TSTP Solution File: SWW655_2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW655_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.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 : Fri Sep 1 00:21:50 EDT 2023
% Result : Theorem 49.47s 49.64s
% Output : Proof 49.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SWW655_2 : TPTP v8.1.2. Released v6.1.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n024.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 : Sun Aug 27 18:05:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_ARI
% 49.47/49.64 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.UL40ICQly7/cvc5---1.0.5_20770.p...
% 49.47/49.64 ------- get file name : TPTP file name is SWW655_2
% 49.47/49.64 ------- cvc5-tfa : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_20770.smt2...
% 49.47/49.64 --- Run --finite-model-find --decision=internal at 15...
% 49.47/49.64 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 49.47/49.64 --- Run --no-e-matching --full-saturate-quant at 15...
% 49.47/49.64 --- Run --cegqi-all --purify-triggers --full-saturate-quant at 15...
% 49.47/49.64 % SZS status Theorem for SWW655_2
% 49.47/49.64 % SZS output start Proof for SWW655_2
% 49.47/49.64 (
% 49.47/49.64 (let ((_let_1 (not (forall ((L tptp.tree1) (K Int) (V Int) (R tptp.tree1)) (=> (and (tptp.lt_tree1 K L) (tptp.gt_tree1 K R) (tptp.bst1 L) (tptp.bst1 R)) (forall ((X tptp.color1) (X1 tptp.tree1) (X2 Int) (X3 Int) (X4 tptp.tree1)) (=> (= R (tptp.node1 X X1 X2 X3 X4)) (and (=> (= X4 tptp.leaf1) (forall ((X5 tptp.color1) (X6 tptp.tree1) (X7 Int) (X8 Int) (X9 tptp.tree1)) (=> (= X1 (tptp.node1 X5 X6 X7 X8 X9)) (=> (= X5 tptp.red1) (=> (= X tptp.red1) (forall ((Kqt Int) (Vqt Int)) (let ((_let_1 (= Kqt K))) (=> (or (and _let_1 (= Vqt V)) (and (not _let_1) (or (tptp.memt1 L Kqt Vqt) (tptp.memt1 R Kqt Vqt)))) (tptp.memt1 (tptp.node1 tptp.red1 (tptp.node1 tptp.black1 L K V X6) X7 X8 (tptp.node1 tptp.black1 X9 X2 X3 X4)) Kqt Vqt))))))))) (forall ((X5 tptp.color1) (X6 tptp.tree1) (X7 Int) (X8 Int) (X9 tptp.tree1)) (=> (= X4 (tptp.node1 X5 X6 X7 X8 X9)) (and (=> (= X5 tptp.red1) (and (=> (= X1 tptp.leaf1) (=> (= X tptp.red1) (forall ((Kqt Int) (Vqt Int)) (let ((_let_1 (= Kqt K))) (=> (or (and _let_1 (= Vqt V)) (and (not _let_1) (or (tptp.memt1 L Kqt Vqt) (tptp.memt1 R Kqt Vqt)))) (tptp.memt1 (tptp.node1 tptp.red1 (tptp.node1 tptp.black1 L K V X1) X2 X3 (tptp.node1 tptp.black1 X6 X7 X8 X9)) Kqt Vqt)))))) (forall ((X10 tptp.color1) (X11 tptp.tree1) (X12 Int) (X13 Int) (X14 tptp.tree1)) (let ((_let_1 (= X tptp.red1))) (=> (= X1 (tptp.node1 X10 X11 X12 X13 X14)) (and (=> (= X10 tptp.red1) (=> _let_1 (forall ((Kqt Int) (Vqt Int)) (let ((_let_1 (= Kqt K))) (=> (or (and _let_1 (= Vqt V)) (and (not _let_1) (or (tptp.memt1 L Kqt Vqt) (tptp.memt1 R Kqt Vqt)))) (tptp.memt1 (tptp.node1 tptp.red1 (tptp.node1 tptp.black1 L K V X11) X12 X13 (tptp.node1 tptp.black1 X14 X2 X3 X4)) Kqt Vqt)))))) (=> (= X10 tptp.black1) (=> _let_1 (forall ((Kqt Int) (Vqt Int)) (let ((_let_1 (= Kqt K))) (=> (or (and _let_1 (= Vqt V)) (and (not _let_1) (or (tptp.memt1 L Kqt Vqt) (tptp.memt1 R Kqt Vqt)))) (tptp.memt1 (tptp.node1 tptp.red1 (tptp.node1 tptp.black1 L K V X1) X2 X3 (tptp.node1 tptp.black1 X6 X7 X8 X9)) Kqt Vqt)))))))))))) (=> (= X5 tptp.black1) (forall ((X10 tptp.color1) (X11 tptp.tree1) (X12 Int) (X13 Int) (X14 tptp.tree1)) (=> (= X1 (tptp.node1 X10 X11 X12 X13 X14)) (=> (= X10 tptp.red1) (=> (= X tptp.red1) (forall ((Kqt Int) (Vqt Int)) (let ((_let_1 (= Kqt K))) (=> (or (and _let_1 (= Vqt V)) (and (not _let_1) (or (tptp.memt1 L Kqt Vqt) (tptp.memt1 R Kqt Vqt)))) (tptp.memt1 (tptp.node1 tptp.red1 (tptp.node1 tptp.black1 L K V X11) X12 X13 (tptp.node1 tptp.black1 X14 X2 X3 X4)) Kqt Vqt)))))))))))))))))))) (let ((_let_2 (tptp.bst1 tptp.leaf1))) (let ((_let_3 (forall ((K Int) (V Int)) (and (not (tptp.memt1 tptp.leaf1 K V)) (forall ((X tptp.color1) (X1 tptp.tree1) (X2 Int) (X3 Int) (X4 tptp.tree1)) (= (tptp.memt1 (tptp.node1 X X1 X2 X3 X4) K V) (or (and (= K X2) (= V X3)) (tptp.memt1 X1 K V) (tptp.memt1 X4 K V)))))))) (let ((_let_4 (forall ((V tptp.color1) (V1 tptp.tree1) (V2 Int) (V3 Int) (V4 tptp.tree1)) (not (= tptp.leaf1 (tptp.node1 V V1 V2 V3 V4)))))) (let ((_let_5 (tptp.node1 