%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET722+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n005.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 14:40:03 EDT 2023

% Result   : Theorem 0.22s 0.61s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : SET722+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.07/0.15  % Command    : do_cvc5 %s %d
% 0.14/0.37  % Computer : n005.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit   : 300
% 0.14/0.37  % WCLimit    : 300
% 0.14/0.37  % DateTime   : Sat Aug 26 10:47:23 EDT 2023
% 0.14/0.37  % CPUTime    : 
% 0.22/0.52  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.61  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.0zZUSvLEFu/cvc5---1.0.5_19660.p...
% 0.22/0.61  ------- get file name : TPTP file name is SET722+4
% 0.22/0.61  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_19660.smt2...
% 0.22/0.61  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.61  % SZS status Theorem for SET722+4
% 0.22/0.61  % SZS output start Proof for SET722+4
% 0.22/0.61  (
% 0.22/0.61  (let ((_let_1 (not (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.maps F A B) (tptp.maps G B C) (tptp.surjective (tptp.compose_function G F A B C) A C)) (tptp.surjective G B C)))))) (let ((_let_2 (forall ((F $$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_3 (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_4 (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))))) (let ((_let_5 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_6 (not _let_5))) (let ((_let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_8 (not _let_7))) (let ((_let_9 (or _let_8 _let_6))) (let ((_let_10 (not _let_4))) (let ((_let_11 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_12 (not _let_11))) (let ((_let_13 (or _let_12 _let_10))) (let ((_let_14 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 E Y))))))))) (let ((_let_15 (not _let_13))) (let ((_let_16 (tptp.surjective SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_17 (= _let_16 _let_14))) (let ((_let_18 (not _let_14))) (let ((_let_19 (forall ((F $$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_20 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_21 (_let_19))) (let ((_let_22 ((tptp.surjective F A B)))) (let ((_let_23 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_24 (tptp.surjective _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or (not (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) _let_25 _let_16))) (let ((_let_27 (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.maps F A B)) (not (tptp.maps G B C)) (not (tptp.surjective (tptp.compose_function G F A B C) A C)) (tptp.surjective G B C))))) (let ((_let_28 (not _let_26))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (or))) (let ((_let_31 (not _let_27))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_29) :args (_let_31))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_27))) (REFL :args (_let_28)) :args _let_30)) _let_29 :args (_let_28 true _let_27)))) (let ((_let_33 (_let_18))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_33)) :args _let_33)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_14))) (REFL :args (_let_15)) :args _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_17)) :args ((or _let_16 _let_18 (not _let_17)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 3)) _let_32 :args ((not _let_16) true _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_22)) :args _let_21)) _let_20 :args (_let_17 false _let_19)) :args (_let_18 true _let_16 false _let_17)) :args (_let_15 true _let_14)))) (let ((_let_35 (REFL :args (_let_13)))) (let ((_let_36 (not _let_9))) (let ((_let_37 (or _let_8 (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)) _let_6))) (let ((_let_38 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))))) (let ((_let_39 (not _let_37))) (let ((_let_40 (not _let_38))) (let ((_let_41 (tptp.apply _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_42 (= _let_41 _let_40))) (let ((_let_43 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_44 _let_12 _let_42))) (let ((_let_46 (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_47 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (not _let_41))) (let ((_let_49 (or _let_44 _let_48))) (let ((_let_50 (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))))) (let ((_let_51 (not _let_49))) (let ((_let_52 (not _let_50))) (let ((_let_53 (or _let_12 _let_52))) (let ((_let_54 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) E Y))))))))) (let ((_let_55 (= _let_24 _let_54))) (let ((_let_56 (_let_54))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 0)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_30)) :args ((or _let_11 _let_13))) _let_34 :args (_let_11 true _let_13)))) (let ((_let_58 (_let_52))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_58)) :args _let_58)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_50))) (REFL :args (_let_51)) :args _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_12 _let_52 (not _let_53)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_56) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false))))) :args _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_55)) :args ((or _let_25 _let_54 (not _let_55)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 2)) (CONG (REFL :args (_let_26)) (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_30)) :args ((or _let_24 _let_26))) _let_32 :args (_let_24 true _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (_let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_22)) :args _let_21)) _let_20 :args (_let_55 false _let_19)) :args (_let_54 false _let_24 false _let_55)) :args (_let_53 false _let_54)) :args (_let_52 false _let_11 false _let_53)) :args (_let_51 true _let_50)))) (let ((_let_60 (REFL :args (_let_49)))) (let ((_let_61 (_let_40))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_61)) :args _let_61)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_38))) (REFL :args (_let_39)) :args _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_42)) :args ((or _let_48 _let_40 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_49 1)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_41))) :args _let_30)) :args ((or _let_41 _let_49))) _let_59 :args (_let_41 true _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_12 _let_44 _let_42 (not _let_45)))) _let_57 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_49 0)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_30)) :args ((or _let_43 _let_49))) _let_59 :args (_let_43 true _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING ((tptp.apply (tptp.compose_function G F A B C) X Z)))) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_42 false _let_11 false _let_43 false _let_45)) :args (_let_40 false _let_41 false _let_42)) :args (_let_39 true _let_38)))) (let ((_let_63 (REFL :args (_let_37)))) (let ((_let_64 (_let_4))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_64) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) :args _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_9)) :args ((or _let_8 _let_6 _let_36))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 0)) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_7))) :args _let_30)) :args ((or _let_7 _let_37))) _let_62 :args (_let_7 true _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 2)) (CONG _let_63 (MACRO_SR_PRED_INTRO :args ((= (not _let_6) _let_5))) :args _let_30)) :args ((or _let_5 _let_37))) _let_62 :args (_let_5 true _let_37)) :args (_let_36 false _let_7 false _let_5)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 1)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_4))) :args _let_30)) :args ((or _let_4 _let_13))) _let_34 :args (_let_4 true _let_13)) :args (false true _let_9 false _let_4)) :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_3 (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.equal_maps F G A B) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y1 B) (tptp.member Y2 B)) (=> (and (tptp.apply F X Y1) (tptp.apply G X Y2)) (= Y1 Y2)))))) (forall ((F $$unsorted) (A $$unsorted)) (= (tptp.identity F A) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.apply F X X))))) (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_2 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.one_to_one F A B) (and (tptp.injective F A B) (tptp.surjective F A B)))) (forall ((G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.inverse_predicate G F A B) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply G Y X)))))) (forall ((F $$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)))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.61  )
% 0.22/0.61  % SZS output end Proof for SET722+4
% 0.22/0.61  % cvc5---1.0.5 exiting
% 0.22/0.61  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------