TSTP Solution File: SEU259+2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU259+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.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 16:30:28 EDT 2023
% Result : Theorem 30.04s 30.27s
% Output : Proof 30.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU259+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 23 13:06:20 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.21/0.52 %----Proving TF0_NAR, FOF, or CNF
% 30.04/30.27 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.U6OuRWYBaK/cvc5---1.0.5_25569.p...
% 30.04/30.27 ------- get file name : TPTP file name is SEU259+2
% 30.04/30.27 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_25569.smt2...
% 30.04/30.27 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 30.04/30.27 --- Run --no-e-matching --full-saturate-quant at 5...
% 30.04/30.27 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 30.04/30.27 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 30.04/30.27 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 30.04/30.27 % SZS status Theorem for SEU259+2
% 30.04/30.27 % SZS output start Proof for SEU259+2
% 30.04/30.27 (
% 30.04/30.27 (let ((_let_1 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (tptp.one_to_one (tptp.function_inverse A))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.function_inverse B))) (=> (and (tptp.relation B) (tptp.function B)) (=> (and (tptp.one_to_one B) (tptp.in A (tptp.relation_rng B))) (and (= A (tptp.apply B (tptp.apply _let_1 A))) (= A (tptp.apply (tptp.relation_composition _let_1 B) A))))))))) (let ((_let_3 (forall ((A $$unsorted)) (let ((_let_1 (tptp.function_inverse A))) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (and (= (tptp.relation_rng A) (tptp.relation_dom _let_1)) (= (tptp.relation_dom A) (tptp.relation_rng _let_1))))))))) (let ((_let_4 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (forall ((B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (= (= B (tptp.function_inverse A)) (and (= (tptp.relation_dom B) (tptp.relation_rng A)) (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (and (tptp.in C (tptp.relation_rng A)) (= D (tptp.apply B C))))) (let ((_let_2 (and (tptp.in D (tptp.relation_dom A)) (= C (tptp.apply A D))))) (and (=> _let_1 _let_2) (=> _let_2 _let_1)))))))))))))) (let ((_let_5 (not (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.relation_isomorphism A B C) (tptp.relation_isomorphism B A (tptp.function_inverse C)))))))))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.relation_field C))) (=> (tptp.relation C) (=> (tptp.in (tptp.ordered_pair A B) C) (and (tptp.in A _let_1) (tptp.in B _let_1)))))))) (let ((_let_7 (tptp.relation tptp.empty_set))) (let ((_let_8 (tptp.empty tptp.empty_set))) (let ((_let_9 (tptp.relation_empty_yielding tptp.empty_set))) (let ((_let_10 (forall ((A $$unsorted)) (let ((_let_1 (tptp.function_inverse A))) (=> (and (tptp.relation A) (tptp.function A)) (and (tptp.relation _let_1) (tptp.function _let_1))))))) (let ((_let_11 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (tptp.relation_isomorphism A B C) (and (= (tptp.relation_dom C) (tptp.relation_field A)) (= (tptp.relation_rng C) (tptp.relation_field B)) (tptp.one_to_one C) (forall ((D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.relation_field A))) (= (tptp.in (tptp.ordered_pair D E) A) (and (tptp.in D _let_1) (tptp.in E _let_1) (tptp.in (tptp.ordered_pair (tptp.apply C D) (tptp.apply C E)) B))))))))))))))) (let ((_let_12 (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_13 (tptp.relation_field SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_14 (= _let_13 _let_12))) (let ((_let_15 (tptp.function_inverse SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_16 (tptp.apply _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_17 (tptp.in _let_16 _let_13))) (let ((_let_18 (tptp.in _let_16 _let_12))) (let ((_let_19 (forall ((D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.relation_field SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (= (tptp.in (tptp.ordered_pair D E) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) (and (tptp.in D _let_1) (tptp.in E _let_1) (tptp.in (tptp.ordered_pair (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 D) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 E)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))))))) (let ((_let_20 (tptp.one_to_one SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_21 (tptp.relation_rng SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_22 (tptp.relation_field SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_23 (= _let_22 _let_21))) (let ((_let_24 (and _let_14 _let_23 _let_20 _let_19))) (let ((_let_25 (tptp.relation_isomorphism SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_26 (= _let_25 _let_24))) (let ((_let_27 (tptp.function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_28 (not _let_27))) (let ((_let_29 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_30 (not _let_29))) (let ((_let_31 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_32 (not _let_31))) (let ((_let_33 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_32 _let_30 _let_28 _let_26))) (let ((_let_36 (forall ((A $$unsorted) (BOUND_VARIABLE_5309 $$unsorted) (BOUND_VARIABLE_5307 $$unsorted)) (or (not (tptp.relation A)) (not (tptp.relation BOUND_VARIABLE_5307)) (not (tptp.relation BOUND_VARIABLE_5309)) (not (tptp.function BOUND_VARIABLE_5309)) (= (tptp.relation_isomorphism A BOUND_VARIABLE_5307 BOUND_VARIABLE_5309) (and (= (tptp.relation_field A) (tptp.relation_dom BOUND_VARIABLE_5309)) (= (tptp.relation_field BOUND_VARIABLE_5307) (tptp.relation_rng BOUND_VARIABLE_5309)) (tptp.one_to_one BOUND_VARIABLE_5309) (forall ((D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.relation_field A))) (= (tptp.in (tptp.ordered_pair D E) A) (and (tptp.in D _let_1) (tptp.in E _let_1) (tptp.in (tptp.ordered_pair (tptp.apply BOUND_VARIABLE_5309 D) (tptp.apply BOUND_VARIABLE_5309 E)) BOUND_VARIABLE_5307))))))))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (_let_36))) (let ((_let_39 ((tptp.relation_isomorphism A BOUND_VARIABLE_5307 BOUND_VARIABLE_5309)))) (let ((_let_40 (tptp.relation_isomorphism SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_15))) (let ((_let_41 (not _let_25))) (let ((_let_42 (or _let_34 _let_32 _let_30 _let_28 _let_41 _let_40))) (let ((_let_43 (forall ((A $$unsorted) (BOUND_VARIABLE_6999 $$unsorted) (BOUND_VARIABLE_6997 $$unsorted)) (or (not (tptp.relation A)) (not (tptp.relation BOUND_VARIABLE_6997)) (not (tptp.relation BOUND_VARIABLE_6999)) (not (tptp.function BOUND_VARIABLE_6999)) (not (tptp.relation_isomorphism A BOUND_VARIABLE_6997 BOUND_VARIABLE_6999)) (tptp.relation_isomorphism BOUND_VARIABLE_6997 A (tptp.function_inverse BOUND_VARIABLE_6999)))))) (let ((_let_44 (not _let_42))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (or))) (let ((_let_47 (not _let_43))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_45) :args (_let_47))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_43))) (REFL :args (_let_44)) :args _let_46)) _let_45 :args (_let_44 true _let_43)))) (let ((_let_49 (REFL :args (_let_42)))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 3)) (CONG _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_46)) :args ((or _let_27 _let_42))) _let_48 :args (_let_27 true _let_42)))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 2)) (CONG _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_46)) :args ((or _let_29 _let_42))) _let_48 :args (_let_29 true _let_42)))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 1)) (CONG _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_46)) :args ((or _let_31 _let_42))) _let_48 :args (_let_31 true _let_42)))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 0)) (CONG _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_46)) :args ((or _let_33 _let_42))) _let_48 :args (_let_33 true _let_42)))) (let ((_let_54 (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_42 4)) (CONG _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_25))) :args _let_46)) :args ((or _let_25 _let_42))) _let_48 :args (_let_25 true _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_34 _let_32 _let_30 _let_28 _let_26 (not _let_35)))) _let_53 _let_52 _let_51 _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_39)) :args _let_38)) _let_37 :args (_let_35 false _let_36)) :args (_let_26 false _let_33 false _let_31 false _let_29 false _let_27 false _let_35)) :args (_let_24 false _let_25 false _let_26)))) (let ((_let_55 (not _let_24))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_24 0)) :args ((or _let_14 _let_55))) _let_54 :args (_let_14 false _let_24)))) (let ((_let_57 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_16))) (let ((_let_58 (tptp.apply _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_59 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_58))) (let ((_let_60 (tptp.in (tptp.ordered_pair _let_59 _let_57) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_61 (tptp.in _let_58 _let_13))) (let ((_let_62 (and _let_61 _let_17 _let_60))) (let ((_let_63 (not _let_17))) (let ((_let_64 (tptp.in (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_65 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 _let_59))) (let ((_let_66 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 _let_57))) (let ((_let_67 (tptp.in (tptp.ordered_pair _let_58 _let_16) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_68 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 _let_22))) (let ((_let_69 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 _let_22))) (let ((_let_70 (and _let_69 _let_68 _let_67))) (let ((_let_71 (= _let_64 _let_70))) (let ((_let_72 (= _let_67 _let_62))) (let ((_let_73 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 _let_21))) (let ((_let_74 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 _let_21))) (let ((_let_75 (tptp.relation_composition _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_76 (and _let_65 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 (tptp.apply _let_75 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))))) (let ((_let_77 (not _let_73))) (let ((_let_78 (not _let_20))) (let ((_let_79 (or _let_30 _let_28 _let_78 _let_77 _let_76))) (let ((_let_80 (and _let_66 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 (tptp.apply _let_75 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))))) (let ((_let_81 (not _let_74))) (let ((_let_82 (or _let_30 _let_28 _let_78 _let_81 _let_80))) (let ((_let_83 (forall ((D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.function_inverse SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_2 (tptp.relation_field SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (= (tptp.in (tptp.ordered_pair D E) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16) (and (tptp.in D _let_2) (tptp.in E _let_2) (tptp.in (tptp.ordered_pair (tptp.apply _let_1 D) (tptp.apply _let_1 E)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))))))) (let ((_let_84 (not _let_71))) (let ((_let_85 (tptp.one_to_one _let_15))) (let ((_let_86 (tptp.relation_rng _let_15))) (let ((_let_87 (= _let_13 _let_86))) (let ((_let_88 (tptp.relation_dom _let_15))) (let ((_let_89 (= _let_22 _let_88))) (let ((_let_90 (and _let_89 _let_87 _let_85 _let_83))) (let ((_let_91 (not _let_83))) (let ((_let_92 (or _let_30 _let_28 _let_78 _let_85))) (let ((_let_93 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (not (tptp.function A)) (not (tptp.one_to_one A)) (tptp.one_to_one (tptp.function_inverse A)))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_24 2)) :args ((or _let_20 _let_55))) _let_54 :args (_let_20 false _let_24)))) (let ((_let_96 (= _let_12 _let_86))) (let ((_let_97 (= _let_21 _let_88))) (let ((_let_98 (and _let_97 _let_96))) (let ((_let_99 (or _let_30 _let_28 _let_78 _let_98))) (let ((_let_100 (forall ((A $$unsorted)) (let ((_let_1 (tptp.function_inverse A))) (or (not (tptp.relation A)) (not (tptp.function A)) (not (tptp.one_to_one A)) (and (= (tptp.relation_rng A) (tptp.relation_dom _let_1)) (= (tptp.relation_dom A) (tptp.relation_rng _let_1)))))))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_99)) :args ((or _let_30 _let_28 _let_78 _let_98 (not _let_99)))) _let_51 _let_50 _let_95 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation A) false))))) :args (_let_100))) _let_101 :args (_let_99 false _let_100)) :args (_let_98 false _let_29 false _let_27 false _let_20 false _let_99)))) (let ((_let_103 (not _let_98))) (let ((_let_104 (not _let_14))) (let ((_let_105 (and _let_14 _let_96))) (let ((_let_106 (ASSUME :args (_let_96)))) (let ((_let_107 (ASSUME :args (_let_14)))) (let ((_let_108 (SYMM (SYMM _let_107)))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_24 1)) :args ((or _let_23 _let_55))) _let_54 :args (_let_23 false _let_24)))) (let ((_let_110 (and _let_23 _let_97))) (let ((_let_111 (ASSUME :args (_let_97)))) (let ((_let_112 (ASSUME :args (_let_23)))) (let ((_let_113 (SYMM _let_112))) (let ((_let_114 (= _let_40 _let_90))) (let ((_let_115 (not _let_90))) (let ((_let_116 (tptp.function _let_15))) (let ((_let_117 (not _let_116))) (let ((_let_118 (tptp.relation _let_15))) (let ((_let_119 (not _let_118))) (let ((_let_120 (or _let_32 _let_34 _let_119 _let_117 _let_114))) (let ((_let_121 (and _let_118 _let_116))) (let ((_let_122 (or _let_30 _let_28 _let_121))) (let ((_let_123 (forall ((A $$unsorted)) (let ((_let_1 (tptp.function_inverse A))) (or (not (tptp.relation A)) (not (tptp.function A)) (and (tptp.relation _let_1) (tptp.function _let_1))))))) (let ((_let_124 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_125 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_122)) :args ((or _let_30 _let_28 _let_121 (not _let_122)))) _let_51 _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_124 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.function_inverse A)))) :args (_let_123))) _let_124 :args (_let_122 false _let_123)) :args (_let_121 false _let_29 false _let_27 false _let_122)))) (let ((_let_126 (not _let_121))) (let ((_let_127 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_121 1)) :args ((or _let_116 _let_126))) _let_125 :args (_let_116 false _let_121)))) (let ((_let_128 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_121 0)) :args ((or _let_118 _let_126))) _let_125 :args (_let_118 false _let_121)))) (let ((_let_129 (_let_91))) (let ((_let_130 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_129)) :args _let_129)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_91) _let_83))) (REFL :args (_let_84)) :args _let_46)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_90)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_114)) :args ((or _let_40 _let_115 (not _let_114)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_42 5)) _let_48 :args ((not _let_40) true _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_120)) :args ((or _let_34 _let_32 _let_119 _let_117 _let_114 (not _let_120)))) _let_53 _let_52 _let_128 _let_127 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 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A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.function A))) (let ((_let_2 (tptp.relation A))) (=> (and _let_2 (tptp.empty A) _let_1) (and _let_2 _let_1 (tptp.one_to_one A)))))) (forall ((A $$unsorted)) (=> (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)) (tptp.ordinal A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (or (tptp.ordinal_subset A B) (tptp.ordinal_subset B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (= B (tptp.identity_relation A)) (forall ((C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair C D) B) (and (tptp.in C A) (= C D))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.subset A B) (tptp.subset B A)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (= C (tptp.relation_dom_restriction A B)) (forall ((D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.ordered_pair D E))) (= (tptp.in _let_1 C) (and (tptp.in D B) (tptp.in _let_1 A)))))))))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.relation_image A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in E (tptp.relation_dom A)) (tptp.in E B) (= D (tptp.apply A E)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (forall ((C $$unsorted)) (=> (tptp.relation C) (= (= C (tptp.relation_rng_restriction A B)) (forall ((D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.ordered_pair D E))) (= (tptp.in _let_1 C) (and (tptp.in E A) (tptp.in _let_1 B)))))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.antisymmetric A) (tptp.is_antisymmetric_in A (tptp.relation_field A))))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.relation_inverse_image A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.relation_dom A)) (tptp.in (tptp.apply A D) B)))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.relation_image A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in (tptp.ordered_pair E D) A) (tptp.in E B))))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.relation_inverse_image A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in (tptp.ordered_pair D E) A) (tptp.in E B))))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.connected A) (tptp.is_connected_in A (tptp.relation_field A))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.transitive A) (tptp.is_transitive_in A (tptp.relation_field A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (= D (tptp.unordered_triple A B C)) (forall ((E $$unsorted)) (= (tptp.in E D) (not (and (not (= E A)) (not (= E B)) (not (= E C)))))))) (forall ((A $$unsorted)) (= (tptp.succ A) (tptp.set_union2 A (tptp.singleton A)))) (forall ((A $$unsorted)) (= (tptp.relation A) (forall ((B $$unsorted)) (not (and (tptp.in B A) (forall ((C $$unsorted) (D $$unsorted)) (not (= B (tptp.ordered_pair C D))))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.is_reflexive_in A B) (forall ((C $$unsorted)) (=> (tptp.in C B) (tptp.in (tptp.ordered_pair C C) A))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (= B (tptp.set_meet A)))) (let ((_let_2 (= A tptp.empty_set))) (and (=> (not _let_2) (= _let_1 (forall ((C $$unsorted)) (= (tptp.in C B) (forall ((D $$unsorted)) (=> (tptp.in