0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : princess-casc +printProof -timeout=%d %s 0.02/0.25 % Computer : n024.star.cs.uiowa.edu 0.02/0.25 % Model : x86_64 x86_64 0.02/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.25 % Memory : 32218.625MB 0.02/0.25 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.25 % CPULimit : 300 0.02/0.25 % DateTime : Sat Jul 14 04:27:09 CDT 2018 0.02/0.26 % CPUTime : 0.06/0.48 ________ _____ 0.06/0.48 ___ __ \_________(_)________________________________ 0.06/0.48 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ 0.06/0.48 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) 0.06/0.48 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ 0.06/0.48 0.06/0.48 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic 0.06/0.48 (CASC 2017-07-17) 0.06/0.48 0.06/0.48 (c) Philipp Rümmer, 2009-2017 0.06/0.48 (contributions by Peter Backeman, Peter Baumgartner, 0.06/0.48 Angelo Brillout, Aleksandar Zeljic) 0.06/0.48 Free software under GNU Lesser General Public License (LGPL). 0.06/0.48 Bug reports to ph_r@gmx.net 0.06/0.48 0.06/0.48 For more information, visit http://www.philipp.ruemmer.org/princess.shtml 0.06/0.48 0.06/0.48 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... 0.06/0.51 Prover 0: Options: +triggersInConjecture -genTotalityAxioms=ctors +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=off 1.93/1.17 Prover 0: Warning: using theory to encode multiplication: GroebnerMultiplication 1.93/1.17 Prover 0: Preprocessing ... 5.52/2.14 Prover 0: Proving ... 12.71/4.35 Prover 1: Options: +triggersInConjecture -genTotalityAxioms=none -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=off 13.26/4.50 Prover 1: Warning: using theory to encode multiplication: GroebnerMultiplication 13.26/4.51 Prover 1: Preprocessing ... 13.91/4.74 Prover 1: Warning: ignoring some quantifiers 14.05/4.83 Prover 1: Constructing countermodel ... 42.86/14.02 Prover 1: Found proof (size 1515) 42.86/14.02 Prover 1: proved (9673ms) 42.86/14.03 Prover 0: stopped 42.86/14.03 42.86/14.03 VALID 42.86/14.03 % SZS status Theorem for theBenchmark 42.86/14.03 43.25/14.11 % SZS output start Proof for theBenchmark 43.25/14.12 Assumptions after simplification: 43.25/14.12 --------------------------------- 43.25/14.12 43.25/14.12 (all_trees_0) 43.25/14.14 in_tree1(empty1) & in_ty(tree) & ? [v0: $int] : ? [v1: $int] : ? [v2: $int] 43.25/14.14 : ? [v3: $int] : (tb2t1(v2) = v3 & all_trees1(0, v3) = 0 & t2tb2(empty1) = v0 43.25/14.14 & nil(tree) = v1 & cons(tree, v0, v1) = v2 & in_list_tree(v3) & in_uni(v2) & 43.25/14.14 in_uni(v1) & in_uni(v0)) 43.25/14.14 43.25/14.14 (all_trees_def) 43.25/14.15 in_ty(tree) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v2 = 0 | ~ 43.25/14.15 (all_trees1(v0, v1) = v2) | ~ in_list_tree(v1) | ? [v3: $int] : ? [v4: 43.25/14.15 $int] : (t2tb1(v1) = v3 & distinct(tree, v3) = v4 & in_uni(v3) & ( ~ (v4 = 43.25/14.15 0) | ? [v5: $int] : ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : 43.25/14.15 (t2tb2(v5) = v6 & size1(v5) = v8 & mem(tree, v6, v3) = v7 & in_tree1(v5) 43.25/14.15 & in_uni(v6) & ( ~ (v8 = v0) | ~ (v7 = 0)) & (v8 = v0 | v7 = 0))))) & 43.25/14.15 ! [v0: $int] : ! [v1: $int] : ( ~ (all_trees1(v0, v1) = 0) | ~ 43.25/14.15 in_list_tree(v1) | ? [v2: $int] : (t2tb1(v1) = v2 & distinct(tree, v2) = 0 43.25/14.15 & in_uni(v2) & ! [v3: $int] : ! [v4: $int] : ! [v5: $int] : (v5 = 0 | 43.25/14.15 ~ (t2tb2(v3) = v4) | ~ (mem(tree, v4, v2) = v5) | ~ in_tree1(v3) | ? 43.25/14.15 [v6: $int] : ( ~ (v6 = v0) & size1(v3) = v6)) & ! [v3: $int] : ! [v4: 43.25/14.15 $int] : ( ~ (t2tb2(v3) = v4) | ~ (mem(tree, v4, v2) = 0) | ~ 43.25/14.15 in_tree1(v3) | size1(v3) = v0))) 43.25/14.15 43.25/14.15 (append_l_nil) 43.25/14.15 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v3 = v1 | ~ 43.25/14.15 (infix_plpl(v0, v1, v2) = v3) | ~ (nil(v0) = v2) | ~ in_ty(v0)) 43.25/14.15 43.25/14.15 (bridgeL) 43.25/14.15 ! [v0: $int] : ! [v1: $int] : ( ~ (t2tb(v0) = v1) | tb2t(v1) = v0) 43.25/14.15 43.25/14.15 (bridgeR1) 43.25/14.15 ! [v0: $int] : ! [v1: $int] : ( ~ (tb2t1(v0) = v1) | ~ in_uni(v0) | 43.25/14.15 t2tb1(v1) = v0) 43.25/14.15 43.25/14.15 (bridgeR3) 43.25/14.15 ! [v0: $int] : ! [v1: $int] : ( ~ (tb2t3(v0) = v1) | ~ in_uni(v0) | 43.25/14.15 t2tb3(v1) = v0) 43.25/14.15 43.25/14.15 (distinct_inversion) 43.40/14.16 ! [v0: $int] : ! [v1: $int] : ( ~ (distinct(v0, v1) = 0) | ~ in_ty(v0) | ? 43.40/14.16 [v2: $int] : ? [v3: $int] : (list(v0) = v3 & nil(v0) = v2 & in_ty(v3) & 43.40/14.16 in_uni(v2) & (v2 = v1 | ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : ( 43.40/14.16 ~ (v6 = 0) & distinct(v0, v5) = 0 & cons(v0, v4, v5) = v1 & mem(v0, 43.40/14.16 v4, v5) = v6 & sort1(v3, v5) = 0 & sort1(v0, v4) = 0 & in_uni(v5) & 43.40/14.16 in_uni(v4) & in_uni(v1)) | ? [v4: $int] : (cons(v0, v4, v2) = v1 & 43.40/14.16 sort1(v0, v4) = 0 & in_uni(v4) & in_uni(v1))))) 43.40/14.16 43.40/14.16 (infix_plpl_sort2) 43.40/14.16 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] 43.40/14.16 : ! [v5: $int] : (v5 = 0 | ~ (infix_plpl(v0, v1, v2) = v4) | ~ (list(v0) = 43.40/14.16 v3) | ~ (sort1(v3, v4) = v5) | ~ in_ty(v0)) 43.40/14.16 43.40/14.16 (mem_append) 43.40/14.16 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] 43.40/14.16 : ! [v5: $int] : (v5 = 0 | ~ (infix_plpl(v0, v2, v3) = v4) | ~ (mem(v0, v1, 43.40/14.16 v4) = v5) | ~ in_ty(v0) | ? [v6: $int] : ? [v7: $int] : ( ~ (v7 = 0) 43.40/14.16 & ~ (v6 = 0) & mem(v0, v1, v3) = v6 & mem(v0, v1, v2) = v7)) & ! [v0: 43.40/14.16 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ( ~ 43.40/14.16 (infix_plpl(v0, v2, v3) = v4) | ~ (mem(v0, v1, v4) = 0) | ~ in_ty(v0) | ? 43.40/14.16 [v5: $int] : ? [v6: $int] : (mem(v0, v1, v3) = v5 & mem(v0, v1, v2) = v6 & 43.40/14.16 (v6 = 0 | v5 = 0))) 43.40/14.16 43.40/14.16 (mem_decomp) 43.40/14.16 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ (mem(v0, v1, v2) = 0) | ~ 43.40/14.16 in_ty(v0) | ? [v3: $int] : (list(v0) = v3 & in_ty(v3) & ? [v4: $int] : ? 43.40/14.16 [v5: $int] : ? [v6: $int] : (infix_plpl(v0, v4, v6) = v2 & cons(v0, v1, 43.40/14.16 v5) = v6 & sort1(v3, v5) = 0 & sort1(v3, v4) = 0 & in_uni(v6) & 43.40/14.16 in_uni(v5) & in_uni(v4) & in_uni(v2)))) 43.40/14.16 43.40/14.16 (nil_Cons1) 43.40/14.16 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ( ~ (cons(v0, 43.40/14.16 v1, v2) = v3) | ~ in_ty(v0) | ? [v4: $int] : ( ~ (v4 = v3) & nil(v0) = 43.40/14.16 v4 & in_uni(v4))) 43.40/14.16 43.40/14.16 (node_proj_1_def1) 43.40/14.16 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ (node1(v0, v1) = v2) | ~ 43.40/14.16 in_tree1(v0) | node_proj_11(v2) = v0) 43.40/14.16 43.40/14.16 (node_proj_2_def1) 43.40/14.16 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ (node1(v0, v1) = v2) | ~ 43.40/14.16 in_tree1(v0) | (node_proj_21(v2) = v1 & in_tree1(v1))) 43.40/14.16 43.40/14.16 (select_eq) 43.40/14.16 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] 43.40/14.16 : ! [v5: $int] : ! [v6: $int] : (v6 = v4 | ~ (set(v1, v0, v2, v3, v4) = v5) 43.40/14.16 | ~ (get(v1, v0, v5, v3) = v6) | ~ in_ty(v0) | ? [v7: $int] : ( ~ (v7 = 43.40/14.16 0) & sort1(v1, v4) = v7)) 43.40/14.16 43.40/14.16 (select_neq) 43.40/14.18 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] 43.40/14.18 : ! [v5: $int] : ( ~ (get(v1, v0, v2, v4) = v5) | ~ (sort1(v0, v3) = 0) | ~ 43.40/14.18 in_ty(v0) | ? [v6: $int] : ( ~ (v6 = 0) & sort1(v0, v4) = v6) | ! [v6: 43.40/14.18 $int] : ! [v7: $int] : ! [v8: $int] : (v8 = v5 | v4 = v3 | ~ (set(v1, 43.40/14.18 v0, v2, v3, v6) = v7) | ~ (get(v1, v0, v7, v4) = v8) | ~ 43.40/14.18 in_uni(v6))) 43.40/14.18 43.40/14.18 (size_def) 43.40/14.18 size1(empty1) = 0 & in_tree1(empty1) & ! [v0: $int] : ! [v1: $int] : ! [v2: 43.40/14.18 $int] : ( ~ (node1(v0, v1) = v2) | ~ in_tree1(v0) | ? [v3: $int] : ? [v4: 43.40/14.18 $int] : (size1(v2) = v3 & $sum(size1(v1), $product(-1, 43.40/14.18 $sum($difference(v3, v4), -1))) = 0 & size1(v0) = v4)) 43.40/14.18 43.40/14.18 (size_left) 43.40/14.18 ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(1, v1)) | ~ (size1(v0) = v1) | 43.40/14.18 ~ in_tree1(v0) | ? [v2: $int] : ? [v3: $int] : ? [v4: $int] : ($lesseq(1, 43.40/14.18 $difference(v1, v4)) & node1(v2, v3) = v0 & size1(v2) = v4 & 43.40/14.18 in_tree1(v3) & in_tree1(v2))) 43.40/14.18 43.40/14.18 (size_nonneg) 43.40/14.18 ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v1, -1)) | ~ (size1(v0) = v1) | 43.40/14.18 ~ in_tree1(v0)) 43.40/14.18 43.40/14.18 (t2tb_sort3) 43.40/14.18 in_ty(int) & ! [v0: $int] : ! [v1: $int] : ( ~ (t2tb(v0) = v1) | sort1(int, 43.40/14.18 v1) = 0) 43.40/14.18 43.40/14.18 (t2tb_sort4) 43.40/14.18 in_ty(tree) & ? [v0: $int] : (list(tree) = v0 & in_ty(v0) & ! [v1: $int] : 43.40/14.18 ! [v2: $int] : ( ~ (t2tb1(v1) = v2) | ~ in_list_tree(v1) | sort1(v0, v2) = 43.40/14.18 0)) 43.40/14.18 43.40/14.18 (t2tb_sort6) 43.40/14.18 in_ty(tree) & in_ty(int) & ? [v0: $int] : ? [v1: $int] : (list(tree) = v0 & 43.40/14.18 map(int, v0) = v1 & in_ty(v1) & in_ty(v0) & ! [v2: $int] : ! [v3: $int] : 43.40/14.18 ( ~ (t2tb3(v2) = v3) | ~ in_map_int_lplist_treerp(v2) | sort1(v1, v3) = 0)) 43.40/14.18 43.40/14.18 (tree_diff) 43.40/14.18 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v3 = v2 | ~ 43.40/14.18 (size1(v1) = v3) | ~ (size1(v0) = v2) | ~ in_tree1(v0) | ! [v4: $int] : 43.40/14.18 ! [v5: $int] : ! [v6: $int] : ( ~ (node1(v1, v5) = v6) | ~ (node1(v0, v4) 43.40/14.18 = v6) | ~ in_tree1(v4))) 43.40/14.18 43.40/14.18 (wP_parameter_all_trees) 43.40/14.19 in_tree1(empty1) & in_ty(tree) & in_ty(int) & ? [v0: $int] : ? [v1: $int] : 43.40/14.19 ? [v2: $int] : ? [v3: $int] : ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : 43.40/14.19 ? [v7: $int] : (t2tb(0) = v3 & set(v0, int, v2, v3, v5) = v6 & const(v0, int, 43.40/14.19 v1) = v2 & list(tree) = v0 & tb2t3(v6) = v7 & t2tb2(empty1) = v4 & 43.40/14.19 nil(tree) = v1 & cons(tree, v4, v1) = v5 & in_map_int_lplist_treerp(v7) & 43.40/14.19 in_ty(v0) & in_uni(v6) & in_uni(v5) & in_uni(v4) & in_uni(v3) & in_uni(v2) & 43.40/14.19 in_uni(v1) & ? [v8: $int] : ($lesseq(1, v8) & ? [v9: $int] : ? [v10: 43.40/14.19 $int] : ? [v11: $int] : ? [v12: $int] : ? [v13: $int] : ? [v14: 43.40/14.19 $int] : ($lesseq(v10, v8) & $lesseq(1, v10) & t2tb(v10) = v12 & set(v0, 43.40/14.19 int, v11, v12, v1) = v13 & t2tb3(v9) = v11 & tb2t3(v13) = v14 & 43.40/14.19 in_map_int_lplist_treerp(v14) & in_map_int_lplist_treerp(v9) & 43.40/14.19 in_uni(v13) & in_uni(v12) & in_uni(v11) & ! [v15: $int] : ! [v16: 43.40/14.19 $int] : ! [v17: $int] : ! [v18: $int] : ! [v19: $int] : (v19 = 0 | 43.40/14.19 ~ ($lesseq(1, $difference(v10, v15))) | ~ ($lesseq(0, v15)) | ~ 43.40/14.19 (t2tb(v15) = v16) | ~ (get(v0, int, v11, v16) = v17) | ~ (tb2t1(v17) 43.40/14.19 = v18) | ~ (all_trees1(v15, v18) = v19)) & ? [v15: $int] : ? 43.40/14.19 [v16: $int] : ? [v17: $int] : ? [v18: $int] : ? [v19: $int] : ? 43.40/14.19 [v20: $int] : ? [v21: $int] : ? [v22: $int] : ? [v23: $int] : ? 43.40/14.19 [v24: $int] : ($lesseq(1, $difference(v10, v16)) & $lesseq(v16, v8) & 43.40/14.19 $lesseq(-1, $sum($difference(v16, v10), v8)) & $lesseq(0, v16) & 43.40/14.19 t2tb($sum($difference(v10, v16), -1)) = v22 & t2tb(v16) = v19 & 43.40/14.19 get(v0, int, v17, v22) = v23 & get(v0, int, v17, v19) = v20 & get(v0, 43.40/14.19 int, v17, v12) = v18 & t2tb3(v15) = v17 & tb2t1(v23) = v24 & 43.40/14.19 tb2t1(v20) = v21 & all_trees1($sum($difference(v10, v16), -1), v24) = 43.40/14.19 0 & all_trees1(v16, v21) = 0 & distinct(tree, v18) = 0 & 43.40/14.19 in_map_int_lplist_treerp(v15) & in_list_tree(v24) & in_list_tree(v21) 43.40/14.19 & in_uni(v23) & in_uni(v22) & in_uni(v20) & in_uni(v19) & in_uni(v18) 43.40/14.19 & in_uni(v17) & ! [v25: $int] : ! [v26: $int] : ! [v27: $int] : ! 43.40/14.19 [v28: $int] : ! [v29: $int] : (v29 = 0 | ~ ($lesseq(1, 43.40/14.19 $difference(v10, v25))) | ~ ($lesseq(0, v25)) | ~ (t2tb(v25) = 43.40/14.19 v26) | ~ (get(v0, int, v17, v26) = v27) | ~ (tb2t1(v27) = v28) | 43.40/14.19 ~ (all_trees1(v25, v28) = v29)) & ! [v25: $int] : ! [v26: $int] : 43.40/14.19 ! [v27: $int] : (v27 = 0 | ~ (t2tb2(v25) = v26) | ~ (mem(tree, v26, 43.40/14.19 v18) = v27) | ~ in_tree1(v25) | ? [v28: $int] : (size1(v25) = 43.40/14.19 v28 & ! [v29: $int] : ! [v30: $int] : ( ~ (v28 = v10) | ~ 43.40/14.19 (node1(v29, v30) = v25) | ~ in_tree1(v29) | ? [v31: $int] : 43.40/14.19 ($lesseq(v16, v31) & size1(v29) = v31)))) & ! [v25: $int] : ! 43.40/14.19 [v26: $int] : ( ~ (t2tb2(v25) = v26) | ~ (mem(tree, v26, v18) = 0) | 43.40/14.19 ~ in_tree1(v25) | ? [v27: $int] : (size1(v25) = v27 & ? [v28: 43.40/14.19 $int] : ? [v29: $int] : ? [v30: $int] : (v27 = v10 & 43.40/14.19 $lesseq(1, $difference(v16, v30)) & node1(v28, v29) = v25 & 43.40/14.19 size1(v28) = v30 & in_tree1(v29) & in_tree1(v28)))) & ? [v25: 43.40/14.19 $int] : ? [v26: $int] : ? [v27: $int] : ? [v28: $int] : ? [v29: 43.40/14.19 $int] : (set(v0, int, v17, v12, v27) = v28 & infix_plpl(tree, v26, 43.40/14.19 v18) = v27 & tb2t3(v28) = v29 & t2tb1(v25) = v26 & distinct(tree, 43.40/14.19 v26) = 0 & in_map_int_lplist_treerp(v29) & in_list_tree(v25) & 43.40/14.19 in_uni(v28) & in_uni(v27) & in_uni(v26) & ! [v30: $int] : ! [v31: 43.40/14.19 $int] : ! [v32: $int] : (v32 = 0 | ~ (t2tb2(v30) = v31) | ~ 43.40/14.19 (mem(tree, v31, v26) = v32) | ~ in_tree1(v30) | ! [v33: $int] : 43.40/14.19 ! [v34: $int] : ( ~ (node1(v33, v34) = v30) | ~ in_tree1(v33) | 43.40/14.19 ? [v35: $int] : ? [v36: $int] : (size1(v34) = v36 & size1(v33) 43.40/14.19 = v35 & ( ~ ($difference($sum(v36, v16), v10) = -1) | ~ (v35 43.40/14.19 = v16))))) & ! [v30: $int] : ! [v31: $int] : ( ~ 43.40/14.19 (t2tb2(v30) = v31) | ~ (mem(tree, v31, v26) = 0) | ~ 43.40/14.19 in_tree1(v30) | ? [v32: $int] : ? [v33: $int] : (node1(v32, v33) 43.40/14.19 = v30 & $sum(size1(v33), $product(-1, $sum($difference(v10, 43.40/14.19 v16), -1))) = 0 & size1(v32) = v16 & in_tree1(v33) & 43.40/14.19 in_tree1(v32))) & ? [v30: $int] : ? [v31: $int] : (get(v0, 43.40/14.19 int, v30, v12) = v31 & t2tb3(v29) = v30 & in_uni(v31) & 43.40/14.19 in_uni(v30) & ? [v32: $int] : ? [v33: $int] : ? [v34: $int] : 43.40/14.19 (t2tb2(v32) = v33 & size1(v32) = v34 & mem(tree, v33, v31) = 0 & 43.40/14.19 in_tree1(v32) & in_uni(v33) & ! [v35: $int] : ! [v36: $int] : 43.40/14.19 ( ~ (v34 = v10) | ~ (node1(v35, v36) = v32) | ~ in_tree1(v35) 43.40/14.20 | ? [v37: $int] : ($lesseq(1, $difference(v37, v16)) & 43.40/14.20 size1(v35) = v37))))))))) 43.40/14.20 43.40/14.20 (axioms) 43.40/14.20 in_map_int_lplist_treerp(constant_in_map_int_lplist_treerp) & 43.40/14.20 in_list_tree(constant_in_list_tree) & in_uni(constant_in_uni) & ! [v0: $int] 43.40/14.20 : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: 43.40/14.20 $int] : ! [v6: $int] : (v1 = v0 | ~ (match_list1(v6, v5, v4, v3, v2) = v1) 43.40/14.20 | ~ (match_list1(v6, v5, v4, v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] 43.40/14.20 : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: $int] : ! [v6: 43.40/14.20 $int] : (v1 = v0 | ~ (set(v6, v5, v4, v3, v2) = v1) | ~ (set(v6, v5, v4, 43.40/14.20 v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: 43.40/14.21 $int] : ! [v4: $int] : ! [v5: $int] : (v1 = v0 | ~ (match_tree1(v5, v4, 43.40/14.21 v3, v2) = v1) | ~ (match_tree1(v5, v4, v3, v2) = v0)) & ! [v0: $int] : 43.40/14.21 ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: $int] 43.40/14.21 : (v1 = v0 | ~ (match_bool1(v5, v4, v3, v2) = v1) | ~ (match_bool1(v5, v4, 43.40/14.21 v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: 43.40/14.21 $int] : ! [v4: $int] : ! [v5: $int] : (v1 = v0 | ~ (set2(v5, v4, v3, v2) 43.40/14.21 = v1) | ~ (set2(v5, v4, v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : 43.40/14.21 ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : ! [v5: $int] : (v1 = v0 | ~ 43.40/14.21 (get(v5, v4, v3, v2) = v1) | ~ (get(v5, v4, v3, v2) = v0)) & ! [v0: $int] 43.40/14.21 : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : (v1 = v0 | 43.40/14.21 ~ (get2(v4, v3, v2) = v1) | ~ (get2(v4, v3, v2) = v0)) & ! [v0: $int] : ! 43.40/14.21 [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : (v1 = v0 | ~ 43.40/14.21 (const(v4, v3, v2) = v1) | ~ (const(v4, v3, v2) = v0)) & ! [v0: $int] : ! 43.40/14.21 [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : (v1 = v0 | ~ 43.40/14.21 (make1(v4, v3, v2) = v1) | ~ (make1(v4, v3, v2) = v0)) & ! [v0: $int] : ! 43.40/14.21 [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : (v1 = v0 | ~ 43.40/14.21 (infix_plpl(v4, v3, v2) = v1) | ~ (infix_plpl(v4, v3, v2) = v0)) & ! [v0: 43.40/14.21 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : (v1 43.40/14.21 = v0 | ~ (cons(v4, v3, v2) = v1) | ~ (cons(v4, v3, v2) = v0)) & ! [v0: 43.40/14.21 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : (v1 43.40/14.21 = v0 | ~ (mem(v4, v3, v2) = v1) | ~ (mem(v4, v3, v2) = v0)) & ! [v0: 43.40/14.21 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : (v1 43.40/14.21 = v0 | ~ (mk_array1(v4, v3, v2) = v1) | ~ (mk_array1(v4, v3, v2) = v0)) & 43.40/14.21 ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 43.40/14.21 (cons_proj_11(v3, v2) = v1) | ~ (cons_proj_11(v3, v2) = v0)) & ! [v0: 43.40/14.21 $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 43.40/14.21 (length2(v3, v2) = v1) | ~ (length2(v3, v2) = v0)) & ! [v0: $int] : ! 43.40/14.21 [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ (cons_proj_21(v3, 43.40/14.21 v2) = v1) | ~ (cons_proj_21(v3, v2) = v0)) & ! [v0: $int] : ! [v1: 43.40/14.21 $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ (length3(v3, v2) = v1) 43.40/14.21 | ~ (length3(v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] 43.40/14.21 : ! [v3: $int] : (v1 = v0 | ~ (node1(v3, v2) = v1) | ~ (node1(v3, v2) = 43.40/14.21 v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 43.40/14.21 = v0 | ~ (all_trees1(v3, v2) = v1) | ~ (all_trees1(v3, v2) = v0)) & ! 43.40/14.21 [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 43.40/14.21 (distinct(v3, v2) = v1) | ~ (distinct(v3, v2) = v0)) & ! [v0: $int] : ! 43.40/14.21 [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ (elts(v3, v2) = v1) 43.40/14.21 | ~ (elts(v3, v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : 43.40/14.21 ! [v3: $int] : (v1 = v0 | ~ (map(v3, v2) = v1) | ~ (map(v3, v2) = v0)) & ! 43.40/14.21 [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 | ~ 43.40/14.21 (sort1(v3, v2) = v1) | ~ (sort1(v3, v2) = v0)) & ! [v0: $int] : ! [v1: 43.40/14.21 $int] : ! [v2: $int] : (v1 = v0 | ~ (witness1(v2) = v1) | ~ (witness1(v2) 43.40/14.21 = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 43.40/14.21 (node_proj_21(v2) = v1) | ~ (node_proj_21(v2) = v0)) & ! [v0: $int] : ! 43.40/14.21 [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t(v2) = v1) | ~ (tb2t(v2) = 43.40/14.21 v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 43.40/14.21 (node_proj_11(v2) = v1) | ~ (node_proj_11(v2) = v0)) & ! [v0: $int] : ! 43.40/14.21 [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (array(v2) = v1) | ~ (array(v2) = 43.40/14.21 v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 43.40/14.21 (tb2t2(v2) = v1) | ~ (tb2t2(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! 43.40/14.21 [v2: $int] : (v1 = v0 | ~ (t2tb(v2) = v1) | ~ (t2tb(v2) = v0)) & ! [v0: 43.40/14.21 $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (list(v2) = v1) | ~ 43.40/14.21 (list(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 43.40/14.21 | ~ (t2tb3(v2) = v1) | ~ (t2tb3(v2) = v0)) & ! [v0: $int] : ! [v1: $int] 43.40/14.21 : ! [v2: $int] : (v1 = v0 | ~ (tb2t3(v2) = v1) | ~ (tb2t3(v2) = v0)) & ! 43.40/14.21 [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (tb2t1(v2) = v1) | 43.40/14.21 ~ (tb2t1(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = 43.40/14.21 v0 | ~ (t2tb1(v2) = v1) | ~ (t2tb1(v2) = v0)) & ! [v0: $int] : ! [v1: 43.40/14.21 $int] : ! [v2: $int] : (v1 = v0 | ~ (t2tb2(v2) = v1) | ~ (t2tb2(v2) = 43.40/14.21 v0)) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 43.40/14.21 (size1(v2) = v1) | ~ (size1(v2) = v0)) & ! [v0: $int] : ! [v1: $int] : ! 43.40/14.21 [v2: $int] : (v1 = v0 | ~ (nil(v2) = v1) | ~ (nil(v2) = v0)) 43.40/14.21 43.40/14.21 Further assumptions not needed in the proof: 43.40/14.21 -------------------------------------------- 43.40/14.21 append_assoc, append_length, array_inversion1, bool_inversion, bridgeL1, 43.40/14.21 bridgeL2, bridgeL3, bridgeR, bridgeR2, compatOrderMult, cons_proj_1_def1, 43.40/14.21 cons_proj_1_sort2, cons_proj_2_def1, cons_proj_2_sort2, cons_sort2, const, 43.40/14.21 const_sort2, distinct_append, distinct_many, distinct_one, distinct_zero, 43.40/14.21 elts_def1, elts_sort2, empty_Node1, get_def, get_sort4, get_sort5, 43.40/14.21 infix_plpl_def, length_def, length_def2, length_nil, length_nonnegative, 43.40/14.21 list_inversion1, make_def, make_sort2, match_bool_False, match_bool_True, 43.40/14.21 match_bool_sort2, match_list_Cons1, match_list_Nil1, match_list_sort2, 43.40/14.21 match_tree_Empty1, match_tree_Node1, match_tree_sort2, mem_def, mk_array_sort2, 43.40/14.21 nil_sort2, set_def, set_sort4, set_sort5, t2tb_sort5, tree_inversion1, 43.40/14.21 true_False, tuple0_inversion, witness_sort1 43.40/14.21 43.40/14.21 Those formulas are unsatisfiable: 43.40/14.21 --------------------------------- 43.40/14.21 43.40/14.21 Begin of proof 43.40/14.21 | 43.40/14.21 | ALPHA: (all_trees_def) implies: 43.40/14.22 | (1) ! [v0: $int] : ! [v1: $int] : ( ~ (all_trees1(v0, v1) = 0) | ~ 43.40/14.22 | in_list_tree(v1) | ? [v2: $int] : (t2tb1(v1) = v2 & distinct(tree, 43.40/14.22 | v2) = 0 & in_uni(v2) & ! [v3: $int] : ! [v4: $int] : ! [v5: 43.40/14.22 | $int] : (v5 = 0 | ~ (t2tb2(v3) = v4) | ~ (mem(tree, v4, v2) = 43.40/14.22 | v5) | ~ in_tree1(v3) | ? [v6: $int] : ( ~ (v6 = v0) & 43.40/14.22 | size1(v3) = v6)) & ! [v3: $int] : ! [v4: $int] : ( ~ 43.40/14.22 | (t2tb2(v3) = v4) | ~ (mem(tree, v4, v2) = 0) | ~ in_tree1(v3) | 43.40/14.22 | size1(v3) = v0))) 43.40/14.22 | 43.40/14.22 | ALPHA: (all_trees_0) implies: 43.40/14.22 | (2) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : 43.40/14.22 | (tb2t1(v2) = v3 & all_trees1(0, v3) = 0 & t2tb2(empty1) = v0 & 43.40/14.22 | nil(tree) = v1 & cons(tree, v0, v1) = v2 & in_list_tree(v3) & 43.40/14.22 | in_uni(v2) & in_uni(v1) & in_uni(v0)) 43.40/14.22 | 43.40/14.22 | ALPHA: (t2tb_sort4) implies: 43.40/14.22 | (3) ? [v0: $int] : (list(tree) = v0 & in_ty(v0) & ! [v1: $int] : ! [v2: 43.40/14.22 | $int] : ( ~ (t2tb1(v1) = v2) | ~ in_list_tree(v1) | sort1(v0, v2) 43.40/14.22 | = 0)) 43.40/14.22 | 43.40/14.22 | ALPHA: (size_def) implies: 43.40/14.22 | (4) size1(empty1) = 0 43.40/14.22 | (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ (node1(v0, v1) = 43.40/14.22 | v2) | ~ in_tree1(v0) | ? [v3: $int] : ? [v4: $int] : (size1(v2) 43.40/14.22 | = v3 & $sum(size1(v1), $product(-1, $sum($difference(v3, v4), -1))) 43.40/14.22 | = 0 & size1(v0) = v4)) 43.40/14.22 | 43.40/14.22 | ALPHA: (t2tb_sort6) implies: 43.40/14.22 | (6) ? [v0: $int] : ? [v1: $int] : (list(tree) = v0 & map(int, v0) = v1 & 43.40/14.22 | in_ty(v1) & in_ty(v0) & ! [v2: $int] : ! [v3: $int] : ( ~ 43.40/14.22 | (t2tb3(v2) = v3) | ~ in_map_int_lplist_treerp(v2) | sort1(v1, v3) 43.40/14.22 | = 0)) 43.40/14.22 | 43.40/14.22 | ALPHA: (mem_append) implies: 43.40/14.22 | (7) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 43.40/14.22 | $int] : ( ~ (infix_plpl(v0, v2, v3) = v4) | ~ (mem(v0, v1, v4) = 0) 43.40/14.22 | | ~ in_ty(v0) | ? [v5: $int] : ? [v6: $int] : (mem(v0, v1, v3) = 43.40/14.22 | v5 & mem(v0, v1, v2) = v6 & (v6 = 0 | v5 = 0))) 43.40/14.22 | 43.40/14.22 | ALPHA: (t2tb_sort3) implies: 43.40/14.22 | (8) ! [v0: $int] : ! [v1: $int] : ( ~ (t2tb(v0) = v1) | sort1(int, v1) = 43.40/14.22 | 0) 43.40/14.22 | 43.40/14.22 | ALPHA: (wP_parameter_all_trees) implies: 43.40/14.23 | (9) in_ty(int) 43.40/14.23 | (10) in_ty(tree) 43.40/14.23 | (11) in_tree1(empty1) 43.40/14.24 | (12) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : ? 43.40/14.24 | [v4: $int] : ? [v5: $int] : ? [v6: $int] : ? [v7: $int] : (t2tb(0) 43.40/14.24 | = v3 & set(v0, int, v2, v3, v5) = v6 & const(v0, int, v1) = v2 & 43.40/14.24 | list(tree) = v0 & tb2t3(v6) = v7 & t2tb2(empty1) = v4 & nil(tree) = 43.40/14.24 | v1 & cons(tree, v4, v1) = v5 & in_map_int_lplist_treerp(v7) & 43.40/14.24 | in_ty(v0) & in_uni(v6) & in_uni(v5) & in_uni(v4) & in_uni(v3) & 43.40/14.24 | in_uni(v2) & in_uni(v1) & ? [v8: $int] : ($lesseq(1, v8) & ? [v9: 43.40/14.24 | $int] : ? [v10: $int] : ? [v11: $int] : ? [v12: $int] : ? 43.40/14.24 | [v13: $int] : ? [v14: $int] : ($lesseq(v10, v8) & $lesseq(1, v10) 43.40/14.24 | & t2tb(v10) = v12 & set(v0, int, v11, v12, v1) = v13 & t2tb3(v9) 43.40/14.24 | = v11 & tb2t3(v13) = v14 & in_map_int_lplist_treerp(v14) & 43.40/14.24 | in_map_int_lplist_treerp(v9) & in_uni(v13) & in_uni(v12) & 43.40/14.24 | in_uni(v11) & ! [v15: $int] : ! [v16: $int] : ! [v17: $int] : 43.40/14.24 | ! [v18: $int] : ! [v19: $int] : (v19 = 0 | ~ ($lesseq(1, 43.40/14.24 | $difference(v10, v15))) | ~ ($lesseq(0, v15)) | ~ 43.40/14.24 | (t2tb(v15) = v16) | ~ (get(v0, int, v11, v16) = v17) | ~ 43.40/14.24 | (tb2t1(v17) = v18) | ~ (all_trees1(v15, v18) = v19)) & ? 43.40/14.24 | [v15: $int] : ? [v16: $int] : ? [v17: $int] : ? [v18: $int] : 43.40/14.24 | ? [v19: $int] : ? [v20: $int] : ? [v21: $int] : ? [v22: 43.40/14.24 | $int] : ? [v23: $int] : ? [v24: $int] : ($lesseq(1, 43.40/14.24 | $difference(v10, v16)) & $lesseq(v16, v8) & $lesseq(-1, 43.40/14.24 | $sum($difference(v16, v10), v8)) & $lesseq(0, v16) & 43.40/14.24 | t2tb($sum($difference(v10, v16), -1)) = v22 & t2tb(v16) = v19 43.40/14.24 | & get(v0, int, v17, v22) = v23 & get(v0, int, v17, v19) = v20 43.40/14.24 | & get(v0, int, v17, v12) = v18 & t2tb3(v15) = v17 & tb2t1(v23) 43.40/14.24 | = v24 & tb2t1(v20) = v21 & all_trees1($sum($difference(v10, 43.40/14.24 | v16), -1), v24) = 0 & all_trees1(v16, v21) = 0 & 43.40/14.24 | distinct(tree, v18) = 0 & in_map_int_lplist_treerp(v15) & 43.40/14.24 | in_list_tree(v24) & in_list_tree(v21) & in_uni(v23) & 43.40/14.24 | in_uni(v22) & in_uni(v20) & in_uni(v19) & in_uni(v18) & 43.40/14.24 | in_uni(v17) & ! [v25: $int] : ! [v26: $int] : ! [v27: $int] 43.40/14.24 | : ! [v28: $int] : ! [v29: $int] : (v29 = 0 | ~ ($lesseq(1, 43.40/14.24 | $difference(v10, v25))) | ~ ($lesseq(0, v25)) | ~ 43.40/14.24 | (t2tb(v25) = v26) | ~ (get(v0, int, v17, v26) = v27) | ~ 43.40/14.24 | (tb2t1(v27) = v28) | ~ (all_trees1(v25, v28) = v29)) & ! 43.40/14.24 | [v25: $int] : ! [v26: $int] : ! [v27: $int] : (v27 = 0 | ~ 43.40/14.24 | (t2tb2(v25) = v26) | ~ (mem(tree, v26, v18) = v27) | ~ 43.40/14.24 | in_tree1(v25) | ? [v28: $int] : (size1(v25) = v28 & ! 43.40/14.24 | [v29: $int] : ! [v30: $int] : ( ~ (v28 = v10) | ~ 43.40/14.24 | (node1(v29, v30) = v25) | ~ in_tree1(v29) | ? [v31: 43.40/14.24 | $int] : ($lesseq(v16, v31) & size1(v29) = v31)))) & ! 43.40/14.24 | [v25: $int] : ! [v26: $int] : ( ~ (t2tb2(v25) = v26) | ~ 43.40/14.24 | (mem(tree, v26, v18) = 0) | ~ in_tree1(v25) | ? [v27: 43.40/14.24 | $int] : (size1(v25) = v27 & ? [v28: $int] : ? [v29: 43.40/14.24 | $int] : ? [v30: $int] : (v27 = v10 & $lesseq(1, 43.40/14.24 | $difference(v16, v30)) & node1(v28, v29) = v25 & 43.40/14.24 | size1(v28) = v30 & in_tree1(v29) & in_tree1(v28)))) & ? 43.40/14.24 | [v25: $int] : ? [v26: $int] : ? [v27: $int] : ? [v28: $int] 43.40/14.24 | : ? [v29: $int] : (set(v0, int, v17, v12, v27) = v28 & 43.40/14.24 | infix_plpl(tree, v26, v18) = v27 & tb2t3(v28) = v29 & 43.40/14.24 | t2tb1(v25) = v26 & distinct(tree, v26) = 0 & 43.40/14.24 | in_map_int_lplist_treerp(v29) & in_list_tree(v25) & 43.40/14.24 | in_uni(v28) & in_uni(v27) & in_uni(v26) & ! [v30: $int] : 43.40/14.24 | ! [v31: $int] : ! [v32: $int] : (v32 = 0 | ~ (t2tb2(v30) = 43.40/14.24 | v31) | ~ (mem(tree, v31, v26) = v32) | ~ in_tree1(v30) 43.40/14.24 | | ! [v33: $int] : ! [v34: $int] : ( ~ (node1(v33, v34) = 43.40/14.24 | v30) | ~ in_tree1(v33) | ? [v35: $int] : ? [v36: 43.40/14.24 | $int] : (size1(v34) = v36 & size1(v33) = v35 & ( ~ 43.40/14.24 | ($difference($sum(v36, v16), v10) = -1) | ~ (v35 = 43.40/14.24 | v16))))) & ! [v30: $int] : ! [v31: $int] : ( ~ 43.40/14.24 | (t2tb2(v30) = v31) | ~ (mem(tree, v31, v26) = 0) | ~ 43.40/14.24 | in_tree1(v30) | ? [v32: $int] : ? [v33: $int] : 43.40/14.24 | (node1(v32, v33) = v30 & $sum(size1(v33), $product(-1, 43.40/14.24 | $sum($difference(v10, v16), -1))) = 0 & size1(v32) = 43.40/14.24 | v16 & in_tree1(v33) & in_tree1(v32))) & ? [v30: $int] : 43.40/14.24 | ? [v31: $int] : (get(v0, int, v30, v12) = v31 & t2tb3(v29) 43.40/14.24 | = v30 & in_uni(v31) & in_uni(v30) & ? [v32: $int] : ? 43.40/14.24 | [v33: $int] : ? [v34: $int] : (t2tb2(v32) = v33 & 43.40/14.24 | size1(v32) = v34 & mem(tree, v33, v31) = 0 & 43.40/14.24 | in_tree1(v32) & in_uni(v33) & ! [v35: $int] : ! [v36: 43.40/14.24 | $int] : ( ~ (v34 = v10) | ~ (node1(v35, v36) = v32) | 43.40/14.24 | ~ in_tree1(v35) | ? [v37: $int] : ($lesseq(1, 43.40/14.24 | $difference(v37, v16)) & size1(v35) = v37))))))))) 43.40/14.24 | 43.40/14.24 | ALPHA: (axioms) implies: 43.40/14.24 | (13) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (nil(v2) 43.40/14.24 | = v1) | ~ (nil(v2) = v0)) 43.40/14.24 | (14) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 43.40/14.24 | (size1(v2) = v1) | ~ (size1(v2) = v0)) 43.40/14.24 | (15) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 43.40/14.24 | (t2tb2(v2) = v1) | ~ (t2tb2(v2) = v0)) 43.40/14.24 | (16) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 43.40/14.24 | (t2tb1(v2) = v1) | ~ (t2tb1(v2) = v0)) 43.40/14.24 | (17) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 43.40/14.24 | (t2tb3(v2) = v1) | ~ (t2tb3(v2) = v0)) 43.40/14.24 | (18) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 43.40/14.24 | (list(v2) = v1) | ~ (list(v2) = v0)) 43.40/14.24 | (19) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 43.40/14.24 | (t2tb(v2) = v1) | ~ (t2tb(v2) = v0)) 43.40/14.24 | (20) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 43.40/14.24 | (node_proj_11(v2) = v1) | ~ (node_proj_11(v2) = v0)) 43.40/14.24 | (21) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ 43.40/14.24 | (tb2t(v2) = v1) | ~ (tb2t(v2) = v0)) 43.40/14.24 | (22) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = 43.40/14.24 | v0 | ~ (sort1(v3, v2) = v1) | ~ (sort1(v3, v2) = v0)) 43.40/14.24 | (23) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! 43.40/14.24 | [v4: $int] : (v1 = v0 | ~ (cons(v4, v3, v2) = v1) | ~ (cons(v4, v3, 43.40/14.24 | v2) = v0)) 43.40/14.24 | 43.40/14.24 | DELTA: instantiating (6) with fresh symbols all_74_0, all_74_1 gives: 43.72/14.25 | (24) list(tree) = all_74_1 & map(int, all_74_1) = all_74_0 & 43.72/14.25 | in_ty(all_74_0) & in_ty(all_74_1) & ! [v0: $int] : ! [v1: $int] : ( 43.72/14.25 | ~ (t2tb3(v0) = v1) | ~ in_map_int_lplist_treerp(v0) | 43.72/14.25 | sort1(all_74_0, v1) = 0) 43.72/14.25 | 43.72/14.25 | ALPHA: (24) implies: 43.72/14.25 | (25) list(tree) = all_74_1 43.72/14.25 | 43.72/14.25 | DELTA: instantiating (12) with fresh symbols all_77_0, all_77_1, all_77_2, 43.72/14.25 | all_77_3, all_77_4, all_77_5, all_77_6, all_77_7 gives: 43.72/14.25 | (26) t2tb(0) = all_77_4 & set(all_77_7, int, all_77_5, all_77_4, all_77_2) 43.72/14.25 | = all_77_1 & const(all_77_7, int, all_77_6) = all_77_5 & list(tree) = 43.72/14.25 | all_77_7 & tb2t3(all_77_1) = all_77_0 & t2tb2(empty1) = all_77_3 & 43.72/14.25 | nil(tree) = all_77_6 & cons(tree, all_77_3, all_77_6) = all_77_2 & 43.72/14.25 | in_map_int_lplist_treerp(all_77_0) & in_ty(all_77_7) & 43.72/14.25 | in_uni(all_77_1) & in_uni(all_77_2) & in_uni(all_77_3) & 43.72/14.25 | in_uni(all_77_4) & in_uni(all_77_5) & in_uni(all_77_6) & ? [v0: $int] 43.72/14.25 | : ($lesseq(1, v0) & ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : ? 43.72/14.25 | [v4: $int] : ? [v5: $int] : ? [v6: $int] : ($lesseq(v2, v0) & 43.72/14.25 | $lesseq(1, v2) & t2tb(v2) = v4 & set(all_77_7, int, v3, v4, 43.72/14.25 | all_77_6) = v5 & t2tb3(v1) = v3 & tb2t3(v5) = v6 & 43.72/14.25 | in_map_int_lplist_treerp(v6) & in_map_int_lplist_treerp(v1) & 43.72/14.25 | in_uni(v5) & in_uni(v4) & in_uni(v3) & ! [v7: $int] : ! [v8: 43.72/14.25 | $int] : ! [v9: $int] : ! [v10: $int] : ! [v11: $int] : (v11 = 43.72/14.25 | 0 | ~ ($lesseq(1, $difference(v2, v7))) | ~ ($lesseq(0, v7)) | 43.72/14.25 | ~ (t2tb(v7) = v8) | ~ (get(all_77_7, int, v3, v8) = v9) | ~ 43.72/14.25 | (tb2t1(v9) = v10) | ~ (all_trees1(v7, v10) = v11)) & ? [v7: 43.72/14.25 | $int] : ? [v8: $int] : ? [v9: $int] : ? [v10: $int] : ? 43.72/14.25 | [v11: $int] : ? [v12: $int] : ? [v13: $int] : ? [v14: $int] : 43.72/14.25 | ? [v15: $int] : ? [v16: $int] : ($lesseq(1, $difference(v2, v8)) 43.72/14.25 | & $lesseq(v8, v0) & $lesseq(-1, $sum($difference(v8, v2), v0)) & 43.72/14.25 | $lesseq(0, v8) & t2tb($sum($difference(v2, v8), -1)) = v14 & 43.72/14.25 | t2tb(v8) = v11 & get(all_77_7, int, v9, v14) = v15 & 43.72/14.25 | get(all_77_7, int, v9, v11) = v12 & get(all_77_7, int, v9, v4) = 43.72/14.25 | v10 & t2tb3(v7) = v9 & tb2t1(v15) = v16 & tb2t1(v12) = v13 & 43.72/14.25 | all_trees1($sum($difference(v2, v8), -1), v16) = 0 & 43.72/14.25 | all_trees1(v8, v13) = 0 & distinct(tree, v10) = 0 & 43.72/14.25 | in_map_int_lplist_treerp(v7) & in_list_tree(v16) & 43.72/14.25 | in_list_tree(v13) & in_uni(v15) & in_uni(v14) & in_uni(v12) & 43.72/14.25 | in_uni(v11) & in_uni(v10) & in_uni(v9) & ! [v17: $int] : ! 43.72/14.25 | [v18: $int] : ! [v19: $int] : ! [v20: $int] : ! [v21: $int] : 43.72/14.25 | (v21 = 0 | ~ ($lesseq(1, $difference(v2, v17))) | ~ 43.72/14.25 | ($lesseq(0, v17)) | ~ (t2tb(v17) = v18) | ~ (get(all_77_7, 43.72/14.25 | int, v9, v18) = v19) | ~ (tb2t1(v19) = v20) | ~ 43.72/14.25 | (all_trees1(v17, v20) = v21)) & ! [v17: $int] : ! [v18: 43.72/14.25 | $int] : ! [v19: $int] : (v19 = 0 | ~ (t2tb2(v17) = v18) | ~ 43.72/14.25 | (mem(tree, v18, v10) = v19) | ~ in_tree1(v17) | ? [v20: 43.72/14.25 | $int] : (size1(v17) = v20 & ! [v21: $int] : ! [v22: $int] 43.72/14.25 | : ( ~ (v20 = v2) | ~ (node1(v21, v22) = v17) | ~ 43.72/14.25 | in_tree1(v21) | ? [v23: $int] : ($lesseq(v8, v23) & 43.72/14.25 | size1(v21) = v23)))) & ! [v17: $int] : ! [v18: $int] : 43.72/14.25 | ( ~ (t2tb2(v17) = v18) | ~ (mem(tree, v18, v10) = 0) | ~ 43.72/14.25 | in_tree1(v17) | ? [v19: $int] : (size1(v17) = v19 & ? [v20: 43.72/14.25 | $int] : ? [v21: $int] : ? [v22: $int] : (v19 = v2 & 43.72/14.25 | $lesseq(1, $difference(v8, v22)) & node1(v20, v21) = v17 & 43.72/14.25 | size1(v20) = v22 & in_tree1(v21) & in_tree1(v20)))) & ? 43.72/14.25 | [v17: $int] : ? [v18: $int] : ? [v19: $int] : ? [v20: $int] : 43.72/14.25 | ? [v21: $int] : (set(all_77_7, int, v9, v4, v19) = v20 & 43.72/14.25 | infix_plpl(tree, v18, v10) = v19 & tb2t3(v20) = v21 & 43.72/14.25 | t2tb1(v17) = v18 & distinct(tree, v18) = 0 & 43.72/14.25 | in_map_int_lplist_treerp(v21) & in_list_tree(v17) & 43.72/14.25 | in_uni(v20) & in_uni(v19) & in_uni(v18) & ! [v22: $int] : ! 43.72/14.25 | [v23: $int] : ! [v24: $int] : (v24 = 0 | ~ (t2tb2(v22) = 43.72/14.25 | v23) | ~ (mem(tree, v23, v18) = v24) | ~ in_tree1(v22) | 43.72/14.25 | ! [v25: $int] : ! [v26: $int] : ( ~ (node1(v25, v26) = 43.72/14.25 | v22) | ~ in_tree1(v25) | ? [v27: $int] : ? [v28: 43.72/14.25 | $int] : (size1(v26) = v28 & size1(v25) = v27 & ( ~ 43.72/14.25 | ($difference($sum(v28, v8), v2) = -1) | ~ (v27 = 43.72/14.25 | v8))))) & ! [v22: $int] : ! [v23: $int] : ( ~ 43.72/14.25 | (t2tb2(v22) = v23) | ~ (mem(tree, v23, v18) = 0) | ~ 43.72/14.25 | in_tree1(v22) | ? [v24: $int] : ? [v25: $int] : 43.72/14.25 | (node1(v24, v25) = v22 & $sum(size1(v25), $product(-1, 43.72/14.25 | $sum($difference(v2, v8), -1))) = 0 & size1(v24) = v8 43.72/14.25 | & in_tree1(v25) & in_tree1(v24))) & ? [v22: $int] : ? 43.72/14.25 | [v23: $int] : (get(all_77_7, int, v22, v4) = v23 & t2tb3(v21) 43.72/14.25 | = v22 & in_uni(v23) & in_uni(v22) & ? [v24: $int] : ? 43.72/14.25 | [v25: $int] : ? [v26: $int] : (t2tb2(v24) = v25 & 43.72/14.25 | size1(v24) = v26 & mem(tree, v25, v23) = 0 & in_tree1(v24) 43.72/14.25 | & in_uni(v25) & ! [v27: $int] : ! [v28: $int] : ( ~ (v26 43.72/14.25 | = v2) | ~ (node1(v27, v28) = v24) | ~ in_tree1(v27) 43.72/14.25 | | ? [v29: $int] : ($lesseq(1, $difference(v29, v8)) & 43.72/14.25 | size1(v27) = v29)))))))) 43.72/14.25 | 43.72/14.25 | ALPHA: (26) implies: 43.72/14.25 | (27) cons(tree, all_77_3, all_77_6) = all_77_2 43.72/14.25 | (28) nil(tree) = all_77_6 43.72/14.25 | (29) t2tb2(empty1) = all_77_3 43.72/14.25 | (30) list(tree) = all_77_7 43.72/14.25 | (31) t2tb(0) = all_77_4 43.72/14.26 | (32) ? [v0: $int] : ($lesseq(1, v0) & ? [v1: $int] : ? [v2: $int] : ? 43.72/14.26 | [v3: $int] : ? [v4: $int] : ? [v5: $int] : ? [v6: $int] : 43.72/14.26 | ($lesseq(v2, v0) & $lesseq(1, v2) & t2tb(v2) = v4 & set(all_77_7, 43.72/14.26 | int, v3, v4, all_77_6) = v5 & t2tb3(v1) = v3 & tb2t3(v5) = v6 & 43.72/14.26 | in_map_int_lplist_treerp(v6) & in_map_int_lplist_treerp(v1) & 43.72/14.26 | in_uni(v5) & in_uni(v4) & in_uni(v3) & ! [v7: $int] : ! [v8: 43.72/14.26 | $int] : ! [v9: $int] : ! [v10: $int] : ! [v11: $int] : (v11 = 43.72/14.26 | 0 | ~ ($lesseq(1, $difference(v2, v7))) | ~ ($lesseq(0, v7)) | 43.72/14.26 | ~ (t2tb(v7) = v8) | ~ (get(all_77_7, int, v3, v8) = v9) | ~ 43.72/14.26 | (tb2t1(v9) = v10) | ~ (all_trees1(v7, v10) = v11)) & ? [v7: 43.72/14.26 | $int] : ? [v8: $int] : ? [v9: $int] : ? [v10: $int] : ? 43.72/14.26 | [v11: $int] : ? [v12: $int] : ? [v13: $int] : ? [v14: $int] : 43.72/14.26 | ? [v15: $int] : ? [v16: $int] : ($lesseq(1, $difference(v2, v8)) 43.72/14.26 | & $lesseq(v8, v0) & $lesseq(-1, $sum($difference(v8, v2), v0)) & 43.72/14.26 | $lesseq(0, v8) & t2tb($sum($difference(v2, v8), -1)) = v14 & 43.72/14.26 | t2tb(v8) = v11 & get(all_77_7, int, v9, v14) = v15 & 43.72/14.26 | get(all_77_7, int, v9, v11) = v12 & get(all_77_7, int, v9, v4) = 43.72/14.26 | v10 & t2tb3(v7) = v9 & tb2t1(v15) = v16 & tb2t1(v12) = v13 & 43.72/14.26 | all_trees1($sum($difference(v2, v8), -1), v16) = 0 & 43.72/14.26 | all_trees1(v8, v13) = 0 & distinct(tree, v10) = 0 & 43.72/14.26 | in_map_int_lplist_treerp(v7) & in_list_tree(v16) & 43.72/14.26 | in_list_tree(v13) & in_uni(v15) & in_uni(v14) & in_uni(v12) & 43.72/14.26 | in_uni(v11) & in_uni(v10) & in_uni(v9) & ! [v17: $int] : ! 43.72/14.26 | [v18: $int] : ! [v19: $int] : ! [v20: $int] : ! [v21: $int] : 43.72/14.26 | (v21 = 0 | ~ ($lesseq(1, $difference(v2, v17))) | ~ 43.72/14.26 | ($lesseq(0, v17)) | ~ (t2tb(v17) = v18) | ~ (get(all_77_7, 43.72/14.26 | int, v9, v18) = v19) | ~ (tb2t1(v19) = v20) | ~ 43.72/14.26 | (all_trees1(v17, v20) = v21)) & ! [v17: $int] : ! [v18: 43.72/14.26 | $int] : ! [v19: $int] : (v19 = 0 | ~ (t2tb2(v17) = v18) | ~ 43.72/14.26 | (mem(tree, v18, v10) = v19) | ~ in_tree1(v17) | ? [v20: 43.72/14.26 | $int] : (size1(v17) = v20 & ! [v21: $int] : ! [v22: $int] 43.72/14.26 | : ( ~ (v20 = v2) | ~ (node1(v21, v22) = v17) | ~ 43.72/14.26 | in_tree1(v21) | ? [v23: $int] : ($lesseq(v8, v23) & 43.72/14.26 | size1(v21) = v23)))) & ! [v17: $int] : ! [v18: $int] : 43.72/14.26 | ( ~ (t2tb2(v17) = v18) | ~ (mem(tree, v18, v10) = 0) | ~ 43.72/14.26 | in_tree1(v17) | ? [v19: $int] : (size1(v17) = v19 & ? [v20: 43.72/14.26 | $int] : ? [v21: $int] : ? [v22: $int] : (v19 = v2 & 43.72/14.26 | $lesseq(1, $difference(v8, v22)) & node1(v20, v21) = v17 & 43.72/14.26 | size1(v20) = v22 & in_tree1(v21) & in_tree1(v20)))) & ? 43.72/14.26 | [v17: $int] : ? [v18: $int] : ? [v19: $int] : ? [v20: $int] : 43.72/14.26 | ? [v21: $int] : (set(all_77_7, int, v9, v4, v19) = v20 & 43.72/14.26 | infix_plpl(tree, v18, v10) = v19 & tb2t3(v20) = v21 & 43.72/14.26 | t2tb1(v17) = v18 & distinct(tree, v18) = 0 & 43.72/14.26 | in_map_int_lplist_treerp(v21) & in_list_tree(v17) & 43.72/14.26 | in_uni(v20) & in_uni(v19) & in_uni(v18) & ! [v22: $int] : ! 43.72/14.26 | [v23: $int] : ! [v24: $int] : (v24 = 0 | ~ (t2tb2(v22) = 43.72/14.26 | v23) | ~ (mem(tree, v23, v18) = v24) | ~ in_tree1(v22) | 43.72/14.26 | ! [v25: $int] : ! [v26: $int] : ( ~ (node1(v25, v26) = 43.72/14.26 | v22) | ~ in_tree1(v25) | ? [v27: $int] : ? [v28: 43.72/14.26 | $int] : (size1(v26) = v28 & size1(v25) = v27 & ( ~ 43.72/14.26 | ($difference($sum(v28, v8), v2) = -1) | ~ (v27 = 43.72/14.26 | v8))))) & ! [v22: $int] : ! [v23: $int] : ( ~ 43.72/14.26 | (t2tb2(v22) = v23) | ~ (mem(tree, v23, v18) = 0) | ~ 43.72/14.26 | in_tree1(v22) | ? [v24: $int] : ? [v25: $int] : 43.72/14.26 | (node1(v24, v25) = v22 & $sum(size1(v25), $product(-1, 43.72/14.26 | $sum($difference(v2, v8), -1))) = 0 & size1(v24) = v8 43.72/14.26 | & in_tree1(v25) & in_tree1(v24))) & ? [v22: $int] : ? 43.72/14.26 | [v23: $int] : (get(all_77_7, int, v22, v4) = v23 & t2tb3(v21) 43.72/14.26 | = v22 & in_uni(v23) & in_uni(v22) & ? [v24: $int] : ? 43.72/14.26 | [v25: $int] : ? [v26: $int] : (t2tb2(v24) = v25 & 43.72/14.26 | size1(v24) = v26 & mem(tree, v25, v23) = 0 & in_tree1(v24) 43.72/14.26 | & in_uni(v25) & ! [v27: $int] : ! [v28: $int] : ( ~ (v26 43.72/14.26 | = v2) | ~ (node1(v27, v28) = v24) | ~ in_tree1(v27) 43.72/14.26 | | ? [v29: $int] : ($lesseq(1, $difference(v29, v8)) & 43.72/14.26 | size1(v27) = v29)))))))) 43.72/14.26 | 43.72/14.26 | DELTA: instantiating (2) with fresh symbols all_79_0, all_79_1, all_79_2, 43.72/14.26 | all_79_3 gives: 43.72/14.26 | (33) tb2t1(all_79_1) = all_79_0 & all_trees1(0, all_79_0) = 0 & 43.72/14.26 | t2tb2(empty1) = all_79_3 & nil(tree) = all_79_2 & cons(tree, all_79_3, 43.72/14.26 | all_79_2) = all_79_1 & in_list_tree(all_79_0) & in_uni(all_79_1) & 43.72/14.26 | in_uni(all_79_2) & in_uni(all_79_3) 43.72/14.26 | 43.72/14.26 | ALPHA: (33) implies: 43.72/14.26 | (34) in_uni(all_79_1) 43.72/14.26 | (35) in_list_tree(all_79_0) 43.72/14.26 | (36) cons(tree, all_79_3, all_79_2) = all_79_1 43.72/14.26 | (37) nil(tree) = all_79_2 43.72/14.26 | (38) t2tb2(empty1) = all_79_3 43.72/14.26 | (39) all_trees1(0, all_79_0) = 0 43.72/14.26 | (40) tb2t1(all_79_1) = all_79_0 43.72/14.26 | 43.72/14.26 | DELTA: instantiating (3) with fresh symbol all_82_0 gives: 43.72/14.26 | (41) list(tree) = all_82_0 & in_ty(all_82_0) & ! [v0: $int] : ! [v1: 43.72/14.26 | $int] : ( ~ (t2tb1(v0) = v1) | ~ in_list_tree(v0) | sort1(all_82_0, 43.72/14.26 | v1) = 0) 43.72/14.26 | 43.72/14.26 | ALPHA: (41) implies: 43.72/14.26 | (42) list(tree) = all_82_0 43.72/14.26 | (43) ! [v0: $int] : ! [v1: $int] : ( ~ (t2tb1(v0) = v1) | ~ 43.72/14.26 | in_list_tree(v0) | sort1(all_82_0, v1) = 0) 43.72/14.26 | 43.72/14.26 | DELTA: instantiating (32) with fresh symbol all_85_0 gives: 43.72/14.27 | (44) $lesseq(1, all_85_0) & ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : 43.72/14.27 | ? [v3: $int] : ? [v4: $int] : ? [v5: $int] : ($lesseq(v1, all_85_0) 43.72/14.27 | & $lesseq(1, v1) & t2tb(v1) = v3 & set(all_77_7, int, v2, v3, 43.72/14.27 | all_77_6) = v4 & t2tb3(v0) = v2 & tb2t3(v4) = v5 & 43.72/14.27 | in_map_int_lplist_treerp(v5) & in_map_int_lplist_treerp(v0) & 43.72/14.27 | in_uni(v4) & in_uni(v3) & in_uni(v2) & ! [v6: $int] : ! [v7: $int] 43.72/14.27 | : ! [v8: $int] : ! [v9: $int] : ! [v10: $int] : (v10 = 0 | ~ 43.72/14.27 | ($lesseq(1, $difference(v1, v6))) | ~ ($lesseq(0, v6)) | ~ 43.72/14.27 | (t2tb(v6) = v7) | ~ (get(all_77_7, int, v2, v7) = v8) | ~ 43.72/14.27 | (tb2t1(v8) = v9) | ~ (all_trees1(v6, v9) = v10)) & ? [v6: $int] 43.72/14.27 | : ? [v7: $int] : ? [v8: $int] : ? [v9: $int] : ? [v10: $int] : 43.72/14.27 | ? [v11: $int] : ? [v12: $int] : ? [v13: $int] : ? [v14: $int] : 43.72/14.27 | ? [v15: $int] : ($lesseq(1, $difference(v1, v7)) & $lesseq(v7, 43.72/14.27 | all_85_0) & $lesseq(-1, $sum($difference(v7, v1), all_85_0)) & 43.72/14.27 | $lesseq(0, v7) & t2tb($sum($difference(v1, v7), -1)) = v13 & 43.72/14.27 | t2tb(v7) = v10 & get(all_77_7, int, v8, v13) = v14 & get(all_77_7, 43.72/14.27 | int, v8, v10) = v11 & get(all_77_7, int, v8, v3) = v9 & 43.72/14.27 | t2tb3(v6) = v8 & tb2t1(v14) = v15 & tb2t1(v11) = v12 & 43.72/14.27 | all_trees1($sum($difference(v1, v7), -1), v15) = 0 & 43.72/14.27 | all_trees1(v7, v12) = 0 & distinct(tree, v9) = 0 & 43.72/14.27 | in_map_int_lplist_treerp(v6) & in_list_tree(v15) & 43.72/14.27 | in_list_tree(v12) & in_uni(v14) & in_uni(v13) & in_uni(v11) & 43.72/14.27 | in_uni(v10) & in_uni(v9) & in_uni(v8) & ! [v16: $int] : ! [v17: 43.72/14.27 | $int] : ! [v18: $int] : ! [v19: $int] : ! [v20: $int] : (v20 43.72/14.27 | = 0 | ~ ($lesseq(1, $difference(v1, v16))) | ~ ($lesseq(0, 43.72/14.27 | v16)) | ~ (t2tb(v16) = v17) | ~ (get(all_77_7, int, v8, 43.72/14.27 | v17) = v18) | ~ (tb2t1(v18) = v19) | ~ (all_trees1(v16, 43.72/14.27 | v19) = v20)) & ! [v16: $int] : ! [v17: $int] : ! [v18: 43.72/14.27 | $int] : (v18 = 0 | ~ (t2tb2(v16) = v17) | ~ (mem(tree, v17, 43.72/14.27 | v9) = v18) | ~ in_tree1(v16) | ? [v19: $int] : (size1(v16) 43.72/14.27 | = v19 & ! [v20: $int] : ! [v21: $int] : ( ~ (v19 = v1) | ~ 43.72/14.27 | (node1(v20, v21) = v16) | ~ in_tree1(v20) | ? [v22: $int] 43.72/14.27 | : ($lesseq(v7, v22) & size1(v20) = v22)))) & ! [v16: $int] 43.72/14.27 | : ! [v17: $int] : ( ~ (t2tb2(v16) = v17) | ~ (mem(tree, v17, v9) 43.72/14.27 | = 0) | ~ in_tree1(v16) | ? [v18: $int] : (size1(v16) = v18 & 43.72/14.27 | ? [v19: $int] : ? [v20: $int] : ? [v21: $int] : (v18 = v1 & 43.72/14.27 | $lesseq(1, $difference(v7, v21)) & node1(v19, v20) = v16 & 43.72/14.27 | size1(v19) = v21 & in_tree1(v20) & in_tree1(v19)))) & ? 43.72/14.27 | [v16: $int] : ? [v17: $int] : ? [v18: $int] : ? [v19: $int] : 43.72/14.27 | ? [v20: $int] : (set(all_77_7, int, v8, v3, v18) = v19 & 43.72/14.27 | infix_plpl(tree, v17, v9) = v18 & tb2t3(v19) = v20 & t2tb1(v16) 43.72/14.27 | = v17 & distinct(tree, v17) = 0 & in_map_int_lplist_treerp(v20) 43.72/14.27 | & in_list_tree(v16) & in_uni(v19) & in_uni(v18) & in_uni(v17) & 43.72/14.27 | ! [v21: $int] : ! [v22: $int] : ! [v23: $int] : (v23 = 0 | ~ 43.72/14.27 | (t2tb2(v21) = v22) | ~ (mem(tree, v22, v17) = v23) | ~ 43.72/14.27 | in_tree1(v21) | ! [v24: $int] : ! [v25: $int] : ( ~ 43.72/14.27 | (node1(v24, v25) = v21) | ~ in_tree1(v24) | ? [v26: $int] 43.72/14.27 | : ? [v27: $int] : (size1(v25) = v27 & size1(v24) = v26 & ( 43.72/14.27 | ~ ($difference($sum(v27, v7), v1) = -1) | ~ (v26 = 43.72/14.27 | v7))))) & ! [v21: $int] : ! [v22: $int] : ( ~ 43.72/14.27 | (t2tb2(v21) = v22) | ~ (mem(tree, v22, v17) = 0) | ~ 43.72/14.27 | in_tree1(v21) | ? [v23: $int] : ? [v24: $int] : (node1(v23, 43.72/14.27 | v24) = v21 & $sum(size1(v24), $product(-1, 43.72/14.27 | $sum($difference(v1, v7), -1))) = 0 & size1(v23) = v7 & 43.72/14.27 | in_tree1(v24) & in_tree1(v23))) & ? [v21: $int] : ? [v22: 43.72/14.27 | $int] : (get(all_77_7, int, v21, v3) = v22 & t2tb3(v20) = v21 43.72/14.27 | & in_uni(v22) & in_uni(v21) & ? [v23: $int] : ? [v24: $int] 43.72/14.27 | : ? [v25: $int] : (t2tb2(v23) = v24 & size1(v23) = v25 & 43.72/14.27 | mem(tree, v24, v22) = 0 & in_tree1(v23) & in_uni(v24) & ! 