TSTP Solution File: SET735+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET735+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n011.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 14:40:07 EDT 2023
% Result : Theorem 61.97s 62.70s
% Output : Proof 61.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET735+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.12/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n011.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 14:10:09 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.51 %----Proving TF0_NAR, FOF, or CNF
% 61.97/62.70 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.gxAfNJ7Rp4/cvc5---1.0.5_9345.p...
% 61.97/62.70 ------- get file name : TPTP file name is SET735+4
% 61.97/62.70 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_9345.smt2...
% 61.97/62.70 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 61.97/62.70 --- Run --no-e-matching --full-saturate-quant at 5...
% 61.97/62.70 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 61.97/62.70 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 61.97/62.70 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 61.97/62.70 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 61.97/62.70 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 61.97/62.70 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 61.97/62.70 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 61.97/62.70 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 61.97/62.70 --- Run --relevant-triggers --full-saturate-quant at 5...
% 61.97/62.70 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 61.97/62.70 % SZS status Theorem for SET735+4
% 61.97/62.70 % SZS output start Proof for SET735+4
% 61.97/62.70 (
% 61.97/62.70 (let ((_let_1 (not (forall ((F1 $$unsorted) (F2 $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (and (tptp.maps F1 A B) (tptp.maps F2 A B) (tptp.maps G B A) (tptp.identity (tptp.compose_function G F1 A B A) A) (tptp.identity (tptp.compose_function G F2 A B A) A) (tptp.equal_set (tptp.image3 F1 A B) (tptp.image3 F2 A B))) (tptp.equal_maps F1 F2 A B)))))) (let ((_let_2 (forall ((F $$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)))))))) (let ((_let_3 (forall ((F $$unsorted) (A $$unsorted)) (= (tptp.identity F A) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.apply F X X))))))) (let ((_let_4 (forall ((F $$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_5 (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_6 (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_7 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_9 (io_tptp.apply_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70))) (let ((_let_10 (io_tptp.apply_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_122 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70))) (let ((_let_11 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_122))) (let ((_let_12 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_59 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70))) (let ((_let_13 (not _let_9))) (let ((_let_14 (io_tptp.apply_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_59))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_59 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19 _let_17 _let_15 _let_13 _let_12))) (let ((_let_23 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24)) (not (io_tptp.apply_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 X Y1)) (not (io_tptp.apply_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 X Y2)) (= Y1 Y2))))) (let ((_let_24 (and (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24)) (not (io_tptp.apply_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 X Y))))))) _let_23))) (let ((_let_25 (io_tptp.maps_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_26 (= _let_25 _let_24))) (let ((_let_27 (forall ((b_F it_57_$$unsorted) (A $$unsorted) (B $$unsorted)) (= (io_tptp.maps_2 b_F A B) (and (forall ((X $$unsorted)) (or (not (tptp.member X A)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (io_tptp.apply_3 b_F X Y))))))) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y1 B)) (not (tptp.member Y2 B)) (not (io_tptp.apply_3 b_F X Y1)) (not (io_tptp.apply_3 b_F X Y2)) (= Y1 Y2)))))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_6)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (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_27))))))) (let ((_let_29 (_let_27))) (let ((_let_30 (io_tptp.equal_maps_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_31 (io_tptp.image3_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_32 (io_tptp.image3_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_33 (tptp.equal_set _let_32 _let_31))) (let ((_let_34 (not _let_33))) (let ((_let_35 (io_tptp.compose_function_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_36 (io_tptp.identity_7 _let_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_37 (not _let_36))) (let ((_let_38 (io_tptp.compose_function_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_39 (io_tptp.identity_7 _let_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_40 (not _let_39))) (let ((_let_41 (not _let_25))) (let ((_let_42 (io_tptp.maps_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_43 (not _let_42))) (let ((_let_44 (io_tptp.maps_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_43 _let_41 _let_40 _let_37 _let_34 _let_30))) (let ((_let_47 (forall ((b_F1 it_57_$$unsorted) (b_F2 it_57_$$unsorted) (b_G it_57_$$unsorted) (A $$unsorted) (B $$unsorted)) (or (not (io_tptp.maps_2 b_F1 A B)) (not (io_tptp.maps_2 b_F2 A B)) (not (io_tptp.maps_2 b_G B A)) (not (io_tptp.identity_7 (io_tptp.compose_function_5 b_G b_F1 A B A) A)) (not (io_tptp.identity_7 (io_tptp.compose_function_5 b_G b_F2 A B A) A)) (not (tptp.equal_set (io_tptp.image3_14 b_F1 A B) (io_tptp.image3_14 b_F2 A B))) (io_tptp.equal_maps_6 b_F1 b_F2 A B))))) (let ((_let_48 (not _let_46))) (let ((_let_49 (not _let_47))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((F1 $$unsorted) (F2 $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (or (not (tptp.maps F1 A B)) (not (tptp.maps F2 A B)) (not (tptp.maps G B A)) (not (tptp.identity (tptp.compose_function G F1 A B A) A)) (not (tptp.identity (tptp.compose_function G F2 A B A) A)) (not (tptp.equal_set (tptp.image3 F1 A B) (tptp.image3 F2 A B))) (tptp.equal_maps F1 F2 A B)))) _let_49))))))) (let ((_let_51 (or))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_50) :args (_let_49))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_47))) (REFL :args (_let_48)) :args _let_51)) _let_50 :args (_let_48 true _let_47)))) (let ((_let_53 (REFL :args (_let_46)))) (let ((_let_54 (_let_23))) (let ((_let_55 (io_tptp.apply_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_59))) (let ((_let_56 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83))) (let ((_let_57 (not _let_55))) (let ((_let_58 (io_tptp.apply_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_59 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83))) (let ((_let_59 (not _let_58))) (let ((_let_60 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_61 (not _let_60))) (let ((_let_62 (or _let_61 _let_59 _let_57))) (let ((_let_63 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25)) (not (io_tptp.apply_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_59 Y)) (not (io_tptp.apply_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_59)))))) (let ((_let_64 (not _let_62))) (let ((_let_65 (not _let_63))) (let ((_let_66 (io_tptp.apply_3 _let_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_59 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_59))) (let ((_let_67 (= _let_66 _let_65))) (let ((_let_68 (or _let_19 _let_19 _let_67))) (let ((_let_69 (forall ((b_G it_57_$$unsorted) (b_F it_57_$$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Z C)) (= (io_tptp.apply_3 (io_tptp.compose_function_5 b_G b_F A B C) X Z) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (io_tptp.apply_3 b_F X Y)) (not (io_tptp.apply_3 b_G Y Z)))))))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((G $$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 $$unsorted)) (or (not (tptp.member Y B)) (not (tptp.apply F X Y)) (not (tptp.apply G Y Z)))))))) _let_69))))))) (let ((_let_71 (_let_69))) (let ((_let_72 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61))) (let ((_let_73 (io_tptp.apply_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_59 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61))) (let ((_let_74 (not _let_73))) (let ((_let_75 (io_tptp.apply_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_59 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60))) (let ((_let_76 (not _let_75))) (let ((_let_77 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_78 (not _let_77))) (let ((_let_79 (or _let_19 _let_78 _let_21 _let_76 _let_74 _let_72))) (let ((_let_80 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25)) (not (io_tptp.apply_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 X Y1)) (not (io_tptp.apply_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 X Y2)) (= Y1 Y2))))) (let ((_let_81 (not _let_79))) (let ((_let_82 (= _let_30 _let_80))) (let ((_let_83 (not _let_80))) (let ((_let_84 (forall ((b_F it_57_$$unsorted) (b_G it_57_$$unsorted) (A $$unsorted) (B $$unsorted)) (= (io_tptp.equal_maps_6 b_F b_G A B) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y1 B)) (not (tptp.member Y2 B)) (not (io_tptp.apply_3 b_F X Y1)) (not (io_tptp.apply_3 b_G X Y2)) (= Y1 