TSTP Solution File: SWW598_2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW598_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:50:51 EDT 2023
% Result : Theorem 25.36s 4.15s
% Output : Proof 26.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWW598_2 : TPTP v8.1.2. Released v6.1.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 17:58:34 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.62 ________ _____
% 0.19/0.62 ___ __ \_________(_)________________________________
% 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62
% 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62 (2023-06-19)
% 0.19/0.62
% 0.19/0.62 (c) Philipp Rümmer, 2009-2023
% 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62 Amanda Stjerna.
% 0.19/0.62 Free software under BSD-3-Clause.
% 0.19/0.62
% 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62
% 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.58/1.22 Prover 0: Preprocessing ...
% 3.58/1.22 Prover 3: Preprocessing ...
% 3.58/1.22 Prover 5: Preprocessing ...
% 3.58/1.23 Prover 2: Preprocessing ...
% 3.58/1.23 Prover 1: Preprocessing ...
% 3.58/1.23 Prover 6: Preprocessing ...
% 3.58/1.23 Prover 4: Preprocessing ...
% 7.50/1.78 Prover 4: Warning: ignoring some quantifiers
% 7.50/1.78 Prover 1: Warning: ignoring some quantifiers
% 7.97/1.82 Prover 4: Constructing countermodel ...
% 7.97/1.83 Prover 0: Proving ...
% 7.97/1.83 Prover 3: Warning: ignoring some quantifiers
% 7.97/1.84 Prover 1: Constructing countermodel ...
% 7.97/1.84 Prover 5: Proving ...
% 7.97/1.85 Prover 3: Constructing countermodel ...
% 8.28/1.89 Prover 6: Proving ...
% 8.28/1.93 Prover 2: Proving ...
% 25.36/4.15 Prover 4: Found proof (size 642)
% 25.36/4.15 Prover 4: proved (3506ms)
% 25.36/4.15 Prover 3: stopped
% 25.36/4.15 Prover 1: stopped
% 25.36/4.15 Prover 0: stopped
% 25.36/4.15 Prover 6: stopped
% 25.36/4.15 Prover 2: stopped
% 25.36/4.15 Prover 5: stopped
% 25.36/4.15
% 25.36/4.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.36/4.15
% 25.43/4.17 % SZS output start Proof for theBenchmark
% 25.43/4.18 Assumptions after simplification:
% 25.43/4.18 ---------------------------------
% 25.43/4.18
% 25.43/4.18 (max_is_ge)
% 25.43/4.19 ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, $difference(v1,
% 25.43/4.19 v2))) | ~ (max(v0, v1) = v2)) & ! [v0: int] : ! [v1: int] : ! [v2:
% 25.43/4.19 int] : ( ~ ($lesseq(1, $difference(v0, v2))) | ~ (max(v0, v1) = v2))
% 25.43/4.19
% 25.43/4.19 (max_is_some)
% 25.43/4.19 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | v2 = v0 | ~ (max(v0,
% 25.43/4.19 v1) = v2))
% 25.43/4.19
% 25.43/4.19 (max_sym)
% 25.43/4.19 ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(v1, v0)) | ~
% 25.43/4.19 (max(v1, v0) = v2) | max(v0, v1) = v2) & ! [v0: int] : ! [v1: int] : !
% 25.43/4.19 [v2: int] : ( ~ ($lesseq(v1, v0)) | ~ (max(v0, v1) = v2) | max(v1, v0) = v2)
% 25.43/4.20
% 25.43/4.20 (max_x)
% 25.43/4.20 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v0 | ~ ($lesseq(v1, v0)) |
% 25.43/4.20 ~ (max(v0, v1) = v2))
% 25.43/4.20
% 25.43/4.20 (max_y)
% 25.43/4.20 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, v1)) |
% 25.43/4.20 ~ (max(v0, v1) = v2))
% 25.43/4.20
% 25.43/4.20 (mem_def)
% 25.43/4.20 tree(empty) & ! [v0: int] : ! [v1: tree] : ! [v2: int] : ! [v3: tree] : !
% 25.43/4.20 [v4: tree] : ! [v5: int] : (v5 = 0 | ~ (mem(v0, v4) = v5) | ~ (node(v1, v2,
% 25.43/4.20 v3) = v4) | ~ tree(v3) | ~ tree(v1) | ? [v6: int] : ? [v7: int] : (
% 25.43/4.20 ~ (v7 = 0) & ~ (v6 = 0) & mem(v0, v3) = v7 & mem(v0, v1) = v6)) & ! [v0:
% 25.43/4.20 int] : ! [v1: tree] : ! [v2: tree] : ! [v3: tree] : ! [v4: int] : (v4 =
% 25.43/4.20 0 | ~ (mem(v0, v3) = v4) | ~ (node(v1, v0, v2) = v3) | ~ tree(v2) | ~
% 25.43/4.20 tree(v1)) & ! [v0: int] : ! [v1: tree] : ! [v2: int] : ! [v3: tree] : !
% 25.43/4.20 [v4: tree] : (v2 = v0 | ~ (mem(v0, v4) = 0) | ~ (node(v1, v2, v3) = v4) | ~
% 25.43/4.20 tree(v3) | ~ tree(v1) | ? [v5: any] : ? [v6: any] : (mem(v0, v3) = v6 &
% 25.43/4.20 mem(v0, v1) = v5 & (v6 = 0 | v5 = 0))) & ! [v0: int] : ~ (mem(v0, empty)
% 25.43/4.20 = 0)
% 25.43/4.20
% 25.43/4.20 (size_def)
% 25.43/4.21 size(empty) = 0 & tree(empty) & ! [v0: tree] : ! [v1: int] : ! [v2: tree] :
% 25.43/4.21 ! [v3: tree] : ( ~ (node(v0, v1, v2) = v3) | ~ tree(v2) | ~ tree(v0) | ?
% 25.43/4.21 [v4: int] : ? [v5: int] : (size(v3) = v4 & size(v2) = $sum($difference(v4,
% 25.43/4.21 v5), -1) & size(v0) = v5))
% 25.43/4.21
% 25.43/4.21 (size_nonneg)
% 25.43/4.21 ! [v0: tree] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | ~ (size(v0) = v1) | ~
% 25.43/4.21 tree(v0))
% 25.43/4.21
% 25.43/4.21 (wP_parameter_maximum)
% 25.67/4.22 tree(empty) & ? [v0: tree] : ? [v1: int] : ? [v2: tree] : ? [v3: int] : ?
% 25.67/4.22 [v4: tree] : ? [v5: any] : ? [v6: int] : ? [v7: int] : ? [v8: tree] : ?
% 25.67/4.22 [v9: int] : ? [v10: tree] : ? [v11: tree] : ? [v12: tree] : ? [v13: int] :
% 25.67/4.22 ? [v14: tree] : ? [v15: tree] : ? [v16: int] : ? [v17: int] : ? [v18:
% 25.67/4.22 int] : ? [v19: int] : ? [v20: int] : ? [v21: int] : ? [v22: any] : ?
% 25.67/4.22 [v23: int] : ? [v24: int] : ? [v25: int] : ? [v26: int] : ? [v27: int] :
% 25.67/4.22 ? [v28: any] : ? [v29: int] : ? [v30: int] : ? [v31: tree] : ? [v32: int]
% 25.67/4.22 : ? [v33: tree] : ? [v34: tree] : ? [v35: int] : ? [v36: int] : ? [v37:
% 25.67/4.22 int] : ? [v38: any] : ? [v39: int] : ? [v40: int] : ? [v41: int] : ?
% 25.67/4.22 [v42: int] : ( ~ (v0 = empty) & mem(v3, v0) = v5 & size(v4) = v7 & size(v2) =
% 25.67/4.22 v6 & size(v0) = v1 & node(v2, v3, v4) = v0 & tree(v33) & tree(v31) &
% 25.67/4.22 tree(v14) & tree(v12) & tree(v10) & tree(v8) & tree(v4) & tree(v2) &
% 25.67/4.22 tree(v0) & ((v11 = v4 & node(v8, v9, v10) = v4 & ((v15 = v2 & node(v12, v13,
% 25.67/4.22 v14) = v2 & (v4 = empty | ~ ($lesseq(1, $difference(v1, v7))) |
% 25.67/4.22 ~ ($lesseq(0, v1)) | (v17 = 0 & mem(v16, v4) = 0 & max(v3, v16) =
% 25.67/4.22 v18 & ! [v43: int] : ( ~ ($lesseq(1, $difference(v43, v16))) |
% 25.67/4.22 ~ (mem(v43, v4) = 0)) & (v2 = empty | ~ ($lesseq(1,
% 25.67/4.22 $difference(v1, v6))) | (v20 = 0 & mem(v21, v0) = v22 &
% 25.67/4.22 mem(v19, v2) = 0 & max(v19, v18) = v21 & ! [v43: int] : ( ~
% 25.67/4.22 ($lesseq(1, $difference(v43, v19))) | ~ (mem(v43, v2) =
% 25.67/4.22 0)) & ( ~ (v22 = 0) | (v24 = 0 & $lesseq(1,
% 25.67/4.22 $difference(v23, v21)) & mem(v23, v0) = 0))))))) | (v2
% 25.67/4.22 = empty & (v4 = empty | ~ ($lesseq(1, $difference(v1, v7))) | ~
% 25.67/4.22 ($lesseq(0, v1)) | (v26 = 0 & mem(v27, v0) = v28 & mem(v25, v4) =
% 25.67/4.22 0 & max(v25, v3) = v27 & ! [v43: int] : ( ~ ($lesseq(1,
% 25.67/4.22 $difference(v43, v25))) | ~ (mem(v43, v4) = 0)) & ( ~
% 25.67/4.22 (v28 = 0) | (v30 = 0 & $lesseq(1, $difference(v29, v27)) &
% 25.67/4.22 mem(v29, v0) = 0))))))) | (v4 = empty & ((v34 = v2 &
% 25.67/4.22 node(v31, v32, v33) = v2 & (v2 = empty | ~ ($lesseq(1,
% 25.67/4.22 $difference(v1, v6))) | ~ ($lesseq(0, v1)) | (v36 = 0 &
% 25.67/4.22 mem(v37, v0) = v38 & mem(v35, v2) = 0 & max(v35, v3) = v37 & !
% 25.67/4.22 [v43: int] : ( ~ ($lesseq(1, $difference(v43, v35))) | ~
% 25.67/4.22 (mem(v43, v2) = 0)) & ( ~ (v38 = 0) | (v40 = 0 & $lesseq(1,
% 25.67/4.22 $difference(v39, v37)) & mem(v39, v0) = 0))))) | (v2 =
% 25.67/4.22 empty & ( ~ (v5 = 0) | (v42 = 0 & $lesseq(1, $difference(v41, v3)) &
% 25.67/4.22 mem(v41, v0) = 0)))))))
% 25.67/4.22
% 25.67/4.22 (function-axioms)
% 25.67/4.22 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: tree] : !
% 25.67/4.22 [v5: ty] : (v1 = v0 | ~ (match_tree(v5, v4, v3, v2) = v1) | ~
% 25.67/4.22 (match_tree(v5, v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2:
% 25.67/4.22 uni] : ! [v3: uni] : ! [v4: bool] : ! [v5: ty] : (v1 = v0 | ~
% 25.67/4.22 (match_bool(v5, v4, v3, v2) = v1) | ~ (match_bool(v5, v4, v3, v2) = v0)) &
% 25.67/4.22 ! [v0: tree] : ! [v1: tree] : ! [v2: tree] : ! [v3: int] : ! [v4: tree] :
% 25.67/4.22 (v1 = v0 | ~ (node(v4, v3, v2) = v1) | ~ (node(v4, v3, v2) = v0)) & ! [v0:
% 25.67/4.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: tree] : ! [v3:
% 25.67/4.22 int] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = v0)) & ! [v0:
% 25.67/4.22 int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 | ~ (min(v3,
% 25.67/4.22 v2) = v1) | ~ (min(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : !
% 25.67/4.22 [v2: int] : ! [v3: int] : (v1 = v0 | ~ (max(v3, v2) = v1) | ~ (max(v3, v2)
% 25.67/4.22 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 25.67/4.22 uni] : ! [v3: ty] : (v1 = v0 | ~ (sort(v3, v2) = v1) | ~ (sort(v3, v2) =
% 25.67/4.22 v0)) & ! [v0: int] : ! [v1: int] : ! [v2: tree] : (v1 = v0 | ~
% 25.67/4.22 (size(v2) = v1) | ~ (size(v2) = v0)) & ! [v0: tree] : ! [v1: tree] : !
% 25.67/4.22 [v2: tree] : (v1 = v0 | ~ (node_proj_3(v2) = v1) | ~ (node_proj_3(v2) = v0))
% 25.67/4.22 & ! [v0: int] : ! [v1: int] : ! [v2: tree] : (v1 = v0 | ~ (node_proj_2(v2)
% 25.67/4.22 = v1) | ~ (node_proj_2(v2) = v0)) & ! [v0: tree] : ! [v1: tree] : !
% 25.67/4.22 [v2: tree] : (v1 = v0 | ~ (node_proj_1(v2) = v1) | ~ (node_proj_1(v2) = v0))
% 25.67/4.22 & ! [v0: uni] : ! [v1: uni] : ! [v2: ty] : (v1 = v0 | ~ (witness(v2) = v1)
% 25.67/4.22 | ~ (witness(v2) = v0))
% 25.67/4.22
% 25.67/4.22 Further assumptions not needed in the proof:
% 25.67/4.22 --------------------------------------------
% 25.67/4.23 bool_inversion, compatOrderMult, empty_Node, match_bool_False, match_bool_True,
% 25.67/4.23 match_bool_sort, match_tree_Empty, match_tree_Node, match_tree_sort, min_is_le,
% 25.67/4.23 min_is_some, min_sym, min_x, min_y, node_proj_1_def, node_proj_2_def,
% 25.67/4.23 node_proj_3_def, tree_inversion, true_False, tuple0_inversion, witness_sort
% 25.67/4.23
% 25.67/4.23 Those formulas are unsatisfiable:
% 25.67/4.23 ---------------------------------
% 25.67/4.23
% 25.67/4.23 Begin of proof
% 25.67/4.23 |
% 25.67/4.23 | ALPHA: (max_is_ge) implies:
% 25.67/4.23 | (1) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1,
% 25.67/4.23 | $difference(v0, v2))) | ~ (max(v0, v1) = v2))
% 25.67/4.23 | (2) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1,
% 25.67/4.23 | $difference(v1, v2))) | ~ (max(v0, v1) = v2))
% 25.67/4.23 |
% 25.67/4.23 | ALPHA: (max_sym) implies:
% 25.67/4.23 | (3) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(v1, v0)) | ~
% 25.67/4.23 | (max(v0, v1) = v2) | max(v1, v0) = v2)
% 25.67/4.23 | (4) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(v1, v0)) | ~
% 25.67/4.23 | (max(v1, v0) = v2) | max(v0, v1) = v2)
% 25.67/4.23 |
% 25.67/4.23 | ALPHA: (size_def) implies:
% 25.67/4.23 | (5) size(empty) = 0
% 25.67/4.23 | (6) ! [v0: tree] : ! [v1: int] : ! [v2: tree] : ! [v3: tree] : ( ~
% 25.67/4.23 | (node(v0, v1, v2) = v3) | ~ tree(v2) | ~ tree(v0) | ? [v4: int] :
% 25.67/4.23 | ? [v5: int] : (size(v3) = v4 & size(v2) = $sum($difference(v4, v5),
% 25.67/4.23 | -1) & size(v0) = v5))
% 25.67/4.23 |
% 25.67/4.23 | ALPHA: (mem_def) implies:
% 25.67/4.23 | (7) ! [v0: int] : ~ (mem(v0, empty) = 0)
% 25.67/4.23 | (8) ! [v0: int] : ! [v1: tree] : ! [v2: int] : ! [v3: tree] : ! [v4:
% 25.67/4.23 | tree] : (v2 = v0 | ~ (mem(v0, v4) = 0) | ~ (node(v1, v2, v3) = v4)
% 25.67/4.23 | | ~ tree(v3) | ~ tree(v1) | ? [v5: any] : ? [v6: any] : (mem(v0,
% 25.67/4.23 | v3) = v6 & mem(v0, v1) = v5 & (v6 = 0 | v5 = 0)))
% 25.67/4.23 | (9) ! [v0: int] : ! [v1: tree] : ! [v2: tree] : ! [v3: tree] : ! [v4:
% 25.67/4.23 | int] : (v4 = 0 | ~ (mem(v0, v3) = v4) | ~ (node(v1, v0, v2) = v3) |
% 25.67/4.23 | ~ tree(v2) | ~ tree(v1))
% 25.67/4.23 | (10) ! [v0: int] : ! [v1: tree] : ! [v2: int] : ! [v3: tree] : ! [v4:
% 25.67/4.23 | tree] : ! [v5: int] : (v5 = 0 | ~ (mem(v0, v4) = v5) | ~
% 25.67/4.23 | (node(v1, v2, v3) = v4) | ~ tree(v3) | ~ tree(v1) | ? [v6: int] :
% 25.67/4.23 | ? [v7: int] : ( ~ (v7 = 0) & ~ (v6 = 0) & mem(v0, v3) = v7 &
% 25.67/4.23 | mem(v0, v1) = v6))
% 25.67/4.23 |
% 25.67/4.23 | ALPHA: (wP_parameter_maximum) implies:
% 25.67/4.24 | (11) ? [v0: tree] : ? [v1: int] : ? [v2: tree] : ? [v3: int] : ? [v4:
% 25.67/4.24 | tree] : ? [v5: any] : ? [v6: int] : ? [v7: int] : ? [v8: tree] :
% 25.67/4.24 | ? [v9: int] : ? [v10: tree] : ? [v11: tree] : ? [v12: tree] : ?
