%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU156+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n001.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 16:29:38 EDT 2023

% Result   : Theorem 0.18s 0.55s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU156+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : do_cvc5 %s %d
% 0.12/0.33  % Computer : n001.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Wed Aug 23 16:35:39 EDT 2023
% 0.12/0.34  % CPUTime    : 
% 0.18/0.46  %----Proving TF0_NAR, FOF, or CNF
% 0.18/0.55  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.sbMcIYsMY5/cvc5---1.0.5_9575.p...
% 0.18/0.55  ------- get file name : TPTP file name is SEU156+2
% 0.18/0.55  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_9575.smt2...
% 0.18/0.55  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.18/0.55  % SZS status Theorem for SEU156+2
% 0.18/0.55  % SZS output start Proof for SEU156+2
% 0.18/0.55  (
% 0.18/0.55  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= A B))))) (let ((_let_2 (forall ((A $$unsorted)) (= (tptp.unordered_pair A A) (tptp.singleton A))))) (let ((_let_3 (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (tptp.ordered_pair A B) (tptp.ordered_pair C D)) (and (= A C) (= B D))))))) (let ((_let_4 (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))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))))) (let ((_let_7 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_8 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_9 (= _let_8 _let_7))) (let ((_let_10 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_11 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_12 (tptp.unordered_pair _let_11 _let_10))) (let ((_let_13 (= _let_8 _let_12))) (let ((_let_14 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_15 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_16 (tptp.unordered_pair _let_15 _let_14))) (let ((_let_17 (= _let_7 _let_16))) (let ((_let_18 (= _let_12 _let_16))) (let ((_let_19 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_20 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_21 (and _let_20 _let_19))) (let ((_let_22 (not _let_9))) (let ((_let_23 (or _let_22 _let_21))) (let ((_let_24 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (or (not (= (tptp.ordered_pair A B) (tptp.ordered_pair C D))) (and (= A C) (= B D)))))) (let ((_let_25 (not _let_23))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (or))) (let ((_let_28 (not _let_24))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_26) :args (_let_28))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_24))) (REFL :args (_let_25)) :args _let_27)) _let_26 :args (_let_25 true _let_24)))) (let ((_let_30 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 0)) (CONG (REFL :args (_let_23)) (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_9))) :args _let_27)) :args ((or _let_9 _let_23))) _let_29 :args (_let_9 true _let_23)))) (let ((_let_31 (_let_5))) (let ((_let_32 (ASSUME :args _let_31))) (let ((_let_33 ((tptp.ordered_pair A B)))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_33)) :args _let_31)) _let_32 :args (_let_13 false _let_5)))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_33)) :args _let_31)) _let_32 :args (_let_17 false _let_5)))) (let ((_let_36 (= _let_10 _let_15))) (let ((_let_37 (= _let_11 _let_15))) (let ((_let_38 (not _let_18))) (let ((_let_39 (or _let_38 _let_37 _let_36))) (let ((_let_40 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (or (not (= (tptp.unordered_pair A B) (tptp.unordered_pair C D))) (= A C) (= A D))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (_let_40))) (let ((_let_43 ((tptp.unordered_pair A B) (tptp.unordered_pair C D)))) (let ((_let_44 (= _let_11 _let_14))) (let ((_let_45 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_46 (= _let_14 _let_45))) (let ((_let_47 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_48 (= _let_10 _let_47))) (let ((_let_49 (not _let_36))) (let ((_let_50 (tptp.unordered_pair _let_14 _let_15))) (let ((_let_51 (= _let_12 _let_50))) (let ((_let_52 (not _let_51))) (let ((_let_53 (or _let_52 _let_44 _let_37))) (let ((_let_54 (= _let_16 _let_50))) (let ((_let_55 (_let_6))) (let ((_let_56 (ASSUME :args _let_55))) (let ((_let_57 ((tptp.unordered_pair A B)))) (let ((_let_58 (and _let_9 _let_13 _let_17 _let_54))) (let ((_let_59 (ASSUME :args (_let_54)))) (let ((_let_60 (ASSUME :args (_let_17)))) (let ((_let_61 (SYMM (SYMM _let_60)))) (let ((_let_62 (ASSUME :args (_let_9)))) (let ((_let_63 (SYMM (SYMM _let_62)))) (let ((_let_64 (ASSUME :args (_let_13)))) (let ((_let_65 (SYMM _let_64))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_58)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_59 _let_60 _let_62 _let_64) (SCOPE (TRANS _let_65 _let_63 _let_61 (SYMM (SYMM _let_59))) :args (_let_54 _let_17 _let_9 _let_13))) :args (_let_9 _let_13 _let_17 _let_54))) :args (true _let_58)) _let_30 _let_34 _let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (_let_15 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_57)) :args _let_55)) _let_56 :args (_let_54 false _let_6)) :args (_let_51 false _let_9 false _let_13 false _let_17 false _let_54)))) (let ((_let_67 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_68 (= _let_15 _let_67))) (let ((_let_69 (= _let_11 _let_67))) (let ((_let_70 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_71 (= _let_11 _let_70))) (let ((_let_72 (= _let_15 _let_70))) (let ((_let_73 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_74 (not _let_69))) (let ((_let_75 (or _let_74 _let_73 _let_19))) (let ((_let_76 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_77 (not _let_72))) (let ((_let_78 (or _let_77 _let_76 _let_19))) (let ((_let_79 (not _let_37))) (let ((_let_80 (and _let_68 _let_37))) (let ((_let_81 (_let_68 _let_37))) (let ((_let_82 (ASSUME :args (_let_68)))) (let ((_let_83 (ASSUME :args (_let_37)))) (let ((_let_84 (SYMM _let_83))) (let ((_let_85 (and _let_71 _let_37))) (let ((_let_86 (_let_71 _let_37))) (let ((_let_87 (ASSUME :args (_let_71)))) (let ((_let_88 (not _let_19))) (let ((_let_89 (= _let_47 _let_45))) (let ((_let_90 (not _let_89))) (let ((_let_91 (or _let_90 _let_20 _let_20))) (let ((_let_92 (not _let_44))) (let ((_let_93 (or _let_92 _let_20))) (let ((_let_94 (= _let_10 _let_14))) (let ((_let_95 (or _let_52 _let_44 _let_94))) (let ((_let_96 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (= (tptp.singleton A) (tptp.unordered_pair B C))) (= A B))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (_let_2))) (let ((_let_99 (ASSUME :args _let_98))) (let ((_let_100 ((tptp.singleton A)))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_99 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_100)) :args _let_98))) _let_99 :args (_let_48 false _let_2)))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_99 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_100)) :args _let_98))) _let_99 :args (_let_46 false _let_2)))) (let ((_let_103 (REFL :args ((not _let_46))))) (let ((_let_104 (REFL :args ((not _let_48))))) (let ((_let_105 (and _let_48 _let_46 _let_90))) (let ((_let_106 (ASSUME :args (_let_90)))) (let ((_let_107 (=))) (let ((_let_108 (ASSUME :args (_let_46)))) (let ((_let_109 (SYMM _let_108))) (let ((_let_110 (SYMM _let_109))) (let ((_let_111 (ASSUME :args (_let_48)))) (let ((_let_112 (SYMM _let_111))) (let ((_let_113 (SYMM _let_112))) (let ((_let_114 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_105)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_106 _let_111 _let_108) (SCOPE (FALSE_ELIM (TRANS (CONG _let_113 _let_110 :args _let_107) (FALSE_INTRO _let_106))) :args (_let_90 _let_48 _let_46))) :args (_let_48 _let_46 _let_90))) :args (true _let_105)) (CONG _let_104 _let_103 (MACRO_SR_PRED_INTRO :args ((= (not _let_90) _let_89))) (REFL :args ((not _let_94))) :args _let_27)) _let_102 _let_101 (REORDERING (CNF_OR_POS :args (_let_95)) :args ((or _let_52 _let_44 _let_94 (not _let_95)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_41 :args (_let_14 _let_15 _let_11 _let_10 QUANTIFIERS_INST_E_MATCHING _let_43)) :args _let_42))) _let_41 :args (_let_95 false _let_40)) _let_66 (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_20 _let_92 (not _let_93)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_97 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((tptp.singleton A) (tptp.unordered_pair B C)))) :args (_let_96)))) _let_97 :args (_let_93 false _let_96)) (REORDERING (FACTORING (CNF_OR_POS :args (_let_91))) :args ((or _let_20 _let_90 (not _let_91)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_43)) :args _let_42))) _let_41 :args (_let_91 false _let_40)) :args (_let_20 false _let_46 false _let_48 false _let_94 false _let_95 false _let_51 true _let_44 false _let_93 true _let_89 false _let_91)))) (let ((_let_115 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_21)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_23 1)) _let_29 :args ((not _let_21) true _let_23)) _let_114 :args (_let_88 true _let_21 false _let_20)))) (let ((_let_116 (not _let_73))) (let ((_let_117 (not _let_76))) (let ((_let_118 (not _let_20))) (let ((_let_119 (REFL :args (_let_118)))) (let ((_let_120 (and _let_20 _let_88 _let_73))) (let ((_let_121 (ASSUME :args (_let_88)))) (let ((_let_122 (ASSUME :args (_let_73)))) (let ((_let_123 (ASSUME :args (_let_20)))) (let ((_let_124 (SYMM _let_123))) (let ((_let_125 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_120)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_121 _let_122 _let_123) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (TRANS _let_124 (SYMM (SYMM _let_122))) :args _let_107) (FALSE_INTRO _let_121))) :args (_let_88 _let_73 _let_20))) :args (_let_20 _let_88 _let_73))) :args (true _let_120)) (CONG _let_119 (MACRO_SR_PRED_INTRO :args ((= (not _let_88) _let_19))) (REFL :args (_let_116)) (REFL :args (_let_117)) :args _let_27)) :args ((or _let_19 _let_118 _let_117 _let_116))) _let_115 _let_114 (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_19 _let_76 _let_77 (not _let_78)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING _let_43)) :args _let_42))) _let_41 :args (_let_78 false _let_40)) _let_115 (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_19 _let_73 _let_74 (not _let_75)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING _let_43)) :args _let_42))) _let_41 :args (_let_75 false _let_40)) _let_115 (RESOLUTION (CNF_AND_NEG :args (_let_85)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_87 _let_83) (SCOPE (TRANS _let_84 (SYMM (SYMM _let_87))) :args _let_86)) :args _let_86)) :args (true _let_85)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_57)) :args _let_55)) _let_56 :args (_let_71 false _let_6)) (RESOLUTION (CNF_AND_NEG :args (_let_80)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_82 _let_83) (SCOPE (TRANS (SYMM _let_84) (SYMM (SYMM _let_82))) :args _let_81)) :args _let_81)) :args (true _let_80)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_57)) :args _let_55)) _let_56 :args (_let_68 false _let_6)) :args (_let_79 true _let_19 false _let_20 false _let_76 false _let_78 true _let_19 false _let_73 false _let_75 true _let_19 false _let_72 false _let_71 false _let_69 false _let_68)))) (let ((_let_126 (and _let_20 _let_48 _let_46 _let_79 _let_44))) (let ((_let_127 (ASSUME :args (_let_79)))) (let ((_let_128 (ASSUME :args (_let_44)))) (let ((_let_129 (ASSUME :args (_let_38)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_129 _let_64 _let_60 _let_62) :args (_let_9 _let_13 _let_17 _let_38)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (TRANS _let_65 _let_63 _let_61))) (FALSE_INTRO _let_129))) :args (_let_38 _let_13 _let_17 _let_9)) :args ((not (and _let_9 _let_13 _let_17 _let_38)) SB_LITERAL))) (CONG (REFL :args (_let_22)) (REFL :args ((not _let_13))) (REFL :args ((not _let_17))) (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_18))) :args _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_37 _let_36 _let_38 (not _let_39)))) _let_125 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_126)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO (MODUS_PONENS (AND_INTRO _let_108 _let_123 _let_111) (SCOPE (TRANS _let_112 (CONG (SYMM _let_124) :args (APPLY_UF tptp.singleton)) _let_110) :args (_let_46 _let_20 _let_48))) _let_128 _let_127 _let_108 _let_111) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS _let_113 (SYMM (SYMM (ASSUME :args (_let_89)))) _let_109 (SYMM _let_128)) (REFL :args (_let_15)) :args _let_107) (FALSE_INTRO _let_127))) :args (_let_89 _let_44 _let_79 _let_46 _let_48))) :args (_let_20 _let_48 _let_46 _let_79 _let_44))) :args (true _let_126)) (CONG _let_119 _let_104 _let_103 (MACRO_SR_PRED_INTRO :args ((= (not _let_79) _let_37))) (REFL :args (_let_92)) (REFL :args (_let_49)) :args _let_27)) _let_114 _let_101 _let_102 _let_125 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_37 _let_52 _let_44 (not _let_53)))) _let_125 _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (_let_11 _let_10 _let_14 _let_15 QUANTIFIERS_INST_E_MATCHING _let_43)) :args _let_42)) _let_41 :args (_let_53 false _let_40)) :args (_let_44 true _let_37 false _let_51 false _let_53)) :args (_let_49 false _let_20 false _let_48 false _let_46 true _let_37 false _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_41 :args (_let_15 _let_14 _let_11 _let_10 QUANTIFIERS_INST_E_MATCHING _let_43)) :args _let_42))) _let_41 :args (_let_39 false _let_40)) :args (_let_38 true _let_37 true _let_36 false _let_39)) _let_35 _let_34 _let_30 :args (false true _let_18 false _let_17 false _let_13 false _let_9)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.proper_subset A B) (not (tptp.proper_subset B A)))) _let_6 (forall ((A $$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 $$unsorted)) (= (= A B) (and (tptp.subset A B) (tptp.subset B A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.singleton A)) (forall ((C $$unsorted)) (= (tptp.in C B) (= C 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) (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) (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 $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))))) (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 $$unsorted) (B $$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 $$unsorted) (B $$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))))))) _let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_intersection2 A B) tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.proper_subset A B) (and (tptp.subset A B) (not (= A B))))) true true true true true true true true true (tptp.empty tptp.empty_set) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.ordered_pair A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 B A))))) (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)) (not (tptp.proper_subset A 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 $$unsorted)) (= (tptp.subset (tptp.singleton A) B) (tptp.in A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (or (tptp.in C A) (tptp.subset A (tptp.set_difference B (tptp.singleton C)))))) (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)))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.disjoint A B) (tptp.disjoint B A))) _let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_union2 A B) B))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_intersection2 A B) A)) (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) (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.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 $$unsorted)) (=> (forall ((C $$unsorted)) (= (tptp.in C A) (tptp.in C B))) (= A B))) (forall ((A $$unsorted)) (tptp.subset tptp.empty_set A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_difference A C) (tptp.set_difference B C)))) _let_3 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_difference A B) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A (tptp.set_difference B A)) (tptp.set_union2 A B))) (forall ((A $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)) (forall ((A $$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 $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= B (tptp.set_union2 A (tptp.set_difference B A))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference A (tptp.set_difference A B)) (tptp.set_intersection2 A B))) (forall ((A $$unsorted)) (= (tptp.set_difference tptp.empty_set A) tptp.empty_set)) (forall ((A $$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) (B $$unsorted)) (not (and (tptp.subset A B) (tptp.proper_subset B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.disjoint B C)) (tptp.disjoint A C))) _let_2 (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 $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$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 $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C B)) (tptp.subset (tptp.set_union2 A C) B))) _let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= B C))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.18/0.56  )
% 0.18/0.56  % SZS output end Proof for SEU156+2
% 0.18/0.56  % cvc5---1.0.5 exiting
% 0.18/0.56  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------