TSTP Solution File: SET710+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET710+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n005.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 14:40:00 EDT 2023
% Result : Theorem 0.21s 0.61s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET710+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 15:04:23 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.61 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.zbByed7bnN/cvc5---1.0.5_25826.p...
% 0.21/0.61 ------- get file name : TPTP file name is SET710+4
% 0.21/0.61 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_25826.smt2...
% 0.21/0.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.61 % SZS status Theorem for SET710+4
% 0.21/0.61 % SZS output start Proof for SET710+4
% 0.21/0.61 (
% 0.21/0.61 (let ((_let_1 (not (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.maps F A B) (tptp.maps G B C) (tptp.maps H C D)) (tptp.equal_maps (tptp.compose_function H (tptp.compose_function G F A B C) A C D) (tptp.compose_function (tptp.compose_function H G B C D) F A B D) A D)))))) (let ((_let_2 (forall ((F $$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 ((_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_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_6 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_7 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_8 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_9 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21))) (let ((_let_10 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_11 (not _let_5))) (let ((_let_12 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_19 (not _let_18))) (let ((_let_20 (or _let_19 _let_17 _let_15 _let_13 _let_11 _let_10))) (let ((_let_21 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y2)) (= Y1 Y2))))) (let ((_let_22 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y))))))))) (let ((_let_23 (and _let_22 _let_21))) (let ((_let_24 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_25 (= _let_24 _let_23))) (let ((_let_26 (forall ((F $$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 $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y1 B)) (not (tptp.member Y2 B)) (not (tptp.apply F X Y1)) (not (tptp.apply F X Y2)) (= Y1 Y2)))))))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (_let_26))) (let ((_let_29 ((tptp.maps F A B)))) (let ((_let_30 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_31 (tptp.compose_function _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_32 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_33 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_34 (tptp.equal_maps _let_33 _let_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_35 (not _let_24))) (let ((_let_36 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_37 _let_35 _let_34))) (let ((_let_41 (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (or (not (tptp.maps F A B)) (not (tptp.maps G B C)) (not (tptp.maps H C D)) (tptp.equal_maps (tptp.compose_function H (tptp.compose_function G F A B C) A C D) (tptp.compose_function (tptp.compose_function H G B C D) F A B D) A D))))) (let ((_let_42 (not _let_40))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (or))) (let ((_let_45 (not _let_41))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_43) :args (_let_45))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_41))) (REFL :args (_let_42)) :args _let_44)) _let_43 :args (_let_42 true _let_41)))) (let ((_let_47 (REFL :args (_let_40)))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_25)) :args ((or _let_35 _let_23 (not _let_25)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 2)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_24))) :args _let_44)) :args ((or _let_24 _let_40))) _let_46 :args (_let_24 true _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 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)))) (let ((_let_49 (not _let_23))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_23 1)) :args ((or _let_21 _let_49))) _let_48 :args (_let_21 false _let_23)))) (let ((_let_51 (_let_21))) (let ((_let_52 (not (= (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) false)))) (let ((_let_53 (ASSUME :args _let_51))) (let ((_let_54 (tptp.apply _let_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_19 _let_55 _let_13))) (let ((_let_57 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))))) (let ((_let_58 (not _let_56))) (let ((_let_59 (not _let_57))) (let ((_let_60 (tptp.apply _let_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_61 (= _let_60 _let_59))) (let ((_let_62 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_63 (not _let_62))) (let ((_let_64 (or _let_63 _let_17 _let_61))) (let ((_let_65 (forall ((G $$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 $$unsorted)) (or (not (tptp.member Y B)) (not (tptp.apply F X Y)) (not (tptp.apply G Y Z)))))))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (_let_65))) (let ((_let_68 ((tptp.apply (tptp.compose_function G F A B C) X Z)))) (let ((_let_69 (tptp.apply _let_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_70 (not _let_69))) (let ((_let_71 (not _let_60))) (let ((_let_72 (or _let_63 _let_17 _let_15 _let_71 _let_70 _let_10))) (let ((_let_73 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (not (tptp.apply (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) X Y1)) (not (tptp.apply (tptp.compose_function (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) X Y2)) (= Y1 Y2))))) (let ((_let_74 (not _let_72))) (let ((_let_75 (= _let_34 _let_73))) (let ((_let_76 (not _let_73))) (let ((_let_77 (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.equal_maps F G A B) (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 G X Y2)) (= Y1 Y2))))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (_let_76))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_79)) :args _let_79)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_73))) (REFL :args (_let_74)) :args _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_75)) :args ((or _let_34 _let_76 (not _let_75)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_40 3)) _let_46 :args ((not _let_34) true _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (_let_33 _let_31 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_maps F G A B)))) :args (_let_77))) _let_78 :args (_let_75 false _let_77)) :args (_let_76 true _let_34 false _let_75)) :args (_let_74 true _let_73)))) (let ((_let_81 (REFL :args (_let_72)))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 1)) (CONG _let_81 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_44)) :args ((or _let_16 _let_72))) _let_80 :args (_let_16 true _let_72)))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 0)) (CONG _let_81 (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_62))) :args _let_44)) :args ((or _let_62 _let_72))) _let_80 :args (_let_62 true _let_72)))) (let ((_let_84 (_let_59))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_84)) :args _let_84)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_57))) (REFL :args (_let_58)) :args _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_61)) :args ((or _let_71 _let_59 (not _let_61)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 3)) (CONG _let_81 (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_60))) :args _let_44)) :args ((or _let_60 _let_72))) _let_80 :args (_let_60 true _let_72)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_63 _let_17 _let_61 (not _let_64)))) _let_83 _let_82 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING _let_68)) :args _let_67)) _let_66 :args (_let_64 false _let_65)) :args (_let_61 false _let_62 false _let_16 false _let_64)) :args (_let_59 false _let_60 false _let_61)) :args (_let_58 true _let_57)))) (let ((_let_86 (REFL :args (_let_56)))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 0)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_44)) :args ((or _let_18 _let_56))) _let_85 :args (_let_18 true _let_56)))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 2)) (CONG _let_81 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_44)) :args ((or _let_14 _let_72))) _let_80 :args (_let_14 true _let_72)))) (let ((_let_89 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_90 (not _let_89))) (let ((_let_91 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_92 (not _let_91))) (let ((_let_93 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_94 (not _let_93))) (let ((_let_95 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_96 (not _let_95))) (let ((_let_97 (or _let_96 _let_94 _let_19 _let_92 _let_90 _let_6))) (let ((_let_98 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y2)) (= Y1 Y2))))) (let ((_let_99 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y))))))))) (let ((_let_100 (and _let_99 _let_98))) (let ((_let_101 (= _let_36 _let_100))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_101)) :args ((or _let_37 _let_100 (not _let_101)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 1)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_44)) :args ((or _let_36 _let_40))) _let_46 :args (_let_36 true _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_28)) _let_27 :args (_let_101 false _let_26)) :args (_let_100 false _let_36 false _let_101)))) (let ((_let_103 (not _let_100))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_100 1)) :args ((or _let_98 _let_103))) _let_102 :args (_let_98 false _let_100)))) (let ((_let_105 (_let_98))) (let ((_let_106 (not (= (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) false)))) (let ((_let_107 (ASSUME :args _let_105))) (let ((_let_108 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_109 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_110 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_111 (not _let_110))) (let ((_let_112 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 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(let ((_let_120 (= _let_38 _let_119))) (let ((_let_121 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_120)) :args ((or _let_39 _let_119 (not _let_120)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 0)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_44)) :args ((or _let_38 _let_40))) _let_46 :args (_let_38 true _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_28)) _let_27 :args (_let_120 false _let_26)) :args (_let_119 false _let_38 false _let_120)))) (let ((_let_122 (not _let_119))) (let ((_let_123 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_119 1)) :args ((or _let_117 _let_122))) _let_121 :args (_let_117 false _let_119)))) (let ((_let_124 (_let_117))) (let ((_let_125 ((not (= (tptp.member X 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true _let_128)))) (let ((_let_135 (REFL :args (_let_127)))) (let ((_let_136 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_127 0)) (CONG _let_135 (MACRO_SR_PRED_INTRO :args ((= (not _let_96) _let_95))) :args _let_44)) :args ((or _let_95 _let_127))) _let_134 :args (_let_95 true _let_127)))) (let ((_let_137 (or _let_115 _let_113))) (let ((_let_138 