43.72/14.27 | [v26: $int] : ! [v27: $int] : ( ~ (v25 = v1) | ~ 43.72/14.27 | (node1(v26, v27) = v23) | ~ in_tree1(v26) | ? [v28: 43.72/14.27 | $int] : ($lesseq(1, $difference(v28, v7)) & size1(v26) = 43.72/14.27 | v28))))))) 43.72/14.27 | 43.72/14.27 | ALPHA: (44) implies: 43.72/14.27 | (45) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : ? 43.72/14.27 | [v4: $int] : ? [v5: $int] : ($lesseq(v1, all_85_0) & $lesseq(1, v1) & 43.72/14.27 | t2tb(v1) = v3 & set(all_77_7, int, v2, v3, all_77_6) = v4 & 43.72/14.27 | t2tb3(v0) = v2 & tb2t3(v4) = v5 & in_map_int_lplist_treerp(v5) & 43.72/14.27 | in_map_int_lplist_treerp(v0) & in_uni(v4) & in_uni(v3) & in_uni(v2) 43.72/14.27 | & ! [v6: $int] : ! [v7: $int] : ! [v8: $int] : ! [v9: $int] : ! 43.72/14.27 | [v10: $int] : (v10 = 0 | ~ ($lesseq(1, $difference(v1, v6))) | ~ 43.72/14.27 | ($lesseq(0, v6)) | ~ (t2tb(v6) = v7) | ~ (get(all_77_7, int, v2, 43.72/14.27 | v7) = v8) | ~ (tb2t1(v8) = v9) | ~ (all_trees1(v6, v9) = 43.72/14.27 | v10)) & ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: 43.72/14.27 | $int] : ? [v10: $int] : ? [v11: $int] : ? [v12: $int] : ? 43.72/14.27 | [v13: $int] : ? [v14: $int] : ? [v15: $int] : ($lesseq(1, 43.72/14.27 | $difference(v1, v7)) & $lesseq(v7, all_85_0) & $lesseq(-1, 43.72/14.27 | $sum($difference(v7, v1), all_85_0)) & $lesseq(0, v7) & 43.72/14.27 | t2tb($sum($difference(v1, v7), -1)) = v13 & t2tb(v7) = v10 & 43.72/14.27 | get(all_77_7, int, v8, v13) = v14 & get(all_77_7, int, v8, v10) = 43.72/14.27 | v11 & get(all_77_7, int, v8, v3) = v9 & t2tb3(v6) = v8 & 43.72/14.27 | tb2t1(v14) = v15 & tb2t1(v11) = v12 & 43.72/14.27 | all_trees1($sum($difference(v1, v7), -1), v15) = 0 & 43.72/14.27 | all_trees1(v7, v12) = 0 & distinct(tree, v9) = 0 & 43.72/14.27 | in_map_int_lplist_treerp(v6) & in_list_tree(v15) & 43.72/14.27 | in_list_tree(v12) & in_uni(v14) & in_uni(v13) & in_uni(v11) & 43.72/14.27 | in_uni(v10) & in_uni(v9) & in_uni(v8) & ! [v16: $int] : ! [v17: 43.72/14.27 | $int] : ! [v18: $int] : ! [v19: $int] : ! [v20: $int] : (v20 43.72/14.27 | = 0 | ~ ($lesseq(1, $difference(v1, v16))) | ~ ($lesseq(0, 43.72/14.27 | v16)) | ~ (t2tb(v16) = v17) | ~ (get(all_77_7, int, v8, 43.72/14.27 | v17) = v18) | ~ (tb2t1(v18) = v19) | ~ (all_trees1(v16, 43.72/14.27 | v19) = v20)) & ! [v16: $int] : ! [v17: $int] : ! [v18: 43.72/14.27 | $int] : (v18 = 0 | ~ (t2tb2(v16) = v17) | ~ (mem(tree, v17, 43.72/14.27 | v9) = v18) | ~ in_tree1(v16) | ? [v19: $int] : (size1(v16) 43.72/14.27 | = v19 & ! [v20: $int] : ! [v21: $int] : ( ~ (v19 = v1) | ~ 43.72/14.27 | (node1(v20, v21) = v16) | ~ in_tree1(v20) | ? [v22: $int] 43.72/14.27 | : ($lesseq(v7, v22) & size1(v20) = v22)))) & ! [v16: $int] 43.72/14.27 | : ! [v17: $int] : ( ~ (t2tb2(v16) = v17) | ~ (mem(tree, v17, v9) 43.72/14.27 | = 0) | ~ in_tree1(v16) | ? [v18: $int] : (size1(v16) = v18 & 43.72/14.27 | ? [v19: $int] : ? [v20: $int] : ? [v21: $int] : (v18 = v1 & 43.72/14.27 | $lesseq(1, $difference(v7, v21)) & node1(v19, v20) = v16 & 43.72/14.27 | size1(v19) = v21 & in_tree1(v20) & in_tree1(v19)))) & ? 43.72/14.27 | [v16: $int] : ? [v17: $int] : ? [v18: $int] : ? [v19: $int] : 43.72/14.27 | ? [v20: $int] : (set(all_77_7, int, v8, v3, v18) = v19 & 43.72/14.27 | infix_plpl(tree, v17, v9) = v18 & tb2t3(v19) = v20 & t2tb1(v16) 43.72/14.27 | = v17 & distinct(tree, v17) = 0 & in_map_int_lplist_treerp(v20) 43.72/14.27 | & in_list_tree(v16) & in_uni(v19) & in_uni(v18) & in_uni(v17) & 43.72/14.27 | ! [v21: $int] : ! [v22: $int] : ! [v23: $int] : (v23 = 0 | ~ 43.72/14.27 | (t2tb2(v21) = v22) | ~ (mem(tree, v22, v17) = v23) | ~ 43.72/14.27 | in_tree1(v21) | ! [v24: $int] : ! [v25: $int] : ( ~ 43.72/14.27 | (node1(v24, v25) = v21) | ~ in_tree1(v24) | ? [v26: $int] 43.72/14.27 | : ? [v27: $int] : (size1(v25) = v27 & size1(v24) = v26 & ( 43.72/14.27 | ~ ($difference($sum(v27, v7), v1) = -1) | ~ (v26 = 43.72/14.27 | v7))))) & ! [v21: $int] : ! [v22: $int] : ( ~ 43.72/14.27 | (t2tb2(v21) = v22) | ~ (mem(tree, v22, v17) = 0) | ~ 43.72/14.27 | in_tree1(v21) | ? [v23: $int] : ? [v24: $int] : (node1(v23, 43.72/14.27 | v24) = v21 & $sum(size1(v24), $product(-1, 43.72/14.27 | $sum($difference(v1, v7), -1))) = 0 & size1(v23) = v7 & 43.72/14.27 | in_tree1(v24) & in_tree1(v23))) & ? [v21: $int] : ? [v22: 43.72/14.27 | $int] : (get(all_77_7, int, v21, v3) = v22 & t2tb3(v20) = v21 43.72/14.27 | & in_uni(v22) & in_uni(v21) & ? [v23: $int] : ? [v24: $int] 43.72/14.27 | : ? [v25: $int] : (t2tb2(v23) = v24 & size1(v23) = v25 & 43.72/14.27 | mem(tree, v24, v22) = 0 & in_tree1(v23) & in_uni(v24) & ! 43.72/14.27 | [v26: $int] : ! [v27: $int] : ( ~ (v25 = v1) | ~ 43.72/14.27 | (node1(v26, v27) = v23) | ~ in_tree1(v26) | ? [v28: 43.72/14.27 | $int] : ($lesseq(1, $difference(v28, v7)) & size1(v26) = 43.72/14.27 | v28))))))) 43.72/14.27 | 43.72/14.27 | DELTA: instantiating (45) with fresh symbols all_88_0, all_88_1, all_88_2, 43.72/14.27 | all_88_3, all_88_4, all_88_5 gives: 43.72/14.28 | (46) $lesseq(all_88_4, all_85_0) & $lesseq(1, all_88_4) & t2tb(all_88_4) = 43.72/14.28 | all_88_2 & set(all_77_7, int, all_88_3, all_88_2, all_77_6) = all_88_1 43.72/14.28 | & t2tb3(all_88_5) = all_88_3 & tb2t3(all_88_1) = all_88_0 & 43.72/14.28 | in_map_int_lplist_treerp(all_88_0) & 43.72/14.28 | in_map_int_lplist_treerp(all_88_5) & in_uni(all_88_1) & 43.72/14.28 | in_uni(all_88_2) & in_uni(all_88_3) & ! [v0: $int] : ! [v1: $int] : 43.72/14.28 | ! [v2: $int] : ! [v3: $int] : ! [v4: $int] : (v4 = 0 | ~ 43.72/14.28 | ($lesseq(1, $difference(all_88_4, v0))) | ~ ($lesseq(0, v0)) | ~ 43.72/14.28 | (t2tb(v0) = v1) | ~ (get(all_77_7, int, all_88_3, v1) = v2) | ~ 43.72/14.28 | (tb2t1(v2) = v3) | ~ (all_trees1(v0, v3) = v4)) & ? [v0: $int] : 43.72/14.28 | ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : ? [v4: $int] : ? [v5: 43.72/14.28 | $int] : ? [v6: $int] : ? [v7: $int] : ? [v8: $int] : ? [v9: 43.72/14.28 | $int] : ($lesseq(1, $difference(all_88_4, v1)) & $lesseq(v1, 43.72/14.28 | all_85_0) & $lesseq(-1, $sum($difference(v1, all_88_4), all_85_0)) 43.72/14.28 | & $lesseq(0, v1) & t2tb($sum($difference(all_88_4, v1), -1)) = v7 & 43.72/14.28 | t2tb(v1) = v4 & get(all_77_7, int, v2, v7) = v8 & get(all_77_7, int, 43.72/14.28 | v2, v4) = v5 & get(all_77_7, int, v2, all_88_2) = v3 & t2tb3(v0) = 43.72/14.28 | v2 & tb2t1(v8) = v9 & tb2t1(v5) = v6 & 43.72/14.28 | all_trees1($sum($difference(all_88_4, v1), -1), v9) = 0 & 43.72/14.28 | all_trees1(v1, v6) = 0 & distinct(tree, v3) = 0 & 43.72/14.28 | in_map_int_lplist_treerp(v0) & in_list_tree(v9) & in_list_tree(v6) & 43.72/14.28 | in_uni(v8) & in_uni(v7) & in_uni(v5) & in_uni(v4) & in_uni(v3) & 43.72/14.28 | in_uni(v2) & ! [v10: $int] : ! [v11: $int] : ! [v12: $int] : ! 43.72/14.28 | [v13: $int] : ! [v14: $int] : (v14 = 0 | ~ ($lesseq(1, 43.72/14.28 | $difference(all_88_4, v10))) | ~ ($lesseq(0, v10)) | ~ 43.72/14.28 | (t2tb(v10) = v11) | ~ (get(all_77_7, int, v2, v11) = v12) | ~ 43.72/14.28 | (tb2t1(v12) = v13) | ~ (all_trees1(v10, v13) = v14)) & ! [v10: 43.72/14.28 | $int] : ! [v11: $int] : ! [v12: $int] : (v12 = 0 | ~ 43.72/14.28 | (t2tb2(v10) = v11) | ~ (mem(tree, v11, v3) = v12) | ~ 43.72/14.28 | in_tree1(v10) | ? [v13: $int] : (size1(v10) = v13 & ! [v14: 43.72/14.28 | $int] : ! [v15: $int] : ( ~ (v13 = all_88_4) | ~ (node1(v14, 43.72/14.28 | v15) = v10) | ~ in_tree1(v14) | ? [v16: $int] : 43.72/14.28 | ($lesseq(v1, v16) & size1(v14) = v16)))) & ! [v10: $int] : ! 43.72/14.28 | [v11: $int] : ( ~ (t2tb2(v10) = v11) | ~ (mem(tree, v11, v3) = 0) | 43.72/14.28 | ~ in_tree1(v10) | ? [v12: $int] : (size1(v10) = v12 & ? [v13: 43.72/14.28 | $int] : ? [v14: $int] : ? [v15: $int] : (v12 = all_88_4 & 43.72/14.28 | $lesseq(1, $difference(v1, v15)) & node1(v13, v14) = v10 & 43.72/14.28 | size1(v13) = v15 & in_tree1(v14) & in_tree1(v13)))) & ? [v10: 43.72/14.28 | $int] : ? [v11: $int] : ? [v12: $int] : ? [v13: $int] : ? 43.72/14.28 | [v14: $int] : (set(all_77_7, int, v2, all_88_2, v12) = v13 & 43.72/14.28 | infix_plpl(tree, v11, v3) = v12 & tb2t3(v13) = v14 & t2tb1(v10) = 43.72/14.28 | v11 & distinct(tree, v11) = 0 & in_map_int_lplist_treerp(v14) & 43.72/14.28 | in_list_tree(v10) & in_uni(v13) & in_uni(v12) & in_uni(v11) & ! 43.72/14.28 | [v15: $int] : ! [v16: $int] : ! [v17: $int] : (v17 = 0 | ~ 43.72/14.28 | (t2tb2(v15) = v16) | ~ (mem(tree, v16, v11) = v17) | ~ 43.72/14.28 | in_tree1(v15) | ! [v18: $int] : ! [v19: $int] : ( ~ 43.72/14.28 | (node1(v18, v19) = v15) | ~ in_tree1(v18) | ? [v20: $int] : 43.72/14.28 | ? [v21: $int] : (size1(v19) = v21 & size1(v18) = v20 & ( ~ 43.72/14.28 | ($difference($sum(v21, v1), all_88_4) = -1) | ~ (v20 = 43.72/14.28 | v1))))) & ! [v15: $int] : ! [v16: $int] : ( ~ 43.72/14.28 | (t2tb2(v15) = v16) | ~ (mem(tree, v16, v11) = 0) | ~ 43.72/14.28 | in_tree1(v15) | ? [v17: $int] : ? [v18: $int] : (node1(v17, 43.72/14.28 | v18) = v15 & $sum(size1(v18), $product(-1, 43.72/14.28 | $sum($difference(all_88_4, v1), -1))) = 0 & size1(v17) = 43.72/14.28 | v1 & in_tree1(v18) & in_tree1(v17))) & ? [v15: $int] : ? 43.72/14.28 | [v16: $int] : (get(all_77_7, int, v15, all_88_2) = v16 & 43.72/14.28 | t2tb3(v14) = v15 & in_uni(v16) & in_uni(v15) & ? [v17: $int] : 43.72/14.28 | ? [v18: $int] : ? [v19: $int] : (t2tb2(v17) = v18 & size1(v17) 43.72/14.28 | = v19 & mem(tree, v18, v16) = 0 & in_tree1(v17) & in_uni(v18) 43.72/14.28 | & ! [v20: $int] : ! [v21: $int] : ( ~ (v19 = all_88_4) | ~ 43.72/14.28 | (node1(v20, v21) = v17) | ~ in_tree1(v20) | ? [v22: $int] 43.72/14.28 | : ($lesseq(1, $difference(v22, v1)) & size1(v20) = v22)))))) 43.72/14.28 | 43.72/14.28 | ALPHA: (46) implies: 43.72/14.28 | (47) t2tb(all_88_4) = all_88_2 43.87/14.28 | (48) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : ? 43.87/14.28 | [v4: $int] : ? [v5: $int] : ? [v6: $int] : ? [v7: $int] : ? [v8: 43.87/14.28 | $int] : ? [v9: $int] : ($lesseq(1, $difference(all_88_4, v1)) & 43.87/14.28 | $lesseq(v1, all_85_0) & $lesseq(-1, $sum($difference(v1, all_88_4), 43.87/14.28 | all_85_0)) & $lesseq(0, v1) & t2tb($sum($difference(all_88_4, 43.87/14.28 | v1), -1)) = v7 & t2tb(v1) = v4 & get(all_77_7, int, v2, v7) = 43.87/14.28 | v8 & get(all_77_7, int, v2, v4) = v5 & get(all_77_7, int, v2, 43.87/14.28 | all_88_2) = v3 & t2tb3(v0) = v2 & tb2t1(v8) = v9 & tb2t1(v5) = v6 43.87/14.28 | & all_trees1($sum($difference(all_88_4, v1), -1), v9) = 0 & 43.87/14.28 | all_trees1(v1, v6) = 0 & distinct(tree, v3) = 0 & 43.87/14.28 | in_map_int_lplist_treerp(v0) & in_list_tree(v9) & in_list_tree(v6) & 43.87/14.28 | in_uni(v8) & in_uni(v7) & in_uni(v5) & in_uni(v4) & in_uni(v3) & 43.87/14.28 | in_uni(v2) & ! [v10: $int] : ! [v11: $int] : ! [v12: $int] : ! 43.87/14.28 | [v13: $int] : ! [v14: $int] : (v14 = 0 | ~ ($lesseq(1, 43.87/14.28 | $difference(all_88_4, v10))) | ~ ($lesseq(0, v10)) | ~ 43.87/14.28 | (t2tb(v10) = v11) | ~ (get(all_77_7, int, v2, v11) = v12) | ~ 43.87/14.28 | (tb2t1(v12) = v13) | ~ (all_trees1(v10, v13) = v14)) & ! [v10: 43.87/14.28 | $int] : ! [v11: $int] : ! [v12: $int] : (v12 = 0 | ~ 43.87/14.28 | (t2tb2(v10) = v11) | ~ (mem(tree, v11, v3) = v12) | ~ 43.87/14.28 | in_tree1(v10) | ? [v13: $int] : (size1(v10) = v13 & ! [v14: 43.87/14.28 | $int] : ! [v15: $int] : ( ~ (v13 = all_88_4) | ~ (node1(v14, 43.87/14.28 | v15) = v10) | ~ in_tree1(v14) | ? [v16: $int] : 43.87/14.28 | ($lesseq(v1, v16) & size1(v14) = v16)))) & ! [v10: $int] : ! 43.87/14.28 | [v11: $int] : ( ~ (t2tb2(v10) = v11) | ~ (mem(tree, v11, v3) = 0) | 43.87/14.28 | ~ in_tree1(v10) | ? [v12: $int] : (size1(v10) = v12 & ? [v13: 43.87/14.28 | $int] : ? [v14: $int] : ? [v15: $int] : (v12 = all_88_4 & 43.87/14.28 | $lesseq(1, $difference(v1, v15)) & node1(v13, v14) = v10 & 43.87/14.28 | size1(v13) = v15 & in_tree1(v14) & in_tree1(v13)))) & ? [v10: 43.87/14.28 | $int] : ? [v11: $int] : ? [v12: $int] : ? [v13: $int] : ? 43.87/14.28 | [v14: $int] : (set(all_77_7, int, v2, all_88_2, v12) = v13 & 43.87/14.28 | infix_plpl(tree, v11, v3) = v12 & tb2t3(v13) = v14 & t2tb1(v10) = 43.87/14.28 | v11 & distinct(tree, v11) = 0 & in_map_int_lplist_treerp(v14) & 43.87/14.28 | in_list_tree(v10) & in_uni(v13) & in_uni(v12) & in_uni(v11) & ! 43.87/14.28 | [v15: $int] : ! [v16: $int] : ! [v17: $int] : (v17 = 0 | ~ 43.87/14.28 | (t2tb2(v15) = v16) | ~ (mem(tree, v16, v11) = v17) | ~ 43.87/14.28 | in_tree1(v15) | ! [v18: $int] : ! [v19: $int] : ( ~ 43.87/14.28 | (node1(v18, v19) = v15) | ~ in_tree1(v18) | ? [v20: $int] : 43.87/14.28 | ? [v21: $int] : (size1(v19) = v21 & size1(v18) = v20 & ( ~ 43.87/14.28 | ($difference($sum(v21, v1), all_88_4) = -1) | ~ (v20 = 43.87/14.28 | v1))))) & ! [v15: $int] : ! [v16: $int] : ( ~ 43.87/14.28 | (t2tb2(v15) = v16) | ~ (mem(tree, v16, v11) = 0) | ~ 43.87/14.28 | in_tree1(v15) | ? [v17: $int] : ? [v18: $int] : (node1(v17, 43.87/14.28 | v18) = v15 & $sum(size1(v18), $product(-1, 43.87/14.28 | $sum($difference(all_88_4, v1), -1))) = 0 & size1(v17) = 43.87/14.28 | v1 & in_tree1(v18) & in_tree1(v17))) & ? [v15: $int] : ? 43.87/14.28 | [v16: $int] : (get(all_77_7, int, v15, all_88_2) = v16 & 43.87/14.28 | t2tb3(v14) = v15 & in_uni(v16) & in_uni(v15) & ? [v17: $int] : 43.87/14.28 | ? [v18: $int] : ? [v19: $int] : (t2tb2(v17) = v18 & size1(v17) 43.87/14.28 | = v19 & mem(tree, v18, v16) = 0 & in_tree1(v17) & in_uni(v18) 43.87/14.28 | & ! [v20: $int] : ! [v21: $int] : ( ~ (v19 = all_88_4) | ~ 43.87/14.28 | (node1(v20, v21) = v17) | ~ in_tree1(v20) | ? [v22: $int] 43.87/14.28 | : ($lesseq(1, $difference(v22, v1)) & size1(v20) = v22)))))) 43.87/14.28 | 43.87/14.28 | DELTA: instantiating (48) with fresh symbols all_92_0, all_92_1, all_92_2, 43.87/14.28 | all_92_3, all_92_4, all_92_5, all_92_6, all_92_7, all_92_8, all_92_9 43.87/14.28 | gives: 43.87/14.29 | (49) $lesseq(1, $difference(all_88_4, all_92_8)) & $lesseq(all_92_8, 43.87/14.29 | all_85_0) & $lesseq(-1, $sum($difference(all_92_8, all_88_4), 43.87/14.29 | all_85_0)) & $lesseq(0, all_92_8) & 43.87/14.29 | t2tb($sum($difference(all_88_4, all_92_8), -1)) = all_92_2 & 43.87/14.29 | t2tb(all_92_8) = all_92_5 & get(all_77_7, int, all_92_7, all_92_2) = 43.87/14.29 | all_92_1 & get(all_77_7, int, all_92_7, all_92_5) = all_92_4 & 43.87/14.29 | get(all_77_7, int, all_92_7, all_88_2) = all_92_6 & t2tb3(all_92_9) = 43.87/14.29 | all_92_7 & tb2t1(all_92_1) = all_92_0 & tb2t1(all_92_4) = all_92_3 & 43.87/14.29 | all_trees1($sum($difference(all_88_4, all_92_8), -1), all_92_0) = 0 & 43.87/14.29 | all_trees1(all_92_8, all_92_3) = 0 & distinct(tree, all_92_6) = 0 & 43.87/14.29 | in_map_int_lplist_treerp(all_92_9) & in_list_tree(all_92_0) & 43.87/14.29 | in_list_tree(all_92_3) & in_uni(all_92_1) & in_uni(all_92_2) & 43.87/14.29 | in_uni(all_92_4) & in_uni(all_92_5) & in_uni(all_92_6) & 43.87/14.29 | in_uni(all_92_7) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! 43.87/14.29 | [v3: $int] : ! [v4: $int] : (v4 = 0 | ~ ($lesseq(1, 43.87/14.29 | $difference(all_88_4, v0))) | ~ ($lesseq(0, v0)) | ~ (t2tb(v0) 43.87/14.29 | = v1) | ~ (get(all_77_7, int, all_92_7, v1) = v2) | ~ (tb2t1(v2) 43.87/14.29 | = v3) | ~ (all_trees1(v0, v3) = v4)) & ! [v0: $int] : ! [v1: 43.87/14.29 | $int] : ! [v2: $int] : (v2 = 0 | ~ (t2tb2(v0) = v1) | ~ 43.87/14.29 | (mem(tree, v1, all_92_6) = v2) | ~ in_tree1(v0) | ? [v3: $int] : 43.87/14.29 | (size1(v0) = v3 & ! [v4: $int] : ! [v5: $int] : ( ~ (v3 = 43.87/14.29 | all_88_4) | ~ (node1(v4, v5) = v0) | ~ in_tree1(v4) | ? 43.87/14.29 | [v6: $int] : ($lesseq(all_92_8, v6) & size1(v4) = v6)))) & ! 43.87/14.29 | [v0: $int] : ! [v1: $int] : ( ~ (t2tb2(v0) = v1) | ~ (mem(tree, v1, 43.87/14.29 | all_92_6) = 0) | ~ in_tree1(v0) | ? [v2: $int] : (size1(v0) = 43.87/14.29 | v2 & ? [v3: $int] : ? [v4: $int] : ? [v5: $int] : (v2 = 43.87/14.29 | all_88_4 & $lesseq(1, $difference(all_92_8, v5)) & node1(v3, v4) 43.87/14.29 | = v0 & size1(v3) = v5 & in_tree1(v4) & in_tree1(v3)))) & ? [v0: 43.87/14.29 | $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : ? [v4: 43.87/14.29 | $int] : (set(all_77_7, int, all_92_7, all_88_2, v2) = v3 & 43.87/14.29 | infix_plpl(tree, v1, all_92_6) = v2 & tb2t3(v3) = v4 & t2tb1(v0) = 43.87/14.29 | v1 & distinct(tree, v1) = 0 & in_map_int_lplist_treerp(v4) & 43.87/14.29 | in_list_tree(v0) & in_uni(v3) & in_uni(v2) & in_uni(v1) & ! [v5: 43.87/14.29 | $int] : ! [v6: $int] : ! [v7: $int] : (v7 = 0 | ~ (t2tb2(v5) = 43.87/14.29 | v6) | ~ (mem(tree, v6, v1) = v7) | ~ in_tree1(v5) | ! [v8: 43.87/14.29 | $int] : ! [v9: $int] : ( ~ (node1(v8, v9) = v5) | ~ 43.87/14.29 | in_tree1(v8) | ? [v10: $int] : ? [v11: $int] : (size1(v9) = 43.87/14.29 | v11 & size1(v8) = v10 & ( ~ ($difference($sum(v11, all_92_8), 43.87/14.29 | all_88_4) = -1) | ~ (v10 = all_92_8))))) & ! [v5: 43.87/14.29 | $int] : ! [v6: $int] : ( ~ (t2tb2(v5) = v6) | ~ (mem(tree, v6, 43.87/14.29 | v1) = 0) | ~ in_tree1(v5) | ? [v7: $int] : ? [v8: $int] : 43.87/14.29 | (node1(v7, v8) = v5 & $sum(size1(v8), $product(-1, 43.87/14.29 | $sum($difference(all_88_4, all_92_8), -1))) = 0 & size1(v7) 43.87/14.29 | = all_92_8 & in_tree1(v8) & in_tree1(v7))) & ? [v5: $int] : ? 43.87/14.29 | [v6: $int] : (get(all_77_7, int, v5, all_88_2) = v6 & t2tb3(v4) = v5 43.87/14.29 | & in_uni(v6) & in_uni(v5) & ? [v7: $int] : ? [v8: $int] : ? 43.87/14.29 | [v9: $int] : (t2tb2(v7) = v8 & size1(v7) = v9 & mem(tree, v8, v6) 43.87/14.29 | = 0 & in_tree1(v7) & in_uni(v8) & ! [v10: $int] : ! [v11: 43.87/14.29 | $int] : ( ~ (v9 = all_88_4) | ~ (node1(v10, v11) = v7) | ~ 43.87/14.29 | in_tree1(v10) | ? [v12: $int] : ($lesseq(1, $difference(v12, 43.87/14.29 | all_92_8)) & size1(v10) = v12))))) 43.87/14.29 | 43.87/14.29 | ALPHA: (49) implies: 43.87/14.29 | (50) $lesseq(0, all_92_8) 43.87/14.29 | (51) $lesseq(1, $difference(all_88_4, all_92_8)) 43.87/14.29 | (52) in_uni(all_92_4) 43.87/14.29 | (53) in_uni(all_92_1) 43.87/14.29 | (54) in_list_tree(all_92_3) 43.87/14.29 | (55) in_list_tree(all_92_0) 43.87/14.30 | (56) distinct(tree, all_92_6) = 0 43.87/14.30 | (57) all_trees1(all_92_8, all_92_3) = 0 43.87/14.30 | (58) all_trees1($sum($difference(all_88_4, all_92_8), -1), all_92_0) = 0 43.87/14.30 | (59) tb2t1(all_92_4) = all_92_3 43.87/14.30 | (60) tb2t1(all_92_1) = all_92_0 43.87/14.30 | (61) get(all_77_7, int, all_92_7, all_88_2) = all_92_6 43.87/14.30 | (62) t2tb(all_92_8) = all_92_5 43.87/14.30 | (63) t2tb($sum($difference(all_88_4, all_92_8), -1)) = all_92_2 43.87/14.30 | (64) ! [v0: $int] : ! [v1: $int] : ( ~ (t2tb2(v0) = v1) | ~ (mem(tree, 43.87/14.30 | v1, all_92_6) = 0) | ~ in_tree1(v0) | ? [v2: $int] : 43.87/14.30 | (size1(v0) = v2 & ? [v3: $int] : ? [v4: $int] : ? [v5: $int] : 43.87/14.30 | (v2 = all_88_4 & $lesseq(1, $difference(all_92_8, v5)) & node1(v3, 43.87/14.30 | v4) = v0 & size1(v3) = v5 & in_tree1(v4) & in_tree1(v3)))) 43.87/14.30 | (65) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v2 = 0 | ~ 43.87/14.30 | (t2tb2(v0) = v1) | ~ (mem(tree, v1, all_92_6) = v2) | ~ 43.87/14.30 | in_tree1(v0) | ? [v3: $int] : (size1(v0) = v3 & ! [v4: $int] : ! 43.87/14.30 | [v5: $int] : ( ~ (v3 = all_88_4) | ~ (node1(v4, v5) = v0) | ~ 43.87/14.30 | in_tree1(v4) | ? [v6: $int] : ($lesseq(all_92_8, v6) & 43.87/14.30 | size1(v4) = v6)))) 43.87/14.30 | (66) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ? [v3: $int] : ? 43.87/14.30 | [v4: $int] : (set(all_77_7, int, all_92_7, all_88_2, v2) = v3 & 43.87/14.30 | infix_plpl(tree, v1, all_92_6) = v2 & tb2t3(v3) = v4 & t2tb1(v0) = 43.87/14.30 | v1 & distinct(tree, v1) = 0 & in_map_int_lplist_treerp(v4) & 43.87/14.30 | in_list_tree(v0) & in_uni(v3) & in_uni(v2) & in_uni(v1) & ! [v5: 43.87/14.30 | $int] : ! [v6: $int] : ! [v7: $int] : (v7 = 0 | ~ (t2tb2(v5) = 43.87/14.30 | v6) | ~ (mem(tree, v6, v1) = v7) | ~ in_tree1(v5) | ! [v8: 43.87/14.30 | $int] : ! [v9: $int] : ( ~ (node1(v8, v9) = v5) | ~ 43.87/14.30 | in_tree1(v8) | ? [v10: $int] : ? [v11: $int] : (size1(v9) = 43.87/14.30 | v11 & size1(v8) = v10 & ( ~ ($difference($sum(v11, all_92_8), 43.87/14.30 | all_88_4) = -1) | ~ (v10 = all_92_8))))) & ! [v5: 43.87/14.30 | $int] : ! [v6: $int] : ( ~ (t2tb2(v5) = v6) | ~ (mem(tree, v6, 43.87/14.30 | v1) = 0) | ~ in_tree1(v5) | ? [v7: $int] : ? [v8: $int] : 43.87/14.30 | (node1(v7, v8) = v5 & $sum(size1(v8), $product(-1, 43.87/14.30 | $sum($difference(all_88_4, all_92_8), -1))) = 0 & size1(v7) 43.87/14.30 | = all_92_8 & in_tree1(v8) & in_tree1(v7))) & ? [v5: $int] : ? 43.87/14.30 | [v6: $int] : (get(all_77_7, int, v5, all_88_2) = v6 & t2tb3(v4) = v5 43.87/14.30 | & in_uni(v6) & in_uni(v5) & ? [v7: $int] : ? [v8: $int] : ? 43.87/14.30 | [v9: $int] : (t2tb2(v7) = v8 & size1(v7) = v9 & mem(tree, v8, v6) 43.87/14.30 | = 0 & in_tree1(v7) & in_uni(v8) & ! [v10: $int] : ! [v11: 43.87/14.30 | $int] : ( ~ (v9 = all_88_4) | ~ (node1(v10, v11) = v7) | ~ 43.87/14.30 | in_tree1(v10) | ? [v12: $int] : ($lesseq(1, $difference(v12, 43.87/14.30 | all_92_8)) & size1(v10) = v12))))) 43.87/14.30 | 43.87/14.30 | DELTA: instantiating (66) with fresh symbols all_96_0, all_96_1, all_96_2, 43.87/14.30 | all_96_3, all_96_4 gives: 43.87/14.30 | (67) set(all_77_7, int, all_92_7, all_88_2, all_96_2) = all_96_1 & 43.87/14.30 | infix_plpl(tree, all_96_3, all_92_6) = all_96_2 & tb2t3(all_96_1) = 43.87/14.30 | all_96_0 & t2tb1(all_96_4) = all_96_3 & distinct(tree, all_96_3) = 0 & 43.87/14.30 | in_map_int_lplist_treerp(all_96_0) & in_list_tree(all_96_4) & 43.87/14.30 | in_uni(all_96_1) & in_uni(all_96_2) & in_uni(all_96_3) & ! [v0: $int] 43.87/14.30 | : ! [v1: $int] : ! [v2: $int] : (v2 = 0 | ~ (t2tb2(v0) = v1) | ~ 43.87/14.30 | (mem(tree, v1, all_96_3) = v2) | ~ in_tree1(v0) | ! [v3: $int] : 43.87/14.30 | ! [v4: $int] : ( ~ (node1(v3, v4) = v0) | ~ in_tree1(v3) | ? [v5: 43.87/14.30 | $int] : ? [v6: $int] : (size1(v4) = v6 & size1(v3) = v5 & ( ~ 43.87/14.30 | ($difference($sum(v6, all_92_8), all_88_4) = -1) | ~ (v5 = 43.87/14.30 | all_92_8))))) & ! [v0: $int] : ! [v1: $int] : ( ~ 43.87/14.30 | (t2tb2(v0) = v1) | ~ (mem(tree, v1, all_96_3) = 0) | ~ 43.87/14.30 | in_tree1(v0) | ? [v2: $int] : ? [v3: $int] : (node1(v2, v3) = v0 & 43.87/14.30 | $sum(size1(v3), $product(-1, $sum($difference(all_88_4, all_92_8), 43.87/14.30 | -1))) = 0 & size1(v2) = all_92_8 & in_tree1(v3) & 43.87/14.30 | in_tree1(v2))) & ? [v0: $int] : ? [v1: $int] : (get(all_77_7, 43.87/14.30 | int, v0, all_88_2) = v1 & t2tb3(all_96_0) = v0 & in_uni(v1) & 43.87/14.30 | in_uni(v0) & ? [v2: $int] : ? [v3: $int] : ? [v4: $int] : 43.87/14.30 | (t2tb2(v2) = v3 & size1(v2) = v4 & mem(tree, v3, v1) = 0 & 43.87/14.30 | in_tree1(v2) & in_uni(v3) & ! [v5: $int] : ! [v6: $int] : ( ~ 43.87/14.30 | (v4 = all_88_4) | ~ (node1(v5, v6) = v2) | ~ in_tree1(v5) | ? 43.87/14.30 | [v7: $int] : ($lesseq(1, $difference(v7, all_92_8)) & size1(v5) 43.87/14.30 | = v7)))) 43.87/14.30 | 43.87/14.30 | ALPHA: (67) implies: 43.87/14.30 | (68) in_uni(all_96_1) 43.87/14.30 | (69) in_list_tree(all_96_4) 43.87/14.30 | (70) distinct(tree, all_96_3) = 0 43.87/14.30 | (71) t2tb1(all_96_4) = all_96_3 43.87/14.30 | (72) tb2t3(all_96_1) = all_96_0 43.87/14.30 | (73) infix_plpl(tree, all_96_3, all_92_6) = all_96_2 43.87/14.30 | (74) set(all_77_7, int, all_92_7, all_88_2, all_96_2) = all_96_1 43.87/14.30 | (75) ! [v0: $int] : ! [v1: $int] : ( ~ (t2tb2(v0) = v1) | ~ (mem(tree, 43.87/14.30 | v1, all_96_3) = 0) | ~ in_tree1(v0) | ? [v2: $int] : ? [v3: 43.87/14.30 | $int] : (node1(v2, v3) = v0 & $sum(size1(v3), $product(-1, 43.87/14.30 | $sum($difference(all_88_4, all_92_8), -1))) = 0 & size1(v2) = 43.87/14.30 | all_92_8 & in_tree1(v3) & in_tree1(v2))) 43.87/14.30 | (76) ? [v0: $int] : ? [v1: $int] : (get(all_77_7, int, v0, all_88_2) = v1 43.87/14.30 | & t2tb3(all_96_0) = v0 & in_uni(v1) & in_uni(v0) & ? [v2: $int] : 43.87/14.30 | ? [v3: $int] : ? [v4: $int] : (t2tb2(v2) = v3 & size1(v2) = v4 & 43.87/14.30 | mem(tree, v3, v1) = 0 & in_tree1(v2) & in_uni(v3) & ! [v5: $int] 43.87/14.30 | : ! [v6: $int] : ( ~ (v4 = all_88_4) | ~ (node1(v5, v6) = v2) | 43.87/14.30 | ~ in_tree1(v5) | ? [v7: $int] : ($lesseq(1, $difference(v7, 43.87/14.30 | all_92_8)) & size1(v5) = v7)))) 43.87/14.30 | 43.87/14.30 | DELTA: instantiating (76) with fresh symbols all_99_0, all_99_1 gives: 43.87/14.30 | (77) get(all_77_7, int, all_99_1, all_88_2) = all_99_0 & t2tb3(all_96_0) = 43.87/14.30 | all_99_1 & in_uni(all_99_0) & in_uni(all_99_1) & ? [v0: $int] : ? 43.87/14.30 | [v1: $int] : ? [v2: $int] : (t2tb2(v0) = v1 & size1(v0) = v2 & 43.87/14.30 | mem(tree, v1, all_99_0) = 0 & in_tree1(v0) & in_uni(v1) & ! [v3: 43.87/14.30 | $int] : ! [v4: $int] : ( ~ (v2 = all_88_4) | ~ (node1(v3, v4) = 43.87/14.30 | v0) | ~ in_tree1(v3) | ? [v5: $int] : ($lesseq(1, 43.87/14.31 | $difference(v5, all_92_8)) & size1(v3) = v5))) 43.87/14.31 | 43.87/14.31 | ALPHA: (77) implies: 43.87/14.31 | (78) t2tb3(all_96_0) = all_99_1 43.87/14.31 | (79) get(all_77_7, int, all_99_1, all_88_2) = all_99_0 43.87/14.31 | (80) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (t2tb2(v0) = v1 & 43.87/14.31 | size1(v0) = v2 & mem(tree, v1, all_99_0) = 0 & in_tree1(v0) & 43.87/14.31 | in_uni(v1) & ! [v3: $int] : ! [v4: $int] : ( ~ (v2 = all_88_4) | 43.87/14.31 | ~ (node1(v3, v4) = v0) | ~ in_tree1(v3) | ? [v5: $int] : 43.87/14.31 | ($lesseq(1, $difference(v5, all_92_8)) & size1(v3) = v5))) 43.87/14.31 | 43.87/14.31 | DELTA: instantiating (80) with fresh symbols all_101_0, all_101_1, all_101_2 43.87/14.31 | gives: 43.87/14.31 | (81) t2tb2(all_101_2) = all_101_1 & size1(all_101_2) = all_101_0 & 43.87/14.31 | mem(tree, all_101_1, all_99_0) = 0 & in_tree1(all_101_2) & 43.87/14.31 | in_uni(all_101_1) & ! [v0: $int] : ! [v1: $int] : ( ~ (all_101_0 = 43.87/14.31 | all_88_4) | ~ (node1(v0, v1) = all_101_2) | ~ in_tree1(v0) | ? 43.87/14.31 | [v2: $int] : ($lesseq(1, $difference(v2, all_92_8)) & size1(v0) = 43.87/14.31 | v2)) 43.87/14.31 | 43.87/14.31 | ALPHA: (81) implies: 43.87/14.31 | (82) in_tree1(all_101_2) 43.87/14.31 | (83) mem(tree, all_101_1, all_99_0) = 0 43.87/14.31 | (84) size1(all_101_2) = all_101_0 43.87/14.31 | (85) t2tb2(all_101_2) = all_101_1 43.87/14.31 | (86) ! [v0: $int] : ! [v1: $int] : ( ~ (all_101_0 = all_88_4) | ~ 43.87/14.31 | (node1(v0, v1) = all_101_2) | ~ in_tree1(v0) | ? [v2: $int] : 43.87/14.31 | ($lesseq(1, $difference(v2, all_92_8)) & size1(v0) = v2)) 43.87/14.31 | 43.87/14.31 | GROUND_INST: instantiating (19) with all_92_2, all_77_4, 0, simplifying with 43.87/14.31 | (31) gives: 43.87/14.31 | (87) all_92_2 = all_77_4 | ~ (t2tb(0) = all_92_2) 43.87/14.31 | 43.87/14.31 | GROUND_INST: instantiating (19) with all_92_5, all_77_4, 0, simplifying with 43.87/14.31 | (31) gives: 43.87/14.31 | (88) all_92_5 = all_77_4 | ~ (t2tb(0) = all_92_5) 43.87/14.31 | 43.87/14.31 | GROUND_INST: instantiating (18) with all_82_0, all_77_7, tree, simplifying 43.87/14.31 | with (30), (42) gives: 43.87/14.31 | (89) all_82_0 = all_77_7 43.87/14.31 | 43.87/14.31 | GROUND_INST: instantiating (18) with all_82_0, all_74_1, tree, simplifying 43.87/14.31 | with (25), (42) gives: 43.87/14.31 | (90) all_82_0 = all_74_1 43.87/14.31 | 43.87/14.32 | GROUND_INST: instantiating (15) with all_79_3, all_77_3, empty1, simplifying 43.87/14.32 | with (29), (38) gives: 43.87/14.32 | (91) all_79_3 = all_77_3 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (size_nonneg) with all_101_2, all_101_0, 43.87/14.32 | simplifying with (82), (84) gives: 43.87/14.32 | (92) $lesseq(0, all_101_0) 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (13) with all_79_2, all_77_6, tree, simplifying 43.87/14.32 | with (28), (37) gives: 43.87/14.32 | (93) all_79_2 = all_77_6 43.87/14.32 | 43.87/14.32 | COMBINE_EQS: (89), (90) imply: 43.87/14.32 | (94) all_77_7 = all_74_1 43.87/14.32 | 43.87/14.32 | REDUCE: (74), (94) imply: 43.87/14.32 | (95) set(all_74_1, int, all_92_7, all_88_2, all_96_2) = all_96_1 43.87/14.32 | 43.87/14.32 | REDUCE: (79), (94) imply: 43.87/14.32 | (96) get(all_74_1, int, all_99_1, all_88_2) = all_99_0 43.87/14.32 | 43.87/14.32 | REDUCE: (61), (94) imply: 43.87/14.32 | (97) get(all_74_1, int, all_92_7, all_88_2) = all_92_6 43.87/14.32 | 43.87/14.32 | REDUCE: (36), (91), (93) imply: 43.87/14.32 | (98) cons(tree, all_77_3, all_77_6) = all_79_1 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (23) with all_77_2, all_79_1, all_77_6, all_77_3, 43.87/14.32 | tree, simplifying with (27), (98) gives: 43.87/14.32 | (99) all_79_1 = all_77_2 43.87/14.32 | 43.87/14.32 | REDUCE: (40), (99) imply: 43.87/14.32 | (100) tb2t1(all_77_2) = all_79_0 43.87/14.32 | 43.87/14.32 | REDUCE: (34), (99) imply: 43.87/14.32 | (101) in_uni(all_77_2) 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (bridgeL) with $sum($difference(all_88_4, 43.87/14.32 | all_92_8), -1), all_92_2, simplifying with (63) gives: 43.87/14.32 | (102) $sum(tb2t(all_92_2), $product(-1, $sum($difference(all_88_4, 43.87/14.32 | all_92_8), -1))) = 0 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (bridgeL) with all_92_8, all_92_5, simplifying with 43.87/14.32 | (62) gives: 43.87/14.32 | (103) tb2t(all_92_5) = all_92_8 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (8) with all_92_8, all_92_5, simplifying with (62) 43.87/14.32 | gives: 43.87/14.32 | (104) sort1(int, all_92_5) = 0 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (8) with all_88_4, all_88_2, simplifying with (47) 43.87/14.32 | gives: 43.87/14.32 | (105) sort1(int, all_88_2) = 0 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (bridgeL) with 0, all_77_4, simplifying with (31) 43.87/14.32 | gives: 43.87/14.32 | (106) tb2t(all_77_4) = 0 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (bridgeR3) with all_96_1, all_96_0, simplifying 43.87/14.32 | with (68), (72) gives: 43.87/14.32 | (107) t2tb3(all_96_0) = all_96_1 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (bridgeR1) with all_92_1, all_92_0, simplifying 43.87/14.32 | with (53), (60) gives: 43.87/14.32 | (108) t2tb1(all_92_0) = all_92_1 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (bridgeR1) with all_92_4, all_92_3, simplifying 43.87/14.32 | with (52), (59) gives: 43.87/14.32 | (109) t2tb1(all_92_3) = all_92_4 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (bridgeR1) with all_77_2, all_79_0, simplifying 43.87/14.32 | with (100), (101) gives: 43.87/14.32 | (110) t2tb1(all_79_0) = all_77_2 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (1) with $sum($difference(all_88_4, all_92_8), -1), 43.87/14.32 | all_92_0, simplifying with (55), (58) gives: 43.87/14.32 | (111) ? [v0: $int] : (t2tb1(all_92_0) = v0 & distinct(tree, v0) = 0 & 43.87/14.32 | in_uni(v0) & ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v3 = 43.87/14.32 | 0 | ~ (t2tb2(v1) = v2) | ~ (mem(tree, v2, v0) = v3) | ~ 43.87/14.32 | in_tree1(v1) | ? [v4: $int] : ( ~ ($difference($sum(v4, 43.87/14.32 | all_92_8), all_88_4) = -1) & size1(v1) = v4)) & ! [v1: 43.87/14.32 | $int] : ! [v2: $int] : ( ~ (t2tb2(v1) = v2) | ~ (mem(tree, v2, 43.87/14.32 | v0) = 0) | ~ in_tree1(v1) | $sum(size1(v1), $product(-1, 43.87/14.32 | $sum($difference(all_88_4, all_92_8), -1))) = 0)) 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (1) with all_92_8, all_92_3, simplifying with (54), 43.87/14.32 | (57) gives: 43.87/14.32 | (112) ? [v0: $int] : (t2tb1(all_92_3) = v0 & distinct(tree, v0) = 0 & 43.87/14.32 | in_uni(v0) & ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v3 = 43.87/14.32 | 0 | ~ (t2tb2(v1) = v2) | ~ (mem(tree, v2, v0) = v3) | ~ 43.87/14.32 | in_tree1(v1) | ? [v4: $int] : ( ~ (v4 = all_92_8) & size1(v1) = 43.87/14.32 | v4)) & ! [v1: $int] : ! [v2: $int] : ( ~ (t2tb2(v1) = v2) | 43.87/14.32 | ~ (mem(tree, v2, v0) = 0) | ~ in_tree1(v1) | size1(v1) = 43.87/14.32 | all_92_8)) 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (1) with 0, all_79_0, simplifying with (35), (39) 43.87/14.32 | gives: 43.87/14.32 | (113) ? [v0: $int] : (t2tb1(all_79_0) = v0 & distinct(tree, v0) = 0 & 43.87/14.32 | in_uni(v0) & ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v3 = 43.87/14.32 | 0 | ~ (t2tb2(v1) = v2) | ~ (mem(tree, v2, v0) = v3) | ~ 43.87/14.32 | in_tree1(v1) | ? [v4: $int] : ( ~ (v4 = 0) & size1(v1) = v4)) & 43.87/14.32 | ! [v1: $int] : ! [v2: $int] : ( ~ (t2tb2(v1) = v2) | ~ (mem(tree, 43.87/14.32 | v2, v0) = 0) | ~ in_tree1(v1) | size1(v1) = 0)) 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (43) with all_96_4, all_96_3, simplifying with 43.87/14.32 | (69), (71) gives: 43.87/14.32 | (114) sort1(all_82_0, all_96_3) = 0 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (distinct_inversion) with tree, all_96_3, 43.87/14.32 | simplifying with (10), (70) gives: 43.87/14.32 | (115) ? [v0: $int] : ? [v1: $int] : (list(tree) = v1 & nil(tree) = v0 & 43.87/14.32 | in_ty(v1) & in_uni(v0) & (v0 = all_96_3 | ? [v2: $int] : ? [v3: 43.87/14.32 | $int] : ? [v4: $int] : ( ~ (v4 = 0) & distinct(tree, v3) = 0 & 43.87/14.32 | cons(tree, v2, v3) = all_96_3 & mem(tree, v2, v3) = v4 & 43.87/14.32 | sort1(v1, v3) = 0 & sort1(tree, v2) = 0 & in_uni(v3) & 43.87/14.32 | in_uni(v2) & in_uni(all_96_3)) | ? [v2: $int] : (cons(tree, 43.87/14.32 | v2, v0) = all_96_3 & sort1(tree, v2) = 0 & in_uni(v2) & 43.87/14.32 | in_uni(all_96_3)))) 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (distinct_inversion) with tree, all_92_6, 43.87/14.32 | simplifying with (10), (56) gives: 43.87/14.32 | (116) ? [v0: $int] : ? [v1: $int] : (list(tree) = v1 & nil(tree) = v0 & 43.87/14.32 | in_ty(v1) & in_uni(v0) & (v0 = all_92_6 | ? [v2: $int] : ? [v3: 43.87/14.32 | $int] : ? [v4: $int] : ( ~ (v4 = 0) & distinct(tree, v3) = 0 & 43.87/14.32 | cons(tree, v2, v3) = all_92_6 & mem(tree, v2, v3) = v4 & 43.87/14.32 | sort1(v1, v3) = 0 & sort1(tree, v2) = 0 & in_uni(v3) & 43.87/14.32 | in_uni(v2) & in_uni(all_92_6)) | ? [v2: $int] : (cons(tree, 43.87/14.32 | v2, v0) = all_92_6 & sort1(tree, v2) = 0 & in_uni(v2) & 43.87/14.32 | in_uni(all_92_6)))) 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (size_left) with all_101_2, all_101_0, simplifying 43.87/14.32 | with (82), (84) gives: 43.87/14.32 | (117) ~ ($lesseq(1, all_101_0)) | ? [v0: $int] : ? [v1: $int] : ? [v2: 43.87/14.32 | $int] : ($lesseq(1, $difference(all_101_0, v2)) & node1(v0, v1) = 43.87/14.32 | all_101_2 & size1(v0) = v2 & in_tree1(v1) & in_tree1(v0)) 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (tree_diff) with empty1, all_101_2, 0, all_101_0, 43.87/14.32 | simplifying with (4), (11), (84) gives: 43.87/14.32 | (118) all_101_0 = 0 | ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ 43.87/14.32 | (node1(all_101_2, v1) = v2) | ~ (node1(empty1, v0) = v2) | ~ 43.87/14.32 | in_tree1(v0)) 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (nil_Cons1) with tree, all_77_3, all_77_6, 43.87/14.32 | all_77_2, simplifying with (10), (27) gives: 43.87/14.32 | (119) ? [v0: $int] : ( ~ (v0 = all_77_2) & nil(tree) = v0 & in_uni(v0)) 43.87/14.32 | 43.87/14.32 | GROUND_INST: instantiating (mem_decomp) with tree, all_101_1, all_99_0, 43.87/14.32 | simplifying with (10), (83) gives: 43.87/14.32 | (120) ? [v0: $int] : (list(tree) = v0 & in_ty(v0) & ? [v1: $int] : ? 43.87/14.32 | [v2: $int] : ? [v3: $int] : (infix_plpl(tree, v1, v3) = all_99_0 & 43.87/14.32 | cons(tree, all_101_1, v2) = v3 & sort1(v0, v2) = 0 & sort1(v0, 43.87/14.32 | v1) = 0 & in_uni(v3) & in_uni(v2) & in_uni(v1) & 43.87/14.32 | in_uni(all_99_0))) 43.87/14.32 | 43.87/14.33 | DELTA: instantiating (115) with fresh symbols all_123_0, all_123_1 gives: 43.87/14.33 | (121) list(tree) = all_123_0 & nil(tree) = all_123_1 & in_ty(all_123_0) & 43.87/14.33 | in_uni(all_123_1) & (all_123_1 = all_96_3 | ? [v0: $int] : ? [v1: 43.87/14.33 | $int] : ? [v2: $int] : ( ~ (v2 = 0) & distinct(tree, v1) = 0 & 43.87/14.33 | cons(tree, v0, v1) = all_96_3 & mem(tree, v0, v1) = v2 & 43.87/14.33 | sort1(all_123_0, v1) = 0 & sort1(tree, v0) = 0 & in_uni(v1) & 43.87/14.33 | in_uni(v0) & in_uni(all_96_3)) | ? [v0: $int] : (cons(tree, v0, 43.87/14.33 | all_123_1) = all_96_3 & sort1(tree, v0) = 0 & in_uni(v0) & 43.87/14.33 | in_uni(all_96_3))) 43.87/14.33 | 43.87/14.33 | ALPHA: (121) implies: 43.87/14.33 | (122) nil(tree) = all_123_1 43.87/14.33 | (123) list(tree) = all_123_0 43.87/14.33 | 43.87/14.33 | DELTA: instantiating (116) with fresh symbols all_125_0, all_125_1 gives: 43.87/14.33 | (124) list(tree) = all_125_0 & nil(tree) = all_125_1 & in_ty(all_125_0) & 43.87/14.33 | in_uni(all_125_1) & (all_125_1 = all_92_6 | ? [v0: $int] : ? [v1: 43.87/14.33 | $int] : ? [v2: $int] : ( ~ (v2 = 0) & distinct(tree, v1) = 0 & 43.87/14.33 | cons(tree, v0, v1) = all_92_6 & mem(tree, v0, v1) = v2 & 43.87/14.33 | sort1(all_125_0, v1) = 0 & sort1(tree, v0) = 0 & in_uni(v1) & 43.87/14.33 | in_uni(v0) & in_uni(all_92_6)) | ? [v0: $int] : (cons(tree, v0, 43.87/14.33 | all_125_1) = all_92_6 & sort1(tree, v0) = 0 & in_uni(v0) & 43.87/14.33 | in_uni(all_92_6))) 43.87/14.33 | 43.87/14.33 | ALPHA: (124) implies: 43.87/14.33 | (125) nil(tree) = all_125_1 43.87/14.33 | (126) list(tree) = all_125_0 43.87/14.33 | (127) all_125_1 = all_92_6 | ? [v0: $int] : ? [v1: $int] : ? [v2: $int] 43.87/14.33 | : ( ~ (v2 = 0) & distinct(tree, v1) = 0 & cons(tree, v0, v1) = 43.87/14.33 | all_92_6 & mem(tree, v0, v1) = v2 & sort1(all_125_0, v1) = 0 & 43.87/14.33 | sort1(tree, v0) = 0 & in_uni(v1) & in_uni(v0) & in_uni(all_92_6)) | 43.87/14.33 | ? [v0: $int] : (cons(tree, v0, all_125_1) = all_92_6 & sort1(tree, 43.87/14.33 | v0) = 0 & in_uni(v0) & in_uni(all_92_6)) 43.87/14.33 | 43.87/14.33 | DELTA: instantiating (113) with fresh symbol all_127_0 gives: 43.87/14.33 | (128) t2tb1(all_79_0) = all_127_0 & distinct(tree, all_127_0) = 0 & 43.87/14.33 | in_uni(all_127_0) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : 43.87/14.33 | (v2 = 0 | ~ (t2tb2(v0) = v1) | ~ (mem(tree, v1, all_127_0) = v2) | 43.87/14.33 | ~ in_tree1(v0) | ? [v3: $int] : ( ~ (v3 = 0) & size1(v0) = v3)) & 43.87/14.33 | ! [v0: $int] : ! [v1: $int] : ( ~ (t2tb2(v0) = v1) | ~ (mem(tree, 43.87/14.33 | v1, all_127_0) = 0) | ~ in_tree1(v0) | size1(v0) = 0) 43.87/14.33 | 43.87/14.33 | ALPHA: (128) implies: 43.87/14.33 | (129) distinct(tree, all_127_0) = 0 43.87/14.33 | (130) t2tb1(all_79_0) = all_127_0 43.87/14.33 | 43.87/14.33 | DELTA: instantiating (120) with fresh symbol all_130_0 gives: 43.87/14.33 | (131) list(tree) = all_130_0 & in_ty(all_130_0) & ? [v0: $int] : ? [v1: 43.87/14.33 | $int] : ? [v2: $int] : (infix_plpl(tree, v0, v2) = all_99_0 & 43.87/14.33 | cons(tree, all_101_1, v1) = v2 & sort1(all_130_0, v1) = 0 & 43.87/14.33 | sort1(all_130_0, v0) = 0 & in_uni(v2) & in_uni(v1) & in_uni(v0) & 43.87/14.33 | in_uni(all_99_0)) 43.87/14.33 | 43.87/14.33 | ALPHA: (131) implies: 43.87/14.33 | (132) list(tree) = all_130_0 43.87/14.33 | (133) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (infix_plpl(tree, v0, 43.87/14.33 | v2) = all_99_0 & cons(tree, all_101_1, v1) = v2 & 43.87/14.33 | sort1(all_130_0, v1) = 0 & sort1(all_130_0, v0) = 0 & in_uni(v2) & 43.87/14.33 | in_uni(v1) & in_uni(v0) & in_uni(all_99_0)) 43.87/14.33 | 43.87/14.33 | DELTA: instantiating (119) with fresh symbol all_132_0 gives: 43.87/14.33 | (134) ~ (all_132_0 = all_77_2) & nil(tree) = all_132_0 & in_uni(all_132_0) 43.87/14.33 | 43.87/14.33 | ALPHA: (134) implies: 43.87/14.33 | (135) ~ (all_132_0 = all_77_2) 43.87/14.33 | (136) nil(tree) = all_132_0 43.87/14.33 | 43.87/14.33 | DELTA: instantiating (112) with fresh symbol all_134_0 gives: 43.87/14.33 | (137) t2tb1(all_92_3) = all_134_0 & distinct(tree, all_134_0) = 0 & 43.87/14.33 | in_uni(all_134_0) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : 43.87/14.33 | (v2 = 0 | ~ (t2tb2(v0) = v1) | ~ (mem(tree, v1, all_134_0) = v2) | 43.87/14.33 | ~ in_tree1(v0) | ? [v3: $int] : ( ~ (v3 = all_92_8) & size1(v0) = 43.87/14.33 | v3)) & ! [v0: $int] : ! [v1: $int] : ( ~ (t2tb2(v0) = v1) | ~ 43.87/14.33 | (mem(tree, v1, all_134_0) = 0) | ~ in_tree1(v0) | size1(v0) = 43.87/14.33 | all_92_8) 43.87/14.33 | 43.87/14.33 | ALPHA: (137) implies: 43.87/14.33 | (138) distinct(tree, all_134_0) = 0 43.87/14.33 | (139) t2tb1(all_92_3) = all_134_0 43.87/14.33 | 43.87/14.33 | DELTA: instantiating (111) with fresh symbol all_137_0 gives: 43.87/14.33 | (140) t2tb1(all_92_0) = all_137_0 & distinct(tree, all_137_0) = 0 & 43.87/14.33 | in_uni(all_137_0) & ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : 43.87/14.33 | (v2 = 0 | ~ (t2tb2(v0) = v1) | ~ (mem(tree, v1, all_137_0) = v2) | 43.87/14.33 | ~ in_tree1(v0) | ? [v3: $int] : ( ~ ($difference($sum(v3, 43.87/14.33 | all_92_8), all_88_4) = -1) & size1(v0) = v3)) & ! [v0: 43.87/14.33 | $int] : ! [v1: $int] : ( ~ (t2tb2(v0) = v1) | ~ (mem(tree, v1, 43.87/14.33 | all_137_0) = 0) | ~ in_tree1(v0) | $sum(size1(v0), 43.87/14.33 | $product(-1, $sum($difference(all_88_4, all_92_8), -1))) = 0) 43.87/14.33 | 43.87/14.33 | ALPHA: (140) implies: 43.87/14.33 | (141) distinct(tree, all_137_0) = 0 43.87/14.33 | (142) t2tb1(all_92_0) = all_137_0 43.87/14.33 | 43.87/14.33 | DELTA: instantiating (133) with fresh symbols all_140_0, all_140_1, all_140_2 43.87/14.33 | gives: 43.87/14.33 | (143) infix_plpl(tree, all_140_2, all_140_0) = all_99_0 & cons(tree, 43.87/14.33 | all_101_1, all_140_1) = all_140_0 & sort1(all_130_0, all_140_1) = 0 43.87/14.33 | & sort1(all_130_0, all_140_2) = 0 & in_uni(all_140_0) & 43.87/14.33 | in_uni(all_140_1) & in_uni(all_140_2) & in_uni(all_99_0) 43.87/14.33 | 43.87/14.33 | ALPHA: (143) implies: 43.87/14.33 | (144) cons(tree, all_101_1, all_140_1) = all_140_0 43.87/14.33 | 43.87/14.33 | REDUCE: (90), (114) imply: 43.87/14.33 | (145) sort1(all_74_1, all_96_3) = 0 43.87/14.33 | 43.87/14.33 | GROUND_INST: instantiating (18) with all_74_1, all_130_0, tree, simplifying 43.87/14.33 | with (25), (132) gives: 43.87/14.33 | (146) all_130_0 = all_74_1 43.87/14.33 | 43.87/14.33 | GROUND_INST: instantiating (18) with all_130_0, all_125_0, tree, simplifying 43.87/14.33 | with (126), (132) gives: 43.87/14.33 | (147) all_130_0 = all_125_0 43.87/14.33 | 43.87/14.33 | GROUND_INST: instantiating (18) with all_130_0, all_123_0, tree, simplifying 43.87/14.33 | with (123), (132) gives: 43.87/14.33 | (148) all_130_0 = all_123_0 43.87/14.33 | 44.04/14.34 | GROUND_INST: instantiating (17) with all_99_1, all_96_1, all_96_0, simplifying 44.04/14.34 | with (78), (107) gives: 44.04/14.34 | (149) all_99_1 = all_96_1 44.04/14.34 | 44.04/14.34 | GROUND_INST: instantiating (16) with all_137_0, all_92_1, all_92_0, 44.04/14.34 | simplifying with (108), (142) gives: 44.04/14.34 | (150) all_137_0 = all_92_1 44.04/14.34 | 44.04/14.34 | GROUND_INST: instantiating (16) with all_134_0, all_92_4, all_92_3, 44.04/14.34 | simplifying with (109), (139) gives: 44.04/14.34 | (151) all_134_0 = all_92_4 44.04/14.34 | 44.04/14.34 | GROUND_INST: instantiating (16) with all_127_0, all_77_2, all_79_0, 44.04/14.34 | simplifying with (110), (130) gives: 44.04/14.34 | (152) all_127_0 = all_77_2 44.04/14.34 | 44.04/14.34 | GROUND_INST: instantiating (13) with all_77_6, all_132_0, tree, simplifying 44.04/14.34 | with (28), (136) gives: 44.04/14.34 | (153) all_132_0 = all_77_6 44.04/14.34 | 44.04/14.34 | GROUND_INST: instantiating (13) with all_132_0, all_125_1, tree, simplifying 44.04/14.34 | with (125), (136) gives: 44.04/14.34 | (154) all_132_0 = all_125_1 44.04/14.34 | 44.04/14.34 | GROUND_INST: instantiating (13) with all_125_1, all_123_1, tree, simplifying 44.04/14.34 | with (122), (125) gives: 44.04/14.34 | (155) all_125_1 = all_123_1 44.04/14.34 | 44.04/14.34 | COMBINE_EQS: (153), (154) imply: 44.04/14.34 | (156) all_125_1 = all_77_6 44.04/14.34 | 44.04/14.34 | SIMP: (156) implies: 44.04/14.34 | (157) all_125_1 = all_77_6 44.04/14.34 | 44.04/14.34 | COMBINE_EQS: (146), (147) imply: 44.04/14.34 | (158) all_125_0 = all_74_1 44.04/14.34 | 44.04/14.34 | COMBINE_EQS: (147), (148) imply: 44.04/14.34 | (159) all_125_0 = all_123_0 44.04/14.34 | 44.04/14.34 | COMBINE_EQS: (158), (159) imply: 44.04/14.34 | (160) all_123_0 = all_74_1 44.04/14.34 | 44.04/14.34 | SIMP: (160) implies: 44.04/14.34 | (161) all_123_0 = all_74_1 44.04/14.34 | 44.04/14.34 | COMBINE_EQS: (155), (157) imply: 44.04/14.34 | (162) all_123_1 = all_77_6 44.04/14.34 | 44.04/14.34 | SIMP: (162) implies: 44.04/14.34 | (163) all_123_1 = all_77_6 44.04/14.34 | 44.04/14.34 | REDUCE: (135), (153) imply: 44.04/14.34 | (164) ~ (all_77_2 = all_77_6) 44.04/14.34 | 44.04/14.34 | SIMP: (164) implies: 44.04/14.34 | (165) ~ (all_77_2 = all_77_6) 44.04/14.34 | 44.04/14.34 | REDUCE: (96), (149) imply: 44.04/14.34 | (166) get(all_74_1, int, all_96_1, all_88_2) = all_99_0 44.04/14.34 | 44.04/14.34 | REDUCE: (141), (150) imply: 44.04/14.34 | (167) distinct(tree, all_92_1) = 0 44.04/14.34 | 44.04/14.34 | REDUCE: (138), (151) imply: 44.04/14.34 | (168) distinct(tree, all_92_4) = 0 44.04/14.34 | 44.04/14.34 | REDUCE: (129), (152) imply: 44.04/14.34 | (169) distinct(tree, all_77_2) = 0 44.04/14.34 | 44.04/14.34 | GROUND_INST: instantiating (select_eq) with int, all_74_1, all_92_7, all_88_2, 44.04/14.34 | all_96_2, all_96_1, all_99_0, simplifying with (9), (95), (166) 44.04/14.34 | gives: 44.04/14.34 | (170) all_99_0 = all_96_2 | ? [v0: $int] : ( ~ (v0 = 0) & sort1(all_74_1, 44.04/14.34 | all_96_2) = v0) 44.04/14.34 | 44.04/14.34 | GROUND_INST: instantiating (distinct_inversion) with tree, all_92_1, 44.04/14.34 | simplifying with (10), (167) gives: 44.04/14.34 | (171) ? [v0: $int] : ? [v1: $int] : (list(tree) = v1 & nil(tree) = v0 & 44.04/14.34 | in_ty(v1) & in_uni(v0) & (v0 = all_92_1 | ? [v2: $int] : ? [v3: 44.04/14.34 | $int] : ? [v4: $int] : ( ~ (v4 = 0) & distinct(tree, v3) = 0 & 44.04/14.34 | cons(tree, v2, v3) = all_92_1 & mem(tree, v2, v3) = v4 & 44.04/14.34 | sort1(v1, v3) = 0 & sort1(tree, v2) = 0 & in_uni(v3) & 44.04/14.34 | in_uni(v2) & in_uni(all_92_1)) | ? [v2: $int] : (cons(tree, 44.04/14.34 | v2, v0) = all_92_1 & sort1(tree, v2) = 0 & in_uni(v2) & 44.04/14.34 | in_uni(all_92_1)))) 44.04/14.34 | 44.04/14.34 | GROUND_INST: instantiating (distinct_inversion) with tree, all_92_4, 44.04/14.34 | simplifying with (10), (168) gives: 44.04/14.34 | (172) ? [v0: $int] : ? [v1: $int] : (list(tree) = v1 & nil(tree) = v0 & 44.04/14.34 | in_ty(v1) & in_uni(v0) & (v0 = all_92_4 | ? [v2: $int] : ? [v3: 44.04/14.34 | $int] : ? [v4: $int] : ( ~ (v4 = 0) & distinct(tree, v3) = 0 & 44.04/14.34 | cons(tree, v2, v3) = all_92_4 & mem(tree, v2, v3) = v4 & 44.04/14.34 | sort1(v1, v3) = 0 & sort1(tree, v2) = 0 & in_uni(v3) & 44.04/14.34 | in_uni(v2) & in_uni(all_92_4)) | ? [v2: $int] : (cons(tree, 44.04/14.34 | v2, v0) = all_92_4 & sort1(tree, v2) = 0 & in_uni(v2) & 44.04/14.34 | in_uni(all_92_4)))) 44.04/14.34 | 44.04/14.34 | GROUND_INST: instantiating (distinct_inversion) with tree, all_77_2, 44.04/14.34 | simplifying with (10), (169) gives: 44.04/14.34 | (173) ? [v0: $int] : ? [v1: $int] : (list(tree) = v1 & nil(tree) = v0 & 44.04/14.34 | in_ty(v1) & in_uni(v0) & (v0 = all_77_2 | ? [v2: $int] : ? [v3: 