D A) (tptp.in C D))))))) (=> _let_2 (= _let_1 (= B tptp.empty_set))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.singleton A)) (forall ((C $$unsorted)) (= (tptp.in C B) (= C A))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.fiber A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (= D B)) (tptp.in (tptp.ordered_pair D B) A)))))))) (forall ((A $$unsorted)) (= (= A tptp.empty_set) (forall ((B $$unsorted)) (not (tptp.in B A))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.powerset A)) (forall ((C $$unsorted)) (= (tptp.in C B) (tptp.subset C A))))) (forall ((A $$unsorted)) (= (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (=> (tptp.in B A) (tptp.subset B A))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (= (= A B) (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ordered_pair C D))) (= (tptp.in _let_1 A) (tptp.in _let_1 B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.element B A))) (let ((_let_2 (tptp.empty A))) (and (=> (not _let_2) (= _let_1 (tptp.in B A))) (=> _let_2 (= _let_1 (tptp.empty B))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.unordered_pair A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (= D A) (= D B)))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.well_founded_relation A) (forall ((B $$unsorted)) (not (and (tptp.subset B (tptp.relation_field A)) (not (= B tptp.empty_set)) (forall ((C $$unsorted)) (not (and (tptp.in C B) (tptp.disjoint (tptp.fiber A C) B)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_union2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (tptp.in D A) (tptp.in D B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.cartesian_product2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted) (F $$unsorted)) (and (tptp.in E A) (tptp.in F B) (= D (tptp.ordered_pair E F)))))))) (forall ((A $$unsorted)) (= (tptp.epsilon_connected A) (forall ((B $$unsorted) (C $$unsorted)) (not (and (tptp.in B A) (tptp.in C A) (not (tptp.in B C)) (not (= B C)) (not (tptp.in C B))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (= (tptp.subset A B) (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ordered_pair C D))) (=> (tptp.in _let_1 A) (tptp.in _let_1 B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.is_well_founded_in A B) (forall ((C $$unsorted)) (not (and (tptp.subset C B) (not (= C tptp.empty_set)) (forall ((D $$unsorted)) (not (and (tptp.in D C) (tptp.disjoint (tptp.fiber A D) C))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_intersection2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (tptp.in D B)))))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (let ((_let_1 (= C (tptp.apply A B)))) (let ((_let_2 (tptp.in B (tptp.relation_dom A)))) (and (=> _let_2 (= _let_1 (tptp.in (tptp.ordered_pair B C) A))) (=> (not _let_2) (= _let_1 (= C tptp.empty_set))))))))) (forall ((A $$unsorted)) (= (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (= B (tptp.relation_dom A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (tptp.in (tptp.ordered_pair C D) A)))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.is_antisymmetric_in A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.in C B) (tptp.in D B) (tptp.in (tptp.ordered_pair C D) A) (tptp.in (tptp.ordered_pair D C) A)) (= C D))))))) (forall ((A $$unsorted)) (= (tptp.cast_to_subset A) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.union A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (and (tptp.in C D) (tptp.in D A))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.well_ordering A) (and (tptp.reflexive A) (tptp.transitive A) (tptp.antisymmetric A) (tptp.connected A) (tptp.well_founded_relation A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_difference A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (not (tptp.in D B))))))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted)) (= (= B (tptp.relation_rng A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (and (tptp.in D (tptp.relation_dom A)) (= C (tptp.apply A D)))))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (= B (tptp.relation_rng A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (tptp.in (tptp.ordered_pair D C) A)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A B) (tptp.set_difference A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.well_orders A B) (and (tptp.is_reflexive_in A B) (tptp.is_transitive_in A B) (tptp.is_antisymmetric_in A B) (tptp.is_connected_in A B) (tptp.is_well_founded_in A B)))))) (forall ((A $$unsorted)) (= (tptp.being_limit_ordinal A) (= A (tptp.union A)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.relation_field A) (tptp.set_union2 (tptp.relation_dom A) (tptp.relation_rng A))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.is_connected_in A B) (forall ((C $$unsorted) (D $$unsorted)) (not (and (tptp.in C B) (tptp.in D B) (not (= C D)) (not (tptp.in (tptp.ordered_pair C D) A)) (not (tptp.in (tptp.ordered_pair D C) A))))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.relation_restriction A B) (tptp.set_intersection2 A (tptp.cartesian_product2 B B)))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (= (= B (tptp.relation_inverse A)) (forall ((C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair C D) B) (tptp.in (tptp.ordered_pair D C) A)))))))) _let_11 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_intersection2 A B) tptp.empty_set))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (= (tptp.one_to_one A) (forall ((B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (=> (and (tptp.in B _let_1) (tptp.in C _let_1) (= (tptp.apply A B) (tptp.apply A C))) (= B C))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (forall ((C $$unsorted)) (=> (tptp.relation C) (= (= C (tptp.relation_composition A B)) (forall ((D $$unsorted) (E $$unsorted)) (= (tptp.in (tptp.ordered_pair D E) C) (exists ((F $$unsorted)) (and (tptp.in (tptp.ordered_pair D F) A) (tptp.in (tptp.ordered_pair F E) B)))))))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.is_transitive_in A B) (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.in C B) (tptp.in