tptp.red1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_90 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_77 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_99 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_93))) (let ((_let_6 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86 _let_5))) (let ((_let_7 (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_78 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_89))) (let ((_let_8 (tptp.memt1 _let_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_78 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_89))) (let ((_let_9 (tptp.node1 tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_93 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_84 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83))) (let ((_let_10 (tptp.node1 tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_90))) (let ((_let_11 (tptp.memt1 (tptp.node1 tptp.red1 _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_77 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_99 _let_9) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_78 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_89))) (let ((_let_12 (tptp.node1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_87 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_84 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83))) (let ((_let_13 (tptp.memt1 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_78 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_89))) (let ((_let_14 (not _let_13))) (let ((_let_15 (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_78 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_89))) (let ((_let_16 (not _let_15))) (let ((_let_17 (and _let_16 _let_14))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_78))) (let ((_let_19 (or _let_18 _let_17))) (let ((_let_20 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_89))) (let ((_let_21 (not _let_20))) (let ((_let_22 (not _let_18))) (let ((_let_23 (or _let_22 _let_21))) (let ((_let_24 (and _let_23 _let_19))) (let ((_let_25 (not _let_6))) (let ((_let_26 (not (= tptp.red1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_87)))) (let ((_let_27 (or (not (= tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_103)) _let_26 _let_25 _let_24 _let_11))) (let ((_let_28 (tptp.node1 tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_100 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_97))) (let ((_let_29 (tptp.node1 tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86))) (let ((_let_30 (tptp.node1 tptp.red1 _let_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_84 _let_28))) (let ((_let_31 (tptp.memt1 _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75))) (let ((_let_32 (tptp.memt1 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75))) (let ((_let_35 (not _let_34))) (let ((_let_36 (and _let_35 _let_33))) (let ((_let_37 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80))) (let ((_let_38 (or _let_37 _let_36))) (let ((_let_39 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75))) (let ((_let_40 (not _let_39))) (let ((_let_41 (not _let_37))) (let ((_let_42 (or _let_41 _let_40))) (let ((_let_43 (and _let_42 _let_38))) (let ((_let_44 (or (not (= tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98)) _let_26 _let_43 _let_31))) (let ((_let_45 (tptp.node1 tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_92 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_84 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83))) (let ((_let_46 (tptp.node1 tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91))) (let ((_let_47 (tptp.memt1 (tptp.node1 tptp.red1 _let_46 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_76 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 _let_45) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_81))) (let ((_let_48 (tptp.memt1 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_81))) (let ((_let_49 (not _let_48))) (let ((_let_50 (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_81))) (let ((_let_51 (not _let_50))) (let ((_let_52 (and _let_51 _let_49))) (let ((_let_53 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82))) (let ((_let_54 (or _let_53 _let_52))) (let ((_let_55 