44.04/14.34 | $int] : ? [v4: $int] : ( ~ (v4 = 0) & distinct(tree, v3) = 0 & 44.04/14.34 | cons(tree, v2, v3) = all_77_2 & mem(tree, v2, v3) = v4 & 44.04/14.34 | sort1(v1, v3) = 0 & sort1(tree, v2) = 0 & in_uni(v3) & 44.04/14.34 | in_uni(v2) & in_uni(all_77_2)) | ? [v2: $int] : (cons(tree, 44.04/14.34 | v2, v0) = all_77_2 & sort1(tree, v2) = 0 & in_uni(v2) & 44.04/14.34 | in_uni(all_77_2)))) 44.04/14.34 | 44.04/14.34 | GROUND_INST: instantiating (nil_Cons1) with tree, all_101_1, all_140_1, 44.04/14.34 | all_140_0, simplifying with (10), (144) gives: 44.04/14.34 | (174) ? [v0: $int] : ( ~ (v0 = all_140_0) & nil(tree) = v0 & in_uni(v0)) 44.04/14.34 | 44.09/14.35 | GROUND_INST: instantiating (select_neq) with int, all_74_1, all_92_7, 44.09/14.35 | all_92_5, all_88_2, all_92_6, simplifying with (9), (97), (104) 44.09/14.35 | gives: 44.09/14.35 | (175) ? [v0: $int] : ( ~ (v0 = 0) & sort1(int, all_88_2) = v0) | ! [v0: 44.09/14.35 | $int] : ! [v1: $int] : ! [v2: $int] : (v2 = all_92_6 | all_92_5 = 44.09/14.35 | all_88_2 | ~ (set(all_74_1, int, all_92_7, all_92_5, v0) = v1) | 44.09/14.35 | ~ (get(all_74_1, int, v1, all_88_2) = v2) | ~ in_uni(v0)) 44.09/14.35 | 44.09/14.35 | DELTA: instantiating (174) with fresh symbol all_154_0 gives: 44.09/14.35 | (176) ~ (all_154_0 = all_140_0) & nil(tree) = all_154_0 & 44.09/14.35 | in_uni(all_154_0) 44.09/14.35 | 44.09/14.35 | ALPHA: (176) implies: 44.09/14.35 | (177) nil(tree) = all_154_0 44.09/14.35 | 44.09/14.35 | DELTA: instantiating (171) with fresh symbols all_156_0, all_156_1 gives: 44.09/14.35 | (178) list(tree) = all_156_0 & nil(tree) = all_156_1 & in_ty(all_156_0) & 44.09/14.35 | in_uni(all_156_1) & (all_156_1 = all_92_1 | ? [v0: $int] : ? [v1: 44.09/14.35 | $int] : ? [v2: $int] : ( ~ (v2 = 0) & distinct(tree, v1) = 0 & 44.09/14.35 | cons(tree, v0, v1) = all_92_1 & mem(tree, v0, v1) = v2 & 44.09/14.35 | sort1(all_156_0, v1) = 0 & sort1(tree, v0) = 0 & in_uni(v1) & 44.09/14.35 | in_uni(v0) & in_uni(all_92_1)) | ? [v0: $int] : (cons(tree, v0, 44.09/14.35 | all_156_1) = all_92_1 & sort1(tree, v0) = 0 & in_uni(v0) & 44.09/14.35 | in_uni(all_92_1))) 44.09/14.35 | 44.09/14.35 | ALPHA: (178) implies: 44.09/14.35 | (179) nil(tree) = all_156_1 44.09/14.35 | (180) list(tree) = all_156_0 44.09/14.35 | 44.09/14.35 | DELTA: instantiating (173) with fresh symbols all_160_0, all_160_1 gives: 44.09/14.35 | (181) list(tree) = all_160_0 & nil(tree) = all_160_1 & in_ty(all_160_0) & 44.09/14.35 | in_uni(all_160_1) & (all_160_1 = all_77_2 | ? [v0: $int] : ? [v1: 44.09/14.35 | $int] : ? [v2: $int] : ( ~ (v2 = 0) & distinct(tree, v1) = 0 & 44.09/14.35 | cons(tree, v0, v1) = all_77_2 & mem(tree, v0, v1) = v2 & 44.09/14.35 | sort1(all_160_0, v1) = 0 & sort1(tree, v0) = 0 & in_uni(v1) & 44.09/14.35 | in_uni(v0) & in_uni(all_77_2)) | ? [v0: $int] : (cons(tree, v0, 44.09/14.35 | all_160_1) = all_77_2 & sort1(tree, v0) = 0 & in_uni(v0) & 44.09/14.35 | in_uni(all_77_2))) 44.09/14.35 | 44.09/14.35 | ALPHA: (181) implies: 44.09/14.35 | (182) nil(tree) = all_160_1 44.09/14.35 | (183) list(tree) = all_160_0 44.09/14.35 | (184) all_160_1 = all_77_2 | ? [v0: $int] : ? [v1: $int] : ? [v2: $int] 44.09/14.35 | : ( ~ (v2 = 0) & distinct(tree, v1) = 0 & cons(tree, v0, v1) = 44.09/14.35 | all_77_2 & mem(tree, v0, v1) = v2 & sort1(all_160_0, v1) = 0 & 44.09/14.35 | sort1(tree, v0) = 0 & in_uni(v1) & in_uni(v0) & in_uni(all_77_2)) | 44.09/14.35 | ? [v0: $int] : (cons(tree, v0, all_160_1) = all_77_2 & sort1(tree, 44.09/14.35 | v0) = 0 & in_uni(v0) & in_uni(all_77_2)) 44.09/14.35 | 44.09/14.35 | DELTA: instantiating (172) with fresh symbols all_162_0, all_162_1 gives: 44.09/14.35 | (185) list(tree) = all_162_0 & nil(tree) = all_162_1 & in_ty(all_162_0) & 44.09/14.35 | in_uni(all_162_1) & (all_162_1 = all_92_4 | ? [v0: $int] : ? [v1: 44.09/14.35 | $int] : ? [v2: $int] : ( ~ (v2 = 0) & distinct(tree, v1) = 0 & 44.09/14.35 | cons(tree, v0, v1) = all_92_4 & mem(tree, v0, v1) = v2 & 44.09/14.35 | sort1(all_162_0, v1) = 0 & sort1(tree, v0) = 0 & in_uni(v1) & 44.09/14.35 | in_uni(v0) & in_uni(all_92_4)) | ? [v0: $int] : (cons(tree, v0, 44.09/14.35 | all_162_1) = all_92_4 & sort1(tree, v0) = 0 & in_uni(v0) & 44.09/14.35 | in_uni(all_92_4))) 44.09/14.35 | 44.09/14.35 | ALPHA: (185) implies: 44.09/14.35 | (186) nil(tree) = all_162_1 44.09/14.35 | (187) list(tree) = all_162_0 44.09/14.35 | 44.09/14.35 | BETA: splitting (175) gives: 44.09/14.35 | 44.09/14.35 | Case 1: 44.09/14.35 | | 44.09/14.35 | | (188) ? [v0: $int] : ( ~ (v0 = 0) & sort1(int, all_88_2) = v0) 44.09/14.35 | | 44.09/14.35 | | DELTA: instantiating (188) with fresh symbol all_182_0 gives: 44.09/14.35 | | (189) ~ (all_182_0 = 0) & sort1(int, all_88_2) = all_182_0 44.09/14.35 | | 44.09/14.35 | | ALPHA: (189) implies: 44.09/14.35 | | (190) ~ (all_182_0 = 0) 44.09/14.35 | | (191) sort1(int, all_88_2) = all_182_0 44.09/14.35 | | 44.09/14.35 | | DELTA: instantiating (188) with fresh symbol all_188_0 gives: 44.09/14.35 | | (192) ~ (all_188_0 = 0) & sort1(int, all_88_2) = all_188_0 44.09/14.35 | | 44.09/14.35 | | ALPHA: (192) implies: 44.09/14.35 | | (193) sort1(int, all_88_2) = all_188_0 44.09/14.35 | | 44.09/14.35 | | DELTA: instantiating (188) with fresh symbol all_190_0 gives: 44.09/14.35 | | (194) ~ (all_190_0 = 0) & sort1(int, all_88_2) = all_190_0 44.09/14.35 | | 44.09/14.35 | | ALPHA: (194) implies: 44.09/14.35 | | (195) sort1(int, all_88_2) = all_190_0 44.09/14.35 | | 44.09/14.35 | | DELTA: instantiating (188) with fresh symbol all_194_0 gives: 44.09/14.35 | | (196) ~ (all_194_0 = 0) & sort1(int, all_88_2) = all_194_0 44.09/14.35 | | 44.09/14.35 | | ALPHA: (196) implies: 44.09/14.35 | | (197) sort1(int, all_88_2) = all_194_0 44.09/14.35 | | 44.09/14.35 | | DELTA: instantiating (188) with fresh symbol all_196_0 gives: 44.09/14.35 | | (198) ~ (all_196_0 = 0) & sort1(int, all_88_2) = all_196_0 44.09/14.35 | | 44.09/14.35 | | ALPHA: (198) implies: 44.09/14.35 | | (199) sort1(int, all_88_2) = all_196_0 44.09/14.35 | | 44.09/14.35 | | DELTA: instantiating (188) with fresh symbol all_198_0 gives: 44.09/14.35 | | (200) ~ (all_198_0 = 0) & sort1(int, all_88_2) = all_198_0 44.09/14.35 | | 44.09/14.35 | | ALPHA: (200) implies: 44.09/14.35 | | (201) sort1(int, all_88_2) = all_198_0 44.09/14.35 | | 44.09/14.35 | | GROUND_INST: instantiating (22) with 0, all_194_0, all_88_2, int, 44.09/14.35 | | simplifying with (105), (197) gives: 44.09/14.35 | | (202) all_194_0 = 0 44.09/14.35 | | 44.09/14.35 | | GROUND_INST: instantiating (22) with all_198_0, all_194_0, all_88_2, int, 44.09/14.35 | | simplifying with (197), (201) gives: 44.09/14.35 | | (203) all_198_0 = all_194_0 44.09/14.35 | | 44.09/14.35 | | GROUND_INST: instantiating (22) with all_196_0, all_194_0, all_88_2, int, 44.09/14.35 | | simplifying with (197), (199) gives: 44.09/14.35 | | (204) all_196_0 = all_194_0 44.09/14.35 | | 44.09/14.35 | | GROUND_INST: instantiating (22) with all_196_0, all_190_0, all_88_2, int, 44.09/14.35 | | simplifying with (195), (199) gives: 44.09/14.35 | | (205) all_196_0 = all_190_0 44.09/14.35 | | 44.09/14.35 | | GROUND_INST: instantiating (22) with all_194_0, all_188_0, all_88_2, int, 44.09/14.35 | | simplifying with (193), (197) gives: 44.09/14.35 | | (206) all_194_0 = all_188_0 44.09/14.35 | | 44.09/14.35 | | GROUND_INST: instantiating (22) with all_198_0, all_182_0, all_88_2, int, 44.09/14.35 | | simplifying with (191), (201) gives: 44.09/14.35 | | (207) all_198_0 = all_182_0 44.09/14.35 | | 44.09/14.35 | | COMBINE_EQS: (203), (207) imply: 44.09/14.35 | | (208) all_194_0 = all_182_0 44.09/14.35 | | 44.09/14.35 | | SIMP: (208) implies: 44.09/14.35 | | (209) all_194_0 = all_182_0 44.09/14.35 | | 44.09/14.36 | | COMBINE_EQS: (204), (205) imply: 44.09/14.36 | | (210) all_194_0 = all_190_0 44.09/14.36 | | 44.09/14.36 | | SIMP: (210) implies: 44.09/14.36 | | (211) all_194_0 = all_190_0 44.09/14.36 | | 44.09/14.36 | | COMBINE_EQS: (206), (211) imply: 44.09/14.36 | | (212) all_190_0 = all_188_0 44.09/14.36 | | 44.09/14.36 | | COMBINE_EQS: (202), (211) imply: 44.09/14.36 | | (213) all_190_0 = 0 44.09/14.36 | | 44.09/14.36 | | COMBINE_EQS: (209), (211) imply: 44.09/14.36 | | (214) all_190_0 = all_182_0 44.09/14.36 | | 44.09/14.36 | | COMBINE_EQS: (212), (213) imply: 44.09/14.36 | | (215) all_188_0 = 0 44.09/14.36 | | 44.09/14.36 | | COMBINE_EQS: (212), (214) imply: 44.09/14.36 | | (216) all_188_0 = all_182_0 44.09/14.36 | | 44.09/14.36 | | COMBINE_EQS: (215), (216) imply: 44.09/14.36 | | (217) all_182_0 = 0 44.09/14.36 | | 44.09/14.36 | | REDUCE: (190), (217) imply: 44.09/14.36 | | (218) ~ (0 = 0) 44.09/14.36 | | 44.09/14.36 | | CLOSE: (218) is inconsistent. 44.09/14.36 | | 44.09/14.36 | Case 2: 44.09/14.36 | | 44.09/14.36 | | 44.09/14.36 | | GROUND_INST: instantiating (18) with all_74_1, all_160_0, tree, simplifying 44.09/14.36 | | with (25), (183) gives: 44.09/14.36 | | (219) all_160_0 = all_74_1 44.09/14.36 | | 44.09/14.36 | | GROUND_INST: instantiating (18) with all_162_0, all_160_0, tree, simplifying 44.09/14.36 | | with (183), (187) gives: 44.09/14.36 | | (220) all_162_0 = all_160_0 44.09/14.36 | | 44.09/14.36 | | GROUND_INST: instantiating (18) with all_162_0, all_156_0, tree, simplifying 44.09/14.36 | | with (180), (187) gives: 44.09/14.36 | | (221) all_162_0 = all_156_0 44.09/14.36 | | 44.09/14.36 | | GROUND_INST: instantiating (13) with all_77_6, all_160_1, tree, simplifying 44.09/14.36 | | with (28), (182) gives: 44.09/14.36 | | (222) all_160_1 = all_77_6 44.09/14.36 | | 44.09/14.36 | | GROUND_INST: instantiating (13) with all_162_1, all_156_1, tree, simplifying 44.09/14.36 | | with (179), (186) gives: 44.09/14.36 | | (223) all_162_1 = all_156_1 44.09/14.36 | | 44.09/14.36 | | GROUND_INST: instantiating (13) with all_160_1, all_156_1, tree, simplifying 44.09/14.36 | | with (179), (182) gives: 44.09/14.36 | | (224) all_160_1 = all_156_1 44.09/14.36 | | 44.09/14.36 | | GROUND_INST: instantiating (13) with all_162_1, all_154_0, tree, simplifying 44.09/14.36 | | with (177), (186) gives: 44.09/14.36 | | (225) all_162_1 = all_154_0 44.09/14.36 | | 44.09/14.36 | | COMBINE_EQS: (220), (221) imply: 44.09/14.36 | | (226) all_160_0 = all_156_0 44.09/14.36 | | 44.09/14.36 | | SIMP: (226) implies: 44.09/14.36 | | (227) all_160_0 = all_156_0 44.09/14.36 | | 44.09/14.36 | | COMBINE_EQS: (223), (225) imply: 44.09/14.36 | | (228) all_156_1 = all_154_0 44.09/14.36 | | 44.09/14.36 | | SIMP: (228) implies: 44.09/14.36 | | (229) all_156_1 = all_154_0 44.09/14.36 | | 44.09/14.36 | | COMBINE_EQS: (219), (227) imply: 44.09/14.36 | | (230) all_156_0 = all_74_1 44.09/14.36 | | 44.09/14.36 | | COMBINE_EQS: (222), (224) imply: 44.09/14.36 | | (231) all_156_1 = all_77_6 44.09/14.36 | | 44.09/14.36 | | SIMP: (231) implies: 44.09/14.36 | | (232) all_156_1 = all_77_6 44.09/14.36 | | 44.09/14.36 | | COMBINE_EQS: (229), (232) imply: 44.09/14.36 | | (233) all_154_0 = all_77_6 44.09/14.36 | | 44.09/14.36 | | BETA: splitting (88) gives: 44.09/14.36 | | 44.09/14.36 | | Case 1: 44.09/14.36 | | | 44.09/14.36 | | | (234) ~ (t2tb(0) = all_92_5) 44.09/14.36 | | | 44.09/14.36 | | | PRED_UNIFY: (62), (234) imply: 44.09/14.36 | | | (235) ~ (all_92_8 = 0) 44.09/14.36 | | | 44.09/14.36 | | | STRENGTHEN: (50), (235) imply: 44.09/14.36 | | | (236) $lesseq(1, all_92_8) 44.09/14.36 | | | 44.09/14.36 | | | BETA: splitting (87) gives: 44.09/14.36 | | | 44.09/14.36 | | | Case 1: 44.09/14.36 | | | | 44.09/14.36 | | | | (237) ~ (t2tb(0) = all_92_2) 44.09/14.36 | | | | 44.09/14.36 | | | | PRED_UNIFY: (63), (237) imply: 44.09/14.36 | | | | (238) ~ ($difference(all_92_8, all_88_4) = -1) 44.09/14.36 | | | | 44.09/14.36 | | | | STRENGTHEN: (51), (238) imply: 44.09/14.36 | | | | (239) $lesseq(2, $difference(all_88_4, all_92_8)) 44.09/14.36 | | | | 44.09/14.36 | | | | BETA: splitting (117) gives: 44.09/14.36 | | | | 44.09/14.36 | | | | Case 1: 44.09/14.36 | | | | | 44.09/14.36 | | | | | (240) $lesseq(all_101_0, 0) 44.09/14.36 | | | | | 44.09/14.36 | | | | | ANTI_SYMM: (92), (240) imply: 44.09/14.36 | | | | | (241) all_101_0 = 0 44.09/14.36 | | | | | 44.09/14.36 | | | | | REDUCE: (84), (241) imply: 44.09/14.36 | | | | | (242) size1(all_101_2) = 0 44.09/14.36 | | | | | 44.09/14.36 | | | | | BETA: splitting (170) gives: 44.09/14.36 | | | | | 44.09/14.36 | | | | | Case 1: 44.09/14.36 | | | | | | 44.09/14.36 | | | | | | (243) all_99_0 = all_96_2 44.09/14.36 | | | | | | 44.09/14.36 | | | | | | REDUCE: (83), (243) imply: 44.09/14.36 | | | | | | (244) mem(tree, all_101_1, all_96_2) = 0 44.09/14.36 | | | | | | 44.09/14.36 | | | | | | BETA: splitting (184) gives: 44.09/14.36 | | | | | | 44.09/14.36 | | | | | | Case 1: 44.09/14.36 | | | | | | | 44.09/14.36 | | | | | | | (245) all_160_1 = all_77_2 44.09/14.36 | | | | | | | 44.09/14.36 | | | | | | | REF_CLOSE: (165), (222), (245) are inconsistent by sub-proof #8. 44.09/14.36 | | | | | | | 44.09/14.36 | | | | | | Case 2: 44.09/14.36 | | | | | | | 44.09/14.36 | | | | | | | 44.09/14.36 | | | | | | | GROUND_INST: instantiating (7) with tree, all_101_1, all_96_3, 44.09/14.36 | | | | | | | all_92_6, all_96_2, simplifying with (10), (73), 44.09/14.36 | | | | | | | (244) gives: 44.09/14.36 | | | | | | | (246) ? [v0: $int] : ? [v1: $int] : (mem(tree, all_101_1, 44.09/14.36 | | | | | | | all_96_3) = v1 & mem(tree, all_101_1, all_92_6) = v0 44.09/14.36 | | | | | | | & (v1 = 0 | v0 = 0)) 44.09/14.36 | | | | | | | 44.09/14.36 | | | | | | | DELTA: instantiating (246) with fresh symbols all_309_0, all_309_1 44.09/14.36 | | | | | | | gives: 44.09/14.36 | | | | | | | (247) mem(tree, all_101_1, all_96_3) = all_309_0 & mem(tree, 44.09/14.36 | | | | | | | all_101_1, all_92_6) = all_309_1 & (all_309_0 = 0 | 44.09/14.36 | | | | | | | all_309_1 = 0) 44.09/14.36 | | | | | | | 44.09/14.36 | | | | | | | ALPHA: (247) implies: 44.09/14.36 | | | | | | | (248) mem(tree, all_101_1, all_92_6) = all_309_1 44.09/14.36 | | | | | | | (249) mem(tree, all_101_1, all_96_3) = all_309_0 44.09/14.36 | | | | | | | (250) all_309_0 = 0 | all_309_1 = 0 44.09/14.36 | | | | | | | 44.09/14.36 | | | | | | | BETA: splitting (250) gives: 44.09/14.36 | | | | | | | 44.09/14.36 | | | | | | | Case 1: 44.09/14.36 | | | | | | | | 44.09/14.36 | | | | | | | | (251) all_309_0 = 0 44.09/14.36 | | | | | | | | 44.09/14.36 | | | | | | | | REDUCE: (249), (251) imply: 44.09/14.36 | | | | | | | | (252) mem(tree, all_101_1, all_96_3) = 0 44.09/14.36 | | | | | | | | 44.09/14.36 | | | | | | | | GROUND_INST: instantiating (75) with all_101_2, all_101_1, 44.09/14.36 | | | | | | | | simplifying with (82), (85), (252) gives: 44.09/14.36 | | | | | | | | (253) ? [v0: $int] : ? [v1: $int] : (node1(v0, v1) = 44.09/14.36 | | | | | | | | all_101_2 & $sum(size1(v1), $product(-1, 44.09/14.36 | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 & 44.09/14.36 | | | | | | | | size1(v0) = all_92_8 & in_tree1(v1) & in_tree1(v0)) 44.09/14.36 | | | | | | | | 44.09/14.36 | | | | | | | | DELTA: instantiating (253) with fresh symbols all_439_0, 44.09/14.36 | | | | | | | | all_439_1 gives: 44.09/14.36 | | | | | | | | (254) node1(all_439_1, all_439_0) = all_101_2 & 44.09/14.36 | | | | | | | | $sum(size1(all_439_0), $product(-1, 44.09/14.36 | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 & 44.09/14.36 | | | | | | | | size1(all_439_1) = all_92_8 & in_tree1(all_439_0) & 44.09/14.36 | | | | | | | | in_tree1(all_439_1) 44.09/14.36 | | | | | | | | 44.09/14.36 | | | | | | | | ALPHA: (254) implies: 44.09/14.36 | | | | | | | | (255) in_tree1(all_439_1) 44.09/14.37 | | | | | | | | (256) size1(all_439_1) = all_92_8 44.09/14.37 | | | | | | | | (257) $sum(size1(all_439_0), $product(-1, 44.09/14.37 | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 44.09/14.37 | | | | | | | | (258) node1(all_439_1, all_439_0) = all_101_2 44.09/14.37 | | | | | | | | 44.09/14.37 | | | | | | | | GROUND_INST: instantiating (5) with all_439_1, all_439_0, 44.09/14.37 | | | | | | | | all_101_2, simplifying with (255), (258) gives: 44.09/14.37 | | | | | | | | (259) ? [v0: $int] : ? [v1: $int] : ($sum(size1(all_439_0), 44.09/14.37 | | | | | | | | $product(-1, $sum($difference(v0, v1), -1))) = 0 & 44.09/14.37 | | | | | | | | size1(all_439_1) = v1 & size1(all_101_2) = v0) 44.09/14.37 | | | | | | | | 44.09/14.37 | | | | | | | | GROUND_INST: instantiating (node_proj_2_def1) with all_439_1, 44.09/14.37 | | | | | | | | all_439_0, all_101_2, simplifying with (255), (258) 44.09/14.37 | | | | | | | | gives: 44.09/14.37 | | | | | | | | (260) node_proj_21(all_101_2) = all_439_0 & 44.09/14.37 | | | | | | | | in_tree1(all_439_0) 44.09/14.37 | | | | | | | | 44.09/14.37 | | | | | | | | ALPHA: (260) implies: 44.09/14.37 | | | | | | | | (261) in_tree1(all_439_0) 44.09/14.37 | | | | | | | | 44.09/14.37 | | | | | | | | GROUND_INST: instantiating (size_left) with all_439_0, 44.09/14.37 | | | | | | | | $sum($difference(all_88_4, all_92_8), -1), 44.09/14.37 | | | | | | | | simplifying with (257), (261) gives: 44.09/14.37 | | | | | | | | (262) ~ ($lesseq(2, $difference(all_88_4, all_92_8))) | ? 44.09/14.37 | | | | | | | | [v0: $int] : ? [v1: $int] : ? [v2: $int] : 44.09/14.37 | | | | | | | | ($lesseq(2, $sum($difference($product(-1, v2), 44.09/14.37 | | | | | | | | all_92_8), all_88_4)) & node1(v0, v1) = 44.09/14.37 | | | | | | | | all_439_0 & size1(v0) = v2 & in_tree1(v1) & 44.09/14.37 | | | | | | | | in_tree1(v0)) 44.09/14.37 | | | | | | | | 44.09/14.37 | | | | | | | | GROUND_INST: instantiating (size_left) with all_439_1, all_92_8, 44.09/14.37 | | | | | | | | simplifying with (255), (256) gives: 44.09/14.37 | | | | | | | | (263) ~ ($lesseq(1, all_92_8)) | ? [v0: $int] : ? [v1: 44.09/14.37 | | | | | | | | $int] : ? [v2: $int] : ($lesseq(1, 44.09/14.37 | | | | | | | | $difference(all_92_8, v2)) & node1(v0, v1) = 44.09/14.37 | | | | | | | | all_439_1 & size1(v0) = v2 & in_tree1(v1) & 44.09/14.37 | | | | | | | | in_tree1(v0)) 44.09/14.37 | | | | | | | | 44.09/14.37 | | | | | | | | DELTA: instantiating (259) with fresh symbols all_464_0, 44.09/14.37 | | | | | | | | all_464_1 gives: 44.09/14.37 | | | | | | | | (264) $sum(size1(all_439_0), $product(-1, 44.09/14.37 | | | | | | | | $sum($difference(all_464_1, all_464_0), -1))) = 0 & 44.09/14.37 | | | | | | | | size1(all_439_1) = all_464_0 & size1(all_101_2) = 44.09/14.37 | | | | | | | | all_464_1 44.09/14.37 | | | | | | | | 44.09/14.37 | | | | | | | | ALPHA: (264) implies: 44.09/14.37 | | | | | | | | (265) size1(all_101_2) = all_464_1 44.09/14.37 | | | | | | | | (266) size1(all_439_1) = all_464_0 44.09/14.37 | | | | | | | | (267) $sum(size1(all_439_0), $product(-1, 44.09/14.37 | | | | | | | | $sum($difference(all_464_1, all_464_0), -1))) = 0 44.09/14.37 | | | | | | | | 44.09/14.37 | | | | | | | | BETA: splitting (262) gives: 44.09/14.37 | | | | | | | | 44.09/14.37 | | | | | | | | Case 1: 44.09/14.37 | | | | | | | | | 44.09/14.37 | | | | | | | | | (268) $lesseq(-1, $difference(all_92_8, all_88_4)) 44.09/14.37 | | | | | | | | | 44.09/14.37 | | | | | | | | | COMBINE_INEQS: (239), (268) imply: 44.09/14.37 | | | | | | | | | (269) $lesseq(0, -1) 44.09/14.37 | | | | | | | | | 44.09/14.37 | | | | | | | | | CLOSE: (269) is inconsistent. 44.09/14.37 | | | | | | | | | 44.09/14.37 | | | | | | | | Case 2: 44.09/14.37 | | | | | | | | | 44.09/14.37 | | | | | | | | | (270) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : 44.09/14.37 | | | | | | | | | ($lesseq(2, $sum($difference($product(-1, v2), 44.09/14.37 | | | | | | | | | all_92_8), all_88_4)) & node1(v0, v1) = 44.09/14.37 | | | | | | | | | all_439_0 & size1(v0) = v2 & in_tree1(v1) & 44.09/14.37 | | | | | | | | | in_tree1(v0)) 44.09/14.37 | | | | | | | | | 44.09/14.37 | | | | | | | | | DELTA: instantiating (270) with fresh symbols all_519_0, 44.09/14.37 | | | | | | | | | all_519_1, all_519_2 gives: 44.09/14.37 | | | | | | | | | (271) $lesseq(2, $sum($difference($product(-1, all_519_0), 44.09/14.37 | | | | | | | | | all_92_8), all_88_4)) & node1(all_519_2, 44.09/14.37 | | | | | | | | | all_519_1) = all_439_0 & size1(all_519_2) = 44.09/14.37 | | | | | | | | | all_519_0 & in_tree1(all_519_1) & in_tree1(all_519_2) 44.09/14.37 | | | | | | | | | 44.09/14.37 | | | | | | | | | ALPHA: (271) implies: 44.09/14.37 | | | | | | | | | (272) $lesseq(2, $sum($difference($product(-1, all_519_0), 44.09/14.37 | | | | | | | | | all_92_8), all_88_4)) 44.09/14.37 | | | | | | | | | (273) in_tree1(all_519_2) 44.09/14.37 | | | | | | | | | (274) size1(all_519_2) = all_519_0 44.09/14.37 | | | | | | | | | 44.09/14.37 | | | | | | | | | BETA: splitting (263) gives: 44.09/14.37 | | | | | | | | | 44.09/14.37 | | | | | | | | | Case 1: 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | (275) $lesseq(all_92_8, 0) 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | COMBINE_INEQS: (236), (275) imply: 44.09/14.37 | | | | | | | | | | (276) $lesseq(0, -1) 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | CLOSE: (276) is inconsistent. 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | Case 2: 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | (277) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : 44.09/14.37 | | | | | | | | | | ($lesseq(1, $difference(all_92_8, v2)) & node1(v0, 44.09/14.37 | | | | | | | | | | v1) = all_439_1 & size1(v0) = v2 & in_tree1(v1) 44.09/14.37 | | | | | | | | | | & in_tree1(v0)) 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | DELTA: instantiating (277) with fresh symbols all_525_0, 44.09/14.37 | | | | | | | | | | all_525_1, all_525_2 gives: 44.09/14.37 | | | | | | | | | | (278) $lesseq(1, $difference(all_92_8, all_525_0)) & 44.09/14.37 | | | | | | | | | | node1(all_525_2, all_525_1) = all_439_1 & 44.09/14.37 | | | | | | | | | | size1(all_525_2) = all_525_0 & in_tree1(all_525_1) 44.09/14.37 | | | | | | | | | | & in_tree1(all_525_2) 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | ALPHA: (278) implies: 44.09/14.37 | | | | | | | | | | (279) $lesseq(1, $difference(all_92_8, all_525_0)) 44.09/14.37 | | | | | | | | | | (280) in_tree1(all_525_2) 44.09/14.37 | | | | | | | | | | (281) size1(all_525_2) = all_525_0 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_525_2, 44.09/14.37 | | | | | | | | | | all_525_0, simplifying with (280), (281) gives: 44.09/14.37 | | | | | | | | | | (282) $lesseq(0, all_525_0) 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_519_2, 44.09/14.37 | | | | | | | | | | all_519_0, simplifying with (273), (274) gives: 44.09/14.37 | | | | | | | | | | (283) $lesseq(0, all_519_0) 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | GROUND_INST: instantiating (14) with $sum($difference(all_88_4, 44.09/14.37 | | | | | | | | | | all_92_8), -1), $sum($difference(all_464_1, 44.09/14.37 | | | | | | | | | | all_464_0), -1), all_439_0, simplifying with 44.09/14.37 | | | | | | | | | | (257), (267) gives: 44.09/14.37 | | | | | | | | | | (284) $sum($difference($difference(all_464_0, all_464_1), 44.09/14.37 | | | | | | | | | | all_92_8), all_88_4) = 0 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | GROUND_INST: instantiating (14) with all_92_8, all_464_0, 44.09/14.37 | | | | | | | | | | all_439_1, simplifying with (256), (266) gives: 44.09/14.37 | | | | | | | | | | (285) all_464_0 = all_92_8 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_464_1, all_101_2, 44.09/14.37 | | | | | | | | | | simplifying with (242), (265) gives: 44.09/14.37 | | | | | | | | | | (286) all_464_1 = 0 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | COMBINE_EQS: (284), (285) imply: 44.09/14.37 | | | | | | | | | | (287) all_464_1 = all_88_4 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | COMBINE_EQS: (286), (287) imply: 44.09/14.37 | | | | | | | | | | (288) all_88_4 = 0 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | SIMP: (288) implies: 44.09/14.37 | | | | | | | | | | (289) all_88_4 = 0 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | REDUCE: (272), (289) imply: 44.09/14.37 | | | | | | | | | | (290) $lesseq(2, $difference($product(-1, all_519_0), 44.09/14.37 | | | | | | | | | | all_92_8)) 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | COMBINE_INEQS: (283), (290) imply: 44.09/14.37 | | | | | | | | | | (291) $lesseq(all_92_8, -2) 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | COMBINE_INEQS: (236), (291) imply: 44.09/14.37 | | | | | | | | | | (292) $lesseq(0, -1) 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | | CLOSE: (292) is inconsistent. 44.09/14.37 | | | | | | | | | | 44.09/14.37 | | | | | | | | | End of split 44.09/14.37 | | | | | | | | | 44.09/14.37 | | | | | | | | End of split 44.09/14.37 | | | | | | | | 44.09/14.37 | | | | | | | Case 2: 44.09/14.37 | | | | | | | | 44.09/14.37 | | | | | | | | (293) all_309_1 = 0 44.09/14.37 | | | | | | | | 44.09/14.37 | | | | | | | | REDUCE: (248), (293) imply: 44.09/14.37 | | | | | | | | (294) mem(tree, all_101_1, all_92_6) = 0 44.09/14.37 | | | | | | | | 44.09/14.37 | | | | | | | | GROUND_INST: instantiating (64) with all_101_2, all_101_1, 44.09/14.37 | | | | | | | | simplifying with (82), (85), (294) gives: 44.09/14.37 | | | | | | | | (295) ? [v0: $int] : (size1(all_101_2) = v0 & ? [v1: $int] 44.09/14.37 | | | | | | | | : ? [v2: $int] : ? [v3: $int] : (v0 = all_88_4 & 44.09/14.37 | | | | | | | | $lesseq(1, $difference(all_92_8, v3)) & node1(v1, 44.09/14.37 | | | | | | | | v2) = all_101_2 & size1(v1) = v3 & in_tree1(v2) & 44.09/14.37 | | | | | | | | in_tree1(v1))) 44.09/14.37 | | | | | | | | 44.09/14.37 | | | | | | | | DELTA: instantiating (295) with fresh symbol all_326_0 gives: 44.09/14.38 | | | | | | | | (296) size1(all_101_2) = all_326_0 & ? [v0: $int] : ? [v1: 44.09/14.38 | | | | | | | | $int] : ? [v2: $int] : (all_326_0 = all_88_4 & 44.09/14.38 | | | | | | | | $lesseq(1, $difference(all_92_8, v2)) & node1(v0, v1) 44.09/14.38 | | | | | | | | = all_101_2 & size1(v0) = v2 & in_tree1(v1) & 44.09/14.38 | | | | | | | | in_tree1(v0)) 44.09/14.38 | | | | | | | | 44.09/14.38 | | | | | | | | ALPHA: (296) implies: 44.09/14.38 | | | | | | | | (297) size1(all_101_2) = all_326_0 44.09/14.38 | | | | | | | | (298) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : 44.09/14.38 | | | | | | | | (all_326_0 = all_88_4 & $lesseq(1, 44.09/14.38 | | | | | | | | $difference(all_92_8, v2)) & node1(v0, v1) = 44.09/14.38 | | | | | | | | all_101_2 & size1(v0) = v2 & in_tree1(v1) & 44.09/14.38 | | | | | | | | in_tree1(v0)) 44.09/14.38 | | | | | | | | 44.09/14.38 | | | | | | | | DELTA: instantiating (298) with fresh symbols all_330_0, 44.09/14.38 | | | | | | | | all_330_1, all_330_2 gives: 44.09/14.38 | | | | | | | | (299) all_326_0 = all_88_4 & $lesseq(1, $difference(all_92_8, 44.09/14.38 | | | | | | | | all_330_0)) & node1(all_330_2, all_330_1) = 44.09/14.38 | | | | | | | | all_101_2 & size1(all_330_2) = all_330_0 & 44.09/14.38 | | | | | | | | in_tree1(all_330_1) & in_tree1(all_330_2) 44.09/14.38 | | | | | | | | 44.09/14.38 | | | | | | | | ALPHA: (299) implies: 44.09/14.38 | | | | | | | | (300) all_326_0 = all_88_4 44.09/14.38 | | | | | | | | (301) $lesseq(1, $difference(all_92_8, all_330_0)) 44.09/14.38 | | | | | | | | (302) in_tree1(all_330_2) 44.09/14.38 | | | | | | | | (303) size1(all_330_2) = all_330_0 44.09/14.38 | | | | | | | | 44.09/14.38 | | | | | | | | REDUCE: (297), (300) imply: 44.09/14.38 | | | | | | | | (304) size1(all_101_2) = all_88_4 44.09/14.38 | | | | | | | | 44.09/14.38 | | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_330_2, 44.09/14.38 | | | | | | | | all_330_0, simplifying with (302), (303) gives: 44.09/14.38 | | | | | | | | (305) $lesseq(0, all_330_0) 44.09/14.38 | | | | | | | | 44.09/14.38 | | | | | | | | GROUND_INST: instantiating (14) with 0, all_88_4, all_101_2, 44.09/14.38 | | | | | | | | simplifying with (242), (304) gives: 44.09/14.38 | | | | | | | | (306) all_88_4 = 0 44.09/14.38 | | | | | | | | 44.09/14.38 | | | | | | | | REDUCE: (239), (306) imply: 44.09/14.38 | | | | | | | | (307) $lesseq(all_92_8, -2) 44.09/14.38 | | | | | | | | 44.09/14.38 | | | | | | | | COMBINE_INEQS: (236), (307) imply: 44.09/14.38 | | | | | | | | (308) $lesseq(0, -1) 44.09/14.38 | | | | | | | | 44.09/14.38 | | | | | | | | CLOSE: (308) is inconsistent. 44.09/14.38 | | | | | | | | 44.09/14.38 | | | | | | | End of split 44.09/14.38 | | | | | | | 44.09/14.38 | | | | | | End of split 44.09/14.38 | | | | | | 44.09/14.38 | | | | | Case 2: 44.09/14.38 | | | | | | 44.09/14.38 | | | | | | (309) ? [v0: $int] : ( ~ (v0 = 0) & sort1(all_74_1, all_96_2) = 44.09/14.38 | | | | | | v0) 44.09/14.38 | | | | | | 44.09/14.38 | | | | | | DELTA: instantiating (309) with fresh symbol all_270_0 gives: 44.09/14.38 | | | | | | (310) ~ (all_270_0 = 0) & sort1(all_74_1, all_96_2) = all_270_0 44.09/14.38 | | | | | | 44.09/14.38 | | | | | | REF_CLOSE: (10), (25), (73), (310), (infix_plpl_sort2) are 44.09/14.38 | | | | | | inconsistent by sub-proof #7. 44.09/14.38 | | | | | | 44.09/14.38 | | | | | End of split 44.09/14.38 | | | | | 44.09/14.38 | | | | Case 2: 44.09/14.38 | | | | | 44.09/14.38 | | | | | (311) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ($lesseq(1, 44.09/14.38 | | | | | $difference(all_101_0, v2)) & node1(v0, v1) = all_101_2 & 44.09/14.38 | | | | | size1(v0) = v2 & in_tree1(v1) & in_tree1(v0)) 44.09/14.38 | | | | | 44.09/14.38 | | | | | DELTA: instantiating (311) with fresh symbols all_248_0, all_248_1, 44.09/14.38 | | | | | all_248_2 gives: 44.09/14.38 | | | | | (312) $lesseq(1, $difference(all_101_0, all_248_0)) & 44.09/14.38 | | | | | node1(all_248_2, all_248_1) = all_101_2 & size1(all_248_2) = 44.09/14.38 | | | | | all_248_0 & in_tree1(all_248_1) & in_tree1(all_248_2) 44.09/14.38 | | | | | 44.09/14.38 | | | | | ALPHA: (312) implies: 44.09/14.38 | | | | | (313) in_tree1(all_248_2) 44.09/14.38 | | | | | (314) size1(all_248_2) = all_248_0 44.09/14.38 | | | | | (315) node1(all_248_2, all_248_1) = all_101_2 44.09/14.38 | | | | | 44.09/14.38 | | | | | BETA: splitting (127) gives: 44.09/14.38 | | | | | 44.09/14.38 | | | | | Case 1: 44.09/14.38 | | | | | | 44.09/14.38 | | | | | | (316) all_125_1 = all_92_6 44.09/14.38 | | | | | | 44.09/14.38 | | | | | | COMBINE_EQS: (157), (316) imply: 44.09/14.38 | | | | | | (317) all_92_6 = all_77_6 44.09/14.38 | | | | | | 44.09/14.38 | | | | | | REDUCE: (73), (317) imply: 44.09/14.38 | | | | | | (318) infix_plpl(tree, all_96_3, all_77_6) = all_96_2 44.09/14.38 | | | | | | 44.09/14.38 | | | | | | GROUND_INST: instantiating (append_l_nil) with tree, all_96_3, 44.09/14.38 | | | | | | all_77_6, all_96_2, simplifying with (10), (28), (318) 44.09/14.38 | | | | | | gives: 44.09/14.38 | | | | | | (319) all_96_2 = all_96_3 44.09/14.38 | | | | | | 44.09/14.38 | | | | | | BETA: splitting (170) gives: 44.09/14.38 | | | | | | 44.09/14.38 | | | | | | Case 1: 44.09/14.38 | | | | | | | 44.09/14.38 | | | | | | | (320) all_99_0 = all_96_2 44.09/14.38 | | | | | | | 44.09/14.38 | | | | | | | COMBINE_EQS: (319), (320) imply: 44.09/14.38 | | | | | | | (321) all_99_0 = all_96_3 44.09/14.38 | | | | | | | 44.09/14.38 | | | | | | | REDUCE: (83), (321) imply: 44.09/14.38 | | | | | | | (322) mem(tree, all_101_1, all_96_3) = 0 44.09/14.38 | | | | | | | 44.09/14.38 | | | | | | | GROUND_INST: instantiating (86) with all_248_2, all_248_1, 44.09/14.38 | | | | | | | simplifying with (313), (315) gives: 44.09/14.38 | | | | | | | (323) ~ (all_101_0 = all_88_4) | ? [v0: $int] : ($lesseq(1, 44.09/14.38 | | | | | | | $difference(v0, all_92_8)) & size1(all_248_2) = v0) 44.09/14.38 | | | | | | | 44.09/14.38 | | | | | | | GROUND_INST: instantiating (node_proj_1_def1) with all_248_2, 44.09/14.38 | | | | | | | all_248_1, all_101_2, simplifying with (313), (315) 44.09/14.38 | | | | | | | gives: 44.09/14.38 | | | | | | | (324) node_proj_11(all_101_2) = all_248_2 44.09/14.38 | | | | | | | 44.09/14.38 | | | | | | | GROUND_INST: instantiating (75) with all_101_2, all_101_1, 44.09/14.38 | | | | | | | simplifying with (82), (85), (322) gives: 44.09/14.38 | | | | | | | (325) ? [v0: $int] : ? [v1: $int] : (node1(v0, v1) = 44.09/14.38 | | | | | | | all_101_2 & $sum(size1(v1), $product(-1, 44.09/14.38 | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 & 44.09/14.38 | | | | | | | size1(v0) = all_92_8 & in_tree1(v1) & in_tree1(v0)) 44.09/14.38 | | | | | | | 44.09/14.38 | | | | | | | DELTA: instantiating (325) with fresh symbols all_301_0, all_301_1 44.09/14.38 | | | | | | | gives: 44.09/14.38 | | | | | | | (326) node1(all_301_1, all_301_0) = all_101_2 & 44.09/14.38 | | | | | | | $sum(size1(all_301_0), $product(-1, 44.09/14.38 | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 & 44.09/14.38 | | | | | | | size1(all_301_1) = all_92_8 & in_tree1(all_301_0) & 44.09/14.38 | | | | | | | in_tree1(all_301_1) 44.09/14.38 | | | | | | | 44.09/14.38 | | | | | | | ALPHA: (326) implies: 44.09/14.38 | | | | | | | (327) in_tree1(all_301_1) 44.09/14.38 | | | | | | | (328) size1(all_301_1) = all_92_8 44.09/14.38 | | | | | | | (329) $sum(size1(all_301_0), $product(-1, 44.09/14.38 | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 44.09/14.38 | | | | | | | (330) node1(all_301_1, all_301_0) = all_101_2 44.09/14.38 | | | | | | | 44.09/14.38 | | | | | | | BETA: splitting (184) gives: 44.09/14.38 | | | | | | | 44.09/14.38 | | | | | | | Case 1: 44.09/14.38 | | | | | | | | 44.09/14.38 | | | | | | | | (331) all_160_1 = all_77_2 44.09/14.38 | | | | | | | | 44.09/14.38 | | | | | | | | COMBINE_EQS: (222), (331) imply: 44.09/14.38 | | | | | | | | (332) all_77_2 = all_77_6 44.09/14.38 | | | | | | | | 44.09/14.38 | | | | | | | | SIMP: (332) implies: 44.09/14.38 | | | | | | | | (333) all_77_2 = all_77_6 44.09/14.38 | | | | | | | | 44.09/14.38 | | | | | | | | REDUCE: (165), (333) imply: 44.09/14.38 | | | | | | | | (334) ~ (0 = 0) 44.09/14.38 | | | | | | | | 44.09/14.38 | | | | | | | | CLOSE: (334) is inconsistent. 44.09/14.38 | | | | | | | | 44.09/14.38 | | | | | | | Case 2: 44.09/14.38 | | | | | | | | 44.09/14.39 | | | | | | | | 44.09/14.39 | | | | | | | | GROUND_INST: instantiating (86) with all_301_1, all_301_0, 44.09/14.39 | | | | | | | | simplifying with (327), (330) gives: 44.09/14.39 | | | | | | | | (335) ~ (all_101_0 = all_88_4) | ? [v0: $int] : ($lesseq(1, 44.09/14.39 | | | | | | | | $difference(v0, all_92_8)) & size1(all_301_1) = v0) 44.09/14.39 | | | | | | | | 44.09/14.39 | | | | | | | | GROUND_INST: instantiating (node_proj_1_def1) with all_301_1, 44.09/14.39 | | | | | | | | all_301_0, all_101_2, simplifying with (327), (330) 44.09/14.39 | | | | | | | | gives: 44.09/14.39 | | | | | | | | (336) node_proj_11(all_101_2) = all_301_1 44.09/14.39 | | | | | | | | 44.09/14.39 | | | | | | | | GROUND_INST: instantiating (5) with all_301_1, all_301_0, 44.09/14.39 | | | | | | | | all_101_2, simplifying with (327), (330) gives: 44.09/14.39 | | | | | | | | (337) ? [v0: $int] : ? [v1: $int] : ($sum(size1(all_301_0), 44.09/14.39 | | | | | | | | $product(-1, $sum($difference(v0, v1), -1))) = 0 & 44.09/14.39 | | | | | | | | size1(all_301_1) = v1 & size1(all_101_2) = v0) 44.09/14.39 | | | | | | | | 44.09/14.39 | | | | | | | | GROUND_INST: instantiating (node_proj_2_def1) with all_301_1, 44.09/14.39 | | | | | | | | all_301_0, all_101_2, simplifying with (327), (330) 44.09/14.39 | | | | | | | | gives: 44.09/14.39 | | | | | | | | (338) node_proj_21(all_101_2) = all_301_0 & 44.09/14.39 | | | | | | | | in_tree1(all_301_0) 44.09/14.39 | | | | | | | | 44.09/14.39 | | | | | | | | ALPHA: (338) implies: 44.09/14.39 | | | | | | | | (339) in_tree1(all_301_0) 44.09/14.39 | | | | | | | | 44.09/14.39 | | | | | | | | GROUND_INST: instantiating (size_left) with all_301_0, 44.09/14.39 | | | | | | | | $sum($difference(all_88_4, all_92_8), -1), 44.09/14.39 | | | | | | | | simplifying with (329), (339) gives: 44.09/14.39 | | | | | | | | (340) ~ ($lesseq(2, $difference(all_88_4, all_92_8))) | ? 44.09/14.39 | | | | | | | | [v0: $int] : ? [v1: $int] : ? [v2: $int] : 44.09/14.39 | | | | | | | | ($lesseq(2, $sum($difference($product(-1, v2), 44.09/14.39 | | | | | | | | all_92_8), all_88_4)) & node1(v0, v1) = 44.09/14.39 | | | | | | | | all_301_0 & size1(v0) = v2 & in_tree1(v1) & 44.09/14.39 | | | | | | | | in_tree1(v0)) 44.09/14.39 | | | | | | | | 44.09/14.39 | | | | | | | | GROUND_INST: instantiating (tree_diff) with all_301_1, 44.09/14.39 | | | | | | | | all_101_2, all_92_8, all_101_0, simplifying with 44.09/14.39 | | | | | | | | (84), (327), (328) gives: 44.09/14.39 | | | | | | | | (341) all_101_0 = all_92_8 | ! [v0: $int] : ! [v1: $int] : 44.09/14.39 | | | | | | | | ! [v2: $int] : ( ~ (node1(all_301_1, v0) = v2) | ~ 44.09/14.39 | | | | | | | | (node1(all_101_2, v1) = v2) | ~ in_tree1(v0)) 44.09/14.39 | | | | | | | | 44.09/14.40 | | | | | | | | DELTA: instantiating (337) with fresh symbols all_369_0, 44.09/14.40 | | | | | | | | all_369_1 gives: 44.09/14.40 | | | | | | | | (342) $sum(size1(all_301_0), $product(-1, 44.09/14.40 | | | | | | | | $sum($difference(all_369_1, all_369_0), -1))) = 0 & 44.09/14.40 | | | | | | | | size1(all_301_1) = all_369_0 & size1(all_101_2) = 44.09/14.40 | | | | | | | | all_369_1 44.09/14.40 | | | | | | | | 44.09/14.40 | | | | | | | | ALPHA: (342) implies: 44.09/14.40 | | | | | | | | (343) size1(all_101_2) = all_369_1 44.09/14.40 | | | | | | | | (344) size1(all_301_1) = all_369_0 44.09/14.40 | | | | | | | | (345) $sum(size1(all_301_0), $product(-1, 44.09/14.40 | | | | | | | | $sum($difference(all_369_1, all_369_0), -1))) = 0 44.09/14.40 | | | | | | | | 44.09/14.40 | | | | | | | | BETA: splitting (340) gives: 44.09/14.40 | | | | | | | | 44.09/14.40 | | | | | | | | Case 1: 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | | (346) $lesseq(-1, $difference(all_92_8, all_88_4)) 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | | COMBINE_INEQS: (239), (346) imply: 44.09/14.40 | | | | | | | | | (347) $lesseq(0, -1) 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | | CLOSE: (347) is inconsistent. 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | Case 2: 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | | (348) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : 44.09/14.40 | | | | | | | | | ($lesseq(2, $sum($difference($product(-1, v2), 44.09/14.40 | | | | | | | | | all_92_8), all_88_4)) & node1(v0, v1) = 44.09/14.40 | | | | | | | | | all_301_0 & size1(v0) = v2 & in_tree1(v1) & 44.09/14.40 | | | | | | | | | in_tree1(v0)) 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | | DELTA: instantiating (348) with fresh symbols all_416_0, 44.09/14.40 | | | | | | | | | all_416_1, all_416_2 gives: 44.09/14.40 | | | | | | | | | (349) $lesseq(2, $sum($difference($product(-1, all_416_0), 44.09/14.40 | | | | | | | | | all_92_8), all_88_4)) & node1(all_416_2, 44.09/14.40 | | | | | | | | | all_416_1) = all_301_0 & size1(all_416_2) = 44.09/14.40 | | | | | | | | | all_416_0 & in_tree1(all_416_1) & in_tree1(all_416_2) 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | | ALPHA: (349) implies: 44.09/14.40 | | | | | | | | | (350) $lesseq(2, $sum($difference($product(-1, all_416_0), 44.09/14.40 | | | | | | | | | all_92_8), all_88_4)) 44.09/14.40 | | | | | | | | | (351) in_tree1(all_416_2) 44.09/14.40 | | | | | | | | | (352) size1(all_416_2) = all_416_0 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | | GROUND_INST: instantiating (20) with all_248_2, all_301_1, 44.09/14.40 | | | | | | | | | all_101_2, simplifying with (324), (336) gives: 44.09/14.40 | | | | | | | | | (353) all_301_1 = all_248_2 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_416_2, 44.09/14.40 | | | | | | | | | all_416_0, simplifying with (351), (352) gives: 44.09/14.40 | | | | | | | | | (354) $lesseq(0, all_416_0) 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | | GROUND_INST: instantiating (14) with $sum($difference(all_88_4, 44.09/14.40 | | | | | | | | | all_92_8), -1), $sum($difference(all_369_1, 44.09/14.40 | | | | | | | | | all_369_0), -1), all_301_0, simplifying with 44.09/14.40 | | | | | | | | | (329), (345) gives: 44.09/14.40 | | | | | | | | | (355) $sum($difference($difference(all_369_0, all_369_1), 44.09/14.40 | | | | | | | | | all_92_8), all_88_4) = 0 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | | GROUND_INST: instantiating (14) with all_92_8, all_369_0, 44.09/14.40 | | | | | | | | | all_301_1, simplifying with (328), (344) gives: 44.09/14.40 | | | | | | | | | (356) all_369_0 = all_92_8 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | | GROUND_INST: instantiating (14) with all_101_0, all_369_1, 44.09/14.40 | | | | | | | | | all_101_2, simplifying with (84), (343) gives: 44.09/14.40 | | | | | | | | | (357) all_369_1 = all_101_0 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | | COMBINE_EQS: (355), (356) imply: 44.09/14.40 | | | | | | | | | (358) all_369_1 = all_88_4 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | | SIMP: (358) implies: 44.09/14.40 | | | | | | | | | (359) all_369_1 = all_88_4 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | | COMBINE_EQS: (357), (359) imply: 44.09/14.40 | | | | | | | | | (360) all_101_0 = all_88_4 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | | REDUCE: (328), (353) imply: 44.09/14.40 | | | | | | | | | (361) size1(all_248_2) = all_92_8 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | | BETA: splitting (323) gives: 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | | Case 1: 44.09/14.40 | | | | | | | | | | 44.09/14.40 | | | | | | | | | | (362) ~ (all_101_0 = all_88_4) 44.09/14.40 | | | | | | | | | | 44.09/14.40 | | | | | | | | | | REDUCE: (360), (362) imply: 44.09/14.40 | | | | | | | | | | (363) ~ (0 = 0) 44.09/14.40 | | | | | | | | | | 44.09/14.40 | | | | | | | | | | CLOSE: (363) is inconsistent. 44.09/14.40 | | | | | | | | | | 44.09/14.40 | | | | | | | | | Case 2: 44.09/14.40 | | | | | | | | | | 44.09/14.40 | | | | | | | | | | (364) ? [v0: $int] : ($lesseq(1, $difference(v0, 44.09/14.40 | | | | | | | | | | all_92_8)) & size1(all_248_2) = v0) 44.09/14.40 | | | | | | | | | | 44.09/14.40 | | | | | | | | | | DELTA: instantiating (364) with fresh symbol all_429_0 44.09/14.40 | | | | | | | | | | gives: 44.09/14.40 | | | | | | | | | | (365) $lesseq(1, $difference(all_429_0, all_92_8)) & 44.09/14.40 | | | | | | | | | | size1(all_248_2) = all_429_0 44.09/14.40 | | | | | | | | | | 44.09/14.40 | | | | | | | | | | ALPHA: (365) implies: 44.09/14.40 | | | | | | | | | | (366) $lesseq(1, $difference(all_429_0, all_92_8)) 44.09/14.40 | | | | | | | | | | (367) size1(all_248_2) = all_429_0 44.09/14.40 | | | | | | | | | | 44.09/14.40 | | | | | | | | | | BETA: splitting (335) gives: 44.09/14.40 | | | | | | | | | | 44.09/14.40 | | | | | | | | | | Case 1: 44.09/14.40 | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | (368) ~ (all_101_0 = all_88_4) 44.09/14.40 | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | REDUCE: (360), (368) imply: 44.09/14.40 | | | | | | | | | | | (369) ~ (0 = 0) 44.09/14.40 | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | CLOSE: (369) is inconsistent. 44.09/14.40 | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | Case 2: 44.09/14.40 | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | (370) ? [v0: $int] : ($lesseq(1, $difference(v0, 44.09/14.40 | | | | | | | | | | | all_92_8)) & size1(all_301_1) = v0) 44.09/14.40 | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | BETA: splitting (341) gives: 44.09/14.40 | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | Case 1: 44.09/14.40 | | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | | (371) all_101_0 = all_92_8 44.09/14.40 | | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | | COMBINE_EQS: (360), (371) imply: 44.09/14.40 | | | | | | | | | | | | (372) all_92_8 = all_88_4 44.09/14.40 | | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | | REDUCE: (350), (372) imply: 44.09/14.40 | | | | | | | | | | | | (373) $lesseq(all_416_0, -2) 44.09/14.40 | | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | | COMBINE_INEQS: (354), (373) imply: 44.09/14.40 | | | | | | | | | | | | (374) $lesseq(0, -1) 44.09/14.40 | | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | | CLOSE: (374) is inconsistent. 44.09/14.40 | | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | Case 2: 44.09/14.40 | | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | | DELTA: instantiating (370) with fresh symbol all_449_0 44.09/14.40 | | | | | | | | | | | | gives: 44.09/14.40 | | | | | | | | | | | | (375) $lesseq(1, $difference(all_449_0, all_92_8)) & 44.09/14.40 | | | | | | | | | | | | size1(all_301_1) = all_449_0 44.09/14.40 | | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | | ALPHA: (375) implies: 44.09/14.40 | | | | | | | | | | | | (376) size1(all_301_1) = all_449_0 44.09/14.40 | | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | | REDUCE: (353), (376) imply: 44.09/14.40 | | | | | | | | | | | | (377) size1(all_248_2) = all_449_0 44.09/14.40 | | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_449_0, all_429_0, 44.09/14.40 | | | | | | | | | | | | all_248_2, simplifying with (367), (377) gives: 44.09/14.40 | | | | | | | | | | | | (378) all_449_0 = all_429_0 44.09/14.40 | | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_449_0, all_92_8, 44.09/14.40 | | | | | | | | | | | | all_248_2, simplifying with (361), (377) gives: 44.09/14.40 | | | | | | | | | | | | (379) all_449_0 = all_92_8 44.09/14.40 | | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | | COMBINE_EQS: (378), (379) imply: 44.09/14.40 | | | | | | | | | | | | (380) all_429_0 = all_92_8 44.09/14.40 | | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | | REDUCE: (366), (380) imply: 44.09/14.40 | | | | | | | | | | | | (381) $lesseq(0, -1) 44.09/14.40 | | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | | CLOSE: (381) is inconsistent. 44.09/14.40 | | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | | End of split 44.09/14.40 | | | | | | | | | | | 44.09/14.40 | | | | | | | | | | End of split 44.09/14.40 | | | | | | | | | | 44.09/14.40 | | | | | | | | | End of split 44.09/14.40 | | | | | | | | | 44.09/14.40 | | | | | | | | End of split 44.09/14.40 | | | | | | | | 44.09/14.40 | | | | | | | End of split 44.09/14.40 | | | | | | | 44.09/14.40 | | | | | | Case 2: 44.09/14.40 | | | | | | | 44.09/14.40 | | | | | | | (382) ? [v0: $int] : ( ~ (v0 = 0) & sort1(all_74_1, all_96_2) 44.09/14.40 | | | | | | | = v0) 44.09/14.40 | | | | | | | 44.09/14.40 | | | | | | | REF_CLOSE: (22), (145), (319), (382) are inconsistent by sub-proof 44.09/14.40 | | | | | | | #6. 