% 25.67/4.24 | [v13: int] : ? [v14: tree] : ? [v15: tree] : ? [v16: int] : ?
% 25.67/4.24 | [v17: int] : ? [v18: int] : ? [v19: int] : ? [v20: int] : ? [v21:
% 25.67/4.24 | int] : ? [v22: any] : ? [v23: int] : ? [v24: int] : ? [v25: int]
% 25.67/4.24 | : ? [v26: int] : ? [v27: int] : ? [v28: any] : ? [v29: int] : ?
% 25.67/4.24 | [v30: int] : ? [v31: tree] : ? [v32: int] : ? [v33: tree] : ?
% 25.67/4.24 | [v34: tree] : ? [v35: int] : ? [v36: int] : ? [v37: int] : ? [v38:
% 25.67/4.24 | any] : ? [v39: int] : ? [v40: int] : ? [v41: int] : ? [v42: int]
% 25.67/4.24 | : ( ~ (v0 = empty) & mem(v3, v0) = v5 & size(v4) = v7 & size(v2) = v6
% 25.67/4.24 | & size(v0) = v1 & node(v2, v3, v4) = v0 & tree(v33) & tree(v31) &
% 25.67/4.24 | tree(v14) & tree(v12) & tree(v10) & tree(v8) & tree(v4) & tree(v2) &
% 25.67/4.24 | tree(v0) & ((v11 = v4 & node(v8, v9, v10) = v4 & ((v15 = v2 &
% 25.67/4.24 | node(v12, v13, v14) = v2 & (v4 = empty | ~ ($lesseq(1,
% 25.67/4.24 | $difference(v1, v7))) | ~ ($lesseq(0, v1)) | (v17 = 0
% 25.67/4.24 | & mem(v16, v4) = 0 & max(v3, v16) = v18 & ! [v43: int]
% 25.67/4.24 | : ( ~ ($lesseq(1, $difference(v43, v16))) | ~ (mem(v43,
% 25.67/4.24 | v4) = 0)) & (v2 = empty | ~ ($lesseq(1,
% 25.67/4.24 | $difference(v1, v6))) | (v20 = 0 & mem(v21, v0) =
% 25.67/4.24 | v22 & mem(v19, v2) = 0 & max(v19, v18) = v21 & !
% 25.67/4.24 | [v43: int] : ( ~ ($lesseq(1, $difference(v43, v19)))
% 25.67/4.24 | | ~ (mem(v43, v2) = 0)) & ( ~ (v22 = 0) | (v24 =
% 25.67/4.24 | 0 & $lesseq(1, $difference(v23, v21)) & mem(v23,
% 25.67/4.24 | v0) = 0))))))) | (v2 = empty & (v4 = empty |
% 25.67/4.24 | ~ ($lesseq(1, $difference(v1, v7))) | ~ ($lesseq(0, v1))
% 25.67/4.24 | | (v26 = 0 & mem(v27, v0) = v28 & mem(v25, v4) = 0 &
% 25.67/4.24 | max(v25, v3) = v27 & ! [v43: int] : ( ~ ($lesseq(1,
% 25.67/4.24 | $difference(v43, v25))) | ~ (mem(v43, v4) = 0)) &
% 25.67/4.24 | ( ~ (v28 = 0) | (v30 = 0 & $lesseq(1, $difference(v29,
% 25.67/4.24 | v27)) & mem(v29, v0) = 0))))))) | (v4 = empty &
% 25.67/4.24 | ((v34 = v2 & node(v31, v32, v33) = v2 & (v2 = empty | ~
% 25.67/4.24 | ($lesseq(1, $difference(v1, v6))) | ~ ($lesseq(0, v1)) |
% 25.67/4.24 | (v36 = 0 & mem(v37, v0) = v38 & mem(v35, v2) = 0 &
% 25.67/4.24 | max(v35, v3) = v37 & ! [v43: int] : ( ~ ($lesseq(1,
% 25.67/4.24 | $difference(v43, v35))) | ~ (mem(v43, v2) = 0)) &
% 25.67/4.24 | ( ~ (v38 = 0) | (v40 = 0 & $lesseq(1, $difference(v39,
% 25.67/4.24 | v37)) & mem(v39, v0) = 0))))) | (v2 = empty & (
% 25.67/4.24 | ~ (v5 = 0) | (v42 = 0 & $lesseq(1, $difference(v41, v3)) &
% 25.67/4.24 | mem(v41, v0) = 0)))))))
% 25.67/4.24 |
% 25.67/4.24 | ALPHA: (function-axioms) implies:
% 25.67/4.24 | (12) ! [v0: int] : ! [v1: int] : ! [v2: tree] : (v1 = v0 | ~ (size(v2)
% 25.67/4.24 | = v1) | ~ (size(v2) = v0))
% 25.67/4.24 | (13) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = v0 |
% 25.67/4.24 | ~ (max(v3, v2) = v1) | ~ (max(v3, v2) = v0))
% 25.67/4.24 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 25.67/4.24 | tree] : ! [v3: int] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~
% 25.67/4.24 | (mem(v3, v2) = v0))
% 25.67/4.24 |
% 25.67/4.24 | DELTA: instantiating (11) with fresh symbols all_42_0, all_42_1, all_42_2,
% 25.67/4.24 | all_42_3, all_42_4, all_42_5, all_42_6, all_42_7, all_42_8, all_42_9,
% 25.67/4.24 | all_42_10, all_42_11, all_42_12, all_42_13, all_42_14, all_42_15,
% 25.67/4.24 | all_42_16, all_42_17, all_42_18, all_42_19, all_42_20, all_42_21,
% 25.67/4.24 | all_42_22, all_42_23, all_42_24, all_42_25, all_42_26, all_42_27,
% 25.67/4.24 | all_42_28, all_42_29, all_42_30, all_42_31, all_42_32, all_42_33,
% 25.67/4.24 | all_42_34, all_42_35, all_42_36, all_42_37, all_42_38, all_42_39,
% 25.67/4.24 | all_42_40, all_42_41, all_42_42 gives:
% 25.67/4.25 | (15) ~ (all_42_42 = empty) & mem(all_42_39, all_42_42) = all_42_37 &
% 25.67/4.25 | size(all_42_38) = all_42_35 & size(all_42_40) = all_42_36 &
% 25.67/4.25 | size(all_42_42) = all_42_41 & node(all_42_40, all_42_39, all_42_38) =
% 25.67/4.25 | all_42_42 & tree(all_42_9) & tree(all_42_11) & tree(all_42_28) &
% 25.67/4.25 | tree(all_42_30) & tree(all_42_32) & tree(all_42_34) & tree(all_42_38)
% 25.67/4.25 | & tree(all_42_40) & tree(all_42_42) & ((all_42_31 = all_42_38 &
% 25.67/4.25 | node(all_42_34, all_42_33, all_42_32) = all_42_38 & ((all_42_27 =
% 25.67/4.25 | all_42_40 & node(all_42_30, all_42_29, all_42_28) = all_42_40
% 25.67/4.25 | & (all_42_38 = empty | ~ ($lesseq(1, $difference(all_42_41,
% 25.67/4.25 | all_42_35))) | ~ ($lesseq(0, all_42_41)) | (all_42_25
% 25.67/4.25 | = 0 & mem(all_42_26, all_42_38) = 0 & max(all_42_39,
% 25.67/4.25 | all_42_26) = all_42_24 & ! [v0: int] : ( ~ ($lesseq(1,
% 25.67/4.25 | $difference(v0, all_42_26))) | ~ (mem(v0,
% 25.67/4.25 | all_42_38) = 0)) & (all_42_40 = empty | ~
% 25.67/4.25 | ($lesseq(1, $difference(all_42_41, all_42_36))) |
% 25.67/4.25 | (all_42_22 = 0 & mem(all_42_21, all_42_42) = all_42_20 &
% 25.67/4.25 | mem(all_42_23, all_42_40) = 0 & max(all_42_23,
% 25.67/4.25 | all_42_24) = all_42_21 & ! [v0: int] : ( ~
% 25.67/4.25 | ($lesseq(1, $difference(v0, all_42_23))) | ~
% 25.67/4.25 | (mem(v0, all_42_40) = 0)) & ( ~ (all_42_20 = 0) |
% 25.67/4.25 | (all_42_18 = 0 & $lesseq(1, $difference(all_42_19,
% 25.67/4.25 | all_42_21)) & mem(all_42_19, all_42_42) =
% 25.67/4.25 | 0))))))) | (all_42_40 = empty & (all_42_38 = empty
% 25.67/4.25 | | ~ ($lesseq(1, $difference(all_42_41, all_42_35))) | ~
% 25.67/4.25 | ($lesseq(0, all_42_41)) | (all_42_16 = 0 & mem(all_42_15,
% 25.67/4.25 | all_42_42) = all_42_14 & mem(all_42_17, all_42_38) = 0 &
% 25.67/4.25 | max(all_42_17, all_42_39) = all_42_15 & ! [v0: int] : ( ~
% 25.67/4.25 | ($lesseq(1, $difference(v0, all_42_17))) | ~ (mem(v0,
% 25.67/4.25 | all_42_38) = 0)) & ( ~ (all_42_14 = 0) | (all_42_12
% 25.88/4.25 | = 0 & $lesseq(1, $difference(all_42_13, all_42_15)) &
% 25.88/4.25 | mem(all_42_13, all_42_42) = 0))))))) | (all_42_38 =
% 25.88/4.25 | empty & ((all_42_8 = all_42_40 & node(all_42_11, all_42_10,
% 25.88/4.25 | all_42_9) = all_42_40 & (all_42_40 = empty | ~ ($lesseq(1,
% 25.88/4.25 | $difference(all_42_41, all_42_36))) | ~ ($lesseq(0,
% 25.88/4.25 | all_42_41)) | (all_42_6 = 0 & mem(all_42_5, all_42_42) =
% 25.88/4.25 | all_42_4 & mem(all_42_7, all_42_40) = 0 & max(all_42_7,
% 25.88/4.25 | all_42_39) = all_42_5 & ! [v0: int] : ( ~ ($lesseq(1,
% 25.88/4.25 | $difference(v0, all_42_7))) | ~ (mem(v0, all_42_40)
% 25.88/4.25 | = 0)) & ( ~ (all_42_4 = 0) | (all_42_2 = 0 &
% 25.88/4.25 | $lesseq(1, $difference(all_42_3, all_42_5)) &
% 25.88/4.25 | mem(all_42_3, all_42_42) = 0))))) | (all_42_40 = empty
% 25.88/4.25 | & ( ~ (all_42_37 = 0) | (all_42_0 = 0 & $lesseq(1,
% 25.88/4.25 | $difference(all_42_1, all_42_39)) & mem(all_42_1,
% 25.88/4.25 | all_42_42) = 0))))))
% 25.88/4.25 |
% 25.88/4.25 | ALPHA: (15) implies:
% 25.88/4.25 | (16) tree(all_42_40)
% 25.88/4.25 | (17) tree(all_42_38)
% 25.88/4.25 | (18) tree(all_42_34)
% 25.88/4.25 | (19) tree(all_42_32)
% 25.88/4.25 | (20) tree(all_42_30)
% 25.88/4.25 | (21) tree(all_42_28)
% 25.88/4.25 | (22) tree(all_42_11)
% 25.88/4.25 | (23) tree(all_42_9)
% 25.88/4.25 | (24) node(all_42_40, all_42_39, all_42_38) = all_42_42
% 25.88/4.25 | (25) size(all_42_42) = all_42_41
% 25.88/4.25 | (26) size(all_42_40) = all_42_36
% 25.88/4.25 | (27) size(all_42_38) = all_42_35
% 25.88/4.25 | (28) mem(all_42_39, all_42_42) = all_42_37
% 25.88/4.25 | (29) (all_42_31 = all_42_38 & node(all_42_34, all_42_33, all_42_32) =
% 25.88/4.25 | all_42_38 & ((all_42_27 = all_42_40 & node(all_42_30, all_42_29,
% 25.88/4.25 | all_42_28) = all_42_40 & (all_42_38 = empty | ~ ($lesseq(1,
% 25.88/4.25 | $difference(all_42_41, all_42_35))) | ~ ($lesseq(0,
% 25.88/4.25 | all_42_41)) | (all_42_25 = 0 & mem(all_42_26, all_42_38) =
% 25.88/4.25 | 0 & max(all_42_39, all_42_26) = all_42_24 & ! [v0: int] : (
% 25.88/4.25 | ~ ($lesseq(1, $difference(v0, all_42_26))) | ~ (mem(v0,
% 25.88/4.25 | all_42_38) = 0)) & (all_42_40 = empty | ~ ($lesseq(1,
% 25.88/4.25 | $difference(all_42_41, all_42_36))) | (all_42_22 = 0 &
% 25.88/4.25 | mem(all_42_21, all_42_42) = all_42_20 & mem(all_42_23,
% 25.88/4.25 | all_42_40) = 0 & max(all_42_23, all_42_24) = all_42_21
% 25.88/4.25 | & ! [v0: int] : ( ~ ($lesseq(1, $difference(v0,
% 25.88/4.25 | all_42_23))) | ~ (mem(v0, all_42_40) = 0)) & (
% 25.88/4.25 | ~ (all_42_20 = 0) | (all_42_18 = 0 & $lesseq(1,
% 25.88/4.25 | $difference(all_42_19, all_42_21)) &
% 25.88/4.25 | mem(all_42_19, all_42_42) = 0))))))) | (all_42_40 =
% 25.88/4.25 | empty & (all_42_38 = empty | ~ ($lesseq(1,
% 25.88/4.25 | $difference(all_42_41, all_42_35))) | ~ ($lesseq(0,
% 25.88/4.25 | all_42_41)) | (all_42_16 = 0 & mem(all_42_15, all_42_42) =
% 25.88/4.25 | all_42_14 & mem(all_42_17, all_42_38) = 0 & max(all_42_17,
% 25.88/4.25 | all_42_39) = all_42_15 & ! [v0: int] : ( ~ ($lesseq(1,
% 25.88/4.25 | $difference(v0, all_42_17))) | ~ (mem(v0, all_42_38)
% 25.88/4.25 | = 0)) & ( ~ (all_42_14 = 0) | (all_42_12 = 0 &
% 25.88/4.25 | $lesseq(1, $difference(all_42_13, all_42_15)) &
% 25.88/4.25 | mem(all_42_13, all_42_42) = 0))))))) | (all_42_38 =
% 25.88/4.26 | empty & ((all_42_8 = all_42_40 & node(all_42_11, all_42_10,
% 25.88/4.26 | all_42_9) = all_42_40 & (all_42_40 = empty | ~ ($lesseq(1,
% 25.88/4.26 | $difference(all_42_41, all_42_36))) | ~ ($lesseq(0,
% 25.88/4.26 | all_42_41)) | (all_42_6 = 0 & mem(all_42_5, all_42_42) =
% 25.88/4.26 | all_42_4 & mem(all_42_7, all_42_40) = 0 & max(all_42_7,
% 25.88/4.26 | all_42_39) = all_42_5 & ! [v0: int] : ( ~ ($lesseq(1,
% 25.88/4.26 | $difference(v0, all_42_7))) | ~ (mem(v0, all_42_40) =
% 25.88/4.26 | 0)) & ( ~ (all_42_4 = 0) | (all_42_2 = 0 & $lesseq(1,
% 25.88/4.26 | $difference(all_42_3, all_42_5)) & mem(all_42_3,
% 25.88/4.26 | all_42_42) = 0))))) | (all_42_40 = empty & ( ~
% 25.88/4.26 | (all_42_37 = 0) | (all_42_0 = 0 & $lesseq(1,
% 25.88/4.26 | $difference(all_42_1, all_42_39)) & mem(all_42_1,
% 25.88/4.26 | all_42_42) = 0)))))
% 25.88/4.26 |
% 25.88/4.26 | GROUND_INST: instantiating (6) with all_42_40, all_42_39, all_42_38,
% 25.88/4.26 | all_42_42, simplifying with (16), (17), (24) gives:
% 25.88/4.26 | (30) ? [v0: int] : ? [v1: int] : (size(all_42_38) = $sum($difference(v0,
% 25.88/4.26 | v1), -1) & size(all_42_40) = v1 & size(all_42_42) = v0)
% 25.88/4.26 |
% 25.88/4.26 | GROUND_INST: instantiating (9) with all_42_39, all_42_40, all_42_38,
% 25.88/4.26 | all_42_42, all_42_37, simplifying with (16), (17), (24), (28)
% 25.88/4.26 | gives:
% 25.88/4.26 | (31) all_42_37 = 0
% 25.88/4.26 |
% 25.88/4.26 | DELTA: instantiating (30) with fresh symbols all_53_0, all_53_1 gives:
% 25.88/4.26 | (32) size(all_42_38) = $sum($difference(all_53_1, all_53_0), -1) &
% 25.88/4.26 | size(all_42_40) = all_53_0 & size(all_42_42) = all_53_1
% 25.88/4.26 |
% 25.88/4.26 | ALPHA: (32) implies:
% 25.88/4.26 | (33) size(all_42_42) = all_53_1
% 25.88/4.26 | (34) size(all_42_40) = all_53_0
% 25.88/4.26 | (35) size(all_42_38) = $sum($difference(all_53_1, all_53_0), -1)
% 25.88/4.26 |
% 25.88/4.26 | GROUND_INST: instantiating (12) with all_42_41, all_53_1, all_42_42,
% 25.88/4.26 | simplifying with (25), (33) gives:
% 25.88/4.26 | (36) all_53_1 = all_42_41
