%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET734+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 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 14:40:07 EDT 2023

% Result   : Theorem 0.21s 0.57s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET734+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.35  % Computer : n020.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sat Aug 26 09:06:15 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.57  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.4iQqH24aEi/cvc5---1.0.5_26185.p...
% 0.21/0.57  ------- get file name : TPTP file name is SET734+4
% 0.21/0.57  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_26185.smt2...
% 0.21/0.57  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.57  % SZS status Theorem for SET734+4
% 0.21/0.57  % SZS output start Proof for SET734+4
% 0.21/0.57  (
% 0.21/0.57  (let ((_let_1 (not (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (and (tptp.maps G A B) (tptp.maps F B A) (tptp.identity (tptp.compose_function G F B A B) B)) (tptp.surjective G A B)))))) (let ((_let_2 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.surjective F A B) (forall ((Y $$unsorted)) (=> (tptp.member Y B) (exists ((E $$unsorted)) (and (tptp.member E A) (tptp.apply F E Y))))))))) (let ((_let_3 (forall ((F $$unsorted) (A $$unsorted)) (= (tptp.identity F A) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.apply F X X))))))) (let ((_let_4 (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_5 (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))))) (let ((_let_6 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_7 (not _let_6))) (let ((_let_8 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_9 (not _let_8))) (let ((_let_10 (or _let_9 _let_7))) (let ((_let_11 (not _let_5))) (let ((_let_12 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_13 (not _let_12))) (let ((_let_14 (or _let_13 _let_11))) (let ((_let_15 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 E Y))))))))) (let ((_let_16 (not _let_14))) (let ((_let_17 (tptp.surjective SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_18 (= _let_17 _let_15))) (let ((_let_19 (not _let_15))) (let ((_let_20 (forall ((F $$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_21 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_22 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_23 (tptp.identity _let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or (not (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_24 _let_17))) (let ((_let_26 (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (or (not (tptp.maps G A B)) (not (tptp.maps F B A)) (not (tptp.identity (tptp.compose_function G F B A B) B)) (tptp.surjective G A B))))) (let ((_let_27 (not _let_25))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (or))) (let ((_let_30 (not _let_26))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_28) :args (_let_30))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_26))) (REFL :args (_let_27)) :args _let_29)) _let_28 :args (_let_27 true _let_26)))) (let ((_let_32 (_let_19))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_32)) :args _let_32)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_15))) (REFL :args (_let_16)) :args _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_18)) :args ((or _let_17 _let_19 (not _let_18)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 3)) _let_31 :args ((not _let_17) true _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.surjective F A B)))) :args (_let_20))) _let_21 :args (_let_18 false _let_20)) :args (_let_19 true _let_17 false _let_18)) :args (_let_16 true _let_15)))) (let ((_let_34 (REFL :args (_let_14)))) (let ((_let_35 (not _let_10))) (let ((_let_36 (or _let_9 (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)) _let_7))) (let ((_let_37 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))))) (let ((_let_38 (not _let_36))) (let ((_let_39 (not _let_37))) (let ((_let_40 (tptp.apply _let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_41 (= _let_40 _let_39))) (let ((_let_42 (or _let_13 _let_13 _let_41))) (let ((_let_43 (forall ((G $$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 $$unsorted)) (or (not (tptp.member Y B)) (not (tptp.apply F X Y)) (not (tptp.apply G Y Z)))))))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 0)) (CONG _let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_29)) :args ((or _let_12 _let_14))) _let_33 :args (_let_12 true _let_14)))) (let ((_let_46 (or _let_13 _let_40))) (let ((_let_47 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.apply (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) X X))))) (let ((_let_48 (= _let_23 _let_47))) (let ((_let_49 (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_50 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (_let_47))) (let ((_let_52 (_let_39))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_52)) :args _let_52)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_37))) (REFL :args (_let_38)) :args _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_41)) :args ((or (not _let_40) _let_39 (not _let_41)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_13 _let_40 (not _let_46)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_51) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) :args _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_48)) :args ((or _let_24 _let_47 (not _let_48)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 2)) (CONG (REFL :args (_let_25)) (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_29)) :args ((or _let_23 _let_25))) _let_31 :args (_let_23 true _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (_let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.identity F A)))) :args (_let_49))) _let_50 :args (_let_48 false _let_49)) :args (_let_47 false _let_23 false _let_48)) :args (_let_46 false _let_47)) :args (_let_40 false _let_12 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_42))) :args ((or _let_13 _let_41 (not _let_42)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING ((tptp.apply (tptp.compose_function G F A B C) X Z)))) :args (_let_43))) _let_44 :args (_let_42 false _let_43)) :args (_let_41 false _let_12 false _let_42)) :args (_let_39 false _let_40 false _let_41)) :args (_let_38 true _let_37)))) (let ((_let_54 (REFL :args (_let_36)))) (let ((_let_55 (_let_5))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_55) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) false))))) :args _let_55)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_10)) :args ((or _let_9 _let_7 _let_35))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 0)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_8))) :args _let_29)) :args ((or _let_8 _let_36))) _let_53 :args (_let_8 true _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 2)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_6))) :args _let_29)) :args ((or _let_6 _let_36))) _let_53 :args (_let_6 true _let_36)) :args (_let_35 false _let_8 false _let_6)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 1)) (CONG _let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_5))) :args _let_29)) :args ((or _let_5 _let_14))) _let_33 :args (_let_5 true _let_14)) :args (false true _let_10 false _let_5)) :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_4 (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.equal_maps F G A B) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y1 B) (tptp.member Y2 B)) (=> (and (tptp.apply F X Y1) (tptp.apply G X Y2)) (= Y1 Y2)))))) _let_3 (forall ((F $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.57  )
% 0.21/0.57  % SZS output end Proof for SET734+4
% 0.21/0.57  % cvc5---1.0.5 exiting
% 0.21/0.57  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------