TSTP Solution File: SET771+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET771+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 14:40:16 EDT 2023
% Result : Theorem 0.22s 0.62s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SET771+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.12/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.21/0.36 % CPULimit : 300
% 0.21/0.36 % WCLimit : 300
% 0.21/0.36 % DateTime : Sat Aug 26 10:57:47 EDT 2023
% 0.21/0.36 % CPUTime :
% 0.22/0.51 %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.62 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.0jcS7diRxv/cvc5---1.0.5_25504.p...
% 0.22/0.62 ------- get file name : TPTP file name is SET771+4
% 0.22/0.62 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_25504.smt2...
% 0.22/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.62 % SZS status Theorem for SET771+4
% 0.22/0.62 % SZS output start Proof for SET771+4
% 0.22/0.62 (
% 0.22/0.62 (let ((_let_1 (not (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (R $$unsorted)) (=> (and (tptp.maps F A B) (forall ((X1 $$unsorted) (X2 $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member X2 A)) (= (tptp.apply R X1 X2) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X1 Y) (tptp.apply F X2 Y))))))) (tptp.equivalence R A)))))) (let ((_let_2 (forall ((A $$unsorted) (R $$unsorted)) (= (tptp.equivalence R A) (and (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A)) (=> (tptp.apply R X Y) (tptp.apply R Y X)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A) (tptp.member Z A)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))))) (let ((_let_3 (forall ((F $$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 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y1 B) (tptp.member Y2 B)) (=> (and (tptp.apply F X Y1) (tptp.apply F X Y2)) (= Y1 Y2))))))))) (let ((_let_4 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_5 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_6 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_7 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_8 (not _let_4))) (let ((_let_9 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_10 (not _let_9))) (let ((_let_11 (or _let_10 _let_8))) (let ((_let_12 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Y)))))) (let ((_let_13 (not _let_11))) (let ((_let_14 (not _let_12))) (let ((_let_15 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_16 (not _let_15))) (let ((_let_17 (or _let_16 _let_14))) (let ((_let_18 (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_19 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y2)) (= Y1 Y2))))) (let ((_let_20 (and _let_18 _let_19))) (let ((_let_21 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_22 (= _let_21 _let_20))) (let ((_let_23 (forall ((F $$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 $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y1 B)) (not (tptp.member Y2 B)) (not (tptp.apply F X Y1)) (not (tptp.apply F X Y2)) (= Y1 Y2)))))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (tptp.equivalence SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_26 (forall ((X1 $$unsorted) (X2 $$unsorted)) (or (not (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 X1 X2) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X1 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X2 Y)))))))))) (let ((_let_27 (not _let_26))) (let ((_let_28 (not _let_21))) (let ((_let_29 (or _let_28 _let_27 _let_25))) (let ((_let_30 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (R $$unsorted)) (or (not (tptp.maps F A B)) (not (forall ((X1 $$unsorted) (X2 $$unsorted)) (or (not (tptp.member X1 A)) (not (tptp.member X2 A)) (= (tptp.apply R X1 X2) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (tptp.apply F X1 Y)) (not (tptp.apply F X2 Y))))))))) (tptp.equivalence R A))))) (let ((_let_31 (not _let_29))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (or))) (let ((_let_34 (not _let_30))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_32) :args (_let_34))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_30))) (REFL :args (_let_31)) :args _let_33)) _let_32 :args (_let_31 true _let_30)))) (let ((_let_36 (REFL :args (_let_29)))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_22)) :args ((or _let_28 _let_20 (not _let_22)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 0)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_21))) :args _let_33)) :args ((or _let_21 _let_29))) _let_35 :args (_let_21 true _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :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_23))) _let_24 :args (_let_22 false _let_23)) :args (_let_20 false _let_21 false _let_22)))) (let ((_let_38 (not _let_20))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_20 0)) :args ((or _let_18 _let_38))) _let_37 :args (_let_18 false _let_20)))) (let ((_let_40 (_let_18))) (let ((_let_41 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false))))) (let ((_let_42 (ASSUME :args _let_40))) (let ((_let_43 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_44 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_45 (not _let_44))) (let ((_let_46 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_47 (not _let_46))) (let ((_let_48 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_49 (not _let_48))) (let ((_let_50 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_49 _let_16 _let_47 _let_45 _let_43))) (let ((_let_53 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 X Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y Z)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 X Z))))) (let ((_let_54 (not _let_52))) (let ((_let_55 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 X Y)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y X))))) (let ((_let_56 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 X X))))) (let ((_let_57 (and _let_56 _let_55 _let_53))) (let ((_let_58 (not _let_53))) (let ((_let_59 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_60 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_61 (not _let_60))) (let ((_let_62 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_63 (not _let_62))) (let ((_let_64 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_65 _let_63 _let_61 _let_59))) (let ((_let_67 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Y)))))) (let ((_let_68 (not _let_67))) (let ((_let_69 (= _let_60 _let_68))) (let ((_let_70 (or _let_65 _let_63 _let_69))) (let ((_let_71 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 Y)))))) (let ((_let_72 (not _let_71))) (let ((_let_73 (= _let_59 _let_72))) (let ((_let_74 (or _let_63 _let_65 _let_73))) (let ((_let_75 (REFL :args (_let_66)))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 1)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_33)) :args ((or _let_26 _let_29))) _let_35 :args (_let_26 true _let_29)))) (let ((_let_77 (_let_26))) (let ((_let_78 ((tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 X1 X2)))) (let ((_let_79 (ASSUME :args _let_77))) (let ((_let_80 (not _let_73))) (let ((_let_81 (not _let_55))) (let ((_let_82 (_let_81))) (let ((_let_83 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_84 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_85 (not _let_84))) (let ((_let_86 (or _let_85 _let_83))) (let ((_let_87 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 Y)))))) (let ((_let_88 (not _let_87))) (let ((_let_89 (= _let_83 _let_88))) (let ((_let_90 (or _let_85 _let_85 _let_89))) (let ((_let_91 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 Y)))))) (let ((_let_92 (not _let_91))) (let ((_let_93 (or _let_85 _let_92))) (let ((_let_94 (not _let_89))) (let ((_let_95 (not _let_56))) (let ((_let_96 (_let_95))) (let ((_let_97 (= _let_25 _let_57))) (let ((_let_98 (not _let_57))) (let ((_let_99 (forall ((A $$unsorted) (R $$unsorted)) (= (tptp.equivalence R A) (and (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y A)) (not (tptp.apply R X Y)) (tptp.apply R Y X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y A)) (not (tptp.member Z A)) (not (tptp.apply R X Y)) (not (tptp.apply R Y Z)) (tptp.apply R X Z)))))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (_let_58))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_101)) :args _let_101)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_53))) (REFL :args (_let_54)) :args _let_33)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_97)) :args ((or _let_25 _let_98 (not _let_97)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 2)) _let_35 :args ((not _let_25) true _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equivalence R A)))) :args (_let_99))) _let_100 :args (_let_97 false _let_99)) :args (_let_98 true _let_25 false _let_97)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_96)) :args _let_96)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_95) _let_56))) (REFL :args ((not _let_86))) :args _let_33)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_87 (= Y Y)))) (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_89)) (CONG (REFL :args (_let_94)) (REFL :args (_let_83)) (MACRO_SR_PRED_INTRO :args ((= (not _let_88) _let_87))) :args _let_33)) :args ((or _let_83 _let_87 _let_94))) (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_85 _let_92 (not _let_93)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_41)) :args _let_40)) _let_39 :args (_let_93 false _let_18)) (REORDERING (FACTORING (CNF_OR_POS :args (_let_90))) :args ((or _let_85 _let_89 (not _let_90)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_79 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_78)) :args _let_77))) _let_76 :args (_let_90 false _let_26)) (CNF_OR_NEG :args (_let_86 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_86 0)) (CONG (REFL :args (_let_86)) (MACRO_SR_PRED_INTRO :args ((= (not _let_85) _let_84))) :args _let_33)) :args ((or _let_84 _let_86))) :args (_let_86 