism1 Morphism2))) _let_19 _let_18 (forall ((Dom $$unsorted) (El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom)) (tptp.element (tptp.subtract Dom El1 El2) Dom))) (forall ((Dom $$unsorted) (El $$unsorted)) (=> (tptp.element El Dom) (= (tptp.subtract Dom El El) (tptp.zero Dom)))) (forall ((Dom $$unsorted) (El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom)) (= (tptp.subtract Dom El1 (tptp.subtract Dom El1 El2)) El2))) (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (tptp.morphism Morphism Dom Cod) (forall ((El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom)) (= (tptp.apply Morphism (tptp.subtract Dom El1 El2)) (tptp.subtract Cod (tptp.apply Morphism El1) (tptp.apply Morphism El2))))))) _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 (tptp.injection tptp.alpha) _let_8 (tptp.surjection tptp.beta) (tptp.surjection tptp.delta) _let_7 (tptp.exact tptp.gammma tptp.delta) _let_6 _let_5 _let_4 _let_3 _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 41.33/41.54 )
% 41.33/41.54 % SZS output end Proof for HAL001+2
% 41.33/41.54 % cvc5---1.0.5 exiting
% 41.41/41.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------