TSTP Solution File: SET715+4 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET715+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n031.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 14:40:02 EDT 2023
% Result : Theorem 0.21s 0.56s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET715+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.11/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n031.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 15:09:53 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.56 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.zAj1rOnJAW/cvc5---1.0.5_20282.p...
% 0.21/0.56 ------- get file name : TPTP file name is SET715+4
% 0.21/0.56 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_20282.smt2...
% 0.21/0.56 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.56 % SZS status Theorem for SET715+4
% 0.21/0.56 % SZS output start Proof for SET715+4
% 0.21/0.56 (
% 0.21/0.56 (let ((_let_1 (not (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (and (tptp.maps F A B) (tptp.one_to_one F A B)) (tptp.identity (tptp.compose_function F (tptp.inverse_function F A B) B A B) B)))))) (let ((_let_2 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply (tptp.inverse_function F A B) Y X)))))) (let ((_let_3 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.one_to_one F A B) (and (tptp.injective F A B) (tptp.surjective F A B)))))) (let ((_let_4 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.surjective F A B) (forall ((Y $$unsorted)) (=> (tptp.member Y B) (exists ((E $$unsorted)) (and (tptp.member E A) (tptp.apply F E Y))))))))) (let ((_let_5 (forall ((F $$unsorted) (A $$unsorted)) (= (tptp.identity F A) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.apply F X X))))))) (let ((_let_6 (forall ((G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted) (X $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X A) (tptp.member Z C)) (= (tptp.apply (tptp.compose_function G F A B C) X Z) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))))) (let ((_let_7 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_8 (tptp.inverse_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_9 (tptp.apply _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_10 (= _let_7 _let_9))) (let ((_let_11 (not _let_7))) (let ((_let_12 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_13 (not _let_12))) (let ((_let_14 (or _let_13 _let_11))) (let ((_let_15 (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))))) (let ((_let_16 (not _let_14))) (let ((_let_17 (not _let_15))) (let ((_let_18 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_19 (not _let_18))) (let ((_let_20 (or _let_19 _let_17))) (let ((_let_21 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 E Y))))))))) (let ((_let_22 (tptp.surjective SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_23 (= _let_22 _let_21))) (let ((_let_24 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.surjective F A B) (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (forall ((E $$unsorted)) (or (not (tptp.member E A)) (not (tptp.apply F E Y))))))))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (and (tptp.injective SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) _let_22))) (let ((_let_27 (tptp.one_to_one SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_28 (= _let_27 _let_26))) (let ((_let_29 (_let_3))) (let ((_let_30 (ASSUME :args _let_29))) (let ((_let_31 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_32 (tptp.identity _let_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_33 (not _let_27))) (let ((_let_34 (or (not (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_33 _let_32))) (let ((_let_35 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (or (not (tptp.maps F A B)) (not (tptp.one_to_one F A B)) (tptp.identity (tptp.compose_function F (tptp.inverse_function F A B) B A B) B))))) (let ((_let_36 (not _let_34))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (or))) (let ((_let_39 (not _let_35))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_37) :args (_let_39))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_35))) (REFL :args (_let_36)) :args _let_38)) _let_37 :args (_let_36 true _let_35)))) (let ((_let_41 (_let_21))) (let ((_let_42 (tptp.apply _let_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_43 (or _let_19 _let_42))) (let ((_let_44 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (tptp.apply (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.inverse_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) X X))))) (let ((_let_45 (not _let_43))) (let ((_let_46 (= _let_32 _let_44))) (let ((_let_47 (not _let_44))) (let ((_let_48 (forall ((F $$unsorted) (A $$unsorted)) (= (tptp.identity F A) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.apply F X X))))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (_let_47))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_50)) :args _let_50)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_44))) (REFL :args (_let_45)) :args _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_46)) :args ((or _let_32 _let_47 (not _let_46)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_34 2)) _let_40 :args ((not _let_32) true _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.identity F A)))) :args (_let_48))) _let_49 :args (_let_46 false _let_48)) :args (_let_47 true _let_32 false _let_46)) :args (_let_45 true _let_44)))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 0)) (CONG (REFL :args (_let_43)) (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_38)) :args ((or _let_18 _let_43))) _let_51 :args (_let_18 true _let_43)))) (let ((_let_53 (_let_17))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_53)) :args _let_53)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_15))) (REFL :args (_let_16)) :args _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_19 _let_17 (not _let_20)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_41) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) false))))) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_23)) :args ((or (not _let_22) _let_21 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_26 1)) :args ((or _let_22 (not _let_26)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_28)) :args ((or _let_33 _let_26 (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 1)) (CONG (REFL :args (_let_34)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_27))) :args _let_38)) :args ((or _let_27 _let_34))) _let_40 :args (_let_27 true _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.one_to_one F A B)))) :args _let_29)) _let_30 :args (_let_28 false _let_3)) :args (_let_26 false _let_27 false _let_28)) :args (_let_22 false _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.surjective F A B)))) :args (_let_24))) _let_25 :args (_let_23 false _let_24)) :args (_let_21 false _let_22 false _let_23)) :args (_let_20 false _let_21)) :args (_let_17 false _let_18 false _let_20)) :args (_let_16 true _let_15)))) (let ((_let_55 (REFL :args (_let_14)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 1)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_7))) :args _let_38)) :args ((or _let_7 _let_14))) _let_54 :args (_let_7 true _let_14)))) (let ((_let_57 (or _let_13 _let_19 _let_10))) (let ((_let_58 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply (tptp.inverse_function F A B) Y X)))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 0)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_38)) :args ((or _let_12 _let_14))) _let_54 :args (_let_12 true _let_14)))) (let ((_let_61 (not _let_9))) (let ((_let_62 (or _let_13 _let_61 _let_11))) (let ((_let_63 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply (tptp.inverse_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))))) (let ((_let_64 (not _let_63))) (let ((_let_65 (= _let_42 _let_64))) (let ((_let_66 (or _let_19 _let_19 _let_65))) (let ((_let_67 (forall ((G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Z C)) (= (tptp.apply (tptp.compose_function G F A B C) X Z) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (tptp.apply F X Y)) (not (tptp.apply G Y Z)))))))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (not _let_65))) (let ((_let_70 (_let_63))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_10)) :args ((or _let_11 _let_9 (not _let_10)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_13 _let_11 _let_61 (not _let_62)))) _let_60 _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_70) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false))))) :args _let_70)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_65)) (CONG (REFL :args (_let_69)) (REFL :args (_let_42)) (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_63))) :args _let_38)) :args ((or _let_42 _let_63 _let_69))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_43 1)) _let_51 :args ((not _let_42) true _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_66))) :args ((or _let_19 _let_65 (not _let_66)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING ((tptp.apply (tptp.compose_function G F A B C) X Z)))) :args (_let_67))) _let_68 :args (_let_66 false _let_67)) :args (_let_65 false _let_18 false _let_66)) :args (_let_63 true _let_42 false _let_65)) :args (_let_62 false _let_63)) :args (_let_61 false _let_12 false _let_7 false _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_19 _let_13 _let_10 (not _let_57)))) _let_52 _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING ((tptp.apply F X Y) (tptp.inverse_function F A B)))) :args (_let_58))) _let_59 :args (_let_57 false _let_58)) :args (_let_10 false _let_18 false _let_12 false _let_57)) _let_56 :args (false true _let_9 false _let_10 false _let_7)) :args ((forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted)) (not (tptp.member X tptp.empty_set))) (forall ((B $$unsorted) (A $$unsorted) (E $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.singleton A)) (= X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.product A)) (forall ((Y $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.maps F A B) (and (forall ((X $$unsorted)) (=> (tptp.member X A) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y))))) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y1 B) (tptp.member Y2 B)) (=> (and (tptp.apply F X Y1) (tptp.apply F X Y2)) (= Y1 Y2))))))) (forall ((H $$unsorted) (G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.compose_predicate H G F A B C) (forall ((X $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X A) (tptp.member Z C)) (= (tptp.apply H X Z) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))))) _let_6 (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.equal_maps F G A B) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y1 B) (tptp.member Y2 B)) (=> (and (tptp.apply F X Y1) (tptp.apply G X Y2)) (= Y1 Y2)))))) _let_5 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.injective F A B) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member X2 A) (tptp.member Y B)) (=> (and (tptp.apply F X1 Y) (tptp.apply F X2 Y)) (= X1 X2)))))) _let_4 _let_3 (forall ((G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.inverse_predicate G F A B) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply G Y X)))))) _let_2 (forall ((F $$unsorted) (A $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.image2 F A)) (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.apply F X Y))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.image3 F A B)) (and (tptp.member Y B) (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.apply F X Y)))))) (forall ((F $$unsorted) (B $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.inverse_image2 F B)) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y))))) (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.inverse_image3 F B A)) (and (tptp.member X A) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y)))))) (forall ((F $$unsorted) (A $$unsorted) (R $$unsorted) (B $$unsorted) (S $$unsorted)) (= (tptp.increasing F A R B S) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member Y1 B) (tptp.member X2 A) (tptp.member Y2 B) (tptp.apply R X1 X2) (tptp.apply F X1 Y1) (tptp.apply F X2 Y2)) (tptp.apply S Y1 Y2))))) (forall ((F $$unsorted) (A $$unsorted) (R $$unsorted) (B $$unsorted) (S $$unsorted)) (= (tptp.decreasing F A R B S) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member Y1 B) (tptp.member X2 A) (tptp.member Y2 B) (tptp.apply R X1 X2) (tptp.apply F X1 Y1) (tptp.apply F X2 Y2)) (tptp.apply S Y2 Y1))))) (forall ((F $$unsorted) (A $$unsorted) (R $$unsorted) (B $$unsorted) (S $$unsorted)) (= (tptp.isomorphism F A R B S) (and (tptp.maps F A B) (tptp.one_to_one F A B) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member Y1 B) (tptp.member X2 A) (tptp.member Y2 B) (tptp.apply F X1 Y1) (tptp.apply F X2 Y2)) (= (tptp.apply R X1 X2) (tptp.apply S Y1 Y2))))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.56 )
% 0.21/0.56 % SZS output end Proof for SET715+4
% 0.21/0.56 % cvc5---1.0.5 exiting
% 0.21/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------