false _let_87 true _let_91 false _let_93 false _let_89 false _let_90 true _let_83 false _let_84)) :args (_let_56 false _let_86)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_82)) :args _let_82)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_81) _let_55))) (REFL :args ((not _let_66))) :args _let_33)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (MACRO_SR_PRED_INTRO :args ((= _let_67 _let_71) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE))) (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_73)) (CONG (REFL :args (_let_80)) (REFL :args (_let_59)) (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_71))) :args _let_33)) :args ((or _let_59 _let_71 _let_80))) (REORDERING (CNF_EQUIV_POS1 :args (_let_69)) :args ((or _let_61 _let_68 (not _let_69)))) (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_65 _let_63 _let_73 (not _let_74)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args 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(MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_165 2)) (CONG _let_173 (MACRO_SR_PRED_INTRO :args ((= (not _let_160) _let_159))) :args _let_33)) :args ((or _let_159 _let_165))) _let_172 :args (_let_159 true _let_165)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_140 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING _let_139)) :args _let_138)) _let_137 :args (_let_163 false _let_19)) :args (_let_157 false _let_15 false _let_9 false _let_4 false _let_161 false _let_159 false _let_163)) :args (_let_154 false _let_158 false _let_157)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_140 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING _let_139)) :args _let_138))) _let_137 :args (_let_156 false _let_19)) :args (_let_7 false _let_48 false _let_9 false _let_134 false _let_141 false _let_154 false _let_156)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_136)) :args ((or _let_51 _let_113 _let_111 _let_135 _let_133 _let_6 (not _let_136)))) _let_119 _let_131 _let_130 _let_153 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_143 1)) (CONG _let_152 (MACRO_SR_PRED_INTRO :args ((= (not _let_133) _let_132))) :args _let_33)) :args ((or _let_132 _let_143))) _let_151 :args (_let_132 true _let_143)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_140 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING _let_139)) :args _let_138))) _let_137 :args (_let_136 false _let_19)) :args (_let_6 false _let_50 false _let_112 false _let_110 false _let_134 false _let_132 false _let_136)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_114)) :args ((or _let_113 _let_111 _let_109 (not _let_114)))) _let_131 _let_130 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_121) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) false))))) :args _let_121)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_117)) (CONG (REFL :args (_let_120)) (REFL :args (_let_43)) (MACRO_SR_PRED_INTRO :args ((= (not _let_116) _let_115))) :args _let_33)) :args ((or _let_43 _let_115 _let_120))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_52 5)) _let_102 :args ((not _let_43) true _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_118)) :args ((or _let_51 _let_16 _let_117 (not _let_118)))) _let_119 _let_104 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_78)) :args _let_77)) _let_76 :args (_let_118 false _let_26)) :args (_let_117 false _let_50 false _let_15 false _let_118)) :args (_let_115 true _let_43 false _let_117)) :args (_let_114 false _let_115)) :args (_let_109 false _let_112 false _let_110 false _let_114)) _let_108 :args (false false _let_7 false _let_6 true _let_5 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 $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) _let_3 (forall ((H $$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 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply (tptp.inverse_function F A B) Y X)))) (forall ((F $$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))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (not (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.member X B)))))) (forall ((A $$unsorted) (E $$unsorted)) (= (tptp.partition A E) (and (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.subset X E))) (forall ((X $$unsorted)) (=> (tptp.member X E) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A)) (=> (exists ((Z $$unsorted)) (and (tptp.member Z X) (tptp.member Z Y))) (= X Y))))))) _let_2 (forall ((R $$unsorted) (E $$unsorted) (A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.equivalence_class A E R)) (and (tptp.member X E) (tptp.apply R A X)))) (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.pre_order R E) (and (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E) (tptp.member Z E)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.62 )
% 0.22/0.62 % SZS output end Proof for SET771+4
% 0.22/0.62 % cvc5---1.0.5 exiting
% 0.22/0.62 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------