% 25.88/4.26 |
% 25.88/4.26 | GROUND_INST: instantiating (12) with all_42_36, all_53_0, all_42_40,
% 25.88/4.26 | simplifying with (26), (34) gives:
% 25.88/4.26 | (37) all_53_0 = all_42_36
% 25.88/4.26 |
% 25.88/4.26 | GROUND_INST: instantiating (12) with all_42_35, $sum($difference(all_53_1,
% 25.88/4.26 | all_53_0), -1), all_42_38, simplifying with (27), (35) gives:
% 25.88/4.26 | (38) $sum($difference(all_53_0, all_53_1), all_42_35) = -1
% 25.88/4.26 |
% 25.88/4.26 | COMBINE_EQS: (37), (38) imply:
% 25.88/4.26 | (39) $difference($difference(all_53_1, all_42_35), all_42_36) = 1
% 25.88/4.26 |
% 25.88/4.26 | COMBINE_EQS: (36), (39) imply:
% 25.88/4.26 | (40) $difference($sum(all_42_35, all_42_36), all_42_41) = -1
% 25.88/4.26 |
% 25.88/4.26 | SIMP: (40) implies:
% 25.88/4.26 | (41) $difference($sum(all_42_35, all_42_36), all_42_41) = -1
% 25.88/4.26 |
% 25.88/4.26 | REDUCE: (27), (41) imply:
% 25.88/4.26 | (42) size(all_42_38) = $sum($difference(all_42_41, all_42_36), -1)
% 25.88/4.26 |
% 25.88/4.26 | BETA: splitting (29) gives:
% 25.88/4.26 |
% 25.88/4.26 | Case 1:
% 25.88/4.26 | |
% 25.88/4.26 | | (43) all_42_31 = all_42_38 & node(all_42_34, all_42_33, all_42_32) =
% 25.88/4.26 | | all_42_38 & ((all_42_27 = all_42_40 & node(all_42_30, all_42_29,
% 25.88/4.26 | | all_42_28) = all_42_40 & (all_42_38 = empty | ~ ($lesseq(1,
% 25.88/4.26 | | $difference(all_42_41, all_42_35))) | ~ ($lesseq(0,
% 25.88/4.26 | | all_42_41)) | (all_42_25 = 0 & mem(all_42_26, all_42_38) =
% 25.88/4.26 | | 0 & max(all_42_39, all_42_26) = all_42_24 & ! [v0: int] : (
% 25.88/4.26 | | ~ ($lesseq(1, $difference(v0, all_42_26))) | ~ (mem(v0,
% 25.88/4.26 | | all_42_38) = 0)) & (all_42_40 = empty | ~ ($lesseq(1,
% 25.88/4.26 | | $difference(all_42_41, all_42_36))) | (all_42_22 = 0 &
% 25.88/4.26 | | mem(all_42_21, all_42_42) = all_42_20 & mem(all_42_23,
% 25.88/4.26 | | all_42_40) = 0 & max(all_42_23, all_42_24) = all_42_21
% 25.88/4.26 | | & ! [v0: int] : ( ~ ($lesseq(1, $difference(v0,
% 25.88/4.26 | | all_42_23))) | ~ (mem(v0, all_42_40) = 0)) & (
% 25.88/4.26 | | ~ (all_42_20 = 0) | (all_42_18 = 0 & $lesseq(1,
% 25.88/4.26 | | $difference(all_42_19, all_42_21)) &
% 25.88/4.26 | | mem(all_42_19, all_42_42) = 0))))))) | (all_42_40 =
% 25.88/4.26 | | empty & (all_42_38 = empty | ~ ($lesseq(1,
% 25.88/4.26 | | $difference(all_42_41, all_42_35))) | ~ ($lesseq(0,
% 25.88/4.26 | | all_42_41)) | (all_42_16 = 0 & mem(all_42_15, all_42_42) =
% 25.88/4.26 | | all_42_14 & mem(all_42_17, all_42_38) = 0 & max(all_42_17,
% 25.88/4.26 | | all_42_39) = all_42_15 & ! [v0: int] : ( ~ ($lesseq(1,
% 25.88/4.26 | | $difference(v0, all_42_17))) | ~ (mem(v0, all_42_38)
% 25.88/4.26 | | = 0)) & ( ~ (all_42_14 = 0) | (all_42_12 = 0 &
% 25.88/4.26 | | $lesseq(1, $difference(all_42_13, all_42_15)) &
% 25.88/4.26 | | mem(all_42_13, all_42_42) = 0))))))
% 25.88/4.26 | |
% 25.88/4.26 | | ALPHA: (43) implies:
% 25.88/4.27 | | (44) node(all_42_34, all_42_33, all_42_32) = all_42_38
% 25.88/4.27 | | (45) (all_42_27 = all_42_40 & node(all_42_30, all_42_29, all_42_28) =
% 25.88/4.27 | | all_42_40 & (all_42_38 = empty | ~ ($lesseq(1,
% 25.88/4.27 | | $difference(all_42_41, all_42_35))) | ~ ($lesseq(0,
% 25.88/4.27 | | all_42_41)) | (all_42_25 = 0 & mem(all_42_26, all_42_38) = 0
% 25.88/4.27 | | & max(all_42_39, all_42_26) = all_42_24 & ! [v0: int] : ( ~
% 25.88/4.27 | | ($lesseq(1, $difference(v0, all_42_26))) | ~ (mem(v0,
% 25.88/4.27 | | all_42_38) = 0)) & (all_42_40 = empty | ~ ($lesseq(1,
% 25.88/4.27 | | $difference(all_42_41, all_42_36))) | (all_42_22 = 0 &
% 25.88/4.27 | | mem(all_42_21, all_42_42) = all_42_20 & mem(all_42_23,
% 25.88/4.27 | | all_42_40) = 0 & max(all_42_23, all_42_24) = all_42_21 &
% 25.88/4.27 | | ! [v0: int] : ( ~ ($lesseq(1, $difference(v0,
% 25.88/4.27 | | all_42_23))) | ~ (mem(v0, all_42_40) = 0)) & ( ~
% 25.88/4.27 | | (all_42_20 = 0) | (all_42_18 = 0 & $lesseq(1,
% 25.88/4.27 | | $difference(all_42_19, all_42_21)) & mem(all_42_19,
% 25.88/4.27 | | all_42_42) = 0))))))) | (all_42_40 = empty &
% 25.88/4.27 | | (all_42_38 = empty | ~ ($lesseq(1, $difference(all_42_41,
% 25.88/4.27 | | all_42_35))) | ~ ($lesseq(0, all_42_41)) | (all_42_16 = 0
% 25.88/4.27 | | & mem(all_42_15, all_42_42) = all_42_14 & mem(all_42_17,
% 25.88/4.27 | | all_42_38) = 0 & max(all_42_17, all_42_39) = all_42_15 & !
% 25.88/4.27 | | [v0: int] : ( ~ ($lesseq(1, $difference(v0, all_42_17))) | ~
% 25.88/4.27 | | (mem(v0, all_42_38) = 0)) & ( ~ (all_42_14 = 0) | (all_42_12
% 25.88/4.27 | | = 0 & $lesseq(1, $difference(all_42_13, all_42_15)) &
% 25.88/4.27 | | mem(all_42_13, all_42_42) = 0)))))
% 25.88/4.27 | |
% 25.88/4.27 | | GROUND_INST: instantiating (6) with all_42_34, all_42_33, all_42_32,
% 25.88/4.27 | | all_42_38, simplifying with (18), (19), (44) gives:
% 25.88/4.27 | | (46) ? [v0: int] : ? [v1: int] : (size(all_42_32) =
% 25.88/4.27 | | $sum($difference(v0, v1), -1) & size(all_42_34) = v1 &
% 25.88/4.27 | | size(all_42_38) = v0)
% 25.88/4.27 | |
% 25.88/4.27 | | DELTA: instantiating (46) with fresh symbols all_86_0, all_86_1 gives:
% 25.88/4.27 | | (47) size(all_42_32) = $sum($difference(all_86_1, all_86_0), -1) &
% 25.88/4.27 | | size(all_42_34) = all_86_0 & size(all_42_38) = all_86_1
% 25.88/4.27 | |
% 25.88/4.27 | | ALPHA: (47) implies:
% 25.88/4.27 | | (48) size(all_42_38) = all_86_1
% 25.88/4.27 | | (49) size(all_42_34) = all_86_0
% 25.88/4.27 | | (50) size(all_42_32) = $sum($difference(all_86_1, all_86_0), -1)
% 25.88/4.27 | |
% 25.88/4.27 | | GROUND_INST: instantiating (12) with $sum($difference(all_42_41, all_42_36),
% 25.88/4.27 | | -1), all_86_1, all_42_38, simplifying with (42), (48) gives:
% 25.88/4.27 | | (51) $difference($sum(all_86_1, all_42_36), all_42_41) = -1
% 25.88/4.27 | |
% 25.88/4.27 | | REDUCE: (50), (51) imply:
% 25.88/4.27 | | (52) size(all_42_32) = $sum($sum($difference($product(-1, all_86_0),
% 25.88/4.27 | | all_42_36), all_42_41), -2)
% 25.88/4.27 | |
% 25.88/4.27 | | GROUND_INST: instantiating (size_nonneg) with all_42_34, all_86_0,
% 25.88/4.27 | | simplifying with (18), (49) gives:
% 25.88/4.27 | | (53) $lesseq(0, all_86_0)
% 25.88/4.27 | |
% 25.88/4.27 | | GROUND_INST: instantiating (size_nonneg) with all_42_32,
% 25.88/4.27 | | $sum($sum($difference($product(-1, all_86_0), all_42_36),
% 25.88/4.27 | | all_42_41), -2), simplifying with (19), (52) gives:
% 25.88/4.27 | | (54) $lesseq(2, $sum($difference($product(-1, all_86_0), all_42_36),
% 25.88/4.27 | | all_42_41))
% 25.88/4.27 | |
% 25.88/4.27 | | COMBINE_INEQS: (53), (54) imply:
% 25.88/4.27 | | (55) $lesseq(2, $difference(all_42_41, all_42_36))
% 25.88/4.27 | |
% 25.88/4.27 | | BETA: splitting (45) gives:
% 25.88/4.27 | |
% 25.88/4.27 | | Case 1:
% 25.88/4.27 | | |
% 25.88/4.27 | | | (56) all_42_27 = all_42_40 & node(all_42_30, all_42_29, all_42_28) =
% 25.88/4.27 | | | all_42_40 & (all_42_38 = empty | ~ ($lesseq(1,
% 25.88/4.27 | | | $difference(all_42_41, all_42_35))) | ~ ($lesseq(0,
% 25.88/4.27 | | | all_42_41)) | (all_42_25 = 0 & mem(all_42_26, all_42_38) = 0
% 25.88/4.27 | | | & max(all_42_39, all_42_26) = all_42_24 & ! [v0: int] : ( ~
% 25.88/4.27 | | | ($lesseq(1, $difference(v0, all_42_26))) | ~ (mem(v0,
% 25.88/4.27 | | | all_42_38) = 0)) & (all_42_40 = empty | ~ ($lesseq(1,
% 25.88/4.27 | | | $difference(all_42_41, all_42_36))) | (all_42_22 = 0 &
% 25.88/4.27 | | | mem(all_42_21, all_42_42) = all_42_20 & mem(all_42_23,
% 25.88/4.27 | | | all_42_40) = 0 & max(all_42_23, all_42_24) = all_42_21 &
% 25.88/4.27 | | | ! [v0: int] : ( ~ ($lesseq(1, $difference(v0,
% 25.88/4.27 | | | all_42_23))) | ~ (mem(v0, all_42_40) = 0)) & ( ~
% 25.88/4.27 | | | (all_42_20 = 0) | (all_42_18 = 0 & $lesseq(1,
% 25.88/4.27 | | | $difference(all_42_19, all_42_21)) & mem(all_42_19,
% 25.88/4.27 | | | all_42_42) = 0))))))
% 25.88/4.28 | | |
% 25.88/4.28 | | | ALPHA: (56) implies:
% 25.88/4.28 | | | (57) node(all_42_30, all_42_29, all_42_28) = all_42_40
% 25.88/4.28 | | | (58) all_42_38 = empty | ~ ($lesseq(1, $difference(all_42_41,
% 25.88/4.28 | | | all_42_35))) | ~ ($lesseq(0, all_42_41)) | (all_42_25 = 0 &
% 25.88/4.28 | | | mem(all_42_26, all_42_38) = 0 & max(all_42_39, all_42_26) =
% 25.88/4.28 | | | all_42_24 & ! [v0: int] : ( ~ ($lesseq(1, $difference(v0,
% 25.88/4.28 | | | all_42_26))) | ~ (mem(v0, all_42_38) = 0)) & (all_42_40
% 25.88/4.28 | | | = empty | ~ ($lesseq(1, $difference(all_42_41, all_42_36))) |
% 25.88/4.28 | | | (all_42_22 = 0 & mem(all_42_21, all_42_42) = all_42_20 &
% 25.88/4.28 | | | mem(all_42_23, all_42_40) = 0 & max(all_42_23, all_42_24) =
% 25.88/4.28 | | | all_42_21 & ! [v0: int] : ( ~ ($lesseq(1, $difference(v0,
% 25.88/4.28 | | | all_42_23))) | ~ (mem(v0, all_42_40) = 0)) & ( ~
% 25.88/4.28 | | | (all_42_20 = 0) | (all_42_18 = 0 & $lesseq(1,
% 25.88/4.28 | | | $difference(all_42_19, all_42_21)) & mem(all_42_19,
% 25.88/4.28 | | | all_42_42) = 0)))))
% 25.88/4.28 | | |
% 25.88/4.28 | | | GROUND_INST: instantiating (6) with all_42_30, all_42_29, all_42_28,
% 25.88/4.28 | | | all_42_40, simplifying with (20), (21), (57) gives:
% 25.88/4.28 | | | (59) ? [v0: int] : ? [v1: int] : (size(all_42_28) =
% 25.88/4.28 | | | $sum($difference(v0, v1), -1) & size(all_42_30) = v1 &
% 25.88/4.28 | | | size(all_42_40) = v0)
% 25.88/4.28 | | |
% 25.88/4.28 | | | DELTA: instantiating (59) with fresh symbols all_138_0, all_138_1 gives:
% 25.88/4.28 | | | (60) size(all_42_28) = $sum($difference(all_138_1, all_138_0), -1) &
% 25.88/4.28 | | | size(all_42_30) = all_138_0 & size(all_42_40) = all_138_1
% 25.88/4.28 | | |
% 25.88/4.28 | | | ALPHA: (60) implies:
% 25.88/4.28 | | | (61) size(all_42_40) = all_138_1
% 25.88/4.28 | | | (62) size(all_42_30) = all_138_0
% 25.88/4.28 | | | (63) size(all_42_28) = $sum($difference(all_138_1, all_138_0), -1)
% 25.88/4.28 | | |
% 25.88/4.28 | | | GROUND_INST: instantiating (12) with all_42_36, all_138_1, all_42_40,
% 25.88/4.28 | | | simplifying with (26), (61) gives:
% 25.88/4.28 | | | (64) all_138_1 = all_42_36
% 25.88/4.28 | | |
% 25.88/4.28 | | | REDUCE: (63), (64) imply:
% 25.88/4.28 | | | (65) size(all_42_28) = $sum($difference(all_42_36, all_138_0), -1)
% 25.88/4.28 | | |
% 25.88/4.28 | | | GROUND_INST: instantiating (size_nonneg) with all_42_30, all_138_0,
% 25.88/4.28 | | | simplifying with (20), (62) gives:
% 25.88/4.28 | | | (66) $lesseq(0, all_138_0)
% 25.88/4.28 | | |
% 25.88/4.28 | | | GROUND_INST: instantiating (size_nonneg) with all_42_28,
% 25.88/4.28 | | | $sum($difference(all_42_36, all_138_0), -1), simplifying with
% 25.88/4.28 | | | (21), (65) gives:
% 25.88/4.28 | | | (67) $lesseq(1, $difference(all_42_36, all_138_0))
% 25.88/4.28 | | |
% 25.88/4.28 | | | COMBINE_INEQS: (66), (67) imply:
% 25.88/4.28 | | | (68) $lesseq(1, all_42_36)
% 25.88/4.28 | | |
% 25.88/4.28 | | | COMBINE_INEQS: (55), (68) imply:
% 25.88/4.28 | | | (69) $lesseq(3, all_42_41)
% 25.88/4.28 | | |
% 25.88/4.28 | | | BETA: splitting (58) gives:
% 25.88/4.28 | | |
% 25.88/4.28 | | | Case 1:
% 25.88/4.28 | | | |
% 25.88/4.28 | | | | (70) $lesseq(all_42_41, -1)
% 25.88/4.28 | | | |
% 25.88/4.28 | | | | COMBINE_INEQS: (69), (70) imply:
% 25.88/4.28 | | | | (71) $false
% 25.88/4.28 | | | |
% 25.88/4.28 | | | | CLOSE: (71) is inconsistent.
