TSTP Solution File: SET733+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET733+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.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 14:40:06 EDT 2023
% Result : Theorem 0.22s 0.63s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET733+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n019.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
% 0.15/0.36 % DateTime : Sat Aug 26 11:41:28 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.63 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.tutmokVDEs/cvc5---1.0.5_10989.p...
% 0.22/0.63 ------- get file name : TPTP file name is SET733+4
% 0.22/0.63 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_10989.smt2...
% 0.22/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.63 % SZS status Theorem for SET733+4
% 0.22/0.63 % SZS output start Proof for SET733+4
% 0.22/0.63 (
% 0.22/0.63 (let ((_let_1 (not (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (and (tptp.maps F A B) (tptp.maps G B A) (tptp.identity (tptp.compose_function G F A B A) A)) (tptp.injective F A B)))))) (let ((_let_2 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.injective F A B) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member X2 A) (tptp.member Y B)) (=> (and (tptp.apply F X1 Y) (tptp.apply F X2 Y)) (= X1 X2)))))))) (let ((_let_3 (forall ((F $$unsorted) (A $$unsorted)) (= (tptp.identity F A) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.apply F X X))))))) (let ((_let_4 (forall ((G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted) (X $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X A) (tptp.member Z C)) (= (tptp.apply (tptp.compose_function G F A B C) X Z) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))))) (let ((_let_5 (forall ((F $$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 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y1 B) (tptp.member Y2 B)) (=> (and (tptp.apply F X Y1) (tptp.apply F X Y2)) (= Y1 Y2))))))))) (let ((_let_6 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_7 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_8 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_9 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_10 (not _let_6))) (let ((_let_11 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_12 (not _let_11))) (let ((_let_13 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_14 (not _let_13))) (let ((_let_15 (or _let_14 _let_12 _let_10))) (let ((_let_16 (forall ((Y $$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)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))))) (let ((_let_17 (not _let_15))) (let ((_let_18 (not _let_16))) (let ((_let_19 (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_4))) (let ((_let_20 (tptp.apply _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_21 (= _let_20 _let_18))) (let ((_let_22 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_23 _let_21))) (let ((_let_25 (forall ((G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Z C)) (= (tptp.apply (tptp.compose_function G F A B C) X Z) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (tptp.apply F X Y)) (not (tptp.apply G Y Z)))))))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (_let_25))) (let ((_let_28 ((tptp.apply (tptp.compose_function G F A B C) X Z)))) (let ((_let_29 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_30 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_31 (not _let_30))) (let ((_let_32 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_23 _let_35 _let_33 _let_31 _let_29))) (let ((_let_39 (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (or (not (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X1 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X2 Y)) (= X1 X2))))) (let ((_let_40 (not _let_38))) (let ((_let_41 (tptp.injective SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_42 (= _let_41 _let_39))) (let ((_let_43 (not _let_39))) (let ((_let_44 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.injective F A B) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (or (not (tptp.member X1 A)) (not (tptp.member X2 A)) (not (tptp.member Y B)) (not (tptp.apply F X1 Y)) (not (tptp.apply F X2 Y)) (= X1 X2))))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (tptp.identity _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_47 (not _let_46))) (let ((_let_48 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_49 (not _let_48))) (let ((_let_50 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_49 _let_47 _let_41))) (let ((_let_53 (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (or (not (tptp.maps F A B)) (not (tptp.maps G B A)) (not (tptp.identity (tptp.compose_function G F A B A) A)) (tptp.injective F A B))))) (let ((_let_54 (not _let_52))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (or))) (let ((_let_57 (not _let_53))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_55) :args (_let_57))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_53))) (REFL :args (_let_54)) :args _let_56)) _let_55 :args (_let_54 true _let_53)))) (let ((_let_59 (_let_43))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_59)) :args _let_59)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_39))) (REFL :args (_let_40)) :args _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_42)) :args ((or _let_41 _let_43 (not _let_42)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_52 3)) _let_58 :args ((not _let_41) true _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.injective F A B)))) :args (_let_44))) _let_45 :args (_let_42 false _let_44)) :args (_let_43 true _let_41 false _let_42)) :args (_let_40 true _let_39)))) (let ((_let_61 (REFL :args (_let_38)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 1)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_56)) :args ((or _let_22 _let_38))) _let_60 :args (_let_22 true _let_38)))) (let ((_let_63 (or _let_23 _let_20))) (let ((_let_64 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (tptp.apply (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_4) X X))))) (let ((_let_65 (= _let_46 _let_64))) (let ((_let_66 (forall ((F $$unsorted) (A $$unsorted)) (= (tptp.identity F A) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.apply F X X))))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (REFL :args (_let_52)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_65)) :args ((or _let_47 _let_64 (not _let_65)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 2)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_56)) :args ((or _let_46 _let_52))) _let_58 :args (_let_46 true _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args (_let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.identity F A)))) :args (_let_66))) _let_67 :args (_let_65 false _let_66)) :args (_let_64 false _let_46 false _let_65)))) (let ((_let_70 (_let_64))) (let ((_let_71 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) false))))) (let ((_let_72 (ASSUME :args _let_70))) (let ((_let_73 (_let_18))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_73)) :args _let_73)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_16))) (REFL :args (_let_17)) :args _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_21)) :args ((or (not _let_20) _let_18 (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_23 _let_20 (not _let_63)))) _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_71)) :args _let_70)) _let_69 :args (_let_63 false _let_64)) :args (_let_20 false _let_22 false _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_24))) :args ((or _let_23 _let_21 (not _let_24)))) _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING _let_28)) :args _let_27)) _let_26 :args (_let_24 false _let_25)) :args (_let_21 false _let_22 false _let_24)) :args (_let_18 false _let_20 false _let_21)) :args (_let_17 true _let_16)))) (let ((_let_75 (REFL :args (_let_15)))) (let ((_let_76 (or _let_23 _let_35 _let_14 _let_31 _let_12 _let_7))) (let ((_let_77 (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_78 (and (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_77))) (let ((_let_79 (= _let_50 _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_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (_let_80))) (let ((_let_83 ((tptp.maps F A B)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_78 1)) :args ((or _let_77 (not _let_78)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_79)) :args ((or _let_51 _let_78 (not _let_79)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 0)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) :args _let_56)) :args ((or _let_50 _let_52))) _let_58 :args (_let_50 true _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_83)) :args _let_82)) _let_81 :args (_let_79 false _let_80)) :args (_let_78 false _let_50 false _let_79)) :args (_let_77 false _let_78)))) (let ((_let_85 (_let_77))) (let ((_let_86 ((not (= (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false)) (not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y2) false))))) (let ((_let_87 (ASSUME :args _let_85))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 2)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_56)) :args ((or _let_34 _let_38))) _let_60 :args (_let_34 true _let_38)))) (let ((_let_89 (not _let_8))) (let ((_let_90 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_91 (not _let_90))) (let ((_let_92 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_93 (not _let_92))) (let ((_let_94 (or _let_93 _let_37 _let_23 _let_91 _let_89 _let_29))) (let ((_let_95 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y2)) (= Y1 Y2))))) (let ((_let_96 (and (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y))))))) _let_95))) (let ((_let_97 (= _let_48 _let_96))) (let ((_let_98 (_let_95))) (let ((_let_99 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_100 (not _let_99))) (let ((_let_101 (or _let_93 _let_100 _let_91))) (let ((_let_102 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))))) (let ((_let_103 (not _let_101))) (let ((_let_104 (not _let_102))) (let ((_let_105 (tptp.apply _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_106 (= _let_105 _let_104))) (let ((_let_107 (or _let_37 _let_37 _let_106))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 0)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_56)) :args ((or _let_36 _let_38))) _let_60 :args (_let_36 true _let_38)))) (let ((_let_109 (or _let_37 _let_105))) (let ((_let_110 (_let_104))) (let ((_let_111 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_110)) :args _let_110)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_104) _let_102))) (REFL :args (_let_103)) :args _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_106)) :args ((or (not _let_105) _let_104 (not _let_106)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_109)) :args ((or _let_37 _let_105 (not _let_109)))) _let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_71)) :args _let_70)) _let_69 :args (_let_109 false _let_64)) :args (_let_105 false _let_36 false _let_109)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_107))) :args ((or _let_37 _let_106 (not _let_107)))) _let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING _let_28)) :args _let_27)) _let_26 :args (_let_107 false _let_25)) :args (_let_106 false _let_36 false _let_107)) :args (_let_104 false _let_105 false _let_106)) :args (_let_103 true _let_102)))) (let ((_let_112 (REFL :args (_let_101)))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_101 0)) (CONG _let_112 (MACRO_SR_PRED_INTRO :args ((= (not _let_93) _let_92))) :args _let_56)) :args ((or _let_92 _let_101))) _let_111 :args (_let_92 true _let_101)))) (let ((_let_114 (or _let_37 _let_35 _let_93 _let_33 _let_100 _let_9))) (let ((_let_115 (not _let_9))) (let ((_let_116 (not _let_7))) (let ((_let_117 (ASSUME :args (_let_6)))) (let ((_let_118 (APPLY_UF tptp.apply))) (let ((_let_119 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (let ((_let_120 (ASSUME :args (_let_7)))) (let ((_let_121 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_122 (ASSUME :args (_let_9)))) (let ((_let_123 (ASSUME :args (_let_89)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_117 _let_120 _let_122 _let_123) :args (_let_6 _let_7 _let_89 _let_9)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_123)) (CONG _let_121 (SYMM _let_122) _let_119 :args _let_118) (CONG _let_121 (SYMM (SYMM _let_120)) _let_119 :args _let_118) (TRUE_INTRO _let_117))) :args (_let_6 _let_7 _let_9 _let_89)) :args ((not (and _let_6 _let_7 _let_89 _let_9)) SB_LITERAL))) (CONG (REFL :args (_let_10)) (REFL :args (_let_116)) (MACRO_SR_PRED_INTRO :args ((= (not _let_89) _let_8))) (REFL :args (_let_115)) :args _let_56)) :args ((or _let_10 _let_8 _let_116 _let_115))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_114)) :args ((or _let_37 _let_35 _let_33 _let_93 _let_100 _let_9 (not _let_114)))) _let_108 _let_88 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 3)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_56)) :args ((or _let_32 _let_38))) _let_60 :args (_let_32 true _let_38)) _let_113 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_101 1)) (CONG _let_112 (MACRO_SR_PRED_INTRO :args ((= (not _let_100) _let_99))) :args _let_56)) :args ((or _let_99 _let_101))) _let_111 :args (_let_99 true _let_101)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 QUANTIFIERS_INST_E_MATCHING _let_86)) :args _let_85)) _let_84 :args (_let_114 false _let_77)) :args (_let_9 false _let_36 false _let_34 false _let_32 false _let_92 false _let_99 false _let_114)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_37 _let_23 _let_29 _let_93 _let_91 _let_89 (not _let_94)))) _let_108 _let_62 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_38 5)) _let_60 :args ((not _let_29) true _let_38)) _let_113 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_101 2)) (CONG _let_112 (MACRO_SR_PRED_INTRO :args ((= (not _let_91) _let_90))) :args _let_56)) :args ((or _let_90 _let_101))) _let_111 :args (_let_90 true _let_101)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_98) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y1) false)) (not (= (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) false))))) :args _let_98)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_96 