TSTP Solution File: HAL002+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : HAL002+1 : 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 0.21s 0.65s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n020.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 : Mon Aug 28 02:30:29 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.65 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.xAxGEW45fV/cvc5---1.0.5_12709.p...
% 0.21/0.65 ------- get file name : TPTP file name is HAL002+1
% 0.21/0.65 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12709.smt2...
% 0.21/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.65 % SZS status Theorem for HAL002+1
% 0.21/0.65 % SZS output start Proof for HAL002+1
% 0.21/0.65 (
% 0.21/0.65 (let ((_let_1 (tptp.injection_2 tptp.x))) (let ((_let_2 (tptp.injection tptp.x))) (let ((_let_3 (not (= _let_2 _let_1)))) (let ((_let_4 (tptp.morphism tptp.x tptp.any1 tptp.any2))) (let ((_let_5 (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_2 Morphism))))) (let ((_let_6 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (and (tptp.injection_2 Morphism) (tptp.morphism Morphism Dom Cod)) (forall ((El $$unsorted)) (=> (and (tptp.element El Dom) (= (tptp.apply Morphism El) (tptp.zero Cod))) (= El (tptp.zero Dom)))))))) (let ((_let_7 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (tptp.morphism Morphism Dom Cod) (forall ((El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom)) (= (tptp.apply Morphism (tptp.subtract Dom El1 El2)) (tptp.subtract Cod (tptp.apply Morphism El1) (tptp.apply Morphism El2))))))))) (let ((_let_8 (forall ((Dom $$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_9 (forall ((Dom $$unsorted) (El $$unsorted)) (=> (tptp.element El Dom) (= (tptp.subtract Dom El El) (tptp.zero Dom)))))) (let ((_let_10 (forall ((Dom $$unsorted) (El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom)) (tptp.element (tptp.subtract Dom El1 El2) Dom))))) (let ((_let_11 (forall ((Morphism $$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_12 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (and (tptp.injection Morphism) (tptp.morphism Morphism Dom Cod)) (forall ((El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom) (= (tptp.apply Morphism El1) (tptp.apply Morphism El2))) (= El1 El2))))))) (let ((_let_13 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (tptp.morphism Morphism Dom Cod) (and (forall ((El $$unsorted)) (=> (tptp.element El Dom) (tptp.element (tptp.apply Morphism El) Cod))) (= (tptp.apply Morphism (tptp.zero Dom)) (tptp.zero Cod))))))) (let ((_let_14 (forall ((Dom $$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_15 (tptp.subtract tptp.any1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_16 (tptp.element _let_15 tptp.any1))) (let ((_let_17 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.any1))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_18 _let_18 _let_16))) (let ((_let_20 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_21 (not _let_19))) (let ((_let_22 (tptp.zero tptp.any1))) (let ((_let_23 (= _let_22 _let_15))) (let ((_let_24 (tptp.element _let_22 tptp.any1))) (let ((_let_25 (not _let_16))) (let ((_let_26 (or _let_18 _let_23))) (let ((_let_27 (forall ((Dom $$unsorted) (El $$unsorted)) (or (not (tptp.element El Dom)) (= (tptp.subtract Dom El El) (tptp.zero Dom)))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (_let_27))) (let ((_let_30 ((not (= (tptp.element El Dom) false))))) (let ((_let_31 (= _let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_32 (tptp.apply tptp.x SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_33 (tptp.zero tptp.any2))) (let ((_let_34 (= _let_33 _let_32))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_18 _let_35 _let_31))) (let ((_let_37 (forall ((El $$unsorted)) (or (not (tptp.element El tptp.any1)) (not (= (tptp.zero tptp.any2) (tptp.apply tptp.x El))) (= El (tptp.zero tptp.any1)))))) (let ((_let_38 (not _let_36))) (let ((_let_39 (not _let_37))) (let ((_let_40 (not _let_4))) (let ((_let_41 (or _let_40 _let_39 _let_1))) (let ((_let_42 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (or (not (tptp.morphism Morphism Dom Cod)) (not (forall ((El $$unsorted)) (or (not (tptp.element El Dom)) (not (= (tptp.apply Morphism El) (tptp.zero Cod))) (= El (tptp.zero Dom))))) (tptp.injection_2 