% 25.88/4.28 | | | |
% 25.88/4.28 | | | Case 2:
% 25.88/4.28 | | | |
% 25.88/4.28 | | | | (72) all_42_38 = empty | ~ ($lesseq(1, $difference(all_42_41,
% 25.88/4.28 | | | | all_42_35))) | (all_42_25 = 0 & mem(all_42_26, all_42_38)
% 25.88/4.28 | | | | = 0 & max(all_42_39, all_42_26) = all_42_24 & ! [v0: int] : (
% 25.88/4.28 | | | | ~ ($lesseq(1, $difference(v0, all_42_26))) | ~ (mem(v0,
% 25.88/4.28 | | | | all_42_38) = 0)) & (all_42_40 = empty | ~ ($lesseq(1,
% 25.88/4.28 | | | | $difference(all_42_41, all_42_36))) | (all_42_22 = 0 &
% 25.88/4.28 | | | | mem(all_42_21, all_42_42) = all_42_20 & mem(all_42_23,
% 25.88/4.28 | | | | all_42_40) = 0 & max(all_42_23, all_42_24) = all_42_21 &
% 25.88/4.28 | | | | ! [v0: int] : ( ~ ($lesseq(1, $difference(v0,
% 25.88/4.28 | | | | all_42_23))) | ~ (mem(v0, all_42_40) = 0)) & ( ~
% 25.88/4.28 | | | | (all_42_20 = 0) | (all_42_18 = 0 & $lesseq(1,
% 25.88/4.28 | | | | $difference(all_42_19, all_42_21)) & mem(all_42_19,
% 25.88/4.28 | | | | all_42_42) = 0)))))
% 25.88/4.28 | | | |
% 25.88/4.28 | | | | BETA: splitting (72) gives:
% 25.88/4.28 | | | |
% 25.88/4.28 | | | | Case 1:
% 25.88/4.28 | | | | |
% 25.88/4.28 | | | | | (73) $lesseq(all_42_41, all_42_35)
% 25.88/4.28 | | | | |
% 25.88/4.28 | | | | | REDUCE: (41), (73) imply:
% 25.88/4.28 | | | | | (74) $lesseq(all_42_36, -1)
% 25.88/4.28 | | | | |
% 25.88/4.28 | | | | | COMBINE_INEQS: (68), (74) imply:
% 25.88/4.28 | | | | | (75) $false
% 25.88/4.28 | | | | |
% 25.88/4.28 | | | | | CLOSE: (75) is inconsistent.
% 25.88/4.28 | | | | |
% 25.88/4.28 | | | | Case 2:
% 25.88/4.28 | | | | |
% 25.88/4.28 | | | | | (76) all_42_38 = empty | (all_42_25 = 0 & mem(all_42_26, all_42_38)
% 25.88/4.28 | | | | | = 0 & max(all_42_39, all_42_26) = all_42_24 & ! [v0: int] :
% 25.88/4.28 | | | | | ( ~ ($lesseq(1, $difference(v0, all_42_26))) | ~ (mem(v0,
% 25.88/4.28 | | | | | all_42_38) = 0)) & (all_42_40 = empty | ~ ($lesseq(1,
% 25.88/4.28 | | | | | $difference(all_42_41, all_42_36))) | (all_42_22 = 0 &
% 25.88/4.28 | | | | | mem(all_42_21, all_42_42) = all_42_20 & mem(all_42_23,
% 25.88/4.28 | | | | | all_42_40) = 0 & max(all_42_23, all_42_24) = all_42_21
% 25.88/4.28 | | | | | & ! [v0: int] : ( ~ ($lesseq(1, $difference(v0,
% 25.88/4.28 | | | | | all_42_23))) | ~ (mem(v0, all_42_40) = 0)) & (
% 25.88/4.28 | | | | | ~ (all_42_20 = 0) | (all_42_18 = 0 & $lesseq(1,
% 25.88/4.28 | | | | | $difference(all_42_19, all_42_21)) &
% 25.88/4.28 | | | | | mem(all_42_19, all_42_42) = 0)))))
% 25.88/4.28 | | | | |
% 25.88/4.29 | | | | | BETA: splitting (76) gives:
% 25.88/4.29 | | | | |
% 25.88/4.29 | | | | | Case 1:
% 25.88/4.29 | | | | | |
% 25.88/4.29 | | | | | | (77) all_42_38 = empty
% 25.88/4.29 | | | | | |
% 25.88/4.29 | | | | | | REDUCE: (42), (77) imply:
% 25.88/4.29 | | | | | | (78) size(empty) = $sum($difference(all_42_41, all_42_36), -1)
% 25.88/4.29 | | | | | |
% 25.88/4.29 | | | | | | GROUND_INST: instantiating (12) with 0, $sum($difference(all_42_41,
% 25.88/4.29 | | | | | | all_42_36), -1), empty, simplifying with (5), (78)
% 25.88/4.29 | | | | | | gives:
% 25.88/4.29 | | | | | | (79) $difference(all_42_36, all_42_41) = -1
% 25.88/4.29 | | | | | |
% 25.88/4.29 | | | | | | REDUCE: (54), (79) imply:
% 25.88/4.29 | | | | | | (80) $lesseq(all_86_0, -1)
% 25.88/4.29 | | | | | |
% 25.88/4.29 | | | | | | COMBINE_INEQS: (53), (80) imply:
% 25.88/4.29 | | | | | | (81) $false
% 25.88/4.29 | | | | | |
% 25.88/4.29 | | | | | | CLOSE: (81) is inconsistent.
% 25.88/4.29 | | | | | |
% 25.88/4.29 | | | | | Case 2:
% 25.88/4.29 | | | | | |
% 25.88/4.29 | | | | | | (82) all_42_25 = 0 & mem(all_42_26, all_42_38) = 0 &
% 25.88/4.29 | | | | | | max(all_42_39, all_42_26) = all_42_24 & ! [v0: int] : ( ~
% 25.88/4.29 | | | | | | ($lesseq(1, $difference(v0, all_42_26))) | ~ (mem(v0,
% 25.88/4.29 | | | | | | all_42_38) = 0)) & (all_42_40 = empty | ~ ($lesseq(1,
% 25.88/4.29 | | | | | | $difference(all_42_41, all_42_36))) | (all_42_22 = 0 &
% 25.88/4.29 | | | | | | mem(all_42_21, all_42_42) = all_42_20 & mem(all_42_23,
% 25.88/4.29 | | | | | | all_42_40) = 0 & max(all_42_23, all_42_24) = all_42_21
% 25.88/4.29 | | | | | | & ! [v0: int] : ( ~ ($lesseq(1, $difference(v0,
% 25.88/4.29 | | | | | | all_42_23))) | ~ (mem(v0, all_42_40) = 0)) & (
% 25.88/4.29 | | | | | | ~ (all_42_20 = 0) | (all_42_18 = 0 & $lesseq(1,
% 25.88/4.29 | | | | | | $difference(all_42_19, all_42_21)) &
% 25.88/4.29 | | | | | | mem(all_42_19, all_42_42) = 0))))
% 25.88/4.29 | | | | | |
% 25.88/4.29 | | | | | | ALPHA: (82) implies:
% 25.88/4.29 | | | | | | (83) max(all_42_39, all_42_26) = all_42_24
% 25.88/4.29 | | | | | | (84) mem(all_42_26, all_42_38) = 0
% 25.88/4.29 | | | | | | (85) all_42_40 = empty | ~ ($lesseq(1, $difference(all_42_41,
% 25.88/4.29 | | | | | | all_42_36))) | (all_42_22 = 0 & mem(all_42_21,
% 25.88/4.29 | | | | | | all_42_42) = all_42_20 & mem(all_42_23, all_42_40) = 0 &
% 25.88/4.29 | | | | | | max(all_42_23, all_42_24) = all_42_21 & ! [v0: int] : ( ~
% 25.88/4.29 | | | | | | ($lesseq(1, $difference(v0, all_42_23))) | ~ (mem(v0,
% 25.88/4.29 | | | | | | all_42_40) = 0)) & ( ~ (all_42_20 = 0) | (all_42_18
% 25.88/4.29 | | | | | | = 0 & $lesseq(1, $difference(all_42_19, all_42_21)) &
% 25.88/4.29 | | | | | | mem(all_42_19, all_42_42) = 0)))
% 25.88/4.29 | | | | | | (86) ! [v0: int] : ( ~ ($lesseq(1, $difference(v0, all_42_26)))
% 25.88/4.29 | | | | | | | ~ (mem(v0, all_42_38) = 0))
% 25.88/4.29 | | | | | |
% 25.88/4.29 | | | | | | GROUND_INST: instantiating (max_y) with all_42_39, all_42_26,
% 25.88/4.29 | | | | | | all_42_24, simplifying with (83) gives:
% 25.88/4.29 | | | | | | (87) all_42_24 = all_42_26 | ~ ($lesseq(all_42_39, all_42_26))
% 25.88/4.29 | | | | | |
% 25.88/4.29 | | | | | | GROUND_INST: instantiating (max_x) with all_42_39, all_42_26,
% 25.88/4.29 | | | | | | all_42_24, simplifying with (83) gives:
% 25.88/4.29 | | | | | | (88) all_42_24 = all_42_39 | ~ ($lesseq(all_42_26, all_42_39))
% 25.88/4.29 | | | | | |
% 25.88/4.29 | | | | | | GROUND_INST: instantiating (1) with all_42_39, all_42_26, all_42_24,
% 25.88/4.29 | | | | | | simplifying with (83) gives:
% 25.88/4.29 | | | | | | (89) $lesseq(all_42_39, all_42_24)
% 25.88/4.29 | | | | | |
% 25.88/4.29 | | | | | | GROUND_INST: instantiating (4) with all_42_26, all_42_39, all_42_24,
% 25.88/4.29 | | | | | | simplifying with (83) gives:
% 25.88/4.29 | | | | | | (90) ~ ($lesseq(all_42_39, all_42_26)) | max(all_42_26,
% 25.88/4.29 | | | | | | all_42_39) = all_42_24
% 25.88/4.29 | | | | | |
% 25.88/4.29 | | | | | | BETA: splitting (85) gives:
% 25.88/4.29 | | | | | |
% 25.88/4.29 | | | | | | Case 1:
% 25.88/4.29 | | | | | | |
% 25.88/4.29 | | | | | | | (91) $lesseq(all_42_41, all_42_36)
% 25.88/4.29 | | | | | | |
% 25.88/4.29 | | | | | | | COMBINE_INEQS: (55), (91) imply:
% 25.88/4.29 | | | | | | | (92) $false
% 25.88/4.29 | | | | | | |
% 25.88/4.29 | | | | | | | CLOSE: (92) is inconsistent.
