TSTP Solution File: SWW602_2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW602_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 00:21:40 EDT 2023
% Result : Theorem 46.52s 46.86s
% Output : Proof 46.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW602_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.12 % Command : do_cvc5 %s %d
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sun Aug 27 18:28:15 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.16/0.41 %----Proving TF0_ARI
% 46.52/46.86 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.rOVVotzy0l/cvc5---1.0.5_14543.p...
% 46.52/46.86 ------- get file name : TPTP file name is SWW602_2
% 46.52/46.86 ------- cvc5-tfa : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_14543.smt2...
% 46.52/46.86 --- Run --finite-model-find --decision=internal at 15...
% 46.52/46.86 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 46.52/46.86 --- Run --no-e-matching --full-saturate-quant at 15...
% 46.52/46.86 --- Run --cegqi-all --purify-triggers --full-saturate-quant at 15...
% 46.52/46.86 % SZS status Theorem for SWW602_2
% 46.52/46.86 % SZS output start Proof for SWW602_2
% 46.52/46.86 (
% 46.52/46.86 (let ((_let_1 (not (forall ((N Int)) (let ((_let_1 (+ N 1))) (let ((_let_2 (<= 0 _let_1))) (=> (<= 0 N) (=> _let_2 (=> _let_2 (=> (and (<= 0 0) (< 0 _let_1)) (forall ((A tptp.map_int_lplist_treerp)) (let ((_let_1 (tptp.nil tptp.tree))) (let ((_let_2 (tptp.list tptp.tree))) (=> (and (<= 0 (+ N 1)) (= A (tptp.tb2t3 (tptp.set _let_2 tptp.int (tptp.const _let_2 tptp.int _let_1) (tptp.t2tb 0) (tptp.cons tptp.tree (tptp.t2tb2 tptp.empty1) _let_1))))) (=> (<= 1 N) (forall ((A1 tptp.map_int_lplist_treerp) (I Int)) (let ((_let_1 (+ N 1))) (=> (and (<= 1 I) (<= I N)) (=> (forall ((K Int)) (=> (and (<= 0 K) (< K I)) (tptp.all_trees1 K (tptp.tb2t1 (tptp.get (tptp.list tptp.tree) tptp.int (tptp.t2tb3 A1) (tptp.t2tb K)))))) (=> (and (<= 0 _let_1) (<= 0 I) (< I _let_1)) (forall ((A2 tptp.map_int_lplist_treerp)) (=> (and (<= 0 (+ N 1)) (= A2 (tptp.tb2t3 (tptp.set (tptp.list tptp.tree) tptp.int (tptp.t2tb3 A1) (tptp.t2tb I) (tptp.nil tptp.tree))))) (=> (<= 0 (- I 1)) (forall ((A3 tptp.map_int_lplist_treerp) (J Int)) (let ((_let_1 (- I 1))) (let ((_let_2 (- _let_1 J))) (let ((_let_3 (tptp.t2tb3 A3))) (let ((_let_4 (tptp.list tptp.tree))) (let ((_let_5 (<= 0 _let_2))) (let ((_let_6 (<= 0 J))) (let ((_let_7 (+ N 1))) (=> (and _let_6 (<= J _let_1)) (=> (and (forall ((K Int)) (=> (and (<= 0 K) (< K I)) (tptp.all_trees1 K (tptp.tb2t1 (tptp.get (tptp.list tptp.tree) tptp.int (tptp.t2tb3 A3) (tptp.t2tb K)))))) (tptp.distinct tptp.tree (tptp.get _let_4 tptp.int _let_3 (tptp.t2tb I))) (forall ((T tptp.tree1)) (= (tptp.mem tptp.tree (tptp.t2tb2 T) (tptp.get (tptp.list tptp.tree) tptp.int (tptp.t2tb3 A3) (tptp.t2tb I))) (exists ((L tptp.tree1) (R tptp.tree1)) (and (= T (tptp.node1 L R)) (= (tptp.size1 T) I) (< (tptp.size1 L) J)))))) (=> (and (<= 0 _let_7) (<= 0 I) (< I _let_7)) (=> (and _let_5 (< _let_2 _let_7)) (=> (and _let_6 (< J _let_7)) (=> (and _let_6 (tptp.all_trees1 J (tptp.tb2t1 (tptp.get _let_4 tptp.int _let_3 (tptp.t2tb J)))) _let_5 (tptp.all_trees1 _let_2 (tptp.tb2t1 (tptp.get _let_4 tptp.int _let_3 (tptp.t2tb _let_2))))) (forall ((O tptp.list_tree)) (=> (and (tptp.distinct tptp.tree (tptp.t2tb1 O)) (forall ((T tptp.tree1)) (= (tptp.mem