Morphism))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (ASSUME :args (_let_4)))) (let ((_let_45 (not _let_1))) (let ((_let_46 (forall ((El1 $$unsorted) (El2 $$unsorted)) (or (not (tptp.element El1 tptp.any1)) (not (tptp.element El2 tptp.any1)) (not (= (tptp.apply tptp.x El1) (tptp.apply tptp.x El2))) (= El1 El2))))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_40 _let_47 _let_2))) (let ((_let_49 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_50 (tptp.apply tptp.x SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_51 (tptp.apply tptp.x SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_52 (= _let_51 _let_50))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.any1))) (let ((_let_55 (not _let_54))) (let ((_let_56 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.any1))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_57 _let_55 _let_53 _let_49))) (let ((_let_59 (tptp.subtract tptp.any1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_60 (= _let_22 _let_59))) (let ((_let_61 (or _let_57 _let_60))) (let ((_let_62 (tptp.subtract tptp.any2 _let_51 _let_51))) (let ((_let_63 (tptp.apply tptp.x _let_59))) (let ((_let_64 (= _let_63 _let_62))) (let ((_let_65 (or _let_40 _let_57 _let_57 _let_64))) (let ((_let_66 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.subtract tptp.any1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_59)))) (let ((_let_67 (or _let_57 _let_57 _let_66))) (let ((_let_68 (tptp.subtract tptp.any1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_69 (tptp.apply tptp.x _let_68))) (let ((_let_70 (= _let_69 (tptp.subtract tptp.any2 _let_51 _let_50)))) (let ((_let_71 (or _let_40 _let_57 _let_55 _let_70))) (let ((_let_72 (tptp.element _let_68 tptp.any1))) (let ((_let_73 (or _let_57 _let_55 _let_72))) (let ((_let_74 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.subtract tptp.any1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_68)))) (let ((_let_75 (or _let_57 _let_55 _let_74))) (let ((_let_76 (tptp.apply tptp.x _let_22))) (let ((_let_77 (= _let_76 _let_33))) (let ((_let_78 (= _let_33 _let_69))) (let ((_let_79 (= _let_22 _let_68))) (let ((_let_80 (not _let_78))) (let ((_let_81 (not _let_72))) (let ((_let_82 (or _let_81 _let_80 _let_79))) (let ((_let_83 (ASSUME :args (_let_3)))) (let ((_let_84 (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_85 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (or))) (let ((_let_87 (_let_47))) (let ((_let_88 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_87)) :args _let_87)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) (REFL :args ((not _let_58))) :args _let_86)))) (let ((_let_89 (REFL :args (_let_58)))) (let ((_let_90 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 0)) (CONG _let_89 (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_56))) :args _let_86)) :args ((or _let_56 _let_58))))) (let ((_let_91 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 1)) (CONG _let_89 (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_86)) :args ((or _let_54 _let_58))))) (let ((_let_92 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 2)) (CONG _let_89 (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) :args _let_86)) :args ((or _let_52 _let_58))))) (let ((_let_93 (CNF_OR_NEG :args (_let_58 3)))) (let ((_let_94 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted) (BOUND_VARIABLE_1201 $$unsorted) (BOUND_VARIABLE_1199 $$unsorted)) (or (not (tptp.morphism Morphism Dom Cod)) (not (tptp.element BOUND_VARIABLE_1199 Dom)) (not (tptp.element BOUND_VARIABLE_1201 Dom)) (= (tptp.apply Morphism (tptp.subtract Dom BOUND_VARIABLE_1199 BOUND_VARIABLE_1201)) (tptp.subtract Cod (tptp.apply Morphism BOUND_VARIABLE_1199) (tptp.apply Morphism BOUND_VARIABLE_1201))))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (_let_94))) (let ((_let_97 (not (= (tptp.morphism Morphism Dom Cod) false)))) (let ((_let_98 (forall ((Dom $$unsorted) (El1 $$unsorted) (El2 $$unsorted)) (or (not (tptp.element El1 Dom)) (not (tptp.element El2 Dom)) (= El2 (tptp.subtract Dom El1 (tptp.subtract Dom El1 El2))))))) (let ((_let_99 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_100 (_let_98))) (let ((_let_101 ((not (= (tptp.element El2 Dom) false)) (not (= (tptp.element El1 Dom) false))))) (let ((_let_102 (_let_14))) (let ((_let_103 ((tptp.subtract Dom El1 