% 25.88/4.29 | | | | | | |
% 25.88/4.29 | | | | | | Case 2:
% 25.88/4.29 | | | | | | |
% 25.88/4.29 | | | | | | | (93) all_42_40 = empty | (all_42_22 = 0 & mem(all_42_21,
% 25.88/4.29 | | | | | | | all_42_42) = all_42_20 & mem(all_42_23, all_42_40) = 0
% 25.88/4.29 | | | | | | | & max(all_42_23, all_42_24) = all_42_21 & ! [v0: int] :
% 25.88/4.29 | | | | | | | ( ~ ($lesseq(1, $difference(v0, all_42_23))) | ~
% 25.88/4.29 | | | | | | | (mem(v0, all_42_40) = 0)) & ( ~ (all_42_20 = 0) |
% 25.88/4.29 | | | | | | | (all_42_18 = 0 & $lesseq(1, $difference(all_42_19,
% 25.88/4.29 | | | | | | | all_42_21)) & mem(all_42_19, all_42_42) = 0)))
% 25.88/4.29 | | | | | | |
% 25.88/4.29 | | | | | | | BETA: splitting (87) gives:
% 25.88/4.29 | | | | | | |
% 25.88/4.29 | | | | | | | Case 1:
% 25.88/4.29 | | | | | | | |
% 25.88/4.29 | | | | | | | | (94) $lesseq(1, $difference(all_42_39, all_42_26))
% 25.88/4.29 | | | | | | | |
% 25.88/4.29 | | | | | | | | BETA: splitting (88) gives:
% 25.88/4.29 | | | | | | | |
% 25.88/4.29 | | | | | | | | Case 1:
% 25.88/4.29 | | | | | | | | |
% 25.88/4.29 | | | | | | | | | (95) $lesseq(1, $difference(all_42_26, all_42_39))
% 25.88/4.29 | | | | | | | | |
% 25.88/4.29 | | | | | | | | | COMBINE_INEQS: (94), (95) imply:
% 25.88/4.29 | | | | | | | | | (96) $false
% 25.88/4.29 | | | | | | | | |
% 25.88/4.29 | | | | | | | | | CLOSE: (96) is inconsistent.
% 25.88/4.29 | | | | | | | | |
% 25.88/4.29 | | | | | | | | Case 2:
% 25.88/4.29 | | | | | | | | |
% 25.88/4.29 | | | | | | | | | (97) all_42_24 = all_42_39
% 25.88/4.29 | | | | | | | | |
% 25.88/4.29 | | | | | | | | | BETA: splitting (93) gives:
% 25.88/4.29 | | | | | | | | |
% 25.88/4.29 | | | | | | | | | Case 1:
% 25.88/4.29 | | | | | | | | | |
% 25.88/4.29 | | | | | | | | | | (98) all_42_40 = empty
% 25.88/4.29 | | | | | | | | | |
% 25.88/4.29 | | | | | | | | | | REDUCE: (26), (98) imply:
% 25.88/4.29 | | | | | | | | | | (99) size(empty) = all_42_36
% 25.88/4.29 | | | | | | | | | |
% 25.88/4.29 | | | | | | | | | | REF_CLOSE: (5), (12), (66), (67), (99) are inconsistent by
% 25.88/4.29 | | | | | | | | | | sub-proof #4.
% 25.88/4.29 | | | | | | | | | |
% 25.88/4.29 | | | | | | | | | Case 2:
% 25.88/4.29 | | | | | | | | | |
% 25.88/4.29 | | | | | | | | | | (100) all_42_22 = 0 & mem(all_42_21, all_42_42) =
% 25.88/4.29 | | | | | | | | | | all_42_20 & mem(all_42_23, all_42_40) = 0 &
% 25.88/4.29 | | | | | | | | | | max(all_42_23, all_42_24) = all_42_21 & ! [v0:
% 25.88/4.29 | | | | | | | | | | int] : ( ~ ($lesseq(1, $difference(v0,
% 25.88/4.29 | | | | | | | | | | all_42_23))) | ~ (mem(v0, all_42_40) = 0))
% 25.88/4.29 | | | | | | | | | | & ( ~ (all_42_20 = 0) | (all_42_18 = 0 & $lesseq(1,
% 25.88/4.29 | | | | | | | | | | $difference(all_42_19, all_42_21)) &
% 25.88/4.29 | | | | | | | | | | mem(all_42_19, all_42_42) = 0))
% 25.88/4.29 | | | | | | | | | |
% 25.88/4.29 | | | | | | | | | | ALPHA: (100) implies:
% 25.88/4.29 | | | | | | | | | | (101) max(all_42_23, all_42_24) = all_42_21
% 25.88/4.29 | | | | | | | | | | (102) mem(all_42_23, all_42_40) = 0
% 25.88/4.29 | | | | | | | | | | (103) mem(all_42_21, all_42_42) = all_42_20
% 25.88/4.29 | | | | | | | | | | (104) ~ (all_42_20 = 0) | (all_42_18 = 0 & $lesseq(1,
% 25.88/4.29 | | | | | | | | | | $difference(all_42_19, all_42_21)) &
% 25.88/4.29 | | | | | | | | | | mem(all_42_19, all_42_42) = 0)
% 25.88/4.29 | | | | | | | | | | (105) ! [v0: int] : ( ~ ($lesseq(1, $difference(v0,
% 25.88/4.29 | | | | | | | | | | all_42_23))) | ~ (mem(v0, all_42_40) = 0))
% 25.88/4.29 | | | | | | | | | |
% 25.88/4.29 | | | | | | | | | | REDUCE: (97), (101) imply:
% 25.88/4.29 | | | | | | | | | | (106) max(all_42_23, all_42_39) = all_42_21
% 25.88/4.29 | | | | | | | | | |
% 25.88/4.29 | | | | | | | | | | GROUND_INST: instantiating (max_y) with all_42_23, all_42_39,
% 25.88/4.29 | | | | | | | | | | all_42_21, simplifying with (106) gives:
% 25.88/4.29 | | | | | | | | | | (107) all_42_21 = all_42_39 | ~ ($lesseq(all_42_23,
% 25.88/4.29 | | | | | | | | | | all_42_39))
% 25.88/4.29 | | | | | | | | | |
% 25.88/4.29 | | | | | | | | | | GROUND_INST: instantiating (max_x) with all_42_23, all_42_39,
% 25.88/4.29 | | | | | | | | | | all_42_21, simplifying with (106) gives:
% 25.88/4.29 | | | | | | | | | | (108) all_42_21 = all_42_23 | ~ ($lesseq(all_42_39,
% 25.88/4.29 | | | | | | | | | | all_42_23))
% 25.88/4.29 | | | | | | | | | |
% 25.88/4.29 | | | | | | | | | | GROUND_INST: instantiating (1) with all_42_23, all_42_39,
% 25.88/4.29 | | | | | | | | | | all_42_21, simplifying with (106) gives:
% 25.88/4.29 | | | | | | | | | | (109) $lesseq(all_42_23, all_42_21)
% 25.88/4.29 | | | | | | | | | |
% 25.88/4.29 | | | | | | | | | | GROUND_INST: instantiating (9) with all_42_39, all_42_40,
% 25.88/4.29 | | | | | | | | | | all_42_38, all_42_42, all_42_20, simplifying with
% 25.88/4.29 | | | | | | | | | | (16), (17), (24) gives:
% 25.88/4.30 | | | | | | | | | | (110) all_42_20 = 0 | ~ (mem(all_42_39, all_42_42) =
% 25.88/4.30 | | | | | | | | | | all_42_20)
% 25.88/4.30 | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | GROUND_INST: instantiating (10) with all_42_21, all_42_40,
% 25.88/4.30 | | | | | | | | | | all_42_39, all_42_38, all_42_42, all_42_20,
% 25.88/4.30 | | | | | | | | | | simplifying with (16), (17), (24), (103) gives:
% 25.88/4.30 | | | | | | | | | | (111) all_42_20 = 0 | ? [v0: int] : ? [v1: int] : ( ~
% 25.88/4.30 | | | | | | | | | | (v1 = 0) & ~ (v0 = 0) & mem(all_42_21,
% 25.88/4.30 | | | | | | | | | | all_42_38) = v1 & mem(all_42_21, all_42_40) =
% 25.88/4.30 | | | | | | | | | | v0)
% 25.88/4.30 | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | BETA: splitting (104) gives:
% 25.88/4.30 | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | Case 1:
% 25.88/4.30 | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | (112) ~ (all_42_20 = 0)
% 25.88/4.30 | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | BETA: splitting (111) gives:
% 25.88/4.30 | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | Case 1:
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | (113) all_42_20 = 0
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | REDUCE: (112), (113) imply:
% 25.88/4.30 | | | | | | | | | | | | (114) $false
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | CLOSE: (114) is inconsistent.
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | Case 2:
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | (115) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~
% 25.88/4.30 | | | | | | | | | | | | (v0 = 0) & mem(all_42_21, all_42_38) = v1 &
% 25.88/4.30 | | | | | | | | | | | | mem(all_42_21, all_42_40) = v0)
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | DELTA: instantiating (115) with fresh symbols all_278_0,
% 25.88/4.30 | | | | | | | | | | | | all_278_1 gives:
% 25.88/4.30 | | | | | | | | | | | | (116) ~ (all_278_0 = 0) & ~ (all_278_1 = 0) &
% 25.88/4.30 | | | | | | | | | | | | mem(all_42_21, all_42_38) = all_278_0 &
% 25.88/4.30 | | | | | | | | | | | | mem(all_42_21, all_42_40) = all_278_1
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | ALPHA: (116) implies:
% 25.88/4.30 | | | | | | | | | | | | (117) ~ (all_278_1 = 0)
% 25.88/4.30 | | | | | | | | | | | | (118) mem(all_42_21, all_42_40) = all_278_1
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_278_1, all_42_40,
% 25.88/4.30 | | | | | | | | | | | | all_42_23, simplifying with (102) gives:
% 25.88/4.30 | | | | | | | | | | | | (119) all_278_1 = 0 | ~ (mem(all_42_23, all_42_40) =
% 25.88/4.30 | | | | | | | | | | | | all_278_1)
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | BETA: splitting (107) gives:
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | Case 1:
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | (120) $lesseq(1, $difference(all_42_23, all_42_39))
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | BETA: splitting (108) gives:
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | Case 1:
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | (121) $lesseq(1, $difference(all_42_39, all_42_23))
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | COMBINE_INEQS: (120), (121) imply:
% 25.88/4.30 | | | | | | | | | | | | | | (122) $false
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | CLOSE: (122) is inconsistent.
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | Case 2:
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | (123) all_42_21 = all_42_23
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | REDUCE: (118), (123) imply:
% 25.88/4.30 | | | | | | | | | | | | | | (124) mem(all_42_23, all_42_40) = all_278_1
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | Case 1:
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | | (125) ~ (mem(all_42_23, all_42_40) = all_278_1)
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | | PRED_UNIFY: (124), (125) imply:
% 25.88/4.30 | | | | | | | | | | | | | | | (126) $false
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | | CLOSE: (126) is inconsistent.
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | Case 2:
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | | (127) all_278_1 = 0
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | | REDUCE: (117), (127) imply:
% 25.88/4.30 | | | | | | | | | | | | | | | (128) $false
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | | CLOSE: (128) is inconsistent.
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | End of split
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | End of split
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | Case 2:
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | (129) all_42_21 = all_42_39
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | REDUCE: (103), (129) imply:
% 25.88/4.30 | | | | | | | | | | | | | (130) mem(all_42_39, all_42_42) = all_42_20
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | BETA: splitting (110) gives:
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | Case 1:
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | (131) ~ (mem(all_42_39, all_42_42) = all_42_20)
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | PRED_UNIFY: (130), (131) imply:
% 25.88/4.30 | | | | | | | | | | | | | | (132) $false
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | CLOSE: (132) is inconsistent.
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | Case 2:
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | (133) all_42_20 = 0
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | REDUCE: (112), (133) imply:
% 25.88/4.30 | | | | | | | | | | | | | | (134) $false
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | CLOSE: (134) is inconsistent.
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | End of split
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | End of split
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | End of split
% 25.88/4.30 | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | Case 2:
% 25.88/4.30 | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | (135) all_42_18 = 0 & $lesseq(1, $difference(all_42_19,
% 25.88/4.30 | | | | | | | | | | | all_42_21)) & mem(all_42_19, all_42_42) = 0
% 25.88/4.30 | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | ALPHA: (135) implies:
% 25.88/4.30 | | | | | | | | | | | (136) $lesseq(1, $difference(all_42_19, all_42_21))
% 25.88/4.30 | | | | | | | | | | | (137) mem(all_42_19, all_42_42) = 0
% 25.88/4.30 | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | GROUND_INST: instantiating (8) with all_42_19, all_42_40,
% 25.88/4.30 | | | | | | | | | | | all_42_39, all_42_38, all_42_42, simplifying with
% 25.88/4.30 | | | | | | | | | | | (16), (17), (24), (137) gives:
% 25.88/4.30 | | | | | | | | | | | (138) all_42_19 = all_42_39 | ? [v0: any] : ? [v1:
% 25.88/4.30 | | | | | | | | | | | any] : (mem(all_42_19, all_42_38) = v1 &
% 25.88/4.30 | | | | | | | | | | | mem(all_42_19, all_42_40) = v0 & (v1 = 0 | v0 =
% 25.88/4.30 | | | | | | | | | | | 0))
% 25.88/4.30 | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | BETA: splitting (107) gives:
% 25.88/4.30 | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | Case 1:
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | (139) $lesseq(1, $difference(all_42_23, all_42_39))
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | BETA: splitting (108) gives:
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | Case 1:
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | (140) $lesseq(1, $difference(all_42_39, all_42_23))
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | COMBINE_INEQS: (139), (140) imply:
% 25.88/4.30 | | | | | | | | | | | | | (141) $false
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | CLOSE: (141) is inconsistent.
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | Case 2:
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | (142) all_42_21 = all_42_23
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | REDUCE: (136), (142) imply:
% 25.88/4.30 | | | | | | | | | | | | | (143) $lesseq(1, $difference(all_42_19, all_42_23))
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | BETA: splitting (138) gives:
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | Case 1:
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | (144) all_42_19 = all_42_39
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | REDUCE: (143), (144) imply:
% 25.88/4.30 | | | | | | | | | | | | | | (145) $lesseq(1, $difference(all_42_39, all_42_23))
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | COMBINE_INEQS: (139), (145) imply:
% 25.88/4.30 | | | | | | | | | | | | | | (146) $false
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | CLOSE: (146) is inconsistent.
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | Case 2:
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | (147) ? [v0: any] : ? [v1: any] : (mem(all_42_19,
% 25.88/4.30 | | | | | | | | | | | | | | all_42_38) = v1 & mem(all_42_19, all_42_40) =
% 25.88/4.30 | | | | | | | | | | | | | | v0 & (v1 = 0 | v0 = 0))
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | DELTA: instantiating (147) with fresh symbols all_366_0,
% 25.88/4.30 | | | | | | | | | | | | | | all_366_1 gives:
% 25.88/4.30 | | | | | | | | | | | | | | (148) mem(all_42_19, all_42_38) = all_366_0 &
% 25.88/4.30 | | | | | | | | | | | | | | mem(all_42_19, all_42_40) = all_366_1 & (all_366_0
% 25.88/4.30 | | | | | | | | | | | | | | = 0 | all_366_1 = 0)
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | ALPHA: (148) implies:
% 25.88/4.30 | | | | | | | | | | | | | | (149) mem(all_42_19, all_42_40) = all_366_1
% 25.88/4.30 | | | | | | | | | | | | | | (150) mem(all_42_19, all_42_38) = all_366_0
% 25.88/4.30 | | | | | | | | | | | | | | (151) all_366_0 = 0 | all_366_1 = 0
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | Case 1:
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | | (152) all_366_0 = 0
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | | REDUCE: (150), (152) imply:
% 25.88/4.30 | | | | | | | | | | | | | | | (153) mem(all_42_19, all_42_38) = 0
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | | GROUND_INST: instantiating (86) with all_42_19, simplifying
% 25.88/4.30 | | | | | | | | | | | | | | | with (153) gives:
% 25.88/4.30 | | | | | | | | | | | | | | | (154) $lesseq(all_42_19, all_42_26)
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | | COMBINE_INEQS: (143), (154) imply:
% 25.88/4.30 | | | | | | | | | | | | | | | (155) $lesseq(1, $difference(all_42_26, all_42_23))
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | | COMBINE_INEQS: (139), (155) imply:
% 25.88/4.30 | | | | | | | | | | | | | | | (156) $lesseq(2, $difference(all_42_26, all_42_39))
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | | COMBINE_INEQS: (94), (156) imply:
% 25.88/4.30 | | | | | | | | | | | | | | | (157) $false
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | | CLOSE: (157) is inconsistent.