Y2))))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((F $$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_84))))))) (let ((_let_86 (_let_83))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_86)) :args _let_86)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_80))) (REFL :args (_let_81)) :args _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_82)) :args ((or _let_30 _let_83 (not _let_82)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_46 6)) _let_52 :args ((not _let_30) true _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((io_tptp.equal_maps_6 b_F b_G A B)))) :args (_let_84))) _let_85 :args (_let_82 false _let_84)) :args (_let_83 true _let_30 false _let_82)) :args (_let_81 true _let_80)))) (let ((_let_88 (REFL :args (_let_79)))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_79 0)) (CONG _let_88 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_51)) :args ((or _let_18 _let_79))) _let_87 :args (_let_18 true _let_79)))) (let ((_let_90 (or _let_19 _let_66))) (let ((_let_91 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24)) (io_tptp.apply_3 (io_tptp.compose_function_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24) X X))))) (let ((_let_92 (= _let_36 _let_91))) (let ((_let_93 (forall ((b_F it_57_$$unsorted) (A $$unsorted)) (= (io_tptp.identity_7 b_F A) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (io_tptp.apply_3 b_F X X))))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((F $$unsorted) (A $$unsorted)) (= (tptp.identity F A) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.apply F X X))))) _let_93))))))) (let ((_let_95 (_let_93))) (let ((_let_96 ((io_tptp.identity_7 b_F A)))) (let ((_let_97 (_let_91))) (let ((_let_98 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_59 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_99 (_let_65))) (let ((_let_100 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_99)) :args _let_99)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_63))) (REFL :args (_let_64)) :args _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_67)) :args ((or _let_65 (not _let_66) (not 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true _let_79)))) (let ((_let_110 (and _let_55 _let_56))) (let ((_let_111 (_let_55 _let_56))) (let ((_let_112 (ASSUME :args (_let_55)))) (let ((_let_113 (APPLY_UF io_tptp.apply_3))) (let ((_let_114 (ASSUME :args (_let_56)))) (let ((_let_115 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23)))) (let ((_let_116 (io_tptp.apply_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_59 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61))) (let ((_let_117 (io_tptp.apply_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105))) (let ((_let_118 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105))) (let ((_let_119 (not _let_12))) (let ((_let_120 (not _let_116))) (let ((_let_121 (or _let_19 _let_78 _let_21 _let_76 _let_120 _let_72))) (let ((_let_122 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24)) (not (tptp.member Y1 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_let_141 _let_192 _let_190 _let_11 (not _let_207)))) _let_109 _let_177 _let_183 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_193 0)) (CONG _let_206 (MACRO_SR_PRED_INTRO :args ((= (not _let_192) _let_191))) :args _let_51)) :args ((or _let_191 _let_193))) _let_205 :args (_let_191 true _let_193)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_193 1)) (CONG _let_206 (MACRO_SR_PRED_INTRO :args ((= (not _let_190) _let_189))) :args _let_51)) :args ((or _let_189 _let_193))) _let_205 :args (_let_189 true _let_193)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_130 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_122 QUANTIFIERS_INST_CBQI_PROP)) :args _let_129)) _let_128 :args (_let_207 false _let_122)) :args (_let_11 false _let_20 false _let_16 false _let_140 false _let_191 false _let_189 false _let_207)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG 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(MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_182)) :args ((or _let_21 _let_17 _let_141 _let_133 _let_131 _let_118 (not _let_182)))) _let_109 _let_177 _let_183 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_134 0)) (CONG _let_180 (MACRO_SR_PRED_INTRO :args ((= (not _let_133) _let_132))) :args _let_51)) :args ((or _let_132 _let_134))) _let_179 :args (_let_132 true _let_134)) _let_181 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_130 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105 QUANTIFIERS_INST_CBQI_PROP)) :args _let_129)) _let_128 :args (_let_182 false _let_122)) :args (_let_118 false _let_20 false _let_16 false _let_140 false _let_132 false _let_117 false _let_182)) _let_181 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_121)) :args ((or _let_19 _let_78 _let_21 _let_76 _let_72 _let_120 (not _let_121)))) _let_89 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_79 1)) (CONG _let_88 (MACRO_SR_PRED_INTRO :args ((= (not _let_78) _let_77))) :args _let_51)) :args ((or _let_77 _let_79))) _let_87 :args (_let_77 true _let_79)) _let_109 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_79 3)) (CONG _let_88 (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_75))) :args _let_51)) :args ((or _let_75 _let_79))) _let_87 :args (_let_75 true _let_79)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_79 5)) _let_87 :args ((not _let_72) true _let_79)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_130 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_59 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_129)) _let_128 :args (_let_121 false _let_122)) :args (_let_120 false _let_18 false _let_77 false _let_20 false _let_75 true _let_72 false _let_121)) :args (_let_119 false _let_118 false _let_117 true _let_116)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_110)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_112 _let_114) (SCOPE (TRUE_ELIM (TRANS (CONG _let_115 (SYMM (SYMM _let_114)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_59)) :args _let_113) (TRUE_INTRO _let_112))) :args _let_111)) :args _let_111)) :args (true _let_110)) :args ((or _let_57 _let_14 (not _let_56)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_19 _let_21 _let_74 _let_61 _let_59 _let_56 (not _let_102)))) _let_89 _let_109 _let_108 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_62 0)) (CONG _let_101 (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_60))) :args _let_51)) :args ((or _let_60 _let_62))) _let_100 :args (_let_60 true _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_62 1)) (CONG _let_101 (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_58))) :args _let_51)) :args ((or _let_58 _let_62))) _let_100 :args (_let_58 true _let_62)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_107) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_59 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 QUANTIFIERS_INST_CBQI_PROP)) :args _let_107)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_104 1)) :args ((or _let_103 (not _let_104)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_105)) :args ((or _let_43 _let_104 (not _let_105)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 1)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_42))) :args _let_51)) :args ((or _let_42 _let_46))) _let_52 :args (_let_42 true _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_106)) :args _let_29)) _let_28 :args (_let_105 false _let_27)) :args (_let_104 false _let_42 false _let_105)) :args (_let_103 false _let_104)) :args (_let_102 false _let_103)) :args (_let_56 false _let_18 false _let_20 false _let_73 false _let_60 false _let_58 false _let_102)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_62 2)) (CONG _let_101 (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_55))) :args _let_51)) :args ((or _let_55 _let_62))) _let_100 :args (_let_55 true _let_62)) :args (_let_14 false _let_56 false _let_55)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_54) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_59 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 QUANTIFIERS_INST_CBQI_PROP)) :args _let_54)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_24 1)) :args ((or _let_23 (not _let_24)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_26)) :args ((or _let_41 _let_24 (not _let_26)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 2)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_25))) :args _let_51)) :args ((or _let_25 _let_46))) _let_52 :args (_let_25 true _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 QUANTIFIERS_INST_CBQI_PROP)) :args _let_29)) _let_28 :args (_let_26 false _let_27)) :args (_let_24 false _let_25 false _let_26)) :args (_let_23 false _let_24)) :args (_let_22 false _let_23)) :args (_let_13 false _let_18 false _let_20 false _let_16 true _let_12 false _let_14 false _let_22)) :args (false false _let_11 false _let_10 true _let_9)) :args (_let_8 _let_7 (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 $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) _let_6 (forall ((H $$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_5 _let_4 _let_3 (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 $$unsorted)) (and (tptp.member X A) (tptp.apply F X Y))))) _let_2 (forall ((F $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 61.97/62.71 )
% 61.97/62.71 % SZS output end Proof for SET735+4
% 61.97/62.71 % cvc5---1.0.5 exiting
% 61.97/62.71 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------