%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET744+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n023.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 14:40:09 EDT 2023

% Result   : Theorem 31.74s 31.97s
% Output   : Proof 31.74s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET744+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.12/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n023.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 13:54:41 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 31.74/31.97  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.aKhAM2UXNd/cvc5---1.0.5_3532.p...
% 31.74/31.97  ------- get file name : TPTP file name is SET744+4
% 31.74/31.97  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_3532.smt2...
% 31.74/31.97  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 31.74/31.97  --- Run --no-e-matching --full-saturate-quant at 5...
% 31.74/31.97  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 31.74/31.97  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 31.74/31.97  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 31.74/31.97  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 31.74/31.97  % SZS status Theorem for SET744+4
% 31.74/31.97  % SZS output start Proof for SET744+4
% 31.74/31.97  (
% 31.74/31.97  (let ((_let_1 (not (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.maps F A B) (tptp.maps G B C) (tptp.maps H C A) (tptp.one_to_one (tptp.compose_function G F A B C) A C) (tptp.one_to_one (tptp.compose_function H G B C A) B A)) (tptp.one_to_one H C A)))))) (let ((_let_2 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.one_to_one F A B) (and (tptp.injective F A B) (tptp.surjective F A B)))))) (let ((_let_3 (forall ((F $$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))))))))) (let ((_let_4 (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_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 ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80)))))) (let ((_let_8 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_92 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80))) (let ((_let_9 (not _let_8))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_92 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_11 (not _let_10))) (let ((_let_12 (or _let_11 _let_9))) (let ((_let_13 (not _let_7))) (let ((_let_14 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_13))) (let ((_let_17 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 E Y))))))))) (let ((_let_18 (not _let_16))) (let ((_let_19 (tptp.surjective SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_20 (= _let_19 _let_17))) (let ((_let_21 (not _let_17))) (let ((_let_22 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.surjective F A B) (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (forall ((E $$unsorted)) (or (not (tptp.member E A)) (not (tptp.apply F E Y))))))))))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (_let_22))) (let ((_let_25 ((tptp.surjective F A B)))) (let ((_let_26 (tptp.injective SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_27 (and _let_26 _let_19))) (let ((_let_28 (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (or (not (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X1 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X2 Y)) (= X1 X2))))) (let ((_let_29 (= _let_26 _let_28))) (let ((_let_30 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.injective F A B) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (or (not (tptp.member X1 A)) (not (tptp.member X2 A)) (not (tptp.member Y B)) (not (tptp.apply F X1 Y)) (not (tptp.apply F X2 Y)) (= X1 X2))))))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (_let_30))) (let ((_let_33 ((tptp.injective F A B)))) (let ((_let_34 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_35 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_36 (not _let_35))) (let ((_let_37 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_38 (not _let_37))) (let ((_let_39 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_40 (not _let_39))) (let ((_let_41 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_42 (not _let_41))) (let ((_let_43 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_44 _let_42 _let_40 _let_38 _let_36 _let_34))) (let ((_let_46 (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (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) E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_44 _let_47))) (let ((_let_49 (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)))))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_42 _let_50))) (let ((_let_52 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_53 (tptp.apply _let_52 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_54 (not _let_53))) (let ((_let_55 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_56 (not _let_55))) (let ((_let_57 (or _let_56 _let_54))) (let ((_let_58 (tptp.apply _let_52 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_59 (not _let_58))) (let ((_let_60 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_61 (not _let_60))) (let ((_let_62 (or _let_61 _let_59))) (let ((_let_63 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))))) (let ((_let_64 (not _let_63))) (let ((_let_65 (= _let_53 _let_64))) (let ((_let_66 (or _let_56 _let_44 _let_65))) (let ((_let_67 