TSTP Solution File: SET748+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET748+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n021.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 14:40:10 EDT 2023
% Result : Theorem 0.21s 0.60s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET748+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.08/0.14 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n021.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
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 11:06:56 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.60 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.dQycuHZDaG/cvc5---1.0.5_11880.p...
% 0.21/0.60 ------- get file name : TPTP file name is SET748+4
% 0.21/0.60 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_11880.smt2...
% 0.21/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.60 % SZS status Theorem for SET748+4
% 0.21/0.60 % SZS output start Proof for SET748+4
% 0.21/0.60 (
% 0.21/0.60 (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.decreasing F A R B S) (tptp.increasing G B S C T)) (tptp.decreasing (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 $$unsorted)) (= (tptp.decreasing F A R B S) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member Y1 B) (tptp.member X2 A) (tptp.member Y2 B) (tptp.apply R X1 X2) (tptp.apply F X1 Y1) (tptp.apply F X2 Y2)) (tptp.apply S Y2 Y1))))))) (let ((_let_3 (forall ((F $$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_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 (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 X1 X2)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X1 Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X2 Y2)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 Y1 Y2))))) (let ((_let_7 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_8 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_9 (not _let_8))) (let ((_let_10 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_11 (not _let_10))) (let ((_let_12 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (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_7))) (let ((_let_23 (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_24 (= _let_23 _let_6))) (let ((_let_25 (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 $$unsorted)) (or (not (tptp.member X1 A)) (not (tptp.member Y1 B)) (not (tptp.member X2 A)) (not (tptp.member Y2 B)) (not (tptp.apply R X1 X2)) (not (tptp.apply F X1 Y1)) (not (tptp.apply F X2 Y2)) (tptp.apply S Y1 Y2))))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_28 (tptp.decreasing _let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_29 (not _let_23))) (let ((_let_30 (tptp.decreasing SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_31 (not _let_30))) (let ((_let_32 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 (not (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) _let_31 _let_29 _let_28))) (let ((_let_35 (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted) (R $$unsorted) (S $$unsorted) (T $$unsorted)) (or (not (tptp.maps F A B)) (not (tptp.maps G B C)) (not (tptp.decreasing F A R B S)) (not (tptp.increasing G B S C T)) (tptp.decreasing (tptp.compose_function G F A B C) A R C T))))) (let ((_let_36 (not _let_34))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (or))) (let ((_let_39 (not _let_35))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_37) :args (_let_39))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_35))) (REFL :args (_let_36)) :args _let_38)) _let_37 :args (_let_36 true _let_35)))) (let ((_let_41 (REFL :args (_let_34)))) (let ((_let_42 (not _let_22))) (let ((_let_43 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_46 (not _let_45))) (let ((_let_47 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_48 (not _let_47))) (let ((_let_49 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_50 (not _let_49))) (let ((_let_51 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_52 (not _let_51))) (let ((_let_53 (or _let_52 _let_17 _let_50 _let_21 _let_48 _let_46 _let_44 _let_12))) (let ((_let_54 (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 X1 X2)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X1 Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X2 Y2)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Y2 Y1))))) (let ((_let_55 (= _let_30 _let_54))) (let ((_let_56 (forall ((F $$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)) (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 Y2 Y1))))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (_let_56))) (let ((_let_59 ((tptp.decreasing F A R B S)))) (let ((_let_60 (_let_54))) (let ((_let_61 (or _let_21 _let_44))) (let ((_let_62 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 Y)))))) (let ((_let_63 (not _let_61))) (let ((_let_64 (not _let_62))) (let ((_let_65 (or _let_50 _let_64))) (let ((_let_66 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y))))))))) (let ((_let_67 (forall ((X $$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_68 (and _let_66 _let_67))) (let ((_let_69 (= _let_32 _let_68))) (let ((_let_70 (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_71 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_69)) :args ((or _let_33 _let_68 (not _let_69)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 0)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_38)) :args ((or _let_32 _let_34))) _let_40 :args (_let_32 true _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :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_70))) _let_71 :args (_let_69 false _let_70)) :args (_let_68 false _let_32 false _let_69)))) (let ((_let_73 (not _let_68))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_68 0)) :args ((or _let_66 _let_73))) _let_72 :args (_let_66 false _let_68)))) (let ((_let_75 (_let_66))) (let ((_let_76 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) false))))) (let ((_let_77 (ASSUME :args _let_75))) (let ((_let_78 (tptp.apply _let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_79 (not _let_78))) (let ((_let_80 (tptp.apply _let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_81 (not _let_80))) (let ((_let_82 (or _let_52 _let_15 _let_50 _let_19 _let_48 _let_81 _let_79 _let_7))) (let ((_let_83 (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 Y2 Y1)))))) (let ((_let_84 (not _let_82))) (let ((_let_85 (= _let_28 _let_83))) (let ((_let_86 (not _let_83))) (let ((_let_87 (_let_86))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_87)) :args _let_87)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_86) _let_83))) (REFL :args (_let_84)) :args _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_85)) :args ((or _let_28 _let_86 (not _let_85)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_34 4)) _let_40 :args ((not _let_28) true _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (_let_27 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_59)) :args _let_58)) _let_57 :args (_let_85 false _let_56)) :args (_let_86 true _let_28 false _let_85)) :args (_let_84 true _let_83)))) (let ((_let_89 (REFL :args (_let_82)))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_82 2)) (CONG _let_89 (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_49))) :args _let_38)) :args ((or _let_49 _let_82))) _let_88 :args (_let_49 true _let_82)))) (let ((_let_91 (_let_64))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_91)) :args _let_91)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_62))) (REFL :args (_let_63)) :args _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_50 _let_64 (not _let_65)))) _let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_76)) :args _let_75)) _let_74 :args (_let_65 false _let_66)) :args (_let_64 false _let_49 false _let_65)) :args (_let_63 true _let_62)))) (let ((_let_93 (REFL :args (_let_61)))) (let ((_let_94 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 1)) (CONG _let_93 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_38)) :args ((or _let_43 _let_61))) _let_92 :args (_let_43 true _let_61)))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 0)) (CONG _let_93 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_38)) :args ((or _let_20 _let_61))) _let_92 :args (_let_20 true _let_61)))) (let ((_let_96 (or _let_17 _let_46))) (let ((_let_97 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Y)))))) (let ((_let_98 (not _let_96))) (let ((_let_99 (not _let_97))) (let ((_let_100 (or _let_52 _let_99))) (let ((_let_101 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_let_34))) _let_40 :args (_let_30 true _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_59)) :args _let_58)) _let_57 :args (_let_55 false _let_56)) :args (_let_54 false _let_30 false _let_55)) :args (_let_53 false _let_54)) :args (_let_12 false _let_51 false _let_49 false _let_47 false _let_16 false _let_45 false _let_20 false _let_43 false _let_53)) :args (_let_42 false _let_14 false _let_18 true _let_7 false _let_16 false _let_20 false _let_8 false _let_10 false _let_12)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_24)) :args ((or _let_29 _let_6 (not _let_24)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 3)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_23))) :args _let_38)) :args ((or _let_23 _let_34))) _let_40 :args (_let_23 true _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.increasing F A R B S)))) :args (_let_25))) _let_26 :args (_let_24 false _let_25)) :args (_let_6 false _let_23 false _let_24)) :args (false true _let_22 false _let_6)) :args ((forall ((A $$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 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y1 B) (tptp.member Y2 B)) (=> (and (tptp.apply F X Y1) (tptp.apply G X Y2)) (= Y1 Y2)))))) (forall ((F $$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 $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y)))))) _let_3 _let_2 (forall ((F $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.61 )
% 0.21/0.61 % SZS output end Proof for SET748+4
% 0.21/0.61 % cvc5---1.0.5 exiting
% 0.21/0.61 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------