TSTP Solution File: SET758+4 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET758+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.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 14:40:13 EDT 2023
% Result : Theorem 0.22s 0.57s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET758+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 15:59:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.57 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.CmSUdX3AEM/cvc5---1.0.5_16499.p...
% 0.22/0.57 ------- get file name : TPTP file name is SET758+4
% 0.22/0.57 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_16499.smt2...
% 0.22/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.57 % SZS status Theorem for SET758+4
% 0.22/0.57 % SZS output start Proof for SET758+4
% 0.22/0.57 (
% 0.22/0.57 (let ((_let_1 (not (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (Y $$unsorted)) (=> (and (tptp.maps F A B) (tptp.subset Y B)) (tptp.subset (tptp.image3 F (tptp.inverse_image3 F Y A) B) Y)))))) (let ((_let_2 (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 $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y)))))))) (let ((_let_3 (forall ((F $$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)))))))) (let ((_let_4 (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_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_6 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_8 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_9 (tptp.inverse_image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_10 (tptp.image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_11 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_10))) (let ((_let_12 (not _let_11))) (let ((_let_13 (or _let_12 _let_6))) (let ((_let_14 (not _let_6))) (let ((_let_15 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.inverse_image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_16 (not _let_13))) (let ((_let_17 (tptp.subset _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_18 (= _let_17 _let_15))) (let ((_let_19 (not _let_15))) (let ((_let_20 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_22 (_let_20))) (let ((_let_23 ((tptp.subset A B)))) (let ((_let_24 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_25 _let_17))) (let ((_let_29 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (Y $$unsorted)) (or (not (tptp.maps F A B)) (not (tptp.subset Y B)) (tptp.subset (tptp.image3 F (tptp.inverse_image3 F Y A) B) Y))))) (let ((_let_30 (not _let_28))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (or))) (let ((_let_33 (not _let_29))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_31) :args (_let_33))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_29))) (REFL :args (_let_30)) :args _let_32)) _let_31 :args (_let_30 true _let_29)))) (let ((_let_35 (_let_19))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_35)) :args _let_35)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_15))) (REFL :args (_let_16)) :args _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_18)) :args ((or _let_17 _let_19 (not _let_18)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_28 2)) _let_34 :args ((not _let_17) true _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (_let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_23)) :args _let_22)) _let_21 :args (_let_18 false _let_20)) :args (_let_19 true _let_17 false _let_18)) :args (_let_16 true _let_15)))) (let ((_let_37 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_38 (not _let_37))) (let ((_let_39 (not _let_7))) (let ((_let_40 (or _let_39 _let_38))) (let ((_let_41 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 Y)))))) (let ((_let_42 (not _let_40))) (let ((_let_43 (not _let_41))) (let ((_let_44 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_45 (and _let_44 _let_43))) (let ((_let_46 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_9))) (let ((_let_47 (= _let_46 _let_45))) (let ((_let_48 (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.inverse_image3 F B A)) (and (tptp.member X A) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (tptp.apply F X Y)))))))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_51 (not _let_50))) (let ((_let_52 (not _let_46))) (let ((_let_53 (or _let_52 _let_51))) (let ((_let_54 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.inverse_image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))))) (let ((_let_55 (not _let_53))) (let ((_let_56 (not _let_54))) (let ((_let_57 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_58 (and _let_57 _let_56))) (let ((_let_59 (= _let_11 _let_58))) (let ((_let_60 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.image3 F A B)) (and (tptp.member Y B) (not (forall ((X $$unsorted)) (or (not (tptp.member X A)) (not (tptp.apply F X Y)))))))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_59)) :args ((or _let_12 _let_58 (not _let_59)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 0)) (CONG (REFL :args (_let_13)) (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_32)) :args ((or _let_11 _let_13))) _let_36 :args (_let_11 true _let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING ((tptp.member Y (tptp.image3 F A B))))) :args (_let_60))) _let_61 :args (_let_59 false _let_60)) :args (_let_58 false _let_11 false _let_59)))) (let ((_let_63 (not _let_58))) (let ((_let_64 (_let_56))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_64)) :args _let_64)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_54))) (REFL :args (_let_55)) :args _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_58 1)) :args ((or _let_56 _let_63))) _let_62 :args (_let_56 false _let_58)) :args (_let_55 true _let_54)))) (let ((_let_66 (REFL :args (_let_53)))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_47)) :args ((or _let_52 _let_45 (not _let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 0)) (CONG _let_66 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_46))) :args _let_32)) :args ((or _let_46 _let_53))) _let_65 :args (_let_46 true _let_53)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING ((tptp.member X (tptp.inverse_image3 F B A))))) :args (_let_48))) _let_49 :args (_let_47 false _let_48)) :args (_let_45 false _let_46 false _let_47)))) (let ((_let_68 (not _let_45))) (let ((_let_69 (_let_43))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_69)) :args _let_69)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_41))) (REFL :args (_let_42)) :args _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_45 1)) :args ((or _let_43 _let_68))) _let_67 :args (_let_43 false _let_45)) :args (_let_42 true _let_41)))) (let ((_let_71 (REFL :args (_let_40)))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 0)) (CONG _let_71 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_7))) :args _let_32)) :args ((or _let_7 _let_40))) _let_70 :args (_let_7 true _let_40)))) (let ((_let_73 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_74 (not _let_73))) (let ((_let_75 (not _let_57))) (let ((_let_76 (not _let_44))) (let ((_let_77 (or _let_76 _let_75 _let_74 _let_51 _let_38 _let_8))) (let ((_let_78 (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 (and (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_78))) (let ((_let_80 (= _let_26 _let_79))) (let ((_let_81 (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_82 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (REFL :args (_let_28)))) (let ((_let_84 (_let_78))) (let ((_let_85 (or _let_39 _let_73))) (let ((_let_86 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_87 (= _let_24 _let_86))) (let ((_let_88 (_let_86))) (let ((_let_89 (ASSUME :args (_let_7)))) (let ((_let_90 (ASSUME :args (_let_8)))) (let ((_let_91 (ASSUME :args (_let_14)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_89 _let_90 _let_91) :args (_let_14 _let_7 _let_8)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_91)) (CONG (SYMM (SYMM _let_90)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) :args (APPLY_UF tptp.member)) (TRUE_INTRO _let_89))) :args (_let_7 _let_8 _let_14)) :args ((not (and _let_14 _let_7 _let_8)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_6))) (REFL :args (_let_39)) (REFL :args ((not _let_8))) :args _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_75 _let_51 _let_76 _let_38 _let_74 _let_8 (not _let_77)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_58 0)) :args ((or _let_57 _let_63))) _let_62 :args (_let_57 false _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 1)) (CONG _let_66 (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) :args _let_32)) :args ((or _let_50 _let_53))) _let_65 :args (_let_50 true _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_45 0)) :args ((or _let_44 _let_68))) _let_67 :args (_let_44 false _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 1)) (CONG _let_71 (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) :args _let_32)) :args ((or _let_37 _let_40))) _let_70 :args (_let_37 true _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_39 _let_73 (not _let_85)))) _let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_88) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) :args _let_88)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_87)) :args ((or _let_25 _let_86 (not _let_87)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 1)) (CONG _let_83 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_32)) :args ((or _let_24 _let_28))) _let_34 :args (_let_24 true _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_23)) :args _let_22)) _let_21 :args (_let_87 false _let_20)) :args (_let_86 false _let_24 false _let_87)) :args (_let_85 false _let_86)) :args (_let_73 false _let_7 false _let_85)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_84) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) false)) (not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y2) false))))) :args _let_84)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_79 1)) :args ((or _let_78 (not _let_79)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_80)) :args ((or _let_27 _let_79 (not _let_80)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 0)) (CONG _let_83 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_32)) :args ((or _let_26 _let_28))) _let_34 :args (_let_26 true _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :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_81))) _let_82 :args (_let_80 false _let_81)) :args (_let_79 false _let_26 false _let_80)) :args (_let_78 false _let_79)) :args (_let_77 false _let_78)) :args (_let_8 false _let_57 false _let_50 false _let_44 false _let_37 false _let_73 false _let_77)) _let_72 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_13 1)) _let_36 :args (_let_14 true _let_13)) :args (false false _let_8 false _let_7 true _let_6)) :args (_let_5 (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))))) _let_4 (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)))) (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_3 (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))))) _let_2 (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.57 )
% 0.22/0.57 % SZS output end Proof for SET758+4
% 0.22/0.57 % cvc5---1.0.5 exiting
% 0.22/0.57 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------