D B) (tptp.in E B) (tptp.in (tptp.ordered_pair C D) A) (tptp.in (tptp.ordered_pair D E) A)) (tptp.in (tptp.ordered_pair C E) A))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.powerset A))) (= (= C (tptp.complements_of_subsets A B)) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.powerset A)) (= (tptp.in D C) (tptp.in (tptp.subset_complement A D) B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.proper_subset A B) (and (tptp.subset A B) (not (= A B))))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (= (tptp.function_inverse A) (tptp.relation_inverse A))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.reflexive A) (tptp.is_reflexive_in A (tptp.relation_field A))))) true true true true true true true true true true _let_10 true (forall ((A $$unsorted)) (tptp.element (tptp.cast_to_subset A) (tptp.powerset A))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_restriction A B)))) true true true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (tptp.element B _let_1) (tptp.element (tptp.subset_complement A B) _let_1)))) true true (forall ((A $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_inverse A)))) true true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.relation_composition A B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (tptp.element B (tptp.powerset _let_1)) (tptp.element (tptp.union_of_subsets A B) _let_1)))) (forall ((A $$unsorted)) (tptp.relation (tptp.identity_relation A))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (tptp.element B (tptp.powerset _let_1)) (tptp.element (tptp.meet_of_subsets A B) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.subset_difference A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_dom_restriction A B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.powerset A)))) (=> (tptp.element B _let_1) (tptp.element (tptp.complements_of_subsets A B) _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.relation (tptp.relation_rng_restriction A B)))) true true (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition B A))) (=> (and (tptp.empty A) (tptp.relation B)) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_inverse A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (and _let_8 _let_7 _let_9) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_dom_restriction A B))) (=> (and (tptp.relation A) (tptp.relation_empty_yielding A)) (and (tptp.relation _let_1) (tptp.relation_empty_yielding _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition A B))) (=> (and (tptp.relation A) (tptp.function A) (tptp.relation B) (tptp.function B)) (and (tptp.relation _let_1) (tptp.function _let_1))))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.succ A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_intersection2 A B)))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_8 (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.ordered_pair A B)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.identity_relation A))) (and (tptp.relation _let_1) (tptp.function _let_1)))) (and _let_7 _let_9 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) _let_8 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_union2 A B)))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.singleton A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_inverse A))) (=> (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A)) (and (tptp.relation _let_1) (tptp.function _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.succ A))) (=> (tptp.ordinal A) (and (not (tptp.empty _let_1)) (tptp.epsilon_transitive _let_1) (tptp.epsilon_connected _let_1) (tptp.ordinal _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_difference A B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.unordered_pair A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 B A))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_dom_restriction A B))) (=> (and (tptp.relation A) (tptp.function A)) (and (tptp.relation _let_1) (tptp.function _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.union A))) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive _let_1) (tptp.epsilon_connected _let_1) (tptp.ordinal _let_1))))) (and _let_8 _let_7) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_rng_restriction A B))) (=> (and (tptp.relation B) (tptp.function B)) (and (tptp.relation _let_1) (tptp.function _let_1))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_dom A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_rng A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_rng A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition A B))) (=> (and (tptp.empty A) (tptp.relation B)) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A (tptp.subset_complement A B)) B))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.relation_inverse (tptp.relation_inverse A)) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.complements_of_subsets A (tptp.complements_of_subsets A B)) B))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.proper_subset A A))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.reflexive A) (forall ((B $$unsorted)) (=> (tptp.in B (tptp.relation_field A)) (tptp.in (tptp.ordered_pair B B) A)))))) (forall ((A $$unsorted)) (not (= (tptp.singleton A) tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (= (tptp.set_union2 (tptp.singleton A) B) B))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.disjoint (tptp.singleton A) B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.in A B)) (tptp.disjoint (tptp.singleton A) B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_dom (tptp.relation_rng_restriction A B)) (tptp.relation_dom B)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.transitive A) (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.in (tptp.ordered_pair B C) A) (tptp.in (tptp.ordered_pair C D) A)) (tptp.in (tptp.ordered_pair B D) A)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset (tptp.singleton A) B) (tptp.in A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.in C B) (tptp.in C A))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.antisymmetric