tptp.tree (tptp.t2tb2 T) (tptp.t2tb1 O)) (exists ((L tptp.tree1) (R tptp.tree1)) (and (= T (tptp.node1 L R)) (= (tptp.size1 L) J) (= (tptp.size1 R) (- (- I 1) J))))))) (=> (and (<= 0 I) (< I (+ N 1))) (forall ((A4 tptp.map_int_lplist_treerp)) (let ((_let_1 (tptp.t2tb I))) (let ((_let_2 (tptp.t2tb3 A3))) (let ((_let_3 (tptp.list tptp.tree))) (=> (and (<= 0 (+ N 1)) (= A4 (tptp.tb2t3 (tptp.set _let_3 tptp.int _let_2 _let_1 (tptp.infix_plpl tptp.tree (tptp.t2tb1 O) (tptp.get _let_3 tptp.int _let_2 _let_1)))))) (forall ((T tptp.tree1)) (=> (tptp.mem tptp.tree (tptp.t2tb2 T) (tptp.get (tptp.list tptp.tree) tptp.int (tptp.t2tb3 A4) (tptp.t2tb I))) (exists ((L tptp.tree1) (R tptp.tree1)) (and (= T (tptp.node1 L R)) (= (tptp.size1 T) I) (< (tptp.size1 L) (+ J 1))))))))))))))))))))))))))))))))))))))))))))))))))) (let ((_let_2 (forall ((J tptp.uni)) (= (tptp.t2tb3 (tptp.tb2t3 J)) J)))) (let ((_let_3 (forall ((T tptp.tree1)) (=> (< 0 (tptp.size1 T)) (exists ((L tptp.tree1) (R tptp.tree1)) (and (= T (tptp.node1 L R)) (< (tptp.size1 L) (tptp.size1 T)))))))) (let ((_let_4 (= (tptp.size1 tptp.empty1) 0))) (let ((_let_5 (and _let_4 (forall ((X tptp.tree1) (X1 tptp.tree1)) (= (tptp.size1 (tptp.node1 X X1)) (+ (+ 1 (tptp.size1 X)) (tptp.size1 X1))))))) (let ((_let_6 (forall ((U tptp.tree1) (U1 tptp.tree1)) (= (tptp.node_proj_11 (tptp.node1 U U1)) U)))) (let ((_let_7 (forall ((A tptp.ty) (B tptp.ty) (M tptp.uni) (A1 tptp.uni) (A2 tptp.uni) (B1 tptp.uni)) (=> (tptp.sort1 B B1) (=> (= A1 A2) (= (tptp.get B A (tptp.set B A M A1 B1) A2) B1)))))) (let ((_let_8 (forall ((A tptp.ty) (X tptp.uni) (L1 tptp.uni) (L2 tptp.uni)) (= (tptp.mem A X (tptp.infix_plpl A L1 L2)) (or (tptp.mem A X L1) (tptp.mem A X L2)))))) (let ((_let_9 (forall ((A tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort1 (tptp.list A) (tptp.infix_plpl A X X1))))) (let ((_let_10 (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98 1))) (let ((_let_11 (tptp.size1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_95))) (let ((_let_12 (* (- 1) _let_11))) (let ((_let_13 (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98 _let_12))) (let ((_let_14 (>= _let_13 1))) (let ((_let_15 (>= _let_11 1))) (let ((_let_16 (forall ((L tptp.tree1) (R tptp.tree1)) (or (not (= (tptp.node1 L R) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_95)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 (* (- 1) (tptp.size1 L))) 0)))))) (let ((_let_17 (not _let_16))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98 _let_11))) (let ((_let_19 (and _let_18 _let_17))) (let ((_let_20 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98))) (let ((_let_21 (tptp.t2tb3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_93))) (let ((_let_22 (tptp.list tptp.tree))) (let ((_let_23 (tptp.get _let_22 tptp.int _let_21 _let_20))) (let ((_let_24 (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_96))) (let ((_let_25 (tptp.infix_plpl tptp.tree _let_24 _let_23))) (let ((_let_26 (tptp.set _let_22 tptp.int _let_21 _let_20 _let_25))) (let ((_let_27 (tptp.t2tb3 (tptp.tb2t3 _let_26)))) (let ((_let_28 (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_95))) (let ((_let_29 (tptp.mem tptp.tree _let_28 (tptp.get _let_22 tptp.int _let_27 _let_20)))) (let ((_let_30 (not _let_29))) (let ((_let_31 (forall ((T tptp.tree1)) (= (tptp.mem tptp.tree (tptp.t2tb2 