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | Case 2:
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | | (158) all_366_1 = 0
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | | REDUCE: (149), (158) imply:
% 25.88/4.30 | | | | | | | | | | | | | | | (159) mem(all_42_19, all_42_40) = 0
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | | REF_CLOSE: (105), (143), (159) are inconsistent by sub-proof
% 25.88/4.30 | | | | | | | | | | | | | | | #3.
% 25.88/4.30 | | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | | End of split
% 25.88/4.30 | | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | End of split
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | End of split
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | Case 2:
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | (160) all_42_21 = all_42_39
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | REDUCE: (136), (160) imply:
% 25.88/4.30 | | | | | | | | | | | | (161) $lesseq(1, $difference(all_42_19, all_42_39))
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | REDUCE: (109), (160) imply:
% 25.88/4.30 | | | | | | | | | | | | (162) $lesseq(all_42_23, all_42_39)
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | BETA: splitting (138) gives:
% 25.88/4.30 | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | Case 1:
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | (163) all_42_19 = all_42_39
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | REDUCE: (161), (163) imply:
% 25.88/4.30 | | | | | | | | | | | | | (164) $false
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | | CLOSE: (164) is inconsistent.
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.30 | | | | | | | | | | | | Case 2:
% 25.88/4.30 | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | (165) ? [v0: any] : ? [v1: any] : (mem(all_42_19,
% 25.88/4.31 | | | | | | | | | | | | | all_42_38) = v1 & mem(all_42_19, all_42_40) =
% 25.88/4.31 | | | | | | | | | | | | | v0 & (v1 = 0 | v0 = 0))
% 25.88/4.31 | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | DELTA: instantiating (165) with fresh symbols all_293_0,
% 25.88/4.31 | | | | | | | | | | | | | all_293_1 gives:
% 25.88/4.31 | | | | | | | | | | | | | (166) mem(all_42_19, all_42_38) = all_293_0 &
% 25.88/4.31 | | | | | | | | | | | | | mem(all_42_19, all_42_40) = all_293_1 & (all_293_0
% 25.88/4.31 | | | | | | | | | | | | | = 0 | all_293_1 = 0)
% 25.88/4.31 | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | ALPHA: (166) implies:
% 25.88/4.31 | | | | | | | | | | | | | (167) mem(all_42_19, all_42_40) = all_293_1
% 25.88/4.31 | | | | | | | | | | | | | (168) mem(all_42_19, all_42_38) = all_293_0
% 25.88/4.31 | | | | | | | | | | | | | (169) all_293_0 = 0 | all_293_1 = 0
% 25.88/4.31 | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_293_1, all_42_40,
% 25.88/4.31 | | | | | | | | | | | | | all_42_23, simplifying with (102) gives:
% 25.88/4.31 | | | | | | | | | | | | | (170) all_293_1 = 0 | ~ (mem(all_42_23, all_42_40) =
% 25.88/4.31 | | | | | | | | | | | | | all_293_1)
% 25.88/4.31 | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_293_0, all_42_38,
% 25.88/4.31 | | | | | | | | | | | | | all_42_26, simplifying with (84) gives:
% 25.88/4.31 | | | | | | | | | | | | | (171) all_293_0 = 0 | ~ (mem(all_42_26, all_42_38) =
% 25.88/4.31 | | | | | | | | | | | | | all_293_0)
% 25.88/4.31 | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | BETA: splitting (171) gives:
% 25.88/4.31 | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | Case 1:
% 25.88/4.31 | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | (172) ~ (mem(all_42_26, all_42_38) = all_293_0)
% 25.88/4.31 | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 25.88/4.31 | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | Case 1:
% 25.88/4.31 | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | (173) ~ (mem(all_42_23, all_42_40) = all_293_1)
% 25.88/4.31 | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 25.88/4.31 | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | Case 1:
% 25.88/4.31 | | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | | (174) all_293_0 = 0
% 25.88/4.31 | | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | | REDUCE: (172), (174) imply:
% 25.88/4.31 | | | | | | | | | | | | | | | | (175) ~ (mem(all_42_26, all_42_38) = 0)
% 25.88/4.31 | | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | | PRED_UNIFY: (84), (175) imply:
% 25.88/4.31 | | | | | | | | | | | | | | | | (176) $false
% 25.88/4.31 | | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | | CLOSE: (176) is inconsistent.
% 25.88/4.31 | | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | Case 2:
% 25.88/4.31 | | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | | (177) all_293_1 = 0
% 25.88/4.31 | | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | | REDUCE: (173), (177) imply:
% 25.88/4.31 | | | | | | | | | | | | | | | | (178) ~ (mem(all_42_23, all_42_40) = 0)
% 25.88/4.31 | | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | | PRED_UNIFY: (102), (178) imply:
% 25.88/4.31 | | | | | | | | | | | | | | | | (179) $false
% 25.88/4.31 | | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | | CLOSE: (179) is inconsistent.
% 25.88/4.31 | | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | End of split
% 25.88/4.31 | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | Case 2:
% 25.88/4.31 | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | (180) all_293_1 = 0
% 25.88/4.31 | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | REDUCE: (167), (180) imply:
% 25.88/4.31 | | | | | | | | | | | | | | | (181) mem(all_42_19, all_42_40) = 0
% 25.88/4.31 | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | GROUND_INST: instantiating (105) with all_42_19, simplifying
% 25.88/4.31 | | | | | | | | | | | | | | | with (181) gives:
% 25.88/4.31 | | | | | | | | | | | | | | | (182) $lesseq(all_42_19, all_42_23)
% 25.88/4.31 | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | COMBINE_INEQS: (161), (182) imply:
% 25.88/4.31 | | | | | | | | | | | | | | | (183) $lesseq(1, $difference(all_42_23, all_42_39))
% 25.88/4.31 | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | COMBINE_INEQS: (162), (183) imply:
% 25.88/4.31 | | | | | | | | | | | | | | | (184) $false
% 25.88/4.31 | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | | CLOSE: (184) is inconsistent.
% 25.88/4.31 | | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | End of split
% 25.88/4.31 | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | Case 2:
% 25.88/4.31 | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | (185) all_293_0 = 0
% 25.88/4.31 | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | REDUCE: (168), (185) imply:
% 25.88/4.31 | | | | | | | | | | | | | | (186) mem(all_42_19, all_42_38) = 0
% 25.88/4.31 | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | GROUND_INST: instantiating (86) with all_42_19, simplifying
% 25.88/4.31 | | | | | | | | | | | | | | with (186) gives:
% 25.88/4.31 | | | | | | | | | | | | | | (187) $lesseq(all_42_19, all_42_26)
% 25.88/4.31 | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | COMBINE_INEQS: (161), (187) imply:
% 25.88/4.31 | | | | | | | | | | | | | | (188) $lesseq(1, $difference(all_42_26, all_42_39))
% 25.88/4.31 | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | COMBINE_INEQS: (94), (188) imply:
% 25.88/4.31 | | | | | | | | | | | | | | (189) $false
% 25.88/4.31 | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | | CLOSE: (189) is inconsistent.
% 25.88/4.31 | | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | | End of split
% 25.88/4.31 | | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | End of split
% 25.88/4.31 | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | End of split
% 25.88/4.31 | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | End of split
% 25.88/4.31 | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | End of split
% 25.88/4.31 | | | | | | | | |
% 25.88/4.31 | | | | | | | | End of split
% 25.88/4.31 | | | | | | | |
% 25.88/4.31 | | | | | | | Case 2:
% 25.88/4.31 | | | | | | | |
% 25.88/4.31 | | | | | | | | (190) all_42_24 = all_42_26
% 25.88/4.31 | | | | | | | |
% 25.88/4.31 | | | | | | | | REDUCE: (89), (190) imply:
% 25.88/4.31 | | | | | | | | (191) $lesseq(all_42_39, all_42_26)
% 25.88/4.31 | | | | | | | |
% 25.88/4.31 | | | | | | | | REDUCE: (83), (190) imply:
% 25.88/4.31 | | | | | | | | (192) max(all_42_39, all_42_26) = all_42_26
% 25.88/4.31 | | | | | | | |
% 25.88/4.31 | | | | | | | | BETA: splitting (90) gives:
% 25.88/4.31 | | | | | | | |
% 25.88/4.31 | | | | | | | | Case 1:
% 25.88/4.31 | | | | | | | | |
% 25.88/4.31 | | | | | | | | | (193) max(all_42_26, all_42_39) = all_42_24
% 25.88/4.31 | | | | | | | | |
% 25.88/4.31 | | | | | | | | | REDUCE: (190), (193) imply:
% 25.88/4.31 | | | | | | | | | (194) max(all_42_26, all_42_39) = all_42_26
% 25.88/4.31 | | | | | | | | |
% 25.88/4.31 | | | | | | | | | BETA: splitting (93) gives:
% 25.88/4.31 | | | | | | | | |
% 25.88/4.31 | | | | | | | | | Case 1:
% 25.88/4.31 | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | (195) all_42_40 = empty
% 25.88/4.31 | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | REDUCE: (26), (195) imply:
% 25.88/4.31 | | | | | | | | | | (196) size(empty) = all_42_36
% 25.88/4.31 | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | REF_CLOSE: (5), (12), (66), (67), (196) are inconsistent by
% 25.88/4.31 | | | | | | | | | | sub-proof #4.
% 25.88/4.31 | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | Case 2:
% 25.88/4.31 | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | (197) all_42_22 = 0 & mem(all_42_21, all_42_42) =
% 25.88/4.31 | | | | | | | | | | all_42_20 & mem(all_42_23, all_42_40) = 0 &
% 25.88/4.31 | | | | | | | | | | max(all_42_23, all_42_24) = all_42_21 & ! [v0:
% 25.88/4.31 | | | | | | | | | | int] : ( ~ ($lesseq(1, $difference(v0,
% 25.88/4.31 | | | | | | | | | | all_42_23))) | ~ (mem(v0, all_42_40) = 0))
% 25.88/4.31 | | | | | | | | | | & ( ~ (all_42_20 = 0) | (all_42_18 = 0 & $lesseq(1,
% 25.88/4.31 | | | | | | | | | | $difference(all_42_19, all_42_21)) &
% 25.88/4.31 | | | | | | | | | | mem(all_42_19, all_42_42) = 0))
% 25.88/4.31 | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | ALPHA: (197) implies:
% 25.88/4.31 | | | | | | | | | | (198) max(all_42_23, all_42_24) = all_42_21
% 25.88/4.31 | | | | | | | | | | (199) mem(all_42_23, all_42_40) = 0
% 25.88/4.31 | | | | | | | | | | (200) mem(all_42_21, all_42_42) = all_42_20
% 25.88/4.31 | | | | | | | | | | (201) ~ (all_42_20 = 0) | (all_42_18 = 0 & $lesseq(1,
% 25.88/4.31 | | | | | | | | | | $difference(all_42_19, all_42_21)) &
% 25.88/4.31 | | | | | | | | | | mem(all_42_19, all_42_42) = 0)
% 25.88/4.31 | | | | | | | | | | (202) ! [v0: int] : ( ~ ($lesseq(1, $difference(v0,
% 25.88/4.31 | | | | | | | | | | all_42_23))) | ~ (mem(v0, all_42_40) = 0))
% 25.88/4.31 | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | REDUCE: (190), (198) imply:
% 25.88/4.31 | | | | | | | | | | (203) max(all_42_23, all_42_26) = all_42_21
% 25.88/4.31 | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | GROUND_INST: instantiating (max_y) with all_42_23, all_42_26,
% 25.88/4.31 | | | | | | | | | | all_42_21, simplifying with (203) gives:
% 25.88/4.31 | | | | | | | | | | (204) all_42_21 = all_42_26 | ~ ($lesseq(all_42_23,
% 25.88/4.31 | | | | | | | | | | all_42_26))
% 25.88/4.31 | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | GROUND_INST: instantiating (max_x) with all_42_23, all_42_26,
% 25.88/4.31 | | | | | | | | | | all_42_21, simplifying with (203) gives:
% 25.88/4.31 | | | | | | | | | | (205) all_42_21 = all_42_23 | ~ ($lesseq(all_42_26,
% 25.88/4.31 | | | | | | | | | | all_42_23))
% 25.88/4.31 | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | GROUND_INST: instantiating (2) with all_42_23, all_42_26,
% 25.88/4.31 | | | | | | | | | | all_42_21, simplifying with (203) gives:
% 25.88/4.31 | | | | | | | | | | (206) $lesseq(all_42_26, all_42_21)
% 25.88/4.31 | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | GROUND_INST: instantiating (13) with all_42_39, all_42_21,
% 25.88/4.31 | | | | | | | | | | all_42_39, all_42_39 gives:
% 25.88/4.31 | | | | | | | | | | (207) all_42_21 = all_42_39 | ~ (max(all_42_39,
% 25.88/4.31 | | | | | | | | | | all_42_39) = all_42_21) | ~ (max(all_42_39,
% 25.88/4.31 | | | | | | | | | | all_42_39) = all_42_39)
% 25.88/4.31 | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | GROUND_INST: instantiating (13) with all_42_26, all_42_21,
% 25.88/4.31 | | | | | | | | | | all_42_26, all_42_39, simplifying with (192)
% 25.88/4.31 | | | | | | | | | | gives:
% 25.88/4.31 | | | | | | | | | | (208) all_42_21 = all_42_26 | ~ (max(all_42_39,
% 25.88/4.31 | | | | | | | | | | all_42_26) = all_42_21)
% 25.88/4.31 | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | GROUND_INST: instantiating (3) with all_42_23, all_42_26,
% 25.88/4.31 | | | | | | | | | | all_42_21, simplifying with (203) gives:
% 25.88/4.31 | | | | | | | | | | (209) ~ ($lesseq(all_42_26, all_42_23)) | max(all_42_26,
% 25.88/4.31 | | | | | | | | | | all_42_23) = all_42_21
% 25.88/4.31 | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | GROUND_INST: instantiating (10) with all_42_21, all_42_40,
% 25.88/4.31 | | | | | | | | | | all_42_39, all_42_38, all_42_42, all_42_20,
% 25.88/4.31 | | | | | | | | | | simplifying with (16), (17), (24), (200) gives:
% 25.88/4.31 | | | | | | | | | | (210) all_42_20 = 0 | ? [v0: int] : ? [v1: int] : ( ~
% 25.88/4.31 | | | | | | | | | | (v1 = 0) & ~ (v0 = 0) & mem(all_42_21,
% 25.88/4.31 | | | | | | | | | | all_42_38) = v1 & mem(all_42_21, all_42_40) =
% 25.88/4.31 | | | | | | | | | | v0)
% 25.88/4.31 | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | BETA: splitting (201) gives:
% 25.88/4.31 | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | Case 1:
% 25.88/4.31 | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | (211) ~ (all_42_20 = 0)
% 25.88/4.31 | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | BETA: splitting (210) gives:
% 25.88/4.31 | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | Case 1:
% 25.88/4.31 | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | (212) all_42_20 = 0
% 25.88/4.31 | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | REDUCE: (211), (212) imply:
% 25.88/4.31 | | | | | | | | | | | | (213) $false
% 25.88/4.31 | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | CLOSE: (213) is inconsistent.