El2)))) (let ((_let_104 (and (or _let_57 (tptp.element _let_51 tptp.any2)) _let_77))) (let ((_let_105 (or _let_40 _let_104))) (let ((_let_106 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted) (BOUND_VARIABLE_913 $$unsorted)) (or (not (tptp.morphism Morphism Dom Cod)) (and (or (not (tptp.element BOUND_VARIABLE_913 Dom)) (tptp.element (tptp.apply Morphism BOUND_VARIABLE_913) Cod)) (= (tptp.apply Morphism (tptp.zero Dom)) (tptp.zero Cod))))))) (let ((_let_107 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_104 1)) :args ((or _let_77 (not _let_104)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_105)) :args ((or _let_40 _let_104 (not _let_105)))) _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args (tptp.x tptp.any1 tptp.any2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.morphism Morphism Dom Cod) false)) (tptp.element BOUND_VARIABLE_913 Dom)))) :args (_let_106))) _let_107 :args (_let_105 false _let_106)) :args (_let_104 false _let_4 false _let_105)) :args (_let_77 false _let_104)))) (let ((_let_109 (and _let_52 _let_77 _let_60 _let_64 _let_70))) (let ((_let_110 (= _let_76 _let_63))) (let ((_let_111 (= _let_62 _let_69))) (let ((_let_112 (ASSUME :args (_let_64)))) (let ((_let_113 (ASSUME :args (_let_77)))) (let ((_let_114 (SYMM _let_113))) (let ((_let_115 (_let_60))) (let ((_let_116 (ASSUME :args _let_115))) (let ((_let_117 (SYMM _let_116))) (let ((_let_118 (ASSUME :args (_let_70)))) (let ((_let_119 (APPLY_UF tptp.subtract))) (let ((_let_120 (ASSUME :args (_let_52)))) (let ((_let_121 (or _let_45 _let_40 _let_18 _let_35 _let_31))) (let ((_let_122 (REFL :args (_let_36)))) (let ((_let_123 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 0)) (CONG _let_122 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_86)) :args ((or _let_17 _let_36))))) (let ((_let_124 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 1)) (CONG _let_122 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_86)) :args ((or _let_34 _let_36))))) (let ((_let_125 (CNF_OR_NEG :args (_let_36 2)))) (let ((_let_126 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted) (BOUND_VARIABLE_1234 $$unsorted)) (or (not (tptp.injection_2 Morphism)) (not (tptp.morphism Morphism Dom Cod)) (not (tptp.element BOUND_VARIABLE_1234 Dom)) (not (= (tptp.zero Cod) (tptp.apply Morphism BOUND_VARIABLE_1234))) (= (tptp.zero Dom) BOUND_VARIABLE_1234))))) (let ((_let_127 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_128 (_let_39))) (let ((_let_129 (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_128)) :args _let_128) (REWRITE :args ((=> _let_39 (not (or _let_18 _let_35 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_22)))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_37))) (REFL :args (_let_38)) :args _let_86)))) (let ((_let_130 (_let_37))) (let ((_let_131 (and _let_60 _let_66 _let_74 _let_79))) (let ((_let_132 (ASSUME :args (_let_74)))) (let ((_let_133 (ASSUME :args (_let_79)))) (let ((_let_134 (REFL :args (tptp.any1)))) (let ((_let_135 (ASSUME :args (_let_66)))) (let ((_let_136 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_131)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_132 _let_133 _let_116 _let_135) (SCOPE (TRANS (SYMM (SYMM _let_135)) (CONG _let_134 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (TRANS _let_117 (SYMM (SYMM _let_133))) :args _let_119) (SYMM _let_132)) :args (_let_74 _let_79 _let_60 _let_66))) :args (_let_60 _let_66 _let_74 _let_79))) :args (true _let_131)) :args ((or _let_49 (not _let_60) (not _let_66) (not _let_74) (not _let_79)))) (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_81 _let_80 _let_79 (not _let_82)))) (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_130) :args (_let_68 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.apply tptp.x El)))) :args _let_130))) _let_129 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_121)) :args ((or _let_40 _let_45 _let_18 _let_35 _let_31 (not _let_121)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_127 :args (tptp.x tptp.any1 tptp.any2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.morphism Morphism Dom Cod) false)) (not (= (tptp.element BOUND_VARIABLE_1234 Dom) false))))) :args (_let_126))) _let_127 :args (_let_121 false _let_126)) _let_44 _let_125 _let_124 _let_123 :args ((or _let_45 _let_36) false _let_121 false _let_4 true _let_31 