T) (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_96)) (not (forall ((L tptp.tree1) (R tptp.tree1)) (or (not (= T (tptp.node1 L R))) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 (tptp.size1 L))) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 (+ (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98 (* (- 1) (tptp.size1 R)))))))))))) (let ((_let_32 (not _let_31))) (let ((_let_33 (not (tptp.distinct tptp.tree _let_24)))) (let ((_let_34 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94))) (let ((_let_35 (+ (- 1) _let_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98))) (let ((_let_36 (not (tptp.all_trees1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 (tptp.tb2t1 (tptp.get _let_22 tptp.int _let_21 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94))))))) (let ((_let_37 (forall ((T tptp.tree1)) (= (tptp.mem tptp.tree (tptp.t2tb2 T) (tptp.get (tptp.list tptp.tree) tptp.int (tptp.t2tb3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_93) (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98))) (and (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98 (tptp.size1 T)) (not (forall ((L tptp.tree1) (R tptp.tree1)) (or (not (= T (tptp.node1 L R))) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 (* (- 1) (tptp.size1 L))) 1)))))))))) (let ((_let_38 (not _let_37))) (let ((_let_39 (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98))) (let ((_let_40 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 0)))) (let ((_let_41 (not (tptp.distinct tptp.tree _let_23)))) (let ((_let_42 (not (forall ((K Int)) (or (not (>= K 0)) (>= (+ K (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98)) 0) (tptp.all_trees1 K (tptp.tb2t1 (tptp.get (tptp.list tptp.tree) tptp.int (tptp.t2tb3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_93) (tptp.t2tb K))))))))) (let ((_let_43 (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98 0)))) (let ((_let_44 (not (forall ((K Int)) (or (not (>= K 0)) (>= (+ K (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98)) 0) (tptp.all_trees1 K (tptp.tb2t1 (tptp.get (tptp.list tptp.tree) tptp.int (tptp.t2tb3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_97) (tptp.t2tb K))))))))) (let ((_let_45 (not _let_10))) (let ((_let_46 (or _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 _let_39) 0) _let_38 _let_36 (not (tptp.all_trees1 _let_35 (tptp.tb2t1 (tptp.get _let_22 tptp.int _let_21 (tptp.t2tb _let_35))))) _let_33 _let_32 _let_30 _let_19))) (let ((_let_47 (forall ((BOUND_VARIABLE_2452 tptp.map_int_lplist_treerp) (BOUND_VARIABLE_2450 Int) (BOUND_VARIABLE_2448 tptp.tree1) (BOUND_VARIABLE_2446 tptp.list_tree) (BOUND_VARIABLE_2444 tptp.map_int_lplist_treerp) (BOUND_VARIABLE_2442 Int)) (let ((_let_1 (tptp.t2tb BOUND_VARIABLE_2442))) (let ((_let_2 (tptp.t2tb3 BOUND_VARIABLE_2452))) (let ((_let_3 (tptp.list tptp.tree))) (let ((_let_4 (tptp.get _let_3 tptp.int _let_2 _let_1))) (let ((_let_5 (tptp.t2tb1 BOUND_VARIABLE_2446))) (let ((_let_6 (* (- 1) BOUND_VARIABLE_2450))) (let ((_let_7 (+ (- 1) BOUND_VARIABLE_2442 _let_6))) (or (not (>= BOUND_VARIABLE_2442 1)) (not (forall ((K Int)) (or (not (>= K 0)) (>= (+ K (* (- 1) BOUND_VARIABLE_2442)) 0) (tptp.all_trees1 K (tptp.tb2t1 (tptp.get (tptp.list tptp.tree) tptp.int (tptp.t2tb3 BOUND_VARIABLE_2444) (tptp.t2tb K))))))) (not (>= BOUND_VARIABLE_2442 0)) (not (forall ((K Int)) (or (not (>= K 0)) (>= (+ K (* (- 1) BOUND_VARIABLE_2442)) 0) (tptp.all_trees1 K (tptp.tb2t1 (tptp.get (tptp.list tptp.tree) tptp.int (tptp.t2tb3 BOUND_VARIABLE_2452) (tptp.t2tb K))))))) (not (tptp.distinct tptp.tree _let_4)) (not (>= BOUND_VARIABLE_2450 0)) (not (>= (+ BOUND_VARIABLE_2442 _let_6) 1)) (not (forall ((T tptp.tree1)) (= (tptp.mem tptp.tree (tptp.t2tb2 T) (tptp.get (tptp.list tptp.tree) tptp.int (tptp.t2tb3 BOUND_VARIABLE_2452) (tptp.t2tb BOUND_VARIABLE_2442))) (and (= BOUND_VARIABLE_2442 (tptp.size1 T)) (not (forall ((L tptp.tree1) (R tptp.tree1)) (or (not (= T (tptp.node1 L R))) (not (>= (+ BOUND_VARIABLE_2450 (* (- 1) (tptp.size1 L))) 1))))))))) (not (tptp.all_trees1 BOUND_VARIABLE_2450 (tptp.tb2t1 (tptp.get _let_3 tptp.int _let_2 (tptp.t2tb BOUND_VARIABLE_2450))))) (not (tptp.all_trees1 _let_7 (tptp.tb2t1 (tptp.get _let_3 tptp.int _let_2 (tptp.t2tb _let_7))))) (not (tptp.distinct tptp.tree _let_5)) (not (forall ((T tptp.tree1)) (= (not (forall ((L tptp.tree1) (R tptp.tree1)) (or (not (= T (tptp.node1 L R))) (not (= BOUND_VARIABLE_2450 (tptp.size1 L))) (not (= BOUND_VARIABLE_2442 (+ 1 BOUND_VARIABLE_2450 (tptp.size1 R))))))) (tptp.mem tptp.tree (tptp.t2tb2 T) (tptp.t2tb1 BOUND_VARIABLE_2446))))) (not (tptp.mem tptp.tree (tptp.t2tb2 BOUND_VARIABLE_2448) (tptp.get _let_3 tptp.int (tptp.t2tb3 (tptp.tb2t3 (tptp.set _let_3 tptp.int _let_2 _let_1 (tptp.infix_plpl tptp.tree _let_5 _let_4)))) _let_1))) (and (= BOUND_VARIABLE_2442 (tptp.size1 BOUND_VARIABLE_2448)) (not (forall ((L tptp.tree1) (R tptp.tree1)) (or (not (= (tptp.node1 L R) BOUND_VARIABLE_2448)) (not (>= (+ BOUND_VARIABLE_2450 (* (- 1) (tptp.size1 L))) 0))))))))))))))))) (let ((_let_48 (not _let_46))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (or))) (let ((_let_51 (not _let_47))) (let ((_let_52 (+ (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98 _let_34))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_49) :args (_let_51)) (REWRITE :args ((=> _let_51 (not (or _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98 _let_34) 1)) _let_38 _let_36 (not (tptp.all_trees1 _let_52 (tptp.tb2t1 (tptp.get _let_22 tptp.int _let_21 (tptp.t2tb _let_52))))) _let_33 (not (forall ((T tptp.tree1)) (= (not (forall ((L tptp.tree1) (R tptp.tree1)) (or (not (= T (tptp.node1 L R))) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 (tptp.size1 L))) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98 (+ 1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 (tptp.size1 R))))))) (tptp.mem tptp.tree (tptp.t2tb2 T) (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_96))))) _let_30 _let_19))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_47))) (REFL :args (_let_48)) :args _let_50)) _let_49 :args (_let_48 true _let_47)))) (let ((_let_54 (REFL :args (_let_46)))) (let ((_let_55 (not _let_14))) (let ((_let_56 (forall ((L tptp.tree1) (R tptp.tree1)) (or (not (= (tptp.node1 L R) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_95)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 (* (- 1) (tptp.size1 L))) 1)))))) (let ((_let_57 (not _let_56))) (let ((_let_58 (and _let_18 _let_57))) (let ((_let_59 (tptp.mem tptp.tree _let_28 _let_23))) (let ((_let_60 (= _let_59 _let_58))) (let ((_let_61 (tptp.mem tptp.tree _let_28 _let_24))) (let ((_let_62 (or _let_61 _let_59))) (let ((_let_63 (forall ((L tptp.tree1) (R tptp.tree1)) (or (not (= (tptp.node1 L R) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_95)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 (tptp.size1 L))) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 (+ (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98 (* (- 1) (tptp.size1 R))))))))) (let ((_let_64 (not _let_63))) (let ((_let_65 (= _let_61 _let_64))) (let ((_let_66 (tptp.size1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_224))) (let ((_let_67 (* (- 1) _let_66))) (let ((_let_68 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 (+ (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_98 _let_67)))) (let ((_let_69 (not _let_68))) (let ((_let_70 (tptp.size1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_223))) (let ((_let_71 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_94 _let_70))) (let ((_let_72 (not _let_71))) (let ((_let_73 (tptp.node1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_223 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_224))) (let ((_let_74 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_95 _let_73))) (let ((_let_75 (not _let_74))) (let ((_let_76 (or _let_75 _let_72 _let_69))) (let ((_let_77 (tptp.size1 _let_73))) (let ((_let_78 (= _let_11 _let_77))) (let ((_let_79 (= _let_70 (+ (- 1) _let_67 _let_77)))) (let ((_let_80 (>= _let_13 0))) (let ((_let_81 (not _let_58))) (let ((_let_82 (_let_37))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_82) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_95 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.t2tb2 T)))) :args _let_82))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 7)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) :args _let_50)) :args ((or _let_37 _let_46))) _let_53 :args (_let_37 true _let_46)) :args (_let_60 false _let_37)))) (let ((_let_84 (REORDERING (CNF_EQUIV_POS1 :args (_let_60)) :args ((or _let_58 (not _let_59) (not _let_60)))))) (let ((_let_85 (tptp.mem tptp.tree _let_28 _let_25))) (let ((_let_86 (= _let_85 _let_62))) (let ((_let_87 (_let_8))) (let ((_let_88 (ASSUME :args _let_87))) (let 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(not _let_168) _let_167))) :args _let_50)) :args ((or _let_167 _let_169))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_207 (MODUS_PONENS (MODUS_PONENS (AND_INTRO _let_210 _let_211 _let_212 _let_213) (SCOPE (CONG (TRANS (SYMM (SYMM _let_213)) (CONG (TRANS (SYMM _let_212) (SYMM (SYMM _let_211))) :args (APPLY_UF tptp.node_proj_11)) (SYMM _let_210)) :args _let_120) :args (_let_174 _let_167 _let_176 _let_181))) (SCOPE (SYMM (ASSUME :args _let_209)) :args _let_209)) _let_208) :args (_let_167 _let_174 _let_180 _let_176 _let_181 _let_172)) (SCOPE (CONTRA _let_208 (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_208 (MACRO_SR_PRED_TRANSFORM (ASSUME :args (_let_204)) :args ((= (+ _let_164 _let_178) 0))) (MACRO_SR_PRED_TRANSFORM _let_207 :args ((< _let_170 0))) :args _let_206) :args _let_132) :args _let_205) :args ((< _let_179 1))) :args _let_203)) :args (_let_172 _let_204 _let_180)) :args ((not (and _let_167 _let_174 _let_180 _let_176 _let_181 _let_172)) SB_LITERAL))) (CONG (REFL :args (_let_168)) (REFL :args ((not _let_174))) (REFL :args _let_203) (REFL :args (_let_191)) (REFL :args ((not _let_181))) (MACRO_SR_PRED_INTRO :args ((= (not _let_172) _let_171))) :args _let_50)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_188 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_301 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_302 QUANTIFIERS_INST_CBQI_PROP)) :args _let_189)) _let_188 :args (_let_181 false _let_187)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_192 1)) (CONG _let_202 (MACRO_SR_PRED_INTRO :args ((= (not _let_190) _let_180))) :args _let_50)) :args ((or _let_180 _let_192))) _let_201 :args (_let_180 true _let_192)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_192 0)) (CONG _let_202 (MACRO_SR_PRED_INTRO :args ((= (not _let_191) _let_176))) :args _let_50)) :args ((or _let_176 _let_192))) _let_201 :args (_let_176 true _let_192)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_188 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_252 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_253 QUANTIFIERS_INST_CBQI_PROP)) :args _let_189)) _let_188 :args (_let_174 false _let_187)) (REORDERING (CNF_OR_POS :args (_let_173)) :args ((or _let_168 _let_172 (not _let_173)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_186 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_252 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_253 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_185)) :args _let_184))) _let_183 :args (_let_173 false _let_16)) :args (_let_168 false _let_181 false _let_180 false _let_176 false _let_174 true _let_171 false _let_173)) :args (_let_169 true _let_167)) :args (_let_158 false _let_169)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_163 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_95 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.size1 T)))) :args (_let_162)))) _let_163 :args (_let_161 false _let_162)) :args (_let_160 false _let_158 false _let_161)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_157 (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_SR_PRED_TRANSFORM (SCOPE (MACRO_SR_PRED_TRANSFORM (MACRO_ARITH_SCALE_SUM_UB _let_143 (MACRO_SR_PRED_TRANSFORM _let_157 :args (_let_152)) :args ((- 1.0) 1.0)) :args _let_132) :args _let_142) :args _let_147) :args _let_148) :args _let_156)) :args _let_156)) _let_155 :args (_let_55 false _let_18)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 0)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_10))) :args _let_50)) :args ((or _let_10 _let_46))) _let_53 :args (_let_10 true _let_46)) :args (false true _let_15 true _let_14 false _let_10)) :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 ((X Int) (Y Int) (Z Int)) (=> (<= X Y) (=> (<= 0 Z) (<= (* X Z) (* Y Z))))) (forall ((A tptp.ty)) (tptp.sort1 (tptp.list A) (tptp.nil A))) (forall ((A tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort1 (tptp.list A) (tptp.cons A X X1))) (forall ((A tptp.ty) (A1 tptp.ty) (X tptp.uni) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort1 A1 (tptp.match_list1 A1 A X X1 X2))) (forall ((A tptp.ty) (A1 tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort1 A1 Z) (= (tptp.match_list1 A1 A (tptp.nil A) Z Z1) Z))) (forall ((A tptp.ty) (A1 tptp.ty) (Z tptp.uni) (Z1 tptp.uni) (U tptp.uni) (U1 tptp.uni)) (=> (tptp.sort1 A1 Z1) (= (tptp.match_list1 A1 A (tptp.cons A U U1) Z Z1) Z1))) (forall ((A tptp.ty) (V tptp.uni) (V1 tptp.uni)) (not (= (tptp.nil A) (tptp.cons A V V1)))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 A (tptp.cons_proj_11 