TSTP Solution File: SET746+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET746+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.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 14:40:09 EDT 2023
% Result : Theorem 0.36s 0.57s
% Output : Proof 0.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET746+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.06/0.14 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 11:47:50 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 0.36/0.57 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.wkdOxdOiQ3/cvc5---1.0.5_22925.p...
% 0.36/0.57 ------- get file name : TPTP file name is SET746+4
% 0.36/0.57 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_22925.smt2...
% 0.36/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.36/0.57 % SZS status Theorem for SET746+4
% 0.36/0.57 % SZS output start Proof for SET746+4
% 0.36/0.57 (
% 0.36/0.57 (let ((_let_1 (not (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted) (R $$unsorted) (S $$unsorted) (T $$unsorted)) (=> (and (tptp.maps F A B) (tptp.maps G B C) (tptp.increasing F A R B S) (tptp.increasing G B S C T)) (tptp.increasing (tptp.compose_function G F A B C) A R C T)))))) (let ((_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 $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member Y1 B) (tptp.member X2 A) (tptp.member Y2 B) (tptp.apply R X1 X2) (tptp.apply F X1 Y1) (tptp.apply F X2 Y2)) (tptp.apply S Y1 Y2))))))) (let ((_let_3 (forall ((G $$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 $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))))) (let ((_let_4 (forall ((F $$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 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y1 B) (tptp.member Y2 B)) (=> (and (tptp.apply F X Y1) (tptp.apply F X Y2)) (= Y1 Y2))))))))) (let ((_let_5 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_6 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_7 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_8 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_9 (not _let_8))) (let ((_let_10 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_11 (not _let_10))) (let ((_let_12 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19 _let_17 _let_15 _let_13 _let_11 _let_9 _let_5))) (let ((_let_23 (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 X1 X2)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X1 Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X2 Y2)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Y1 Y2))))) (let ((_let_24 (tptp.increasing SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_25 (= _let_24 _let_23))) (let ((_let_26 (forall ((F $$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)) (or (not (tptp.member X1 A)) (not (tptp.member Y1 B)) (not (tptp.member X2 A)) (not (tptp.member Y2 B)) (not (tptp.apply R X1 X2)) (not (tptp.apply F X1 Y1)) (not (tptp.apply F X2 Y2)) (tptp.apply S Y1 Y2))))))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (_let_26))) (let ((_let_29 ((tptp.increasing F A R B S)))) (let ((_let_30 (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_31 (tptp.increasing _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_32 (tptp.increasing SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_33 (not _let_32))) (let ((_let_34 (not _let_24))) (let ((_let_35 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_36 (not _let_35))) (let ((_let_37 (or _let_36 (not (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) _let_34 _let_33 _let_31))) (let ((_let_38 (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted) (R $$unsorted) (S $$unsorted) (T $$unsorted)) (or (not (tptp.maps F A B)) (not (tptp.maps G B C)) (not (tptp.increasing F A R B S)) (not (tptp.increasing G B S C T)) (tptp.increasing (tptp.compose_function G F A B C) A R C T))))) (let ((_let_39 (not _let_37))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (or))) (let ((_let_42 (not _let_38))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_40) :args (_let_42))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_38))) (REFL :args (_let_39)) :args _let_41)) _let_40 :args (_let_39 true _let_38)))) (let ((_let_44 (REFL :args (_let_37)))) (let ((_let_45 (_let_23))) (let ((_let_46 (or _let_15 _let_9))) (let ((_let_47 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 Y)))))) (let ((_let_48 (not _let_46))) (let ((_let_49 (not _let_47))) (let ((_let_50 (or _let_17 _let_49))) (let ((_let_51 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y))))))))) (let ((_let_52 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y2)) (= Y1 Y2))))) (let ((_let_53 (and _let_51 _let_52))) (let ((_let_54 (= _let_35 _let_53))) (let ((_let_55 (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_56 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_54)) :args ((or _let_36 _let_53 (not _let_54)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 0)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_41)) :args ((or _let_35 _let_37))) _let_43 :args (_let_35 true _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.maps F A B)))) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_53 false _let_35 false _let_54)))) (let ((_let_58 (not _let_53))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_53 0)) :args ((or _let_51 _let_58))) _let_57 :args (_let_51 false _let_53)))) (let ((_let_60 (_let_51))) (let ((_let_61 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) false))))) (let ((_let_62 (ASSUME :args _let_60))) (let ((_let_63 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_64 (tptp.apply _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_65 (not _let_64))) (let ((_let_66 (tptp.apply _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_67 (not _let_66))) (let ((_let_68 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_69 (not _let_68))) (let ((_let_70 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_71 (not _let_70))) (let ((_let_72 (or _let_21 _let_71 _let_17 _let_69 _let_13 _let_67 _let_65 _let_63))) (let ((_let_73 (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (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))) (or (not (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 X1 X2)) (not (tptp.apply _let_1 X1 Y1)) (not (tptp.apply _let_1 X2 Y2)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 Y1 Y2)))))) (let ((_let_74 (not _let_72))) (let ((_let_75 (= _let_31 _let_73))) (let ((_let_76 (not _let_73))) (let ((_let_77 (_let_76))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_77)) :args _let_77)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_73))) (REFL :args (_let_74)) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_75)) :args ((or _let_31 _let_76 (not _let_75)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_37 4)) _let_43 :args ((not _let_31) true _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (_let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_28)) _let_27 :args (_let_75 false _let_26)) :args (_let_76 true _let_31 false _let_75)) :args (_let_74 true _let_73)))) (let ((_let_79 (REFL :args (_let_72)))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 2)) (CONG _let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_41)) :args ((or _let_16 _let_72))) _let_78 :args (_let_16 true _let_72)))) (let ((_let_81 (_let_49))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_81)) :args _let_81)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_47))) (REFL :args (_let_48)) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_17 _let_49 (not _let_50)))) _let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_61)) :args _let_60)) _let_59 :args (_let_50 false _let_51)) :args (_let_49 false _let_16 false _let_50)) :args (_let_48 true _let_47)))) (let ((_let_83 (REFL :args (_let_46)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 1)) (CONG _let_83 (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_8))) :args _let_41)) :args ((or _let_8 _let_46))) _let_82 :args (_let_8 true _let_46)))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 0)) (CONG _let_83 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_41)) :args ((or _let_14 _let_46))) _let_82 :args (_let_14 true _let_46)))) (let ((_let_86 (or _let_19 _let_11))) (let ((_let_87 (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_12 Y)))))) (let ((_let_88 (not _let_86))) (let ((_let_89 (not _let_87))) (let ((_let_90 (or _let_21 _let_89))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 0)) (CONG _let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_41)) :args ((or _let_20 _let_72))) _let_78 :args (_let_20 true _let_72)))) (let ((_let_92 (_let_89))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_92)) :args _let_92)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_89) _let_87))) (REFL :args (_let_88)) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_21 _let_89 (not _let_90)))) _let_91 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_61)) :args _let_60)) _let_59 :args (_let_90 false _let_51)) :args (_let_89 false _let_20 false _let_90)) :args (_let_88 true _let_87)))) (let ((_let_94 (REFL :args (_let_86)))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_86 1)) (CONG _let_94 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_10))) :args _let_41)) :args ((or _let_10 _let_86))) _let_93 :args (_let_10 true _let_86)))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_86 0)) (CONG _let_94 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_41)) :args ((or _let_18 _let_86))) _let_93 :args (_let_18 true _let_86)))) (let ((_let_97 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_98 (not _let_97))) (let ((_let_99 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_100 (not _let_99))) (let ((_let_101 (or _let_21 _let_19 _let_100 _let_11 _let_98 _let_6))) (let ((_let_102 (MACRO_RESOLUTION_TRUST 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(MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_41)) :args ((or _let_12 _let_72))) _let_78 :args (_let_12 true _let_72)) _let_96 _let_95 _let_85 _let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_45) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) false)) (not (= (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false)) (not (= (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) false)) (not (= (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_25)) :args ((or _let_34 _let_23 (not _let_25)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 2)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_24))) :args _let_41)) :args ((or _let_24 _let_37))) _let_43 :args (_let_24 true _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_28)) _let_27 :args (_let_25 false _let_26)) :args (_let_23 false _let_24 false _let_25)) :args (_let_22 false _let_23)) :args (_let_5 false _let_20 false _let_16 false _let_12 false _let_18 false _let_10 false _let_14 false _let_8 false _let_22)) :args (false true _let_7 false _let_6 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 $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) _let_4 (forall ((H $$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)))))))) _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)))))) (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 $$unsorted)) (and (tptp.member X A) (tptp.apply F X Y))))) (forall ((F $$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 $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y)))))) _let_2 (forall ((F $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.36/0.58 )
% 0.36/0.58 % SZS output end Proof for SET746+4
% 0.36/0.58 % cvc5---1.0.5 exiting
% 0.36/0.58 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------