TSTP Solution File: SWW654_2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW654_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n016.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 17.09s 17.27s
% Output : Proof 17.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW654_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.17/0.36 % Computer : n016.cluster.edu
% 0.17/0.36 % Model : x86_64 x86_64
% 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36 % Memory : 8042.1875MB
% 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36 % CPULimit : 300
% 0.17/0.36 % WCLimit : 300
% 0.17/0.36 % DateTime : Sun Aug 27 22:19:44 EDT 2023
% 0.17/0.36 % CPUTime :
% 0.20/0.50 %----Proving TF0_ARI
% 17.09/17.27 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.bdY0rg7B6P/cvc5---1.0.5_27230.p...
% 17.09/17.27 ------- get file name : TPTP file name is SWW654_2
% 17.09/17.27 ------- cvc5-tfa : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_27230.smt2...
% 17.09/17.27 --- Run --finite-model-find --decision=internal at 15...
% 17.09/17.27 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 17.09/17.27 % SZS status Theorem for SWW654_2
% 17.09/17.27 % SZS output start Proof for SWW654_2
% 17.09/17.27 (
% 17.09/17.27 (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)) (=> (= L (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) (tptp.bst1 (tptp.node1 tptp.red1 (tptp.node1 tptp.black1 X6 X7 X8 X9) X2 X3 (tptp.node1 tptp.black1 X4 K V R)))))))) (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) (tptp.bst1 (tptp.node1 tptp.red1 (tptp.node1 tptp.black1 X1 X2 X3 X6) X7 X8 (tptp.node1 tptp.black1 X9 K V R))))) (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 (tptp.bst1 (tptp.node1 tptp.red1 (tptp.node1 tptp.black1 X11 X12 X13 X14) X2 X3 (tptp.node1 tptp.black1 X4 K V R))))) (=> (= X10 tptp.black1) (=> _let_1 (tptp.bst1 (tptp.node1 tptp.red1 (tptp.node1 tptp.black1 X1 X2 X3 X6) X7 X8 (tptp.node1 tptp.black1 X9 K V R))))))))))) (=> (= 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) (tptp.bst1 (tptp.node1 tptp.red1 (tptp.node1 tptp.black1 X11 X12 X13 X14) X2 X3 (tptp.node1 tptp.black1 X4 K V R))))))))))))))))))) (let ((_let_2 (forall ((C tptp.color1) (Cqt tptp.color1) (K Int) (V Int) (L tptp.tree1) (R tptp.tree1)) (=> (tptp.bst1 (tptp.node1 C L K V R)) (tptp.bst1 (tptp.node1 Cqt L K V R)))))) (let ((_let_3 (forall ((K Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C tptp.color1)) (=> (tptp.bst1 (tptp.node1 C L K V R)) (tptp.bst1 R))))) (let ((_let_4 (forall ((K Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C tptp.color1)) (=> (tptp.bst1 (tptp.node1 C L K V R)) (tptp.bst1 L))))) (let ((_let_5 (tptp.bst1 tptp.leaf1))) (let ((_let_6 (forall ((X tptp.color1) (X1 tptp.tree1) (X2 Int) (X3 Int) (X4 tptp.tree1)) (= (tptp.bst1 (tptp.node1 X X1 X2 X3 X4)) (and (tptp.bst1 X1) (tptp.bst1 X4) (tptp.lt_tree1 X2 X1) (tptp.gt_tree1 X2 X4)))))) (let ((_let_7 (and _let_5 _let_6))) (let ((_let_8 (forall ((X Int) (Y Int)) (=> (< Y X) (forall ((T tptp.tree1)) (=> (tptp.gt_tree1 X T) (tptp.gt_tree1 Y T))))))) (let ((_let_9 (forall ((X Int) (Y Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C tptp.color1)) (=> (tptp.gt_tree1 X (tptp.node1 C L Y V R)) (tptp.gt_tree1 X L))))) (let ((_let_10 (forall ((X Int) (Y Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C tptp.color1)) (=> (tptp.lt_tree1 X (tptp.node1 C L Y V R)) (tptp.lt_tree1 X R))))) (let ((_let_11 (forall ((X Int) (Y Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C tptp.color1)) (=> (tptp.lt_tree1 X (tptp.node1 C L Y V R)) (tptp.lt_tree1 X L))))) (let ((_let_12 (forall ((X Int) (Y Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C tptp.color1)) (=> (tptp.gt_tree1 X (tptp.node1 C L Y V R)) (< X Y))))) (let ((_let_13 (forall ((X Int) (Y Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C tptp.color1)) (=> (tptp.lt_tree1 X (tptp.node1 C L Y V R)) (< Y X))))) (let ((_let_14 (forall ((X Int) (Y Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C tptp.color1)) (=> (tptp.gt_tree1 X L) (=> (tptp.gt_tree1 X R) (=> (< X Y) (tptp.gt_tree1 X (tptp.node1 C L Y V R)))))))) (let ((_let_15 (forall ((X Int) (Y Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C tptp.color1)) (=> (tptp.lt_tree1 X L) (=> (tptp.lt_tree1 X R) (=> (< Y