TSTP Solution File: SET763+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET763+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 14:40:14 EDT 2023
% Result : Theorem 27.48s 27.67s
% Output : Proof 27.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET763+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.11/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n007.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 10:21:41 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 27.48/27.67 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.oUtfVtkhO6/cvc5---1.0.5_3655.p...
% 27.48/27.67 ------- get file name : TPTP file name is SET763+4
% 27.48/27.67 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_3655.smt2...
% 27.48/27.67 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 27.48/27.67 --- Run --no-e-matching --full-saturate-quant at 5...
% 27.48/27.67 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 27.48/27.67 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 27.48/27.67 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 27.48/27.67 % SZS status Theorem for SET763+4
% 27.48/27.67 % SZS output start Proof for SET763+4
% 27.48/27.67 (
% 27.48/27.67 (let ((_let_1 (not (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (X $$unsorted)) (=> (and (tptp.maps F A B) (tptp.subset X A) (tptp.equal_set (tptp.image2 F X) tptp.empty_set)) (tptp.equal_set X tptp.empty_set)))))) (let ((_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))))))) (let ((_let_3 (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))))))))) (let ((_let_4 (forall ((X $$unsorted)) (not (tptp.member X tptp.empty_set))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85 tptp.empty_set))) (let ((_let_8 (_let_4))) (let ((_let_9 (ASSUME :args _let_8))) (let ((_let_10 (not _let_7))) (let ((_let_11 (or _let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_12 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.empty_set)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_13 (not _let_11))) (let ((_let_14 (tptp.subset tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_15 (= _let_14 _let_12))) (let ((_let_16 (not _let_12))) (let ((_let_17 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (_let_17))) (let ((_let_20 ((tptp.subset A B)))) (let ((_let_21 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.empty_set))) (let ((_let_22 (and _let_21 _let_14))) (let ((_let_23 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.member X tptp.empty_set))))) (let ((_let_24 (= _let_21 _let_23))) (let ((_let_25 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.empty_set)))) (let ((_let_28 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_29 (or _let_26 _let_28))) (let ((_let_30 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_26 _let_31))) (let ((_let_33 (forall ((Y $$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)))))) (let ((_let_34 (not _let_33))) (let ((_let_35 (not _let_28))) (let ((_let_36 (or _let_35 _let_34))) (let ((_let_37 (or (not (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_31))) (let ((_let_38 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_39 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_40 (= _let_39 _let_38))) (let ((_let_41 (tptp.equal_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.empty_set))) (let ((_let_42 (tptp.image2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_43 (tptp.equal_set _let_42 tptp.empty_set))) (let ((_let_44 (not _let_43))) (let ((_let_45 (not _let_39))) (let ((_let_46 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_47 _let_45 _let_44 _let_41))) (let ((_let_49 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (X $$unsorted)) (or (not (tptp.maps F A B)) (not (tptp.subset X A)) (not (tptp.equal_set (tptp.image2 F X) tptp.empty_set)) (tptp.equal_set X tptp.empty_set))))) (let ((_let_50 (not _let_48))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (or))) (let ((_let_53 (not _let_49))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_51) :args (_let_53))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_49))) (REFL :args (_let_50)) :args _let_52)) _let_51 :args (_let_50 true _let_49)))) (let ((_let_55 (REFL :args (_let_48)))) (let ((_let_56 (_let_38))) (let ((_let_57 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))))) (let ((_let_58 (not _let_57))) (let ((_let_59 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_42))) (let ((_let_60 (= _let_59 _let_58))) (let ((_let_61 (forall ((F $$unsorted) (A $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.image2 F A)) (not (forall ((X $$unsorted)) (or (not (tptp.member X A)) (not (tptp.apply F X Y))))))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.empty_set))) (let ((_let_64 (not _let_59))) (let ((_let_65 (or _let_64 _let_63))) (let ((_let_66 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.image2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (tptp.member X tptp.empty_set))))) (let ((_let_67 (tptp.subset _let_42 tptp.empty_set))) (let ((_let_68 (= _let_67 _let_66))) (let ((_let_69 (and _let_67 (tptp.subset tptp.empty_set _let_42)))) (let ((_let_70 (= _let_43 _let_69))) (let ((_let_71 (_let_5))) (let ((_let_72 (ASSUME :args _let_71))) (let ((_let_73 ((tptp.equal_set A B)))) (let ((_let_74 (_let_66))) (let ((_let_75 (not _let_60))) (let ((_let_76 (_let_57))) (let ((_let_77 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y))))))))) (let ((_let_78 (and _let_77 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y2)) (= Y1 Y2)))))) (let ((_let_79 (= _let_46 _let_78))) (let ((_let_80 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.maps F A B) (and (forall ((X $$unsorted)) (or (not (tptp.member X A)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (tptp.apply F X Y))))))) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y1 B)) (not (tptp.member Y2 B)) (not (tptp.apply F X Y1)) (not (tptp.apply F X Y2)) (= Y1 Y2)))))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (_let_77))) (let ((_let_83 (_let_34))) (let ((_let_84 (not _let_23))) (let ((_let_85 (_let_84))) (let ((_let_86 (= _let_41 _let_22))) (let ((_let_87 (not _let_22))) (let ((_let_88 (_let_16))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_9 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_8)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_11 0)) (CONG (REFL :args (_let_11)) (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_7))) :args _let_52)) :args ((or _let_7 _let_11))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_88)) :args _let_88)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_12))) (REFL :args (_let_13)) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_15)) :args ((or _let_14 _let_16 (not _let_15)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_86)) :args ((or _let_41 _let_87 (not _let_86)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_48 3)) _let_54 :args ((not _let_41) true _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.empty_set QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_73)) :args _let_71)) _let_72 :args (_let_86 false _let_5)) :args (_let_87 true _let_41 false _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_24)) :args ((or _let_21 _let_84 (not _let_24)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_85)) :args _let_85)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_84) _let_23))) (REFL :args ((not _let_27))) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 0)) (CONG (REFL :args (_let_27)) (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_52)) :args ((or _let_25 _let_27))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_83)) :args _let_83)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) (REFL :args ((not _let_37))) :args _let_52)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 1)) (CONG (REFL :args (_let_37)) (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_52)) :args ((or _let_30 _let_37))) (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_35 _let_34 (not _let_36)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_82) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false))))) :args _let_82)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_78 0)) :args ((or _let_77 (not _let_78)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_79)) :args ((or _let_47 _let_78 (not _let_79)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 0)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_52)) :args ((or _let_46 _let_48))) _let_54 :args (_let_46 true _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.maps F A B)))) :args (_let_80))) _let_81 :args (_let_79 false _let_80)) :args (_let_78 false _let_46 false _let_79)) :args (_let_77 false _let_78)) :args (_let_36 false _let_77)) (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_26 _let_31 (not _let_32)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_76) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_76)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_60)) (CONG (REFL :args (_let_75)) (REFL :args (_let_59)) (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_57))) :args _let_52)) :args ((or _let_59 _let_57 _let_75))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_63 _let_64 (not _let_65)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_9 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X tptp.empty_set) false))))) :args _let_8)) _let_9 :args ((not _let_63) false _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_74) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X tptp.empty_set) true))))) :args _let_74)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_68)) :args ((or (not _let_67) _let_66 (not _let_68)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_69 0)) :args ((or _let_67 (not _let_69)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_70)) :args ((or _let_44 _let_69 (not _let_70)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 2)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_52)) :args ((or _let_43 _let_48))) _let_54 :args (_let_43 true _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (_let_42 tptp.empty_set QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_73)) :args _let_71)) _let_72 :args (_let_70 false _let_5)) :args (_let_69 false _let_43 false _let_70)) :args (_let_67 false _let_69)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (_let_42 tptp.empty_set QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_20)) :args _let_19)) _let_18 :args (_let_68 false _let_17)) :args (_let_66 false _let_67 false _let_68)) :args (_let_65 false _let_66)) :args (_let_64 true _let_63 false _let_65)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING ((tptp.member Y (tptp.image2 F A))))) :args (_let_61))) _let_62 :args (_let_60 false _let_61)) :args (_let_57 true _let_59 false _let_60)) :args (_let_32 false _let_57)) (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_26 _let_28 (not _let_29)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_56) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) :args _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_40)) :args ((or _let_45 _let_38 (not _let_40)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 1)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_39))) :args _let_52)) :args ((or _let_39 _let_48))) _let_54 :args (_let_39 true _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_20)) :args _let_19)) _let_18 :args (_let_40 false _let_17)) :args (_let_38 false _let_39 false _let_40)) :args (_let_29 false _let_38)) :args (_let_26 false _let_37 true _let_33 false _let_36 true _let_30 false _let_32 false _let_28 false _let_29)) :args (_let_27 true _let_25)) :args (_let_23 false _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.empty_set QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_20)) :args _let_19)) _let_18 :args (_let_24 false _let_17)) :args (_let_21 false _let_23 false _let_24)) :args ((not _let_14) true _let_22 false _let_21)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_20)) :args _let_19)) _let_18 :args (_let_15 false _let_17)) :args (_let_16 true _let_14 false _let_15)) :args (_let_13 true _let_12)) :args (_let_7 true _let_11)) _let_9 :args (false false _let_7 false _let_4)) :args (_let_6 _let_5 (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)))) _let_4 (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))))) _let_3 (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 $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))))) (forall ((G $$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 $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))) (forall ((F $$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 $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member X2 A) (tptp.member Y B)) (=> (and (tptp.apply F X1 Y) (tptp.apply F X2 Y)) (= X1 X2)))))) (forall ((F $$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))))))) (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)))) _let_2 (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 27.48/27.68 )
% 27.48/27.68 % SZS output end Proof for SET763+4
% 27.48/27.68 % cvc5---1.0.5 exiting
% 27.48/27.68 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------