A X))) (forall ((A tptp.ty) (U tptp.uni) (U1 tptp.uni)) (=> (tptp.sort1 A U) (= (tptp.cons_proj_11 A (tptp.cons A U U1)) U))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.list A) (tptp.cons_proj_21 A X))) (forall ((A tptp.ty) (U tptp.uni) (U1 tptp.uni)) (= (tptp.cons_proj_21 A (tptp.cons A U U1)) U1)) (forall ((A tptp.ty) (U tptp.uni)) (or (= U (tptp.nil A)) (= U (tptp.cons A (tptp.cons_proj_11 A U) (tptp.cons_proj_21 A U))))) (forall ((A tptp.ty) (X tptp.uni)) (=> (tptp.sort1 A X) (and (not (tptp.mem A X (tptp.nil A))) (forall ((X1 tptp.uni) (X2 tptp.uni)) (=> (tptp.sort1 A X1) (= (tptp.mem A X (tptp.cons A X1 X2)) (or (= X X1) (tptp.mem A X X2)))))))) _let_9 (forall ((A tptp.ty) (L2 tptp.uni)) (and (= (tptp.infix_plpl A (tptp.nil A) L2) L2) (forall ((X tptp.uni) (X1 tptp.uni)) (= (tptp.infix_plpl A (tptp.cons A X X1) L2) (tptp.cons A X (tptp.infix_plpl A X1 L2)))))) (forall ((A tptp.ty) (L1 tptp.uni) (L2 tptp.uni) (L3 tptp.uni)) (= (tptp.infix_plpl A L1 (tptp.infix_plpl A L2 L3)) (tptp.infix_plpl A (tptp.infix_plpl A L1 L2) L3))) (forall ((A tptp.ty) (L tptp.uni)) (= (tptp.infix_plpl A L (tptp.nil A)) L)) (forall ((A tptp.ty)) (and (= (tptp.length2 A (tptp.nil A)) 0) (forall ((X tptp.uni) (X1 tptp.uni)) (= (tptp.length2 A (tptp.cons A X X1)) (+ 1 (tptp.length2 A X1)))))) (forall ((A tptp.ty) (L tptp.uni)) (<= 0 (tptp.length2 A L))) (forall ((A tptp.ty) (L tptp.uni)) (= (= (tptp.length2 A L) 0) (= L (tptp.nil A)))) (forall ((A tptp.ty) (L1 tptp.uni) (L2 tptp.uni)) (= (tptp.length2 A (tptp.infix_plpl A L1 L2)) (+ (tptp.length2 A L1) (tptp.length2 A L2)))) _let_8 (forall ((A tptp.ty) (X tptp.uni) (L tptp.uni)) (=> (tptp.mem A X L) (exists ((L1 tptp.uni) (L2 tptp.uni)) (let ((_let_1 (tptp.list A))) (and (tptp.sort1 _let_1 L1) (tptp.sort1 _let_1 L2) (= L (tptp.infix_plpl A L1 (tptp.cons A X L2)))))))) (forall ((A tptp.ty)) (tptp.distinct A (tptp.nil A))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.distinct A (tptp.cons A X (tptp.nil A)))) (forall ((A tptp.ty) (X tptp.uni) (L tptp.uni)) (=> (not (tptp.mem A X L)) (=> (tptp.distinct A L) (tptp.distinct A (tptp.cons A X L))))) (forall ((A tptp.ty) (Z tptp.uni)) (=> (tptp.distinct A Z) (or (= Z (tptp.nil A)) (exists ((X tptp.uni)) (and (tptp.sort1 A X) (= Z (tptp.cons A X (tptp.nil A))))) (exists ((X tptp.uni) (L tptp.uni)) (and (tptp.sort1 A X) (tptp.sort1 (tptp.list A) L) (not (tptp.mem A X L)) (tptp.distinct A L) (= Z (tptp.cons A X L))))))) (forall ((A tptp.ty) (L1 tptp.uni) (L2 tptp.uni)) (=> (tptp.distinct A L1) (=> (tptp.distinct A L2) (=> (forall ((X tptp.uni)) (=> (tptp.sort1 A X) (=> (tptp.mem A X L1) (not (tptp.mem A X L2))))) (tptp.distinct A (tptp.infix_plpl A L1 L2)))))) (forall ((A tptp.ty) (B tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort1 B (tptp.get B A X X1))) (forall ((A tptp.ty) (B tptp.ty) (X tptp.uni) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort1 (tptp.map A B) (tptp.set B A X X1 X2))) _let_7 (forall ((A tptp.ty) (B tptp.ty) (M tptp.uni) (A1 tptp.uni) (A2 tptp.uni)) (=> (tptp.sort1 A A1) (=> (tptp.sort1 A A2) (forall ((B1 tptp.uni)) (=> (not (= A1 A2)) (= (tptp.get B A (tptp.set B A M A1 B1) A2) (tptp.get B A M A2))))))) (forall ((A tptp.ty) (B tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.map A B) (tptp.const B A X))) (forall ((A tptp.ty) (B tptp.ty) (B1 tptp.uni) (A1 