TSTP Solution File: SET750+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET750+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 1.00s 1.22s
% Output : Proof 1.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SET750+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.10/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n007.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 13:10:56 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 1.00/1.22 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.qsWrBfjTrh/cvc5---1.0.5_16548.p...
% 1.00/1.22 ------- get file name : TPTP file name is SET750+4
% 1.00/1.22 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_16548.smt2...
% 1.00/1.22 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.00/1.22 % SZS status Theorem for SET750+4
% 1.00/1.22 % SZS output start Proof for SET750+4
% 1.00/1.22 (
% 1.00/1.22 (let ((_let_1 (not (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (R $$unsorted) (S $$unsorted)) (=> (and (tptp.maps F A B) (tptp.one_to_one F A B)) (= (tptp.isomorphism F A R B S) (and (tptp.increasing F A R B S) (tptp.increasing (tptp.inverse_function F A B) B S A R)))))))) (let ((_let_2 (forall ((F $$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 ((_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 $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member Y1 B) (tptp.member X2 A) (tptp.member Y2 B) (tptp.apply R X1 X2) (tptp.apply F X1 Y1) (tptp.apply F X2 Y2)) (tptp.apply S Y1 Y2))))))) (let ((_let_4 (forall ((F $$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)))))) (let ((_let_5 (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 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_6 Y1 Y2))))) (let ((_let_6 (tptp.increasing SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_7 (= _let_6 _let_5))) (let ((_let_8 (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_9 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_10 (_let_8))) (let ((_let_11 ((tptp.increasing F A R B S)))) (let ((_let_12 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_9 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_11)) :args _let_10)) _let_9 :args (_let_7 false _let_8)))) (let ((_let_13 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35))) (let ((_let_14 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_34))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_25 _let_23 _let_21 _let_19 _let_17 _let_15 _let_13))) (let ((_let_29 (= _let_18 _let_13))) (let ((_let_30 (or _let_27 _let_25 _let_23 _let_21 _let_17 _let_15 _let_29))) (let ((_let_31 (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (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_5 X1 X2) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Y1 Y2)))))) (let ((_let_32 (tptp.one_to_one SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_33 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_34 (and _let_33 _let_32 _let_31))) (let ((_let_35 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_36 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_37 (= _let_36 _let_35))) (let ((_let_38 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_41 (not _let_40))) (let ((_let_42 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_43 (not _let_42))) (let ((_let_44 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_45 (not _let_44))) (let ((_let_46 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_47 (not _let_46))) (let ((_let_48 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_49 _let_47 _let_45 _let_43 _let_41 _let_39 _let_37))) (let ((_let_51 (tptp.isomorphism SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_52 (= _let_51 _let_34))) (let ((_let_53 (tptp.inverse_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_54 (tptp.apply _let_53 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_55 (= _let_38 _let_54))) (let ((_let_56 (tptp.increasing _let_53 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_57 (and _let_6 _let_56))) (let ((_let_58 (= _let_51 _let_57))) (let ((_let_59 (not _let_36))) (let ((_let_60 (or _let_49 _let_47 _let_45 _let_43 _let_59 _let_41 _let_39 _let_35))) (let ((_let_61 (not _let_34))) (let ((_let_62 (REORDERING (CNF_AND_POS :args (_let_34 2)) :args ((or _let_31 _let_61))))) (let ((_let_63 (or))) (let ((_let_64 (not _let_31))) (let ((_let_65 (_let_64))) (let ((_let_66 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_65)) :args _let_65)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_31))) (REFL :args ((not _let_50))) :args _let_63)))) (let ((_let_67 (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)) (or (not (tptp.member X1 A)) (not (tptp.member Y1 B)) (not (tptp.member X2 A)) (not (tptp.member Y2 B)) (not (tptp.apply F X1 Y1)) (not (tptp.apply F X2 Y2)) (= (tptp.apply R X1 X2) (tptp.apply S Y1 Y2))))))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.isomorphism F A R B S)))) :args (_let_67))) _let_68 :args (_let_52 false _let_67)))) (let ((_let_70 (not _let_52))) (let ((_let_71 (_let_52))) (let ((_let_72 (REORDERING (CNF_EQUIV_POS1 :args _let_71) :args ((or (not _let_51) _let_34 _let_70))))) (let ((_let_73 (REFL :args (_let_50)))) (let ((_let_74 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 2)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_63)) :args ((or _let_44 _let_50))))) (let ((_let_75 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 3)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_42))) :args _let_63)) :args ((or _let_42 _let_50))))) (let ((_let_76 (CNF_OR_NEG :args (_let_50 6)))) (let ((_let_77 (or _let_45 _let_43 _let_55))) (let ((_let_78 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply (tptp.inverse_function F A B) Y X)))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (_let_78))) (let ((_let_81 ((tptp.apply (tptp.inverse_function F A B) Y X)))) (let ((_let_82 (not _let_32))) (let ((_let_83 (not _let_33))) (let ((_let_84 (or _let_83 _let_82 _let_58))) (let ((_let_85 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (R $$unsorted) (S $$unsorted)) (or (not (tptp.maps F A B)) (not (tptp.one_to_one F A B)) (= (tptp.isomorphism F A R B S) (and (tptp.increasing F A R B S) (tptp.increasing (tptp.inverse_function F A B) B S A R))))))) (let ((_let_86 (not _let_84))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (not _let_85))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_87) :args (_let_88))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_88) _let_85))) (REFL :args (_let_86)) :args _let_63)) _let_87 :args (_let_86 true _let_85)))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_84 2)) _let_89 :args ((not _let_58) true _let_84)))) (let ((_let_91 (_let_58))) (let ((_let_92 (REORDERING (CNF_EQUIV_NEG1 :args _let_91) :args ((or _let_51 _let_57 _let_58))))) (let ((_let_93 (not _let_57))) (let ((_let_94 (tptp.apply _let_53 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_95 (= _let_40 _let_94))) (let ((_let_96 (or _let_49 _let_47 _let_95))) (let ((_let_97 (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.inverse_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (or (not (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 X1 X2)) (not (tptp.apply _let_1 X1 Y1)) (not (tptp.apply _let_1 X2 Y2)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y1 Y2)))))) (let ((_let_98 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_99 (tptp.apply _let_53 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_100 (not _let_99))) (let ((_let_101 (tptp.apply _let_53 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_102 (not _let_101))) (let ((_let_103 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_104 (not _let_103))) (let ((_let_105 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_106 (not _let_105))) (let ((_let_107 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_108 (not _let_107))) (let ((_let_109 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_110 (not _let_109))) (let ((_let_111 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_112 (not _let_111))) (let ((_let_113 (or _let_112 _let_110 _let_108 _let_106 _let_104 _let_102 _let_100 _let_98))) (let ((_let_114 (not _let_54))) (let ((_let_115 (not _let_35))) (let ((_let_116 (= _let_56 _let_97))) (let ((_let_117 (not _let_94))) (let ((_let_118 (or _let_47 _let_49 _let_43 _let_45 _let_115 _let_117 _let_114 _let_36))) (let ((_let_119 (not _let_97))) (let ((_let_120 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_9 :args (_let_53 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_11)) :args _let_10)) _let_9 :args (_let_116 false _let_8)))) (let ((_let_121 (not _let_116))) (let ((_let_122 (_let_116))) (let ((_let_123 (REORDERING (CNF_EQUIV_POS2 :args _let_122) :args ((or _let_56 _let_119 _let_121))))) (let ((_let_124 (_let_97))) (let ((_let_125 (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_124) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) false)) (not (= (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false)) (not (= (tptp.apply _let_53 X1 Y1) false))))) :args _let_124)))) (let ((_let_126 (REORDERING (CNF_OR_POS :args (_let_118)) :args ((or _let_49 _let_47 _let_45 _let_43 _let_36 _let_115 _let_117 _let_114 (not _let_118)))))) (let ((_let_127 (_let_37))) (let ((_let_128 (CNF_EQUIV_NEG2 :args _let_127))) (let ((_let_129 (REFL :args (_let_84)))) (let ((_let_130 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_84 0)) (CONG _let_129 (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_33))) :args _let_63)) 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_let_142) _let_5))) (REFL :args ((not _let_28))) :args _let_63)))) (let ((_let_145 (CNF_AND_NEG :args (_let_57)))) (let ((_let_146 (not _let_7))) (let ((_let_147 (_let_7))) (let ((_let_148 (REORDERING (CNF_EQUIV_POS2 :args _let_147) :args ((or _let_6 _let_142 _let_146))))) (let ((_let_149 (_let_119))) (let ((_let_150 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_149)) :args _let_149)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_119) _let_97))) (REFL :args ((not _let_113))) :args _let_63)))) (let ((_let_151 (REFL :args (_let_113)))) (let ((_let_152 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_113 2)) (CONG _let_151 (MACRO_SR_PRED_INTRO :args ((= (not _let_108) _let_107))) :args _let_63)) :args ((or _let_107 _let_113))))) (let ((_let_153 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_113 3)) (CONG _let_151 (MACRO_SR_PRED_INTRO :args ((= (not _let_106) _let_105))) :args _let_63)) :args ((or _let_105 _let_113))))) (let ((_let_154 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_155 (= _let_99 _let_154))) (let ((_let_156 (or _let_106 _let_108 _let_155))) (let ((_let_157 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_158 (= _let_101 _let_157))) (let ((_let_159 (or _let_110 _let_112 _let_158))) (let ((_let_160 (= _let_103 _let_98))) (let ((_let_161 (not _let_154))) (let ((_let_162 (not _let_157))) (let ((_let_163 (or _let_110 _let_112 _let_106 _let_108 _let_162 _let_161 _let_160))) (let ((_let_164 (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_79 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING _let_81)) :args _let_80))))) (let ((_let_165 (REORDERING (CNF_OR_POS :args (_let_156)) :args ((or _let_108 _let_106 _let_155 (not _let_156)))))) (let ((_let_166 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_113 0)) (CONG _let_151 (MACRO_SR_PRED_INTRO :args ((= (not _let_112) _let_111))) :args _let_63)) :args ((or _let_111 _let_113))))) (let ((_let_167 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_113 1)) (CONG _let_151 (MACRO_SR_PRED_INTRO :args ((= (not _let_110) _let_109))) :args _let_63)) :args ((or _let_109 _let_113))))) (let ((_let_168 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_113 4)) (CONG _let_151 (MACRO_SR_PRED_INTRO :args ((= (not _let_104) _let_103))) :args _let_63)) :args ((or _let_103 _let_113))))) (let ((_let_169 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_113 5)) (CONG _let_151 (MACRO_SR_PRED_INTRO :args ((= (not _let_102) _let_101))) :args _let_63)) :args ((or _let_101 _let_113))))) (let ((_let_170 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_113 6)) (CONG _let_151 (MACRO_SR_PRED_INTRO :args ((= (not _let_100) _let_99))) :args _let_63)) :args ((or _let_99 _let_113))))) (let ((_let_171 (CNF_OR_NEG :args (_let_113 7)))) (let ((_let_172 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_79 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING _let_81)) :args _let_80))) _let_79 :args (_let_159 false _let_78)))) (let ((_let_173 (REORDERING (CNF_OR_POS :args (_let_159)) :args ((or _let_112 _let_110 _let_158 (not _let_159)))))) (let ((_let_174 (REORDERING (CNF_EQUIV_POS1 :args (_let_158)) :args ((or _let_102 _let_157 (not _let_158)))))) (let ((_let_175 (REORDERING (CNF_EQUIV_POS1 :args (_let_155)) :args ((or _let_100 _let_154 (not _let_155)))))) (let ((_let_176 (REORDERING (CNF_EQUIV_POS1 :args (_let_160)) :args ((or _let_104 _let_98 (not _let_160)))))) (let ((_let_177 (REORDERING (CNF_OR_POS :args (_let_163)) :args ((or _let_112 _let_110 _let_108 _let_106 _let_162 _let_161 _let_160 (not _let_163)))))) (let ((_let_178 (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_135 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING _let_134)) :args _let_133))))) (let ((_let_179 (MACRO_RESOLUTION_TRUST _let_178 _let_62 _let_177 _let_72 _let_69 _let_176 _let_175 _let_174 _let_173 _let_172 _let_92 _let_90 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 (REORDERING (CNF_AND_POS :args (_let_57 1)) :args ((or _let_56 _let_93))) _let_150 (REORDERING (CNF_EQUIV_POS1 :args _let_122) :args ((or (not _let_56) _let_97 _let_121))) _let_120 _let_165 _let_164 _let_79 :args ((or _let_97 _let_108 _let_106) false _let_31 true _let_163 false _let_34 false _let_52 true _let_160 false _let_154 false _let_157 false _let_158 false _let_159 false _let_51 true _let_58 true _let_98 false _let_99 false _let_101 false _let_103 false _let_109 false _let_111 true _let_57 true _let_113 true _let_56 false _let_116 false _let_155 false _let_156 false _let_78)))) (let ((_let_180 (not _let_6))) (let ((_let_181 (_let_5))) (let ((_let_182 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_49 _let_47 _let_45 _let_43 _let_41 _let_39 _let_35 _let_59 (not _let_60)))) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_181) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false)) (not (= (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) false)) (not (= (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false)) (not (= (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) false))))) :args _let_181)) (REORDERING (CNF_EQUIV_NEG1 :args _let_127) :args ((or _let_36 _let_35 _let_37))) (REORDERING 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(SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING _let_81)) :args _let_80)) _let_79 :args (_let_96 false _let_78)) :args ((or _let_49 _let_47 _let_45 _let_43 _let_41 _let_115 _let_114) false _let_105 false _let_107 true _let_113 true _let_97 false _let_94 false _let_95 false _let_96)) (REORDERING (CNF_AND_POS :args (_let_57 0)) :args ((or _let_6 _let_93))) (REORDERING (CNF_EQUIV_POS1 :args (_let_55)) :args ((or _let_39 _let_54 (not _let_55)))) _let_92 _let_90 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_45 _let_43 _let_55 (not _let_77)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 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(_let_28 false _let_30)) :args (_let_5 false _let_28)) _let_12 :args (false true _let_6 false _let_5 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))))) (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))))))) (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 $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))))) (forall ((G $$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 $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))) (forall ((F $$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 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply G Y X)))))) _let_4 (forall ((F $$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 $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y)))))) _let_3 (forall ((F $$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_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.00/1.22 )
% 1.00/1.22 % SZS output end Proof for SET750+4
% 1.00/1.22 % cvc5---1.0.5 exiting
% 1.00/1.23 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------