false _let_34 false _let_17)) (RESOLUTION (CNF_AND_NEG :args (_let_109)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO (MODUS_PONENS (AND_INTRO _let_118 _let_120) (SCOPE (TRANS (CONG (REFL :args (tptp.any2)) (REFL :args (_let_51)) (SYMM (SYMM _let_120)) :args _let_119) (SYMM _let_118)) :args (_let_70 _let_52))) _let_112 (MODUS_PONENS _let_116 (SCOPE (CONG (REFL :args (tptp.x)) (SYMM _let_117) :args (APPLY_UF tptp.apply)) :args _let_115)) _let_113) (SCOPE (TRANS _let_114 (SYMM (SYMM (ASSUME :args (_let_110)))) (SYMM (SYMM _let_112)) (SYMM (SYMM (ASSUME :args (_let_111))))) :args (_let_111 _let_64 _let_110 _let_77))) :args (_let_52 _let_77 _let_60 _let_64 _let_70))) :args (true _let_109)) _let_108 (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_57 _let_55 _let_74 (not _let_75)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_99 :args (tptp.any1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING _let_101)) :args _let_100)) _let_99 :args (_let_75 false _let_98)) (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_57 _let_55 _let_72 (not _let_73)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (tptp.any1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_103)) :args _let_102)) _let_20 :args (_let_73 false _let_14)) (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_40 _let_57 _let_55 _let_70 (not _let_71)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (tptp.x tptp.any1 tptp.any2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING (_let_97 (tptp.subtract Cod (tptp.apply Morphism BOUND_VARIABLE_1199) (tptp.apply Morphism BOUND_VARIABLE_1201))))) :args _let_96)) _let_95 :args (_let_71 false _let_94)) _let_44 (REORDERING (FACTORING (CNF_OR_POS :args (_let_67))) :args ((or _let_57 _let_66 (not _let_67)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_99 :args (tptp.any1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_101)) :args _let_100)) _let_99 :args (_let_67 false _let_98)) (REORDERING (FACTORING (CNF_OR_POS :args (_let_65))) :args ((or _let_40 _let_57 _let_64 (not _let_65)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (tptp.x tptp.any1 tptp.any2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING (_let_97 (not (= (tptp.element BOUND_VARIABLE_1199 Dom) false)) (not (= (tptp.element BOUND_VARIABLE_1201 Dom) false))))) :args _let_96)) _let_95 :args (_let_65 false _let_94)) _let_44 (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_57 _let_60 (not _let_61)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_28 :args (tptp.any1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_29))) _let_28 :args (_let_61 false _let_27)) _let_93 _let_92 _let_91 _let_90 _let_88 (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_2 _let_40 _let_47 (not _let_48)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (tptp.x tptp.any1 tptp.any2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.morphism Morphism Dom Cod) false))))) :args (_let_84))) _let_85 :args (_let_48 false _let_84)) _let_44 (NOT_EQUIV_ELIM1 _let_83) :args (_let_2 false _let_79 false _let_82 false _let_37 false _let_36 false _let_78 false _let_77 false _let_74 false _let_75 false _let_72 false _let_73 false _let_70 false _let_71 false _let_4 false _let_66 false _let_67 false _let_64 false _let_65 false _let_4 false _let_60 false _let_61 true _let_49 false _let_52 false _let_54 false _let_56 true _let_58 true _let_46 false _let_48 false _let_4 false _let_1)))) (let ((_let_137 (MACRO_RESOLUTION_TRUST _let_129 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_1 _let_40 _let_39 (not _let_41)))) (MACRO_RESOLUTION_TRUST (NOT_EQUIV_ELIM2 _let_83) _let_136 :args (_let_45 false _let_2)) _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_43 :args (tptp.x tptp.any1 tptp.any2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.morphism Morphism Dom Cod) false))))) :args (_let_42)))) _let_43 :args (_let_41 false _let_42)) :args (_let_39 true _let_1 false _let_4 false _let_41)) :args (_let_38 true _let_37)))) (let ((_let_138 (MACRO_RESOLUTION_TRUST _let_123 _let_137 :args (_let_17 true _let_36)))) (let ((_let_139 (= _let_76 _let_32))) (let ((_let_140 (not _let_139))) (let ((_let_141 (not _let_24))) (let ((_let_142 (or _let_18 _let_141 _let_140 _let_31))) (let ((_let_143 (not _let_2))) (let ((_let_144 (or _let_143 _let_40 _let_55 _let_57 _let_53 _let_49))) (let ((_let_145 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted) (BOUND_VARIABLE_942 $$unsorted) (BOUND_VARIABLE_940 $$unsorted)) (or (not (tptp.injection Morphism)) (not (tptp.morphism Morphism Dom Cod)) (not (tptp.element BOUND_VARIABLE_940 Dom)) (not (tptp.element BOUND_VARIABLE_942 Dom)) (not (= (tptp.apply Morphism BOUND_VARIABLE_940) (tptp.apply Morphism BOUND_VARIABLE_942))) (= BOUND_VARIABLE_940 BOUND_VARIABLE_942))))) (let ((_let_146 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_147 (_let_46))) (let ((_let_148 (and _let_77 _let_34))) (let ((_let_149 (ASSUME :args (_let_34)))) (let ((_let_150 (and _let_141 _let_23))) (let ((_let_151 (_let_141 _let_23))) (let ((_let_152 (ASSUME :args (_let_141)))) (let ((_let_153 (ASSUME :args (_let_23)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (tptp.any1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_103)) :args _let_102)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_19))) :args ((or _let_18 _let_16 _let_21))) _let_138 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_150)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_152 _let_153) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_153) _let_134 :args (APPLY_UF tptp.element)) (FALSE_INTRO _let_152))) :args _let_151)) :args _let_151)) :args (true _let_150)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_141) _let_24))) (REFL :args ((not _let_23))) (REFL :args (_let_25)) :args _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_142)) :args ((or _let_141 _let_18 _let_31 _let_140 (not _let_142)))) _let_138 (MACRO_RESOLUTION_TRUST _let_125 _let_137 :args ((not _let_31) true _let_36)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_148)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_149 _let_113) (SCOPE (TRANS (SYMM _let_114) (SYMM (SYMM _let_149))) :args (_let_34 _let_77))) :args (_let_77 _let_34))) :args (true _let_148)) _let_108 (MACRO_RESOLUTION_TRUST _let_124 _let_137 :args (_let_34 true _let_36)) :args (_let_139 false _let_77 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_147) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_22 QUANTIFIERS_INST_E_MATCHING ((tptp.apply tptp.x El2) (not (= (tptp.element El1 tptp.any1) false))))) :args _let_147))) (MACRO_RESOLUTION_TRUST _let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_144)) :args ((or _let_40 _let_143 _let_57 _let_55 _let_53 _let_49 (not _let_144)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_146 :args (tptp.x tptp.any1 tptp.any2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.morphism Morphism Dom Cod) false)) (not (= (tptp.element BOUND_VARIABLE_940 Dom) false)) (not (= (tptp.element BOUND_VARIABLE_942 Dom) false))))) :args (_let_145)))) _let_146 :args (_let_144 false _let_145)) _let_136 _let_44 _let_93 _let_92 _let_91 _let_90 :args (_let_58 false _let_144 false _let_2 false _let_4 true _let_49 false _let_52 false _let_54 false _let_56)) :args (_let_46 false _let_58)) :args (_let_142 false _let_46)) :args (_let_141 false _let_17 true _let_31 false _let_139 false _let_142)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_18 _let_23 (not _let_26)))) _let_138 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_28 :args (tptp.any1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_29))) _let_28 :args (_let_26 false _let_27)) :args (_let_23 false _let_17 false _let_26)) :args (_let_25 true _let_24 false _let_23)) :args (_let_21 false _let_17 true _let_16)) _let_20 :args (false true _let_19 false _let_14)) :args (_let_13 _let_12 _let_11 (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 $$unsorted)) (and (tptp.element ElDom Dom) (= (tptp.apply Morphism ElDom) ElCod)))))) (tptp.surjection Morphism))) (forall ((Morphism1 $$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))))))) (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 $$unsorted)) (and (tptp.element ElDom Dom) (= (tptp.apply Morphism1 ElDom) ElCodDom)))))) (tptp.exact Morphism1 Morphism2))) (forall ((M1 $$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))))))) (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_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.65 )
% 0.21/0.65 % SZS output end Proof for HAL002+1
% 0.21/0.66 % cvc5---1.0.5 exiting
% 0.21/0.66 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------