TSTP Solution File: HAL006+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : HAL006+1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n027.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 01:53:30 EDT 2023
% Result : Theorem 44.47s 44.66s
% Output : Proof 44.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : HAL006+1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.16/0.35 % Computer : n027.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Mon Aug 28 02:55:51 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 44.47/44.66 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.85QDbfvLcb/cvc5---1.0.5_32607.p...
% 44.47/44.66 ------- get file name : TPTP file name is HAL006+1
% 44.47/44.66 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_32607.smt2...
% 44.47/44.66 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 44.47/44.66 --- Run --no-e-matching --full-saturate-quant at 5...
% 44.47/44.66 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 44.47/44.66 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 44.47/44.66 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 44.47/44.66 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 44.47/44.66 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 44.47/44.66 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 44.47/44.66 % SZS status Theorem for HAL006+1
% 44.47/44.66 % SZS output start Proof for HAL006+1
% 44.47/44.66 (
% 44.47/44.66 (let ((_let_1 (not (forall ((E $$unsorted)) (=> (tptp.element E tptp.e) (exists ((B1 $$unsorted) (B2 $$unsorted)) (and (tptp.element B1 tptp.b) (tptp.element B2 tptp.b) (= (tptp.apply tptp.g (tptp.subtract tptp.b B1 B2)) E)))))))) (let ((_let_2 (forall ((E $$unsorted)) (=> (tptp.element E tptp.e) (exists ((B1 $$unsorted) (E1 $$unsorted) (A $$unsorted)) (and (tptp.element B1 tptp.b) (tptp.element E1 tptp.e) (= (tptp.subtract tptp.e (tptp.apply tptp.g B1) E) E1) (tptp.element A tptp.a) (= (tptp.apply tptp.gamma (tptp.apply tptp.f A)) E1) (= (tptp.apply tptp.g (tptp.apply tptp.alpha A)) E1))))))) (let ((_let_3 (tptp.morphism tptp.g tptp.b tptp.e))) (let ((_let_4 (tptp.morphism tptp.alpha tptp.a tptp.b))) (let ((_let_5 (forall ((Morphism $$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_6 (forall ((Dom $$unsorted) (El1 $$unsorted) (El2 $$unsorted)) (=> (and (tptp.element El1 Dom) (tptp.element El2 Dom)) (= (tptp.subtract Dom El1 (tptp.subtract Dom El1 El2)) El2))))) (let ((_let_7 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted)) (=> (tptp.morphism Morphism Dom Cod) (and (forall ((El $$unsorted)) (=> (tptp.element El Dom) (tptp.element (tptp.apply Morphism El) Cod))) (= (tptp.apply Morphism (tptp.zero Dom)) (tptp.zero Cod))))))) (let ((_let_8 (tptp.apply tptp.alpha SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_9 (tptp.apply tptp.g _let_8))) (let ((_let_10 (tptp.apply tptp.g SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_11 (tptp.subtract tptp.e _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_12 (= _let_11 _let_9))) (let ((_let_13 (tptp.apply tptp.g (tptp.subtract tptp.b SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_8)))) (let ((_let_14 (= _let_13 (tptp.subtract tptp.e _let_10 _let_9)))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_13))) (let ((_let_16 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.subtract tptp.e _let_10 _let_11)))) (let ((_let_17 (not _let_12))) (let ((_let_18 (tptp.apply tptp.gamma (tptp.apply tptp.f SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_19 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.a))) (let ((_let_20 (not _let_19))) (let ((_let_21 (not (tptp.element _let_11 tptp.e)))) (let ((_let_22 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.b))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_21 _let_20 (not (= _let_11 _let_18)) _let_17))) (let ((_let_25 (forall ((B1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.subtract tptp.e (tptp.apply tptp.g B1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (or (not (tptp.element B1 tptp.b)) (not (tptp.element _let_1 tptp.e)) (not (tptp.element A tptp.a)) (not (= (tptp.apply tptp.gamma (tptp.apply tptp.f A)) _let_1)) (not (= (tptp.apply tptp.g (tptp.apply tptp.alpha A)) _let_1))))))) (let ((_let_26 (not _let_24))) (let ((_let_27 (not _let_25))) (let ((_let_28 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.e))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_27))) (let ((_let_31 (forall ((E $$unsorted)) (or (not (tptp.element E tptp.e)) (not (forall ((B1 $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.subtract tptp.e (tptp.apply tptp.g B1) E))) (or (not (tptp.element B1 tptp.b)) (not (tptp.element _let_1 tptp.e)) (not (tptp.element A tptp.a)) (not (= _let_1 (tptp.apply tptp.gamma (tptp.apply