% 25.88/4.31 | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | Case 2:
% 25.88/4.31 | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | (214) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~
% 25.88/4.31 | | | | | | | | | | | | (v0 = 0) & mem(all_42_21, all_42_38) = v1 &
% 25.88/4.31 | | | | | | | | | | | | mem(all_42_21, all_42_40) = v0)
% 25.88/4.31 | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | DELTA: instantiating (214) with fresh symbols all_291_0,
% 25.88/4.31 | | | | | | | | | | | | all_291_1 gives:
% 25.88/4.31 | | | | | | | | | | | | (215) ~ (all_291_0 = 0) & ~ (all_291_1 = 0) &
% 25.88/4.31 | | | | | | | | | | | | mem(all_42_21, all_42_38) = all_291_0 &
% 25.88/4.31 | | | | | | | | | | | | mem(all_42_21, all_42_40) = all_291_1
% 25.88/4.31 | | | | | | | | | | | |
% 25.88/4.31 | | | | | | | | | | | | ALPHA: (215) implies:
% 25.88/4.31 | | | | | | | | | | | | (216) ~ (all_291_1 = 0)
% 25.88/4.31 | | | | | | | | | | | | (217) ~ (all_291_0 = 0)
% 25.88/4.31 | | | | | | | | | | | | (218) mem(all_42_21, all_42_40) = all_291_1
% 25.88/4.31 | | | | | | | | | | | | (219) mem(all_42_21, all_42_38) = all_291_0
% 25.88/4.31 | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_291_1, all_42_40,
% 25.88/4.32 | | | | | | | | | | | | all_42_23, simplifying with (199) gives:
% 25.88/4.32 | | | | | | | | | | | | (220) all_291_1 = 0 | ~ (mem(all_42_23, all_42_40) =
% 25.88/4.32 | | | | | | | | | | | | all_291_1)
% 25.88/4.32 | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_291_0, all_42_38,
% 25.88/4.32 | | | | | | | | | | | | all_42_26, simplifying with (84) gives:
% 25.88/4.32 | | | | | | | | | | | | (221) all_291_0 = 0 | ~ (mem(all_42_26, all_42_38) =
% 25.88/4.32 | | | | | | | | | | | | all_291_0)
% 25.88/4.32 | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | BETA: splitting (205) gives:
% 25.88/4.32 | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | Case 1:
% 25.88/4.32 | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | (222) $lesseq(1, $difference(all_42_26, all_42_23))
% 25.88/4.32 | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | BETA: splitting (204) gives:
% 25.88/4.32 | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | Case 1:
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | (223) $lesseq(1, $difference(all_42_23, all_42_26))
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | COMBINE_INEQS: (222), (223) imply:
% 25.88/4.32 | | | | | | | | | | | | | | (224) $false
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | CLOSE: (224) is inconsistent.
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | Case 2:
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | (225) all_42_21 = all_42_26
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | REDUCE: (219), (225) imply:
% 25.88/4.32 | | | | | | | | | | | | | | (226) mem(all_42_26, all_42_38) = all_291_0
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | Case 1:
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | (227) ~ (mem(all_42_26, all_42_38) = all_291_0)
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | PRED_UNIFY: (226), (227) imply:
% 25.88/4.32 | | | | | | | | | | | | | | | (228) $false
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | CLOSE: (228) is inconsistent.
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | Case 2:
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | (229) all_291_0 = 0
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | REDUCE: (217), (229) imply:
% 25.88/4.32 | | | | | | | | | | | | | | | (230) $false
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | CLOSE: (230) is inconsistent.
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | End of split
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | End of split
% 25.88/4.32 | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | Case 2:
% 25.88/4.32 | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | (231) all_42_21 = all_42_23
% 25.88/4.32 | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | REDUCE: (218), (231) imply:
% 25.88/4.32 | | | | | | | | | | | | | (232) mem(all_42_23, all_42_40) = all_291_1
% 25.88/4.32 | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | BETA: splitting (220) gives:
% 25.88/4.32 | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | Case 1:
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | (233) ~ (mem(all_42_23, all_42_40) = all_291_1)
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | PRED_UNIFY: (232), (233) imply:
% 25.88/4.32 | | | | | | | | | | | | | | (234) $false
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | CLOSE: (234) is inconsistent.
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | Case 2:
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | (235) all_291_1 = 0
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | REDUCE: (216), (235) imply:
% 25.88/4.32 | | | | | | | | | | | | | | (236) $false
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | CLOSE: (236) is inconsistent.
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | End of split
% 25.88/4.32 | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | End of split
% 25.88/4.32 | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | End of split
% 25.88/4.32 | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | Case 2:
% 25.88/4.32 | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | (237) all_42_18 = 0 & $lesseq(1, $difference(all_42_19,
% 25.88/4.32 | | | | | | | | | | | all_42_21)) & mem(all_42_19, all_42_42) = 0
% 25.88/4.32 | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | ALPHA: (237) implies:
% 25.88/4.32 | | | | | | | | | | | (238) $lesseq(1, $difference(all_42_19, all_42_21))
% 25.88/4.32 | | | | | | | | | | | (239) mem(all_42_19, all_42_42) = 0
% 25.88/4.32 | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | GROUND_INST: instantiating (8) with all_42_19, all_42_40,
% 25.88/4.32 | | | | | | | | | | | all_42_39, all_42_38, all_42_42, simplifying with
% 25.88/4.32 | | | | | | | | | | | (16), (17), (24), (239) gives:
% 25.88/4.32 | | | | | | | | | | | (240) all_42_19 = all_42_39 | ? [v0: any] : ? [v1:
% 25.88/4.32 | | | | | | | | | | | any] : (mem(all_42_19, all_42_38) = v1 &
% 25.88/4.32 | | | | | | | | | | | mem(all_42_19, all_42_40) = v0 & (v1 = 0 | v0 =
% 25.88/4.32 | | | | | | | | | | | 0))
% 25.88/4.32 | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | BETA: splitting (205) gives:
% 25.88/4.32 | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | Case 1:
% 25.88/4.32 | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | (241) $lesseq(1, $difference(all_42_26, all_42_23))
% 25.88/4.32 | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | REF_CLOSE: (14), (86), (191), (194), (199), (202), (204),
% 25.88/4.32 | | | | | | | | | | | | (207), (238), (240), (241), (max_is_some) are
% 25.88/4.32 | | | | | | | | | | | | inconsistent by sub-proof #1.
% 25.88/4.32 | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | Case 2:
% 25.88/4.32 | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | (242) all_42_21 = all_42_23
% 25.88/4.32 | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | REDUCE: (238), (242) imply:
% 25.88/4.32 | | | | | | | | | | | | (243) $lesseq(1, $difference(all_42_19, all_42_23))
% 25.88/4.32 | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | REDUCE: (206), (242) imply:
% 25.88/4.32 | | | | | | | | | | | | (244) $lesseq(all_42_26, all_42_23)
% 25.88/4.32 | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | BETA: splitting (209) gives:
% 25.88/4.32 | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | Case 1:
% 25.88/4.32 | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | (245) max(all_42_26, all_42_23) = all_42_21
% 25.88/4.32 | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | REDUCE: (242), (245) imply:
% 25.88/4.32 | | | | | | | | | | | | | (246) max(all_42_26, all_42_23) = all_42_23
% 25.88/4.32 | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | BETA: splitting (208) gives:
% 25.88/4.32 | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | Case 1:
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | (247) ~ (max(all_42_39, all_42_26) = all_42_21)
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | REDUCE: (242), (247) imply:
% 25.88/4.32 | | | | | | | | | | | | | | (248) ~ (max(all_42_39, all_42_26) = all_42_23)
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | PRED_UNIFY: (192), (248) imply:
% 25.88/4.32 | | | | | | | | | | | | | | (249) ~ (all_42_23 = all_42_26)
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | STRENGTHEN: (244), (249) imply:
% 25.88/4.32 | | | | | | | | | | | | | | (250) $lesseq(1, $difference(all_42_23, all_42_26))
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | Case 1:
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | (251) all_42_19 = all_42_39
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | REDUCE: (243), (251) imply:
% 25.88/4.32 | | | | | | | | | | | | | | | (252) $lesseq(1, $difference(all_42_39, all_42_23))
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | COMBINE_INEQS: (250), (252) imply:
% 25.88/4.32 | | | | | | | | | | | | | | | (253) $lesseq(2, $difference(all_42_39, all_42_26))
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | COMBINE_INEQS: (191), (253) imply:
% 25.88/4.32 | | | | | | | | | | | | | | | (254) $false
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | CLOSE: (254) is inconsistent.
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | Case 2:
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | (255) ? [v0: any] : ? [v1: any] : (mem(all_42_19,
% 25.88/4.32 | | | | | | | | | | | | | | | all_42_38) = v1 & mem(all_42_19, all_42_40) =
% 25.88/4.32 | | | | | | | | | | | | | | | v0 & (v1 = 0 | v0 = 0))
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | DELTA: instantiating (255) with fresh symbols all_383_0,
% 25.88/4.32 | | | | | | | | | | | | | | | all_383_1 gives:
% 25.88/4.32 | | | | | | | | | | | | | | | (256) mem(all_42_19, all_42_38) = all_383_0 &
% 25.88/4.32 | | | | | | | | | | | | | | | mem(all_42_19, all_42_40) = all_383_1 & (all_383_0
% 25.88/4.32 | | | | | | | | | | | | | | | = 0 | all_383_1 = 0)
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | ALPHA: (256) implies:
% 25.88/4.32 | | | | | | | | | | | | | | | (257) mem(all_42_19, all_42_40) = all_383_1
% 25.88/4.32 | | | | | | | | | | | | | | | (258) mem(all_42_19, all_42_38) = all_383_0
% 25.88/4.32 | | | | | | | | | | | | | | | (259) all_383_0 = 0 | all_383_1 = 0
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_383_0, all_42_38,
% 25.88/4.32 | | | | | | | | | | | | | | | all_42_26, simplifying with (84) gives:
% 25.88/4.32 | | | | | | | | | | | | | | | (260) all_383_0 = 0 | ~ (mem(all_42_26, all_42_38) =
% 25.88/4.32 | | | | | | | | | | | | | | | all_383_0)
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | Case 1:
% 25.88/4.32 | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | (261) ~ (mem(all_42_26, all_42_38) = all_383_0)
% 25.88/4.32 | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | BETA: splitting (259) gives:
% 25.88/4.32 | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | Case 1:
% 25.88/4.32 | | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | | (262) all_383_0 = 0
% 25.88/4.32 | | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | | REDUCE: (261), (262) imply:
% 25.88/4.32 | | | | | | | | | | | | | | | | | (263) ~ (mem(all_42_26, all_42_38) = 0)
% 25.88/4.32 | | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | | PRED_UNIFY: (84), (263) imply:
% 25.88/4.32 | | | | | | | | | | | | | | | | | (264) $false
% 25.88/4.32 | | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | | CLOSE: (264) is inconsistent.
% 25.88/4.32 | | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | Case 2:
% 25.88/4.32 | | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | | (265) all_383_1 = 0
% 25.88/4.32 | | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | | REDUCE: (257), (265) imply:
% 25.88/4.32 | | | | | | | | | | | | | | | | | (266) mem(all_42_19, all_42_40) = 0
% 25.88/4.32 | | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | | REF_CLOSE: (202), (243), (266) are inconsistent by sub-proof
% 25.88/4.32 | | | | | | | | | | | | | | | | | #3.
% 25.88/4.32 | | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | End of split
% 25.88/4.32 | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | Case 2:
% 25.88/4.32 | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | (267) all_383_0 = 0
% 25.88/4.32 | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | REDUCE: (258), (267) imply:
% 25.88/4.32 | | | | | | | | | | | | | | | | (268) mem(all_42_19, all_42_38) = 0
% 25.88/4.32 | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (86) with all_42_19, simplifying
% 25.88/4.32 | | | | | | | | | | | | | | | | with (268) gives:
% 25.88/4.32 | | | | | | | | | | | | | | | | (269) $lesseq(all_42_19, all_42_26)
% 25.88/4.32 | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | COMBINE_INEQS: (243), (269) imply:
% 25.88/4.32 | | | | | | | | | | | | | | | | (270) $lesseq(1, $difference(all_42_26, all_42_23))
% 25.88/4.32 | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | COMBINE_INEQS: (250), (270) imply:
% 25.88/4.32 | | | | | | | | | | | | | | | | (271) $false
% 25.88/4.32 | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | CLOSE: (271) is inconsistent.
% 25.88/4.32 | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | End of split
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | End of split
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | Case 2:
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | (272) all_42_21 = all_42_26
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | COMBINE_EQS: (242), (272) imply:
% 25.88/4.32 | | | | | | | | | | | | | | (273) all_42_23 = all_42_26
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | SIMP: (273) implies:
% 25.88/4.32 | | | | | | | | | | | | | | (274) all_42_23 = all_42_26
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | REDUCE: (243), (274) imply:
% 25.88/4.32 | | | | | | | | | | | | | | (275) $lesseq(1, $difference(all_42_19, all_42_26))
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | REDUCE: (246), (274) imply:
% 25.88/4.32 | | | | | | | | | | | | | | (276) max(all_42_26, all_42_26) = all_42_26
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 25.88/4.32 | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | Case 1:
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | (277) ~ (max(all_42_39, all_42_39) = all_42_21)
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | REDUCE: (272), (277) imply:
% 25.88/4.32 | | | | | | | | | | | | | | | (278) ~ (max(all_42_39, all_42_39) = all_42_26)
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | PRED_UNIFY: (276), (278) imply:
% 25.88/4.32 | | | | | | | | | | | | | | | (279) ~ (all_42_26 = all_42_39)
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | STRENGTHEN: (191), (279) imply:
% 25.88/4.32 | | | | | | | | | | | | | | | (280) $lesseq(1, $difference(all_42_26, all_42_39))
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 25.88/4.32 | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | Case 1:
% 25.88/4.32 | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | (281) all_42_19 = all_42_39
% 25.88/4.32 | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | REDUCE: (275), (281) imply:
% 25.88/4.32 | | | | | | | | | | | | | | | | (282) $lesseq(1, $difference(all_42_39, all_42_26))
% 25.88/4.32 | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | COMBINE_INEQS: (280), (282) imply:
% 25.88/4.32 | | | | | | | | | | | | | | | | (283) $false
% 25.88/4.32 | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | CLOSE: (283) is inconsistent.
% 25.88/4.32 | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | Case 2:
% 25.88/4.32 | | | | | | | | | | | | | | | |
% 25.88/4.32 | | | | | | | | | | | | | | | | (284) ? [v0: any] : ? [v1: any] : (mem(all_42_19,
% 25.88/4.33 | | | | | | | | | | | | | | | | all_42_38) = v1 & mem(all_42_19, all_42_40) =
% 25.88/4.33 | | | | | | | | | | | | | | | | v0 & (v1 = 0 | v0 = 0))
% 25.88/4.33 | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | DELTA: instantiating (284) with fresh symbols all_371_0,
% 25.88/4.33 | | | | | | | | | | | | | | | | all_371_1 gives:
% 25.88/4.33 | | | | | | | | | | | | | | | | (285) mem(all_42_19, all_42_38) = all_371_0 &
% 25.88/4.33 | | | | | | | | | | | | | | | | mem(all_42_19, all_42_40) = all_371_1 & (all_371_0
% 25.88/4.33 | | | | | | | | | | | | | | | | = 0 | all_371_1 = 0)
% 25.88/4.33 | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | ALPHA: (285) implies:
% 25.88/4.33 | | | | | | | | | | | | | | | | (286) mem(all_42_19, all_42_40) = all_371_1
% 25.88/4.33 | | | | | | | | | | | | | | | | (287) mem(all_42_19, all_42_38) = all_371_0
% 25.88/4.33 | | | | | | | | | | | | | | | | (288) all_371_0 = 0 | all_371_1 = 0
% 25.88/4.33 | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | BETA: splitting (288) gives:
% 25.88/4.33 | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | Case 1:
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | | (289) all_371_0 = 0
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | | REDUCE: (287), (289) imply:
% 25.88/4.33 | | | | | | | | | | | | | | | | | (290) mem(all_42_19, all_42_38) = 0
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (86) with all_42_19, simplifying
% 25.88/4.33 | | | | | | | | | | | | | | | | | with (290) gives:
% 25.88/4.33 | | | | | | | | | | | | | | | | | (291) $lesseq(all_42_19, all_42_26)
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | | COMBINE_INEQS: (275), (291) imply:
% 25.88/4.33 | | | | | | | | | | | | | | | | | (292) $false
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | | CLOSE: (292) is inconsistent.