X) (tptp.lt_tree1 X (tptp.node1 C L Y V R)))))))) (let ((_let_16 (forall ((X Int) (T tptp.tree1)) (= (tptp.lt_tree1 X T) (forall ((K Int) (V Int)) (=> (tptp.memt1 T K V) (< K X))))))) (let ((_let_17 (forall ((L tptp.tree1) (R tptp.tree1) (K Int) (Kqt Int) (V Int) (Vqt Int) (C tptp.color1) (Cqt tptp.color1)) (=> (tptp.memt1 (tptp.node1 C L K V R) Kqt Vqt) (tptp.memt1 (tptp.node1 Cqt L K V R) Kqt Vqt))))) (let ((_let_18 (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_19 (tptp.node1 tptp.red1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_20 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_19))) (let ((_let_21 (tptp.memt1 _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_122 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_123))) (let ((_let_22 (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_122 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_123))) (let ((_let_23 (tptp.node1 tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_24 (tptp.node1 tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_25 (tptp.bst1 (tptp.node1 tptp.red1 _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_23)))) (let ((_let_26 (not _let_20))) (let ((_let_27 (not (= tptp.red1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)))) (let ((_let_28 (or (not (= tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) _let_27 _let_26 _let_25))) (let ((_let_29 (tptp.node1 tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_30 (tptp.node1 tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_31 (tptp.bst1 (tptp.node1 tptp.red1 _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_29)))) (let ((_let_32 (or (not (= tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21)) _let_27 _let_31))) (let ((_let_33 (tptp.node1 tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_34 (tptp.bst1 (tptp.node1 tptp.red1 _let_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_23)))) (let ((_let_35 (or (not (= tptp.red1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21)) _let_27 _let_34))) (let ((_let_36 (and _let_35 _let_32))) (let ((_let_37 (tptp.node1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_38 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_37))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_36))) (let ((_let_41 (or (not (= tptp.leaf1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)) _let_27 _let_31))) (let ((_let_42 (and _let_41 _let_40))) (let ((_let_43 (or (not (= tptp.red1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) _let_42))) (let ((_let_44 (and _let_43 _let_28))) (let ((_let_45 (tptp.bst1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_46 (tptp.bst1 _let_37))) (let ((_let_47 (and (tptp.bst1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23) (tptp.bst1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27) (tptp.lt_tree1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23) (tptp.gt_tree1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27)))) (let ((_let_48 (= _let_46 _let_47))) (let ((_let_49 (tptp.bst1 _let_33))) (let ((_let_50 (= _let_49 _let_47))) (let ((_let_51 (tptp.gt_tree1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_23))) (let ((_let_52 (tptp.lt_tree1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_33))) (let ((_let_53 (tptp.bst1 _let_23))) (let ((_let_54 (and _let_49 _let_53 _let_52 _let_51))) (let ((_let_55 (= _let_34 _let_54))) (let ((_let_56 (forall ((K Int) (V Int)) (or (not (tptp.memt1 (tptp.node1 tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27) K V)) (not (>= (+ K (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)) 0)))))) (let ((_let_57 (= _let_52 _let_56))) (let ((_let_58 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_130)) 1))) (let ((_let_59 (tptp.memt1 _let_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_130 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_131))) (let ((_let_60 (not _let_59))) (let ((_let_61 (or _let_60 _let_58))) (let ((_let_62 (tptp.memt1 _let_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_130 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_131))) (let ((_let_63 (or _let_60 _let_62))) (let ((_let_64 (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_130 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_131))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_65 _let_58))) (let ((_let_67 (or))) (let ((_let_68 (tptp.gt_tree1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_69 (tptp.lt_tree1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_70 (tptp.bst1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_71 (and _let_45 _let_70 _let_69 _let_68))) (let ((_let_72 (tptp.node1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_73 (tptp.bst1 _let_72))) (let ((_let_74 (= _let_73 _let_71))) (let ((_let_75 (1))) (let ((_let_76 (AND_ELIM (ASSUME :args (_let_7)) :args _let_75))) (let ((_let_77 (_let_6))) (let ((_let_78 ((tptp.node1 X X1 X2 X3 X4)))) (let ((_let_79 (ASSUME :args _let_77))) (let ((_let_80 (tptp.node1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_81 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_80))) (let ((_let_82 (not _let_81))) (let ((_let_83 (or _let_82 _let_44))) (let ((_let_84 (tptp.node1 tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_85 (tptp.bst1 (tptp.node1 tptp.red1 _let_84 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_23)))) (let ((_let_86 (tptp.node1 tptp.red1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_87 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_86))) (let ((_let_88 (not _let_87))) (let ((_let_89 (or (not (= tptp.leaf1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20)) _let_27 _let_88 _let_85))) (let ((_let_90 (and _let_89 _let_83))) (let ((_let_91 (tptp.bst1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_92 (not _let_91))) (let ((_let_93 (not _let_73))) (let ((_let_94 (tptp.gt_tree1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_95 (not _let_94))) (let ((_let_96 (tptp.lt_tree1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_72))) (let ((_let_97 (not _let_96))) (let ((_let_98 (or _let_97 _let_95 _let_93 _let_92 _let_90))) (let ((_let_99 (forall ((K Int) (V Int) (R tptp.tree1) (BOUND_VARIABLE_2401 tptp.tree1) (BOUND_VARIABLE_2399 Int) (BOUND_VARIABLE_2397 Int) (BOUND_VARIABLE_2395 tptp.tree1) (BOUND_VARIABLE_2393 tptp.color1) (BOUND_VARIABLE_2391 Int) (BOUND_VARIABLE_2389 tptp.tree1) (BOUND_VARIABLE_2387 Int) (BOUND_VARIABLE_2385 Int) (BOUND_VARIABLE_2383 tptp.tree1) (BOUND_VARIABLE_2357 tptp.color1) (BOUND_VARIABLE_2359 tptp.tree1) (BOUND_VARIABLE_2361 Int) (BOUND_VARIABLE_2363 Int) (BOUND_VARIABLE_2365 tptp.tree1) (BOUND_VARIABLE_2367 tptp.color1) (BOUND_VARIABLE_2369 tptp.tree1) (BOUND_VARIABLE_2371 tptp.tree1) (BOUND_VARIABLE_2373 Int) (BOUND_VARIABLE_2375 Int) (BOUND_VARIABLE_2377 tptp.tree1) (BOUND_VARIABLE_2379 tptp.tree1) (BOUND_VARIABLE_2381 Int)) (let ((_let_1 (tptp.node1 tptp.black1 BOUND_VARIABLE_2365 K V R))) (let ((_let_2 (not (= tptp.red1 BOUND_VARIABLE_2357)))) (let ((_let_3 (tptp.bst1 (tptp.node1 tptp.red1 (tptp.node1 tptp.black1 BOUND_VARIABLE_2359 BOUND_VARIABLE_2361 BOUND_VARIABLE_2363 BOUND_VARIABLE_2395) BOUND_VARIABLE_2397 BOUND_VARIABLE_2399 (tptp.node1 tptp.black1 BOUND_VARIABLE_2401 K V R))))) (let ((_let_4 (tptp.node1 BOUND_VARIABLE_2357 BOUND_VARIABLE_2359 BOUND_VARIABLE_2361 BOUND_VARIABLE_2363 BOUND_VARIABLE_2365))) (or (not (tptp.lt_tree1 K _let_4)) (not (tptp.gt_tree1 K R)) (not (tptp.bst1 _let_4)) (not (tptp.bst1 R)) (and (or (not (= tptp.leaf1 BOUND_VARIABLE_2365)) _let_2 (not (= BOUND_VARIABLE_2359 (tptp.node1 tptp.red1 BOUND_VARIABLE_2377 BOUND_VARIABLE_2381 BOUND_VARIABLE_2385 BOUND_VARIABLE_2389))) (tptp.bst1 (tptp.node1 tptp.red1 (tptp.node1 tptp.black1 BOUND_VARIABLE_2377 BOUND_VARIABLE_2381 BOUND_VARIABLE_2385 BOUND_VARIABLE_2389) BOUND_VARIABLE_2361 BOUND_VARIABLE_2363 _let_1))) (or (not (= BOUND_VARIABLE_2365 (tptp.node1 BOUND_VARIABLE_2393 BOUND_VARIABLE_2395 BOUND_VARIABLE_2397 BOUND_VARIABLE_2399 BOUND_VARIABLE_2401))) (and (or (not (= tptp.red1 BOUND_VARIABLE_2393)) (and (or (not (= tptp.leaf1 BOUND_VARIABLE_2359)) _let_2 _let_3) (or (not (= BOUND_VARIABLE_2359 (tptp.node1 BOUND_VARIABLE_2367 BOUND_VARIABLE_2371 BOUND_VARIABLE_2375 BOUND_VARIABLE_2387 BOUND_VARIABLE_2379))) (and (or (not (= tptp.red1 BOUND_VARIABLE_2367)) _let_2 (tptp.bst1 (tptp.node1 tptp.red1 (tptp.node1 tptp.black1 BOUND_VARIABLE_2371 BOUND_VARIABLE_2375 BOUND_VARIABLE_2387 BOUND_VARIABLE_2379) BOUND_VARIABLE_2361 BOUND_VARIABLE_2363 _let_1))) (or (not (= tptp.black1 BOUND_VARIABLE_2367)) _let_2 _let_3))))) (or (not (= tptp.black1 BOUND_VARIABLE_2393)) _let_2 (not (= BOUND_VARIABLE_2359 (tptp.node1 tptp.red1 BOUND_VARIABLE_2369 BOUND_VARIABLE_2373 BOUND_VARIABLE_2391 BOUND_VARIABLE_2383))) (tptp.bst1 (tptp.node1 tptp.red1 (tptp.node1 tptp.black1 BOUND_VARIABLE_2369 BOUND_VARIABLE_2373 BOUND_VARIABLE_2391 BOUND_VARIABLE_2383) BOUND_VARIABLE_2361 BOUND_VARIABLE_2363 _let_1)))))))))))))) (let ((_let_100 (not _let_98))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (not _let_99))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_101) :args (_let_102))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_102) _let_99))) (REFL :args (_let_100)) :args _let_67)) _let_101 :args (_let_100 true _let_99)))) (let ((_let_104 (REFL :args (_let_98)))) (let ((_let_105 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_74)) :args ((or _let_93 _let_71 (not _let_74)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_98 2)) (CONG _let_104 (MACRO_SR_PRED_INTRO :args ((= (not _let_93) _let_73))) :args _let_67)) :args ((or _let_73 _let_98))) _let_103 :args (_let_73 true _let_98)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_78)) :args _let_77)) _let_76 :args (_let_74 false _let_6)) :args (_let_71 false _let_73 false _let_74)))) (let ((_let_106 (not _let_71))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_71 0)) :args ((or _let_45 _let_106))) _let_105 :args (_let_45 false _let_71)))) (let ((_let_108 (not _let_45))) (let ((_let_109 (not _let_46))) (let ((_let_110 (REFL :args (_let_108)))) (let ((_let_111 (ASSUME :args (_let_45)))) (let ((_let_112 (TRUE_INTRO _let_111))) (let ((_let_113 (APPLY_UF tptp.bst1))) (let ((_let_114 (ASSUME :args (_let_38)))) (let ((_let_115 (SYMM _let_114))) (let ((_let_116 (ASSUME :args (_let_109)))) (let ((_let_117 (tptp.gt_tree1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_29))) (let ((_let_118 (tptp.lt_tree1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_30))) (let ((_let_119 (tptp.bst1 _let_29))) (let ((_let_120 (tptp.bst1 _let_30))) (let ((_let_121 (and _let_120 _let_119 _let_118 _let_117))) (let ((_let_122 (= _let_31 _let_121))) (let ((_let_123 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_124 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_123) 1))) (let ((_let_125 (not _let_124))) (let ((_let_126 (tptp.gt_tree1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_127 (not _let_126))) (let ((_let_128 (tptp.gt_tree1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_129 (not _let_128))) (let ((_let_130 (or _let_129 _let_127 _let_125 _let_117))) (let ((_let_131 (forall ((X Int) (Y Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C tptp.color1)) (or (not (tptp.gt_tree1 X L)) (not (tptp.gt_tree1 X R)) (>= (+ X (* (- 1) Y)) 0) (tptp.gt_tree1 X (tptp.node1 C L Y V R)))))) (let ((_let_132 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_133 (_let_131))) (let ((_let_134 ((not (= (tptp.gt_tree1 X (tptp.node1 C L Y V R)) true))))) (let ((_let_135 (tptp.lt_tree1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_80))) (let ((_let_136 (not _let_135))) (let ((_let_137 (or _let_136 _let_124))) (let ((_let_138 (forall ((X Int) (Y Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C tptp.color1)) (or (not (tptp.lt_tree1 X (tptp.node1 C L Y V R))) (>= (+ X (* (- 1) Y)) 1))))) (let ((_let_139 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_140 (_let_138))) (let ((_let_141 ((not (= (tptp.lt_tree1 X (tptp.node1 C L Y V R)) false))))) (let ((_let_142 (tptp.lt_tree1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_143 (or _let_97 _let_142))) (let ((_let_144 (forall ((X Int) (Y Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C tptp.color1)) (or (not (tptp.lt_tree1 X (tptp.node1 C L Y V R))) (tptp.lt_tree1 X R))))) (let ((_let_145 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_146 (_let_144))) (let ((_let_147 ((not (= (tptp.lt_tree1 X (tptp.node1 C L Y V R)) false))))) (let ((_let_148 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_98 0)) (CONG _let_104 (MACRO_SR_PRED_INTRO :args ((= (not _let_97) _let_96))) :args _let_67)) :args ((or _let_96 _let_98))) _let_103 :args (_let_96 true _let_98)))) (let ((_let_149 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_143)) :args ((or _let_97 _let_142 (not _let_143)))) _let_148 