tptp.f A)))) (not (= _let_1 (tptp.apply tptp.g (tptp.apply tptp.alpha A)))))))))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (forall ((B1 $$unsorted) (B2 $$unsorted)) (or (not (tptp.element B1 tptp.b)) (not (tptp.element B2 tptp.b)) (not (= (tptp.apply tptp.g (tptp.subtract tptp.b B1 B2)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_29 _let_34))) (let ((_let_36 (forall ((E $$unsorted)) (or (not (tptp.element E tptp.e)) (not (forall ((B1 $$unsorted) (B2 $$unsorted)) (or (not (tptp.element B1 tptp.b)) (not (tptp.element B2 tptp.b)) (not (= E (tptp.apply tptp.g (tptp.subtract tptp.b B1 B2))))))))))) (let ((_let_37 (not _let_35))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (or))) (let ((_let_40 (not _let_36))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_38) :args (_let_40)) (REWRITE :args ((=> _let_40 (not (or _let_29 (not (forall ((B1 $$unsorted) (B2 $$unsorted)) (or (not (tptp.element B1 tptp.b)) (not (tptp.element B2 tptp.b)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.apply tptp.g (tptp.subtract tptp.b B1 B2)))))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_36))) (REFL :args (_let_37)) :args _let_39)) _let_38 :args (_let_37 true _let_36)))) (let ((_let_42 (REFL :args (_let_35)))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 0)) (CONG _let_42 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_39)) :args ((or _let_28 _let_35))) _let_41 :args (_let_28 true _let_35)))) (let ((_let_44 (_let_27))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_44)) :args _let_44) (REWRITE :args ((=> _let_27 (not (or _let_23 _let_21 _let_20 (not (= _let_18 _let_11)) (not (= _let_9 _let_11))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_25))) (REFL :args (_let_26)) :args _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_29 _let_27 (not _let_30)))) _let_43 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.element E tptp.e) false))))) :args (_let_31)))) _let_32 :args (_let_30 false _let_31)) :args (_let_27 false _let_28 false _let_30)) :args (_let_26 true _let_25)))) (let ((_let_46 (REFL :args (_let_24)))) (let ((_let_47 (tptp.element _let_8 tptp.b))) (let ((_let_48 (not _let_47))) (let ((_let_49 (not _let_3))) (let ((_let_50 (or _let_49 _let_23 _let_48 _let_14))) (let ((_let_51 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted) (BOUND_VARIABLE_1242 $$unsorted) (BOUND_VARIABLE_1240 $$unsorted)) (or (not (tptp.morphism Morphism Dom Cod)) (not (tptp.element BOUND_VARIABLE_1240 Dom)) (not (tptp.element BOUND_VARIABLE_1242 Dom)) (= (tptp.apply Morphism (tptp.subtract Dom BOUND_VARIABLE_1240 BOUND_VARIABLE_1242)) (tptp.subtract Cod (tptp.apply Morphism BOUND_VARIABLE_1240) (tptp.apply Morphism BOUND_VARIABLE_1242))))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (or _let_20 _let_47))) (let ((_let_54 (tptp.zero tptp.b))) (let ((_let_55 (and _let_53 (= _let_54 (tptp.apply tptp.alpha (tptp.zero tptp.a)))))) (let ((_let_56 (not _let_4))) (let ((_let_57 (or _let_56 _let_55))) (let ((_let_58 (forall ((Morphism $$unsorted) (Dom $$unsorted) (Cod $$unsorted) (BOUND_VARIABLE_954 $$unsorted)) (or (not (tptp.morphism Morphism Dom Cod)) (and (or (not (tptp.element BOUND_VARIABLE_954 Dom)) (tptp.element (tptp.apply Morphism BOUND_VARIABLE_954) Cod)) (= (tptp.apply Morphism (tptp.zero Dom)) (tptp.zero Cod))))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (_let_58))) (let ((_let_61 ((not (= (tptp.morphism Morphism Dom Cod) false)) (tptp.element BOUND_VARIABLE_954 Dom)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_20 _let_47 (not _let_53)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 2)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_39)) :args ((or _let_19 _let_24))) _let_45 :args (_let_19 true _let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_55 0)) :args ((or _let_53 (not _let_55)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_56 _let_55 (not _let_57)))) (ASSUME :args (_let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_59 :args (tptp.alpha tptp.a tptp.b SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_MT _let_61)) :args _let_60))) _let_59 :args (_let_57 false _let_58)) :args (_let_55 false _let_4 false _let_57)) :args (_let_53 false _let_55)) :args (_let_47 false _let_19 false _let_53)))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 0)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_39)) :args ((or _let_22 _let_24))) _let_45 :args (_let_22 true _let_24)))) (let ((_let_64 (ASSUME :args (_let_3)))) (let ((_let_65 (not _let_15))) (let ((_let_66 (or _let_23 _let_48 _let_65))) (let ((_let_67 (_let_33))) (let ((_let_68 (tptp.element _let_10 tptp.e))) (let ((_let_69 (not _let_68))) (let ((_let_70 (or _let_69 _let_29 _let_16))) (let ((_let_71 (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_72 