44.09/14.40 | | | | | | | 44.09/14.40 | | | | | | End of split 44.09/14.40 | | | | | | 44.09/14.40 | | | | | Case 2: 44.09/14.40 | | | | | | 44.09/14.40 | | | | | | 44.09/14.40 | | | | | | GROUND_INST: instantiating (86) with all_248_2, all_248_1, 44.09/14.40 | | | | | | simplifying with (313), (315) gives: 44.09/14.40 | | | | | | (383) ~ (all_101_0 = all_88_4) | ? [v0: $int] : ($lesseq(1, 44.09/14.40 | | | | | | $difference(v0, all_92_8)) & size1(all_248_2) = v0) 44.09/14.40 | | | | | | 44.09/14.40 | | | | | | GROUND_INST: instantiating (5) with all_248_2, all_248_1, all_101_2, 44.09/14.40 | | | | | | simplifying with (313), (315) gives: 44.09/14.40 | | | | | | (384) ? [v0: $int] : ? [v1: $int] : ($sum(size1(all_248_1), 44.09/14.40 | | | | | | $product(-1, $sum($difference(v0, v1), -1))) = 0 & 44.09/14.40 | | | | | | size1(all_248_2) = v1 & size1(all_101_2) = v0) 44.09/14.40 | | | | | | 44.09/14.40 | | | | | | GROUND_INST: instantiating (node_proj_2_def1) with all_248_2, 44.09/14.40 | | | | | | all_248_1, all_101_2, simplifying with (313), (315) 44.09/14.40 | | | | | | gives: 44.09/14.40 | | | | | | (385) node_proj_21(all_101_2) = all_248_1 & in_tree1(all_248_1) 44.09/14.40 | | | | | | 44.09/14.40 | | | | | | ALPHA: (385) implies: 44.09/14.40 | | | | | | (386) in_tree1(all_248_1) 44.09/14.40 | | | | | | 44.09/14.40 | | | | | | GROUND_INST: instantiating (tree_diff) with all_248_2, empty1, 44.09/14.40 | | | | | | all_248_0, 0, simplifying with (4), (313), (314) gives: 44.09/14.40 | | | | | | (387) all_248_0 = 0 | ! [v0: $int] : ! [v1: $int] : ! [v2: 44.09/14.40 | | | | | | $int] : ( ~ (node1(all_248_2, v0) = v2) | ~ 44.09/14.40 | | | | | | (node1(empty1, v1) = v2) | ~ in_tree1(v0)) 44.09/14.40 | | | | | | 44.09/14.40 | | | | | | GROUND_INST: instantiating (size_left) with all_248_2, all_248_0, 44.09/14.40 | | | | | | simplifying with (313), (314) gives: 44.09/14.40 | | | | | | (388) ~ ($lesseq(1, all_248_0)) | ? [v0: $int] : ? [v1: $int] 44.09/14.40 | | | | | | : ? [v2: $int] : ($lesseq(1, $difference(all_248_0, v2)) & 44.09/14.40 | | | | | | node1(v0, v1) = all_248_2 & size1(v0) = v2 & in_tree1(v1) 44.09/14.40 | | | | | | & in_tree1(v0)) 44.09/14.40 | | | | | | 44.09/14.40 | | | | | | DELTA: instantiating (384) with fresh symbols all_287_0, all_287_1 44.09/14.40 | | | | | | gives: 44.09/14.40 | | | | | | (389) $sum(size1(all_248_1), $product(-1, 44.09/14.40 | | | | | | $sum($difference(all_287_1, all_287_0), -1))) = 0 & 44.09/14.40 | | | | | | size1(all_248_2) = all_287_0 & size1(all_101_2) = all_287_1 44.09/14.40 | | | | | | 44.09/14.40 | | | | | | ALPHA: (389) implies: 44.09/14.40 | | | | | | (390) size1(all_101_2) = all_287_1 44.09/14.40 | | | | | | (391) size1(all_248_2) = all_287_0 44.09/14.40 | | | | | | (392) $sum(size1(all_248_1), $product(-1, 44.09/14.40 | | | | | | $sum($difference(all_287_1, all_287_0), -1))) = 0 44.09/14.40 | | | | | | 44.09/14.40 | | | | | | GROUND_INST: instantiating (14) with all_248_0, all_287_0, 44.09/14.40 | | | | | | all_248_2, simplifying with (314), (391) gives: 44.09/14.40 | | | | | | (393) all_287_0 = all_248_0 44.09/14.40 | | | | | | 44.09/14.40 | | | | | | GROUND_INST: instantiating (size_nonneg) with all_248_2, all_287_0, 44.09/14.40 | | | | | | simplifying with (313), (391) gives: 44.09/14.40 | | | | | | (394) $lesseq(0, all_287_0) 44.09/14.40 | | | | | | 44.09/14.40 | | | | | | GROUND_INST: instantiating (14) with all_101_0, all_287_1, 44.09/14.40 | | | | | | all_101_2, simplifying with (84), (390) gives: 44.09/14.40 | | | | | | (395) all_287_1 = all_101_0 44.09/14.40 | | | | | | 44.09/14.40 | | | | | | REDUCE: (393), (394) imply: 44.09/14.40 | | | | | | (396) $lesseq(0, all_248_0) 44.09/14.40 | | | | | | 44.09/14.40 | | | | | | REDUCE: (392), (393), (395) imply: 44.09/14.40 | | | | | | (397) $sum(size1(all_248_1), $product(-1, 44.09/14.40 | | | | | | $sum($difference(all_101_0, all_248_0), -1))) = 0 44.09/14.40 | | | | | | 44.09/14.40 | | | | | | BETA: splitting (170) gives: 44.09/14.40 | | | | | | 44.09/14.40 | | | | | | Case 1: 44.09/14.40 | | | | | | | 44.09/14.40 | | | | | | | (398) all_99_0 = all_96_2 44.09/14.40 | | | | | | | 44.09/14.40 | | | | | | | REDUCE: (83), (398) imply: 44.09/14.40 | | | | | | | (399) mem(tree, all_101_1, all_96_2) = 0 44.09/14.40 | | | | | | | 44.09/14.40 | | | | | | | BETA: splitting (184) gives: 44.09/14.40 | | | | | | | 44.09/14.40 | | | | | | | Case 1: 44.09/14.40 | | | | | | | | 44.09/14.40 | | | | | | | | (400) all_160_1 = all_77_2 44.09/14.40 | | | | | | | | 44.09/14.40 | | | | | | | | COMBINE_EQS: (222), (400) imply: 44.09/14.40 | | | | | | | | (401) all_77_2 = all_77_6 44.09/14.40 | | | | | | | | 44.09/14.40 | | | | | | | | SIMP: (401) implies: 44.09/14.40 | | | | | | | | (402) all_77_2 = all_77_6 44.09/14.40 | | | | | | | | 44.09/14.40 | | | | | | | | REDUCE: (165), (402) imply: 44.09/14.40 | | | | | | | | (403) ~ (0 = 0) 44.09/14.40 | | | | | | | | 44.09/14.40 | | | | | | | | CLOSE: (403) is inconsistent. 44.09/14.40 | | | | | | | | 44.09/14.40 | | | | | | | Case 2: 44.09/14.40 | | | | | | | | 44.09/14.40 | | | | | | | | (404) ~ (all_160_1 = all_77_2) 44.09/14.40 | | | | | | | | 44.09/14.41 | | | | | | | | GROUND_INST: instantiating (tree_diff) with all_248_1, 44.09/14.41 | | | | | | | | all_101_2, $sum($difference(all_101_0, all_248_0), 44.09/14.41 | | | | | | | | -1), all_101_0, simplifying with (84), (386), 44.09/14.41 | | | | | | | | (397) gives: 44.09/14.41 | | | | | | | | (405) all_248_0 = -1 | ! [v0: $int] : ! [v1: $int] : ! 44.09/14.41 | | | | | | | | [v2: $int] : ( ~ (node1(all_248_1, v0) = v2) | ~ 44.09/14.41 | | | | | | | | (node1(all_101_2, v1) = v2) | ~ in_tree1(v0)) 44.09/14.41 | | | | | | | | 44.09/14.41 | | | | | | | | GROUND_INST: instantiating (7) with tree, all_101_1, all_96_3, 44.09/14.41 | | | | | | | | all_92_6, all_96_2, simplifying with (10), (73), 44.09/14.41 | | | | | | | | (399) gives: 44.09/14.41 | | | | | | | | (406) ? [v0: $int] : ? [v1: $int] : (mem(tree, all_101_1, 44.09/14.41 | | | | | | | | all_96_3) = v1 & mem(tree, all_101_1, all_92_6) = 44.09/14.41 | | | | | | | | v0 & (v1 = 0 | v0 = 0)) 44.09/14.41 | | | | | | | | 44.09/14.41 | | | | | | | | DELTA: instantiating (406) with fresh symbols all_350_0, 44.09/14.41 | | | | | | | | all_350_1 gives: 44.09/14.41 | | | | | | | | (407) mem(tree, all_101_1, all_96_3) = all_350_0 & mem(tree, 44.09/14.41 | | | | | | | | all_101_1, all_92_6) = all_350_1 & (all_350_0 = 0 | 44.09/14.41 | | | | | | | | all_350_1 = 0) 44.09/14.41 | | | | | | | | 44.09/14.41 | | | | | | | | ALPHA: (407) implies: 44.09/14.41 | | | | | | | | (408) mem(tree, all_101_1, all_92_6) = all_350_1 44.09/14.41 | | | | | | | | (409) mem(tree, all_101_1, all_96_3) = all_350_0 44.09/14.41 | | | | | | | | (410) all_350_0 = 0 | all_350_1 = 0 44.09/14.41 | | | | | | | | 44.09/14.41 | | | | | | | | BETA: splitting (405) gives: 44.09/14.41 | | | | | | | | 44.09/14.41 | | | | | | | | Case 1: 44.09/14.41 | | | | | | | | | 44.09/14.41 | | | | | | | | | (411) all_248_0 = -1 44.09/14.41 | | | | | | | | | 44.09/14.41 | | | | | | | | | REDUCE: (396), (411) imply: 44.09/14.41 | | | | | | | | | (412) $lesseq(0, -1) 44.09/14.41 | | | | | | | | | 44.09/14.41 | | | | | | | | | CLOSE: (412) is inconsistent. 44.09/14.41 | | | | | | | | | 44.09/14.41 | | | | | | | | Case 2: 44.09/14.41 | | | | | | | | | 44.09/14.41 | | | | | | | | | 44.09/14.41 | | | | | | | | | GROUND_INST: instantiating (65) with all_101_2, all_101_1, 44.09/14.41 | | | | | | | | | all_350_1, simplifying with (82), (85), (408) 44.09/14.41 | | | | | | | | | gives: 44.09/14.41 | | | | | | | | | (413) all_350_1 = 0 | ? [v0: $int] : (size1(all_101_2) = 44.09/14.41 | | | | | | | | | v0 & ! [v1: $int] : ! [v2: $int] : ( ~ (v0 = 44.09/14.41 | | | | | | | | | all_88_4) | ~ (node1(v1, v2) = all_101_2) | ~ 44.09/14.41 | | | | | | | | | in_tree1(v1) | ? [v3: $int] : ($lesseq(all_92_8, 44.09/14.41 | | | | | | | | | v3) & size1(v1) = v3))) 44.09/14.41 | | | | | | | | | 44.09/14.41 | | | | | | | | | BETA: splitting (387) gives: 44.09/14.41 | | | | | | | | | 44.09/14.41 | | | | | | | | | Case 1: 44.09/14.41 | | | | | | | | | | 44.09/14.41 | | | | | | | | | | (414) all_248_0 = 0 44.09/14.41 | | | | | | | | | | 44.09/14.41 | | | | | | | | | | REDUCE: (314), (414) imply: 44.09/14.41 | | | | | | | | | | (415) size1(all_248_2) = 0 44.09/14.41 | | | | | | | | | | 44.09/14.41 | | | | | | | | | | BETA: splitting (410) gives: 44.09/14.41 | | | | | | | | | | 44.09/14.41 | | | | | | | | | | Case 1: 44.09/14.41 | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | (416) all_350_0 = 0 44.09/14.41 | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | REDUCE: (409), (416) imply: 44.09/14.41 | | | | | | | | | | | (417) mem(tree, all_101_1, all_96_3) = 0 44.09/14.41 | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | GROUND_INST: instantiating (75) with all_101_2, all_101_1, 44.09/14.41 | | | | | | | | | | | simplifying with (82), (85), (417) gives: 44.09/14.41 | | | | | | | | | | | (418) ? [v0: $int] : ? [v1: $int] : (node1(v0, v1) = 44.09/14.41 | | | | | | | | | | | all_101_2 & $sum(size1(v1), $product(-1, 44.09/14.41 | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) 44.09/14.41 | | | | | | | | | | | = 0 & size1(v0) = all_92_8 & in_tree1(v1) & 44.09/14.41 | | | | | | | | | | | in_tree1(v0)) 44.09/14.41 | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | DELTA: instantiating (418) with fresh symbols all_504_0, 44.09/14.41 | | | | | | | | | | | all_504_1 gives: 44.09/14.41 | | | | | | | | | | | (419) node1(all_504_1, all_504_0) = all_101_2 & 44.09/14.41 | | | | | | | | | | | $sum(size1(all_504_0), $product(-1, 44.09/14.41 | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 44.09/14.41 | | | | | | | | | | | 0 & size1(all_504_1) = all_92_8 & 44.09/14.41 | | | | | | | | | | | in_tree1(all_504_0) & in_tree1(all_504_1) 44.09/14.41 | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | ALPHA: (419) implies: 44.09/14.41 | | | | | | | | | | | (420) size1(all_504_1) = all_92_8 44.09/14.41 | | | | | | | | | | | (421) node1(all_504_1, all_504_0) = all_101_2 44.09/14.41 | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | GROUND_INST: instantiating (tree_diff) with all_248_2, 44.09/14.41 | | | | | | | | | | | all_504_1, 0, all_92_8, simplifying with (313), 44.09/14.41 | | | | | | | | | | | (415), (420) gives: 44.09/14.41 | | | | | | | | | | | (422) all_92_8 = 0 | ! [v0: $int] : ! [v1: $int] : ! 44.09/14.41 | | | | | | | | | | | [v2: $int] : ( ~ (node1(all_504_1, v1) = v2) | ~ 44.09/14.41 | | | | | | | | | | | (node1(all_248_2, v0) = v2) | ~ in_tree1(v0)) 44.09/14.41 | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | BETA: splitting (422) gives: 44.09/14.41 | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | Case 1: 44.09/14.41 | | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | | (423) all_92_8 = 0 44.09/14.41 | | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | | REDUCE: (236), (423) imply: 44.09/14.41 | | | | | | | | | | | | (424) $lesseq(0, -1) 44.09/14.41 | | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | | CLOSE: (424) is inconsistent. 44.09/14.41 | | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | Case 2: 44.09/14.41 | | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | | (425) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( 44.09/14.41 | | | | | | | | | | | | ~ (node1(all_504_1, v1) = v2) | ~ 44.09/14.41 | | | | | | | | | | | | (node1(all_248_2, v0) = v2) | ~ in_tree1(v0)) 44.09/14.41 | | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | | GROUND_INST: instantiating (425) with all_248_1, all_504_0, 44.09/14.41 | | | | | | | | | | | | all_101_2, simplifying with (315), (386), (421) 44.09/14.41 | | | | | | | | | | | | gives: 44.09/14.41 | | | | | | | | | | | | (426) $false 44.09/14.41 | | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | | CLOSE: (426) is inconsistent. 44.09/14.41 | | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | End of split 44.09/14.41 | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | Case 2: 44.09/14.41 | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | (427) all_350_1 = 0 44.09/14.41 | | | | | | | | | | | 44.09/14.41 | | | | | | | | | | | REDUCE: (408), (427) imply: 44.09/14.41 | | | | | | | | | | | (428) mem(tree, all_101_1, all_92_6) = 0 44.09/14.41 | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | REF_CLOSE: (5), (14), (64), (82), (84), (85), (86), (165), 44.34/14.42 | | | | | | | | | | | (184), (222), (386), (396), (397), (428), 44.34/14.42 | | | | | | | | | | | (tree_diff) are inconsistent by sub-proof #5. 44.34/14.42 | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | End of split 44.34/14.42 | | | | | | | | | | 44.34/14.42 | | | | | | | | | Case 2: 44.34/14.42 | | | | | | | | | | 44.34/14.42 | | | | | | | | | | (429) ~ (all_248_0 = 0) 44.34/14.42 | | | | | | | | | | 44.34/14.42 | | | | | | | | | | STRENGTHEN: (396), (429) imply: 44.34/14.42 | | | | | | | | | | (430) $lesseq(1, all_248_0) 44.34/14.42 | | | | | | | | | | 44.34/14.42 | | | | | | | | | | BETA: splitting (388) gives: 44.34/14.42 | | | | | | | | | | 44.34/14.42 | | | | | | | | | | Case 1: 44.34/14.42 | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | (431) $lesseq(all_248_0, 0) 44.34/14.42 | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | COMBINE_INEQS: (430), (431) imply: 44.34/14.42 | | | | | | | | | | | (432) $lesseq(0, -1) 44.34/14.42 | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | CLOSE: (432) is inconsistent. 44.34/14.42 | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | Case 2: 44.34/14.42 | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | (433) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : 44.34/14.42 | | | | | | | | | | | ($lesseq(1, $difference(all_248_0, v2)) & 44.34/14.42 | | | | | | | | | | | node1(v0, v1) = all_248_2 & size1(v0) = v2 & 44.34/14.42 | | | | | | | | | | | in_tree1(v1) & in_tree1(v0)) 44.34/14.42 | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | DELTA: instantiating (433) with fresh symbols all_445_0, 44.34/14.42 | | | | | | | | | | | all_445_1, all_445_2 gives: 44.34/14.42 | | | | | | | | | | | (434) $lesseq(1, $difference(all_248_0, all_445_0)) & 44.34/14.42 | | | | | | | | | | | node1(all_445_2, all_445_1) = all_248_2 & 44.34/14.42 | | | | | | | | | | | size1(all_445_2) = all_445_0 & in_tree1(all_445_1) 44.34/14.42 | | | | | | | | | | | & in_tree1(all_445_2) 44.34/14.42 | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | ALPHA: (434) implies: 44.34/14.42 | | | | | | | | | | | (435) $lesseq(1, $difference(all_248_0, all_445_0)) 44.34/14.42 | | | | | | | | | | | (436) in_tree1(all_445_2) 44.34/14.42 | | | | | | | | | | | (437) size1(all_445_2) = all_445_0 44.34/14.42 | | | | | | | | | | | (438) node1(all_445_2, all_445_1) = all_248_2 44.34/14.42 | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | BETA: splitting (383) gives: 44.34/14.42 | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | Case 1: 44.34/14.42 | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | (439) ~ (all_101_0 = all_88_4) 44.34/14.42 | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_445_2, all_445_1, 44.34/14.42 | | | | | | | | | | | | all_248_2, simplifying with (436), (438) gives: 44.34/14.42 | | | | | | | | | | | | (440) ? [v0: $int] : ? [v1: $int] : 44.34/14.42 | | | | | | | | | | | | ($sum(size1(all_445_1), $product(-1, 44.34/14.42 | | | | | | | | | | | | $sum($difference(v0, v1), -1))) = 0 & 44.34/14.42 | | | | | | | | | | | | size1(all_445_2) = v1 & size1(all_248_2) = v0) 44.34/14.42 | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | GROUND_INST: instantiating (tree_diff) with all_248_2, 44.34/14.42 | | | | | | | | | | | | all_445_2, all_248_0, all_445_0, simplifying with 44.34/14.42 | | | | | | | | | | | | (313), (314), (437) gives: 44.34/14.42 | | | | | | | | | | | | (441) all_445_0 = all_248_0 | ! [v0: $int] : ! [v1: 44.34/14.42 | | | | | | | | | | | | $int] : ! [v2: $int] : ( ~ (node1(all_445_2, 44.34/14.42 | | | | | | | | | | | | v1) = v2) | ~ (node1(all_248_2, v0) = v2) | 44.34/14.42 | | | | | | | | | | | | ~ in_tree1(v0)) 44.34/14.42 | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | DELTA: instantiating (440) with fresh symbols all_471_0, 44.34/14.42 | | | | | | | | | | | | all_471_1 gives: 44.34/14.42 | | | | | | | | | | | | (442) $sum(size1(all_445_1), $product(-1, 44.34/14.42 | | | | | | | | | | | | $sum($difference(all_471_1, all_471_0), -1))) 44.34/14.42 | | | | | | | | | | | | = 0 & size1(all_445_2) = all_471_0 & 44.34/14.42 | | | | | | | | | | | | size1(all_248_2) = all_471_1 44.34/14.42 | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | ALPHA: (442) implies: 44.34/14.42 | | | | | | | | | | | | (443) size1(all_248_2) = all_471_1 44.34/14.42 | | | | | | | | | | | | (444) size1(all_445_2) = all_471_0 44.34/14.42 | | | | | | | | | | | | (445) $sum(size1(all_445_1), $product(-1, 44.34/14.42 | | | | | | | | | | | | $sum($difference(all_471_1, all_471_0), -1))) 44.34/14.42 | | | | | | | | | | | | = 0 44.34/14.42 | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | BETA: splitting (441) gives: 44.34/14.42 | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | Case 1: 44.34/14.42 | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | (446) all_445_0 = all_248_0 44.34/14.42 | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | REDUCE: (435), (446) imply: 44.34/14.42 | | | | | | | | | | | | | (447) $lesseq(0, -1) 44.34/14.42 | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | CLOSE: (447) is inconsistent. 44.34/14.42 | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | Case 2: 44.34/14.42 | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_445_0, all_471_0, 44.34/14.42 | | | | | | | | | | | | | all_445_2, simplifying with (437), (444) gives: 44.34/14.42 | | | | | | | | | | | | | (448) all_471_0 = all_445_0 44.34/14.42 | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_445_2, 44.34/14.42 | | | | | | | | | | | | | all_471_0, simplifying with (436), (444) gives: 44.34/14.42 | | | | | | | | | | | | | (449) $lesseq(0, all_471_0) 44.34/14.42 | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_248_0, all_471_1, 44.34/14.42 | | | | | | | | | | | | | all_248_2, simplifying with (314), (443) gives: 44.34/14.42 | | | | | | | | | | | | | (450) all_471_1 = all_248_0 44.34/14.42 | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | REDUCE: (448), (449) imply: 44.34/14.42 | | | | | | | | | | | | | (451) $lesseq(0, all_445_0) 44.34/14.42 | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | REDUCE: (445), (448), (450) imply: 44.34/14.42 | | | | | | | | | | | | | (452) $sum(size1(all_445_1), $product(-1, 44.34/14.42 | | | | | | | | | | | | | $sum($difference(all_248_0, all_445_0), -1))) 44.34/14.42 | | | | | | | | | | | | | = 0 44.34/14.42 | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | BETA: splitting (410) gives: 44.34/14.42 | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | Case 1: 44.34/14.42 | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | (453) all_350_0 = 0 44.34/14.42 | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | REDUCE: (409), (453) imply: 44.34/14.42 | | | | | | | | | | | | | | (454) mem(tree, all_101_1, all_96_3) = 0 44.34/14.42 | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | GROUND_INST: instantiating (tree_diff) with all_248_2, 44.34/14.42 | | | | | | | | | | | | | | all_445_1, all_248_0, $sum($difference(all_248_0, 44.34/14.42 | | | | | | | | | | | | | | all_445_0), -1), simplifying with (313), 44.34/14.42 | | | | | | | | | | | | | | (314), (452) gives: 44.34/14.42 | | | | | | | | | | | | | | (455) all_445_0 = -1 | ! [v0: $int] : ! [v1: $int] : 44.34/14.42 | | | | | | | | | | | | | | ! [v2: $int] : ( ~ (node1(all_445_1, v1) = v2) | 44.34/14.42 | | | | | | | | | | | | | | ~ (node1(all_248_2, v0) = v2) | ~ in_tree1(v0)) 44.34/14.42 | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | GROUND_INST: instantiating (75) with all_101_2, all_101_1, 44.34/14.42 | | | | | | | | | | | | | | simplifying with (82), (85), (454) gives: 44.34/14.42 | | | | | | | | | | | | | | (456) ? [v0: $int] : ? [v1: $int] : (node1(v0, v1) = 44.34/14.42 | | | | | | | | | | | | | | all_101_2 & $sum(size1(v1), $product(-1, 44.34/14.42 | | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) 44.34/14.42 | | | | | | | | | | | | | | = 0 & size1(v0) = all_92_8 & in_tree1(v1) & 44.34/14.42 | | | | | | | | | | | | | | in_tree1(v0)) 44.34/14.42 | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | DELTA: instantiating (456) with fresh symbols all_553_0, 44.34/14.42 | | | | | | | | | | | | | | all_553_1 gives: 44.34/14.42 | | | | | | | | | | | | | | (457) node1(all_553_1, all_553_0) = all_101_2 & 44.34/14.42 | | | | | | | | | | | | | | $sum(size1(all_553_0), $product(-1, 44.34/14.42 | | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 44.34/14.42 | | | | | | | | | | | | | | 0 & size1(all_553_1) = all_92_8 & 44.34/14.42 | | | | | | | | | | | | | | in_tree1(all_553_0) & in_tree1(all_553_1) 44.34/14.42 | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | ALPHA: (457) implies: 44.34/14.42 | | | | | | | | | | | | | | (458) in_tree1(all_553_1) 44.34/14.42 | | | | | | | | | | | | | | (459) size1(all_553_1) = all_92_8 44.34/14.42 | | | | | | | | | | | | | | (460) $sum(size1(all_553_0), $product(-1, 44.34/14.42 | | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 44.34/14.42 | | | | | | | | | | | | | | 0 44.34/14.42 | | | | | | | | | | | | | | (461) node1(all_553_1, all_553_0) = all_101_2 44.34/14.42 | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | BETA: splitting (455) gives: 44.34/14.42 | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | Case 1: 44.34/14.42 | | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | | (462) all_445_0 = -1 44.34/14.42 | | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | | REDUCE: (451), (462) imply: 44.34/14.42 | | | | | | | | | | | | | | | (463) $lesseq(0, -1) 44.34/14.42 | | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | | CLOSE: (463) is inconsistent. 44.34/14.42 | | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | Case 2: 44.34/14.42 | | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_553_1, all_553_0, 44.34/14.42 | | | | | | | | | | | | | | | all_101_2, simplifying with (458), (461) gives: 44.34/14.42 | | | | | | | | | | | | | | | (464) ? [v0: $int] : ? [v1: $int] : 44.34/14.42 | | | | | | | | | | | | | | | ($sum(size1(all_553_0), $product(-1, 44.34/14.42 | | | | | | | | | | | | | | | $sum($difference(v0, v1), -1))) = 0 & 44.34/14.42 | | | | | | | | | | | | | | | size1(all_553_1) = v1 & size1(all_101_2) = v0) 44.34/14.42 | | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | | DELTA: instantiating (464) with fresh symbols all_621_0, 44.34/14.42 | | | | | | | | | | | | | | | all_621_1 gives: 44.34/14.42 | | | | | | | | | | | | | | | (465) $sum(size1(all_553_0), $product(-1, 44.34/14.42 | | | | | | | | | | | | | | | $sum($difference(all_621_1, all_621_0), -1))) 44.34/14.42 | | | | | | | | | | | | | | | = 0 & size1(all_553_1) = all_621_0 & 44.34/14.42 | | | | | | | | | | | | | | | size1(all_101_2) = all_621_1 44.34/14.42 | | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | | ALPHA: (465) implies: 44.34/14.42 | | | | | | | | | | | | | | | (466) size1(all_101_2) = all_621_1 44.34/14.42 | | | | | | | | | | | | | | | (467) size1(all_553_1) = all_621_0 44.34/14.42 | | | | | | | | | | | | | | | (468) $sum(size1(all_553_0), $product(-1, 44.34/14.42 | | | | | | | | | | | | | | | $sum($difference(all_621_1, all_621_0), -1))) 44.34/14.42 | | | | | | | | | | | | | | | = 0 44.34/14.42 | | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with $sum($difference(all_88_4, 44.34/14.42 | | | | | | | | | | | | | | | all_92_8), -1), $sum($difference(all_621_1, 44.34/14.42 | | | | | | | | | | | | | | | all_621_0), -1), all_553_0, simplifying with 44.34/14.42 | | | | | | | | | | | | | | | (460), (468) gives: 44.34/14.42 | | | | | | | | | | | | | | | (469) $sum($difference($difference(all_621_0, 44.34/14.42 | | | | | | | | | | | | | | | all_621_1), all_92_8), all_88_4) = 0 44.34/14.42 | | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_92_8, all_621_0, 44.34/14.42 | | | | | | | | | | | | | | | all_553_1, simplifying with (459), (467) gives: 44.34/14.42 | | | | | | | | | | | | | | | (470) all_621_0 = all_92_8 44.34/14.42 | | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_101_0, all_621_1, 44.34/14.42 | | | | | | | | | | | | | | | all_101_2, simplifying with (84), (466) gives: 44.34/14.42 | | | | | | | | | | | | | | | (471) all_621_1 = all_101_0 44.34/14.42 | | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | | COMBINE_EQS: (469), (470) imply: 44.34/14.42 | | | | | | | | | | | | | | | (472) all_621_1 = all_88_4 44.34/14.42 | | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | | COMBINE_EQS: (471), (472) imply: 44.34/14.42 | | | | | | | | | | | | | | | (473) all_101_0 = all_88_4 44.34/14.42 | | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | | REDUCE: (439), (473) imply: 44.34/14.42 | | | | | | | | | | | | | | | (474) ~ (0 = 0) 44.34/14.42 | | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | | CLOSE: (474) is inconsistent. 44.34/14.42 | | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | End of split 44.34/14.42 | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | Case 2: 44.34/14.42 | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | (475) all_350_1 = 0 44.34/14.42 | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | REDUCE: (408), (475) imply: 44.34/14.42 | | | | | | | | | | | | | | (476) mem(tree, all_101_1, all_92_6) = 0 44.34/14.42 | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | | REF_CLOSE: (5), (14), (64), (82), (84), (85), (86), (165), 44.34/14.42 | | | | | | | | | | | | | | (184), (222), (386), (396), (397), (476), 44.34/14.42 | | | | | | | | | | | | | | (tree_diff) are inconsistent by sub-proof #5. 44.34/14.42 | | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | | End of split 44.34/14.42 | | | | | | | | | | | | | 44.34/14.42 | | | | | | | | | | | | End of split 44.34/14.42 | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | Case 2: 44.34/14.43 | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | (477) ? [v0: $int] : ($lesseq(1, $difference(v0, 44.34/14.43 | | | | | | | | | | | | all_92_8)) & size1(all_248_2) = v0) 44.34/14.43 | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | DELTA: instantiating (477) with fresh symbol all_460_0 44.34/14.43 | | | | | | | | | | | | gives: 44.34/14.43 | | | | | | | | | | | | (478) $lesseq(1, $difference(all_460_0, all_92_8)) & 44.34/14.43 | | | | | | | | | | | | size1(all_248_2) = all_460_0 44.34/14.43 | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | ALPHA: (478) implies: 44.34/14.43 | | | | | | | | | | | | (479) $lesseq(1, $difference(all_460_0, all_92_8)) 44.34/14.43 | | | | | | | | | | | | (480) size1(all_248_2) = all_460_0 44.34/14.43 | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_248_0, all_460_0, 44.34/14.43 | | | | | | | | | | | | all_248_2, simplifying with (314), (480) gives: 44.34/14.43 | | | | | | | | | | | | (481) all_460_0 = all_248_0 44.34/14.43 | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_248_2, 44.34/14.43 | | | | | | | | | | | | all_460_0, simplifying with (313), (480) gives: 44.34/14.43 | | | | | | | | | | | | (482) $lesseq(0, all_460_0) 44.34/14.43 | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | REDUCE: (479), (481) imply: 44.34/14.43 | | | | | | | | | | | | (483) $lesseq(1, $difference(all_248_0, all_92_8)) 44.34/14.43 | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | BETA: splitting (410) gives: 44.34/14.43 | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | Case 1: 44.34/14.43 | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | (484) all_350_0 = 0 44.34/14.43 | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | REDUCE: (409), (484) imply: 44.34/14.43 | | | | | | | | | | | | | (485) mem(tree, all_101_1, all_96_3) = 0 44.34/14.43 | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | GROUND_INST: instantiating (75) with all_101_2, all_101_1, 44.34/14.43 | | | | | | | | | | | | | simplifying with (82), (85), (485) gives: 44.34/14.43 | | | | | | | | | | | | | (486) ? [v0: $int] : ? [v1: $int] : (node1(v0, v1) = 44.34/14.43 | | | | | | | | | | | | | all_101_2 & $sum(size1(v1), $product(-1, 44.34/14.43 | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) 44.34/14.43 | | | | | | | | | | | | | = 0 & size1(v0) = all_92_8 & in_tree1(v1) & 44.34/14.43 | | | | | | | | | | | | | in_tree1(v0)) 44.34/14.43 | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | DELTA: instantiating (486) with fresh symbols all_561_0, 44.34/14.43 | | | | | | | | | | | | | all_561_1 gives: 44.34/14.43 | | | | | | | | | | | | | (487) node1(all_561_1, all_561_0) = all_101_2 & 44.34/14.43 | | | | | | | | | | | | | $sum(size1(all_561_0), $product(-1, 44.34/14.43 | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 44.34/14.43 | | | | | | | | | | | | | 0 & size1(all_561_1) = all_92_8 & 44.34/14.43 | | | | | | | | | | | | | in_tree1(all_561_0) & in_tree1(all_561_1) 44.34/14.43 | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | ALPHA: (487) implies: 44.34/14.43 | | | | | | | | | | | | | (488) size1(all_561_1) = all_92_8 44.34/14.43 | | | | | | | | | | | | | (489) node1(all_561_1, all_561_0) = all_101_2 44.34/14.43 | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | BETA: splitting (413) gives: 44.34/14.43 | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | Case 1: 44.34/14.43 | | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | | (490) all_350_1 = 0 44.34/14.43 | | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | | REDUCE: (408), (490) imply: 44.34/14.43 | | | | | | | | | | | | | | (491) mem(tree, all_101_1, all_92_6) = 0 44.34/14.43 | | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | | REF_CLOSE: (5), (14), (64), (82), (84), (85), (86), (165), 44.34/14.43 | | | | | | | | | | | | | | (184), (222), (386), (396), (397), (491), 44.34/14.43 | | | | | | | | | | | | | | (tree_diff) are inconsistent by sub-proof #5. 44.34/14.43 | | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | Case 2: 44.34/14.43 | | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | | GROUND_INST: instantiating (tree_diff) with all_248_2, 44.34/14.43 | | | | | | | | | | | | | | all_561_1, all_248_0, all_92_8, simplifying with 44.34/14.43 | | | | | | | | | | | | | | (313), (314), (488) gives: 44.34/14.43 | | | | | | | | | | | | | | (492) all_248_0 = all_92_8 | ! [v0: $int] : ! [v1: 44.34/14.43 | | | | | | | | | | | | | | $int] : ! [v2: $int] : ( ~ (node1(all_561_1, 44.34/14.43 | | | | | | | | | | | | | | v1) = v2) | ~ (node1(all_248_2, v0) = v2) | 44.34/14.43 | | | | | | | | | | | | | | ~ in_tree1(v0)) 44.34/14.43 | | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | | BETA: splitting (492) gives: 44.34/14.43 | | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | | Case 1: 44.34/14.43 | | | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | | | (493) all_248_0 = all_92_8 44.34/14.43 | | | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | | | REDUCE: (483), (493) imply: 44.34/14.43 | | | | | | | | | | | | | | | (494) $lesseq(0, -1) 44.34/14.43 | | | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | | | CLOSE: (494) is inconsistent. 44.34/14.43 | | | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | | Case 2: 44.34/14.43 | | | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | | | (495) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( 44.34/14.43 | | | | | | | | | | | | | | | ~ (node1(all_561_1, v1) = v2) | ~ 44.34/14.43 | | | | | | | | | | | | | | | (node1(all_248_2, v0) = v2) | ~ in_tree1(v0)) 44.34/14.43 | | | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | | | GROUND_INST: instantiating (495) with all_248_1, all_561_0, 44.34/14.43 | | | | | | | | | | | | | | | all_101_2, simplifying with (315), (386), (489) 44.34/14.43 | | | | | | | | | | | | | | | gives: 44.34/14.43 | | | | | | | | | | | | | | | (496) $false 44.34/14.43 | | | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | | | CLOSE: (496) is inconsistent. 44.34/14.43 | | | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | | End of split 44.34/14.43 | | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | End of split 44.34/14.43 | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | Case 2: 44.34/14.43 | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | (497) all_350_1 = 0 44.34/14.43 | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | REDUCE: (408), (497) imply: 44.34/14.43 | | | | | | | | | | | | | (498) mem(tree, all_101_1, all_92_6) = 0 44.34/14.43 | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | | REF_CLOSE: (5), (14), (64), (82), (84), (85), (86), (165), 44.34/14.43 | | | | | | | | | | | | | (184), (222), (386), (396), (397), (498), 44.34/14.43 | | | | | | | | | | | | | (tree_diff) are inconsistent by sub-proof #5. 44.34/14.43 | | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | | End of split 44.34/14.43 | | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | | End of split 44.34/14.43 | | | | | | | | | | | 44.34/14.43 | | | | | | | | | | End of split 44.34/14.43 | | | | | | | | | | 44.34/14.43 | | | | | | | | | End of split 44.34/14.43 | | | | | | | | | 44.34/14.43 | | | | | | | | End of split 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | End of split 44.34/14.43 | | | | | | | 44.34/14.43 | | | | | | Case 2: 44.34/14.43 | | | | | | | 44.34/14.43 | | | | | | | (499) ? [v0: $int] : ( ~ (v0 = 0) & sort1(all_74_1, all_96_2) 44.34/14.43 | | | | | | | = v0) 44.34/14.43 | | | | | | | 44.34/14.43 | | | | | | | DELTA: instantiating (499) with fresh symbol all_270_0 gives: 44.34/14.43 | | | | | | | (500) ~ (all_270_0 = 0) & sort1(all_74_1, all_96_2) = 44.34/14.43 | | | | | | | all_270_0 44.34/14.43 | | | | | | | 44.34/14.43 | | | | | | | REF_CLOSE: (10), (25), (73), (500), (infix_plpl_sort2) are 44.34/14.43 | | | | | | | inconsistent by sub-proof #7. 44.34/14.43 | | | | | | | 44.34/14.43 | | | | | | End of split 44.34/14.43 | | | | | | 44.34/14.43 | | | | | End of split 44.34/14.43 | | | | | 44.34/14.43 | | | | End of split 44.34/14.43 | | | | 44.34/14.43 | | | Case 2: 44.34/14.43 | | | | 44.34/14.43 | | | | (501) all_92_2 = all_77_4 44.34/14.43 | | | | 44.34/14.43 | | | | REDUCE: (102), (501) imply: 44.34/14.43 | | | | (502) $sum(tb2t(all_77_4), $product(-1, $sum($difference(all_88_4, 44.34/14.43 | | | | all_92_8), -1))) = 0 44.34/14.43 | | | | 44.34/14.43 | | | | GROUND_INST: instantiating (21) with 0, $sum($difference(all_88_4, 44.34/14.43 | | | | all_92_8), -1), all_77_4, simplifying with (106), (502) 44.34/14.43 | | | | gives: 44.34/14.43 | | | | (503) $difference(all_92_8, all_88_4) = -1 44.34/14.43 | | | | 44.34/14.43 | | | | REDUCE: (236), (503) imply: 44.34/14.43 | | | | (504) $lesseq(2, all_88_4) 44.34/14.43 | | | | 44.34/14.43 | | | | BETA: splitting (118) gives: 44.34/14.43 | | | | 44.34/14.43 | | | | Case 1: 44.34/14.43 | | | | | 44.34/14.43 | | | | | (505) all_101_0 = 0 44.34/14.43 | | | | | 44.34/14.43 | | | | | REDUCE: (84), (505) imply: 44.34/14.43 | | | | | (506) size1(all_101_2) = 0 44.34/14.43 | | | | | 44.34/14.43 | | | | | BETA: splitting (170) gives: 44.34/14.43 | | | | | 44.34/14.43 | | | | | Case 1: 44.34/14.43 | | | | | | 44.34/14.43 | | | | | | (507) all_99_0 = all_96_2 44.34/14.43 | | | | | | 44.34/14.43 | | | | | | REDUCE: (83), (507) imply: 44.34/14.43 | | | | | | (508) mem(tree, all_101_1, all_96_2) = 0 44.34/14.43 | | | | | | 44.34/14.43 | | | | | | BETA: splitting (184) gives: 44.34/14.43 | | | | | | 44.34/14.43 | | | | | | Case 1: 44.34/14.43 | | | | | | | 44.34/14.43 | | | | | | | (509) all_160_1 = all_77_2 44.34/14.43 | | | | | | | 44.34/14.43 | | | | | | | REF_CLOSE: (165), (222), (509) are inconsistent by sub-proof #8. 44.34/14.43 | | | | | | | 44.34/14.43 | | | | | | Case 2: 44.34/14.43 | | | | | | | 44.34/14.43 | | | | | | | 44.34/14.43 | | | | | | | GROUND_INST: instantiating (7) with tree, all_101_1, all_96_3, 44.34/14.43 | | | | | | | all_92_6, all_96_2, simplifying with (10), (73), 44.34/14.43 | | | | | | | (508) gives: 44.34/14.43 | | | | | | | (510) ? [v0: $int] : ? [v1: $int] : (mem(tree, all_101_1, 44.34/14.43 | | | | | | | all_96_3) = v1 & mem(tree, all_101_1, all_92_6) = v0 44.34/14.43 | | | | | | | & (v1 = 0 | v0 = 0)) 44.34/14.43 | | | | | | | 44.34/14.43 | | | | | | | DELTA: instantiating (510) with fresh symbols all_292_0, all_292_1 44.34/14.43 | | | | | | | gives: 44.34/14.43 | | | | | | | (511) mem(tree, all_101_1, all_96_3) = all_292_0 & mem(tree, 44.34/14.43 | | | | | | | all_101_1, all_92_6) = all_292_1 & (all_292_0 = 0 | 44.34/14.43 | | | | | | | all_292_1 = 0) 44.34/14.43 | | | | | | | 44.34/14.43 | | | | | | | ALPHA: (511) implies: 44.34/14.43 | | | | | | | (512) mem(tree, all_101_1, all_92_6) = all_292_1 44.34/14.43 | | | | | | | (513) mem(tree, all_101_1, all_96_3) = all_292_0 44.34/14.43 | | | | | | | (514) all_292_0 = 0 | all_292_1 = 0 44.34/14.43 | | | | | | | 44.34/14.43 | | | | | | | BETA: splitting (514) gives: 44.34/14.43 | | | | | | | 44.34/14.43 | | | | | | | Case 1: 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | (515) all_292_0 = 0 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | REDUCE: (513), (515) imply: 44.34/14.43 | | | | | | | | (516) mem(tree, all_101_1, all_96_3) = 0 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | GROUND_INST: instantiating (75) with all_101_2, all_101_1, 44.34/14.43 | | | | | | | | simplifying with (82), (85), (516) gives: 44.34/14.43 | | | | | | | | (517) ? [v0: $int] : ? [v1: $int] : (node1(v0, v1) = 44.34/14.43 | | | | | | | | all_101_2 & $sum(size1(v1), $product(-1, 44.34/14.43 | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 & 44.34/14.43 | | | | | | | | size1(v0) = all_92_8 & in_tree1(v1) & in_tree1(v0)) 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | DELTA: instantiating (517) with fresh symbols all_434_0, 44.34/14.43 | | | | | | | | all_434_1 gives: 44.34/14.43 | | | | | | | | (518) node1(all_434_1, all_434_0) = all_101_2 & 44.34/14.43 | | | | | | | | $sum(size1(all_434_0), $product(-1, 44.34/14.43 | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 & 44.34/14.43 | | | | | | | | size1(all_434_1) = all_92_8 & in_tree1(all_434_0) & 44.34/14.43 | | | | | | | | in_tree1(all_434_1) 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | ALPHA: (518) implies: 44.34/14.43 | | | | | | | | (519) in_tree1(all_434_1) 44.34/14.43 | | | | | | | | (520) size1(all_434_1) = all_92_8 44.34/14.43 | | | | | | | | (521) $sum(size1(all_434_0), $product(-1, 44.34/14.43 | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 44.34/14.43 | | | | | | | | (522) node1(all_434_1, all_434_0) = all_101_2 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | REDUCE: (503), (521) imply: 44.34/14.43 | | | | | | | | (523) size1(all_434_0) = 0 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | REDUCE: (503), (520) imply: 44.34/14.43 | | | | | | | | (524) $sum(size1(all_434_1), $product(-1, $sum(all_88_4, 44.34/14.43 | | | | | | | | -1))) = 0 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | GROUND_INST: instantiating (5) with all_434_1, all_434_0, 44.34/14.43 | | | | | | | | all_101_2, simplifying with (519), (522) gives: 44.34/14.43 | | | | | | | | (525) ? [v0: $int] : ? [v1: $int] : ($sum(size1(all_434_0), 44.34/14.43 | | | | | | | | $product(-1, $sum($difference(v0, v1), -1))) = 0 & 44.34/14.43 | | | | | | | | size1(all_434_1) = v1 & size1(all_101_2) = v0) 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | DELTA: instantiating (525) with fresh symbols all_463_0, 44.34/14.43 | | | | | | | | all_463_1 gives: 44.34/14.43 | | | | | | | | (526) $sum(size1(all_434_0), $product(-1, 44.34/14.43 | | | | | | | | $sum($difference(all_463_1, all_463_0), -1))) = 0 & 44.34/14.43 | | | | | | | | size1(all_434_1) = all_463_0 & size1(all_101_2) = 44.34/14.43 | | | | | | | | all_463_1 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | ALPHA: (526) implies: 44.34/14.43 | | | | | | | | (527) size1(all_101_2) = all_463_1 44.34/14.43 | | | | | | | | (528) size1(all_434_1) = all_463_0 44.34/14.43 | | | | | | | | (529) $sum(size1(all_434_0), $product(-1, 44.34/14.43 | | | | | | | | $sum($difference(all_463_1, all_463_0), -1))) = 0 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | GROUND_INST: instantiating (14) with 0, 44.34/14.43 | | | | | | | | $sum($difference(all_463_1, all_463_0), -1), 44.34/14.43 | | | | | | | | all_434_0, simplifying with (523), (529) gives: 44.34/14.43 | | | | | | | | (530) $difference(all_463_0, all_463_1) = -1 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | GROUND_INST: instantiating (14) with $sum(all_88_4, -1), 44.34/14.43 | | | | | | | | all_463_0, all_434_1, simplifying with (524), (528) 44.34/14.43 | | | | | | | | gives: 44.34/14.43 | | | | | | | | (531) $difference(all_463_0, all_88_4) = -1 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_434_1, 44.34/14.43 | | | | | | | | all_463_0, simplifying with (519), (528) gives: 44.34/14.43 | | | | | | | | (532) $lesseq(0, all_463_0) 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | GROUND_INST: instantiating (14) with 0, all_463_1, all_101_2, 44.34/14.43 | | | | | | | | simplifying with (506), (527) gives: 44.34/14.43 | | | | | | | | (533) all_463_1 = 0 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | COMBINE_EQS: (530), (531) imply: 44.34/14.43 | | | | | | | | (534) all_463_1 = all_88_4 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | SIMP: (534) implies: 44.34/14.43 | | | | | | | | (535) all_463_1 = all_88_4 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | COMBINE_EQS: (533), (535) imply: 44.34/14.43 | | | | | | | | (536) all_88_4 = 0 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | SIMP: (536) implies: 44.34/14.43 | | | | | | | | (537) all_88_4 = 0 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | COMBINE_EQS: (531), (537) imply: 44.34/14.43 | | | | | | | | (538) all_463_0 = -1 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | REDUCE: (532), (538) imply: 44.34/14.43 | | | | | | | | (539) $lesseq(0, -1) 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | CLOSE: (539) is inconsistent. 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | Case 2: 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | (540) all_292_1 = 0 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | REDUCE: (512), (540) imply: 44.34/14.43 | | | | | | | | (541) mem(tree, all_101_1, all_92_6) = 0 44.34/14.43 | | | | | | | | 44.34/14.43 | | | | | | | | GROUND_INST: instantiating (64) with all_101_2, all_101_1, 44.34/14.43 | | | | | | | | simplifying with (82), (85), (541) gives: 44.34/14.44 | | | | | | | | (542) ? [v0: $int] : (size1(all_101_2) = v0 & ? [v1: $int] 44.34/14.44 | | | | | | | | : ? [v2: $int] : ? [v3: $int] : (v0 = all_88_4 & 44.34/14.44 | | | | | | | | $lesseq(1, $difference(all_92_8, v3)) & node1(v1, 44.34/14.44 | | | | | | | | v2) = all_101_2 & size1(v1) = v3 & in_tree1(v2) & 44.34/14.44 | | | | | | | | in_tree1(v1))) 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | DELTA: instantiating (542) with fresh symbol all_321_0 gives: 44.34/14.44 | | | | | | | | (543) size1(all_101_2) = all_321_0 & ? [v0: $int] : ? [v1: 44.34/14.44 | | | | | | | | $int] : ? [v2: $int] : (all_321_0 = all_88_4 & 44.34/14.44 | | | | | | | | $lesseq(1, $difference(all_92_8, v2)) & node1(v0, v1) 44.34/14.44 | | | | | | | | = all_101_2 & size1(v0) = v2 & in_tree1(v1) & 44.34/14.44 | | | | | | | | in_tree1(v0)) 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | ALPHA: (543) implies: 44.34/14.44 | | | | | | | | (544) size1(all_101_2) = all_321_0 44.34/14.44 | | | | | | | | (545) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : 44.34/14.44 | | | | | | | | (all_321_0 = all_88_4 & $lesseq(1, 44.34/14.44 | | | | | | | | $difference(all_92_8, v2)) & node1(v0, v1) = 44.34/14.44 | | | | | | | | all_101_2 & size1(v0) = v2 & in_tree1(v1) & 44.34/14.44 | | | | | | | | in_tree1(v0)) 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | DELTA: instantiating (545) with fresh symbols all_325_0, 44.34/14.44 | | | | | | | | all_325_1, all_325_2 gives: 44.34/14.44 | | | | | | | | (546) all_321_0 = all_88_4 & $lesseq(1, $difference(all_92_8, 44.34/14.44 | | | | | | | | all_325_0)) & node1(all_325_2, all_325_1) = 44.34/14.44 | | | | | | | | all_101_2 & size1(all_325_2) = all_325_0 & 44.34/14.44 | | | | | | | | in_tree1(all_325_1) & in_tree1(all_325_2) 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | ALPHA: (546) implies: 44.34/14.44 | | | | | | | | (547) all_321_0 = all_88_4 44.34/14.44 | | | | | | | | (548) $lesseq(1, $difference(all_92_8, all_325_0)) 44.34/14.44 | | | | | | | | (549) in_tree1(all_325_2) 44.34/14.44 | | | | | | | | (550) size1(all_325_2) = all_325_0 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | REDUCE: (503), (548) imply: 44.34/14.44 | | | | | | | | (551) $lesseq(2, $difference(all_88_4, all_325_0)) 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | REDUCE: (544), (547) imply: 44.34/14.44 | | | | | | | | (552) size1(all_101_2) = all_88_4 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_325_2, 44.34/14.44 | | | | | | | | all_325_0, simplifying with (549), (550) gives: 44.34/14.44 | | | | | | | | (553) $lesseq(0, all_325_0) 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | GROUND_INST: instantiating (14) with 0, all_88_4, all_101_2, 44.34/14.44 | | | | | | | | simplifying with (506), (552) gives: 44.34/14.44 | | | | | | | | (554) all_88_4 = 0 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | REDUCE: (551), (554) imply: 44.34/14.44 | | | | | | | | (555) $lesseq(all_325_0, -2) 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | COMBINE_INEQS: (553), (555) imply: 44.34/14.44 | | | | | | | | (556) $lesseq(0, -1) 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | CLOSE: (556) is inconsistent. 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | End of split 44.34/14.44 | | | | | | | 44.34/14.44 | | | | | | End of split 44.34/14.44 | | | | | | 44.34/14.44 | | | | | Case 2: 44.34/14.44 | | | | | | 44.34/14.44 | | | | | | (557) ? [v0: $int] : ( ~ (v0 = 0) & sort1(all_74_1, all_96_2) = 44.34/14.44 | | | | | | v0) 44.34/14.44 | | | | | | 44.34/14.44 | | | | | | DELTA: instantiating (557) with fresh symbol all_270_0 gives: 44.34/14.44 | | | | | | (558) ~ (all_270_0 = 0) & sort1(all_74_1, all_96_2) = all_270_0 44.34/14.44 | | | | | | 44.34/14.44 | | | | | | REF_CLOSE: (10), (25), (73), (558), (infix_plpl_sort2) are 44.34/14.44 | | | | | | inconsistent by sub-proof #7. 