%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : HAL001+1 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n014.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 32.55s 32.77s
% Output   : Proof 32.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : HAL001+1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.17/0.35  % Computer : n014.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit   : 300
% 0.17/0.35  % WCLimit    : 300
% 0.17/0.35  % DateTime   : Mon Aug 28 02:28:46 EDT 2023
% 0.17/0.35  % CPUTime    : 
% 0.21/0.48  %----Proving TF0_NAR, FOF, or CNF
% 32.55/32.77  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.UUmRNUYPyE/cvc5---1.0.5_32033.p...
% 32.55/32.77  ------- get file name : TPTP file name is HAL001+1
% 32.55/32.77  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_32033.smt2...
% 32.55/32.77  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 32.55/32.77  --- Run --no-e-matching --full-saturate-quant at 5...
% 32.55/32.77  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 32.55/32.77  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 32.55/32.77  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 32.55/32.77  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 32.55/32.77  % SZS status Theorem for HAL001+1
% 32.55/32.77  % SZS output start Proof for HAL001+1
% 32.55/32.77  (
% 32.55/32.77  (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.injection tptp.alpha))) (let ((_let_10 (tptp.morphism tptp.h tptp.c tptp.r))) (let ((_let_11 (tptp.morphism tptp.g tptp.b tptp.e))) (let ((_let_12 (tptp.morphism tptp.f tptp.a tptp.d))) (let ((_let_13 (tptp.morphism tptp.delta tptp.e tptp.r))) (let ((_let_14 (tptp.morphism tptp.gamma tptp.d tptp.e))) (let ((_let_15 (tptp.morphism tptp.beta tptp.b tptp.c))) (let ((_let_16 (tptp.morphism tptp.alpha tptp.a tptp.b))) (let ((_let_17 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (tptp.morphism Morphism Dom Cod) (forall ((El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom)) (= (tptp.apply Morphism (tptp.subtract Dom El1 El2)) (tptp.subtract Cod (tptp.apply Morphism El1) (tptp.apply Morphism El2))))))))) (let ((_let_18 (forall ((Dom $$unsorted) (El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom)) (= (tptp.subtract Dom El1 (tptp.subtract Dom El1 El2)) El2))))) (let ((_let_19 (forall ((Dom $$unsorted) (El $$unsorted)) (=> (tptp.element El Dom) (= (tptp.subtract Dom El El) (tptp.zero Dom)))))) (let ((_let_20 (forall ((Dom $$unsorted) (El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom)) (tptp.element (tptp.subtract Dom El1 El2) Dom))))) (let ((_let_21 (forall ((M1 $$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_22 (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 $$unsorted)) (and (tptp.element ElDom Dom) (= (tptp.apply Morphism1 ElDom) ElCodDom))))))))) (let ((_let_23 (forall ((Morphism $$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))))) (let ((_let_24 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (and (tptp.injection Morphism) (tptp.morphism Morphism Dom Cod)) (forall ((El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom) (= (tptp.apply Morphism El1) (tptp.apply Morphism El2))) (= El1 El2))))))) (let ((_let_25 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (tptp.morphism Morphism Dom Cod) (and (forall ((El $$unsorted)) (=> (tptp.element El Dom) (tptp.element (tptp.apply Morphism El) Cod))) (= (tptp.apply Morphism (tptp.zero Dom)) (tptp.zero Cod))))))) (let ((_let_26 (tptp.apply tptp.f SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29))) (let ((_let_27 (tptp.element _let_26 tptp.d))) (let ((_let_28 (tptp.apply tptp.f SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38))) (let ((_let_29 (tptp.element _let_28 tptp.d))) (let ((_let_30 (= _let_26 _let_28))) (let ((_let_31 (tptp.apply tptp.gamma _let_28))) (let ((_let_32 (tptp.apply tptp.gamma _let_26))) (let ((_let_33 (= _let_32 _let_31))) (let ((_let_34 (not _let_33))) (let ((_let_35 (not _let_29))) (let ((_let_36 (not _let_27))) (let ((_let_37 (not _let_14))) (let ((_let_38 (not _let_8))) (let ((_let_39 (or _let_38 _let_37 _let_36 _let_35 _let_34 _let_30))) (let ((_let_40 (ASSUME :args (_let_14)))) (let ((_let_41 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 tptp.a))) (let ((_let_42 (not _let_41))) (let ((_let_43 (or _let_42 _let_27))) (let ((_let_44 (tptp.zero tptp.a))) (let ((_let_45 (tptp.apply tptp.f _let_44))) (let ((_let_46 (= (tptp.zero tptp.d) _let_45))) (let ((_let_47 (and _let_43 _let_46))) (let ((_let_48 (not _let_12))) (let ((_let_49 (or _let_48 _let_47))) (let ((_let_50 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted) (BOUND_VARIABLE_897 $$unsorted)) (or (not (tptp.morphism Morphism Dom Cod)) (and (or (not (tptp.element BOUND_VARIABLE_897 Dom)) (tptp.element (tptp.apply Morphism BOUND_VARIABLE_897) Cod)) (= (tptp.apply Morphism (tptp.zero Dom)) (tptp.zero Cod))))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (_let_50))) (let ((_let_53 ((not (= (tptp.morphism Morphism Dom Cod) false)) (tptp.element BOUND_VARIABLE_897 Dom)))) (let ((_let_54 (ASSUME :args (_let_12)))) (let ((_let_55 (tptp.apply tptp.alpha SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29))) (let ((_let_56 (tptp.subtract tptp.b SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_57 (= _let_56 _let_55))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_42 _let_58))) (let ((_let_60 (forall ((ElDom $$unsorted)) (or (not (tptp.element ElDom tptp.a)) (not (= (tptp.apply tptp.alpha ElDom) (tptp.subtract tptp.b SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))) (let ((_let_61 (not _let_59))) (let ((_let_62 (not _let_60))) (let ((_let_63 (tptp.apply tptp.beta _let_56))) (let ((_let_64 (tptp.zero tptp.c))) (let ((_let_65 (= _let_64 _let_63))) (let ((_let_66 (tptp.element _let_56 tptp.b))) (let ((_let_67 (and _let_66 _let_65))) (let ((_let_68 (= _let_67 _let_62))) (let ((_let_69 (not _let_15))) (let ((_let_70 (not _let_16))) (let ((_let_71 (not _let_7))) (let ((_let_72 (or _let_71 _let_70 _let_69 _let_68))) (let ((_let_73 (forall ((Morphism1 $$unsorted) (Morphism2 $$unsorted) (Dom $$unsorted) (CodDom $$unsorted) (Cod $$unsorted) (BOUND_VARIABLE_1055 $$unsorted)) (or (not (tptp.exact Morphism1 Morphism2)) (not (tptp.morphism Morphism1 Dom CodDom)) (not (tptp.morphism Morphism2 CodDom Cod)) (= (and (tptp.element BOUND_VARIABLE_1055 CodDom) (= (tptp.zero Cod) (tptp.apply Morphism2 BOUND_VARIABLE_1055))) (not (forall ((ElDom $$unsorted)) (or (not (tptp.element ElDom Dom)) (not (= (tptp.apply Morphism1 ElDom) BOUND_VARIABLE_1055)))))))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (_let_73))) (let ((_let_76 (not (= (tptp.morphism Morphism2 CodDom Cod) false)))) (let ((_let_77 (not (= (tptp.morphism Morphism1 Dom CodDom) false)))) (let ((_let_78 (ASSUME :args (_let_7)))) (let ((_let_79 (ASSUME :args (_let_15)))) (let ((_let_80 (ASSUME :args (_let_16)))) (let ((_let_81 (tptp.zero tptp.b))) (let ((_let_82 (= _let_81 _let_56))) (let ((_let_83 (= (tptp.apply tptp.beta _let_81) _let_64))) (let ((_let_84 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.b))) (let ((_let_85 (not _let_84))) (let ((_let_86 (or _let_85 _let_82))) (let ((_let_87 (forall ((Dom $$unsorted) (El $$unsorted)) (or (not (tptp.element El Dom)) (= (tptp.subtract Dom El El) (tptp.zero Dom)))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (_let_87))) (let ((_let_90 ((not (= (tptp.element El Dom) false))))) (let ((_let_91 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_92 (tptp.apply tptp.g SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_93 (tptp.apply tptp.g SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_94 (= _let_93 _let_92))) (let ((_let_95 (not _let_94))) (let ((_let_96 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.b))) (let ((_let_97 (not _let_96))) (let ((_let_98 (or _let_85 _let_97 _let_95 _let_91))) (let ((_let_99 (forall ((El1 $$unsorted) (El2 $$unsorted)) (or (not (tptp.element El1 tptp.b)) (not (tptp.element El2 tptp.b)) (not (= (tptp.apply tptp.g El1) (tptp.apply tptp.g El2))) (= El1 El2))))) (let ((_let_100 (not _let_98))) (let ((_let_101 (not _let_99))) (let ((_let_102 (not _let_11))) (let ((_let_103 (or _let_102 _let_101 _let_1))) (let ((_let_104 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (or (not (tptp.morphism