A) (forall ((B $$unsorted) (C $$unsorted)) (=> (and (tptp.in (tptp.ordered_pair B C) A) (tptp.in (tptp.ordered_pair C B) A)) (= B C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (or (tptp.in C A) (tptp.subset A (tptp.set_difference B (tptp.singleton C)))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.connected A) (forall ((B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.relation_field A))) (not (and (tptp.in B _let_1) (tptp.in C _let_1) (not (= B C)) (not (tptp.in (tptp.ordered_pair B C) A)) (not (tptp.in (tptp.ordered_pair C B) A))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.singleton B))) (= (tptp.subset A _let_1) (or (= A tptp.empty_set) (= A _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D)) (and (tptp.in A C) (tptp.in B D)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))) (tptp.element A (tptp.powerset B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (tptp.in B (tptp.relation_dom (tptp.relation_dom_restriction C A))) (and (tptp.in B (tptp.relation_dom C)) (tptp.in B A))))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A) (tptp.empty A) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A) (tptp.function A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.union_of_subsets A B) (tptp.union B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.meet_of_subsets A B) (tptp.set_meet B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_difference A B C) (tptp.set_difference B C))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (= (tptp.ordinal_subset A B) (tptp.subset A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (tptp.ordinal_subset A A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.disjoint A B) (tptp.disjoint B A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D)) (and (tptp.in A C) (tptp.in B D)))) (forall ((A $$unsorted)) (tptp.in A (tptp.succ A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (= (tptp.unordered_pair A B) (tptp.unordered_pair C D)) (not (= A C)) (not (= A D))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_rng (tptp.relation_rng_restriction B C))) (and (tptp.in A B) (tptp.in A (tptp.relation_rng C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng (tptp.relation_rng_restriction A B)) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng_restriction A B) B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng (tptp.relation_rng_restriction A B)) (tptp.relation_rng B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (and (tptp.subset (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B C)) (tptp.subset (tptp.cartesian_product2 C A) (tptp.cartesian_product2 C B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_rng (tptp.relation_rng_restriction A B)) (tptp.set_intersection2 (tptp.relation_rng B) A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C D)) (tptp.subset (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B D)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_union2 A B) B))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.in A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.in C B) (tptp.subset D C)) (tptp.in D B))) (forall ((C $$unsorted)) (=> (tptp.in C B) (tptp.in (tptp.powerset C) B))) (forall ((C $$unsorted)) (not (and (tptp.subset C B) (not (tptp.are_equipotent C B)) (not (tptp.in C B)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.relation_dom_restriction (tptp.relation_rng_restriction A C) B) (tptp.relation_rng_restriction A (tptp.relation_dom_restriction C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_image C B)) (exists ((D $$unsorted)) (and (tptp.in D (tptp.relation_dom C)) (tptp.in (tptp.ordered_pair D A) C) (tptp.in D B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_image B A) (tptp.relation_rng B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (tptp.subset (tptp.relation_image B (tptp.relation_inverse_image B A)) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_image B A) (tptp.relation_image B (tptp.set_intersection2 (tptp.relation_dom B) A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.subset A (tptp.relation_dom B)) (tptp.subset A (tptp.relation_inverse_image B (tptp.relation_image B A)))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.relation_image A (tptp.relation_dom A)) (tptp.relation_rng A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (=> (tptp.subset A (tptp.relation_rng B)) (= (tptp.relation_image B (tptp.relation_inverse_image B A)) A)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_rng (tptp.relation_composition A B)) (tptp.relation_image B (tptp.relation_rng A))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_inverse_image C B)) (exists ((D $$unsorted)) (and (tptp.in D (tptp.relation_rng C)) (tptp.in (tptp.ordered_pair A D) C) (tptp.in D B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_inverse_image B A) (tptp.relation_dom B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_restriction C B)) (and (tptp.in A C) (tptp.in A (tptp.cartesian_product2 B B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (not (and (not (= A tptp.empty_set)) (tptp.subset A (tptp.relation_rng B)) (= (tptp.relation_inverse_image B A) tptp.empty_set))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (=> (tptp.subset A B) (tptp.subset (tptp.relation_inverse_image C A) (tptp.relation_inverse_image C B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_restriction B A) (tptp.relation_dom_restriction (tptp.relation_rng_restriction A B) A)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_intersection2 A B) A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_restriction B A) (tptp.relation_rng_restriction A (tptp.relation_dom_restriction B A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (=> (tptp.in A (tptp.relation_field (tptp.relation_restriction C B))) (and (tptp.in A (tptp.relation_field C)) (tptp.in A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset A C)) (tptp.subset A (tptp.set_intersection2 B C)))) (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset B C)) (tptp.subset A C))) (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (=> (tptp.in (tptp.ordered_pair A B) C) (and (tptp.in A (tptp.relation_dom C)) (tptp.in B (tptp.relation_rng C)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_field (tptp.relation_restriction B A)))) (=> (tptp.relation B) (and (tptp.subset _let_1 (tptp.relation_field B)) (tptp.subset _let_1 A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (tptp.in A (tptp.relation_dom (tptp.relation_composition C B))) (and (tptp.in A (tptp.relation_dom C)) (tptp.in (tptp.apply C A) (tptp.relation_dom B)))))))) (forall ((A $$unsorted)) (=> (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (=> (tptp.proper_subset A B) (tptp.in A B)))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (tptp.subset A (tptp.cartesian_product2 (tptp.relation_dom A) (tptp.relation_rng A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (tptp.subset (tptp.fiber (tptp.relation_restriction C A) B) (tptp.fiber C B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.relation_composition C B))) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in A (tptp.relation_dom _let_1)) (= (tptp.apply _let_1 A) (tptp.apply B (tptp.apply C A))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.reflexive B) (tptp.reflexive (tptp.relation_restriction B A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in A (tptp.relation_dom B)) (= (tptp.apply (tptp.relation_composition B C) A) (tptp.apply C (tptp.apply B A)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.ordinal B) (=> (tptp.in A B) (tptp.ordinal A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.connected B) (tptp.connected (tptp.relation_restriction B A))))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (not (and (not (tptp.in A B)) (not (= A B)) (not (tptp.in B A)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.transitive B) (tptp.transitive (tptp.relation_restriction B A))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (=> (tptp.subset A B) (and (tptp.subset (tptp.relation_dom A) (tptp.relation_dom B)) (tptp.subset (tptp.relation_rng A) (tptp.relation_rng B)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.antisymmetric B) (tptp.antisymmetric (tptp.relation_restriction B A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_intersection2 A C) (tptp.set_intersection2 B C)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_intersection2 A B) A))) (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (= (tptp.in C A) (tptp.in C B))) (= A B))) (forall ((A $$unsorted)) (tptp.subset tptp.empty_set A)) _let_6 (forall ((A $$unsorted)) (=> (forall ((B $$unsorted)) (=> (tptp.in B A) (and (tptp.ordinal B) (tptp.subset B A)))) (tptp.ordinal A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.well_founded_relation B) (tptp.well_founded_relation (tptp.relation_restriction B A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.ordinal B) (not (and (tptp.subset A B) (not (= A tptp.empty_set)) (forall ((C $$unsorted)) (=> (tptp.ordinal C) (not (and (tptp.in C A) (forall ((D $$unsorted)) (=> (tptp.ordinal D) (=> (tptp.in D A) (tptp.ordinal_subset C D)))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.well_ordering B) (tptp.well_ordering (tptp.relation_restriction B A))))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (= (tptp.in A B) (tptp.ordinal_subset (tptp.succ A) B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_difference A C) (tptp.set_difference B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (tptp.ordered_pair A B) (tptp.ordered_pair C D)) (and (= A C) (= B D)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (= (= B (tptp.identity_relation A)) (and (= (tptp.relation_dom B) A) (forall ((C $$unsorted)) (=> (tptp.in C A) (= (tptp.apply B C) C))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in B A) (= (tptp.apply (tptp.identity_relation A) B) B))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_difference A B) A)) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_inverse A))) (=> (tptp.relation A) (and (= (tptp.relation_rng A) (tptp.relation_dom _let_1)) (= (tptp.relation_dom A) (tptp.relation_rng _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset (tptp.singleton A) B) (tptp.in A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.subset (tptp.unordered_pair A B) C) (and (tptp.in A C) (tptp.in B C)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (and (tptp.well_ordering B) (tptp.subset A (tptp.relation_field B))) (= (tptp.relation_field (tptp.relation_restriction B A)) A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A (tptp.set_difference B A)) (tptp.set_union2 A B))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.singleton B))) (= (tptp.subset A _let_1) (or (= A tptp.empty_set) (= A _let_1))))) (forall ((A $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.in B C) (tptp.in C A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.disjoint A B))) (and (not (and (not _let_1) (forall ((C $$unsorted)) (not (and (tptp.in C A) (tptp.in C B)))))) (not (and (exists ((C $$unsorted)) (and (tptp.in C A) (tptp.in C B))) _let_1))))) (forall ((A $$unsorted)) (=> (tptp.subset A tptp.empty_set) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference (tptp.set_union2 A B) B) (tptp.set_difference A B))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (= (tptp.being_limit_ordinal A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (=> (tptp.in B A) (tptp.in (tptp.succ B) A))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.being_limit_ordinal A))) (=> (tptp.ordinal A) (and (not (and (not _let_1) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (not (= A (tptp.succ B))))))) (not (and (exists ((B $$unsorted)) (and (tptp.ordinal B) (= A (tptp.succ B)))) _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset A)) (= (tptp.disjoint B C) (tptp.subset B (tptp.subset_complement A C))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_dom (tptp.relation_composition A B)) (tptp.relation_dom A)))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng (tptp.relation_composition A B)) (tptp.relation_rng B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= B (tptp.set_union2 A (tptp.set_difference B A))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (=> (tptp.subset (tptp.relation_rng A) (tptp.relation_dom B)) (= (tptp.relation_dom (tptp.relation_composition A B)) (tptp.relation_dom A))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (not (and (not (= B tptp.empty_set)) (= (tptp.complements_of_subsets A B) tptp.empty_set))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (= (tptp.set_union2 (tptp.singleton A) B) B))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (=> (tptp.subset (tptp.relation_dom A) (tptp.relation_rng B)) (= (tptp.relation_rng (tptp.relation_composition B A)) (tptp.relation_rng A))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (=> (not (= B tptp.empty_set)) (= (tptp.subset_difference A (tptp.cast_to_subset A) (tptp.union_of_subsets A B)) (tptp.meet_of_subsets A (tptp.complements_of_subsets A B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (=> (not (= B tptp.empty_set)) (= (tptp.union_of_subsets A (tptp.complements_of_subsets A B)) (tptp.subset_difference A (tptp.cast_to_subset A) (tptp.meet_of_subsets A B)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference A (tptp.set_difference A B)) (tptp.set_intersection2 A B))) _let_5 (forall ((A $$unsorted)) (= (tptp.set_difference tptp.empty_set A) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.disjoint A B))) (and (not (and (not _let_1) (forall ((C $$unsorted)) (not (tptp.in C (tptp.set_intersection2 A B)))))) (not (and (exists ((C $$unsorted)) (tptp.in C (tptp.set_intersection2 A B))) _let_1))))) (forall ((A $$unsorted)) (=> (not (= A tptp.empty_set)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.element C A) (=> (not (tptp.in C B)) (tptp.in C (tptp.subset_complement A B))))))))) _let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset A)) (not (and (tptp.in B (tptp.subset_complement A C)) (tptp.in B C))))) _let_3 (forall ((A $$unsorted)) (=> (tptp.relation A) (=> (forall ((B $$unsorted) (C $$unsorted)) (not (tptp.in (tptp.ordered_pair B C) A))) (= A tptp.empty_set)))) _let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.well_founded_relation A) (tptp.is_well_founded_in A (tptp.relation_field A))))) (and (= (tptp.relation_dom tptp.empty_set) tptp.empty_set) (= (tptp.relation_rng tptp.empty_set) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.subset A B) (tptp.proper_subset B A)))) _let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.disjoint B C)) (tptp.disjoint A C))) (forall ((A $$unsorted)) (=> (tptp.relation A) (=> (or (= (tptp.relation_dom A) tptp.empty_set) (= (tptp.relation_rng A) tptp.empty_set)) (= A tptp.empty_set)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (= (tptp.relation_dom A) tptp.empty_set) (= (tptp.relation_rng A) tptp.empty_set)))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A (tptp.singleton B)) A) (not (tptp.in B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (= B (tptp.relation_dom_restriction C A)) (and (= (tptp.relation_dom B) (tptp.set_intersection2 (tptp.relation_dom C) A)) (forall ((D $$unsorted)) (=> (tptp.in D (tptp.relation_dom B)) (= (tptp.apply B D) (tptp.apply C D)))))))))) (forall ((A $$unsorted)) (= (tptp.unordered_pair A A) (tptp.singleton A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset (tptp.singleton A) (tptp.singleton B)) (= A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.relation_dom_restriction C A))) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in B (tptp.relation_dom _let_1)) (= (tptp.apply _let_1 B) (tptp.apply C B)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.identity_relation A))) (and (= (tptp.relation_dom _let_1) A) (= (tptp.relation_rng _let_1) A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in B A) (= (tptp.apply (tptp.relation_dom_restriction C A) B) (tptp.apply C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ordered_pair A B))) (=> (tptp.relation D) (= (tptp.in _let_1 (tptp.relation_composition (tptp.identity_relation C) D)) (and (tptp.in A C) (tptp.in _let_1 D)))))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (forall ((C $$unsorted)) (not (and (tptp.in C B) (forall ((D $$unsorted)) (not (and (tptp.in D B) (tptp.in D C)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A (tptp.set_union2 A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_difference A B) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_dom (tptp.relation_dom_restriction C B))) (and (tptp.in A B) (tptp.in A (tptp.relation_dom C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_dom_restriction B A) B))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (tptp.in (tptp.ordered_pair A B) C) (and (tptp.in A (tptp.relation_dom C)) (= B (tptp.apply C A)))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.well_orders A (tptp.relation_field A)) (tptp.well_ordering A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C B)) (tptp.subset (tptp.set_union2 A C) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_dom (tptp.relation_dom_restriction B A)) (tptp.set_intersection2 (tptp.relation_dom B) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_dom_restriction B A) (tptp.relation_composition (tptp.identity_relation A) B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng (tptp.relation_dom_restriction B A)) (tptp.relation_rng B)))) (forall ((A $$unsorted)) (= (tptp.union (tptp.powerset A)) A)) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.in A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.in C B) (tptp.subset D C)) (tptp.in D B))) (forall ((C $$unsorted)) (not (and (tptp.in C B) (forall ((D $$unsorted)) (not (and (tptp.in D B) (forall ((E $$unsorted)) (=> (tptp.subset E C) (tptp.in E D))))))))) (forall ((C $$unsorted)) (not (and (tptp.subset C B) (not (tptp.are_equipotent C B)) (not (tptp.in C B)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= B C))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 30.04/30.28 )
% 30.04/30.28 % SZS output end Proof for SEU259+2
% 30.04/30.28 % cvc5---1.0.5 exiting
% 30.04/30.28 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------