44.34/14.44 | | | | | | 44.34/14.44 | | | | | End of split 44.34/14.44 | | | | | 44.34/14.44 | | | | Case 2: 44.34/14.44 | | | | | 44.34/14.44 | | | | | (559) ~ (all_101_0 = 0) 44.34/14.44 | | | | | 44.34/14.44 | | | | | STRENGTHEN: (92), (559) imply: 44.34/14.44 | | | | | (560) $lesseq(1, all_101_0) 44.34/14.44 | | | | | 44.34/14.44 | | | | | BETA: splitting (117) gives: 44.34/14.44 | | | | | 44.34/14.44 | | | | | Case 1: 44.34/14.44 | | | | | | 44.34/14.44 | | | | | | (561) $lesseq(all_101_0, 0) 44.34/14.44 | | | | | | 44.34/14.44 | | | | | | COMBINE_INEQS: (560), (561) imply: 44.34/14.44 | | | | | | (562) $lesseq(0, -1) 44.34/14.44 | | | | | | 44.34/14.44 | | | | | | CLOSE: (562) is inconsistent. 44.34/14.44 | | | | | | 44.34/14.44 | | | | | Case 2: 44.34/14.44 | | | | | | 44.34/14.44 | | | | | | (563) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ($lesseq(1, 44.34/14.44 | | | | | | $difference(all_101_0, v2)) & node1(v0, v1) = all_101_2 44.34/14.44 | | | | | | & size1(v0) = v2 & in_tree1(v1) & in_tree1(v0)) 44.34/14.44 | | | | | | 44.34/14.44 | | | | | | DELTA: instantiating (563) with fresh symbols all_253_0, all_253_1, 44.34/14.44 | | | | | | all_253_2 gives: 44.34/14.44 | | | | | | (564) $lesseq(1, $difference(all_101_0, all_253_0)) & 44.34/14.44 | | | | | | node1(all_253_2, all_253_1) = all_101_2 & size1(all_253_2) 44.34/14.44 | | | | | | = all_253_0 & in_tree1(all_253_1) & in_tree1(all_253_2) 44.34/14.44 | | | | | | 44.34/14.44 | | | | | | ALPHA: (564) implies: 44.34/14.44 | | | | | | (565) $lesseq(1, $difference(all_101_0, all_253_0)) 44.34/14.44 | | | | | | (566) in_tree1(all_253_2) 44.34/14.44 | | | | | | (567) size1(all_253_2) = all_253_0 44.34/14.44 | | | | | | (568) node1(all_253_2, all_253_1) = all_101_2 44.34/14.44 | | | | | | 44.34/14.44 | | | | | | BETA: splitting (127) gives: 44.34/14.44 | | | | | | 44.34/14.44 | | | | | | Case 1: 44.34/14.44 | | | | | | | 44.34/14.44 | | | | | | | (569) all_125_1 = all_92_6 44.34/14.44 | | | | | | | 44.34/14.44 | | | | | | | COMBINE_EQS: (157), (569) imply: 44.34/14.44 | | | | | | | (570) all_92_6 = all_77_6 44.34/14.44 | | | | | | | 44.34/14.44 | | | | | | | REDUCE: (73), (570) imply: 44.34/14.44 | | | | | | | (571) infix_plpl(tree, all_96_3, all_77_6) = all_96_2 44.34/14.44 | | | | | | | 44.34/14.44 | | | | | | | GROUND_INST: instantiating (append_l_nil) with tree, all_96_3, 44.34/14.44 | | | | | | | all_77_6, all_96_2, simplifying with (10), (28), 44.34/14.44 | | | | | | | (571) gives: 44.34/14.44 | | | | | | | (572) all_96_2 = all_96_3 44.34/14.44 | | | | | | | 44.34/14.44 | | | | | | | BETA: splitting (170) gives: 44.34/14.44 | | | | | | | 44.34/14.44 | | | | | | | Case 1: 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | (573) all_99_0 = all_96_2 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | COMBINE_EQS: (572), (573) imply: 44.34/14.44 | | | | | | | | (574) all_99_0 = all_96_3 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | REDUCE: (83), (574) imply: 44.34/14.44 | | | | | | | | (575) mem(tree, all_101_1, all_96_3) = 0 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | GROUND_INST: instantiating (86) with all_253_2, all_253_1, 44.34/14.44 | | | | | | | | simplifying with (566), (568) gives: 44.34/14.44 | | | | | | | | (576) ~ (all_101_0 = all_88_4) | ? [v0: $int] : ($lesseq(1, 44.34/14.44 | | | | | | | | $difference(v0, all_92_8)) & size1(all_253_2) = v0) 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | GROUND_INST: instantiating (75) with all_101_2, all_101_1, 44.34/14.44 | | | | | | | | simplifying with (82), (85), (575) gives: 44.34/14.44 | | | | | | | | (577) ? [v0: $int] : ? [v1: $int] : (node1(v0, v1) = 44.34/14.44 | | | | | | | | all_101_2 & $sum(size1(v1), $product(-1, 44.34/14.44 | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 & 44.34/14.44 | | | | | | | | size1(v0) = all_92_8 & in_tree1(v1) & in_tree1(v0)) 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | DELTA: instantiating (577) with fresh symbols all_296_0, 44.34/14.44 | | | | | | | | all_296_1 gives: 44.34/14.44 | | | | | | | | (578) node1(all_296_1, all_296_0) = all_101_2 & 44.34/14.44 | | | | | | | | $sum(size1(all_296_0), $product(-1, 44.34/14.44 | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 & 44.34/14.44 | | | | | | | | size1(all_296_1) = all_92_8 & in_tree1(all_296_0) & 44.34/14.44 | | | | | | | | in_tree1(all_296_1) 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | ALPHA: (578) implies: 44.34/14.44 | | | | | | | | (579) in_tree1(all_296_1) 44.34/14.44 | | | | | | | | (580) size1(all_296_1) = all_92_8 44.34/14.44 | | | | | | | | (581) $sum(size1(all_296_0), $product(-1, 44.34/14.44 | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 44.34/14.44 | | | | | | | | (582) node1(all_296_1, all_296_0) = all_101_2 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | REDUCE: (503), (581) imply: 44.34/14.44 | | | | | | | | (583) size1(all_296_0) = 0 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | REDUCE: (503), (580) imply: 44.34/14.44 | | | | | | | | (584) $sum(size1(all_296_1), $product(-1, $sum(all_88_4, 44.34/14.44 | | | | | | | | -1))) = 0 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | BETA: splitting (184) gives: 44.34/14.44 | | | | | | | | 44.34/14.44 | | | | | | | | Case 1: 44.34/14.44 | | | | | | | | | 44.34/14.44 | | | | | | | | | (585) all_160_1 = all_77_2 44.34/14.44 | | | | | | | | | 44.34/14.44 | | | | | | | | | COMBINE_EQS: (222), (585) imply: 44.34/14.44 | | | | | | | | | (586) all_77_2 = all_77_6 44.34/14.44 | | | | | | | | | 44.34/14.44 | | | | | | | | | SIMP: (586) implies: 44.34/14.44 | | | | | | | | | (587) all_77_2 = all_77_6 44.34/14.44 | | | | | | | | | 44.34/14.44 | | | | | | | | | REDUCE: (165), (587) imply: 44.34/14.44 | | | | | | | | | (588) ~ (0 = 0) 44.34/14.44 | | | | | | | | | 44.34/14.44 | | | | | | | | | CLOSE: (588) is inconsistent. 44.34/14.44 | | | | | | | | | 44.34/14.44 | | | | | | | | Case 2: 44.34/14.44 | | | | | | | | | 44.34/14.44 | | | | | | | | | 44.34/14.44 | | | | | | | | | GROUND_INST: instantiating (5) with all_296_1, all_296_0, 44.34/14.44 | | | | | | | | | all_101_2, simplifying with (579), (582) gives: 44.34/14.44 | | | | | | | | | (589) ? [v0: $int] : ? [v1: $int] : 44.34/14.44 | | | | | | | | | ($sum(size1(all_296_0), $product(-1, 44.34/14.44 | | | | | | | | | $sum($difference(v0, v1), -1))) = 0 & 44.34/14.44 | | | | | | | | | size1(all_296_1) = v1 & size1(all_101_2) = v0) 44.34/14.44 | | | | | | | | | 44.34/14.44 | | | | | | | | | GROUND_INST: instantiating (size_left) with all_296_1, 44.34/14.44 | | | | | | | | | $sum(all_88_4, -1), simplifying with (579), (584) 44.34/14.44 | | | | | | | | | gives: 44.34/14.44 | | | | | | | | | (590) ~ ($lesseq(2, all_88_4)) | ? [v0: $int] : ? [v1: 44.34/14.44 | | | | | | | | | $int] : ? [v2: $int] : ($lesseq(2, 44.34/14.44 | | | | | | | | | $difference(all_88_4, v2)) & node1(v0, v1) = 44.34/14.44 | | | | | | | | | all_296_1 & size1(v0) = v2 & in_tree1(v1) & 44.34/14.44 | | | | | | | | | in_tree1(v0)) 44.34/14.44 | | | | | | | | | 44.34/14.45 | | | | | | | | | DELTA: instantiating (589) with fresh symbols all_364_0, 44.34/14.45 | | | | | | | | | all_364_1 gives: 44.34/14.45 | | | | | | | | | (591) $sum(size1(all_296_0), $product(-1, 44.34/14.45 | | | | | | | | | $sum($difference(all_364_1, all_364_0), -1))) = 0 44.34/14.45 | | | | | | | | | & size1(all_296_1) = all_364_0 & size1(all_101_2) = 44.34/14.45 | | | | | | | | | all_364_1 44.34/14.45 | | | | | | | | | 44.34/14.45 | | | | | | | | | ALPHA: (591) implies: 44.34/14.45 | | | | | | | | | (592) size1(all_101_2) = all_364_1 44.34/14.45 | | | | | | | | | (593) size1(all_296_1) = all_364_0 44.34/14.45 | | | | | | | | | (594) $sum(size1(all_296_0), $product(-1, 44.34/14.45 | | | | | | | | | $sum($difference(all_364_1, all_364_0), -1))) = 0 44.34/14.45 | | | | | | | | | 44.34/14.45 | | | | | | | | | BETA: splitting (590) gives: 44.34/14.45 | | | | | | | | | 44.34/14.45 | | | | | | | | | Case 1: 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | | (595) $lesseq(all_88_4, 1) 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | | COMBINE_INEQS: (504), (595) imply: 44.34/14.45 | | | | | | | | | | (596) $lesseq(0, -1) 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | | CLOSE: (596) is inconsistent. 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | Case 2: 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | | GROUND_INST: instantiating (14) with 0, 44.34/14.45 | | | | | | | | | | $sum($difference(all_364_1, all_364_0), -1), 44.34/14.45 | | | | | | | | | | all_296_0, simplifying with (583), (594) gives: 44.34/14.45 | | | | | | | | | | (597) $difference(all_364_0, all_364_1) = -1 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | | GROUND_INST: instantiating (14) with $sum(all_88_4, -1), 44.34/14.45 | | | | | | | | | | all_364_0, all_296_1, simplifying with (584), 44.34/14.45 | | | | | | | | | | (593) gives: 44.34/14.45 | | | | | | | | | | (598) $difference(all_364_0, all_88_4) = -1 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | | GROUND_INST: instantiating (14) with all_101_0, all_364_1, 44.34/14.45 | | | | | | | | | | all_101_2, simplifying with (84), (592) gives: 44.34/14.45 | | | | | | | | | | (599) all_364_1 = all_101_0 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | | COMBINE_EQS: (597), (598) imply: 44.34/14.45 | | | | | | | | | | (600) all_364_1 = all_88_4 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | | SIMP: (600) implies: 44.34/14.45 | | | | | | | | | | (601) all_364_1 = all_88_4 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | | COMBINE_EQS: (599), (601) imply: 44.34/14.45 | | | | | | | | | | (602) all_101_0 = all_88_4 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | | REDUCE: (84), (602) imply: 44.34/14.45 | | | | | | | | | | (603) size1(all_101_2) = all_88_4 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | | REF_CLOSE: (14), (84), (503), (565), (567), (576), (603) are 44.34/14.45 | | | | | | | | | | inconsistent by sub-proof #4. 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | End of split 44.34/14.45 | | | | | | | | | 44.34/14.45 | | | | | | | | End of split 44.34/14.45 | | | | | | | | 44.34/14.45 | | | | | | | Case 2: 44.34/14.45 | | | | | | | | 44.34/14.45 | | | | | | | | (604) ? [v0: $int] : ( ~ (v0 = 0) & sort1(all_74_1, 44.34/14.45 | | | | | | | | all_96_2) = v0) 44.34/14.45 | | | | | | | | 44.34/14.45 | | | | | | | | REF_CLOSE: (22), (145), (572), (604) are inconsistent by 44.34/14.45 | | | | | | | | sub-proof #6. 44.34/14.45 | | | | | | | | 44.34/14.45 | | | | | | | End of split 44.34/14.45 | | | | | | | 44.34/14.45 | | | | | | Case 2: 44.34/14.45 | | | | | | | 44.34/14.45 | | | | | | | 44.34/14.45 | | | | | | | GROUND_INST: instantiating (86) with all_253_2, all_253_1, 44.34/14.45 | | | | | | | simplifying with (566), (568) gives: 44.34/14.45 | | | | | | | (605) ~ (all_101_0 = all_88_4) | ? [v0: $int] : ($lesseq(1, 44.34/14.45 | | | | | | | $difference(v0, all_92_8)) & size1(all_253_2) = v0) 44.34/14.45 | | | | | | | 44.34/14.45 | | | | | | | GROUND_INST: instantiating (5) with all_253_2, all_253_1, 44.34/14.45 | | | | | | | all_101_2, simplifying with (566), (568) gives: 44.34/14.45 | | | | | | | (606) ? [v0: $int] : ? [v1: $int] : ($sum(size1(all_253_1), 44.34/14.45 | | | | | | | $product(-1, $sum($difference(v0, v1), -1))) = 0 & 44.34/14.45 | | | | | | | size1(all_253_2) = v1 & size1(all_101_2) = v0) 44.34/14.45 | | | | | | | 44.34/14.45 | | | | | | | GROUND_INST: instantiating (node_proj_2_def1) with all_253_2, 44.34/14.45 | | | | | | | all_253_1, all_101_2, simplifying with (566), (568) 44.34/14.45 | | | | | | | gives: 44.34/14.45 | | | | | | | (607) node_proj_21(all_101_2) = all_253_1 & in_tree1(all_253_1) 44.34/14.45 | | | | | | | 44.34/14.45 | | | | | | | ALPHA: (607) implies: 44.34/14.45 | | | | | | | (608) in_tree1(all_253_1) 44.34/14.45 | | | | | | | 44.34/14.45 | | | | | | | GROUND_INST: instantiating (tree_diff) with all_253_2, empty1, 44.34/14.45 | | | | | | | all_253_0, 0, simplifying with (4), (566), (567) 44.34/14.45 | | | | | | | gives: 44.34/14.45 | | | | | | | (609) all_253_0 = 0 | ! [v0: $int] : ! [v1: $int] : ! [v2: 44.34/14.45 | | | | | | | $int] : ( ~ (node1(all_253_2, v0) = v2) | ~ 44.34/14.45 | | | | | | | (node1(empty1, v1) = v2) | ~ in_tree1(v0)) 44.34/14.45 | | | | | | | 44.34/14.45 | | | | | | | GROUND_INST: instantiating (size_left) with all_253_2, all_253_0, 44.34/14.45 | | | | | | | simplifying with (566), (567) gives: 44.34/14.45 | | | | | | | (610) ~ ($lesseq(1, all_253_0)) | ? [v0: $int] : ? [v1: 44.34/14.45 | | | | | | | $int] : ? [v2: $int] : ($lesseq(1, 44.34/14.45 | | | | | | | $difference(all_253_0, v2)) & node1(v0, v1) = 44.34/14.45 | | | | | | | all_253_2 & size1(v0) = v2 & in_tree1(v1) & 44.34/14.45 | | | | | | | in_tree1(v0)) 44.34/14.45 | | | | | | | 44.34/14.45 | | | | | | | DELTA: instantiating (606) with fresh symbols all_282_0, all_282_1 44.34/14.45 | | | | | | | gives: 44.34/14.45 | | | | | | | (611) $sum(size1(all_253_1), $product(-1, 44.34/14.45 | | | | | | | $sum($difference(all_282_1, all_282_0), -1))) = 0 & 44.34/14.45 | | | | | | | size1(all_253_2) = all_282_0 & size1(all_101_2) = 44.34/14.45 | | | | | | | all_282_1 44.34/14.45 | | | | | | | 44.34/14.45 | | | | | | | ALPHA: (611) implies: 44.34/14.45 | | | | | | | (612) size1(all_101_2) = all_282_1 44.34/14.45 | | | | | | | (613) size1(all_253_2) = all_282_0 44.34/14.45 | | | | | | | (614) $sum(size1(all_253_1), $product(-1, 44.34/14.45 | | | | | | | $sum($difference(all_282_1, all_282_0), -1))) = 0 44.34/14.45 | | | | | | | 44.34/14.45 | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_253_1, 44.34/14.45 | | | | | | | $sum($difference(all_282_1, all_282_0), -1), 44.34/14.45 | | | | | | | simplifying with (608), (614) gives: 44.34/14.45 | | | | | | | (615) $lesseq(1, $difference(all_282_1, all_282_0)) 44.34/14.45 | | | | | | | 44.34/14.45 | | | | | | | GROUND_INST: instantiating (14) with all_253_0, all_282_0, 44.34/14.45 | | | | | | | all_253_2, simplifying with (567), (613) gives: 44.34/14.45 | | | | | | | (616) all_282_0 = all_253_0 44.34/14.45 | | | | | | | 44.34/14.45 | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_253_2, 44.34/14.45 | | | | | | | all_282_0, simplifying with (566), (613) gives: 44.34/14.45 | | | | | | | (617) $lesseq(0, all_282_0) 44.34/14.45 | | | | | | | 44.34/14.45 | | | | | | | GROUND_INST: instantiating (14) with all_101_0, all_282_1, 44.34/14.45 | | | | | | | all_101_2, simplifying with (84), (612) gives: 44.34/14.45 | | | | | | | (618) all_282_1 = all_101_0 44.34/14.45 | | | | | | | 44.34/14.45 | | | | | | | REDUCE: (616), (617) imply: 44.34/14.45 | | | | | | | (619) $lesseq(0, all_253_0) 44.34/14.45 | | | | | | | 44.34/14.45 | | | | | | | BETA: splitting (170) gives: 44.34/14.45 | | | | | | | 44.34/14.45 | | | | | | | Case 1: 44.34/14.45 | | | | | | | | 44.34/14.45 | | | | | | | | (620) all_99_0 = all_96_2 44.34/14.45 | | | | | | | | 44.34/14.45 | | | | | | | | REDUCE: (83), (620) imply: 44.34/14.45 | | | | | | | | (621) mem(tree, all_101_1, all_96_2) = 0 44.34/14.45 | | | | | | | | 44.34/14.45 | | | | | | | | BETA: splitting (184) gives: 44.34/14.45 | | | | | | | | 44.34/14.45 | | | | | | | | Case 1: 44.34/14.45 | | | | | | | | | 44.34/14.45 | | | | | | | | | (622) all_160_1 = all_77_2 44.34/14.45 | | | | | | | | | 44.34/14.45 | | | | | | | | | COMBINE_EQS: (222), (622) imply: 44.34/14.45 | | | | | | | | | (623) all_77_2 = all_77_6 44.34/14.45 | | | | | | | | | 44.34/14.45 | | | | | | | | | SIMP: (623) implies: 44.34/14.45 | | | | | | | | | (624) all_77_2 = all_77_6 44.34/14.45 | | | | | | | | | 44.34/14.45 | | | | | | | | | REDUCE: (165), (624) imply: 44.34/14.45 | | | | | | | | | (625) ~ (0 = 0) 44.34/14.45 | | | | | | | | | 44.34/14.45 | | | | | | | | | CLOSE: (625) is inconsistent. 44.34/14.45 | | | | | | | | | 44.34/14.45 | | | | | | | | Case 2: 44.34/14.45 | | | | | | | | | 44.34/14.45 | | | | | | | | | (626) ~ (all_160_1 = all_77_2) 44.34/14.45 | | | | | | | | | 44.34/14.45 | | | | | | | | | GROUND_INST: instantiating (7) with tree, all_101_1, all_96_3, 44.34/14.45 | | | | | | | | | all_92_6, all_96_2, simplifying with (10), (73), 44.34/14.45 | | | | | | | | | (621) gives: 44.34/14.45 | | | | | | | | | (627) ? [v0: $int] : ? [v1: $int] : (mem(tree, all_101_1, 44.34/14.45 | | | | | | | | | all_96_3) = v1 & mem(tree, all_101_1, all_92_6) = 44.34/14.45 | | | | | | | | | v0 & (v1 = 0 | v0 = 0)) 44.34/14.45 | | | | | | | | | 44.34/14.45 | | | | | | | | | DELTA: instantiating (627) with fresh symbols all_345_0, 44.34/14.45 | | | | | | | | | all_345_1 gives: 44.34/14.45 | | | | | | | | | (628) mem(tree, all_101_1, all_96_3) = all_345_0 & 44.34/14.45 | | | | | | | | | mem(tree, all_101_1, all_92_6) = all_345_1 & 44.34/14.45 | | | | | | | | | (all_345_0 = 0 | all_345_1 = 0) 44.34/14.45 | | | | | | | | | 44.34/14.45 | | | | | | | | | ALPHA: (628) implies: 44.34/14.45 | | | | | | | | | (629) mem(tree, all_101_1, all_92_6) = all_345_1 44.34/14.45 | | | | | | | | | (630) mem(tree, all_101_1, all_96_3) = all_345_0 44.34/14.45 | | | | | | | | | (631) all_345_0 = 0 | all_345_1 = 0 44.34/14.45 | | | | | | | | | 44.34/14.45 | | | | | | | | | BETA: splitting (609) gives: 44.34/14.45 | | | | | | | | | 44.34/14.45 | | | | | | | | | Case 1: 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | | (632) all_253_0 = 0 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | | REDUCE: (567), (632) imply: 44.34/14.45 | | | | | | | | | | (633) size1(all_253_2) = 0 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | | BETA: splitting (631) gives: 44.34/14.45 | | | | | | | | | | 44.34/14.45 | | | | | | | | | | Case 1: 44.34/14.45 | | | | | | | | | | | 44.34/14.45 | | | | | | | | | | | (634) all_345_0 = 0 44.34/14.45 | | | | | | | | | | | 44.34/14.45 | | | | | | | | | | | REDUCE: (630), (634) imply: 44.34/14.45 | | | | | | | | | | | (635) mem(tree, all_101_1, all_96_3) = 0 44.34/14.45 | | | | | | | | | | | 44.34/14.45 | | | | | | | | | | | GROUND_INST: instantiating (75) with all_101_2, all_101_1, 44.34/14.45 | | | | | | | | | | | simplifying with (82), (85), (635) gives: 44.34/14.45 | | | | | | | | | | | (636) ? [v0: $int] : ? [v1: $int] : (node1(v0, v1) = 44.34/14.45 | | | | | | | | | | | all_101_2 & $sum(size1(v1), $product(-1, 44.34/14.45 | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) 44.34/14.45 | | | | | | | | | | | = 0 & size1(v0) = all_92_8 & in_tree1(v1) & 44.34/14.45 | | | | | | | | | | | in_tree1(v0)) 44.34/14.45 | | | | | | | | | | | 44.34/14.45 | | | | | | | | | | | DELTA: instantiating (636) with fresh symbols all_499_0, 44.34/14.45 | | | | | | | | | | | all_499_1 gives: 44.34/14.45 | | | | | | | | | | | (637) node1(all_499_1, all_499_0) = all_101_2 & 44.34/14.45 | | | | | | | | | | | $sum(size1(all_499_0), $product(-1, 44.34/14.45 | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 44.34/14.45 | | | | | | | | | | | 0 & size1(all_499_1) = all_92_8 & 44.34/14.45 | | | | | | | | | | | in_tree1(all_499_0) & in_tree1(all_499_1) 44.34/14.45 | | | | | | | | | | | 44.34/14.45 | | | | | | | | | | | ALPHA: (637) implies: 44.34/14.46 | | | | | | | | | | | (638) size1(all_499_1) = all_92_8 44.34/14.46 | | | | | | | | | | | (639) node1(all_499_1, all_499_0) = all_101_2 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | REDUCE: (503), (638) imply: 44.34/14.46 | | | | | | | | | | | (640) $sum(size1(all_499_1), $product(-1, $sum(all_88_4, 44.34/14.46 | | | | | | | | | | | -1))) = 0 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | GROUND_INST: instantiating (tree_diff) with all_253_2, 44.34/14.46 | | | | | | | | | | | all_499_1, 0, $sum(all_88_4, -1), simplifying with 44.34/14.46 | | | | | | | | | | | (566), (633), (640) gives: 44.34/14.46 | | | | | | | | | | | (641) all_88_4 = 1 | ! [v0: $int] : ! [v1: $int] : ! 44.34/14.46 | | | | | | | | | | | [v2: $int] : ( ~ (node1(all_499_1, v1) = v2) | ~ 44.34/14.46 | | | | | | | | | | | (node1(all_253_2, v0) = v2) | ~ in_tree1(v0)) 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | BETA: splitting (641) gives: 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | Case 1: 44.34/14.46 | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | (642) all_88_4 = 1 44.34/14.46 | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | REDUCE: (504), (642) imply: 44.34/14.46 | | | | | | | | | | | | (643) $lesseq(0, -1) 44.34/14.46 | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | CLOSE: (643) is inconsistent. 44.34/14.46 | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | Case 2: 44.34/14.46 | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | (644) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( 44.34/14.46 | | | | | | | | | | | | ~ (node1(all_499_1, v1) = v2) | ~ 44.34/14.46 | | | | | | | | | | | | (node1(all_253_2, v0) = v2) | ~ in_tree1(v0)) 44.34/14.46 | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | GROUND_INST: instantiating (644) with all_253_1, all_499_0, 44.34/14.46 | | | | | | | | | | | | all_101_2, simplifying with (568), (608), (639) 44.34/14.46 | | | | | | | | | | | | gives: 44.34/14.46 | | | | | | | | | | | | (645) $false 44.34/14.46 | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | CLOSE: (645) is inconsistent. 44.34/14.46 | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | End of split 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | Case 2: 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | (646) all_345_1 = 0 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | REDUCE: (629), (646) imply: 44.34/14.46 | | | | | | | | | | | (647) mem(tree, all_101_1, all_92_6) = 0 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | REF_CLOSE: (14), (64), (82), (84), (85), (165), (184), (222), 44.34/14.46 | | | | | | | | | | | (503), (565), (567), (605), (647) are inconsistent 44.34/14.46 | | | | | | | | | | | by sub-proof #3. 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | End of split 44.34/14.46 | | | | | | | | | | 44.34/14.46 | | | | | | | | | Case 2: 44.34/14.46 | | | | | | | | | | 44.34/14.46 | | | | | | | | | | (648) ~ (all_253_0 = 0) 44.34/14.46 | | | | | | | | | | 44.34/14.46 | | | | | | | | | | STRENGTHEN: (619), (648) imply: 44.34/14.46 | | | | | | | | | | (649) $lesseq(1, all_253_0) 44.34/14.46 | | | | | | | | | | 44.34/14.46 | | | | | | | | | | BETA: splitting (610) gives: 44.34/14.46 | | | | | | | | | | 44.34/14.46 | | | | | | | | | | Case 1: 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | (650) $lesseq(all_253_0, 0) 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | COMBINE_INEQS: (649), (650) imply: 44.34/14.46 | | | | | | | | | | | (651) $lesseq(0, -1) 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | CLOSE: (651) is inconsistent. 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | Case 2: 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | (652) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : 44.34/14.46 | | | | | | | | | | | ($lesseq(1, $difference(all_253_0, v2)) & 44.34/14.46 | | | | | | | | | | | node1(v0, v1) = all_253_2 & size1(v0) = v2 & 44.34/14.46 | | | | | | | | | | | in_tree1(v1) & in_tree1(v0)) 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | DELTA: instantiating (652) with fresh symbols all_440_0, 44.34/14.46 | | | | | | | | | | | all_440_1, all_440_2 gives: 44.34/14.46 | | | | | | | | | | | (653) $lesseq(1, $difference(all_253_0, all_440_0)) & 44.34/14.46 | | | | | | | | | | | node1(all_440_2, all_440_1) = all_253_2 & 44.34/14.46 | | | | | | | | | | | size1(all_440_2) = all_440_0 & in_tree1(all_440_1) 44.34/14.46 | | | | | | | | | | | & in_tree1(all_440_2) 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | ALPHA: (653) implies: 44.34/14.46 | | | | | | | | | | | (654) $lesseq(1, $difference(all_253_0, all_440_0)) 44.34/14.46 | | | | | | | | | | | (655) in_tree1(all_440_2) 44.34/14.46 | | | | | | | | | | | (656) size1(all_440_2) = all_440_0 44.34/14.46 | | | | | | | | | | | (657) node1(all_440_2, all_440_1) = all_253_2 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | BETA: splitting (605) gives: 44.34/14.46 | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | Case 1: 44.34/14.46 | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | (658) ~ (all_101_0 = all_88_4) 44.34/14.46 | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_440_2, all_440_1, 44.34/14.46 | | | | | | | | | | | | all_253_2, simplifying with (655), (657) gives: 44.34/14.46 | | | | | | | | | | | | (659) ? [v0: $int] : ? [v1: $int] : 44.34/14.46 | | | | | | | | | | | | ($sum(size1(all_440_1), $product(-1, 44.34/14.46 | | | | | | | | | | | | $sum($difference(v0, v1), -1))) = 0 & 44.34/14.46 | | | | | | | | | | | | size1(all_440_2) = v1 & size1(all_253_2) = v0) 44.34/14.46 | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | GROUND_INST: instantiating (tree_diff) with all_253_2, 44.34/14.46 | | | | | | | | | | | | all_440_2, all_253_0, all_440_0, simplifying with 44.34/14.46 | | | | | | | | | | | | (566), (567), (656) gives: 44.34/14.46 | | | | | | | | | | | | (660) all_440_0 = all_253_0 | ! [v0: $int] : ! [v1: 44.34/14.46 | | | | | | | | | | | | $int] : ! [v2: $int] : ( ~ (node1(all_440_2, 44.34/14.46 | | | | | | | | | | | | v1) = v2) | ~ (node1(all_253_2, v0) = v2) | 44.34/14.46 | | | | | | | | | | | | ~ in_tree1(v0)) 44.34/14.46 | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | DELTA: instantiating (659) with fresh symbols all_466_0, 44.34/14.46 | | | | | | | | | | | | all_466_1 gives: 44.34/14.46 | | | | | | | | | | | | (661) $sum(size1(all_440_1), $product(-1, 44.34/14.46 | | | | | | | | | | | | $sum($difference(all_466_1, all_466_0), -1))) 44.34/14.46 | | | | | | | | | | | | = 0 & size1(all_440_2) = all_466_0 & 44.34/14.46 | | | | | | | | | | | | size1(all_253_2) = all_466_1 44.34/14.46 | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | ALPHA: (661) implies: 44.34/14.46 | | | | | | | | | | | | (662) size1(all_253_2) = all_466_1 44.34/14.46 | | | | | | | | | | | | (663) size1(all_440_2) = all_466_0 44.34/14.46 | | | | | | | | | | | | (664) $sum(size1(all_440_1), $product(-1, 44.34/14.46 | | | | | | | | | | | | $sum($difference(all_466_1, all_466_0), -1))) 44.34/14.46 | | | | | | | | | | | | = 0 44.34/14.46 | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | BETA: splitting (660) gives: 44.34/14.46 | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | Case 1: 44.34/14.46 | | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | | (665) all_440_0 = all_253_0 44.34/14.46 | | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | | REDUCE: (654), (665) imply: 44.34/14.46 | | | | | | | | | | | | | (666) $lesseq(0, -1) 44.34/14.46 | | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | | CLOSE: (666) is inconsistent. 44.34/14.46 | | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | Case 2: 44.34/14.46 | | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_440_0, all_466_0, 44.34/14.46 | | | | | | | | | | | | | all_440_2, simplifying with (656), (663) gives: 44.34/14.46 | | | | | | | | | | | | | (667) all_466_0 = all_440_0 44.34/14.46 | | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_440_2, 44.34/14.46 | | | | | | | | | | | | | all_466_0, simplifying with (655), (663) gives: 44.34/14.46 | | | | | | | | | | | | | (668) $lesseq(0, all_466_0) 44.34/14.46 | | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_253_0, all_466_1, 44.34/14.46 | | | | | | | | | | | | | all_253_2, simplifying with (567), (662) gives: 44.34/14.46 | | | | | | | | | | | | | (669) all_466_1 = all_253_0 44.34/14.46 | | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | | REDUCE: (667), (668) imply: 44.34/14.46 | | | | | | | | | | | | | (670) $lesseq(0, all_440_0) 44.34/14.46 | | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | | REDUCE: (664), (667), (669) imply: 44.34/14.46 | | | | | | | | | | | | | (671) $sum(size1(all_440_1), $product(-1, 44.34/14.46 | | | | | | | | | | | | | $sum($difference(all_253_0, all_440_0), -1))) 44.34/14.46 | | | | | | | | | | | | | = 0 44.34/14.46 | | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | | BETA: splitting (631) gives: 44.34/14.46 | | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | | Case 1: 44.34/14.46 | | | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | | | (672) all_345_0 = 0 44.34/14.46 | | | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | | | REDUCE: (630), (672) imply: 44.34/14.46 | | | | | | | | | | | | | | (673) mem(tree, all_101_1, all_96_3) = 0 44.34/14.46 | | | | | | | | | | | | | | 44.34/14.46 | | | | | | | | | | | | | | GROUND_INST: instantiating (tree_diff) with all_253_2, 44.34/14.46 | | | | | | | | | | | | | | all_440_1, all_253_0, $sum($difference(all_253_0, 44.34/14.46 | | | | | | | | | | | | | | all_440_0), -1), simplifying with (566), 44.34/14.46 | | | | | | | | | | | | | | (567), (671) gives: 44.34/14.46 | | | | | | | | | | | | | | (674) all_440_0 = -1 | ! [v0: $int] : ! [v1: $int] : 44.34/14.46 | | | | | | | | | | | | | | ! [v2: $int] : ( ~ (node1(all_440_1, v1) = v2) | 44.34/14.46 | | | | | | | | | | | | | | ~ (node1(all_253_2, v0) = v2) | ~ in_tree1(v0)) 44.34/14.46 | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | GROUND_INST: instantiating (75) with all_101_2, all_101_1, 44.49/14.47 | | | | | | | | | | | | | | simplifying with (82), (85), (673) gives: 44.49/14.47 | | | | | | | | | | | | | | (675) ? [v0: $int] : ? [v1: $int] : (node1(v0, v1) = 44.49/14.47 | | | | | | | | | | | | | | all_101_2 & $sum(size1(v1), $product(-1, 44.49/14.47 | | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) 44.49/14.47 | | | | | | | | | | | | | | = 0 & size1(v0) = all_92_8 & in_tree1(v1) & 44.49/14.47 | | | | | | | | | | | | | | in_tree1(v0)) 44.49/14.47 | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | DELTA: instantiating (675) with fresh symbols all_548_0, 44.49/14.47 | | | | | | | | | | | | | | all_548_1 gives: 44.49/14.47 | | | | | | | | | | | | | | (676) node1(all_548_1, all_548_0) = all_101_2 & 44.49/14.47 | | | | | | | | | | | | | | $sum(size1(all_548_0), $product(-1, 44.49/14.47 | | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 44.49/14.47 | | | | | | | | | | | | | | 0 & size1(all_548_1) = all_92_8 & 44.49/14.47 | | | | | | | | | | | | | | in_tree1(all_548_0) & in_tree1(all_548_1) 44.49/14.47 | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | ALPHA: (676) implies: 44.49/14.47 | | | | | | | | | | | | | | (677) in_tree1(all_548_1) 44.49/14.47 | | | | | | | | | | | | | | (678) size1(all_548_1) = all_92_8 44.49/14.47 | | | | | | | | | | | | | | (679) $sum(size1(all_548_0), $product(-1, 44.49/14.47 | | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 44.49/14.47 | | | | | | | | | | | | | | 0 44.49/14.47 | | | | | | | | | | | | | | (680) node1(all_548_1, all_548_0) = all_101_2 44.49/14.47 | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | REDUCE: (503), (679) imply: 44.49/14.47 | | | | | | | | | | | | | | (681) size1(all_548_0) = 0 44.49/14.47 | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | REDUCE: (503), (678) imply: 44.49/14.47 | | | | | | | | | | | | | | (682) $sum(size1(all_548_1), $product(-1, $sum(all_88_4, 44.49/14.47 | | | | | | | | | | | | | | -1))) = 0 44.49/14.47 | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | BETA: splitting (674) gives: 44.49/14.47 | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | Case 1: 44.49/14.47 | | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | | (683) all_440_0 = -1 44.49/14.47 | | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | | REDUCE: (670), (683) imply: 44.49/14.47 | | | | | | | | | | | | | | | (684) $lesseq(0, -1) 44.49/14.47 | | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | | CLOSE: (684) is inconsistent. 44.49/14.47 | | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | Case 2: 44.49/14.47 | | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_548_1, all_548_0, 44.49/14.47 | | | | | | | | | | | | | | | all_101_2, simplifying with (677), (680) gives: 44.49/14.47 | | | | | | | | | | | | | | | (685) ? [v0: $int] : ? [v1: $int] : 44.49/14.47 | | | | | | | | | | | | | | | ($sum(size1(all_548_0), $product(-1, 44.49/14.47 | | | | | | | | | | | | | | | $sum($difference(v0, v1), -1))) = 0 & 44.49/14.47 | | | | | | | | | | | | | | | size1(all_548_1) = v1 & size1(all_101_2) = v0) 44.49/14.47 | | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | | DELTA: instantiating (685) with fresh symbols all_616_0, 44.49/14.47 | | | | | | | | | | | | | | | all_616_1 gives: 44.49/14.47 | | | | | | | | | | | | | | | (686) $sum(size1(all_548_0), $product(-1, 44.49/14.47 | | | | | | | | | | | | | | | $sum($difference(all_616_1, all_616_0), -1))) 44.49/14.47 | | | | | | | | | | | | | | | = 0 & size1(all_548_1) = all_616_0 & 44.49/14.47 | | | | | | | | | | | | | | | size1(all_101_2) = all_616_1 44.49/14.47 | | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | | ALPHA: (686) implies: 44.49/14.47 | | | | | | | | | | | | | | | (687) size1(all_101_2) = all_616_1 44.49/14.47 | | | | | | | | | | | | | | | (688) size1(all_548_1) = all_616_0 44.49/14.47 | | | | | | | | | | | | | | | (689) $sum(size1(all_548_0), $product(-1, 44.49/14.47 | | | | | | | | | | | | | | | $sum($difference(all_616_1, all_616_0), -1))) 44.49/14.47 | | | | | | | | | | | | | | | = 0 44.49/14.47 | | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, 44.49/14.47 | | | | | | | | | | | | | | | $sum($difference(all_616_1, all_616_0), -1), 44.49/14.47 | | | | | | | | | | | | | | | all_548_0, simplifying with (681), (689) gives: 44.49/14.47 | | | | | | | | | | | | | | | (690) $difference(all_616_0, all_616_1) = -1 44.49/14.47 | | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with $sum(all_88_4, -1), 44.49/14.47 | | | | | | | | | | | | | | | all_616_0, all_548_1, simplifying with (682), 44.49/14.47 | | | | | | | | | | | | | | | (688) gives: 44.49/14.47 | | | | | | | | | | | | | | | (691) $difference(all_616_0, all_88_4) = -1 44.49/14.47 | | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_101_0, all_616_1, 44.49/14.47 | | | | | | | | | | | | | | | all_101_2, simplifying with (84), (687) gives: 44.49/14.47 | | | | | | | | | | | | | | | (692) all_616_1 = all_101_0 44.49/14.47 | | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | | COMBINE_EQS: (690), (691) imply: 44.49/14.47 | | | | | | | | | | | | | | | (693) all_616_1 = all_88_4 44.49/14.47 | | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | | COMBINE_EQS: (692), (693) imply: 44.49/14.47 | | | | | | | | | | | | | | | (694) all_101_0 = all_88_4 44.49/14.47 | | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | | REDUCE: (658), (694) imply: 44.49/14.47 | | | | | | | | | | | | | | | (695) ~ (0 = 0) 44.49/14.47 | | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | | CLOSE: (695) is inconsistent. 44.49/14.47 | | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | End of split 44.49/14.47 | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | Case 2: 44.49/14.47 | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | (696) all_345_1 = 0 44.49/14.47 | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | REDUCE: (629), (696) imply: 44.49/14.47 | | | | | | | | | | | | | | (697) mem(tree, all_101_1, all_92_6) = 0 44.49/14.47 | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | | REF_CLOSE: (14), (64), (82), (84), (85), (165), (184), (222), 44.49/14.47 | | | | | | | | | | | | | | (503), (565), (567), (605), (697) are inconsistent 44.49/14.47 | | | | | | | | | | | | | | by sub-proof #3. 44.49/14.47 | | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | | End of split 44.49/14.47 | | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | End of split 44.49/14.47 | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | Case 2: 44.49/14.47 | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | (698) all_101_0 = all_88_4 44.49/14.47 | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | REDUCE: (84), (698) imply: 44.49/14.47 | | | | | | | | | | | | (699) size1(all_101_2) = all_88_4 44.49/14.47 | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | | REF_CLOSE: (14), (84), (503), (565), (567), (605), (699) are 44.49/14.47 | | | | | | | | | | | | inconsistent by sub-proof #4. 44.49/14.47 | | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | | End of split 44.49/14.47 | | | | | | | | | | | 44.49/14.47 | | | | | | | | | | End of split 44.49/14.47 | | | | | | | | | | 44.49/14.47 | | | | | | | | | End of split 44.49/14.47 | | | | | | | | | 44.49/14.47 | | | | | | | | End of split 44.49/14.47 | | | | | | | | 44.49/14.47 | | | | | | | Case 2: 44.49/14.47 | | | | | | | | 44.49/14.47 | | | | | | | | (700) ? [v0: $int] : ( ~ (v0 = 0) & sort1(all_74_1, 44.49/14.47 | | | | | | | | all_96_2) = v0) 44.49/14.47 | | | | | | | | 44.49/14.47 | | | | | | | | DELTA: instantiating (700) with fresh symbol all_270_0 gives: 44.49/14.47 | | | | | | | | (701) ~ (all_270_0 = 0) & sort1(all_74_1, all_96_2) = 44.49/14.47 | | | | | | | | all_270_0 44.49/14.47 | | | | | | | | 44.49/14.47 | | | | | | | | REF_CLOSE: (10), (25), (73), (701), (infix_plpl_sort2) are 44.49/14.47 | | | | | | | | inconsistent by sub-proof #7. 44.49/14.47 | | | | | | | | 44.49/14.47 | | | | | | | End of split 44.49/14.47 | | | | | | | 44.49/14.47 | | | | | | End of split 44.49/14.47 | | | | | | 44.49/14.47 | | | | | End of split 44.49/14.47 | | | | | 44.49/14.47 | | | | End of split 44.49/14.47 | | | | 44.49/14.47 | | | End of split 44.49/14.47 | | | 44.49/14.47 | | Case 2: 44.49/14.47 | | | 44.49/14.47 | | | (702) all_92_5 = all_77_4 44.49/14.47 | | | 44.49/14.47 | | | REDUCE: (103), (702) imply: 44.49/14.47 | | | (703) tb2t(all_77_4) = all_92_8 44.49/14.47 | | | 44.49/14.47 | | | GROUND_INST: instantiating (21) with 0, all_92_8, all_77_4, simplifying 44.49/14.47 | | | with (106), (703) gives: 44.49/14.47 | | | (704) all_92_8 = 0 44.49/14.47 | | | 44.49/14.47 | | | REDUCE: (51), (704) imply: 44.49/14.47 | | | (705) $lesseq(1, all_88_4) 44.49/14.47 | | | 44.49/14.47 | | | REDUCE: (102), (704) imply: 44.49/14.47 | | | (706) $sum(tb2t(all_92_2), $product(-1, $sum(all_88_4, -1))) = 0 44.49/14.47 | | | 44.49/14.47 | | | REDUCE: (63), (704) imply: 44.49/14.47 | | | (707) t2tb($sum(all_88_4, -1)) = all_92_2 44.49/14.47 | | | 44.49/14.47 | | | BETA: splitting (87) gives: 44.49/14.47 | | | 44.49/14.47 | | | Case 1: 44.49/14.47 | | | | 44.49/14.47 | | | | (708) ~ (t2tb(0) = all_92_2) 44.49/14.47 | | | | 44.49/14.47 | | | | PRED_UNIFY: (707), (708) imply: 44.49/14.47 | | | | (709) ~ (all_88_4 = 1) 44.49/14.47 | | | | 44.49/14.47 | | | | STRENGTHEN: (705), (709) imply: 44.49/14.47 | | | | (710) $lesseq(2, all_88_4) 44.49/14.47 | | | | 44.49/14.47 | | | | BETA: splitting (118) gives: 44.49/14.47 | | | | 44.49/14.47 | | | | Case 1: 44.49/14.47 | | | | | 44.49/14.47 | | | | | (711) all_101_0 = 0 44.49/14.47 | | | | | 44.49/14.47 | | | | | REDUCE: (84), (711) imply: 44.49/14.47 | | | | | (712) size1(all_101_2) = 0 44.49/14.47 | | | | | 44.49/14.47 | | | | | REF_CLOSE: (5), (7), (10), (14), (25), (64), (73), (75), (82), (83), 44.49/14.47 | | | | | (85), (165), (170), (184), (222), (704), (712), 44.49/14.47 | | | | | (infix_plpl_sort2), (node_proj_2_def1), (size_nonneg) are 44.49/14.47 | | | | | inconsistent by sub-proof #1. 44.49/14.47 | | | | | 44.49/14.47 | | | | Case 2: 44.49/14.47 | | | | | 44.49/14.47 | | | | | (713) ~ (all_101_0 = 0) 44.49/14.47 | | | | | 44.49/14.47 | | | | | STRENGTHEN: (92), (713) imply: 44.49/14.47 | | | | | (714) $lesseq(1, all_101_0) 44.49/14.47 | | | | | 44.49/14.47 | | | | | BETA: splitting (117) gives: 44.49/14.47 | | | | | 44.49/14.47 | | | | | Case 1: 44.49/14.47 | | | | | | 44.49/14.47 | | | | | | (715) $lesseq(all_101_0, 0) 44.49/14.47 | | | | | | 44.49/14.47 | | | | | | COMBINE_INEQS: (714), (715) imply: 44.49/14.47 | | | | | | (716) $lesseq(0, -1) 44.49/14.47 | | | | | | 44.49/14.47 | | | | | | CLOSE: (716) is inconsistent. 44.49/14.47 | | | | | | 44.49/14.47 | | | | | Case 2: 44.49/14.47 | | | | | | 44.49/14.47 | | | | | | (717) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ($lesseq(1, 44.49/14.47 | | | | | | $difference(all_101_0, v2)) & node1(v0, v1) = all_101_2 44.49/14.47 | | | | | | & size1(v0) = v2 & in_tree1(v1) & in_tree1(v0)) 44.49/14.47 | | | | | | 44.49/14.47 | | | | | | DELTA: instantiating (717) with fresh symbols all_253_0, all_253_1, 44.49/14.47 | | | | | | all_253_2 gives: 44.49/14.47 | | | | | | (718) $lesseq(1, $difference(all_101_0, all_253_0)) & 44.49/14.47 | | | | | | node1(all_253_2, all_253_1) = all_101_2 & size1(all_253_2) 44.49/14.47 | | | | | | = all_253_0 & in_tree1(all_253_1) & in_tree1(all_253_2) 44.49/14.47 | | | | | | 44.49/14.47 | | | | | | ALPHA: (718) implies: 44.49/14.47 | | | | | | (719) in_tree1(all_253_2) 44.49/14.47 | | | | | | (720) size1(all_253_2) = all_253_0 44.49/14.47 | | | | | | (721) node1(all_253_2, all_253_1) = all_101_2 44.49/14.47 | | | | | | 44.49/14.47 | | | | | | BETA: splitting (127) gives: 44.49/14.47 | | | | | | 44.49/14.47 | | | | | | Case 1: 44.49/14.47 | | | | | | | 44.49/14.47 | | | | | | | (722) all_125_1 = all_92_6 44.49/14.47 | | | | | | | 44.49/14.47 | | | | | | | COMBINE_EQS: (157), (722) imply: 44.49/14.47 | | | | | | | (723) all_92_6 = all_77_6 44.49/14.47 | | | | | | | 44.49/14.47 | | | | | | | REDUCE: (73), (723) imply: 44.49/14.47 | | | | | | | (724) infix_plpl(tree, all_96_3, all_77_6) = all_96_2 44.49/14.47 | | | | | | | 44.49/14.47 | | | | | | | GROUND_INST: instantiating (append_l_nil) with tree, all_96_3, 44.49/14.47 | | | | | | | all_77_6, all_96_2, simplifying with (10), (28), 44.49/14.47 | | | | | | | (724) gives: 44.49/14.48 | | | | | | | (725) all_96_2 = all_96_3 44.49/14.48 | | | | | | | 44.49/14.48 | | | | | | | BETA: splitting (170) gives: 44.49/14.48 | | | | | | | 44.49/14.48 | | | | | | | Case 1: 44.49/14.48 | | | | | | | | 44.49/14.48 | | | | | | | | (726) all_99_0 = all_96_2 44.49/14.48 | | | | | | | | 44.49/14.48 | | | | | | | | COMBINE_EQS: (725), (726) imply: 44.49/14.48 | | | | | | | | (727) all_99_0 = all_96_3 44.49/14.48 | | | | | | | | 44.49/14.48 | | | | | | | | REDUCE: (83), (727) imply: 44.49/14.48 | | | | | | | | (728) mem(tree, all_101_1, all_96_3) = 0 44.49/14.48 | | | | | | | | 44.49/14.48 | | | | | | | | GROUND_INST: instantiating (86) with all_253_2, all_253_1, 44.49/14.48 | | | | | | | | simplifying with (719), (721) gives: 44.49/14.48 | | | | | | | | (729) ~ (all_101_0 = all_88_4) | ? [v0: $int] : ($lesseq(1, 44.49/14.48 | | | | | | | | $difference(v0, all_92_8)) & size1(all_253_2) = v0) 44.49/14.48 | | | | | | | | 44.49/14.48 | | | | | | | | GROUND_INST: instantiating (node_proj_1_def1) with all_253_2, 44.49/14.48 | | | | | | | | all_253_1, all_101_2, simplifying with (719), (721) 44.49/14.48 | | | | | | | | gives: 44.49/14.48 | | | | | | | | (730) node_proj_11(all_101_2) = all_253_2 44.49/14.48 | | | | | | | | 44.49/14.48 | | | | | | | | GROUND_INST: instantiating (75) with all_101_2, all_101_1, 44.49/14.48 | | | | | | | | simplifying with (82), (85), (728) gives: 44.49/14.48 | | | | | | | | (731) ? [v0: $int] : ? [v1: $int] : (node1(v0, v1) = 44.49/14.48 | | | | | | | | all_101_2 & $sum(size1(v1), $product(-1, 44.49/14.48 | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 & 44.49/14.48 | | | | | | | | size1(v0) = all_92_8 & in_tree1(v1) & in_tree1(v0)) 44.49/14.48 | | | | | | | | 44.49/14.48 | | | | | | | | DELTA: instantiating (731) with fresh symbols all_296_0, 44.49/14.48 | | | | | | | | all_296_1 gives: 44.49/14.48 | | | | | | | | (732) node1(all_296_1, all_296_0) = all_101_2 & 44.49/14.48 | | | | | | | | $sum(size1(all_296_0), $product(-1, 44.49/14.48 | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 & 44.49/14.48 | | | | | | | | size1(all_296_1) = all_92_8 & in_tree1(all_296_0) & 44.49/14.48 | | | | | | | | in_tree1(all_296_1) 44.49/14.48 | | | | | | | | 44.49/14.48 | | | | | | | | ALPHA: (732) implies: 44.49/14.48 | | | | | | | | (733) in_tree1(all_296_1) 44.49/14.48 | | | | | | | | (734) size1(all_296_1) = all_92_8 44.49/14.48 | | | | | | | | (735) $sum(size1(all_296_0), $product(-1, 44.49/14.48 | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 44.49/14.48 | | | | | | | | (736) node1(all_296_1, all_296_0) = all_101_2 44.49/14.48 | | | | | | | | 44.49/14.48 | | | | | | | | REDUCE: (704), (735) imply: 44.49/14.48 | | | | | | | | (737) $sum(size1(all_296_0), $product(-1, $sum(all_88_4, 44.49/14.48 | | | | | | | | -1))) = 0 44.49/14.48 | | | | | | | | 44.49/14.48 | | | | | | | | REDUCE: (704), (734) imply: 44.49/14.48 | | | | | | | | (738) size1(all_296_1) = 0 44.49/14.48 | | | | | | | | 44.49/14.48 | | | | | | | | BETA: splitting (184) gives: 44.49/14.48 | | | | | | | | 44.49/14.48 | | | | | | | | Case 1: 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | (739) all_160_1 = all_77_2 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | COMBINE_EQS: (222), (739) imply: 44.49/14.48 | | | | | | | | | (740) all_77_2 = all_77_6 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | SIMP: (740) implies: 44.49/14.48 | | | | | | | | | (741) all_77_2 = all_77_6 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | REDUCE: (165), (741) imply: 44.49/14.48 | | | | | | | | | (742) ~ (0 = 0) 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | CLOSE: (742) is inconsistent. 