Morphism Dom Cod)) (not (forall ((El1 $$unsorted) (El2 $$unsorted)) (or (not (tptp.element El1 Dom)) (not (tptp.element El2 Dom)) (not (= (tptp.apply Morphism El1) (tptp.apply Morphism El2))) (= El1 El2)))) (tptp.injection Morphism))))) (let ((_let_105 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_106 (ASSUME :args (_let_11)))) (let ((_let_107 (or))) (let ((_let_108 (_let_101))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_108)) :args _let_108)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_101) _let_99))) (REFL :args (_let_100)) :args _let_107)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_103)) :args ((or _let_1 _let_102 _let_101 (not _let_103)))) (ASSUME :args (_let_2)) _let_106 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_105 :args (tptp.g tptp.b tptp.e QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.morphism Morphism Dom Cod) false))))) :args (_let_104))) _let_105 :args (_let_103 false _let_104)) :args (_let_101 true _let_1 false _let_11 false _let_103)) :args (_let_100 true _let_99)))) (let ((_let_110 (REFL :args (_let_98)))) (let ((_let_111 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_98 0)) (CONG _let_110 (MACRO_SR_PRED_INTRO :args ((= (not _let_85) _let_84))) :args _let_107)) :args ((or _let_84 _let_98))) _let_109 :args (_let_84 true _let_98)))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_85 _let_82 (not _let_86)))) _let_111 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_88 :args (tptp.b SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_90)) :args _let_89))) _let_88 :args (_let_86 false _let_87)) :args (_let_82 false _let_84 false _let_86)))) (let ((_let_113 (tptp.apply tptp.beta SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_114 (tptp.element _let_113 tptp.c))) (let ((_let_115 (or _let_85 _let_114))) (let ((_let_116 (and _let_115 _let_83))) (let ((_let_117 (or _let_69 _let_116))) (let ((_let_118 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_117)) :args ((or _let_69 _let_116 (not _let_117)))) _let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (tptp.beta tptp.b tptp.c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_53)) :args _let_52)) _let_51 :args (_let_117 false _let_50)) :args (_let_116 false _let_15 false _let_117)))) (let ((_let_119 (not _let_116))) (let ((_let_120 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_116 1)) :args ((or _let_83 _let_119))) _let_118 :args (_let_83 false _let_116)))) (let ((_let_121 (and _let_83 _let_82))) (let ((_let_122 (APPLY_UF tptp.apply))) (let ((_let_123 (ASSUME :args (_let_82)))) (let ((_let_124 (SYMM _let_123))) (let ((_let_125 (SYMM _let_124))) (let ((_let_126 (CONG (REFL :args (tptp.beta)) _let_125 :args _let_122))) (let ((_let_127 (ASSUME :args (_let_83)))) (let ((_let_128 (SYMM _let_127))) (let ((_let_129 (or _let_85 _let_85 _let_66))) (let ((_let_130 (forall ((Dom $$unsorted) (El1 $$unsorted) (El2 $$unsorted)) (or (not (tptp.element El1 Dom)) (not (tptp.element El2 Dom)) (tptp.element (tptp.subtract Dom El1 El2) Dom))))) (let ((_let_131 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_132 (_let_130))) (let ((_let_133 (_let_62))) (let ((_let_134 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_133)) :args _let_133) (REWRITE :args ((=> _let_62 (not (or _let_42 (not (= _let_55 _let_56))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_60))) (REFL :args (_let_61)) :args _let_107)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_68)) :args ((or _let_62 (not _let_67) (not _let_68)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_129))) :args ((or _let_85 _let_66 (not _let_129)))) _let_111 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_131 :args (tptp.b SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_132)) _let_131 :args (_let_129 false _let_130)) :args (_let_66 false _let_84 false _let_129)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_121)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_123 _let_127) (SCOPE (TRANS _let_128 _let_126) :args (_let_82 _let_83))) :args (_let_83 _let_82))) :args (true _let_121)) _let_120 _let_112 :args (_let_65 false _let_83 false _let_82)) :args (_let_67 