1)) :args ((or _let_95 (not _let_96)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_97)) :args ((or _let_49 _let_96 (not _let_97)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 1)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_56)) :args ((or _let_48 _let_52))) _let_58 :args (_let_48 true _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_83)) :args _let_82)) _let_81 :args (_let_97 false _let_80)) :args (_let_96 false _let_48 false _let_97)) :args (_let_95 false _let_96)) :args (_let_94 false _let_95)) :args (_let_89 false _let_36 false _let_22 true _let_29 false _let_92 false _let_90 false _let_94)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_23 _let_35 _let_31 _let_14 _let_12 _let_7 (not _let_76)))) _let_62 _let_88 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 4)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_56)) :args ((or _let_30 _let_38))) _let_60 :args (_let_30 true _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_15 0)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_56)) :args ((or _let_13 _let_15))) _let_74 :args (_let_13 true _let_15)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_15 1)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_56)) :args ((or _let_11 _let_15))) _let_74 :args (_let_11 true _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING _let_86)) :args _let_85)) _let_84 :args (_let_76 false _let_77)) :args (_let_7 false _let_22 false _let_34 false _let_30 false _let_13 false _let_11 false _let_76)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_15 2)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_6))) :args _let_56)) :args ((or _let_6 _let_15))) _let_74 :args (_let_6 true _let_15)) :args (false false _let_9 true _let_8 false _let_7 false _let_6)) :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_5 (forall ((H $$unsorted) (G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.compose_predicate H G F A B C) (forall ((X $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X A) (tptp.member Z C)) (= (tptp.apply H X Z) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))))) _let_4 (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.equal_maps F G A B) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y1 B) (tptp.member Y2 B)) (=> (and (tptp.apply F X Y1) (tptp.apply G X Y2)) (= Y1 Y2)))))) _let_3 _let_2 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.surjective F A B) (forall ((Y $$unsorted)) (=> (tptp.member Y B) (exists ((E $$unsorted)) (and (tptp.member E A) (tptp.apply F E Y))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.one_to_one F A B) (and (tptp.injective F A B) (tptp.surjective F A B)))) (forall ((G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.inverse_predicate G F A B) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply G Y X)))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply (tptp.inverse_function F A B) Y X)))) (forall ((F $$unsorted) (A $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.image2 F A)) (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.apply F X Y))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.image3 F A B)) (and (tptp.member Y B) (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.apply F X Y)))))) (forall ((F $$unsorted) (B $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.inverse_image2 F B)) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y))))) (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.inverse_image3 F B A)) (and (tptp.member X A) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y)))))) (forall ((F $$unsorted) (A $$unsorted) (R $$unsorted) (B $$unsorted) (S $$unsorted)) (= (tptp.increasing F A R B S) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member Y1 B) (tptp.member X2 A) (tptp.member Y2 B) (tptp.apply R X1 X2) (tptp.apply F X1 Y1) (tptp.apply F X2 Y2)) (tptp.apply S Y1 Y2))))) (forall ((F $$unsorted) (A $$unsorted) (R $$unsorted) (B $$unsorted) (S $$unsorted)) (= (tptp.decreasing F A R B S) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member Y1 B) (tptp.member X2 A) (tptp.member Y2 B) (tptp.apply R X1 X2) (tptp.apply F X1 Y1) (tptp.apply F X2 Y2)) (tptp.apply S Y2 Y1))))) (forall ((F $$unsorted) (A $$unsorted) (R $$unsorted) (B $$unsorted) (S $$unsorted)) (= (tptp.isomorphism F A R B S) (and (tptp.maps F A B) (tptp.one_to_one F A B) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member Y1 B) (tptp.member X2 A) (tptp.member Y2 B) (tptp.apply F X1 Y1) (tptp.apply F X2 Y2)) (= (tptp.apply R X1 X2) (tptp.apply S Y1 Y2))))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.63 )
% 0.22/0.63 % SZS output end Proof for SET733+4
% 0.22/0.63 % cvc5---1.0.5 exiting
% 0.22/0.63 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------