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | Case 2: 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | GROUND_INST: instantiating (86) with all_296_1, all_296_0, 44.49/14.48 | | | | | | | | | simplifying with (733), (736) gives: 44.49/14.48 | | | | | | | | | (743) ~ (all_101_0 = all_88_4) | ? [v0: $int] : 44.49/14.48 | | | | | | | | | ($lesseq(1, $difference(v0, all_92_8)) & 44.49/14.48 | | | | | | | | | size1(all_296_1) = v0) 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | GROUND_INST: instantiating (node_proj_1_def1) with all_296_1, 44.49/14.48 | | | | | | | | | all_296_0, all_101_2, simplifying with (733), 44.49/14.48 | | | | | | | | | (736) gives: 44.49/14.48 | | | | | | | | | (744) node_proj_11(all_101_2) = all_296_1 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | GROUND_INST: instantiating (5) with all_296_1, all_296_0, 44.49/14.48 | | | | | | | | | all_101_2, simplifying with (733), (736) gives: 44.49/14.48 | | | | | | | | | (745) ? [v0: $int] : ? [v1: $int] : 44.49/14.48 | | | | | | | | | ($sum(size1(all_296_0), $product(-1, 44.49/14.48 | | | | | | | | | $sum($difference(v0, v1), -1))) = 0 & 44.49/14.48 | | | | | | | | | size1(all_296_1) = v1 & size1(all_101_2) = v0) 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | DELTA: instantiating (745) with fresh symbols all_364_0, 44.49/14.48 | | | | | | | | | all_364_1 gives: 44.49/14.48 | | | | | | | | | (746) $sum(size1(all_296_0), $product(-1, 44.49/14.48 | | | | | | | | | $sum($difference(all_364_1, all_364_0), -1))) = 0 44.49/14.48 | | | | | | | | | & size1(all_296_1) = all_364_0 & size1(all_101_2) = 44.49/14.48 | | | | | | | | | all_364_1 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | ALPHA: (746) implies: 44.49/14.48 | | | | | | | | | (747) size1(all_101_2) = all_364_1 44.49/14.48 | | | | | | | | | (748) size1(all_296_1) = all_364_0 44.49/14.48 | | | | | | | | | (749) $sum(size1(all_296_0), $product(-1, 44.49/14.48 | | | | | | | | | $sum($difference(all_364_1, all_364_0), -1))) = 0 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | GROUND_INST: instantiating (20) with all_253_2, all_296_1, 44.49/14.48 | | | | | | | | | all_101_2, simplifying with (730), (744) gives: 44.49/14.48 | | | | | | | | | (750) all_296_1 = all_253_2 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | GROUND_INST: instantiating (14) with $sum(all_88_4, -1), 44.49/14.48 | | | | | | | | | $sum($difference(all_364_1, all_364_0), -1), 44.49/14.48 | | | | | | | | | all_296_0, simplifying with (737), (749) gives: 44.49/14.48 | | | | | | | | | (751) $sum($difference(all_364_0, all_364_1), all_88_4) = 0 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_364_0, all_296_1, 44.49/14.48 | | | | | | | | | simplifying with (738), (748) gives: 44.49/14.48 | | | | | | | | | (752) all_364_0 = 0 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | GROUND_INST: instantiating (14) with all_101_0, all_364_1, 44.49/14.48 | | | | | | | | | all_101_2, simplifying with (84), (747) gives: 44.49/14.48 | | | | | | | | | (753) all_364_1 = all_101_0 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | COMBINE_EQS: (751), (752) imply: 44.49/14.48 | | | | | | | | | (754) all_364_1 = all_88_4 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | SIMP: (754) implies: 44.49/14.48 | | | | | | | | | (755) all_364_1 = all_88_4 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | COMBINE_EQS: (753), (755) imply: 44.49/14.48 | | | | | | | | | (756) all_101_0 = all_88_4 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | REDUCE: (738), (750) imply: 44.49/14.48 | | | | | | | | | (757) size1(all_253_2) = 0 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | BETA: splitting (743) gives: 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | | Case 1: 44.49/14.48 | | | | | | | | | | 44.49/14.48 | | | | | | | | | | (758) ~ (all_101_0 = all_88_4) 44.49/14.48 | | | | | | | | | | 44.49/14.48 | | | | | | | | | | REDUCE: (756), (758) imply: 44.49/14.48 | | | | | | | | | | (759) ~ (0 = 0) 44.49/14.48 | | | | | | | | | | 44.49/14.48 | | | | | | | | | | CLOSE: (759) is inconsistent. 44.49/14.48 | | | | | | | | | | 44.49/14.48 | | | | | | | | | Case 2: 44.49/14.48 | | | | | | | | | | 44.49/14.48 | | | | | | | | | | (760) ? [v0: $int] : ($lesseq(1, $difference(v0, 44.49/14.48 | | | | | | | | | | all_92_8)) & size1(all_296_1) = v0) 44.49/14.48 | | | | | | | | | | 44.49/14.48 | | | | | | | | | | DELTA: instantiating (760) with fresh symbol all_418_0 44.49/14.48 | | | | | | | | | | gives: 44.49/14.48 | | | | | | | | | | (761) $lesseq(1, $difference(all_418_0, all_92_8)) & 44.49/14.48 | | | | | | | | | | size1(all_296_1) = all_418_0 44.49/14.48 | | | | | | | | | | 44.49/14.48 | | | | | | | | | | ALPHA: (761) implies: 44.49/14.48 | | | | | | | | | | (762) $lesseq(1, $difference(all_418_0, all_92_8)) 44.49/14.48 | | | | | | | | | | (763) size1(all_296_1) = all_418_0 44.49/14.48 | | | | | | | | | | 44.49/14.48 | | | | | | | | | | REDUCE: (704), (762) imply: 44.49/14.48 | | | | | | | | | | (764) $lesseq(1, all_418_0) 44.49/14.48 | | | | | | | | | | 44.49/14.48 | | | | | | | | | | REDUCE: (750), (763) imply: 44.49/14.48 | | | | | | | | | | (765) size1(all_253_2) = all_418_0 44.49/14.48 | | | | | | | | | | 44.49/14.48 | | | | | | | | | | BETA: splitting (729) gives: 44.49/14.48 | | | | | | | | | | 44.49/14.48 | | | | | | | | | | Case 1: 44.49/14.48 | | | | | | | | | | | 44.49/14.48 | | | | | | | | | | | (766) ~ (all_101_0 = all_88_4) 44.49/14.48 | | | | | | | | | | | 44.49/14.48 | | | | | | | | | | | REDUCE: (756), (766) imply: 44.49/14.48 | | | | | | | | | | | (767) ~ (0 = 0) 44.49/14.48 | | | | | | | | | | | 44.49/14.48 | | | | | | | | | | | CLOSE: (767) is inconsistent. 44.49/14.48 | | | | | | | | | | | 44.49/14.48 | | | | | | | | | | Case 2: 44.49/14.48 | | | | | | | | | | | 44.49/14.48 | | | | | | | | | | | (768) ? [v0: $int] : ($lesseq(1, $difference(v0, 44.49/14.48 | | | | | | | | | | | all_92_8)) & size1(all_253_2) = v0) 44.49/14.48 | | | | | | | | | | | 44.49/14.48 | | | | | | | | | | | DELTA: instantiating (768) with fresh symbol all_426_0 44.49/14.48 | | | | | | | | | | | gives: 44.49/14.48 | | | | | | | | | | | (769) $lesseq(1, $difference(all_426_0, all_92_8)) & 44.49/14.48 | | | | | | | | | | | size1(all_253_2) = all_426_0 44.49/14.48 | | | | | | | | | | | 44.49/14.48 | | | | | | | | | | | ALPHA: (769) implies: 44.49/14.48 | | | | | | | | | | | (770) size1(all_253_2) = all_426_0 44.49/14.48 | | | | | | | | | | | 44.49/14.48 | | | | | | | | | | | GROUND_INST: instantiating (14) with all_426_0, all_418_0, 44.49/14.48 | | | | | | | | | | | all_253_2, simplifying with (765), (770) gives: 44.49/14.48 | | | | | | | | | | | (771) all_426_0 = all_418_0 44.49/14.48 | | | | | | | | | | | 44.49/14.48 | | | | | | | | | | | GROUND_INST: instantiating (14) with all_426_0, 0, all_253_2, 44.49/14.48 | | | | | | | | | | | simplifying with (757), (770) gives: 44.49/14.48 | | | | | | | | | | | (772) all_426_0 = 0 44.49/14.48 | | | | | | | | | | | 44.49/14.48 | | | | | | | | | | | COMBINE_EQS: (771), (772) imply: 44.49/14.48 | | | | | | | | | | | (773) all_418_0 = 0 44.49/14.48 | | | | | | | | | | | 44.49/14.48 | | | | | | | | | | | REDUCE: (764), (773) imply: 44.49/14.48 | | | | | | | | | | | (774) $lesseq(0, -1) 44.49/14.48 | | | | | | | | | | | 44.49/14.48 | | | | | | | | | | | CLOSE: (774) is inconsistent. 44.49/14.48 | | | | | | | | | | | 44.49/14.48 | | | | | | | | | | End of split 44.49/14.48 | | | | | | | | | | 44.49/14.48 | | | | | | | | | End of split 44.49/14.48 | | | | | | | | | 44.49/14.48 | | | | | | | | End of split 44.49/14.48 | | | | | | | | 44.49/14.48 | | | | | | | Case 2: 44.49/14.48 | | | | | | | | 44.49/14.48 | | | | | | | | (775) ? [v0: $int] : ( ~ (v0 = 0) & sort1(all_74_1, 44.49/14.48 | | | | | | | | all_96_2) = v0) 44.49/14.48 | | | | | | | | 44.49/14.48 | | | | | | | | REF_CLOSE: (22), (145), (725), (775) are inconsistent by 44.49/14.48 | | | | | | | | sub-proof #6. 44.49/14.48 | | | | | | | | 44.49/14.48 | | | | | | | End of split 44.49/14.48 | | | | | | | 44.49/14.48 | | | | | | Case 2: 44.49/14.48 | | | | | | | 44.49/14.48 | | | | | | | 44.49/14.48 | | | | | | | GROUND_INST: instantiating (86) with all_253_2, all_253_1, 44.49/14.48 | | | | | | | simplifying with (719), (721) gives: 44.49/14.48 | | | | | | | (776) ~ (all_101_0 = all_88_4) | ? [v0: $int] : ($lesseq(1, 44.49/14.48 | | | | | | | $difference(v0, all_92_8)) & size1(all_253_2) = v0) 44.49/14.48 | | | | | | | 44.49/14.48 | | | | | | | GROUND_INST: instantiating (5) with all_253_2, all_253_1, 44.49/14.48 | | | | | | | all_101_2, simplifying with (719), (721) gives: 44.49/14.48 | | | | | | | (777) ? [v0: $int] : ? [v1: $int] : ($sum(size1(all_253_1), 44.49/14.48 | | | | | | | $product(-1, $sum($difference(v0, v1), -1))) = 0 & 44.49/14.48 | | | | | | | size1(all_253_2) = v1 & size1(all_101_2) = v0) 44.49/14.48 | | | | | | | 44.49/14.48 | | | | | | | GROUND_INST: instantiating (node_proj_2_def1) with all_253_2, 44.49/14.48 | | | | | | | all_253_1, all_101_2, simplifying with (719), (721) 44.49/14.48 | | | | | | | gives: 44.49/14.48 | | | | | | | (778) node_proj_21(all_101_2) = all_253_1 & in_tree1(all_253_1) 44.49/14.48 | | | | | | | 44.49/14.48 | | | | | | | ALPHA: (778) implies: 44.49/14.48 | | | | | | | (779) in_tree1(all_253_1) 44.49/14.48 | | | | | | | 44.49/14.48 | | | | | | | GROUND_INST: instantiating (tree_diff) with all_253_2, empty1, 44.49/14.48 | | | | | | | all_253_0, 0, simplifying with (4), (719), (720) 44.49/14.48 | | | | | | | gives: 44.49/14.48 | | | | | | | (780) all_253_0 = 0 | ! [v0: $int] : ! [v1: $int] : ! [v2: 44.49/14.48 | | | | | | | $int] : ( ~ (node1(all_253_2, v0) = v2) | ~ 44.49/14.48 | | | | | | | (node1(empty1, v1) = v2) | ~ in_tree1(v0)) 44.49/14.48 | | | | | | | 44.49/14.48 | | | | | | | GROUND_INST: instantiating (size_left) with all_253_2, all_253_0, 44.49/14.48 | | | | | | | simplifying with (719), (720) gives: 44.49/14.48 | | | | | | | (781) ~ ($lesseq(1, all_253_0)) | ? [v0: $int] : ? [v1: 44.49/14.48 | | | | | | | $int] : ? [v2: $int] : ($lesseq(1, 44.49/14.48 | | | | | | | $difference(all_253_0, v2)) & node1(v0, v1) = 44.49/14.49 | | | | | | | all_253_2 & size1(v0) = v2 & in_tree1(v1) & 44.49/14.49 | | | | | | | in_tree1(v0)) 44.49/14.49 | | | | | | | 44.49/14.49 | | | | | | | DELTA: instantiating (777) with fresh symbols all_282_0, all_282_1 44.49/14.49 | | | | | | | gives: 44.49/14.49 | | | | | | | (782) $sum(size1(all_253_1), $product(-1, 44.49/14.49 | | | | | | | $sum($difference(all_282_1, all_282_0), -1))) = 0 & 44.49/14.49 | | | | | | | size1(all_253_2) = all_282_0 & size1(all_101_2) = 44.49/14.49 | | | | | | | all_282_1 44.49/14.49 | | | | | | | 44.49/14.49 | | | | | | | ALPHA: (782) implies: 44.49/14.49 | | | | | | | (783) size1(all_101_2) = all_282_1 44.49/14.49 | | | | | | | (784) size1(all_253_2) = all_282_0 44.49/14.49 | | | | | | | (785) $sum(size1(all_253_1), $product(-1, 44.49/14.49 | | | | | | | $sum($difference(all_282_1, all_282_0), -1))) = 0 44.49/14.49 | | | | | | | 44.49/14.49 | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_253_1, 44.49/14.49 | | | | | | | $sum($difference(all_282_1, all_282_0), -1), 44.49/14.49 | | | | | | | simplifying with (779), (785) gives: 44.49/14.49 | | | | | | | (786) $lesseq(1, $difference(all_282_1, all_282_0)) 44.49/14.49 | | | | | | | 44.49/14.49 | | | | | | | GROUND_INST: instantiating (14) with all_253_0, all_282_0, 44.49/14.49 | | | | | | | all_253_2, simplifying with (720), (784) gives: 44.49/14.49 | | | | | | | (787) all_282_0 = all_253_0 44.49/14.49 | | | | | | | 44.49/14.49 | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_253_2, 44.49/14.49 | | | | | | | all_282_0, simplifying with (719), (784) gives: 44.49/14.49 | | | | | | | (788) $lesseq(0, all_282_0) 44.49/14.49 | | | | | | | 44.49/14.49 | | | | | | | GROUND_INST: instantiating (14) with all_101_0, all_282_1, 44.49/14.49 | | | | | | | all_101_2, simplifying with (84), (783) gives: 44.49/14.49 | | | | | | | (789) all_282_1 = all_101_0 44.49/14.49 | | | | | | | 44.49/14.49 | | | | | | | REDUCE: (786), (787), (789) imply: 44.49/14.49 | | | | | | | (790) $lesseq(1, $difference(all_101_0, all_253_0)) 44.49/14.49 | | | | | | | 44.49/14.49 | | | | | | | REDUCE: (787), (788) imply: 44.49/14.49 | | | | | | | (791) $lesseq(0, all_253_0) 44.49/14.49 | | | | | | | 44.49/14.49 | | | | | | | REDUCE: (785), (787), (789) imply: 44.49/14.49 | | | | | | | (792) $sum(size1(all_253_1), $product(-1, 44.49/14.49 | | | | | | | $sum($difference(all_101_0, all_253_0), -1))) = 0 44.49/14.49 | | | | | | | 44.49/14.49 | | | | | | | BETA: splitting (170) gives: 44.49/14.49 | | | | | | | 44.49/14.49 | | | | | | | Case 1: 44.49/14.49 | | | | | | | | 44.49/14.49 | | | | | | | | (793) all_99_0 = all_96_2 44.49/14.49 | | | | | | | | 44.49/14.49 | | | | | | | | REDUCE: (83), (793) imply: 44.49/14.49 | | | | | | | | (794) mem(tree, all_101_1, all_96_2) = 0 44.49/14.49 | | | | | | | | 44.49/14.49 | | | | | | | | BETA: splitting (184) gives: 44.49/14.49 | | | | | | | | 44.49/14.49 | | | | | | | | Case 1: 44.49/14.49 | | | | | | | | | 44.49/14.49 | | | | | | | | | (795) all_160_1 = all_77_2 44.49/14.49 | | | | | | | | | 44.49/14.49 | | | | | | | | | COMBINE_EQS: (222), (795) imply: 44.49/14.49 | | | | | | | | | (796) all_77_2 = all_77_6 44.49/14.49 | | | | | | | | | 44.49/14.49 | | | | | | | | | SIMP: (796) implies: 44.49/14.49 | | | | | | | | | (797) all_77_2 = all_77_6 44.49/14.49 | | | | | | | | | 44.49/14.49 | | | | | | | | | REDUCE: (165), (797) imply: 44.49/14.49 | | | | | | | | | (798) ~ (0 = 0) 44.49/14.49 | | | | | | | | | 44.49/14.49 | | | | | | | | | CLOSE: (798) is inconsistent. 44.49/14.49 | | | | | | | | | 44.49/14.49 | | | | | | | | Case 2: 44.49/14.49 | | | | | | | | | 44.49/14.49 | | | | | | | | | 44.49/14.49 | | | | | | | | | GROUND_INST: instantiating (tree_diff) with all_253_1, 44.49/14.49 | | | | | | | | | all_253_2, $sum($difference(all_101_0, all_253_0), 44.49/14.49 | | | | | | | | | -1), all_253_0, simplifying with (720), (779), 44.49/14.49 | | | | | | | | | (792) gives: 44.49/14.49 | | | | | | | | | (799) $difference($product(2, all_253_0), all_101_0) = -1 | 44.49/14.49 | | | | | | | | | ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ 44.49/14.49 | | | | | | | | | (node1(all_253_1, v0) = v2) | ~ (node1(all_253_2, 44.49/14.49 | | | | | | | | | v1) = v2) | ~ in_tree1(v0)) 44.49/14.49 | | | | | | | | | 44.49/14.49 | | | | | | | | | GROUND_INST: instantiating (tree_diff) with all_253_1, 44.49/14.49 | | | | | | | | | all_101_2, $sum($difference(all_101_0, all_253_0), 44.49/14.49 | | | | | | | | | -1), all_101_0, simplifying with (84), (779), 44.49/14.49 | | | | | | | | | (792) gives: 44.49/14.49 | | | | | | | | | (800) all_253_0 = -1 | ! [v0: $int] : ! [v1: $int] : ! 44.49/14.49 | | | | | | | | | [v2: $int] : ( ~ (node1(all_253_1, v0) = v2) | ~ 44.49/14.49 | | | | | | | | | (node1(all_101_2, v1) = v2) | ~ in_tree1(v0)) 44.49/14.49 | | | | | | | | | 44.49/14.49 | | | | | | | | | GROUND_INST: instantiating (size_left) with all_253_1, 44.49/14.49 | | | | | | | | | $sum($difference(all_101_0, all_253_0), -1), 44.49/14.49 | | | | | | | | | simplifying with (779), (792) gives: 44.49/14.49 | | | | | | | | | (801) ~ ($lesseq(2, $difference(all_101_0, all_253_0))) | 44.49/14.49 | | | | | | | | | ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : 44.49/14.49 | | | | | | | | | ($lesseq(2, $sum($difference($product(-1, v2), 44.49/14.49 | | | | | | | | | all_253_0), all_101_0)) & node1(v0, v1) = 44.49/14.49 | | | | | | | | | all_253_1 & size1(v0) = v2 & in_tree1(v1) & 44.49/14.49 | | | | | | | | | in_tree1(v0)) 44.49/14.49 | | | | | | | | | 44.49/14.49 | | | | | | | | | GROUND_INST: instantiating (7) with tree, all_101_1, all_96_3, 44.49/14.49 | | | | | | | | | all_92_6, all_96_2, simplifying with (10), (73), 44.49/14.49 | | | | | | | | | (794) gives: 44.49/14.49 | | | | | | | | | (802) ? [v0: $int] : ? [v1: $int] : (mem(tree, all_101_1, 44.49/14.49 | | | | | | | | | all_96_3) = v1 & mem(tree, all_101_1, all_92_6) = 44.49/14.49 | | | | | | | | | v0 & (v1 = 0 | v0 = 0)) 44.49/14.49 | | | | | | | | | 44.49/14.49 | | | | | | | | | DELTA: instantiating (802) with fresh symbols all_345_0, 44.49/14.49 | | | | | | | | | all_345_1 gives: 44.49/14.49 | | | | | | | | | (803) mem(tree, all_101_1, all_96_3) = all_345_0 & 44.49/14.49 | | | | | | | | | mem(tree, all_101_1, all_92_6) = all_345_1 & 44.49/14.49 | | | | | | | | | (all_345_0 = 0 | all_345_1 = 0) 44.49/14.49 | | | | | | | | | 44.49/14.49 | | | | | | | | | ALPHA: (803) implies: 44.49/14.49 | | | | | | | | | (804) mem(tree, all_101_1, all_92_6) = all_345_1 44.49/14.49 | | | | | | | | | (805) mem(tree, all_101_1, all_96_3) = all_345_0 44.49/14.49 | | | | | | | | | (806) all_345_0 = 0 | all_345_1 = 0 44.49/14.49 | | | | | | | | | 44.49/14.49 | | | | | | | | | BETA: splitting (800) gives: 44.49/14.49 | | | | | | | | | 44.49/14.49 | | | | | | | | | Case 1: 44.49/14.49 | | | | | | | | | | 44.49/14.49 | | | | | | | | | | (807) all_253_0 = -1 44.49/14.49 | | | | | | | | | | 44.49/14.49 | | | | | | | | | | REDUCE: (791), (807) imply: 44.49/14.49 | | | | | | | | | | (808) $lesseq(0, -1) 44.49/14.49 | | | | | | | | | | 44.49/14.49 | | | | | | | | | | CLOSE: (808) is inconsistent. 44.49/14.49 | | | | | | | | | | 44.49/14.49 | | | | | | | | | Case 2: 44.49/14.49 | | | | | | | | | | 44.49/14.49 | | | | | | | | | | 44.49/14.49 | | | | | | | | | | GROUND_INST: instantiating (65) with all_101_2, all_101_1, 44.49/14.49 | | | | | | | | | | all_345_1, simplifying with (82), (85), (804) 44.49/14.49 | | | | | | | | | | gives: 44.49/14.49 | | | | | | | | | | (809) all_345_1 = 0 | ? [v0: $int] : (size1(all_101_2) = 44.49/14.49 | | | | | | | | | | v0 & ! [v1: $int] : ! [v2: $int] : ( ~ (v0 = 44.49/14.49 | | | | | | | | | | all_88_4) | ~ (node1(v1, v2) = all_101_2) | 44.49/14.49 | | | | | | | | | | ~ in_tree1(v1) | ? [v3: $int] : 44.49/14.49 | | | | | | | | | | ($lesseq(all_92_8, v3) & size1(v1) = v3))) 44.49/14.49 | | | | | | | | | | 44.49/14.49 | | | | | | | | | | BETA: splitting (780) gives: 44.49/14.49 | | | | | | | | | | 44.49/14.49 | | | | | | | | | | Case 1: 44.49/14.49 | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | (810) all_253_0 = 0 44.49/14.49 | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | REDUCE: (720), (810) imply: 44.49/14.49 | | | | | | | | | | | (811) size1(all_253_2) = 0 44.49/14.49 | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | BETA: splitting (776) gives: 44.49/14.49 | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | Case 1: 44.49/14.49 | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | (812) ~ (all_101_0 = all_88_4) 44.49/14.49 | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | BETA: splitting (799) gives: 44.49/14.49 | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | Case 1: 44.49/14.49 | | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | | (813) $difference($product(2, all_253_0), all_101_0) = 44.49/14.49 | | | | | | | | | | | | | -1 44.49/14.49 | | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | | COMBINE_EQS: (810), (813) imply: 44.49/14.49 | | | | | | | | | | | | | (814) all_101_0 = 1 44.49/14.49 | | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | | SIMP: (814) implies: 44.49/14.49 | | | | | | | | | | | | | (815) all_101_0 = 1 44.49/14.49 | | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | | REDUCE: (84), (815) imply: 44.49/14.49 | | | | | | | | | | | | | (816) size1(all_101_2) = 1 44.49/14.49 | | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | | BETA: splitting (806) gives: 44.49/14.49 | | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | | Case 1: 44.49/14.49 | | | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | | | (817) all_345_0 = 0 44.49/14.49 | | | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | | | REDUCE: (805), (817) imply: 44.49/14.49 | | | | | | | | | | | | | | (818) mem(tree, all_101_1, all_96_3) = 0 44.49/14.49 | | | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | | | GROUND_INST: instantiating (75) with all_101_2, all_101_1, 44.49/14.49 | | | | | | | | | | | | | | simplifying with (82), (85), (818) gives: 44.49/14.49 | | | | | | | | | | | | | | (819) ? [v0: $int] : ? [v1: $int] : (node1(v0, v1) = 44.49/14.49 | | | | | | | | | | | | | | all_101_2 & $sum(size1(v1), $product(-1, 44.49/14.49 | | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) 44.49/14.49 | | | | | | | | | | | | | | = 0 & size1(v0) = all_92_8 & in_tree1(v1) & 44.49/14.49 | | | | | | | | | | | | | | in_tree1(v0)) 44.49/14.49 | | | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | | | DELTA: instantiating (819) with fresh symbols all_499_0, 44.49/14.49 | | | | | | | | | | | | | | all_499_1 gives: 44.49/14.49 | | | | | | | | | | | | | | (820) node1(all_499_1, all_499_0) = all_101_2 & 44.49/14.49 | | | | | | | | | | | | | | $sum(size1(all_499_0), $product(-1, 44.49/14.49 | | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 44.49/14.49 | | | | | | | | | | | | | | 0 & size1(all_499_1) = all_92_8 & 44.49/14.49 | | | | | | | | | | | | | | in_tree1(all_499_0) & in_tree1(all_499_1) 44.49/14.49 | | | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | | | ALPHA: (820) implies: 44.49/14.49 | | | | | | | | | | | | | | (821) in_tree1(all_499_1) 44.49/14.49 | | | | | | | | | | | | | | (822) size1(all_499_1) = all_92_8 44.49/14.49 | | | | | | | | | | | | | | (823) $sum(size1(all_499_0), $product(-1, 44.49/14.49 | | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 44.49/14.49 | | | | | | | | | | | | | | 0 44.49/14.49 | | | | | | | | | | | | | | (824) node1(all_499_1, all_499_0) = all_101_2 44.49/14.49 | | | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | | | REDUCE: (704), (823) imply: 44.49/14.49 | | | | | | | | | | | | | | (825) $sum(size1(all_499_0), $product(-1, $sum(all_88_4, 44.49/14.49 | | | | | | | | | | | | | | -1))) = 0 44.49/14.49 | | | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | | | REDUCE: (704), (822) imply: 44.49/14.49 | | | | | | | | | | | | | | (826) size1(all_499_1) = 0 44.49/14.49 | | | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_499_1, all_499_0, 44.49/14.49 | | | | | | | | | | | | | | all_101_2, simplifying with (821), (824) gives: 44.49/14.49 | | | | | | | | | | | | | | (827) ? [v0: $int] : ? [v1: $int] : 44.49/14.49 | | | | | | | | | | | | | | ($sum(size1(all_499_0), $product(-1, 44.49/14.49 | | | | | | | | | | | | | | $sum($difference(v0, v1), -1))) = 0 & 44.49/14.49 | | | | | | | | | | | | | | size1(all_499_1) = v1 & size1(all_101_2) = v0) 44.49/14.49 | | | | | | | | | | | | | | 44.49/14.49 | | | | | | | | | | | | | | GROUND_INST: instantiating (node_proj_2_def1) with all_499_1, 44.49/14.49 | | | | | | | | | | | | | | all_499_0, all_101_2, simplifying with (821), 44.49/14.49 | | | | | | | | | | | | | | (824) gives: 44.49/14.49 | | | | | | | | | | | | | | (828) node_proj_21(all_101_2) = all_499_0 & 44.49/14.50 | | | | | | | | | | | | | | in_tree1(all_499_0) 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | ALPHA: (828) implies: 44.49/14.50 | | | | | | | | | | | | | | (829) in_tree1(all_499_0) 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | GROUND_INST: instantiating (size_left) with all_499_0, 44.49/14.50 | | | | | | | | | | | | | | $sum(all_88_4, -1), simplifying with (825), (829) 44.49/14.50 | | | | | | | | | | | | | | gives: 44.49/14.50 | | | | | | | | | | | | | | (830) ~ ($lesseq(2, all_88_4)) | ? [v0: $int] : ? 44.49/14.50 | | | | | | | | | | | | | | [v1: $int] : ? [v2: $int] : ($lesseq(2, 44.49/14.50 | | | | | | | | | | | | | | $difference(all_88_4, v2)) & node1(v0, v1) = 44.49/14.50 | | | | | | | | | | | | | | all_499_0 & size1(v0) = v2 & in_tree1(v1) & 44.49/14.50 | | | | | | | | | | | | | | in_tree1(v0)) 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | DELTA: instantiating (827) with fresh symbols all_537_0, 44.49/14.50 | | | | | | | | | | | | | | all_537_1 gives: 44.49/14.50 | | | | | | | | | | | | | | (831) $sum(size1(all_499_0), $product(-1, 44.49/14.50 | | | | | | | | | | | | | | $sum($difference(all_537_1, all_537_0), -1))) 44.49/14.50 | | | | | | | | | | | | | | = 0 & size1(all_499_1) = all_537_0 & 44.49/14.50 | | | | | | | | | | | | | | size1(all_101_2) = all_537_1 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | ALPHA: (831) implies: 44.49/14.50 | | | | | | | | | | | | | | (832) size1(all_101_2) = all_537_1 44.49/14.50 | | | | | | | | | | | | | | (833) size1(all_499_1) = all_537_0 44.49/14.50 | | | | | | | | | | | | | | (834) $sum(size1(all_499_0), $product(-1, 44.49/14.50 | | | | | | | | | | | | | | $sum($difference(all_537_1, all_537_0), -1))) 44.49/14.50 | | | | | | | | | | | | | | = 0 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | BETA: splitting (830) gives: 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | Case 1: 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | (835) $lesseq(all_88_4, 1) 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | COMBINE_INEQS: (710), (835) imply: 44.49/14.50 | | | | | | | | | | | | | | | (836) $lesseq(0, -1) 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | CLOSE: (836) is inconsistent. 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | Case 2: 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | (837) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : 44.49/14.50 | | | | | | | | | | | | | | | ($lesseq(2, $difference(all_88_4, v2)) & node1(v0, 44.49/14.50 | | | | | | | | | | | | | | | v1) = all_499_0 & size1(v0) = v2 & 44.49/14.50 | | | | | | | | | | | | | | | in_tree1(v1) & in_tree1(v0)) 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | DELTA: instantiating (837) with fresh symbols all_588_0, 44.49/14.50 | | | | | | | | | | | | | | | all_588_1, all_588_2 gives: 44.49/14.50 | | | | | | | | | | | | | | | (838) $lesseq(2, $difference(all_88_4, all_588_0)) & 44.49/14.50 | | | | | | | | | | | | | | | node1(all_588_2, all_588_1) = all_499_0 & 44.49/14.50 | | | | | | | | | | | | | | | size1(all_588_2) = all_588_0 & in_tree1(all_588_1) 44.49/14.50 | | | | | | | | | | | | | | | & in_tree1(all_588_2) 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | ALPHA: (838) implies: 44.49/14.50 | | | | | | | | | | | | | | | (839) $lesseq(2, $difference(all_88_4, all_588_0)) 44.49/14.50 | | | | | | | | | | | | | | | (840) in_tree1(all_588_2) 44.49/14.50 | | | | | | | | | | | | | | | (841) size1(all_588_2) = all_588_0 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_588_2, 44.49/14.50 | | | | | | | | | | | | | | | all_588_0, simplifying with (840), (841) gives: 44.49/14.50 | | | | | | | | | | | | | | | (842) $lesseq(0, all_588_0) 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with $sum(all_88_4, -1), 44.49/14.50 | | | | | | | | | | | | | | | $sum($difference(all_537_1, all_537_0), -1), 44.49/14.50 | | | | | | | | | | | | | | | all_499_0, simplifying with (825), (834) gives: 44.49/14.50 | | | | | | | | | | | | | | | (843) $sum($difference(all_537_0, all_537_1), all_88_4) 44.49/14.50 | | | | | | | | | | | | | | | = 0 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_537_0, all_499_1, 44.49/14.50 | | | | | | | | | | | | | | | simplifying with (826), (833) gives: 44.49/14.50 | | | | | | | | | | | | | | | (844) all_537_0 = 0 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 1, all_537_1, all_101_2, 44.49/14.50 | | | | | | | | | | | | | | | simplifying with (816), (832) gives: 44.49/14.50 | | | | | | | | | | | | | | | (845) all_537_1 = 1 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | COMBINE_EQS: (843), (844) imply: 44.49/14.50 | | | | | | | | | | | | | | | (846) all_537_1 = all_88_4 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | SIMP: (846) implies: 44.49/14.50 | | | | | | | | | | | | | | | (847) all_537_1 = all_88_4 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | COMBINE_EQS: (845), (847) imply: 44.49/14.50 | | | | | | | | | | | | | | | (848) all_88_4 = 1 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | SIMP: (848) implies: 44.49/14.50 | | | | | | | | | | | | | | | (849) all_88_4 = 1 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | REDUCE: (839), (849) imply: 44.49/14.50 | | | | | | | | | | | | | | | (850) $lesseq(all_588_0, -1) 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | COMBINE_INEQS: (842), (850) imply: 44.49/14.50 | | | | | | | | | | | | | | | (851) $lesseq(0, -1) 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | CLOSE: (851) is inconsistent. 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | End of split 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | Case 2: 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | (852) all_345_1 = 0 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | REDUCE: (804), (852) imply: 44.49/14.50 | | | | | | | | | | | | | | (853) mem(tree, all_101_1, all_92_6) = 0 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | REF_CLOSE: (64), (82), (85), (704), (853), (size_nonneg) are 44.49/14.50 | | | | | | | | | | | | | | inconsistent by sub-proof #2. 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | End of split 44.49/14.50 | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | Case 2: 44.49/14.50 | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | (854) ~ ($difference($product(2, all_253_0), all_101_0) 44.49/14.50 | | | | | | | | | | | | | = -1) 44.49/14.50 | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | REDUCE: (810), (854) imply: 44.49/14.50 | | | | | | | | | | | | | (855) ~ (all_101_0 = 1) 44.49/14.50 | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | SIMP: (855) implies: 44.49/14.50 | | | | | | | | | | | | | (856) ~ (all_101_0 = 1) 44.49/14.50 | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | STRENGTHEN: (714), (856) imply: 44.49/14.50 | | | | | | | | | | | | | (857) $lesseq(2, all_101_0) 44.49/14.50 | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | BETA: splitting (801) gives: 44.49/14.50 | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | Case 1: 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | (858) $lesseq(-1, $difference(all_253_0, all_101_0)) 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | REDUCE: (810), (858) imply: 44.49/14.50 | | | | | | | | | | | | | | (859) $lesseq(all_101_0, 1) 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | COMBINE_INEQS: (857), (859) imply: 44.49/14.50 | | | | | | | | | | | | | | (860) $lesseq(0, -1) 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | CLOSE: (860) is inconsistent. 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | Case 2: 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | (861) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : 44.49/14.50 | | | | | | | | | | | | | | ($lesseq(2, $sum($difference($product(-1, v2), 44.49/14.50 | | | | | | | | | | | | | | all_253_0), all_101_0)) & node1(v0, v1) = 44.49/14.50 | | | | | | | | | | | | | | all_253_1 & size1(v0) = v2 & in_tree1(v1) & 44.49/14.50 | | | | | | | | | | | | | | in_tree1(v0)) 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | DELTA: instantiating (861) with fresh symbols all_496_0, 44.49/14.50 | | | | | | | | | | | | | | all_496_1, all_496_2 gives: 44.49/14.50 | | | | | | | | | | | | | | (862) $lesseq(2, $sum($difference($product(-1, 44.49/14.50 | | | | | | | | | | | | | | all_496_0), all_253_0), all_101_0)) & 44.49/14.50 | | | | | | | | | | | | | | node1(all_496_2, all_496_1) = all_253_1 & 44.49/14.50 | | | | | | | | | | | | | | size1(all_496_2) = all_496_0 & in_tree1(all_496_1) 44.49/14.50 | | | | | | | | | | | | | | & in_tree1(all_496_2) 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | ALPHA: (862) implies: 44.49/14.50 | | | | | | | | | | | | | | (863) $lesseq(2, $sum($difference($product(-1, 44.49/14.50 | | | | | | | | | | | | | | all_496_0), all_253_0), all_101_0)) 44.49/14.50 | | | | | | | | | | | | | | (864) in_tree1(all_496_2) 44.49/14.50 | | | | | | | | | | | | | | (865) size1(all_496_2) = all_496_0 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | REDUCE: (810), (863) imply: 44.49/14.50 | | | | | | | | | | | | | | (866) $lesseq(2, $difference(all_101_0, all_496_0)) 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | BETA: splitting (806) gives: 44.49/14.50 | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | Case 1: 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | (867) all_345_0 = 0 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | REDUCE: (805), (867) imply: 44.49/14.50 | | | | | | | | | | | | | | | (868) mem(tree, all_101_1, all_96_3) = 0 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | GROUND_INST: instantiating (tree_diff) with all_496_2, 44.49/14.50 | | | | | | | | | | | | | | | all_101_2, all_496_0, all_101_0, simplifying with 44.49/14.50 | | | | | | | | | | | | | | | (84), (864), (865) gives: 44.49/14.50 | | | | | | | | | | | | | | | (869) all_496_0 = all_101_0 | ! [v0: $int] : ! [v1: 44.49/14.50 | | | | | | | | | | | | | | | $int] : ! [v2: $int] : ( ~ (node1(all_496_2, 44.49/14.50 | | | | | | | | | | | | | | | v0) = v2) | ~ (node1(all_101_2, v1) = v2) | 44.49/14.50 | | | | | | | | | | | | | | | ~ in_tree1(v0)) 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | GROUND_INST: instantiating (75) with all_101_2, all_101_1, 44.49/14.50 | | | | | | | | | | | | | | | simplifying with (82), (85), (868) gives: 44.49/14.50 | | | | | | | | | | | | | | | (870) ? [v0: $int] : ? [v1: $int] : (node1(v0, v1) = 44.49/14.50 | | | | | | | | | | | | | | | all_101_2 & $sum(size1(v1), $product(-1, 44.49/14.50 | | | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) 44.49/14.50 | | | | | | | | | | | | | | | = 0 & size1(v0) = all_92_8 & in_tree1(v1) & 44.49/14.50 | | | | | | | | | | | | | | | in_tree1(v0)) 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | DELTA: instantiating (870) with fresh symbols all_520_0, 44.49/14.50 | | | | | | | | | | | | | | | all_520_1 gives: 44.49/14.50 | | | | | | | | | | | | | | | (871) node1(all_520_1, all_520_0) = all_101_2 & 44.49/14.50 | | | | | | | | | | | | | | | $sum(size1(all_520_0), $product(-1, 44.49/14.50 | | | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 44.49/14.50 | | | | | | | | | | | | | | | 0 & size1(all_520_1) = all_92_8 & 44.49/14.50 | | | | | | | | | | | | | | | in_tree1(all_520_0) & in_tree1(all_520_1) 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | ALPHA: (871) implies: 44.49/14.50 | | | | | | | | | | | | | | | (872) in_tree1(all_520_1) 44.49/14.50 | | | | | | | | | | | | | | | (873) size1(all_520_1) = all_92_8 44.49/14.50 | | | | | | | | | | | | | | | (874) $sum(size1(all_520_0), $product(-1, 44.49/14.50 | | | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 44.49/14.50 | | | | | | | | | | | | | | | 0 44.49/14.50 | | | | | | | | | | | | | | | (875) node1(all_520_1, all_520_0) = all_101_2 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | REDUCE: (704), (874) imply: 44.49/14.50 | | | | | | | | | | | | | | | (876) $sum(size1(all_520_0), $product(-1, $sum(all_88_4, 44.49/14.50 | | | | | | | | | | | | | | | -1))) = 0 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | REDUCE: (704), (873) imply: 44.49/14.50 | | | | | | | | | | | | | | | (877) size1(all_520_1) = 0 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | BETA: splitting (869) gives: 44.49/14.50 | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | Case 1: 44.49/14.50 | | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | | (878) all_496_0 = all_101_0 44.49/14.50 | | | | | | | | | | | | | | | | 44.49/14.50 | | | | | | | | | | | | | | | | REDUCE: (866), (878) imply: 44.49/14.51 | | | | | | | | | | | | | | | | (879) $lesseq(0, -1) 44.49/14.51 | | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | | CLOSE: (879) is inconsistent. 44.49/14.51 | | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | Case 2: 44.49/14.51 | | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_520_1, all_520_0, 44.49/14.51 | | | | | | | | | | | | | | | | all_101_2, simplifying with (872), (875) gives: 44.49/14.51 | | | | | | | | | | | | | | | | (880) ? [v0: $int] : ? [v1: $int] : 44.49/14.51 | | | | | | | | | | | | | | | | ($sum(size1(all_520_0), $product(-1, 44.49/14.51 | | | | | | | | | | | | | | | | $sum($difference(v0, v1), -1))) = 0 & 44.49/14.51 | | | | | | | | | | | | | | | | size1(all_520_1) = v1 & size1(all_101_2) = v0) 44.49/14.51 | | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | | DELTA: instantiating (880) with fresh symbols all_581_0, 44.49/14.51 | | | | | | | | | | | | | | | | all_581_1 gives: 44.49/14.51 | | | | | | | | | | | | | | | | (881) $sum(size1(all_520_0), $product(-1, 44.49/14.51 | | | | | | | | | | | | | | | | $sum($difference(all_581_1, all_581_0), -1))) 44.49/14.51 | | | | | | | | | | | | | | | | = 0 & size1(all_520_1) = all_581_0 & 44.49/14.51 | | | | | | | | | | | | | | | | size1(all_101_2) = all_581_1 44.49/14.51 | | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | | ALPHA: (881) implies: 44.49/14.51 | | | | | | | | | | | | | | | | (882) size1(all_101_2) = all_581_1 44.49/14.51 | | | | | | | | | | | | | | | | (883) size1(all_520_1) = all_581_0 44.49/14.51 | | | | | | | | | | | | | | | | (884) $sum(size1(all_520_0), $product(-1, 44.49/14.51 | | | | | | | | | | | | | | | | $sum($difference(all_581_1, all_581_0), -1))) 44.49/14.51 | | | | | | | | | | | | | | | | = 0 44.49/14.51 | | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with $sum(all_88_4, -1), 44.49/14.51 | | | | | | | | | | | | | | | | $sum($difference(all_581_1, all_581_0), -1), 44.49/14.51 | | | | | | | | | | | | | | | | all_520_0, simplifying with (876), (884) gives: 44.49/14.51 | | | | | | | | | | | | | | | | (885) $sum($difference(all_581_0, all_581_1), all_88_4) 44.49/14.51 | | | | | | | | | | | | | | | | = 0 44.49/14.51 | | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_581_0, all_520_1, 44.49/14.51 | | | | | | | | | | | | | | | | simplifying with (877), (883) gives: 44.49/14.51 | | | | | | | | | | | | | | | | (886) all_581_0 = 0 44.49/14.51 | | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_101_0, all_581_1, 44.49/14.51 | | | | | | | | | | | | | | | | all_101_2, simplifying with (84), (882) gives: 44.49/14.51 | | | | | | | | | | | | | | | | (887) all_581_1 = all_101_0 44.49/14.51 | | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | | COMBINE_EQS: (885), (886) imply: 44.49/14.51 | | | | | | | | | | | | | | | | (888) all_581_1 = all_88_4 44.49/14.51 | | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | | COMBINE_EQS: (887), (888) imply: 44.49/14.51 | | | | | | | | | | | | | | | | (889) all_101_0 = all_88_4 44.49/14.51 | | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | | REDUCE: (812), (889) imply: 44.49/14.51 | | | | | | | | | | | | | | | | (890) ~ (0 = 0) 44.49/14.51 | | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | | CLOSE: (890) is inconsistent. 44.49/14.51 | | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | End of split 44.49/14.51 | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | Case 2: 44.49/14.51 | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | (891) all_345_1 = 0 44.49/14.51 | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | REDUCE: (804), (891) imply: 44.49/14.51 | | | | | | | | | | | | | | | (892) mem(tree, all_101_1, all_92_6) = 0 44.49/14.51 | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | REF_CLOSE: (64), (82), (85), (704), (892), (size_nonneg) are 44.49/14.51 | | | | | | | | | | | | | | | inconsistent by sub-proof #2. 44.49/14.51 | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | End of split 44.49/14.51 | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | End of split 44.49/14.51 | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | End of split 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | Case 2: 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | (893) ? [v0: $int] : ($lesseq(1, $difference(v0, 44.49/14.51 | | | | | | | | | | | | all_92_8)) & size1(all_253_2) = v0) 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | DELTA: instantiating (893) with fresh symbol all_435_0 44.49/14.51 | | | | | | | | | | | | gives: 44.49/14.51 | | | | | | | | | | | | (894) $lesseq(1, $difference(all_435_0, all_92_8)) & 44.49/14.51 | | | | | | | | | | | | size1(all_253_2) = all_435_0 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | ALPHA: (894) implies: 44.49/14.51 | | | | | | | | | | | | (895) $lesseq(1, $difference(all_435_0, all_92_8)) 44.49/14.51 | | | | | | | | | | | | (896) size1(all_253_2) = all_435_0 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | REDUCE: (704), (895) imply: 44.49/14.51 | | | | | | | | | | | | (897) $lesseq(1, all_435_0) 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_435_0, 0, all_253_2, 44.49/14.51 | | | | | | | | | | | | simplifying with (811), (896) gives: 44.49/14.51 | | | | | | | | | | | | (898) all_435_0 = 0 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | REDUCE: (897), (898) imply: 44.49/14.51 | | | | | | | | | | | | (899) $lesseq(0, -1) 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | CLOSE: (899) is inconsistent. 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | End of split 44.49/14.51 | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | Case 2: 44.49/14.51 | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | (900) ~ (all_253_0 = 0) 44.49/14.51 | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | STRENGTHEN: (791), (900) imply: 44.49/14.51 | | | | | | | | | | | (901) $lesseq(1, all_253_0) 44.49/14.51 | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | BETA: splitting (781) gives: 44.49/14.51 | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | Case 1: 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | (902) $lesseq(all_253_0, 0) 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | COMBINE_INEQS: (901), (902) imply: 44.49/14.51 | | | | | | | | | | | | (903) $lesseq(0, -1) 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | CLOSE: (903) is inconsistent. 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | Case 2: 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | (904) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : 44.49/14.51 | | | | | | | | | | | | ($lesseq(1, $difference(all_253_0, v2)) & 44.49/14.51 | | | | | | | | | | | | node1(v0, v1) = all_253_2 & size1(v0) = v2 & 44.49/14.51 | | | | | | | | | | | | in_tree1(v1) & in_tree1(v0)) 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | DELTA: instantiating (904) with fresh symbols all_440_0, 44.49/14.51 | | | | | | | | | | | | all_440_1, all_440_2 gives: 44.49/14.51 | | | | | | | | | | | | (905) $lesseq(1, $difference(all_253_0, all_440_0)) & 44.49/14.51 | | | | | | | | | | | | node1(all_440_2, all_440_1) = all_253_2 & 44.49/14.51 | | | | | | | | | | | | size1(all_440_2) = all_440_0 & in_tree1(all_440_1) 44.49/14.51 | | | | | | | | | | | | & in_tree1(all_440_2) 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | ALPHA: (905) implies: 44.49/14.51 | | | | | | | | | | | | (906) $lesseq(1, $difference(all_253_0, all_440_0)) 44.49/14.51 | | | | | | | | | | | | (907) in_tree1(all_440_2) 44.49/14.51 | | | | | | | | | | | | (908) size1(all_440_2) = all_440_0 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_440_2, 44.49/14.51 | | | | | | | | | | | | all_440_0, simplifying with (907), (908) gives: 44.49/14.51 | | | | | | | | | | | | (909) $lesseq(0, all_440_0) 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | BETA: splitting (806) gives: 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | Case 1: 44.49/14.51 | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | (910) all_345_0 = 0 44.49/14.51 | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | REDUCE: (805), (910) imply: 44.49/14.51 | | | | | | | | | | | | | (911) mem(tree, all_101_1, all_96_3) = 0 44.49/14.51 | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | GROUND_INST: instantiating (75) with all_101_2, all_101_1, 44.49/14.51 | | | | | | | | | | | | | simplifying with (82), (85), (911) gives: 44.49/14.51 | | | | | | | | | | | | | (912) ? [v0: $int] : ? [v1: $int] : (node1(v0, v1) = 44.49/14.51 | | | | | | | | | | | | | all_101_2 & $sum(size1(v1), $product(-1, 44.49/14.51 | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) 44.49/14.51 | | | | | | | | | | | | | = 0 & size1(v0) = all_92_8 & in_tree1(v1) & 44.49/14.51 | | | | | | | | | | | | | in_tree1(v0)) 44.49/14.51 | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | DELTA: instantiating (912) with fresh symbols all_541_0, 44.49/14.51 | | | | | | | | | | | | | all_541_1 gives: 44.49/14.51 | | | | | | | | | | | | | (913) node1(all_541_1, all_541_0) = all_101_2 & 44.49/14.51 | | | | | | | | | | | | | $sum(size1(all_541_0), $product(-1, 44.49/14.51 | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 44.49/14.51 | | | | | | | | | | | | | 0 & size1(all_541_1) = all_92_8 & 44.49/14.51 | | | | | | | | | | | | | in_tree1(all_541_0) & in_tree1(all_541_1) 44.49/14.51 | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | ALPHA: (913) implies: 44.49/14.51 | | | | | | | | | | | | | (914) in_tree1(all_541_1) 44.49/14.51 | | | | | | | | | | | | | (915) size1(all_541_1) = all_92_8 44.49/14.51 | | | | | | | | | | | | | (916) node1(all_541_1, all_541_0) = all_101_2 44.49/14.51 | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | REDUCE: (704), (915) imply: 44.49/14.51 | | | | | | | | | | | | | (917) size1(all_541_1) = 0 44.49/14.51 | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | BETA: splitting (809) gives: 44.49/14.51 | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | Case 1: 44.49/14.51 | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | (918) all_345_1 = 0 44.49/14.51 | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | REDUCE: (804), (918) imply: 44.49/14.51 | | | | | | | | | | | | | | (919) mem(tree, all_101_1, all_92_6) = 0 44.49/14.51 | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | REF_CLOSE: (64), (82), (85), (704), (919), (size_nonneg) are 44.49/14.51 | | | | | | | | | | | | | | inconsistent by sub-proof #2. 44.49/14.51 | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | Case 2: 44.49/14.51 | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | GROUND_INST: instantiating (node_proj_2_def1) with all_541_1, 44.49/14.51 | | | | | | | | | | | | | | all_541_0, all_101_2, simplifying with (914), 44.49/14.51 | | | | | | | | | | | | | | (916) gives: 44.49/14.51 | | | | | | | | | | | | | | (920) node_proj_21(all_101_2) = all_541_0 & 44.49/14.51 | | | | | | | | | | | | | | in_tree1(all_541_0) 44.49/14.51 | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | ALPHA: (920) implies: 44.49/14.51 | | | | | | | | | | | | | | (921) in_tree1(all_541_0) 44.49/14.51 | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | GROUND_INST: instantiating (tree_diff) with all_541_1, 44.49/14.51 | | | | | | | | | | | | | | all_253_2, 0, all_253_0, simplifying with (720), 44.49/14.51 | | | | | | | | | | | | | | (914), (917) gives: 44.49/14.51 | | | | | | | | | | | | | | (922) all_253_0 = 0 | ! [v0: $int] : ! [v1: $int] : ! 44.49/14.51 | | | | | | | | | | | | | | [v2: $int] : ( ~ (node1(all_541_1, v0) = v2) | ~ 44.49/14.51 | | | | | | | | | | | | | | (node1(all_253_2, v1) = v2) | ~ in_tree1(v0)) 44.49/14.51 | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | BETA: splitting (922) gives: 44.49/14.51 | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | Case 1: 44.49/14.51 | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | (923) all_253_0 = 0 44.49/14.51 | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | REDUCE: (906), (923) imply: 44.49/14.51 | | | | | | | | | | | | | | | (924) $lesseq(all_440_0, -1) 44.49/14.51 | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | COMBINE_INEQS: (909), (924) imply: 44.49/14.51 | | | | | | | | | | | | | | | (925) $lesseq(0, -1) 44.49/14.51 | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | CLOSE: (925) is inconsistent. 