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_81))) (let ((_let_56 (not _let_55))) (let ((_let_57 (not _let_53))) (let ((_let_58 (or _let_57 _let_56))) (let ((_let_59 (and _let_58 _let_54))) (let ((_let_60 (or (not (= tptp.red1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98)) _let_26 _let_59 _let_47))) (let ((_let_61 (and _let_60 _let_44))) (let ((_let_62 (tptp.node1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_76 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_92))) (let ((_let_63 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86 _let_62))) (let ((_let_64 (not _let_63))) (let ((_let_65 (or _let_64 _let_61))) (let ((_let_66 (tptp.memt1 _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_88 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_79))) (let ((_let_67 (tptp.memt1 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_88 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_79))) (let ((_let_68 (not _let_67))) (let ((_let_69 (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_88 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_79))) (let ((_let_70 (not _let_69))) (let ((_let_71 (and _let_70 _let_68))) (let ((_let_72 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_69 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_88))) (let ((_let_73 (or _let_72 _let_71))) (let ((_let_74 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_79))) (let ((_let_75 (not _let_74))) (let ((_let_76 (not _let_72))) (let ((_let_77 (or _let_76 _let_75))) (let ((_let_78 (and _let_77 _let_73))) (let ((_let_79 (= tptp.leaf1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86))) (let ((_let_80 (not _let_79))) (let ((_let_81 (or _let_80 _let_26 _let_78 _let_66))) (let ((_let_82 (and _let_81 _let_65))) (let ((_let_83 (or (not (= tptp.red1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_103)) _let_82))) (let ((_let_84 (and _let_83 _let_27))) (let ((_let_85 (or))) (let ((_let_86 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 0)) (CONG (REFL :args (_let_65)) (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_63))) :args _let_85)) :args ((or _let_63 _let_65))))) (let ((_let_87 (tptp.memt1 _let_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_81))) (let ((_let_88 (tptp.memt1 _let_46 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_81))) (let ((_let_89 (and (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_76 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82) (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_81 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94)))) (let ((_let_90 (or _let_89 _let_88 _let_87))) (let ((_let_91 (= _let_47 _let_90))) (let ((_let_92 (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_81))) (let ((_let_93 (and _let_53 _let_55))) (let ((_let_94 (or _let_93 _let_50 _let_92))) (let ((_let_95 (= _let_88 _let_94))) (let ((_let_96 (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_81))) (let ((_let_97 (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_92 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_81))) (let ((_let_98 (and (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85) (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_81 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_84)))) (let ((_let_99 (or _let_98 _let_97 _let_96))) (let ((_let_100 (= _let_87 _let_99))) (let ((_let_101 (or _let_89 _let_92 _let_97))) (let ((_let_102 (tptp.memt1 _let_62 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_81))) (let ((_let_103 (= _let_102 _let_101))) (let ((_let_104 (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_82 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_81))) (let ((_let_105 (or _let_98 _let_104 _let_96))) (let ((_let_106 (= _let_48 _let_105))) (let ((_let_107 (forall ((BOUND_VARIABLE_1541 Int) (BOUND_VARIABLE_1543 Int) (X tptp.color1) (X1 tptp.tree1) (X2 Int) (X3 Int) (X4 tptp.tree1)) (= (tptp.memt1 (tptp.node1 X X1 X2 X3 X4) BOUND_VARIABLE_1541 BOUND_VARIABLE_1543) (or (and (= X2 BOUND_VARIABLE_1541) (= X3 BOUND_VARIABLE_1543)) (tptp.memt1 X1 BOUND_VARIABLE_1541 BOUND_VARIABLE_1543) (tptp.memt1 X4 BOUND_VARIABLE_1541 BOUND_VARIABLE_1543)))))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (AND_ELIM _let_108 :args (1)))) (let ((_let_110 (_let_107))) (let ((_let_111 ((tptp.memt1 (tptp.node1 X X1 X2 X3 X4) BOUND_VARIABLE_1541 BOUND_VARIABLE_1543)))) (let ((_let_112 (ASSUME :args _let_110))) (let ((_let_113 (CNF_AND_NEG :args (_let_59)))) (let ((_let_114 (REFL :args (_let_58)))) (let ((_let_115 (not _let_102))) (let ((_let_116 (_let_52))) (let ((_let_117 (not _let_104))) (let ((_let_118 (REFL :args (_let_64)))) (let ((_let_119 (and _let_63 _let_115))) (let ((_let_120 (ASSUME :args (_let_115)))) (let ((_let_121 (APPLY_UF tptp.memt1))) (let ((_let_122 (ASSUME :args (_let_63)))) (let ((_let_123 (tptp.memt1 _let_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75))) (let ((_let_124 (tptp.memt1 _let_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75))) (let ((_let_125 (and (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85) (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_84)))) (let ((_let_126 (or _let_125 _let_124 _let_123))) (let ((_let_127 (= _let_31 _let_126))) (let ((_let_128 (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75))) (let ((_let_129 (and _let_37 _let_39))) (let ((_let_130 (or _let_129 _let_34 _let_128))) (let ((_let_131 (= _let_124 _let_130))) (let ((_let_132 (or (and (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80) (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_100)) (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75) (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_97 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75)))) (let ((_let_133 (= _let_123 _let_132))) (let ((_let_134 (tptp.node1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_103 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_73 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_100 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_97))) (let ((_let_135 (tptp.memt1 _let_134 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75))) (let ((_let_136 (= _let_132 _let_135))) (let ((_let_137 (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75))) (let ((_let_138 (or _let_125 _let_128 _let_137))) (let ((_let_139 (= _let_32 _let_138))) (let ((_let_140 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 _let_134))) (let ((_let_141 (not _let_135))) (let ((_let_142 (CNF_AND_NEG :args (_let_43)))) (let ((_let_143 (REFL :args (_let_42)))) (let ((_let_144 (_let_36))) (let ((_let_145 (not _let_140))) (let ((_let_146 (or _let_145 _let_84))) (let ((_let_147 (tptp.node1 tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_74 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85 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SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_72))) (let ((_let_158 (not _let_157))) (let ((_let_159 (not _let_155))) (let ((_let_160 (or _let_159 _let_158))) (let ((_let_161 (and _let_160 _let_156))) (let ((_let_162 (tptp.node1 tptp.red1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_95 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_96 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_102 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_74))) (let ((_let_163 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86 _let_162))) (let ((_let_164 (not _let_163))) (let ((_let_165 (= tptp.leaf1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83))) (let ((_let_166 (not _let_165))) (let ((_let_167 (or _let_166 _let_26 _let_164 _let_161 _let_149))) (let ((_let_168 (and _let_167 _let_146))) (let ((_let_169 (= tptp.leaf1 _let_134))) (let ((_let_170 (tptp.memt1 tptp.leaf1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_72))) (let ((_let_171 (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101 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(IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_112 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_87 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_84 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_83 QUANTIFIERS_INST_E_MATCHING _let_111)) :args _let_110))) _let_109 :args (_let_139 false _let_107)) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_144) (CONG (REFL :args _let_144) (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_85)) :args ((or _let_34 _let_32 _let_36))) (CNF_OR_NEG :args (_let_38 