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 Y)))))) (let ((_let_139 (not _let_137))) (let ((_let_140 (not _let_138))) (let ((_let_141 (or _let_63 _let_140))) (let ((_let_142 (_let_118))) (let ((_let_143 (_let_140))) (let ((_let_144 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_143)) :args _let_143)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_140) _let_138))) (REFL :args (_let_139)) :args _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS 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(MACRO_SR_PRED_INTRO :args ((= (not _let_115) _let_114))) :args _let_44)) :args ((or _let_114 _let_137))) _let_144 :args (_let_114 true _let_137)))) (let ((_let_148 (not _let_109))) (let ((_let_149 (or _let_94 _let_148))) (let ((_let_150 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 Y)))))) (let ((_let_151 (not _let_149))) (let ((_let_152 (not _let_150))) (let ((_let_153 (or _let_115 _let_152))) (let ((_let_154 (_let_99))) (let ((_let_155 (_let_152))) (let ((_let_156 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_155)) :args _let_155)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_152) _let_150))) (REFL :args (_let_151)) :args _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_153)) :args ((or _let_115 _let_152 (not _let_153)))) _let_147 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE 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(MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_149 0)) (CONG _let_157 (MACRO_SR_PRED_INTRO :args ((= (not _let_94) _let_93))) :args _let_44)) :args ((or _let_93 _let_149))) _let_156 :args (_let_93 true _let_149)))) (let ((_let_165 (not _let_7))) (let ((_let_166 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_167 (not _let_166))) (let ((_let_168 (or _let_167 _let_165))) (let ((_let_169 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 Y)))))) (let ((_let_170 (not _let_168))) (let ((_let_171 (not _let_169))) (let ((_let_172 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_173 (not _let_172))) (let ((_let_174 (or _let_173 _let_171))) (let ((_let_175 (_let_22))) (let ((_let_176 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_177 (not _let_176))) (let ((_let_178 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21))) (let ((_let_179 (not _let_178))) (let ((_let_180 (or _let_173 _let_179 _let_177))) (let ((_let_181 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)))))) (let ((_let_182 (not _let_180))) (let ((_let_183 (not _let_181))) (let ((_let_184 (tptp.apply _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_185 (= _let_184 _let_183))) (let ((_let_186 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_187 (not _let_186))) (let ((_let_188 (or _let_187 _let_15 _let_185))) (let ((_let_189 (not _let_184))) (let ((_let_190 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_191 (not _let_190))) (let ((_let_192 (or _let_187 _let_191 _let_189))) (let ((_let_193 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 Y)) (not (tptp.apply (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)))))) (let ((_let_194 (not _let_192))) (let ((_let_195 (not _let_193))) (let ((_let_196 (= _let_69 _let_195))) (let ((_let_197 (or _let_63 _let_15 _let_196))) (let ((_let_198 (_let_195))) (let ((_let_199 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE 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(REORDERING (CNF_OR_POS :args (_let_116)) :args ((or _let_63 _let_115 _let_113 _let_96 _let_111 _let_108 (not _let_116)))) _let_83 _let_147 _let_146 _let_136 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_127 1)) (CONG _let_135 (MACRO_SR_PRED_INTRO :args ((= (not _let_111) _let_110))) :args _let_44)) :args ((or _let_110 _let_127))) _let_134 :args (_let_110 true _let_127)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_126 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 QUANTIFIERS_INST_E_MATCHING _let_125)) :args _let_124)) _let_123 :args (_let_116 false _let_117)) :args (_let_108 false _let_62 false _let_114 false _let_112 false _let_95 false _let_110 false _let_116)) :args (_let_91 false _let_109 false _let_108)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_107 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false)) (not (= (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) false)) _let_106))) :args _let_105))) _let_104 :args (_let_97 false _let_98)) :args (_let_6 false _let_18 false _let_93 false _let_95 false _let_89 false _let_91 false _let_97)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_17 _let_15 _let_10 _let_19 _let_13 _let_11 (not _let_20)))) _let_82 _let_88 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_72 5)) _let_80 :args ((not _let_10) true _let_72)) _let_87 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 2)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_44)) :args ((or _let_12 _let_56))) _let_85 :args (_let_12 true _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) false)) _let_52 (not (= (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) false))))) :args _let_51)) _let_50 :args (_let_20 false _let_21)) :args (_let_11 false _let_16 false _let_14 true _let_10 false _let_18 false _let_12 false _let_20)) :args (false false _let_9 false _let_8 false _let_7 false _let_6 true _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 _let_2 (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))))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.61 )
% 0.21/0.61 % SZS output end Proof for SET710+4
% 0.21/0.61 % cvc5---1.0.5 exiting
% 0.21/0.62 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------