44.49/14.51 | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | Case 2: 44.49/14.51 | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | (926) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( 44.49/14.51 | | | | | | | | | | | | | | | ~ (node1(all_541_1, v0) = v2) | ~ 44.49/14.51 | | | | | | | | | | | | | | | (node1(all_253_2, v1) = v2) | ~ in_tree1(v0)) 44.49/14.51 | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | GROUND_INST: instantiating (926) with all_541_0, all_253_1, 44.49/14.51 | | | | | | | | | | | | | | | all_101_2, simplifying with (721), (916), (921) 44.49/14.51 | | | | | | | | | | | | | | | gives: 44.49/14.51 | | | | | | | | | | | | | | | (927) $false 44.49/14.51 | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | | CLOSE: (927) is inconsistent. 44.49/14.51 | | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | | End of split 44.49/14.51 | | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | End of split 44.49/14.51 | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | Case 2: 44.49/14.51 | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | (928) all_345_1 = 0 44.49/14.51 | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | REDUCE: (804), (928) imply: 44.49/14.51 | | | | | | | | | | | | | (929) mem(tree, all_101_1, all_92_6) = 0 44.49/14.51 | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | | REF_CLOSE: (64), (82), (85), (704), (929), (size_nonneg) are 44.49/14.51 | | | | | | | | | | | | | inconsistent by sub-proof #2. 44.49/14.51 | | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | | End of split 44.49/14.51 | | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | | End of split 44.49/14.51 | | | | | | | | | | | 44.49/14.51 | | | | | | | | | | End of split 44.49/14.51 | | | | | | | | | | 44.49/14.51 | | | | | | | | | End of split 44.49/14.51 | | | | | | | | | 44.49/14.51 | | | | | | | | End of split 44.49/14.51 | | | | | | | | 44.49/14.51 | | | | | | | Case 2: 44.49/14.51 | | | | | | | | 44.49/14.52 | | | | | | | | (930) ? [v0: $int] : ( ~ (v0 = 0) & sort1(all_74_1, 44.49/14.52 | | | | | | | | all_96_2) = v0) 44.49/14.52 | | | | | | | | 44.49/14.52 | | | | | | | | DELTA: instantiating (930) with fresh symbol all_270_0 gives: 44.49/14.52 | | | | | | | | (931) ~ (all_270_0 = 0) & sort1(all_74_1, all_96_2) = 44.49/14.52 | | | | | | | | all_270_0 44.49/14.52 | | | | | | | | 44.49/14.52 | | | | | | | | REF_CLOSE: (10), (25), (73), (931), (infix_plpl_sort2) are 44.49/14.52 | | | | | | | | inconsistent by sub-proof #7. 44.49/14.52 | | | | | | | | 44.49/14.52 | | | | | | | End of split 44.49/14.52 | | | | | | | 44.49/14.52 | | | | | | End of split 44.49/14.52 | | | | | | 44.49/14.52 | | | | | End of split 44.49/14.52 | | | | | 44.49/14.52 | | | | End of split 44.49/14.52 | | | | 44.49/14.52 | | | Case 2: 44.49/14.52 | | | | 44.49/14.52 | | | | (932) all_92_2 = all_77_4 44.49/14.52 | | | | 44.49/14.52 | | | | REDUCE: (706), (932) imply: 44.49/14.52 | | | | (933) $sum(tb2t(all_77_4), $product(-1, $sum(all_88_4, -1))) = 0 44.49/14.52 | | | | 44.49/14.52 | | | | GROUND_INST: instantiating (21) with 0, $sum(all_88_4, -1), all_77_4, 44.49/14.52 | | | | simplifying with (106), (933) gives: 44.49/14.52 | | | | (934) all_88_4 = 1 44.49/14.52 | | | | 44.49/14.52 | | | | BETA: splitting (117) gives: 44.49/14.52 | | | | 44.49/14.52 | | | | Case 1: 44.49/14.52 | | | | | 44.49/14.52 | | | | | (935) $lesseq(all_101_0, 0) 44.49/14.52 | | | | | 44.49/14.52 | | | | | ANTI_SYMM: (92), (935) imply: 44.49/14.52 | | | | | (936) all_101_0 = 0 44.49/14.52 | | | | | 44.49/14.52 | | | | | REDUCE: (84), (936) imply: 44.49/14.52 | | | | | (937) size1(all_101_2) = 0 44.49/14.52 | | | | | 44.49/14.52 | | | | | REF_CLOSE: (5), (7), (10), (14), (25), (64), (73), (75), (82), (83), 44.49/14.52 | | | | | (85), (165), (170), (184), (222), (704), (937), 44.49/14.52 | | | | | (infix_plpl_sort2), (node_proj_2_def1), (size_nonneg) are 44.49/14.52 | | | | | inconsistent by sub-proof #1. 44.49/14.52 | | | | | 44.49/14.52 | | | | Case 2: 44.49/14.52 | | | | | 44.49/14.52 | | | | | (938) $lesseq(1, all_101_0) 44.49/14.52 | | | | | (939) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ($lesseq(1, 44.49/14.52 | | | | | $difference(all_101_0, v2)) & node1(v0, v1) = all_101_2 & 44.49/14.52 | | | | | size1(v0) = v2 & in_tree1(v1) & in_tree1(v0)) 44.49/14.52 | | | | | 44.49/14.52 | | | | | DELTA: instantiating (939) with fresh symbols all_248_0, all_248_1, 44.49/14.52 | | | | | all_248_2 gives: 44.49/14.52 | | | | | (940) $lesseq(1, $difference(all_101_0, all_248_0)) & 44.49/14.52 | | | | | node1(all_248_2, all_248_1) = all_101_2 & size1(all_248_2) = 44.49/14.52 | | | | | all_248_0 & in_tree1(all_248_1) & in_tree1(all_248_2) 44.49/14.52 | | | | | 44.49/14.52 | | | | | ALPHA: (940) implies: 44.49/14.52 | | | | | (941) $lesseq(1, $difference(all_101_0, all_248_0)) 44.49/14.52 | | | | | (942) in_tree1(all_248_2) 44.49/14.52 | | | | | (943) size1(all_248_2) = all_248_0 44.49/14.52 | | | | | (944) node1(all_248_2, all_248_1) = all_101_2 44.49/14.52 | | | | | 44.49/14.52 | | | | | BETA: splitting (118) gives: 44.49/14.52 | | | | | 44.49/14.52 | | | | | Case 1: 44.49/14.52 | | | | | | 44.49/14.52 | | | | | | (945) all_101_0 = 0 44.49/14.52 | | | | | | 44.49/14.52 | | | | | | REDUCE: (938), (945) imply: 44.49/14.52 | | | | | | (946) $lesseq(0, -1) 44.49/14.52 | | | | | | 44.49/14.52 | | | | | | CLOSE: (946) is inconsistent. 44.49/14.52 | | | | | | 44.49/14.52 | | | | | Case 2: 44.49/14.52 | | | | | | 44.49/14.52 | | | | | | 44.49/14.52 | | | | | | GROUND_INST: instantiating (size_nonneg) with all_248_2, all_248_0, 44.49/14.52 | | | | | | simplifying with (942), (943) gives: 44.49/14.52 | | | | | | (947) $lesseq(0, all_248_0) 44.49/14.52 | | | | | | 44.49/14.52 | | | | | | BETA: splitting (127) gives: 44.49/14.52 | | | | | | 44.49/14.52 | | | | | | Case 1: 44.49/14.52 | | | | | | | 44.49/14.52 | | | | | | | (948) all_125_1 = all_92_6 44.49/14.52 | | | | | | | 44.49/14.52 | | | | | | | COMBINE_EQS: (157), (948) imply: 44.49/14.52 | | | | | | | (949) all_92_6 = all_77_6 44.49/14.52 | | | | | | | 44.49/14.52 | | | | | | | REDUCE: (73), (949) imply: 44.49/14.52 | | | | | | | (950) infix_plpl(tree, all_96_3, all_77_6) = all_96_2 44.49/14.52 | | | | | | | 44.49/14.52 | | | | | | | GROUND_INST: instantiating (append_l_nil) with tree, all_96_3, 44.49/14.52 | | | | | | | all_77_6, all_96_2, simplifying with (10), (28), 44.49/14.52 | | | | | | | (950) gives: 44.49/14.52 | | | | | | | (951) all_96_2 = all_96_3 44.49/14.52 | | | | | | | 44.49/14.52 | | | | | | | BETA: splitting (170) gives: 44.49/14.52 | | | | | | | 44.49/14.52 | | | | | | | Case 1: 44.49/14.52 | | | | | | | | 44.49/14.52 | | | | | | | | (952) all_99_0 = all_96_2 44.49/14.52 | | | | | | | | 44.49/14.52 | | | | | | | | COMBINE_EQS: (951), (952) imply: 44.49/14.52 | | | | | | | | (953) all_99_0 = all_96_3 44.49/14.52 | | | | | | | | 44.49/14.52 | | | | | | | | REDUCE: (83), (953) imply: 44.49/14.52 | | | | | | | | (954) mem(tree, all_101_1, all_96_3) = 0 44.49/14.52 | | | | | | | | 44.49/14.52 | | | | | | | | GROUND_INST: instantiating (86) with all_248_2, all_248_1, 44.49/14.52 | | | | | | | | simplifying with (942), (944) gives: 44.49/14.52 | | | | | | | | (955) ~ (all_101_0 = all_88_4) | ? [v0: $int] : ($lesseq(1, 44.49/14.52 | | | | | | | | $difference(v0, all_92_8)) & size1(all_248_2) = v0) 44.49/14.52 | | | | | | | | 44.49/14.52 | | | | | | | | GROUND_INST: instantiating (node_proj_1_def1) with all_248_2, 44.49/14.52 | | | | | | | | all_248_1, all_101_2, simplifying with (942), (944) 44.49/14.52 | | | | | | | | gives: 44.49/14.52 | | | | | | | | (956) node_proj_11(all_101_2) = all_248_2 44.49/14.52 | | | | | | | | 44.49/14.52 | | | | | | | | GROUND_INST: instantiating (75) with all_101_2, all_101_1, 44.49/14.52 | | | | | | | | simplifying with (82), (85), (954) gives: 44.49/14.52 | | | | | | | | (957) ? [v0: $int] : ? [v1: $int] : (node1(v0, v1) = 44.49/14.52 | | | | | | | | all_101_2 & $sum(size1(v1), $product(-1, 44.49/14.52 | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 & 44.49/14.52 | | | | | | | | size1(v0) = all_92_8 & in_tree1(v1) & in_tree1(v0)) 44.49/14.52 | | | | | | | | 44.49/14.52 | | | | | | | | DELTA: instantiating (957) with fresh symbols all_301_0, 44.49/14.52 | | | | | | | | all_301_1 gives: 44.49/14.52 | | | | | | | | (958) node1(all_301_1, all_301_0) = all_101_2 & 44.49/14.52 | | | | | | | | $sum(size1(all_301_0), $product(-1, 44.49/14.52 | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 & 44.49/14.52 | | | | | | | | size1(all_301_1) = all_92_8 & in_tree1(all_301_0) & 44.49/14.52 | | | | | | | | in_tree1(all_301_1) 44.49/14.52 | | | | | | | | 44.49/14.52 | | | | | | | | ALPHA: (958) implies: 44.49/14.52 | | | | | | | | (959) in_tree1(all_301_1) 44.49/14.52 | | | | | | | | (960) size1(all_301_1) = all_92_8 44.49/14.52 | | | | | | | | (961) $sum(size1(all_301_0), $product(-1, 44.49/14.52 | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 0 44.49/14.52 | | | | | | | | (962) node1(all_301_1, all_301_0) = all_101_2 44.49/14.52 | | | | | | | | 44.49/14.52 | | | | | | | | REDUCE: (704), (934), (961) imply: 44.49/14.52 | | | | | | | | (963) size1(all_301_0) = 0 44.49/14.52 | | | | | | | | 44.49/14.52 | | | | | | | | REDUCE: (704), (960) imply: 44.49/14.52 | | | | | | | | (964) size1(all_301_1) = 0 44.49/14.52 | | | | | | | | 44.49/14.52 | | | | | | | | BETA: splitting (184) gives: 44.49/14.52 | | | | | | | | 44.49/14.52 | | | | | | | | Case 1: 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | (965) all_160_1 = all_77_2 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | COMBINE_EQS: (222), (965) imply: 44.49/14.52 | | | | | | | | | (966) all_77_2 = all_77_6 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | SIMP: (966) implies: 44.49/14.52 | | | | | | | | | (967) all_77_2 = all_77_6 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | REDUCE: (165), (967) imply: 44.49/14.52 | | | | | | | | | (968) ~ (0 = 0) 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | CLOSE: (968) is inconsistent. 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | Case 2: 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | GROUND_INST: instantiating (86) with all_301_1, all_301_0, 44.49/14.52 | | | | | | | | | simplifying with (959), (962) gives: 44.49/14.52 | | | | | | | | | (969) ~ (all_101_0 = all_88_4) | ? [v0: $int] : 44.49/14.52 | | | | | | | | | ($lesseq(1, $difference(v0, all_92_8)) & 44.49/14.52 | | | | | | | | | size1(all_301_1) = v0) 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | GROUND_INST: instantiating (node_proj_1_def1) with all_301_1, 44.49/14.52 | | | | | | | | | all_301_0, all_101_2, simplifying with (959), 44.49/14.52 | | | | | | | | | (962) gives: 44.49/14.52 | | | | | | | | | (970) node_proj_11(all_101_2) = all_301_1 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | GROUND_INST: instantiating (5) with all_301_1, all_301_0, 44.49/14.52 | | | | | | | | | all_101_2, simplifying with (959), (962) gives: 44.49/14.52 | | | | | | | | | (971) ? [v0: $int] : ? [v1: $int] : 44.49/14.52 | | | | | | | | | ($sum(size1(all_301_0), $product(-1, 44.49/14.52 | | | | | | | | | $sum($difference(v0, v1), -1))) = 0 & 44.49/14.52 | | | | | | | | | size1(all_301_1) = v1 & size1(all_101_2) = v0) 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | DELTA: instantiating (971) with fresh symbols all_350_0, 44.49/14.52 | | | | | | | | | all_350_1 gives: 44.49/14.52 | | | | | | | | | (972) $sum(size1(all_301_0), $product(-1, 44.49/14.52 | | | | | | | | | $sum($difference(all_350_1, all_350_0), -1))) = 0 44.49/14.52 | | | | | | | | | & size1(all_301_1) = all_350_0 & size1(all_101_2) = 44.49/14.52 | | | | | | | | | all_350_1 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | ALPHA: (972) implies: 44.49/14.52 | | | | | | | | | (973) size1(all_101_2) = all_350_1 44.49/14.52 | | | | | | | | | (974) size1(all_301_1) = all_350_0 44.49/14.52 | | | | | | | | | (975) $sum(size1(all_301_0), $product(-1, 44.49/14.52 | | | | | | | | | $sum($difference(all_350_1, all_350_0), -1))) = 0 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | GROUND_INST: instantiating (20) with all_248_2, all_301_1, 44.49/14.52 | | | | | | | | | all_101_2, simplifying with (956), (970) gives: 44.49/14.52 | | | | | | | | | (976) all_301_1 = all_248_2 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | GROUND_INST: instantiating (14) with 0, 44.49/14.52 | | | | | | | | | $sum($difference(all_350_1, all_350_0), -1), 44.49/14.52 | | | | | | | | | all_301_0, simplifying with (963), (975) gives: 44.49/14.52 | | | | | | | | | (977) $difference(all_350_0, all_350_1) = -1 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_350_0, all_301_1, 44.49/14.52 | | | | | | | | | simplifying with (964), (974) gives: 44.49/14.52 | | | | | | | | | (978) all_350_0 = 0 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | GROUND_INST: instantiating (14) with all_101_0, all_350_1, 44.49/14.52 | | | | | | | | | all_101_2, simplifying with (84), (973) gives: 44.49/14.52 | | | | | | | | | (979) all_350_1 = all_101_0 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | COMBINE_EQS: (977), (978) imply: 44.49/14.52 | | | | | | | | | (980) all_350_1 = 1 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | COMBINE_EQS: (979), (980) imply: 44.49/14.52 | | | | | | | | | (981) all_101_0 = 1 44.49/14.52 | | | | | | | | | 44.49/14.52 | | | | | | | | | REDUCE: (941), (981) imply: 44.49/14.52 | | | | | | | | | (982) $lesseq(all_248_0, 0) 44.49/14.52 | | | | | | | | | 44.49/14.53 | | | | | | | | | ANTI_SYMM: (947), (982) imply: 44.49/14.53 | | | | | | | | | (983) all_248_0 = 0 44.49/14.53 | | | | | | | | | 44.49/14.53 | | | | | | | | | REDUCE: (943), (983) imply: 44.49/14.53 | | | | | | | | | (984) size1(all_248_2) = 0 44.49/14.53 | | | | | | | | | 44.49/14.53 | | | | | | | | | BETA: splitting (969) gives: 44.49/14.53 | | | | | | | | | 44.49/14.53 | | | | | | | | | Case 1: 44.49/14.53 | | | | | | | | | | 44.49/14.53 | | | | | | | | | | (985) ~ (all_101_0 = all_88_4) 44.49/14.53 | | | | | | | | | | 44.49/14.53 | | | | | | | | | | REDUCE: (934), (981), (985) imply: 44.49/14.53 | | | | | | | | | | (986) ~ (0 = 0) 44.49/14.53 | | | | | | | | | | 44.49/14.53 | | | | | | | | | | CLOSE: (986) is inconsistent. 44.49/14.53 | | | | | | | | | | 44.49/14.53 | | | | | | | | | Case 2: 44.49/14.53 | | | | | | | | | | 44.49/14.53 | | | | | | | | | | (987) all_101_0 = all_88_4 44.49/14.53 | | | | | | | | | | (988) ? [v0: $int] : ($lesseq(1, $difference(v0, 44.49/14.53 | | | | | | | | | | all_92_8)) & size1(all_301_1) = v0) 44.49/14.53 | | | | | | | | | | 44.49/14.53 | | | | | | | | | | DELTA: instantiating (988) with fresh symbol all_394_0 44.49/14.53 | | | | | | | | | | gives: 44.49/14.53 | | | | | | | | | | (989) $lesseq(1, $difference(all_394_0, all_92_8)) & 44.49/14.53 | | | | | | | | | | size1(all_301_1) = all_394_0 44.49/14.53 | | | | | | | | | | 44.49/14.53 | | | | | | | | | | ALPHA: (989) implies: 44.49/14.53 | | | | | | | | | | (990) $lesseq(1, $difference(all_394_0, all_92_8)) 44.49/14.53 | | | | | | | | | | (991) size1(all_301_1) = all_394_0 44.49/14.53 | | | | | | | | | | 44.49/14.53 | | | | | | | | | | REDUCE: (704), (990) imply: 44.49/14.53 | | | | | | | | | | (992) $lesseq(1, all_394_0) 44.49/14.53 | | | | | | | | | | 44.49/14.53 | | | | | | | | | | REDUCE: (976), (991) imply: 44.49/14.53 | | | | | | | | | | (993) size1(all_248_2) = all_394_0 44.49/14.53 | | | | | | | | | | 44.49/14.53 | | | | | | | | | | BETA: splitting (955) gives: 44.49/14.53 | | | | | | | | | | 44.49/14.53 | | | | | | | | | | Case 1: 44.49/14.53 | | | | | | | | | | | 44.49/14.53 | | | | | | | | | | | (994) ~ (all_101_0 = all_88_4) 44.49/14.53 | | | | | | | | | | | 44.49/14.53 | | | | | | | | | | | REDUCE: (934), (981), (994) imply: 44.49/14.53 | | | | | | | | | | | (995) ~ (0 = 0) 44.49/14.53 | | | | | | | | | | | 44.49/14.53 | | | | | | | | | | | CLOSE: (995) is inconsistent. 44.49/14.53 | | | | | | | | | | | 44.49/14.53 | | | | | | | | | | Case 2: 44.49/14.53 | | | | | | | | | | | 44.49/14.53 | | | | | | | | | | | (996) ? [v0: $int] : ($lesseq(1, $difference(v0, 44.49/14.53 | | | | | | | | | | | all_92_8)) & size1(all_248_2) = v0) 44.49/14.53 | | | | | | | | | | | 44.49/14.53 | | | | | | | | | | | DELTA: instantiating (996) with fresh symbol all_402_0 44.49/14.53 | | | | | | | | | | | gives: 44.49/14.53 | | | | | | | | | | | (997) $lesseq(1, $difference(all_402_0, all_92_8)) & 44.49/14.53 | | | | | | | | | | | size1(all_248_2) = all_402_0 44.49/14.53 | | | | | | | | | | | 44.49/14.53 | | | | | | | | | | | ALPHA: (997) implies: 44.49/14.53 | | | | | | | | | | | (998) size1(all_248_2) = all_402_0 44.49/14.53 | | | | | | | | | | | 44.49/14.53 | | | | | | | | | | | GROUND_INST: instantiating (14) with all_402_0, all_394_0, 44.49/14.53 | | | | | | | | | | | all_248_2, simplifying with (993), (998) gives: 44.49/14.53 | | | | | | | | | | | (999) all_402_0 = all_394_0 44.49/14.53 | | | | | | | | | | | 44.49/14.53 | | | | | | | | | | | GROUND_INST: instantiating (14) with all_402_0, 0, all_248_2, 44.49/14.53 | | | | | | | | | | | simplifying with (984), (998) gives: 44.49/14.53 | | | | | | | | | | | (1000) all_402_0 = 0 44.49/14.53 | | | | | | | | | | | 44.49/14.53 | | | | | | | | | | | COMBINE_EQS: (999), (1000) imply: 44.49/14.53 | | | | | | | | | | | (1001) all_394_0 = 0 44.49/14.53 | | | | | | | | | | | 44.49/14.53 | | | | | | | | | | | SIMP: (1001) implies: 44.49/14.53 | | | | | | | | | | | (1002) all_394_0 = 0 44.49/14.54 | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | REDUCE: (992), (1002) imply: 44.49/14.54 | | | | | | | | | | | (1003) $lesseq(0, -1) 44.49/14.54 | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | CLOSE: (1003) is inconsistent. 44.49/14.54 | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | End of split 44.49/14.54 | | | | | | | | | | 44.49/14.54 | | | | | | | | | End of split 44.49/14.54 | | | | | | | | | 44.49/14.54 | | | | | | | | End of split 44.49/14.54 | | | | | | | | 44.49/14.54 | | | | | | | Case 2: 44.49/14.54 | | | | | | | | 44.49/14.54 | | | | | | | | (1004) ? [v0: $int] : ( ~ (v0 = 0) & sort1(all_74_1, 44.49/14.54 | | | | | | | | all_96_2) = v0) 44.49/14.54 | | | | | | | | 44.49/14.54 | | | | | | | | REF_CLOSE: (22), (145), (951), (1004) are inconsistent by 44.49/14.54 | | | | | | | | sub-proof #6. 44.49/14.54 | | | | | | | | 44.49/14.54 | | | | | | | End of split 44.49/14.54 | | | | | | | 44.49/14.54 | | | | | | Case 2: 44.49/14.54 | | | | | | | 44.49/14.54 | | | | | | | 44.49/14.54 | | | | | | | GROUND_INST: instantiating (86) with all_248_2, all_248_1, 44.49/14.54 | | | | | | | simplifying with (942), (944) gives: 44.49/14.54 | | | | | | | (1005) ~ (all_101_0 = all_88_4) | ? [v0: $int] : ($lesseq(1, 44.49/14.54 | | | | | | | $difference(v0, all_92_8)) & size1(all_248_2) = v0) 44.49/14.54 | | | | | | | 44.49/14.54 | | | | | | | GROUND_INST: instantiating (5) with all_248_2, all_248_1, 44.49/14.54 | | | | | | | all_101_2, simplifying with (942), (944) gives: 44.49/14.54 | | | | | | | (1006) ? [v0: $int] : ? [v1: $int] : ($sum(size1(all_248_1), 44.49/14.54 | | | | | | | $product(-1, $sum($difference(v0, v1), -1))) = 0 & 44.49/14.54 | | | | | | | size1(all_248_2) = v1 & size1(all_101_2) = v0) 44.49/14.54 | | | | | | | 44.49/14.54 | | | | | | | GROUND_INST: instantiating (node_proj_2_def1) with all_248_2, 44.49/14.54 | | | | | | | all_248_1, all_101_2, simplifying with (942), (944) 44.49/14.54 | | | | | | | gives: 44.49/14.54 | | | | | | | (1007) node_proj_21(all_101_2) = all_248_1 & 44.49/14.54 | | | | | | | in_tree1(all_248_1) 44.49/14.54 | | | | | | | 44.49/14.54 | | | | | | | ALPHA: (1007) implies: 44.49/14.54 | | | | | | | (1008) in_tree1(all_248_1) 44.49/14.54 | | | | | | | 44.49/14.54 | | | | | | | GROUND_INST: instantiating (tree_diff) with all_248_2, empty1, 44.49/14.54 | | | | | | | all_248_0, 0, simplifying with (4), (942), (943) 44.49/14.54 | | | | | | | gives: 44.49/14.54 | | | | | | | (1009) all_248_0 = 0 | ! [v0: $int] : ! [v1: $int] : ! [v2: 44.49/14.54 | | | | | | | $int] : ( ~ (node1(all_248_2, v0) = v2) | ~ 44.49/14.54 | | | | | | | (node1(empty1, v1) = v2) | ~ in_tree1(v0)) 44.49/14.54 | | | | | | | 44.49/14.54 | | | | | | | GROUND_INST: instantiating (size_left) with all_248_2, all_248_0, 44.49/14.54 | | | | | | | simplifying with (942), (943) gives: 44.49/14.54 | | | | | | | (1010) ~ ($lesseq(1, all_248_0)) | ? [v0: $int] : ? [v1: 44.49/14.54 | | | | | | | $int] : ? [v2: $int] : ($lesseq(1, 44.49/14.54 | | | | | | | $difference(all_248_0, v2)) & node1(v0, v1) = 44.49/14.54 | | | | | | | all_248_2 & size1(v0) = v2 & in_tree1(v1) & 44.49/14.54 | | | | | | | in_tree1(v0)) 44.49/14.54 | | | | | | | 44.49/14.54 | | | | | | | DELTA: instantiating (1006) with fresh symbols all_287_0, 44.49/14.54 | | | | | | | all_287_1 gives: 44.49/14.54 | | | | | | | (1011) $sum(size1(all_248_1), $product(-1, 44.49/14.54 | | | | | | | $sum($difference(all_287_1, all_287_0), -1))) = 0 & 44.49/14.54 | | | | | | | size1(all_248_2) = all_287_0 & size1(all_101_2) = 44.49/14.54 | | | | | | | all_287_1 44.49/14.54 | | | | | | | 44.49/14.54 | | | | | | | ALPHA: (1011) implies: 44.49/14.54 | | | | | | | (1012) size1(all_101_2) = all_287_1 44.49/14.54 | | | | | | | (1013) size1(all_248_2) = all_287_0 44.49/14.54 | | | | | | | (1014) $sum(size1(all_248_1), $product(-1, 44.49/14.54 | | | | | | | $sum($difference(all_287_1, all_287_0), -1))) = 0 44.49/14.54 | | | | | | | 44.49/14.54 | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_248_1, 44.49/14.54 | | | | | | | $sum($difference(all_287_1, all_287_0), -1), 44.49/14.54 | | | | | | | simplifying with (1008), (1014) gives: 44.49/14.54 | | | | | | | (1015) $lesseq(1, $difference(all_287_1, all_287_0)) 44.49/14.54 | | | | | | | 44.49/14.54 | | | | | | | GROUND_INST: instantiating (14) with all_248_0, all_287_0, 44.49/14.54 | | | | | | | all_248_2, simplifying with (943), (1013) gives: 44.49/14.54 | | | | | | | (1016) all_287_0 = all_248_0 44.49/14.54 | | | | | | | 44.49/14.54 | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_248_2, 44.49/14.54 | | | | | | | all_287_0, simplifying with (942), (1013) gives: 44.49/14.54 | | | | | | | (1017) $lesseq(0, all_287_0) 44.49/14.54 | | | | | | | 44.49/14.54 | | | | | | | GROUND_INST: instantiating (14) with all_101_0, all_287_1, 44.49/14.54 | | | | | | | all_101_2, simplifying with (84), (1012) gives: 44.49/14.54 | | | | | | | (1018) all_287_1 = all_101_0 44.49/14.54 | | | | | | | 44.49/14.54 | | | | | | | REDUCE: (1014), (1016), (1018) imply: 44.49/14.54 | | | | | | | (1019) $sum(size1(all_248_1), $product(-1, 44.49/14.54 | | | | | | | $sum($difference(all_101_0, all_248_0), -1))) = 0 44.49/14.54 | | | | | | | 44.49/14.54 | | | | | | | BETA: splitting (170) gives: 44.49/14.54 | | | | | | | 44.49/14.54 | | | | | | | Case 1: 44.49/14.54 | | | | | | | | 44.49/14.54 | | | | | | | | (1020) all_99_0 = all_96_2 44.49/14.54 | | | | | | | | 44.49/14.54 | | | | | | | | REDUCE: (83), (1020) imply: 44.49/14.54 | | | | | | | | (1021) mem(tree, all_101_1, all_96_2) = 0 44.49/14.54 | | | | | | | | 44.49/14.54 | | | | | | | | BETA: splitting (184) gives: 44.49/14.54 | | | | | | | | 44.49/14.54 | | | | | | | | Case 1: 44.49/14.54 | | | | | | | | | 44.49/14.54 | | | | | | | | | (1022) all_160_1 = all_77_2 44.49/14.54 | | | | | | | | | 44.49/14.54 | | | | | | | | | COMBINE_EQS: (222), (1022) imply: 44.49/14.54 | | | | | | | | | (1023) all_77_2 = all_77_6 44.49/14.54 | | | | | | | | | 44.49/14.54 | | | | | | | | | SIMP: (1023) implies: 44.49/14.54 | | | | | | | | | (1024) all_77_2 = all_77_6 44.49/14.54 | | | | | | | | | 44.49/14.54 | | | | | | | | | REDUCE: (165), (1024) imply: 44.49/14.54 | | | | | | | | | (1025) ~ (0 = 0) 44.49/14.54 | | | | | | | | | 44.49/14.54 | | | | | | | | | CLOSE: (1025) is inconsistent. 44.49/14.54 | | | | | | | | | 44.49/14.54 | | | | | | | | Case 2: 44.49/14.54 | | | | | | | | | 44.49/14.54 | | | | | | | | | 44.49/14.54 | | | | | | | | | GROUND_INST: instantiating (size_left) with all_248_1, 44.49/14.54 | | | | | | | | | $sum($difference(all_101_0, all_248_0), -1), 44.49/14.54 | | | | | | | | | simplifying with (1008), (1019) gives: 44.49/14.54 | | | | | | | | | (1026) ~ ($lesseq(2, $difference(all_101_0, all_248_0))) | 44.49/14.54 | | | | | | | | | ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : 44.49/14.54 | | | | | | | | | ($lesseq(2, $sum($difference($product(-1, v2), 44.49/14.54 | | | | | | | | | all_248_0), all_101_0)) & node1(v0, v1) = 44.49/14.54 | | | | | | | | | all_248_1 & size1(v0) = v2 & in_tree1(v1) & 44.49/14.54 | | | | | | | | | in_tree1(v0)) 44.49/14.54 | | | | | | | | | 44.49/14.54 | | | | | | | | | GROUND_INST: instantiating (7) with tree, all_101_1, all_96_3, 44.49/14.54 | | | | | | | | | all_92_6, all_96_2, simplifying with (10), (73), 44.49/14.54 | | | | | | | | | (1021) gives: 44.49/14.54 | | | | | | | | | (1027) ? [v0: $int] : ? [v1: $int] : (mem(tree, 44.49/14.54 | | | | | | | | | all_101_1, all_96_3) = v1 & mem(tree, all_101_1, 44.49/14.54 | | | | | | | | | all_92_6) = v0 & (v1 = 0 | v0 = 0)) 44.49/14.54 | | | | | | | | | 44.49/14.54 | | | | | | | | | DELTA: instantiating (1027) with fresh symbols all_338_0, 44.49/14.54 | | | | | | | | | all_338_1 gives: 44.49/14.54 | | | | | | | | | (1028) mem(tree, all_101_1, all_96_3) = all_338_0 & 44.49/14.54 | | | | | | | | | mem(tree, all_101_1, all_92_6) = all_338_1 & 44.49/14.54 | | | | | | | | | (all_338_0 = 0 | all_338_1 = 0) 44.49/14.54 | | | | | | | | | 44.49/14.54 | | | | | | | | | ALPHA: (1028) implies: 44.49/14.54 | | | | | | | | | (1029) mem(tree, all_101_1, all_92_6) = all_338_1 44.49/14.54 | | | | | | | | | (1030) mem(tree, all_101_1, all_96_3) = all_338_0 44.49/14.54 | | | | | | | | | (1031) all_338_0 = 0 | all_338_1 = 0 44.49/14.54 | | | | | | | | | 44.49/14.54 | | | | | | | | | BETA: splitting (1005) gives: 44.49/14.54 | | | | | | | | | 44.49/14.54 | | | | | | | | | Case 1: 44.49/14.54 | | | | | | | | | | 44.49/14.54 | | | | | | | | | | (1032) ~ (all_101_0 = all_88_4) 44.49/14.54 | | | | | | | | | | 44.49/14.54 | | | | | | | | | | REDUCE: (934), (1032) imply: 44.49/14.54 | | | | | | | | | | (1033) ~ (all_101_0 = 1) 44.49/14.54 | | | | | | | | | | 44.49/14.54 | | | | | | | | | | BETA: splitting (1009) gives: 44.49/14.54 | | | | | | | | | | 44.49/14.54 | | | | | | | | | | Case 1: 44.49/14.54 | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | (1034) all_248_0 = 0 44.49/14.54 | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | STRENGTHEN: (938), (1033) imply: 44.49/14.54 | | | | | | | | | | | (1035) $lesseq(2, all_101_0) 44.49/14.54 | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | REDUCE: (1019), (1034) imply: 44.49/14.54 | | | | | | | | | | | (1036) $sum(size1(all_248_1), $product(-1, 44.49/14.54 | | | | | | | | | | | $sum(all_101_0, -1))) = 0 44.49/14.54 | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | BETA: splitting (1026) gives: 44.49/14.54 | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | Case 1: 44.49/14.54 | | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | | (1037) $lesseq(-1, $difference(all_248_0, all_101_0)) 44.49/14.54 | | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | | REDUCE: (1034), (1037) imply: 44.49/14.54 | | | | | | | | | | | | (1038) $lesseq(all_101_0, 1) 44.49/14.54 | | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | | COMBINE_INEQS: (1035), (1038) imply: 44.49/14.54 | | | | | | | | | | | | (1039) $lesseq(0, -1) 44.49/14.54 | | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | | CLOSE: (1039) is inconsistent. 44.49/14.54 | | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | Case 2: 44.49/14.54 | | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | | (1040) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : 44.49/14.54 | | | | | | | | | | | | ($lesseq(2, $sum($difference($product(-1, v2), 44.49/14.54 | | | | | | | | | | | | all_248_0), all_101_0)) & node1(v0, v1) = 44.49/14.54 | | | | | | | | | | | | all_248_1 & size1(v0) = v2 & in_tree1(v1) & 44.49/14.54 | | | | | | | | | | | | in_tree1(v0)) 44.49/14.54 | | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | | DELTA: instantiating (1040) with fresh symbols all_461_0, 44.49/14.54 | | | | | | | | | | | | all_461_1, all_461_2 gives: 44.49/14.54 | | | | | | | | | | | | (1041) $lesseq(2, $sum($difference($product(-1, 44.49/14.54 | | | | | | | | | | | | all_461_0), all_248_0), all_101_0)) & 44.49/14.54 | | | | | | | | | | | | node1(all_461_2, all_461_1) = all_248_1 & 44.49/14.54 | | | | | | | | | | | | size1(all_461_2) = all_461_0 & in_tree1(all_461_1) 44.49/14.54 | | | | | | | | | | | | & in_tree1(all_461_2) 44.49/14.54 | | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | | ALPHA: (1041) implies: 44.49/14.54 | | | | | | | | | | | | (1042) $lesseq(2, $sum($difference($product(-1, 44.49/14.54 | | | | | | | | | | | | all_461_0), all_248_0), all_101_0)) 44.49/14.54 | | | | | | | | | | | | (1043) in_tree1(all_461_2) 44.49/14.54 | | | | | | | | | | | | (1044) size1(all_461_2) = all_461_0 44.49/14.54 | | | | | | | | | | | | (1045) node1(all_461_2, all_461_1) = all_248_1 44.49/14.54 | | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | | REDUCE: (1034), (1042) imply: 44.49/14.54 | | | | | | | | | | | | (1046) $lesseq(2, $difference(all_101_0, all_461_0)) 44.49/14.54 | | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_461_2, 44.49/14.54 | | | | | | | | | | | | all_461_0, simplifying with (1043), (1044) gives: 44.49/14.54 | | | | | | | | | | | | (1047) $lesseq(0, all_461_0) 44.49/14.54 | | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | | GROUND_INST: instantiating (node_proj_1_def1) with all_461_2, 44.49/14.54 | | | | | | | | | | | | all_461_1, all_248_1, simplifying with (1043), 44.49/14.54 | | | | | | | | | | | | (1045) gives: 44.49/14.54 | | | | | | | | | | | | (1048) node_proj_11(all_248_1) = all_461_2 44.49/14.54 | | | | | | | | | | | | 44.49/14.54 | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_461_2, all_461_1, 44.49/14.54 | | | | | | | | | | | | all_248_1, simplifying with (1043), (1045) gives: 44.49/14.54 | | | | | | | | | | | | (1049) ? [v0: $int] : ? [v1: $int] : 44.49/14.54 | | | | | | | | | | | | ($sum(size1(all_461_1), $product(-1, 44.49/14.54 | | | | | | | | | | | | $sum($difference(v0, v1), -1))) = 0 & 44.49/14.54 | | | | | | | | | | | | size1(all_461_2) = v1 & size1(all_248_1) = v0) 44.49/14.54 | | | | | | | | | | | | 44.49/14.55 | | | | | | | | | | | | GROUND_INST: instantiating (size_left) with all_248_1, 44.49/14.55 | | | | | | | | | | | | $sum(all_101_0, -1), simplifying with (1008), 44.49/14.55 | | | | | | | | | | | | (1036) gives: 44.49/14.55 | | | | | | | | | | | | (1050) ~ ($lesseq(2, all_101_0)) | ? [v0: $int] : ? 44.49/14.55 | | | | | | | | | | | | [v1: $int] : ? [v2: $int] : ($lesseq(2, 44.49/14.55 | | | | | | | | | | | | $difference(all_101_0, v2)) & node1(v0, v1) = 44.49/14.55 | | | | | | | | | | | | all_248_1 & size1(v0) = v2 & in_tree1(v1) & 44.49/14.55 | | | | | | | | | | | | in_tree1(v0)) 44.49/14.55 | | | | | | | | | | | | 44.49/14.55 | | | | | | | | | | | | DELTA: instantiating (1049) with fresh symbols all_480_0, 44.49/14.55 | | | | | | | | | | | | all_480_1 gives: 44.49/14.55 | | | | | | | | | | | | (1051) $sum(size1(all_461_1), $product(-1, 44.49/14.55 | | | | | | | | | | | | $sum($difference(all_480_1, all_480_0), -1))) 44.49/14.55 | | | | | | | | | | | | = 0 & size1(all_461_2) = all_480_0 & 44.49/14.55 | | | | | | | | | | | | size1(all_248_1) = all_480_1 44.49/14.55 | | | | | | | | | | | | 44.49/14.55 | | | | | | | | | | | | ALPHA: (1051) implies: 44.49/14.55 | | | | | | | | | | | | (1052) size1(all_248_1) = all_480_1 44.49/14.55 | | | | | | | | | | | | (1053) size1(all_461_2) = all_480_0 44.49/14.55 | | | | | | | | | | | | 44.49/14.55 | | | | | | | | | | | | BETA: splitting (1050) gives: 44.49/14.55 | | | | | | | | | | | | 44.49/14.55 | | | | | | | | | | | | Case 1: 44.49/14.55 | | | | | | | | | | | | | 44.49/14.55 | | | | | | | | | | | | | (1054) $lesseq(all_101_0, 1) 44.49/14.55 | | | | | | | | | | | | | 44.49/14.55 | | | | | | | | | | | | | COMBINE_INEQS: (1035), (1054) imply: 44.49/14.55 | | | | | | | | | | | | | (1055) $lesseq(0, -1) 44.49/14.55 | | | | | | | | | | | | | 44.49/14.55 | | | | | | | | | | | | | CLOSE: (1055) is inconsistent. 44.49/14.55 | | | | | | | | | | | | | 44.49/14.55 | | | | | | | | | | | | Case 2: 44.49/14.55 | | | | | | | | | | | | | 44.49/14.55 | | | | | | | | | | | | | (1056) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : 44.49/14.55 | | | | | | | | | | | | | ($lesseq(2, $difference(all_101_0, v2)) & 44.49/14.55 | | | | | | | | | | | | | node1(v0, v1) = all_248_1 & size1(v0) = v2 & 44.49/14.55 | | | | | | | | | | | | | in_tree1(v1) & in_tree1(v0)) 44.49/14.55 | | | | | | | | | | | | | 44.49/14.55 | | | | | | | | | | | | | DELTA: instantiating (1056) with fresh symbols all_527_0, 44.49/14.55 | | | | | | | | | | | | | all_527_1, all_527_2 gives: 44.49/14.55 | | | | | | | | | | | | | (1057) $lesseq(2, $difference(all_101_0, all_527_0)) & 44.49/14.55 | | | | | | | | | | | | | node1(all_527_2, all_527_1) = all_248_1 & 44.49/14.55 | | | | | | | | | | | | | size1(all_527_2) = all_527_0 & in_tree1(all_527_1) 44.49/14.55 | | | | | | | | | | | | | & in_tree1(all_527_2) 44.49/14.55 | | | | | | | | | | | | | 44.49/14.55 | | | | | | | | | | | | | ALPHA: (1057) implies: 44.49/14.55 | | | | | | | | | | | | | (1058) $lesseq(2, $difference(all_101_0, all_527_0)) 44.49/14.55 | | | | | | | | | | | | | (1059) in_tree1(all_527_2) 44.49/14.55 | | | | | | | | | | | | | (1060) size1(all_527_2) = all_527_0 44.49/14.55 | | | | | | | | | | | | | (1061) node1(all_527_2, all_527_1) = all_248_1 44.49/14.55 | | | | | | | | | | | | | 44.49/14.55 | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_461_0, all_480_0, 44.49/14.55 | | | | | | | | | | | | | all_461_2, simplifying with (1044), (1053) gives: 44.76/14.55 | | | | | | | | | | | | | (1062) all_480_0 = all_461_0 44.76/14.55 | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | GROUND_INST: instantiating (14) with $sum(all_101_0, -1), 44.76/14.55 | | | | | | | | | | | | | all_480_1, all_248_1, simplifying with (1036), 44.76/14.55 | | | | | | | | | | | | | (1052) gives: 44.76/14.55 | | | | | | | | | | | | | (1063) $difference(all_480_1, all_101_0) = -1 44.76/14.55 | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | BETA: splitting (1031) gives: 44.76/14.55 | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | Case 1: 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | (1064) all_338_0 = 0 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | REDUCE: (1030), (1064) imply: 44.76/14.55 | | | | | | | | | | | | | | (1065) mem(tree, all_101_1, all_96_3) = 0 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | GROUND_INST: instantiating (node_proj_1_def1) with all_527_2, 44.76/14.55 | | | | | | | | | | | | | | all_527_1, all_248_1, simplifying with (1059), 44.76/14.55 | | | | | | | | | | | | | | (1061) gives: 44.76/14.55 | | | | | | | | | | | | | | (1066) node_proj_11(all_248_1) = all_527_2 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_527_2, all_527_1, 44.76/14.55 | | | | | | | | | | | | | | all_248_1, simplifying with (1059), (1061) gives: 44.76/14.55 | | | | | | | | | | | | | | (1067) ? [v0: $int] : ? [v1: $int] : 44.76/14.55 | | | | | | | | | | | | | | ($sum(size1(all_527_1), $product(-1, 44.76/14.55 | | | | | | | | | | | | | | $sum($difference(v0, v1), -1))) = 0 & 44.76/14.55 | | | | | | | | | | | | | | size1(all_527_2) = v1 & size1(all_248_1) = v0) 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | GROUND_INST: instantiating (node_proj_2_def1) with all_527_2, 44.76/14.55 | | | | | | | | | | | | | | all_527_1, all_248_1, simplifying with (1059), 44.76/14.55 | | | | | | | | | | | | | | (1061) gives: 44.76/14.55 | | | | | | | | | | | | | | (1068) node_proj_21(all_248_1) = all_527_1 & 44.76/14.55 | | | | | | | | | | | | | | in_tree1(all_527_1) 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | ALPHA: (1068) implies: 44.76/14.55 | | | | | | | | | | | | | | (1069) in_tree1(all_527_1) 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | GROUND_INST: instantiating (tree_diff) with all_527_2, 44.76/14.55 | | | | | | | | | | | | | | all_248_1, all_527_0, $sum(all_101_0, -1), 44.76/14.55 | | | | | | | | | | | | | | simplifying with (1036), (1059), (1060) gives: 44.76/14.55 | | | | | | | | | | | | | | (1070) $difference(all_527_0, all_101_0) = -1 | ! [v0: 44.76/14.55 | | | | | | | | | | | | | | $int] : ! [v1: $int] : ! [v2: $int] : ( ~ 44.76/14.55 | | | | | | | | | | | | | | (node1(all_527_2, v0) = v2) | ~ 44.76/14.55 | | | | | | | | | | | | | | (node1(all_248_1, v1) = v2) | ~ in_tree1(v0)) 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | GROUND_INST: instantiating (75) with all_101_2, all_101_1, 44.76/14.55 | | | | | | | | | | | | | | simplifying with (82), (85), (1065) gives: 44.76/14.55 | | | | | | | | | | | | | | (1071) ? [v0: $int] : ? [v1: $int] : (node1(v0, v1) = 44.76/14.55 | | | | | | | | | | | | | | all_101_2 & $sum(size1(v1), $product(-1, 44.76/14.55 | | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) 44.76/14.55 | | | | | | | | | | | | | | = 0 & size1(v0) = all_92_8 & in_tree1(v1) & 44.76/14.55 | | | | | | | | | | | | | | in_tree1(v0)) 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | DELTA: instantiating (1071) with fresh symbols all_568_0, 44.76/14.55 | | | | | | | | | | | | | | all_568_1 gives: 44.76/14.55 | | | | | | | | | | | | | | (1072) node1(all_568_1, all_568_0) = all_101_2 & 44.76/14.55 | | | | | | | | | | | | | | $sum(size1(all_568_0), $product(-1, 44.76/14.55 | | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 44.76/14.55 | | | | | | | | | | | | | | 0 & size1(all_568_1) = all_92_8 & 44.76/14.55 | | | | | | | | | | | | | | in_tree1(all_568_0) & in_tree1(all_568_1) 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | ALPHA: (1072) implies: 44.76/14.55 | | | | | | | | | | | | | | (1073) in_tree1(all_568_1) 44.76/14.55 | | | | | | | | | | | | | | (1074) size1(all_568_1) = all_92_8 44.76/14.55 | | | | | | | | | | | | | | (1075) $sum(size1(all_568_0), $product(-1, 44.76/14.55 | | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 44.76/14.55 | | | | | | | | | | | | | | 0 44.76/14.55 | | | | | | | | | | | | | | (1076) node1(all_568_1, all_568_0) = all_101_2 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | DELTA: instantiating (1067) with fresh symbols all_572_0, 44.76/14.55 | | | | | | | | | | | | | | all_572_1 gives: 44.76/14.55 | | | | | | | | | | | | | | (1077) $sum(size1(all_527_1), $product(-1, 44.76/14.55 | | | | | | | | | | | | | | $sum($difference(all_572_1, all_572_0), -1))) 44.76/14.55 | | | | | | | | | | | | | | = 0 & size1(all_527_2) = all_572_0 & 44.76/14.55 | | | | | | | | | | | | | | size1(all_248_1) = all_572_1 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | ALPHA: (1077) implies: 44.76/14.55 | | | | | | | | | | | | | | (1078) size1(all_248_1) = all_572_1 44.76/14.55 | | | | | | | | | | | | | | (1079) size1(all_527_2) = all_572_0 44.76/14.55 | | | | | | | | | | | | | | (1080) $sum(size1(all_527_1), $product(-1, 44.76/14.55 | | | | | | | | | | | | | | $sum($difference(all_572_1, all_572_0), -1))) 44.76/14.55 | | | | | | | | | | | | | | = 0 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | REDUCE: (704), (934), (1075) imply: 44.76/14.55 | | | | | | | | | | | | | | (1081) size1(all_568_0) = 0 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | REDUCE: (704), (1074) imply: 44.76/14.55 | | | | | | | | | | | | | | (1082) size1(all_568_1) = 0 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | BETA: splitting (1070) gives: 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | Case 1: 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | (1083) $difference(all_527_0, all_101_0) = -1 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | REDUCE: (1058), (1083) imply: 44.76/14.55 | | | | | | | | | | | | | | | (1084) $lesseq(0, -1) 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | CLOSE: (1084) is inconsistent. 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | Case 2: 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_461_2, all_527_2, 44.76/14.55 | | | | | | | | | | | | | | | all_248_1, simplifying with (1048), (1066) gives: 44.76/14.55 | | | | | | | | | | | | | | | (1085) all_527_2 = all_461_2 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_527_1, 44.76/14.55 | | | | | | | | | | | | | | | $sum($difference(all_572_1, all_572_0), -1), 44.76/14.55 | | | | | | | | | | | | | | | simplifying with (1069), (1080) gives: 44.76/14.55 | | | | | | | | | | | | | | | (1086) $lesseq(1, $difference(all_572_1, all_572_0)) 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_527_0, all_572_0, 44.76/14.55 | | | | | | | | | | | | | | | all_527_2, simplifying with (1060), (1079) gives: 44.76/14.55 | | | | | | | | | | | | | | | (1087) all_572_0 = all_527_0 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_527_2, 44.76/14.55 | | | | | | | | | | | | | | | all_572_0, simplifying with (1059), (1079) gives: 44.76/14.55 | | | | | | | | | | | | | | | (1088) $lesseq(0, all_572_0) 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with $sum(all_101_0, -1), 44.76/14.55 | | | | | | | | | | | | | | | all_572_1, all_248_1, simplifying with (1036), 44.76/14.55 | | | | | | | | | | | | | | | (1078) gives: 44.76/14.55 | | | | | | | | | | | | | | | (1089) $difference(all_572_1, all_101_0) = -1 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | REDUCE: (1087), (1088) imply: 44.76/14.55 | | | | | | | | | | | | | | | (1090) $lesseq(0, all_527_0) 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | REDUCE: (1060), (1085) imply: 44.76/14.55 | | | | | | | | | | | | | | | (1091) size1(all_461_2) = all_527_0 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_461_0, all_527_0, 44.76/14.55 | | | | | | | | | | | | | | | all_461_2, simplifying with (1044), (1091) gives: 44.76/14.55 | | | | | | | | | | | | | | | (1092) all_527_0 = all_461_0 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_568_1, all_568_0, 44.76/14.55 | | | | | | | | | | | | | | | all_101_2, simplifying with (1073), (1076) gives: 44.76/14.55 | | | | | | | | | | | | | | | (1093) ? [v0: $int] : ? [v1: $int] : 44.76/14.55 | | | | | | | | | | | | | | | ($sum(size1(all_568_0), $product(-1, 44.76/14.55 | | | | | | | | | | | | | | | $sum($difference(v0, v1), -1))) = 0 & 44.76/14.55 | | | | | | | | | | | | | | | size1(all_568_1) = v1 & size1(all_101_2) = v0) 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | DELTA: instantiating (1093) with fresh symbols all_659_0, 44.76/14.55 | | | | | | | | | | | | | | | all_659_1 gives: 44.76/14.55 | | | | | | | | | | | | | | | (1094) $sum(size1(all_568_0), $product(-1, 44.76/14.55 | | | | | | | | | | | | | | | $sum($difference(all_659_1, all_659_0), -1))) 44.76/14.55 | | | | | | | | | | | | | | | = 0 & size1(all_568_1) = all_659_0 & 44.76/14.55 | | | | | | | | | | | | | | | size1(all_101_2) = all_659_1 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | ALPHA: (1094) implies: 44.76/14.55 | | | | | | | | | | | | | | | (1095) size1(all_101_2) = all_659_1 44.76/14.55 | | | | | | | | | | | | | | | (1096) size1(all_568_1) = all_659_0 44.76/14.55 | | | | | | | | | | | | | | | (1097) $sum(size1(all_568_0), $product(-1, 44.76/14.55 | | | | | | | | | | | | | | | $sum($difference(all_659_1, all_659_0), -1))) 44.76/14.55 | | | | | | | | | | | | | | | = 0 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, 44.76/14.55 | | | | | | | | | | | | | | | $sum($difference(all_659_1, all_659_0), -1), 44.76/14.55 | | | | | | | | | | | | | | | all_568_0, simplifying with (1081), (1097) gives: 44.76/14.55 | | | | | | | | | | | | | | | (1098) $difference(all_659_0, all_659_1) = -1 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_659_0, all_568_1, 44.76/14.55 | | | | | | | | | | | | | | | simplifying with (1082), (1096) gives: 44.76/14.55 | | | | | | | | | | | | | | | (1099) all_659_0 = 0 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_101_0, all_659_1, 44.76/14.55 | | | | | | | | | | | | | | | all_101_2, simplifying with (84), (1095) gives: 44.76/14.55 | | | | | | | | | | | | | | | (1100) all_659_1 = all_101_0 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | COMBINE_EQS: (1098), (1099) imply: 44.76/14.55 | | | | | | | | | | | | | | | (1101) all_659_1 = 1 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | SIMP: (1101) implies: 44.76/14.55 | | | | | | | | | | | | | | | (1102) all_659_1 = 1 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | COMBINE_EQS: (1100), (1102) imply: 44.76/14.55 | | | | | | | | | | | | | | | (1103) all_101_0 = 1 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | REDUCE: (1046), (1103) imply: 44.76/14.55 | | | | | | | | | | | | | | | (1104) $lesseq(all_461_0, -1) 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | COMBINE_INEQS: (1047), (1104) imply: 44.76/14.55 | | | | | | | | | | | | | | | (1105) $lesseq(0, -1) 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | | CLOSE: (1105) is inconsistent. 44.76/14.55 | | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | End of split 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | Case 2: 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | (1106) all_338_1 = 0 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | REDUCE: (1029), (1106) imply: 44.76/14.55 | | | | | | | | | | | | | | (1107) mem(tree, all_101_1, all_92_6) = 0 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | | REF_CLOSE: (64), (82), (85), (704), (1107), (size_nonneg) are 44.76/14.55 | | | | | | | | | | | | | | inconsistent by sub-proof #2. 44.76/14.55 | | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | End of split 44.76/14.55 | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | End of split 44.76/14.55 | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | End of split 44.76/14.55 | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | Case 2: 44.76/14.55 | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | (1108) ~ (all_248_0 = 0) 44.76/14.55 | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | STRENGTHEN: (947), (1108) imply: 44.76/14.55 | | | | | | | | | | | (1109) $lesseq(1, all_248_0) 44.76/14.55 | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | BETA: splitting (1010) gives: 44.76/14.55 | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | Case 1: 44.76/14.55 | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | (1110) $lesseq(all_248_0, 0) 44.76/14.55 | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | COMBINE_INEQS: (1109), (1110) imply: 44.76/14.55 | | | | | | | | | | | | (1111) $lesseq(0, -1) 44.76/14.55 | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | CLOSE: (1111) is inconsistent. 