false _let_66 false _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_70 _let_69 _let_71 _let_68 (not _let_72)))) _let_80 _let_79 _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (tptp.alpha tptp.beta tptp.a tptp.b tptp.c _let_56 QUANTIFIERS_INST_E_MATCHING (_let_77 (tptp.apply Morphism2 BOUND_VARIABLE_1055) _let_76))) :args _let_75)) _let_74 :args (_let_72 false _let_73)) :args (_let_68 false _let_16 false _let_15 false _let_7 false _let_72)) :args (_let_62 false _let_67 false _let_68)) :args (_let_61 true _let_60)))) (let ((_let_135 (REFL :args (_let_59)))) (let ((_let_136 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 0)) (CONG _let_135 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) :args _let_107)) :args ((or _let_41 _let_59))) _let_134 :args (_let_41 true _let_59)))) (let ((_let_137 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 tptp.a))) (let ((_let_138 (not _let_137))) (let ((_let_139 (or _let_138 _let_29))) (let ((_let_140 (and _let_139 _let_46))) (let ((_let_141 (or _let_48 _let_140))) (let ((_let_142 (tptp.apply tptp.alpha SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38))) (let ((_let_143 (tptp.subtract tptp.b SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_144 (= _let_143 _let_142))) (let ((_let_145 (not _let_144))) (let ((_let_146 (or _let_138 _let_145))) (let ((_let_147 (forall ((ElDom $$unsorted)) (or (not (tptp.element ElDom tptp.a)) (not (= (tptp.apply tptp.alpha ElDom) (tptp.subtract tptp.b SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))) (let ((_let_148 (not _let_146))) (let ((_let_149 (not _let_147))) (let ((_let_150 (tptp.apply tptp.beta _let_143))) (let ((_let_151 (= _let_64 _let_150))) (let ((_let_152 (tptp.element _let_143 tptp.b))) (let ((_let_153 (and _let_152 _let_151))) (let ((_let_154 (= _let_153 _let_149))) (let ((_let_155 (or _let_71 _let_70 _let_69 _let_154))) (let ((_let_156 (tptp.apply tptp.beta SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_157 (= _let_150 (tptp.subtract tptp.c _let_156 _let_113)))) (let ((_let_158 (= _let_63 (tptp.subtract tptp.c _let_113 _let_113)))) (let ((_let_159 (= _let_113 _let_156))) (let ((_let_160 (or _let_69 _let_97 _let_85 _let_157))) (let ((_let_161 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted) (BOUND_VARIABLE_1185 $$unsorted) (BOUND_VARIABLE_1183 $$unsorted)) (or (not (tptp.morphism Morphism Dom Cod)) (not (tptp.element BOUND_VARIABLE_1183 Dom)) 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(MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_131 :args (tptp.a SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_132)) _let_131 :args (_let_256 false _let_130)) :args (_let_254 false _let_41 false _let_256)) :args (_let_219 false _let_255 false _let_254)))) (let ((_let_262 (= _let_227 _let_55))) (let ((_let_263 (not _let_262))) (let ((_let_264 (not _let_9))) (let ((_let_265 (or _let_264 _let_70 _let_220 _let_42 _let_263 _let_215))) (let ((_let_266 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 1)) (CONG _let_135 (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_57))) :args _let_107)) :args ((or _let_57 _let_59))) _let_134 :args (_let_57 true _let_59)))) (let ((_let_267 (and _let_82 _let_228 _let_57))) (let ((_let_268 (ASSUME :args (_let_57)))) (let ((_let_269 (SYMM _let_268))) (let ((_let_270 (and _let_215 _let_218))) (let ((_let_271 (_let_215 _let_218))) (let ((_let_272 (ASSUME :args (_let_218)))) (let ((_let_273 (ASSUME :args (_let_215)))) (let ((_let_274 (= (tptp.apply tptp.g _let_142) _let_31))) (let ((_let_275 (= (tptp.apply tptp.g _let_55) _let_32))) (let ((_let_276 (= (tptp.apply tptp.g _let_143) (tptp.subtract tptp.e _let_92 _let_93)))) (let ((_let_277 (= (tptp.apply tptp.g _let_225) (tptp.subtract tptp.e _let_92 _let_92)))) (let ((_let_278 (not _let_6))) (let ((_let_279 (or _let_278 _let_70 _let_102 _let_48 _let_37 _let_138 _let_274))) (let ((_let_280 (_let_189 _let_188 (not (= (tptp.morphism M1 Dom DomCod1) false)) (not (= (tptp.morphism M4 DomCod2 Cod) false))))) (let ((_let_281 (ASSUME :args (_let_6)))) (let ((_let_282 (or _let_278 _let_70 _let_102 _let_48 _let_37 _let_42 _let_275))) (let ((_let_283 (or _let_102 _let_97 _let_85 _let_276))) (let ((_let_284 (or _let_102 _let_97 _let_97 _let_277))) (let ((_let_285 (and _let_94 _let_82 _let_229 _let_277 _let_276 _let_57 _let_275 _let_144 _let_274))) (let ((_let_286 (ASSUME :args (_let_274)))) (let ((_let_287 (REFL :args (tptp.g)))) (let ((_let_288 (ASSUME :args (_let_276)))) (let ((_let_289 (ASSUME :args (_let_277)))) (let ((_let_290 (ASSUME :args (_let_275)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_37 _let_38 _let_36 _let_35 _let_34 _let_30 (not _let_39)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_285)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_286 _let_250 _let_288 _let_198 _let_289 _let_245 _let_123 _let_268 _let_290) (SCOPE (TRANS (SYMM _let_290) (CONG _let_287 (TRANS _let_269 _let_124) :args _let_122) (CONG _let_287 _let_246 :args _let_122) (SYMM (SYMM _let_289)) (CONG (REFL :args (tptp.e)) (REFL :args (_let_92)) _let_199 :args _let_206) (SYMM _let_288) (CONG _let_287 _let_251 :args _let_122) (SYMM (SYMM _let_286))) :args (_let_274 _let_144 _let_276 _let_94 _let_277 _let_229 _let_82 _let_57 _let_275))) :args (_let_94 _let_82 _let_229 _let_277 _let_276 _let_57 _let_275 _let_144 _let_274))) :args (true _let_285)) _let_195 _let_112 _let_242 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_284))) :args ((or _let_102 _let_97 _let_277 (not _let_284)))) _let_106 _let_164 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_162 :args (tptp.g tptp.b tptp.e SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING _let_166)) :args _let_163)) _let_162 :args (_let_284 false _let_161)) :args (_let_277 false _let_11 false _let_96 false _let_284)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_283)) :args ((or _let_102 _let_85 _let_97 _let_276 (not _let_283)))) _let_106 _let_111 _let_164 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_162 :args (tptp.g tptp.b tptp.e SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING _let_166)) :args _let_163)) _let_162 :args (_let_283 false _let_161)) :args (_let_276 false _let_11 false _let_84 false _let_96 false _let_283)) _let_266 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_282)) :args ((or _let_70 _let_37 _let_48 _let_102 _let_278 _let_42 _let_275 (not _let_282)))) _let_80 _let_40 _let_54 _let_106 _let_281 _let_136 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_186 :args (tptp.alpha tptp.g tptp.f tptp.gamma tptp.a tptp.b tptp.d tptp.e SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 QUANTIFIERS_INST_E_MATCHING _let_280)) :args _let_187)) _let_186 :args (_let_282 false _let_185)) :args (_let_275 false _let_16 false _let_14 false _let_12 false _let_11 false _let_6 false _let_41 false _let_282)) _let_231 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_279)) :args ((or _let_70 _let_37 _let_48 _let_102 _let_278 _let_138 _let_274 (not _let_279)))) _let_80 _let_40 _let_54 _let_106 _let_281 _let_213 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_186 :args (tptp.alpha tptp.g tptp.f tptp.gamma tptp.a tptp.b tptp.d tptp.e 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_let_263 _let_215 (not _let_265)))) _let_80 (ASSUME :args (_let_9)) _let_136 _let_261 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_267)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_268 _let_123 _let_247) (SCOPE (TRANS _let_248 _let_125 (SYMM _let_269)) :args (_let_57 _let_82 _let_228))) :args (_let_82 _let_228 _let_57))) :args (true _let_267)) _let_112 _let_240 _let_266 :args (_let_262 false _let_82 false _let_228 false _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_178 :args (tptp.alpha tptp.a tptp.b SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 _let_44 QUANTIFIERS_INST_E_MATCHING _let_223)) :args _let_179)) _let_178 :args (_let_265 false _let_177)) :args (_let_215 false _let_16 false _let_9 false _let_41 false _let_219 false _let_262 false _let_265)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_222)) :args ((or _let_48 _let_221 _let_220 _let_138 _let_218 _let_217 (not _let_222)))) _let_54 (ASSUME :args (_let_4)) _let_261 _let_213 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_243)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_244 _let_245 _let_247 _let_249 _let_250 _let_252) (SCOPE (TRANS (SYMM (SYMM _let_252)) (CONG (REFL :args (tptp.b)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (TRANS _let_251 (CONG (REFL :args (tptp.alpha)) (SYMM _let_249) :args _let_122) _let_248 _let_246) :args _let_206) (SYMM _let_244)) :args (_let_226 _let_229 _let_228 _let_217 _let_144 _let_224))) :args (_let_229 _let_228 _let_226 _let_224 _let_144 _let_217))) :args (true _let_243)) :args ((or _let_91 (not _let_229) (not _let_228) (not _let_226) (not _let_224) _let_145 _let_230))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_98 3)) _let_109 :args ((not _let_91) true _let_98)) _let_242 _let_240 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_237))) :args ((or _let_97 _let_226 (not _let_237)))) _let_164 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_234 :args (tptp.b SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING _let_236)) :args _let_235)) _let_234 :args (_let_237 false _let_233)) :args (_let_226 false _let_96 false _let_237)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_232)) :args ((or _let_85 _let_97 _let_224 (not _let_232)))) _let_111 _let_164 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_234 :args (tptp.b SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_236)) :args _let_235)) _let_234 :args (_let_232 false _let_233)) :args (_let_224 false _let_84 false _let_96 false _let_232)) _let_231 :args (_let_230 true _let_91 false _let_229 false _let_228 false _let_226 false _let_224 false _let_144)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_178 :args (tptp.f tptp.a tptp.d SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 _let_44 QUANTIFIERS_INST_E_MATCHING _let_223)) :args _let_179)) _let_178 :args (_let_222 false _let_177)) :args (_let_218 false _let_12 false _let_4 false _let_219 false _let_137 true _let_217 false _let_222)) :args (_let_216 false _let_215 true _let_214)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_178 :args (tptp.gamma tptp.d tptp.e _let_28 _let_26 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_179)) _let_178 :args (_let_39 false _let_177)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_139)) :args ((or _let_138 _let_29 (not _let_139)))) _let_213 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_140 0)) :args ((or _let_139 (not _let_140)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_141)) :args ((or _let_48 _let_140 (not _let_141)))) _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_51 :args (tptp.f tptp.a tptp.d SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 QUANTIFIERS_INST_E_MATCHING _let_53)) :args _let_52))) _let_51 :args (_let_141 false _let_50)) :args (_let_140 false _let_12 false _let_141)) :args (_let_139 false _let_140)) :args (_let_29 false _let_137 false _let_139)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_42 _let_27 (not _let_43)))) _let_136 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_47 0)) :args ((or _let_43 (not _let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_48 _let_47 (not _let_49)))) _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_51 :args (tptp.f tptp.a tptp.d SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 QUANTIFIERS_INST_E_MATCHING _let_53)) :args _let_52))) _let_51 :args (_let_49 false _let_50)) :args (_let_47 false _let_12 false _let_49)) :args (_let_43 false _let_47)) :args (_let_27 false _let_41 false _let_43)) (ASSUME :args (_let_8)) _let_40 :args (false false _let_33 true _let_30 false _let_39 false _let_29 false _let_27 false _let_8 false _let_14)) :args (_let_25 _let_24 _let_23 (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 $$unsorted)) (and (tptp.element ElDom Dom) (= (tptp.apply Morphism ElDom) ElCod)))))) (tptp.surjection Morphism))) _let_22 (forall ((Morphism1 $$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_21 (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_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 32.55/32.78  )
% 32.55/32.78  % SZS output end Proof for HAL001+1
% 32.55/32.78  % cvc5---1.0.5 exiting
% 32.55/32.78  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------