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE 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(let ((_let_160 (or _let_157 _let_159))) (let ((_let_161 (tptp.lt_tree1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26))) (let ((_let_162 (or _let_157 _let_161))) (let ((_let_163 (not _let_155))) (let ((_let_164 (or _let_163 _let_151))) (let ((_let_165 (not _let_156))) (let ((_let_166 (not _let_159))) (let ((_let_167 (not _let_161))) (let ((_let_168 (or _let_167 _let_166 _let_165 _let_150))) (let ((_let_169 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_71 2)) :args ((or _let_69 _let_106))) _let_105 :args (_let_69 false _let_71)))) (let ((_let_170 (and _let_87 _let_69))) (let ((_let_171 (ASSUME :args (_let_69)))) (let ((_let_172 (APPLY_UF tptp.lt_tree1))) (let ((_let_173 (ASSUME :args (_let_87)))) (let ((_let_174 (SYMM _let_173))) (let ((_let_175 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)))) (let ((_let_176 (and _let_87 _let_45))) (let ((_let_177 (forall ((X Int) (Y Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C tptp.color1)) (or (not 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SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 tptp.red1 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.lt_tree1 X (tptp.node1 C L Y V R)) false))))) :args (_let_177))) _let_178 :args (_let_162 false _let_177)) (REORDERING (CNF_OR_POS :args (_let_160)) :args ((or _let_159 _let_157 (not _let_160)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_145 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 tptp.red1 QUANTIFIERS_INST_E_MATCHING _let_147)) :args _let_146)) _let_145 :args (_let_160 false _let_144)) (REORDERING (CNF_OR_POS :args (_let_158)) :args ((or _let_156 _let_157 (not _let_158)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_139 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 tptp.red1 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_let_78)) :args _let_77)) _let_76 :args (_let_153 false _let_6)) (CNF_OR_NEG :args (_let_89 3)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_89 2)) (CONG (REFL :args (_let_89)) (MACRO_SR_PRED_INTRO :args ((= (not _let_88) _let_87))) :args _let_67)) :args ((or _let_87 _let_89))) :args (_let_89 false _let_53 false _let_51 false _let_150 false _let_168 false _let_151 false _let_164 false _let_161 false _let_162 false _let_159 false _let_160 false _let_156 false _let_158 false _let_155 false _let_45 false _let_154 false _let_69 true _let_152 false _let_153 true _let_85 false _let_87)) :args ((not _let_83) true _let_90 false _let_89)))) (let ((_let_211 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_83 0)) (CONG (REFL :args (_let_83)) (MACRO_SR_PRED_INTRO :args ((= (not _let_82) _let_81))) :args _let_67)) :args ((or _let_81 _let_83))) _let_210 :args (_let_81 true _let_83)))) (let ((_let_212 (and _let_81 _let_142))) (let ((_let_213 (ASSUME :args (_let_142)))) (let ((_let_214 (ASSUME :args (_let_81)))) (let ((_let_215 (SYMM _let_214))) (let ((_let_216 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_212)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_213 _let_214) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_215 :args _let_172) (TRUE_INTRO _let_213))) :args (_let_142 _let_81))) :args (_let_81 _let_142))) :args (true _let_212)) _let_211 _let_149 :args (_let_135 false _let_81 false _let_142)))) (let ((_let_217 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_137)) :args ((or _let_124 _let_136 (not _let_137)))) _let_216 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_139 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING _let_141)) :args _let_140)) _let_139 :args (_let_137 false _let_138)) :args (_let_124 false _let_135 false _let_137)))) (let ((_let_218 (or _let_125 _let_95 _let_126))) (let ((_let_219 (tptp.lt_tree1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_220 (tptp.bst1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_221 (tptp.bst1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_222 (and _let_221 _let_220 _let_219 _let_128))) (let ((_let_223 (tptp.bst1 _let_80))) (let ((_let_224 (= _let_223 _let_222))) (let ((_let_225 (not _let_223))) (let ((_let_226 (ASSUME :args (_let_70)))) (let ((_let_227 (ASSUME :args (_let_225)))) (let ((_let_228 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_226 _let_214 _let_227) :args (_let_81 _let_70 _let_225)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_227)) (CONG _let_215 :args _let_113) (TRUE_INTRO _let_226))) :args (_let_70 _let_81 _let_225)) :args ((not (and _let_81 _let_70 _let_225)) SB_LITERAL))) (CONG (REFL :args (_let_82)) (REFL :args (_let_206)) (MACRO_SR_PRED_INTRO :args ((= (not _let_225) _let_223))) :args _let_67)) :args ((or _let_82 _let_223 _let_206))) _let_211 _let_204 :args (_let_223 false _let_81 false _let_70)))) (let ((_let_229 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_224)) :args ((or _let_222 _let_225 (not _let_224)))) _let_228 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_78)) :args _let_77)) _let_76 :args (_let_224 false _let_6)) :args (_let_222 false _let_223 false _let_224)))) (let ((_let_230 (not _let_222))) (let ((_let_231 (forall ((K Int) (V Int)) (or (not (tptp.memt1 (tptp.node1 tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 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SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_127))) (let ((_let_244 (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_126 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_127))) (let ((_let_245 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_126))) (let ((_let_246 (and _let_245 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_127)))) (let ((_let_247 (or _let_246 _let_244 _let_243))) (let ((_let_248 (= _let_240 _let_247))) (let ((_let_249 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_185))) (let ((_let_250 (>= _let_249 1))) (let ((_let_251 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_237))) (let ((_let_252 (>= _let_251 1))) (let ((_let_253 (not _let_243))) (let ((_let_254 (or _let_253 _let_239))) (let ((_let_255 (not _let_244))) (let ((_let_256 (or _let_255 _let_252))) (let ((_let_257 (not _let_239))) (let ((_let_258 (forall ((BOUND_VARIABLE_1467 Int) (BOUND_VARIABLE_1469 Int) (X tptp.color1) (X1 tptp.tree1) (X2 Int) (X3 Int) (X4 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(TRUE_ELIM (TRANS (CONG _let_175 _let_215 :args (APPLY_UF tptp.gt_tree1)) (TRUE_INTRO _let_266))) :args (_let_68 _let_81))) :args (_let_81 _let_68))) :args (true _let_265)) _let_211 _let_200 :args (_let_260 false _let_81 false _let_68)))) (let ((_let_268 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_262)) :args ((or _let_250 _let_261 (not _let_262)))) _let_267 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_264 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.gt_tree1 X (tptp.node1 C L Y V R)) false))))) :args (_let_263)))) _let_264 :args (_let_262 false _let_263)) :args (_let_250 false _let_260 false _let_262)))) (let ((_let_269 (not _let_250))) (let ((_let_270 (not _let_252))) (let ((_let_271 (false))) (let ((_let_272 (_let_250))) (let ((_let_273 (ASSUME :args _let_272))) (let ((_let_274 (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_257)) :args ((< _let_238 1))))) (let ((_let_275 (forall ((K Int) (V Int)) (or (not (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 K V)) (not (>= (+ K (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) 0)))))) (let ((_let_276 (= _let_219 _let_275))) (let ((_let_277 (_let_275))) (let ((_let_278 (forall ((K Int) (V Int)) (or (not (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 K V)) (not (>= (+ K (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)) 0)))))) (let ((_let_279 (= _let_69 _let_278))) (let ((_let_280 (not _let_69))) (let ((_let_281 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_279)) :args ((or _let_280 _let_278 (not _let_279)))) _let_169 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_234 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_236)) :args _let_235))) _let_234 :args (_let_279 false _let_233)) :args (_let_278 false _let_69 false _let_279)))) (let ((_let_282 (_let_278))) (let ((_let_283 ((not (= (tptp.memt1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 K V) false))))) (let ((_let_284 (ASSUME :args _let_282))) (let ((_let_285 (_let_269))) (let ((_let_286 (not _let_231))) (let ((_let_287 (_let_286))) (let ((_let_288 (tptp.gt_tree1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_289 (and _let_45 _let_221 _let_69 _let_288))) (let ((_let_290 (= _let_120 _let_289))) (let ((_let_291 (or _let_261 _let_288))) (let ((_let_292 (forall ((X Int) (Y Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C tptp.color1)) (or (not (tptp.gt_tree1 X (tptp.node1 C L Y V R))) (tptp.gt_tree1 X L))))) (let ((_let_293 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_294 (or _let_225 _let_221))) (let ((_let_295 (forall ((K Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C 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((_let_328 (not _let_323))) (let ((_let_329 (tptp.bst1 _let_19))) (let ((_let_330 (not _let_329))) (let ((_let_331 (or _let_330 _let_326))) (let ((_let_332 (REFL :args (_let_26)))) (let ((_let_333 (ASSUME :args (_let_20)))) (let ((_let_334 (SYMM _let_333))) (let ((_let_335 (ASSUME :args (_let_330)))) (let ((_let_336 (= _let_25 _let_327))) (let ((_let_337 (not _let_327))) (let ((_let_338 (_let_325))) (let ((_let_339 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_338)) :args _let_338) (REWRITE :args ((=> _let_325 (not (or _let_317 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_122 _let_185) 0))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_325) _let_321))) (REFL :args (_let_322)) :args _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_324)) :args ((or _let_323 _let_325 (not _let_324)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_327)) :args ((or _let_327 (not _let_326) _let_209 _let_208 _let_328))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_336)) :args ((or _let_25 _let_337 (not _let_336)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_28 3)) _let_314 :args ((not _let_25) true _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (tptp.red1 _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_78)) :args _let_77)) _let_76 :args (_let_336 false _let_6)) :args (_let_337 true _let_25 false _let_336)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_331)) :args ((or _let_326 _let_330 (not _let_331)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_111 _let_333 _let_335) :args (_let_20 _let_45 _let_330)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_335)) (CONG _let_334 :args _let_113) _let_112)) :args (_let_45 _let_20 _let_330)) :args ((not (and _let_20 _let_45 _let_330)) SB_LITERAL))) (CONG _let_332 _let_110 (MACRO_SR_PRED_INTRO :args ((= (not _let_330) _let_329))) :args _let_67)) :args ((or _let_26 _let_329 _let_108))) _let_315 _let_107 :args (_let_329 false _let_20 false _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_180 :args (tptp.red1 tptp.black1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING _let_182)) :args _let_181)) _let_180 :args (_let_331 false _let_179)) :args (_let_326 false _let_329 false _let_331)) _let_207 _let_201 :args (_let_328 true _let_327 false _let_326 false _let_53 false _let_51)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_234 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_236)) :args _let_235))) _let_234 :args (_let_324 false _let_233)) :args (_let_325 true _let_323 false _let_324)) :args (_let_322 true _let_321)))) (let ((_let_340 (not _let_22))) (let ((_let_341 (or _let_340 _let_319))) (let ((_let_342 (not _let_319))) (let ((_let_343 (ASSUME :args (_let_340)))) (let ((_let_344 (ASSUME :args (_let_21)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_343 _let_333 _let_344) :args (_let_20 _let_21 _let_340)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_344)) (CONG _let_334 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_122)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_123)) :args _let_313) (FALSE_INTRO _let_343))) :args (_let_340 _let_20 _let_21)) :args ((not (and _let_20 _let_21 _let_340)) SB_LITERAL))) (CONG _let_332 (REFL :args ((not _let_21))) (MACRO_SR_PRED_INTRO :args ((= (not _let_340) _let_22))) :args _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_341)) :args ((or _let_319 _let_340 (not _let_341)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_320 1)) :args ((or _let_342 _let_320))) _let_339 :args (_let_342 true _let_320)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_284 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_122 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_123 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_283)) :args _let_282))) _let_281 :args (_let_341 false _let_278)) :args (_let_340 true _let_319 false _let_341)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_318)) :args ((or _let_317 _let_21 (not _let_318)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_320 0)) (CONG (REFL :args (_let_320)) (MACRO_SR_PRED_INTRO :args ((= (not _let_317) _let_316))) :args _let_67)) :args ((or _let_316 _let_320))) _let_339 :args (_let_316 true _let_320)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_308 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_122 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_123 tptp.black1 tptp.red1 QUANTIFIERS_INST_E_MATCHING _let_310)) :args _let_309)) _let_308 :args (_let_318 false _let_307)) :args (_let_21 false _let_316 false _let_318)) _let_315 :args (false true _let_22 false _let_21 false _let_20)) :args ((forall ((A tptp.ty)) (tptp.sort1 A (tptp.witness1 A))) (forall ((A tptp.ty) (X tptp.bool1) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort1 A (tptp.match_bool1 A X X1 X2))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort1 A Z) (= (tptp.match_bool1 A tptp.true1 Z Z1) Z))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort1 A Z1) (= (tptp.match_bool1 A tptp.false1 Z Z1) Z1))) (not (= tptp.true1 tptp.false1)) (forall ((U tptp.bool1)) (or (= U tptp.true1) (= U tptp.false1))) (forall ((U tptp.tuple02)) (= U tptp.tuple03)) (forall ((A tptp.ty) (X tptp.color1) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort1 A (tptp.match_color1 A X X1 X2))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort1 A Z) (= (tptp.match_color1 A tptp.red1 Z Z1) Z))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort1 A Z1) (= (tptp.match_color1 A tptp.black1 Z Z1) Z1))) (not (= tptp.red1 tptp.black1)) (forall ((U tptp.color1)) (or (= U tptp.red1) (= U tptp.black1))) (forall ((A tptp.ty) (X tptp.tree1) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort1 A (tptp.match_tree1 A X X1 X2))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort1 A Z) (= (tptp.match_tree1 A tptp.leaf1 Z Z1) Z))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni) (U tptp.color1) (U1 tptp.tree1) (U2 Int) (U3 Int) (U4 tptp.tree1)) (=> (tptp.sort1 A Z1) (= (tptp.match_tree1 A (tptp.node1 U U1 U2 U3 U4) Z Z1) Z1))) (forall ((V tptp.color1) (V1 tptp.tree1) (V2 Int) (V3 Int) (V4 tptp.tree1)) (not (= tptp.leaf1 (tptp.node1 V V1 V2 V3 V4)))) (forall ((U tptp.color1) (U1 tptp.tree1) (U2 Int) (U3 Int) (U4 tptp.tree1)) (= (tptp.node_proj_11 (tptp.node1 U U1 U2 U3 U4)) U)) (forall ((U tptp.color1) (U1 tptp.tree1) (U2 Int) (U3 Int) (U4 tptp.tree1)) (= (tptp.node_proj_21 (tptp.node1 U U1 U2 U3 U4)) U1)) (forall ((U tptp.color1) (U1 tptp.tree1) (U2 Int) (U3 Int) (U4 tptp.tree1)) (= (tptp.node_proj_31 (tptp.node1 U U1 U2 U3 U4)) U2)) (forall ((U tptp.color1) (U1 tptp.tree1) (U2 Int) (U3 Int) (U4 tptp.tree1)) (= (tptp.node_proj_41 (tptp.node1 U U1 U2 U3 U4)) U3)) (forall ((U tptp.color1) (U1 tptp.tree1) (U2 Int) (U3 Int) (U4 tptp.tree1)) (= (tptp.node_proj_51 (tptp.node1 U U1 U2 U3 U4)) U4)) (forall ((U tptp.tree1)) (or (= U tptp.leaf1) (= U (tptp.node1 (tptp.node_proj_11 U) (tptp.node_proj_21 U) (tptp.node_proj_31 U) (tptp.node_proj_41 U) (tptp.node_proj_51 U))))) _let_18 _let_17 (forall ((X Int) (Y Int) (Z Int)) (=> (<= X Y) (=> (<= 0 Z) (<= (* X Z) (* Y Z))))) _let_16 (forall ((X Int) (T tptp.tree1)) (= (tptp.gt_tree1 X T) (forall ((K Int) (V Int)) (=> (tptp.memt1 T K V) (< X K))))) (forall ((X Int)) (tptp.lt_tree1 X tptp.leaf1)) (forall ((X Int)) (tptp.gt_tree1 X tptp.leaf1)) _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 (forall ((X Int) (Y Int) (V Int) (L tptp.tree1) (R tptp.tree1) (C tptp.color1)) (=> (tptp.gt_tree1 X (tptp.node1 C L Y V R)) (tptp.gt_tree1 X R))) (forall ((X Int) (T tptp.tree1)) (=> (tptp.lt_tree1 X T) (forall ((V Int)) (not (tptp.memt1 T X V))))) (forall ((X Int) (Y Int)) (=> (< X Y) (forall ((T tptp.tree1)) (=> (tptp.lt_tree1 X T) (tptp.lt_tree1 Y T))))) (forall ((X Int) (T tptp.tree1)) (=> (tptp.gt_tree1 X T) (forall ((V Int)) (not (tptp.memt1 T X V))))) _let_8 _let_7 _let_5 _let_4 _let_3 _let_2 (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 17.09/17.28 )
% 17.09/17.28 % SZS output end Proof for SWW654_2
% 17.09/17.28 % cvc5---1.0.5 exiting
% 17.09/17.28 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------