44.76/14.55 | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | Case 2: 44.76/14.55 | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | (1112) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : 44.76/14.55 | | | | | | | | | | | | ($lesseq(1, $difference(all_248_0, v2)) & 44.76/14.55 | | | | | | | | | | | | node1(v0, v1) = all_248_2 & size1(v0) = v2 & 44.76/14.55 | | | | | | | | | | | | in_tree1(v1) & in_tree1(v0)) 44.76/14.55 | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | DELTA: instantiating (1112) with fresh symbols all_450_0, 44.76/14.55 | | | | | | | | | | | | all_450_1, all_450_2 gives: 44.76/14.55 | | | | | | | | | | | | (1113) $lesseq(1, $difference(all_248_0, all_450_0)) & 44.76/14.55 | | | | | | | | | | | | node1(all_450_2, all_450_1) = all_248_2 & 44.76/14.55 | | | | | | | | | | | | size1(all_450_2) = all_450_0 & in_tree1(all_450_1) 44.76/14.55 | | | | | | | | | | | | & in_tree1(all_450_2) 44.76/14.55 | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | ALPHA: (1113) implies: 44.76/14.55 | | | | | | | | | | | | (1114) $lesseq(1, $difference(all_248_0, all_450_0)) 44.76/14.55 | | | | | | | | | | | | (1115) in_tree1(all_450_2) 44.76/14.55 | | | | | | | | | | | | (1116) size1(all_450_2) = all_450_0 44.76/14.55 | | | | | | | | | | | | (1117) node1(all_450_2, all_450_1) = all_248_2 44.76/14.55 | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_450_2, all_450_1, 44.76/14.55 | | | | | | | | | | | | all_248_2, simplifying with (1115), (1117) gives: 44.76/14.55 | | | | | | | | | | | | (1118) ? [v0: $int] : ? [v1: $int] : 44.76/14.55 | | | | | | | | | | | | ($sum(size1(all_450_1), $product(-1, 44.76/14.55 | | | | | | | | | | | | $sum($difference(v0, v1), -1))) = 0 & 44.76/14.55 | | | | | | | | | | | | size1(all_450_2) = v1 & size1(all_248_2) = v0) 44.76/14.55 | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | GROUND_INST: instantiating (node_proj_2_def1) with all_450_2, 44.76/14.55 | | | | | | | | | | | | all_450_1, all_248_2, simplifying with (1115), 44.76/14.55 | | | | | | | | | | | | (1117) gives: 44.76/14.55 | | | | | | | | | | | | (1119) node_proj_21(all_248_2) = all_450_1 & 44.76/14.55 | | | | | | | | | | | | in_tree1(all_450_1) 44.76/14.55 | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | ALPHA: (1119) implies: 44.76/14.55 | | | | | | | | | | | | (1120) in_tree1(all_450_1) 44.76/14.55 | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | GROUND_INST: instantiating (tree_diff) with all_248_2, 44.76/14.55 | | | | | | | | | | | | all_450_2, all_248_0, all_450_0, simplifying with 44.76/14.55 | | | | | | | | | | | | (942), (943), (1116) gives: 44.76/14.55 | | | | | | | | | | | | (1121) all_450_0 = all_248_0 | ! [v0: $int] : ! [v1: 44.76/14.55 | | | | | | | | | | | | $int] : ! [v2: $int] : ( ~ (node1(all_450_2, 44.76/14.55 | | | | | | | | | | | | v1) = v2) | ~ (node1(all_248_2, v0) = v2) | 44.76/14.55 | | | | | | | | | | | | ~ in_tree1(v0)) 44.76/14.55 | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | DELTA: instantiating (1118) with fresh symbols all_465_0, 44.76/14.55 | | | | | | | | | | | | all_465_1 gives: 44.76/14.55 | | | | | | | | | | | | (1122) $sum(size1(all_450_1), $product(-1, 44.76/14.55 | | | | | | | | | | | | $sum($difference(all_465_1, all_465_0), -1))) 44.76/14.55 | | | | | | | | | | | | = 0 & size1(all_450_2) = all_465_0 & 44.76/14.55 | | | | | | | | | | | | size1(all_248_2) = all_465_1 44.76/14.55 | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | ALPHA: (1122) implies: 44.76/14.55 | | | | | | | | | | | | (1123) size1(all_248_2) = all_465_1 44.76/14.55 | | | | | | | | | | | | (1124) size1(all_450_2) = all_465_0 44.76/14.55 | | | | | | | | | | | | (1125) $sum(size1(all_450_1), $product(-1, 44.76/14.55 | | | | | | | | | | | | $sum($difference(all_465_1, all_465_0), -1))) 44.76/14.55 | | | | | | | | | | | | = 0 44.76/14.55 | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | BETA: splitting (1121) gives: 44.76/14.55 | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | Case 1: 44.76/14.55 | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | (1126) all_450_0 = all_248_0 44.76/14.55 | | | | | | | | | | | | | 44.76/14.55 | | | | | | | | | | | | | REDUCE: (1114), (1126) imply: 44.76/14.56 | | | | | | | | | | | | | (1127) $lesseq(0, -1) 44.76/14.56 | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | CLOSE: (1127) is inconsistent. 44.76/14.56 | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | Case 2: 44.76/14.56 | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_450_1, 44.76/14.56 | | | | | | | | | | | | | $sum($difference(all_465_1, all_465_0), -1), 44.76/14.56 | | | | | | | | | | | | | simplifying with (1120), (1125) gives: 44.76/14.56 | | | | | | | | | | | | | (1128) $lesseq(1, $difference(all_465_1, all_465_0)) 44.76/14.56 | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_450_0, all_465_0, 44.76/14.56 | | | | | | | | | | | | | all_450_2, simplifying with (1116), (1124) gives: 44.76/14.56 | | | | | | | | | | | | | (1129) all_465_0 = all_450_0 44.76/14.56 | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | GROUND_INST: instantiating (size_nonneg) with all_450_2, 44.76/14.56 | | | | | | | | | | | | | all_465_0, simplifying with (1115), (1124) gives: 44.76/14.56 | | | | | | | | | | | | | (1130) $lesseq(0, all_465_0) 44.76/14.56 | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_248_0, all_465_1, 44.76/14.56 | | | | | | | | | | | | | all_248_2, simplifying with (943), (1123) gives: 44.76/14.56 | | | | | | | | | | | | | (1131) all_465_1 = all_248_0 44.76/14.56 | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | REDUCE: (1129), (1130) imply: 44.76/14.56 | | | | | | | | | | | | | (1132) $lesseq(0, all_450_0) 44.76/14.56 | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | REDUCE: (1125), (1129), (1131) imply: 44.76/14.56 | | | | | | | | | | | | | (1133) $sum(size1(all_450_1), $product(-1, 44.76/14.56 | | | | | | | | | | | | | $sum($difference(all_248_0, all_450_0), -1))) 44.76/14.56 | | | | | | | | | | | | | = 0 44.76/14.56 | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | BETA: splitting (1031) gives: 44.76/14.56 | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | Case 1: 44.76/14.56 | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | (1134) all_338_0 = 0 44.76/14.56 | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | REDUCE: (1030), (1134) imply: 44.76/14.56 | | | | | | | | | | | | | | (1135) mem(tree, all_101_1, all_96_3) = 0 44.76/14.56 | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | GROUND_INST: instantiating (tree_diff) with all_248_2, 44.76/14.56 | | | | | | | | | | | | | | all_450_1, all_248_0, $sum($difference(all_248_0, 44.76/14.56 | | | | | | | | | | | | | | all_450_0), -1), simplifying with (942), 44.76/14.56 | | | | | | | | | | | | | | (943), (1133) gives: 44.76/14.56 | | | | | | | | | | | | | | (1136) all_450_0 = -1 | ! [v0: $int] : ! [v1: $int] : 44.76/14.56 | | | | | | | | | | | | | | ! [v2: $int] : ( ~ (node1(all_450_1, v1) = v2) | 44.76/14.56 | | | | | | | | | | | | | | ~ (node1(all_248_2, v0) = v2) | ~ in_tree1(v0)) 44.76/14.56 | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | GROUND_INST: instantiating (75) with all_101_2, all_101_1, 44.76/14.56 | | | | | | | | | | | | | | simplifying with (82), (85), (1135) gives: 44.76/14.56 | | | | | | | | | | | | | | (1137) ? [v0: $int] : ? [v1: $int] : (node1(v0, v1) = 44.76/14.56 | | | | | | | | | | | | | | all_101_2 & $sum(size1(v1), $product(-1, 44.76/14.56 | | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) 44.76/14.56 | | | | | | | | | | | | | | = 0 & size1(v0) = all_92_8 & in_tree1(v1) & 44.76/14.56 | | | | | | | | | | | | | | in_tree1(v0)) 44.76/14.56 | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | DELTA: instantiating (1137) with fresh symbols all_549_0, 44.76/14.56 | | | | | | | | | | | | | | all_549_1 gives: 44.76/14.56 | | | | | | | | | | | | | | (1138) node1(all_549_1, all_549_0) = all_101_2 & 44.76/14.56 | | | | | | | | | | | | | | $sum(size1(all_549_0), $product(-1, 44.76/14.56 | | | | | | | | | | | | | | $sum($difference(all_88_4, all_92_8), -1))) = 44.76/14.56 | | | | | | | | | | | | | | 0 & size1(all_549_1) = all_92_8 & 44.76/14.56 | | | | | | | | | | | | | | in_tree1(all_549_0) & in_tree1(all_549_1) 44.76/14.56 | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | ALPHA: (1138) implies: 44.76/14.56 | | | | | | | | | | | | | | (1139) size1(all_549_1) = all_92_8 44.76/14.56 | | | | | | | | | | | | | | (1140) node1(all_549_1, all_549_0) = all_101_2 44.76/14.56 | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | REDUCE: (704), (1139) imply: 44.76/14.56 | | | | | | | | | | | | | | (1141) size1(all_549_1) = 0 44.76/14.56 | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | BETA: splitting (1136) gives: 44.76/14.56 | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | Case 1: 44.76/14.56 | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | | (1142) all_450_0 = -1 44.76/14.56 | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | | REDUCE: (1132), (1142) imply: 44.76/14.56 | | | | | | | | | | | | | | | (1143) $lesseq(0, -1) 44.76/14.56 | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | | CLOSE: (1143) is inconsistent. 44.76/14.56 | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | Case 2: 44.76/14.56 | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | | GROUND_INST: instantiating (tree_diff) with all_248_2, 44.76/14.56 | | | | | | | | | | | | | | | all_549_1, all_248_0, 0, simplifying with (942), 44.76/14.56 | | | | | | | | | | | | | | | (943), (1141) gives: 44.76/14.56 | | | | | | | | | | | | | | | (1144) all_248_0 = 0 | ! [v0: $int] : ! [v1: $int] : ! 44.76/14.56 | | | | | | | | | | | | | | | [v2: $int] : ( ~ (node1(all_549_1, v1) = v2) | ~ 44.76/14.56 | | | | | | | | | | | | | | | (node1(all_248_2, v0) = v2) | ~ in_tree1(v0)) 44.76/14.56 | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | | BETA: splitting (1144) gives: 44.76/14.56 | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | | Case 1: 44.76/14.56 | | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | | | (1145) all_248_0 = 0 44.76/14.56 | | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | | | REDUCE: (1114), (1145) imply: 44.76/14.56 | | | | | | | | | | | | | | | | (1146) $lesseq(all_450_0, -1) 44.76/14.56 | | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | | | COMBINE_INEQS: (1132), (1146) imply: 44.76/14.56 | | | | | | | | | | | | | | | | (1147) $lesseq(0, -1) 44.76/14.56 | | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | | | CLOSE: (1147) is inconsistent. 44.76/14.56 | | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | | Case 2: 44.76/14.56 | | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | | | (1148) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( 44.76/14.56 | | | | | | | | | | | | | | | | ~ (node1(all_549_1, v1) = v2) | ~ 44.76/14.56 | | | | | | | | | | | | | | | | (node1(all_248_2, v0) = v2) | ~ in_tree1(v0)) 44.76/14.56 | | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1148) with all_248_1, all_549_0, 44.76/14.56 | | | | | | | | | | | | | | | | all_101_2, simplifying with (944), (1008), (1140) 44.76/14.56 | | | | | | | | | | | | | | | | gives: 44.76/14.56 | | | | | | | | | | | | | | | | (1149) $false 44.76/14.56 | | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | | | CLOSE: (1149) is inconsistent. 44.76/14.56 | | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | | End of split 44.76/14.56 | | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | End of split 44.76/14.56 | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | Case 2: 44.76/14.56 | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | (1150) all_338_1 = 0 44.76/14.56 | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | REDUCE: (1029), (1150) imply: 44.76/14.56 | | | | | | | | | | | | | | (1151) mem(tree, all_101_1, all_92_6) = 0 44.76/14.56 | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | | REF_CLOSE: (64), (82), (85), (704), (1151), (size_nonneg) are 44.76/14.56 | | | | | | | | | | | | | | inconsistent by sub-proof #2. 44.76/14.56 | | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | | End of split 44.76/14.56 | | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | | End of split 44.76/14.56 | | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | | End of split 44.76/14.56 | | | | | | | | | | | 44.76/14.56 | | | | | | | | | | End of split 44.76/14.56 | | | | | | | | | | 44.76/14.56 | | | | | | | | | Case 2: 44.76/14.56 | | | | | | | | | | 44.76/14.56 | | | | | | | | | | (1152) all_101_0 = all_88_4 44.76/14.56 | | | | | | | | | | (1153) ? [v0: $int] : ($lesseq(1, $difference(v0, 44.76/14.56 | | | | | | | | | | all_92_8)) & size1(all_248_2) = v0) 44.76/14.56 | | | | | | | | | | 44.76/14.56 | | | | | | | | | | COMBINE_EQS: (934), (1152) imply: 44.76/14.56 | | | | | | | | | | (1154) all_101_0 = 1 44.76/14.56 | | | | | | | | | | 44.76/14.56 | | | | | | | | | | DELTA: instantiating (1153) with fresh symbol all_433_0 44.76/14.56 | | | | | | | | | | gives: 44.76/14.56 | | | | | | | | | | (1155) $lesseq(1, $difference(all_433_0, all_92_8)) & 44.76/14.56 | | | | | | | | | | size1(all_248_2) = all_433_0 44.76/14.56 | | | | | | | | | | 44.76/14.56 | | | | | | | | | | ALPHA: (1155) implies: 44.76/14.56 | | | | | | | | | | (1156) $lesseq(1, $difference(all_433_0, all_92_8)) 44.76/14.56 | | | | | | | | | | (1157) size1(all_248_2) = all_433_0 44.76/14.56 | | | | | | | | | | 44.76/14.56 | | | | | | | | | | REDUCE: (704), (1156) imply: 44.76/14.56 | | | | | | | | | | (1158) $lesseq(1, all_433_0) 44.76/14.56 | | | | | | | | | | 44.76/14.56 | | | | | | | | | | REDUCE: (941), (1154) imply: 44.76/14.56 | | | | | | | | | | (1159) $lesseq(all_248_0, 0) 44.76/14.56 | | | | | | | | | | 44.76/14.56 | | | | | | | | | | ANTI_SYMM: (947), (1159) imply: 44.76/14.56 | | | | | | | | | | (1160) all_248_0 = 0 44.76/14.56 | | | | | | | | | | 44.76/14.56 | | | | | | | | | | REDUCE: (943), (1160) imply: 44.76/14.56 | | | | | | | | | | (1161) size1(all_248_2) = 0 44.76/14.56 | | | | | | | | | | 44.76/14.56 | | | | | | | | | | GROUND_INST: instantiating (14) with all_433_0, 0, all_248_2, 44.76/14.56 | | | | | | | | | | simplifying with (1157), (1161) gives: 44.76/14.56 | | | | | | | | | | (1162) all_433_0 = 0 44.76/14.56 | | | | | | | | | | 44.76/14.56 | | | | | | | | | | REDUCE: (1158), (1162) imply: 44.76/14.56 | | | | | | | | | | (1163) $lesseq(0, -1) 44.76/14.56 | | | | | | | | | | 44.76/14.56 | | | | | | | | | | CLOSE: (1163) is inconsistent. 44.76/14.56 | | | | | | | | | | 44.76/14.56 | | | | | | | | | End of split 44.76/14.56 | | | | | | | | | 44.76/14.56 | | | | | | | | End of split 44.76/14.56 | | | | | | | | 44.76/14.56 | | | | | | | Case 2: 44.76/14.56 | | | | | | | | 44.76/14.56 | | | | | | | | (1164) ? [v0: $int] : ( ~ (v0 = 0) & sort1(all_74_1, 44.76/14.56 | | | | | | | | all_96_2) = v0) 44.76/14.56 | | | | | | | | 44.76/14.56 | | | | | | | | DELTA: instantiating (1164) with fresh symbol all_270_0 gives: 44.76/14.56 | | | | | | | | (1165) ~ (all_270_0 = 0) & sort1(all_74_1, all_96_2) = 44.76/14.56 | | | | | | | | all_270_0 44.76/14.56 | | | | | | | | 44.76/14.56 | | | | | | | | REF_CLOSE: (10), (25), (73), (1165), (infix_plpl_sort2) are 44.76/14.56 | | | | | | | | inconsistent by sub-proof #7. 44.76/14.56 | | | | | | | | 44.76/14.56 | | | | | | | End of split 44.76/14.56 | | | | | | | 44.76/14.56 | | | | | | End of split 44.76/14.56 | | | | | | 44.76/14.56 | | | | | End of split 44.76/14.56 | | | | | 44.76/14.56 | | | | End of split 44.76/14.56 | | | | 44.76/14.56 | | | End of split 44.76/14.56 | | | 44.76/14.56 | | End of split 44.76/14.56 | | 44.76/14.56 | End of split 44.76/14.56 | 44.76/14.56 End of proof 44.76/14.56 44.76/14.56 Sub-proof #1 shows that the following formulas are inconsistent: 44.76/14.56 ---------------------------------------------------------------- 44.76/14.56 (1) size1(all_101_2) = 0 44.76/14.56 (2) in_ty(tree) 44.76/14.56 (3) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (size1(v2) 44.76/14.56 = v1) | ~ (size1(v2) = v0)) 44.76/14.56 (4) t2tb2(all_101_2) = all_101_1 44.76/14.56 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 44.76/14.56 $int] : ( ~ (infix_plpl(v0, v2, v3) = v4) | ~ (mem(v0, v1, v4) = 0) | 44.76/14.56 ~ in_ty(v0) | ? [v5: $int] : ? [v6: $int] : (mem(v0, v1, v3) = v5 & 44.76/14.56 mem(v0, v1, v2) = v6 & (v6 = 0 | v5 = 0))) 44.76/14.56 (6) list(tree) = all_74_1 44.76/14.57 (7) ! [v0: $int] : ! [v1: $int] : ( ~ (t2tb2(v0) = v1) | ~ (mem(tree, v1, 44.76/14.57 all_92_6) = 0) | ~ in_tree1(v0) | ? [v2: $int] : (size1(v0) = v2 44.76/14.57 & ? [v3: $int] : ? [v4: $int] : ? [v5: $int] : (v2 = all_88_4 & 44.76/14.57 $lesseq(1, $difference(all_92_8, v5)) & node1(v3, v4) = v0 & 44.76/14.57 size1(v3) = v5 & in_tree1(v4) & in_tree1(v3)))) 44.76/14.57 (8) all_160_1 = all_77_6 44.76/14.57 (9) ~ (all_77_2 = all_77_6) 44.76/14.57 (10) all_99_0 = all_96_2 | ? [v0: $int] : ( ~ (v0 = 0) & sort1(all_74_1, 44.76/14.57 all_96_2) = v0) 44.76/14.57 (11) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ (node1(v0, v1) = v2) 44.76/14.57 | ~ in_tree1(v0) | (node_proj_21(v2) = v1 & in_tree1(v1))) 44.76/14.57 (12) all_160_1 = all_77_2 | ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ( 44.76/14.57 ~ (v2 = 0) & distinct(tree, v1) = 0 & cons(tree, v0, v1) = all_77_2 & 44.76/14.57 mem(tree, v0, v1) = v2 & sort1(all_160_0, v1) = 0 & sort1(tree, v0) = 44.76/14.57 0 & in_uni(v1) & in_uni(v0) & in_uni(all_77_2)) | ? [v0: $int] : 44.76/14.57 (cons(tree, v0, all_160_1) = all_77_2 & sort1(tree, v0) = 0 & in_uni(v0) 44.76/14.57 & in_uni(all_77_2)) 44.76/14.57 (13) infix_plpl(tree, all_96_3, all_92_6) = all_96_2 44.76/14.57 (14) all_92_8 = 0 44.76/14.57 (15) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v1, -1)) | ~ (size1(v0) = 44.76/14.57 v1) | ~ in_tree1(v0)) 44.76/14.57 (16) mem(tree, all_101_1, all_99_0) = 0 44.76/14.57 (17) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ (node1(v0, v1) = v2) 44.76/14.57 | ~ in_tree1(v0) | ? [v3: $int] : ? [v4: $int] : (size1(v2) = v3 & 44.76/14.57 $sum(size1(v1), $product(-1, $sum($difference(v3, v4), -1))) = 0 & 44.76/14.57 size1(v0) = v4)) 44.76/14.57 (18) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 44.76/14.57 $int] : ! [v5: $int] : (v5 = 0 | ~ (infix_plpl(v0, v1, v2) = v4) | 44.76/14.57 ~ (list(v0) = v3) | ~ (sort1(v3, v4) = v5) | ~ in_ty(v0)) 44.76/14.57 (19) ! [v0: $int] : ! [v1: $int] : ( ~ (t2tb2(v0) = v1) | ~ (mem(tree, v1, 44.76/14.57 all_96_3) = 0) | ~ in_tree1(v0) | ? [v2: $int] : ? [v3: $int] : 44.76/14.57 (node1(v2, v3) = v0 & $sum(size1(v3), $product(-1, 44.76/14.57 $sum($difference(all_88_4, all_92_8), -1))) = 0 & size1(v2) = 44.76/14.57 all_92_8 & in_tree1(v3) & in_tree1(v2))) 44.76/14.57 (20) in_tree1(all_101_2) 44.76/14.57 44.76/14.57 Begin of proof 44.76/14.57 | 44.76/14.57 | BETA: splitting (10) gives: 44.76/14.57 | 44.76/14.57 | Case 1: 44.76/14.57 | | 44.76/14.57 | | (21) all_99_0 = all_96_2 44.76/14.57 | | 44.76/14.57 | | REDUCE: (16), (21) imply: 44.76/14.57 | | (22) mem(tree, all_101_1, all_96_2) = 0 44.76/14.57 | | 44.76/14.57 | | BETA: splitting (12) gives: 44.76/14.57 | | 44.76/14.57 | | Case 1: 44.76/14.57 | | | 44.76/14.57 | | | (23) all_160_1 = all_77_2 44.76/14.57 | | | 44.76/14.57 | | | REF_CLOSE: (8), (9), (23) are inconsistent by sub-proof #8. 44.76/14.57 | | | 44.76/14.57 | | Case 2: 44.76/14.57 | | | 44.76/14.57 | | | 44.76/14.57 | | | GROUND_INST: instantiating (5) with tree, all_101_1, all_96_3, all_92_6, 44.76/14.57 | | | all_96_2, simplifying with (2), (13), (22) gives: 44.76/14.57 | | | (24) ? [v0: $int] : ? [v1: $int] : (mem(tree, all_101_1, all_96_3) = 44.76/14.57 | | | v1 & mem(tree, all_101_1, all_92_6) = v0 & (v1 = 0 | v0 = 0)) 44.76/14.57 | | | 44.76/14.57 | | | DELTA: instantiating (24) with fresh symbols all_292_0, all_292_1 gives: 44.76/14.57 | | | (25) mem(tree, all_101_1, all_96_3) = all_292_0 & mem(tree, all_101_1, 44.76/14.57 | | | all_92_6) = all_292_1 & (all_292_0 = 0 | all_292_1 = 0) 44.76/14.57 | | | 44.76/14.57 | | | ALPHA: (25) implies: 44.76/14.57 | | | (26) mem(tree, all_101_1, all_92_6) = all_292_1 44.76/14.57 | | | (27) mem(tree, all_101_1, all_96_3) = all_292_0 44.76/14.57 | | | (28) all_292_0 = 0 | all_292_1 = 0 44.76/14.57 | | | 44.76/14.57 | | | BETA: splitting (28) gives: 44.76/14.57 | | | 44.76/14.57 | | | Case 1: 44.76/14.57 | | | | 44.76/14.57 | | | | (29) all_292_0 = 0 44.76/14.57 | | | | 44.76/14.57 | | | | REDUCE: (27), (29) imply: 44.76/14.57 | | | | (30) mem(tree, all_101_1, all_96_3) = 0 44.76/14.57 | | | | 44.76/14.57 | | | | GROUND_INST: instantiating (19) with all_101_2, all_101_1, simplifying 44.76/14.57 | | | | with (4), (20), (30) gives: 44.76/14.57 | | | | (31) ? [v0: $int] : ? [v1: $int] : (node1(v0, v1) = all_101_2 & 44.76/14.57 | | | | $sum(size1(v1), $product(-1, $sum($difference(all_88_4, 44.76/14.57 | | | | all_92_8), -1))) = 0 & size1(v0) = all_92_8 & 44.76/14.57 | | | | in_tree1(v1) & in_tree1(v0)) 44.76/14.57 | | | | 44.76/14.57 | | | | DELTA: instantiating (31) with fresh symbols all_434_0, all_434_1 gives: 44.76/14.57 | | | | (32) node1(all_434_1, all_434_0) = all_101_2 & $sum(size1(all_434_0), 44.76/14.57 | | | | $product(-1, $sum($difference(all_88_4, all_92_8), -1))) = 0 & 44.76/14.57 | | | | size1(all_434_1) = all_92_8 & in_tree1(all_434_0) & 44.76/14.57 | | | | in_tree1(all_434_1) 44.76/14.57 | | | | 44.76/14.57 | | | | ALPHA: (32) implies: 44.76/14.57 | | | | (33) in_tree1(all_434_1) 44.76/14.57 | | | | (34) size1(all_434_1) = all_92_8 44.76/14.57 | | | | (35) node1(all_434_1, all_434_0) = all_101_2 44.76/14.57 | | | | 44.76/14.57 | | | | REDUCE: (14), (34) imply: 44.76/14.57 | | | | (36) size1(all_434_1) = 0 44.76/14.57 | | | | 44.76/14.57 | | | | GROUND_INST: instantiating (17) with all_434_1, all_434_0, all_101_2, 44.76/14.57 | | | | simplifying with (33), (35) gives: 44.76/14.57 | | | | (37) ? [v0: $int] : ? [v1: $int] : ($sum(size1(all_434_0), 44.76/14.57 | | | | $product(-1, $sum($difference(v0, v1), -1))) = 0 & 44.76/14.57 | | | | size1(all_434_1) = v1 & size1(all_101_2) = v0) 44.76/14.57 | | | | 44.76/14.57 | | | | GROUND_INST: instantiating (11) with all_434_1, all_434_0, all_101_2, 44.76/14.57 | | | | simplifying with (33), (35) gives: 44.76/14.57 | | | | (38) node_proj_21(all_101_2) = all_434_0 & in_tree1(all_434_0) 44.76/14.57 | | | | 44.76/14.57 | | | | ALPHA: (38) implies: 44.76/14.57 | | | | (39) in_tree1(all_434_0) 44.76/14.57 | | | | 44.76/14.57 | | | | DELTA: instantiating (37) with fresh symbols all_463_0, all_463_1 gives: 44.76/14.57 | | | | (40) $sum(size1(all_434_0), $product(-1, $sum($difference(all_463_1, 44.76/14.57 | | | | all_463_0), -1))) = 0 & size1(all_434_1) = all_463_0 & 44.76/14.57 | | | | size1(all_101_2) = all_463_1 44.76/14.57 | | | | 44.76/14.57 | | | | ALPHA: (40) implies: 44.76/14.57 | | | | (41) size1(all_101_2) = all_463_1 44.76/14.57 | | | | (42) size1(all_434_1) = all_463_0 44.76/14.57 | | | | (43) $sum(size1(all_434_0), $product(-1, $sum($difference(all_463_1, 44.76/14.57 | | | | all_463_0), -1))) = 0 44.76/14.57 | | | | 44.76/14.57 | | | | GROUND_INST: instantiating (15) with all_434_0, 44.76/14.57 | | | | $sum($difference(all_463_1, all_463_0), -1), simplifying 44.76/14.57 | | | | with (39), (43) gives: 44.76/14.57 | | | | (44) $lesseq(1, $difference(all_463_1, all_463_0)) 44.76/14.57 | | | | 44.76/14.57 | | | | GROUND_INST: instantiating (3) with 0, all_463_0, all_434_1, simplifying 44.76/14.57 | | | | with (36), (42) gives: 44.76/14.57 | | | | (45) all_463_0 = 0 44.76/14.57 | | | | 44.76/14.57 | | | | GROUND_INST: instantiating (3) with 0, all_463_1, all_101_2, simplifying 44.76/14.57 | | | | with (1), (41) gives: 44.76/14.57 | | | | (46) all_463_1 = 0 44.76/14.57 | | | | 44.76/14.57 | | | | REDUCE: (44), (45), (46) imply: 44.76/14.57 | | | | (47) $lesseq(0, -1) 44.76/14.57 | | | | 44.76/14.57 | | | | CLOSE: (47) is inconsistent. 44.76/14.57 | | | | 44.76/14.57 | | | Case 2: 44.76/14.57 | | | | 44.76/14.57 | | | | (48) all_292_1 = 0 44.76/14.57 | | | | 44.76/14.57 | | | | REDUCE: (26), (48) imply: 44.76/14.57 | | | | (49) mem(tree, all_101_1, all_92_6) = 0 44.76/14.57 | | | | 44.76/14.57 | | | | REF_CLOSE: (4), (7), (14), (15), (20), (49) are inconsistent by 44.76/14.57 | | | | sub-proof #2. 44.76/14.57 | | | | 44.76/14.57 | | | End of split 44.76/14.57 | | | 44.76/14.58 | | End of split 44.76/14.58 | | 44.76/14.58 | Case 2: 44.76/14.58 | | 44.76/14.58 | | (50) ? [v0: $int] : ( ~ (v0 = 0) & sort1(all_74_1, all_96_2) = v0) 44.76/14.58 | | 44.76/14.58 | | DELTA: instantiating (50) with fresh symbol all_270_0 gives: 44.76/14.58 | | (51) ~ (all_270_0 = 0) & sort1(all_74_1, all_96_2) = all_270_0 44.76/14.58 | | 44.76/14.58 | | REF_CLOSE: (2), (6), (13), (18), (51) are inconsistent by sub-proof #7. 44.76/14.58 | | 44.76/14.58 | End of split 44.76/14.58 | 44.76/14.58 End of proof 44.76/14.58 44.76/14.58 Sub-proof #2 shows that the following formulas are inconsistent: 44.76/14.58 ---------------------------------------------------------------- 44.76/14.58 (1) t2tb2(all_101_2) = all_101_1 44.76/14.58 (2) ! [v0: $int] : ! [v1: $int] : ( ~ (t2tb2(v0) = v1) | ~ (mem(tree, v1, 44.76/14.58 all_92_6) = 0) | ~ in_tree1(v0) | ? [v2: $int] : (size1(v0) = v2 44.76/14.58 & ? [v3: $int] : ? [v4: $int] : ? [v5: $int] : (v2 = all_88_4 & 44.76/14.58 $lesseq(1, $difference(all_92_8, v5)) & node1(v3, v4) = v0 & 44.76/14.58 size1(v3) = v5 & in_tree1(v4) & in_tree1(v3)))) 44.76/14.58 (3) mem(tree, all_101_1, all_92_6) = 0 44.76/14.58 (4) all_92_8 = 0 44.76/14.58 (5) ! [v0: $int] : ! [v1: $int] : ( ~ ($lesseq(v1, -1)) | ~ (size1(v0) = 44.76/14.58 v1) | ~ in_tree1(v0)) 44.76/14.58 (6) in_tree1(all_101_2) 44.76/14.58 44.76/14.58 Begin of proof 44.76/14.58 | 44.76/14.58 | GROUND_INST: instantiating (2) with all_101_2, all_101_1, simplifying with 44.76/14.58 | (1), (3), (6) gives: 44.76/14.58 | (7) ? [v0: $int] : (size1(all_101_2) = v0 & ? [v1: $int] : ? [v2: $int] 44.76/14.58 | : ? [v3: $int] : (v0 = all_88_4 & $lesseq(1, $difference(all_92_8, 44.76/14.58 | v3)) & node1(v1, v2) = all_101_2 & size1(v1) = v3 & 44.76/14.58 | in_tree1(v2) & in_tree1(v1))) 44.76/14.58 | 44.76/14.58 | DELTA: instantiating (7) with fresh symbol all_321_0 gives: 44.76/14.58 | (8) size1(all_101_2) = all_321_0 & ? [v0: $int] : ? [v1: $int] : ? [v2: 44.76/14.58 | $int] : (all_321_0 = all_88_4 & $lesseq(1, $difference(all_92_8, v2)) 44.76/14.58 | & node1(v0, v1) = all_101_2 & size1(v0) = v2 & in_tree1(v1) & 44.76/14.58 | in_tree1(v0)) 44.76/14.58 | 44.76/14.58 | ALPHA: (8) implies: 44.76/14.58 | (9) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (all_321_0 = all_88_4 & 44.76/14.58 | $lesseq(1, $difference(all_92_8, v2)) & node1(v0, v1) = all_101_2 & 44.76/14.58 | size1(v0) = v2 & in_tree1(v1) & in_tree1(v0)) 44.76/14.58 | 44.76/14.58 | DELTA: instantiating (9) with fresh symbols all_325_0, all_325_1, all_325_2 44.76/14.58 | gives: 44.76/14.58 | (10) all_321_0 = all_88_4 & $lesseq(1, $difference(all_92_8, all_325_0)) & 44.76/14.58 | node1(all_325_2, all_325_1) = all_101_2 & size1(all_325_2) = all_325_0 44.76/14.58 | & in_tree1(all_325_1) & in_tree1(all_325_2) 44.76/14.58 | 44.76/14.58 | ALPHA: (10) implies: 44.76/14.58 | (11) $lesseq(1, $difference(all_92_8, all_325_0)) 44.76/14.58 | (12) in_tree1(all_325_2) 44.76/14.58 | (13) size1(all_325_2) = all_325_0 44.76/14.58 | 44.76/14.58 | REDUCE: (4), (11) imply: 44.76/14.58 | (14) $lesseq(all_325_0, -1) 44.76/14.58 | 44.76/14.58 | GROUND_INST: instantiating (5) with all_325_2, all_325_0, simplifying with 44.76/14.58 | (12), (13) gives: 44.76/14.58 | (15) $lesseq(0, all_325_0) 44.76/14.58 | 44.76/14.58 | COMBINE_INEQS: (14), (15) imply: 44.76/14.58 | (16) $lesseq(0, -1) 44.76/14.58 | 44.76/14.58 | CLOSE: (16) is inconsistent. 44.76/14.58 | 44.76/14.58 End of proof 44.76/14.58 44.76/14.58 Sub-proof #3 shows that the following formulas are inconsistent: 44.76/14.58 ---------------------------------------------------------------- 44.76/14.58 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (size1(v2) 44.76/14.58 = v1) | ~ (size1(v2) = v0)) 44.76/14.58 (2) t2tb2(all_101_2) = all_101_1 44.76/14.58 (3) size1(all_101_2) = all_101_0 44.76/14.58 (4) ! [v0: $int] : ! [v1: $int] : ( ~ (t2tb2(v0) = v1) | ~ (mem(tree, v1, 44.76/14.58 all_92_6) = 0) | ~ in_tree1(v0) | ? [v2: $int] : (size1(v0) = v2 44.76/14.58 & ? [v3: $int] : ? [v4: $int] : ? [v5: $int] : (v2 = all_88_4 & 44.76/14.58 $lesseq(1, $difference(all_92_8, v5)) & node1(v3, v4) = v0 & 44.76/14.58 size1(v3) = v5 & in_tree1(v4) & in_tree1(v3)))) 44.76/14.58 (5) ~ (all_101_0 = all_88_4) | ? [v0: $int] : ($lesseq(1, $difference(v0, 44.76/14.58 all_92_8)) & size1(all_253_2) = v0) 44.76/14.58 (6) $lesseq(1, $difference(all_101_0, all_253_0)) 44.76/14.58 (7) all_160_1 = all_77_6 44.76/14.58 (8) ~ (all_77_2 = all_77_6) 44.76/14.58 (9) $difference(all_92_8, all_88_4) = -1 44.76/14.58 (10) all_160_1 = all_77_2 | ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ( 44.76/14.58 ~ (v2 = 0) & distinct(tree, v1) = 0 & cons(tree, v0, v1) = all_77_2 & 44.76/14.58 mem(tree, v0, v1) = v2 & sort1(all_160_0, v1) = 0 & sort1(tree, v0) = 44.76/14.58 0 & in_uni(v1) & in_uni(v0) & in_uni(all_77_2)) | ? [v0: $int] : 44.76/14.58 (cons(tree, v0, all_160_1) = all_77_2 & sort1(tree, v0) = 0 & in_uni(v0) 44.76/14.58 & in_uni(all_77_2)) 44.76/14.58 (11) mem(tree, all_101_1, all_92_6) = 0 44.76/14.58 (12) in_tree1(all_101_2) 44.76/14.58 (13) size1(all_253_2) = all_253_0 44.76/14.58 44.76/14.58 Begin of proof 44.76/14.58 | 44.76/14.58 | BETA: splitting (10) gives: 44.76/14.58 | 44.76/14.58 | Case 1: 44.76/14.58 | | 44.76/14.58 | | (14) all_160_1 = all_77_2 44.76/14.58 | | 44.76/14.58 | | COMBINE_EQS: (7), (14) imply: 44.76/14.58 | | (15) all_77_2 = all_77_6 44.76/14.58 | | 44.76/14.58 | | SIMP: (15) implies: 44.76/14.58 | | (16) all_77_2 = all_77_6 44.76/14.58 | | 44.76/14.58 | | REDUCE: (8), (16) imply: 44.76/14.58 | | (17) ~ (0 = 0) 44.76/14.58 | | 44.76/14.58 | | CLOSE: (17) is inconsistent. 44.76/14.58 | | 44.76/14.58 | Case 2: 44.76/14.58 | | 44.76/14.58 | | 44.85/14.58 | | GROUND_INST: instantiating (4) with all_101_2, all_101_1, simplifying with 44.85/14.58 | | (2), (11), (12) gives: 44.85/14.58 | | (18) ? [v0: $int] : (size1(all_101_2) = v0 & ? [v1: $int] : ? [v2: 44.85/14.58 | | $int] : ? [v3: $int] : (v0 = all_88_4 & $lesseq(1, 44.85/14.58 | | $difference(all_92_8, v3)) & node1(v1, v2) = all_101_2 & 44.85/14.58 | | size1(v1) = v3 & in_tree1(v2) & in_tree1(v1))) 44.85/14.58 | | 44.85/14.58 | | DELTA: instantiating (18) with fresh symbol all_360_0 gives: 44.85/14.58 | | (19) size1(all_101_2) = all_360_0 & ? [v0: $int] : ? [v1: $int] : ? 44.85/14.58 | | [v2: $int] : (all_360_0 = all_88_4 & $lesseq(1, 44.85/14.58 | | $difference(all_92_8, v2)) & node1(v0, v1) = all_101_2 & 44.85/14.58 | | size1(v0) = v2 & in_tree1(v1) & in_tree1(v0)) 44.85/14.58 | | 44.85/14.58 | | ALPHA: (19) implies: 44.85/14.58 | | (20) size1(all_101_2) = all_360_0 44.85/14.58 | | (21) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (all_360_0 = 44.85/14.58 | | all_88_4 & $lesseq(1, $difference(all_92_8, v2)) & node1(v0, v1) = 44.85/14.58 | | all_101_2 & size1(v0) = v2 & in_tree1(v1) & in_tree1(v0)) 44.85/14.58 | | 44.85/14.58 | | DELTA: instantiating (21) with fresh symbols all_364_0, all_364_1, all_364_2 44.85/14.58 | | gives: 44.85/14.58 | | (22) all_360_0 = all_88_4 & $lesseq(1, $difference(all_92_8, all_364_0)) 44.85/14.58 | | & node1(all_364_2, all_364_1) = all_101_2 & size1(all_364_2) = 44.85/14.58 | | all_364_0 & in_tree1(all_364_1) & in_tree1(all_364_2) 44.85/14.58 | | 44.85/14.58 | | ALPHA: (22) implies: 44.85/14.58 | | (23) all_360_0 = all_88_4 44.85/14.58 | | 44.85/14.58 | | REDUCE: (20), (23) imply: 44.85/14.58 | | (24) size1(all_101_2) = all_88_4 44.85/14.58 | | 44.85/14.58 | | REF_CLOSE: (1), (3), (5), (6), (9), (13), (24) are inconsistent by sub-proof 44.85/14.58 | | #4. 44.85/14.58 | | 44.85/14.58 | End of split 44.85/14.58 | 44.85/14.58 End of proof 44.85/14.58 44.85/14.58 Sub-proof #4 shows that the following formulas are inconsistent: 44.85/14.58 ---------------------------------------------------------------- 44.85/14.58 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (size1(v2) 44.85/14.58 = v1) | ~ (size1(v2) = v0)) 44.85/14.58 (2) size1(all_101_2) = all_101_0 44.85/14.58 (3) size1(all_101_2) = all_88_4 44.85/14.58 (4) ~ (all_101_0 = all_88_4) | ? [v0: $int] : ($lesseq(1, $difference(v0, 44.85/14.58 all_92_8)) & size1(all_253_2) = v0) 44.85/14.58 (5) $lesseq(1, $difference(all_101_0, all_253_0)) 44.85/14.58 (6) $difference(all_92_8, all_88_4) = -1 44.85/14.58 (7) size1(all_253_2) = all_253_0 44.85/14.58 44.85/14.58 Begin of proof 44.85/14.58 | 44.85/14.58 | GROUND_INST: instantiating (1) with all_101_0, all_88_4, all_101_2, 44.85/14.58 | simplifying with (2), (3) gives: 44.85/14.58 | (8) all_101_0 = all_88_4 44.85/14.58 | 44.85/14.58 | REDUCE: (5), (8) imply: 44.85/14.58 | (9) $lesseq(1, $difference(all_88_4, all_253_0)) 44.85/14.58 | 44.85/14.58 | BETA: splitting (4) gives: 44.85/14.58 | 44.85/14.58 | Case 1: 44.85/14.58 | | 44.85/14.58 | | (10) ~ (all_101_0 = all_88_4) 44.85/14.58 | | 44.85/14.58 | | REDUCE: (8), (10) imply: 44.85/14.58 | | (11) ~ (0 = 0) 44.85/14.58 | | 44.85/14.58 | | CLOSE: (11) is inconsistent. 44.85/14.58 | | 44.85/14.58 | Case 2: 44.85/14.58 | | 44.85/14.58 | | (12) ? [v0: $int] : ($lesseq(1, $difference(v0, all_92_8)) & 44.85/14.58 | | size1(all_253_2) = v0) 44.85/14.58 | | 44.85/14.58 | | DELTA: instantiating (12) with fresh symbol all_389_0 gives: 44.85/14.58 | | (13) $lesseq(1, $difference(all_389_0, all_92_8)) & size1(all_253_2) = 44.85/14.58 | | all_389_0 44.85/14.59 | | 44.85/14.59 | | ALPHA: (13) implies: 44.85/14.59 | | (14) $lesseq(1, $difference(all_389_0, all_92_8)) 44.85/14.59 | | (15) size1(all_253_2) = all_389_0 44.85/14.59 | | 44.85/14.59 | | REDUCE: (6), (14) imply: 44.85/14.59 | | (16) $lesseq(all_88_4, all_389_0) 44.85/14.59 | | 44.85/14.59 | | GROUND_INST: instantiating (1) with all_253_0, all_389_0, all_253_2, 44.85/14.59 | | simplifying with (7), (15) gives: 44.85/14.59 | | (17) all_389_0 = all_253_0 44.85/14.59 | | 44.85/14.59 | | REDUCE: (16), (17) imply: 44.85/14.59 | | (18) $lesseq(all_88_4, all_253_0) 44.85/14.59 | | 44.85/14.59 | | COMBINE_INEQS: (9), (18) imply: 44.85/14.59 | | (19) $lesseq(0, -1) 44.85/14.59 | | 44.85/14.59 | | CLOSE: (19) is inconsistent. 44.85/14.59 | | 44.85/14.59 | End of split 44.85/14.59 | 44.85/14.59 End of proof 44.85/14.59 44.85/14.59 Sub-proof #5 shows that the following formulas are inconsistent: 44.85/14.59 ---------------------------------------------------------------- 44.85/14.59 (1) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : (v1 = v0 | ~ (size1(v2) 44.85/14.59 = v1) | ~ (size1(v2) = v0)) 44.85/14.59 (2) t2tb2(all_101_2) = all_101_1 44.85/14.59 (3) size1(all_101_2) = all_101_0 44.85/14.59 (4) in_tree1(all_248_1) 44.85/14.59 (5) ! [v0: $int] : ! [v1: $int] : ( ~ (t2tb2(v0) = v1) | ~ (mem(tree, v1, 44.85/14.59 all_92_6) = 0) | ~ in_tree1(v0) | ? [v2: $int] : (size1(v0) = v2 44.85/14.59 & ? [v3: $int] : ? [v4: $int] : ? [v5: $int] : (v2 = all_88_4 & 44.85/14.59 $lesseq(1, $difference(all_92_8, v5)) & node1(v3, v4) = v0 & 44.85/14.59 size1(v3) = v5 & in_tree1(v4) & in_tree1(v3)))) 44.85/14.59 (6) $sum(size1(all_248_1), $product(-1, $sum($difference(all_101_0, 44.85/14.59 all_248_0), -1))) = 0 44.85/14.59 (7) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v3 = v2 44.85/14.59 | ~ (size1(v1) = v3) | ~ (size1(v0) = v2) | ~ in_tree1(v0) | ! [v4: 44.85/14.59 $int] : ! [v5: $int] : ! [v6: $int] : ( ~ (node1(v1, v5) = v6) | ~ 44.85/14.59 (node1(v0, v4) = v6) | ~ in_tree1(v4))) 44.85/14.59 (8) all_160_1 = all_77_6 44.85/14.59 (9) ~ (all_77_2 = all_77_6) 44.85/14.59 (10) ! [v0: $int] : ! [v1: $int] : ( ~ (all_101_0 = all_88_4) | ~ 44.85/14.59 (node1(v0, v1) = all_101_2) | ~ in_tree1(v0) | ? [v2: $int] : 44.85/14.59 ($lesseq(1, $difference(v2, all_92_8)) & size1(v0) = v2)) 44.85/14.59 (11) all_160_1 = all_77_2 | ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : ( 44.85/14.59 ~ (v2 = 0) & distinct(tree, v1) = 0 & cons(tree, v0, v1) = all_77_2 & 44.85/14.59 mem(tree, v0, v1) = v2 & sort1(all_160_0, v1) = 0 & sort1(tree, v0) = 44.85/14.59 0 & in_uni(v1) & in_uni(v0) & in_uni(all_77_2)) | ? [v0: $int] : 44.85/14.59 (cons(tree, v0, all_160_1) = all_77_2 & sort1(tree, v0) = 0 & in_uni(v0) 44.85/14.59 & in_uni(all_77_2)) 44.85/14.59 (12) mem(tree, all_101_1, all_92_6) = 0 44.85/14.59 (13) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ (node1(v0, v1) = v2) 44.85/14.59 | ~ in_tree1(v0) | ? [v3: $int] : ? [v4: $int] : (size1(v2) = v3 & 44.85/14.59 $sum(size1(v1), $product(-1, $sum($difference(v3, v4), -1))) = 0 & 44.85/14.59 size1(v0) = v4)) 44.85/14.59 (14) $lesseq(0, all_248_0) 44.85/14.59 (15) in_tree1(all_101_2) 44.85/14.59 44.85/14.59 Begin of proof 44.85/14.59 | 44.85/14.59 | BETA: splitting (11) gives: 44.85/14.59 | 44.85/14.59 | Case 1: 44.85/14.59 | | 44.85/14.59 | | (16) all_160_1 = all_77_2 44.85/14.59 | | 44.85/14.59 | | COMBINE_EQS: (8), (16) imply: 44.85/14.59 | | (17) all_77_2 = all_77_6 44.85/14.59 | | 44.85/14.59 | | SIMP: (17) implies: 44.85/14.59 | | (18) all_77_2 = all_77_6 44.85/14.59 | | 44.85/14.59 | | REDUCE: (9), (18) imply: 44.85/14.59 | | (19) ~ (0 = 0) 44.85/14.59 | | 44.85/14.59 | | CLOSE: (19) is inconsistent. 44.85/14.59 | | 44.85/14.59 | Case 2: 44.85/14.59 | | 44.85/14.59 | | 44.85/14.59 | | GROUND_INST: instantiating (7) with all_248_1, all_101_2, 44.85/14.59 | | $sum($difference(all_101_0, all_248_0), -1), all_101_0, 44.85/14.59 | | simplifying with (3), (4), (6) gives: 44.85/14.59 | | (20) all_248_0 = -1 | ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ( ~ 44.85/14.59 | | (node1(all_248_1, v0) = v2) | ~ (node1(all_101_2, v1) = v2) | ~ 44.85/14.59 | | in_tree1(v0)) 44.85/14.59 | | 44.85/14.59 | | GROUND_INST: instantiating (5) with all_101_2, all_101_1, simplifying with 44.85/14.59 | | (2), (12), (15) gives: 44.85/14.59 | | (21) ? [v0: $int] : (size1(all_101_2) = v0 & ? [v1: $int] : ? [v2: 44.85/14.59 | | $int] : ? [v3: $int] : (v0 = all_88_4 & $lesseq(1, 44.85/14.59 | | $difference(all_92_8, v3)) & node1(v1, v2) = all_101_2 & 44.85/14.59 | | size1(v1) = v3 & in_tree1(v2) & in_tree1(v1))) 44.85/14.59 | | 44.85/14.59 | | DELTA: instantiating (21) with fresh symbol all_365_0 gives: 44.85/14.59 | | (22) size1(all_101_2) = all_365_0 & ? [v0: $int] : ? [v1: $int] : ? 44.85/14.59 | | [v2: $int] : (all_365_0 = all_88_4 & $lesseq(1, 44.85/14.59 | | $difference(all_92_8, v2)) & node1(v0, v1) = all_101_2 & 44.85/14.59 | | size1(v0) = v2 & in_tree1(v1) & in_tree1(v0)) 44.85/14.59 | | 44.85/14.59 | | ALPHA: (22) implies: 44.85/14.59 | | (23) size1(all_101_2) = all_365_0 44.85/14.59 | | (24) ? [v0: $int] : ? [v1: $int] : ? [v2: $int] : (all_365_0 = 44.85/14.59 | | all_88_4 & $lesseq(1, $difference(all_92_8, v2)) & node1(v0, v1) = 44.85/14.59 | | all_101_2 & size1(v0) = v2 & in_tree1(v1) & in_tree1(v0)) 44.85/14.59 | | 44.85/14.59 | | DELTA: instantiating (24) with fresh symbols all_369_0, all_369_1, all_369_2 44.85/14.59 | | gives: 44.85/14.59 | | (25) all_365_0 = all_88_4 & $lesseq(1, $difference(all_92_8, all_369_0)) 44.85/14.59 | | & node1(all_369_2, all_369_1) = all_101_2 & size1(all_369_2) = 44.85/14.59 | | all_369_0 & in_tree1(all_369_1) & in_tree1(all_369_2) 44.85/14.59 | | 44.85/14.59 | | ALPHA: (25) implies: 44.85/14.59 | | (26) all_365_0 = all_88_4 44.85/14.59 | | (27) $lesseq(1, $difference(all_92_8, all_369_0)) 44.85/14.59 | | (28) in_tree1(all_369_2) 44.85/14.59 | | (29) size1(all_369_2) = all_369_0 44.85/14.59 | | (30) node1(all_369_2, all_369_1) = all_101_2 44.85/14.59 | | 44.85/14.59 | | REDUCE: (23), (26) imply: 44.85/14.59 | | (31) size1(all_101_2) = all_88_4 44.85/14.59 | | 44.85/14.59 | | BETA: splitting (20) gives: 44.85/14.59 | | 44.85/14.59 | | Case 1: 44.85/14.59 | | | 44.85/14.59 | | | (32) all_248_0 = -1 44.85/14.59 | | | 44.85/14.59 | | | REDUCE: (14), (32) imply: 44.85/14.59 | | | (33) $lesseq(0, -1) 44.85/14.59 | | | 44.85/14.59 | | | CLOSE: (33) is inconsistent. 44.85/14.59 | | | 44.85/14.59 | | Case 2: 44.85/14.59 | | | 44.85/14.59 | | | 44.85/14.59 | | | GROUND_INST: instantiating (1) with all_101_0, all_88_4, all_101_2, 44.85/14.59 | | | simplifying with (3), (31) gives: 44.85/14.59 | | | (34) all_101_0 = all_88_4 44.85/14.59 | | | 44.85/14.59 | | | GROUND_INST: instantiating (10) with all_369_2, all_369_1, simplifying 44.85/14.59 | | | with (28), (30) gives: 44.85/14.59 | | | (35) ~ (all_101_0 = all_88_4) | ? [v0: $int] : ($lesseq(1, 44.85/14.59 | | | $difference(v0, all_92_8)) & size1(all_369_2) = v0) 44.85/14.59 | | | 44.85/14.59 | | | GROUND_INST: instantiating (13) with all_369_2, all_369_1, all_101_2, 44.85/14.59 | | | simplifying with (28), (30) gives: 44.85/14.59 | | | (36) ? [v0: $int] : ? [v1: $int] : ($sum(size1(all_369_1), 44.85/14.59 | | | $product(-1, $sum($difference(v0, v1), -1))) = 0 & 44.85/14.59 | | | size1(all_369_2) = v1 & size1(all_101_2) = v0) 44.85/14.59 | | | 44.85/14.59 | | | DELTA: instantiating (36) with fresh symbols all_409_0, all_409_1 gives: 44.85/14.59 | | | (37) $sum(size1(all_369_1), $product(-1, $sum($difference(all_409_1, 44.85/14.59 | | | all_409_0), -1))) = 0 & size1(all_369_2) = all_409_0 & 44.85/14.59 | | | size1(all_101_2) = all_409_1 44.85/14.59 | | | 44.85/14.59 | | | ALPHA: (37) implies: 44.85/14.60 | | | (38) size1(all_369_2) = all_409_0 44.85/14.60 | | | 44.85/14.60 | | | BETA: splitting (35) gives: 44.85/14.60 | | | 44.85/14.60 | | | Case 1: 44.85/14.60 | | | | 44.85/14.60 | | | | (39) ~ (all_101_0 = all_88_4) 44.85/14.60 | | | | 44.85/14.60 | | | | REDUCE: (34), (39) imply: 44.85/14.60 | | | | (40) ~ (0 = 0) 44.85/14.60 | | | | 44.85/14.60 | | | | CLOSE: (40) is inconsistent. 44.85/14.60 | | | | 44.85/14.60 | | | Case 2: 44.85/14.60 | | | | 44.85/14.60 | | | | (41) ? [v0: $int] : ($lesseq(1, $difference(v0, all_92_8)) & 44.85/14.60 | | | | size1(all_369_2) = v0) 44.85/14.60 | | | | 44.85/14.60 | | | | DELTA: instantiating (41) with fresh symbol all_422_0 gives: 44.85/14.60 | | | | (42) $lesseq(1, $difference(all_422_0, all_92_8)) & size1(all_369_2) 44.85/14.60 | | | | = all_422_0 44.85/14.60 | | | | 44.85/14.60 | | | | ALPHA: (42) implies: 44.85/14.60 | | | | (43) $lesseq(1, $difference(all_422_0, all_92_8)) 44.85/14.60 | | | | (44) size1(all_369_2) = all_422_0 44.85/14.60 | | | | 44.85/14.60 | | | | GROUND_INST: instantiating (1) with all_369_0, all_422_0, all_369_2, 44.85/14.60 | | | | simplifying with (29), (44) gives: 44.85/14.60 | | | | (45) all_422_0 = all_369_0 44.85/14.60 | | | | 44.85/14.60 | | | | GROUND_INST: instantiating (1) with all_422_0, all_409_0, all_369_2, 44.85/14.60 | | | | simplifying with (38), (44) gives: 44.85/14.60 | | | | (46) all_422_0 = all_409_0 44.85/14.60 | | | | 44.85/14.60 | | | | COMBINE_EQS: (45), (46) imply: 44.85/14.60 | | | | (47) all_409_0 = all_369_0 44.85/14.60 | | | | 44.85/14.60 | | | | REDUCE: (43), (45) imply: 44.85/14.60 | | | | (48) $lesseq(1, $difference(all_369_0, all_92_8)) 44.85/14.60 | | | | 44.85/14.60 | | | | COMBINE_INEQS: (27), (48) imply: 44.85/14.60 | | | | (49) $lesseq(0, -1) 44.85/14.60 | | | | 44.85/14.60 | | | | CLOSE: (49) is inconsistent. 44.85/14.60 | | | | 44.85/14.60 | | | End of split 44.85/14.60 | | | 44.85/14.60 | | End of split 44.85/14.60 | | 44.85/14.60 | End of split 44.85/14.60 | 44.85/14.60 End of proof 44.85/14.60 44.85/14.60 Sub-proof #6 shows that the following formulas are inconsistent: 44.85/14.60 ---------------------------------------------------------------- 44.85/14.60 (1) ? [v0: $int] : ( ~ (v0 = 0) & sort1(all_74_1, all_96_2) = v0) 44.85/14.60 (2) all_96_2 = all_96_3 44.85/14.60 (3) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : (v1 = v0 44.85/14.60 | ~ (sort1(v3, v2) = v1) | ~ (sort1(v3, v2) = v0)) 44.85/14.60 (4) sort1(all_74_1, all_96_3) = 0 44.85/14.60 44.85/14.60 Begin of proof 44.85/14.60 | 44.85/14.60 | DELTA: instantiating (1) with fresh symbol all_272_0 gives: 44.85/14.60 | (5) ~ (all_272_0 = 0) & sort1(all_74_1, all_96_2) = all_272_0 44.85/14.60 | 44.85/14.60 | ALPHA: (5) implies: 44.85/14.60 | (6) ~ (all_272_0 = 0) 44.85/14.60 | (7) sort1(all_74_1, all_96_2) = all_272_0 44.85/14.60 | 44.85/14.60 | REDUCE: (2), (7) imply: 44.85/14.60 | (8) sort1(all_74_1, all_96_3) = all_272_0 44.85/14.60 | 44.85/14.60 | GROUND_INST: instantiating (3) with 0, all_272_0, all_96_3, all_74_1, 44.85/14.60 | simplifying with (4), (8) gives: 44.85/14.60 | (9) all_272_0 = 0 44.85/14.60 | 44.85/14.60 | REDUCE: (6), (9) imply: 44.85/14.60 | (10) ~ (0 = 0) 44.85/14.60 | 44.85/14.60 | CLOSE: (10) is inconsistent. 44.85/14.60 | 44.85/14.60 End of proof 44.85/14.60 44.85/14.60 Sub-proof #7 shows that the following formulas are inconsistent: 44.85/14.60 ---------------------------------------------------------------- 44.85/14.60 (1) in_ty(tree) 44.85/14.60 (2) list(tree) = all_74_1 44.85/14.60 (3) infix_plpl(tree, all_96_3, all_92_6) = all_96_2 44.85/14.60 (4) ~ (all_270_0 = 0) & sort1(all_74_1, all_96_2) = all_270_0 44.85/14.60 (5) ! [v0: $int] : ! [v1: $int] : ! [v2: $int] : ! [v3: $int] : ! [v4: 44.85/14.60 $int] : ! [v5: $int] : (v5 = 0 | ~ (infix_plpl(v0, v1, v2) = v4) | ~ 44.85/14.60 (list(v0) = v3) | ~ (sort1(v3, v4) = v5) | ~ in_ty(v0)) 44.85/14.60 44.85/14.60 Begin of proof 44.85/14.60 | 44.85/14.60 | ALPHA: (4) implies: 44.85/14.60 | (6) ~ (all_270_0 = 0) 44.85/14.60 | (7) sort1(all_74_1, all_96_2) = all_270_0 44.85/14.60 | 44.85/14.60 | GROUND_INST: instantiating (5) with tree, all_96_3, all_92_6, all_74_1, 44.85/14.60 | all_96_2, all_270_0, simplifying with (1), (2), (3), (7) gives: 44.85/14.60 | (8) all_270_0 = 0 44.85/14.60 | 44.85/14.60 | REDUCE: (6), (8) imply: 44.85/14.60 | (9) ~ (0 = 0) 44.85/14.60 | 44.85/14.60 | CLOSE: (9) is inconsistent. 44.85/14.60 | 44.85/14.60 End of proof 44.85/14.60 44.85/14.60 Sub-proof #8 shows that the following formulas are inconsistent: 44.85/14.60 ---------------------------------------------------------------- 44.85/14.60 (1) all_160_1 = all_77_2 44.85/14.60 (2) all_160_1 = all_77_6 44.85/14.60 (3) ~ (all_77_2 = all_77_6) 44.85/14.60 44.85/14.60 Begin of proof 44.85/14.60 | 44.85/14.60 | COMBINE_EQS: (1), (2) imply: 44.85/14.60 | (4) all_77_2 = all_77_6 44.85/14.60 | 44.85/14.60 | SIMP: (4) implies: 44.85/14.60 | (5) all_77_2 = all_77_6 44.85/14.60 | 44.85/14.60 | REDUCE: (3), (5) imply: 44.85/14.60 | (6) ~ (0 = 0) 44.85/14.60 | 44.85/14.60 | CLOSE: (6) is inconsistent. 44.85/14.60 | 44.85/14.60 End of proof 44.85/14.60 % SZS output end Proof for theBenchmark 44.85/14.60 44.85/14.60 14113ms 44.96/14.68 EOF