tptp.uni)) (=> (tptp.sort1 B B1) (= (tptp.get B A (tptp.const B A B1) A1) B1))) (forall ((A tptp.ty) (X Int) (X1 tptp.uni)) (tptp.sort1 (tptp.array A) (tptp.mk_array1 A X X1))) (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (= (tptp.length3 A (tptp.mk_array1 A U U1)) U)) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.map tptp.int A) (tptp.elts A X))) (forall ((A tptp.ty) (U Int) (U1 tptp.uni)) (=> (tptp.sort1 (tptp.map tptp.int A) U1) (= (tptp.elts A (tptp.mk_array1 A U U1)) U1))) (forall ((A tptp.ty) (U tptp.uni)) (= U (tptp.mk_array1 A (tptp.length3 A U) (tptp.elts A U)))) (forall ((A tptp.ty) (X tptp.uni) (X1 Int)) (tptp.sort1 A (tptp.get2 A X X1))) (forall ((X Int)) (tptp.sort1 tptp.int (tptp.t2tb X))) (forall ((I Int)) (= (tptp.tb2t (tptp.t2tb I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb (tptp.tb2t J)) J)) (forall ((A tptp.ty) (A1 tptp.uni) (I Int)) (= (tptp.get2 A A1 I) (tptp.get A tptp.int (tptp.elts A A1) (tptp.t2tb I)))) (forall ((A tptp.ty) (X tptp.uni) (X1 Int) (X2 tptp.uni)) (tptp.sort1 (tptp.array A) (tptp.set2 A X X1 X2))) (forall ((A tptp.ty) (A1 tptp.uni) (I Int) (V tptp.uni)) (= (tptp.set2 A A1 I V) (tptp.mk_array1 A (tptp.length3 A A1) (tptp.set A tptp.int (tptp.elts A A1) (tptp.t2tb I) V)))) (forall ((A tptp.ty) (X Int) (X1 tptp.uni)) (tptp.sort1 (tptp.array A) (tptp.make1 A X X1))) (forall ((A tptp.ty) (N Int) (V tptp.uni)) (= (tptp.make1 A N V) (tptp.mk_array1 A N (tptp.const A tptp.int V)))) (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.empty1 Z Z1) Z))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni) (U tptp.tree1) (U1 tptp.tree1)) (=> (tptp.sort1 A Z1) (= (tptp.match_tree1 A (tptp.node1 U U1) Z Z1) Z1))) (forall ((V tptp.tree1) (V1 tptp.tree1)) (not (= tptp.empty1 (tptp.node1 V V1)))) _let_6 (forall ((U tptp.tree1) (U1 tptp.tree1)) (= (tptp.node_proj_21 (tptp.node1 U U1)) U1)) (forall ((U tptp.tree1)) (or (= U tptp.empty1) (= U (tptp.node1 (tptp.node_proj_11 U) (tptp.node_proj_21 U))))) _let_5 (forall ((T tptp.tree1)) (<= 0 (tptp.size1 T))) _let_3 (forall ((X tptp.list_tree)) (tptp.sort1 (tptp.list tptp.tree) (tptp.t2tb1 X))) (forall ((I tptp.list_tree)) (= (tptp.tb2t1 (tptp.t2tb1 I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb1 (tptp.tb2t1 J)) J)) (forall ((X tptp.tree1)) (tptp.sort1 tptp.tree (tptp.t2tb2 X))) (forall ((I tptp.tree1)) (= (tptp.tb2t2 (tptp.t2tb2 I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb2 (tptp.tb2t2 J)) J)) (forall ((N Int) (L tptp.list_tree)) (= (tptp.all_trees1 N L) (and (tptp.distinct tptp.tree (tptp.t2tb1 L)) (forall ((T tptp.tree1)) (= (= (tptp.size1 T) N) (tptp.mem tptp.tree (tptp.t2tb2 T) (tptp.t2tb1 L))))))) (tptp.all_trees1 0 (tptp.tb2t1 (tptp.cons tptp.tree (tptp.t2tb2 tptp.empty1) (tptp.nil tptp.tree)))) (forall ((L1 tptp.tree1) (L2 tptp.tree1)) (=> (not (= (tptp.size1 L1) (tptp.size1 L2))) (forall ((R1 tptp.tree1) (R2 tptp.tree1)) (not (= (tptp.node1 L1 R1) (tptp.node1 L2 R2)))))) (forall ((X tptp.map_int_lplist_treerp)) (tptp.sort1 (tptp.map tptp.int (tptp.list tptp.tree)) (tptp.t2tb3 X))) (forall ((I tptp.map_int_lplist_treerp)) (= (tptp.tb2t3 (tptp.t2tb3 I)) I)) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 46.52/46.86 )
% 46.52/46.86 % SZS output end Proof for SWW602_2
% 46.52/46.86 % cvc5---1.0.5 exiting
% 46.52/46.86 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------