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (or _let_23 _let_68))) (let ((_let_74 (and _let_73 (= (tptp.zero tptp.e) (tptp.apply tptp.g _let_54))))) (let ((_let_75 (or _let_49 _let_74))) (let ((_let_76 (and _let_12 _let_14 _let_65))) (let ((_let_77 (ASSUME :args (_let_65)))) (let ((_let_78 (ASSUME :args (_let_14)))) (let ((_let_79 (ASSUME :args (_let_12)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_76)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_77 _let_78 _let_79) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (TRANS (CONG (REFL :args (tptp.e)) (REFL :args (_let_10)) (SYMM (SYMM _let_79)) :args (APPLY_UF tptp.subtract)) (SYMM _let_78)) :args (=)) (FALSE_INTRO _let_77))) :args (_let_65 _let_14 _let_12))) :args (_let_12 _let_14 _let_65))) :args (true _let_76)) (CONG (REFL :args (_let_17)) (REFL :args ((not _let_14))) (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_15))) (REFL :args ((not _let_16))) :args _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_29 _let_69 _let_16 (not _let_70)))) _let_43 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_23 _let_68 (not _let_73)))) _let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_74 0)) :args ((or _let_73 (not _let_74)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_49 _let_74 (not _let_75)))) _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_59 :args (tptp.g tptp.b tptp.e SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_MT _let_61)) :args _let_60))) _let_59 :args (_let_75 false _let_58)) :args (_let_74 false _let_3 false _let_75)) :args (_let_73 false _let_74)) :args (_let_68 false _let_22 false _let_73)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (tptp.e _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_71))) _let_72 :args (_let_70 false _let_71)) :args (_let_16 false _let_28 false _let_68 false _let_70)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_23 _let_48 _let_65 (not _let_66)))) _let_63 _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_67) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_8 QUANTIFIERS_INST_CBQI_PROP)) :args _let_67))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 1)) (CONG _let_42 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_39)) :args ((or _let_33 _let_35))) _let_41 :args (_let_33 true _let_35)) :args (_let_66 false _let_33)) :args (_let_65 false _let_22 false _let_47 false _let_66)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_49 _let_23 _let_48 _let_14 (not _let_50)))) _let_64 _let_63 _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.g tptp.b tptp.e _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_MT ((not (= (tptp.morphism Morphism Dom Cod) false)) (not (= (tptp.element BOUND_VARIABLE_1240 Dom) false)) (not (= (tptp.element BOUND_VARIABLE_1242 Dom) false))))) :args (_let_51))) _let_52 :args (_let_50 false _let_51)) :args (_let_14 false _let_3 false _let_22 false _let_47 false _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 4)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_12))) :args _let_39)) :args ((or _let_12 _let_24))) _let_45 :args (_let_12 true _let_24)) :args (false false _let_16 true _let_15 false _let_14 false _let_12)) :args (_let_7 (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 $$unsorted)) (and (tptp.element ElDom Dom) (= (tptp.apply Morphism ElDom) ElCod)))))) (tptp.surjection Morphism))) (forall ((Morphism1 $$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 $$unsorted)) (=> (tptp.element ElDom Dom) (= (tptp.apply M2 (tptp.apply M1 ElDom)) (tptp.apply M4 (tptp.apply M3 ElDom)))))) (tptp.commute M1 M2 M3 M4))) (forall ((Dom $$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)))) _let_6 _let_5 _let_4 (tptp.morphism tptp.beta tptp.b tptp.c) (tptp.morphism tptp.gamma tptp.d tptp.e) (tptp.morphism tptp.delta tptp.e tptp.r) (tptp.morphism tptp.f tptp.a tptp.d) _let_3 (tptp.morphism tptp.h tptp.c tptp.r) (tptp.injection tptp.alpha) (tptp.injection tptp.gamma) (tptp.surjection tptp.beta) (tptp.surjection tptp.delta) (tptp.exact tptp.alpha tptp.beta) (tptp.exact tptp.gammma tptp.delta) (tptp.commute tptp.alpha tptp.g tptp.f tptp.gamma) (tptp.commute tptp.beta tptp.h tptp.g tptp.delta) (tptp.surjection tptp.f) (tptp.surjection tptp.h) (forall ((E $$unsorted)) (=> (tptp.element E tptp.e) (exists ((R $$unsorted) (B1 $$unsorted)) (and (tptp.element R tptp.r) (= (tptp.apply tptp.delta E) R) (tptp.element B1 tptp.b) (= (tptp.apply tptp.h (tptp.apply tptp.beta B1)) R) (= (tptp.apply tptp.delta (tptp.apply tptp.g B1)) R))))) _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 44.47/44.68 )
% 44.47/44.68 % SZS output end Proof for HAL006+1
% 44.47/44.68 % cvc5---1.0.5 exiting
% 44.47/44.68 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------