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)))))) (let ((_let_68 (not _let_67))) (let ((_let_69 (= _let_58 _let_68))) (let ((_let_70 (or _let_61 _let_42 _let_69))) (let ((_let_71 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_72 (not _let_71))) (let ((_let_73 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_74 (not _let_73))) (let ((_let_75 (or _let_74 (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26)) _let_72))) (let ((_let_76 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_77 (not _let_76))) (let ((_let_78 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_79 (not _let_78))) (let ((_let_80 (or _let_79 (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27)) _let_77))) (let ((_let_81 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))))) (let ((_let_82 (not _let_81))) (let ((_let_83 (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_5))) (let ((_let_84 (tptp.apply _let_83 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_85 (= _let_84 _let_82))) (let ((_let_86 (or _let_74 _let_40 _let_85))) (let ((_let_87 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_88 (not _let_87))) (let ((_let_89 (or _let_74 _let_44 _let_42 _let_72 _let_88 _let_34))) (let ((_let_90 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))))) (let ((_let_91 (not _let_90))) (let ((_let_92 (tptp.apply _let_83 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_93 (= _let_92 _let_91))) (let ((_let_94 (or _let_79 _let_40 _let_93))) (let ((_let_95 (or _let_42 _let_77 _let_36))) (let ((_let_96 (or _let_44 _let_72 _let_38))) (let ((_let_97 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_98 (not _let_84))) (let ((_let_99 (not _let_92))) (let ((_let_100 (or _let_79 _let_74 _let_40 _let_99 _let_98 _let_97))) (let ((_let_101 (or))) (let ((_let_102 (REFL :args (_let_45)))) (let ((_let_103 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) E Y))))))))) (let ((_let_104 (tptp.surjective _let_52 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_105 (= _let_104 _let_103))) (let ((_let_106 (and (tptp.injective _let_52 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) _let_104))) (let ((_let_107 (tptp.one_to_one _let_52 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_108 (= _let_107 _let_106))) (let ((_let_109 (_let_2))) (let ((_let_110 (ASSUME :args _let_109))) (let ((_let_111 ((tptp.one_to_one F A B)))) (let ((_let_112 (tptp.one_to_one SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_113 (tptp.one_to_one _let_83 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_114 (not _let_113))) (let ((_let_115 (not _let_107))) (let ((_let_116 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_117 (not _let_116))) (let ((_let_118 (or (not (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) _let_117 (not (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) _let_115 _let_114 _let_112))) (let ((_let_119 (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.maps F A B)) (not (tptp.maps G B C)) (not (tptp.maps H C A)) (not (tptp.one_to_one (tptp.compose_function G F A B C) A C)) (not (tptp.one_to_one (tptp.compose_function H G B C A) B A)) (tptp.one_to_one H C A))))) (let ((_let_120 (not _let_118))) (let ((_let_121 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_122 (not _let_119))) (let ((_let_123 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_121) :args (_let_122))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_122) _let_119))) (REFL :args (_let_120)) :args _let_101)) _let_121 :args (_let_120 true _let_119)))) (let ((_let_124 (REFL :args (_let_118)))) (let ((_let_125 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_105)) :args ((or (not _let_104) _let_103 (not _let_105)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_106 1)) :args ((or _let_104 (not _let_106)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_108)) :args ((or _let_115 _let_106 (not _let_108)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_118 3)) (CONG _let_124 (MACRO_SR_PRED_INTRO :args ((= (not _let_115) _let_107))) :args _let_101)) :args ((or _let_107 _let_118))) _let_123 :args (_let_107 true _let_118)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_110 :args (_let_52 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_111)) :args _let_109)) _let_110 :args (_let_108 false _let_2)) :args (_let_106 false _let_107 false _let_108)) :args (_let_104 false _let_106)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (_let_52 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_24)) _let_23 :args (_let_105 false _let_22)) :args (_let_103 false _let_104 false _let_105)))) (let ((_let_126 (_let_103))) (let ((_let_127 ((not (= (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) false))))) (let ((_let_128 (ASSUME :args _let_126))) (let ((_let_129 (_let_47))) (let ((_let_130 (_let_50))) (let ((_let_131 (REFL :args (_let_57)))) (let ((_let_132 (REFL :args (_let_62)))) (let 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_let_30)) :args (_let_26 false _let_28 false _let_29)) :args ((not _let_19) true _let_27 false _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_24)) _let_23 :args (_let_20 false _let_22)) :args (_let_21 true _let_19 false _let_20)) :args (_let_18 true _let_17)))) (let ((_let_167 (REFL :args (_let_16)))) (let ((_let_168 (not _let_12))) (let ((_let_169 (or _let_11 (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_89 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_92)) _let_9))) (let ((_let_170 (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_89 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80)))))) (let ((_let_171 (not _let_169))) (let ((_let_172 (not _let_170))) (let ((_let_173 (tptp.apply _let_83 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_89 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80))) (let ((_let_174 (= _let_173 _let_172))) (let ((_let_175 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_89 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_176 (not _let_175))) (let ((_let_177 (or _let_176 _let_15 _let_174))) (let ((_let_178 (not _let_173))) (let ((_let_179 (or _let_176 _let_178))) (let ((_let_180 (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80)))))) (let ((_let_181 (not _let_179))) (let ((_let_182 (not _let_180))) (let ((_let_183 (or _let_15 _let_182))) (let ((_let_184 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (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_5) E Y))))))))) (let ((_let_185 (= _let_154 _let_184))) (let ((_let_186 (_let_184))) (let ((_let_187 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_16 0)) (CONG _let_167 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_101)) :args ((or _let_14 _let_16))) _let_166 :args (_let_14 true _let_16)))) (let ((_let_188 (_let_182))) (let ((_let_189 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_188)) :args _let_188)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_182) _let_180))) (REFL :args (_let_181)) :args _let_101)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_183)) :args ((or _let_15 _let_182 (not _let_183)))) _let_187 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_186) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) :args _let_186)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_185)) :args ((or (not _let_154) _let_184 (not _let_185)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_155 1)) :args ((or _let_154 _let_158))) _let_157 :args (_let_154 false _let_155)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (_let_83 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_24)) _let_23 :args (_let_185 false _let_22)) :args (_let_184 false _let_154 false _let_185)) :args (_let_183 false _let_184)) :args (_let_182 false _let_14 false _let_183)) :args (_let_181 true _let_180)))) (let ((_let_190 (REFL :args (_let_179)))) (let ((_let_191 (_let_172))) (let ((_let_192 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_191)) :args _let_191)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_172) _let_170))) (REFL :args (_let_171)) :args _let_101)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_174)) :args ((or _let_178 _let_172 (not _let_174)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_179 1)) (CONG _let_190 (MACRO_SR_PRED_INTRO :args ((= (not _let_178) _let_173))) :args _let_101)) :args ((or _let_173 _let_179))) _let_189 :args (_let_173 true _let_179)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_177)) :args ((or _let_15 _let_176 _let_174 (not _let_177)))) _let_187 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_179 0)) (CONG _let_190 (MACRO_SR_PRED_INTRO :args ((= (not _let_176) _let_175))) :args _let_101)) :args ((or _let_175 _let_179))) _let_189 :args (_let_175 true _let_179)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_134 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_89 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80 QUANTIFIERS_INST_E_MATCHING _let_136)) :args _let_135)) _let_134 :args (_let_177 false _let_133)) :args (_let_174 false _let_14 false _let_175 false _let_177)) :args (_let_172 false _let_173 false _let_174)) :args (_let_171 true _let_170)))) (let ((_let_193 (REFL :args (_let_169)))) (let ((_let_194 (_let_7))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_194) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_92 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_194)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_12)) :args ((or _let_11 _let_9 _let_168))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_169 0)) (CONG _let_193 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_10))) :args _let_101)) :args ((or _let_10 _let_169))) _let_192 :args (_let_10 true _let_169)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_169 2)) (CONG _let_193 (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_8))) :args _let_101)) :args ((or _let_8 _let_169))) _let_192 :args (_let_8 true _let_169)) :args (_let_168 false _let_10 false _let_8)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_16 1)) (CONG _let_167 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_7))) :args _let_101)) :args ((or _let_7 _let_16))) _let_166 :args (_let_7 true _let_16)) :args (false true _let_12 false _let_7)) :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 $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) _let_6 (forall ((H $$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 (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))))) _let_4 _let_3 _let_2 (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 31.74/31.98  )
% 31.74/31.98  % SZS output end Proof for SET744+4
% 31.74/31.98  % cvc5---1.0.5 exiting
% 31.74/31.98  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------