1)) _let_142 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 0)) (CONG _let_143 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_37))) :args _let_85)) :args ((or _let_37 _let_42))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 1)) (CONG _let_143 (MACRO_SR_PRED_INTRO :args 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:args _let_110)) _let_109 :args (_let_131 false _let_107)) (CNF_OR_NEG :args (_let_126 2)) (CNF_OR_NEG :args (_let_126 1)) (CNF_OR_NEG :args (_let_126 0)) (REORDERING (CNF_EQUIV_POS2 :args (_let_127)) :args ((or _let_31 (not _let_126) (not _let_127)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_112 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_80 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75 tptp.red1 _let_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_85 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_84 _let_28 QUANTIFIERS_INST_E_MATCHING _let_111)) :args _let_110))) _let_109 :args (_let_127 false _let_107)) (CNF_OR_NEG :args (_let_44 3)) (CNF_OR_NEG :args (_let_44 2)) :args (_let_44 false _let_140 false _let_137 false _let_138 false _let_139 false _let_32 true _let_36 true _let_38 false _let_42 true _let_37 true _let_135 false _let_136 true _let_128 true _let_34 true _let_129 true _let_132 false _let_133 true _let_130 false _let_131 true _let_123 true _let_124 true _let_125 true 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L K V R)) (tptp.bst1 (tptp.node1 Cqt L K V R)))) (forall ((Kx Int) (Ky Int) (Vx Int) (Vy Int) (A tptp.tree1) (B tptp.tree1) (C tptp.tree1) (C1 tptp.color1) (C2 tptp.color1) (C3 tptp.color1) (C4 tptp.color1)) (=> (tptp.bst1 (tptp.node1 C1 A Kx Vx (tptp.node1 C2 B Ky Vy C))) (tptp.bst1 (tptp.node1 C3 (tptp.node1 C4 A Kx Vx B) Ky Vy C)))) (forall ((Kx Int) (Ky Int) (Vx Int) (Vy Int) (A tptp.tree1) (B tptp.tree1) (C tptp.tree1) (C1 tptp.color1) (C2 tptp.color1) (C3 tptp.color1) (C4 tptp.color1)) (=> (tptp.bst1 (tptp.node1 C3 (tptp.node1 C4 A Kx Vx B) Ky Vy C)) (tptp.bst1 (tptp.node1 C1 A Kx Vx (tptp.node1 C2 B Ky Vy C))))) (and (tptp.is_not_red1 tptp.leaf1) (forall ((X tptp.color1) (X1 tptp.tree1) (X2 Int) (X3 Int) (X4 tptp.tree1)) (let ((_let_1 (tptp.is_not_red1 (tptp.node1 X X1 X2 X3 X4)))) (and (=> (= X tptp.red1) (not _let_1)) (=> (= X tptp.black1) _let_1))))) (forall ((N Int)) (and (= (tptp.rbtree1 N tptp.leaf1) (= N 0)) (forall ((X tptp.color1) (X1 tptp.tree1) (X2 Int) (X3 Int) (X4 tptp.tree1)) (let ((_let_1 (- N 1))) (let ((_let_2 (tptp.rbtree1 N (tptp.node1 X X1 X2 X3 X4)))) (and (=> (= X tptp.red1) (= _let_2 (and (tptp.rbtree1 N X1) (tptp.rbtree1 N X4) (tptp.is_not_red1 X1) (tptp.is_not_red1 X4)))) (=> (= X tptp.black1) (= _let_2 (and (tptp.rbtree1 _let_1 X1) (tptp.rbtree1 _let_1 X4)))))))))) (tptp.rbtree1 0 tptp.leaf1) (forall ((K Int) (V Int)) (tptp.rbtree1 0 (tptp.node1 tptp.red1 tptp.leaf1 K V tptp.leaf1))) (forall ((X Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C tptp.color1)) (=> (exists ((N Int)) (tptp.rbtree1 N (tptp.node1 C L X V R))) (exists ((N Int)) (tptp.rbtree1 N L)))) (forall ((X Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C tptp.color1)) (=> (exists ((N Int)) (tptp.rbtree1 N (tptp.node1 C L X V R))) (exists ((N Int)) (tptp.rbtree1 N R)))) (forall ((N Int)) (and (= (tptp.almost_rbtree1 N tptp.leaf1) (= N 0)) (forall ((X tptp.color1) (X1 tptp.tree1) (X2 Int) (X3 Int) (X4 tptp.tree1)) (let ((_let_1 (- N 1))) (let ((_let_2 (tptp.almost_rbtree1 N (tptp.node1 X X1 X2 X3 X4)))) (and (=> (= X tptp.red1) (= _let_2 (and (tptp.rbtree1 N X1) (tptp.rbtree1 N X4)))) (=> (= X tptp.black1) (= _let_2 (and (tptp.rbtree1 _let_1 X1) (tptp.rbtree1 _let_1 X4)))))))))) (forall ((N Int) (T tptp.tree1)) (=> (tptp.rbtree1 N T) (tptp.almost_rbtree1 N T))) (forall ((S tptp.tree1)) (=> (exists ((N Int)) (tptp.rbtree1 N S)) (exists ((N Int)) (tptp.almost_rbtree1 N S)))) (forall ((X Int) (V Int) (L tptp.tree1) (R tptp.tree1) (N Int)) (let ((_let_1 (tptp.node1 tptp.black1 L X V R))) (=> (tptp.almost_rbtree1 N _let_1) (tptp.rbtree1 N _let_1)))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 49.47/49.65 )
% 49.47/49.65 % SZS output end Proof for SWW655_2
% 49.47/49.65 % cvc5---1.0.5 exiting
% 49.47/49.65 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------