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | Case 2:
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | | (293) all_371_1 = 0
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | | REDUCE: (286), (293) imply:
% 25.88/4.33 | | | | | | | | | | | | | | | | | (294) mem(all_42_19, all_42_40) = 0
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | | REF_CLOSE: (202), (243), (294) are inconsistent by sub-proof
% 25.88/4.33 | | | | | | | | | | | | | | | | | #3.
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | End of split
% 25.88/4.33 | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | End of split
% 25.88/4.33 | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | Case 2:
% 25.88/4.33 | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | (295) max(all_42_39, all_42_39) = all_42_21
% 25.88/4.33 | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | REDUCE: (272), (295) imply:
% 25.88/4.33 | | | | | | | | | | | | | | | (296) max(all_42_39, all_42_39) = all_42_26
% 25.88/4.33 | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | GROUND_INST: instantiating (max_is_some) with all_42_39,
% 25.88/4.33 | | | | | | | | | | | | | | | all_42_39, all_42_26, simplifying with (296)
% 25.88/4.33 | | | | | | | | | | | | | | | gives:
% 25.88/4.33 | | | | | | | | | | | | | | | (297) all_42_26 = all_42_39
% 25.88/4.33 | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | REDUCE: (275), (297) imply:
% 25.88/4.33 | | | | | | | | | | | | | | | (298) $lesseq(1, $difference(all_42_19, all_42_39))
% 25.88/4.33 | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 25.88/4.33 | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | Case 1:
% 25.88/4.33 | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | (299) all_42_19 = all_42_39
% 25.88/4.33 | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | REDUCE: (298), (299) imply:
% 25.88/4.33 | | | | | | | | | | | | | | | | (300) $false
% 25.88/4.33 | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | CLOSE: (300) is inconsistent.
% 25.88/4.33 | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | Case 2:
% 25.88/4.33 | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | (301) ? [v0: any] : ? [v1: any] : (mem(all_42_19,
% 25.88/4.33 | | | | | | | | | | | | | | | | all_42_38) = v1 & mem(all_42_19, all_42_40) =
% 25.88/4.33 | | | | | | | | | | | | | | | | v0 & (v1 = 0 | v0 = 0))
% 25.88/4.33 | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | DELTA: instantiating (301) with fresh symbols all_338_0,
% 25.88/4.33 | | | | | | | | | | | | | | | | all_338_1 gives:
% 25.88/4.33 | | | | | | | | | | | | | | | | (302) mem(all_42_19, all_42_38) = all_338_0 &
% 25.88/4.33 | | | | | | | | | | | | | | | | mem(all_42_19, all_42_40) = all_338_1 & (all_338_0
% 25.88/4.33 | | | | | | | | | | | | | | | | = 0 | all_338_1 = 0)
% 25.88/4.33 | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | ALPHA: (302) implies:
% 25.88/4.33 | | | | | | | | | | | | | | | | (303) mem(all_42_19, all_42_40) = all_338_1
% 25.88/4.33 | | | | | | | | | | | | | | | | (304) mem(all_42_19, all_42_38) = all_338_0
% 25.88/4.33 | | | | | | | | | | | | | | | | (305) all_338_0 = 0 | all_338_1 = 0
% 25.88/4.33 | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 25.88/4.33 | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | Case 1:
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | | (306) all_338_0 = 0
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | | REDUCE: (304), (306) imply:
% 25.88/4.33 | | | | | | | | | | | | | | | | | (307) mem(all_42_19, all_42_38) = 0
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (297), (298), (307) are inconsistent by
% 25.88/4.33 | | | | | | | | | | | | | | | | | sub-proof #2.
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | Case 2:
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | | (308) all_338_1 = 0
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | | REDUCE: (303), (308) imply:
% 25.88/4.33 | | | | | | | | | | | | | | | | | (309) mem(all_42_19, all_42_40) = 0
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | | REF_CLOSE: (202), (243), (309) are inconsistent by sub-proof
% 25.88/4.33 | | | | | | | | | | | | | | | | | #3.
% 25.88/4.33 | | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | | End of split
% 25.88/4.33 | | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | | End of split
% 25.88/4.33 | | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | | End of split
% 25.88/4.33 | | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | End of split
% 25.88/4.33 | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | Case 2:
% 25.88/4.33 | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | (310) $lesseq(1, $difference(all_42_26, all_42_23))
% 25.88/4.33 | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | | REF_CLOSE: (14), (86), (191), (194), (199), (202), (204),
% 25.88/4.33 | | | | | | | | | | | | | (207), (238), (240), (310), (max_is_some) are
% 25.88/4.33 | | | | | | | | | | | | | inconsistent by sub-proof #1.
% 25.88/4.33 | | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | | End of split
% 25.88/4.33 | | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | | End of split
% 25.88/4.33 | | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | | End of split
% 25.88/4.33 | | | | | | | | | |
% 25.88/4.33 | | | | | | | | | End of split
% 25.88/4.33 | | | | | | | | |
% 25.88/4.33 | | | | | | | | Case 2:
% 25.88/4.33 | | | | | | | | |
% 25.88/4.33 | | | | | | | | | (311) $lesseq(1, $difference(all_42_39, all_42_26))
% 25.88/4.33 | | | | | | | | |
% 25.88/4.33 | | | | | | | | | COMBINE_INEQS: (191), (311) imply:
% 25.88/4.33 | | | | | | | | | (312) $false
% 25.88/4.33 | | | | | | | | |
% 25.88/4.33 | | | | | | | | | CLOSE: (312) is inconsistent.
% 25.88/4.33 | | | | | | | | |
% 25.88/4.33 | | | | | | | | End of split
% 25.88/4.33 | | | | | | | |
% 25.88/4.33 | | | | | | | End of split
% 25.88/4.33 | | | | | | |
% 25.88/4.33 | | | | | | End of split
% 25.88/4.33 | | | | | |
% 25.88/4.33 | | | | | End of split
% 25.88/4.33 | | | | |
% 25.88/4.33 | | | | End of split
% 25.88/4.33 | | | |
% 25.88/4.33 | | | End of split
% 25.88/4.33 | | |
% 25.88/4.33 | | Case 2:
% 25.88/4.33 | | |
% 25.88/4.33 | | | (313) all_42_40 = empty & (all_42_38 = empty | ~ ($lesseq(1,
% 25.88/4.33 | | | $difference(all_42_41, all_42_35))) | ~ ($lesseq(0,
% 25.88/4.33 | | | all_42_41)) | (all_42_16 = 0 & mem(all_42_15, all_42_42) =
% 25.88/4.33 | | | all_42_14 & mem(all_42_17, all_42_38) = 0 & max(all_42_17,
% 25.88/4.33 | | | all_42_39) = all_42_15 & ! [v0: int] : ( ~ ($lesseq(1,
% 25.88/4.33 | | | $difference(v0, all_42_17))) | ~ (mem(v0, all_42_38) =
% 25.88/4.33 | | | 0)) & ( ~ (all_42_14 = 0) | (all_42_12 = 0 & $lesseq(1,
% 25.88/4.33 | | | $difference(all_42_13, all_42_15)) & mem(all_42_13,
% 25.88/4.33 | | | all_42_42) = 0))))
% 25.88/4.33 | | |
% 25.88/4.33 | | | ALPHA: (313) implies:
% 25.88/4.33 | | | (314) all_42_40 = empty
% 25.88/4.33 | | | (315) all_42_38 = empty | ~ ($lesseq(1, $difference(all_42_41,
% 25.88/4.33 | | | all_42_35))) | ~ ($lesseq(0, all_42_41)) | (all_42_16 = 0
% 25.88/4.33 | | | & mem(all_42_15, all_42_42) = all_42_14 & mem(all_42_17,
% 25.88/4.33 | | | all_42_38) = 0 & max(all_42_17, all_42_39) = all_42_15 & !
% 25.88/4.33 | | | [v0: int] : ( ~ ($lesseq(1, $difference(v0, all_42_17))) | ~
% 25.88/4.33 | | | (mem(v0, all_42_38) = 0)) & ( ~ (all_42_14 = 0) | (all_42_12
% 25.88/4.33 | | | = 0 & $lesseq(1, $difference(all_42_13, all_42_15)) &
% 25.88/4.33 | | | mem(all_42_13, all_42_42) = 0)))
% 25.88/4.33 | | |
% 25.88/4.33 | | | REDUCE: (26), (314) imply:
% 25.88/4.33 | | | (316) size(empty) = all_42_36
% 25.88/4.33 | | |
% 25.88/4.33 | | | REDUCE: (24), (314) imply:
% 25.88/4.33 | | | (317) node(empty, all_42_39, all_42_38) = all_42_42
% 25.88/4.33 | | |
% 25.88/4.33 | | | REDUCE: (16), (314) imply:
% 25.88/4.33 | | | (318) tree(empty)
% 25.88/4.33 | | |
% 25.88/4.33 | | | GROUND_INST: instantiating (12) with 0, all_42_36, empty, simplifying with
% 25.88/4.33 | | | (5), (316) gives:
% 25.88/4.33 | | | (319) all_42_36 = 0
% 25.88/4.33 | | |
% 25.88/4.33 | | | COMBINE_EQS: (41), (319) imply:
% 25.88/4.33 | | | (320) $difference(all_42_35, all_42_41) = -1
% 25.88/4.33 | | |
% 25.88/4.33 | | | REDUCE: (54), (319) imply:
% 25.88/4.33 | | | (321) $lesseq(2, $difference(all_42_41, all_86_0))
% 25.88/4.33 | | |
% 25.88/4.33 | | | COMBINE_INEQS: (53), (321) imply:
% 25.88/4.33 | | | (322) $lesseq(2, all_42_41)
% 25.88/4.33 | | |
% 25.88/4.33 | | | REDUCE: (42), (319) imply:
% 25.88/4.33 | | | (323) size(all_42_38) = $sum(all_42_41, -1)
% 25.88/4.33 | | |
% 25.88/4.33 | | | BETA: splitting (315) gives:
% 25.88/4.33 | | |
% 25.88/4.33 | | | Case 1:
% 25.88/4.33 | | | |
% 25.88/4.33 | | | | (324) $lesseq(all_42_41, -1)
% 25.88/4.33 | | | |
% 25.88/4.33 | | | | COMBINE_INEQS: (322), (324) imply:
% 25.88/4.33 | | | | (325) $false
% 25.88/4.33 | | | |
% 25.88/4.33 | | | | CLOSE: (325) is inconsistent.
% 25.88/4.33 | | | |
% 25.88/4.33 | | | Case 2:
% 25.88/4.33 | | | |
% 25.88/4.33 | | | | (326) all_42_38 = empty | ~ ($lesseq(1, $difference(all_42_41,
% 25.88/4.33 | | | | all_42_35))) | (all_42_16 = 0 & mem(all_42_15, all_42_42)
% 25.88/4.33 | | | | = all_42_14 & mem(all_42_17, all_42_38) = 0 & max(all_42_17,
% 25.88/4.33 | | | | all_42_39) = all_42_15 & ! [v0: int] : ( ~ ($lesseq(1,
% 25.88/4.33 | | | | $difference(v0, all_42_17))) | ~ (mem(v0, all_42_38) =
% 25.88/4.33 | | | | 0)) & ( ~ (all_42_14 = 0) | (all_42_12 = 0 & $lesseq(1,
% 25.88/4.33 | | | | $difference(all_42_13, all_42_15)) & mem(all_42_13,
% 25.88/4.33 | | | | all_42_42) = 0)))
% 25.88/4.33 | | | |
% 25.88/4.33 | | | | BETA: splitting (326) gives:
% 25.88/4.33 | | | |
% 25.88/4.33 | | | | Case 1:
% 25.88/4.33 | | | | |
% 25.88/4.33 | | | | | (327) $lesseq(all_42_41, all_42_35)
% 25.88/4.33 | | | | |
% 25.88/4.33 | | | | | REDUCE: (320), (327) imply:
% 25.88/4.33 | | | | | (328) $false
% 25.88/4.33 | | | | |
% 25.88/4.33 | | | | | CLOSE: (328) is inconsistent.
% 25.88/4.33 | | | | |
% 25.88/4.33 | | | | Case 2:
% 25.88/4.33 | | | | |
% 25.88/4.33 | | | | | (329) all_42_38 = empty | (all_42_16 = 0 & mem(all_42_15,
% 25.88/4.33 | | | | | all_42_42) = all_42_14 & mem(all_42_17, all_42_38) = 0 &
% 25.88/4.33 | | | | | max(all_42_17, all_42_39) = all_42_15 & ! [v0: int] : ( ~
% 25.88/4.33 | | | | | ($lesseq(1, $difference(v0, all_42_17))) | ~ (mem(v0,
% 25.88/4.33 | | | | | all_42_38) = 0)) & ( ~ (all_42_14 = 0) | (all_42_12 =
% 25.88/4.33 | | | | | 0 & $lesseq(1, $difference(all_42_13, all_42_15)) &
% 25.88/4.33 | | | | | mem(all_42_13, all_42_42) = 0)))
% 25.88/4.33 | | | | |
% 25.88/4.33 | | | | | BETA: splitting (329) gives:
% 25.88/4.33 | | | | |
% 25.88/4.33 | | | | | Case 1:
% 25.88/4.33 | | | | | |
% 25.88/4.33 | | | | | | (330) all_42_38 = empty
% 25.88/4.33 | | | | | |
% 25.88/4.33 | | | | | | REDUCE: (323), (330) imply:
% 25.88/4.33 | | | | | | (331) size(empty) = $sum(all_42_41, -1)
% 25.88/4.33 | | | | | |
% 25.88/4.33 | | | | | | GROUND_INST: instantiating (12) with 0, $sum(all_42_41, -1), empty,
% 25.88/4.33 | | | | | | simplifying with (5), (331) gives:
% 25.88/4.33 | | | | | | (332) all_42_41 = 1
% 25.88/4.33 | | | | | |
% 25.88/4.33 | | | | | | REDUCE: (321), (332) imply:
% 25.88/4.33 | | | | | | (333) $lesseq(all_86_0, -1)
% 25.88/4.33 | | | | | |
% 25.88/4.33 | | | | | | COMBINE_INEQS: (53), (333) imply:
% 25.88/4.33 | | | | | | (334) $false
% 25.88/4.33 | | | | | |
% 25.88/4.33 | | | | | | CLOSE: (334) is inconsistent.
% 25.88/4.33 | | | | | |
% 25.88/4.33 | | | | | Case 2:
% 25.88/4.33 | | | | | |
% 25.88/4.34 | | | | | | (335) all_42_16 = 0 & mem(all_42_15, all_42_42) = all_42_14 &
% 25.88/4.34 | | | | | | mem(all_42_17, all_42_38) = 0 & max(all_42_17, all_42_39) =
% 25.88/4.34 | | | | | | all_42_15 & ! [v0: int] : ( ~ ($lesseq(1, $difference(v0,
% 25.88/4.34 | | | | | | all_42_17))) | ~ (mem(v0, all_42_38) = 0)) & ( ~
% 25.88/4.34 | | | | | | (all_42_14 = 0) | (all_42_12 = 0 & $lesseq(1,
% 25.88/4.34 | | | | | | $difference(all_42_13, all_42_15)) & mem(all_42_13,
% 25.88/4.34 | | | | | | all_42_42) = 0))
% 25.88/4.34 | | | | | |
% 25.88/4.34 | | | | | | ALPHA: (335) implies:
% 25.88/4.34 | | | | | | (336) max(all_42_17, all_42_39) = all_42_15
% 25.88/4.34 | | | | | | (337) mem(all_42_17, all_42_38) = 0
% 25.88/4.34 | | | | | | (338) mem(all_42_15, all_42_42) = all_42_14
% 25.88/4.34 | | | | | | (339) ~ (all_42_14 = 0) | (all_42_12 = 0 & $lesseq(1,
% 25.88/4.34 | | | | | | $difference(all_42_13, all_42_15)) & mem(all_42_13,
% 25.88/4.34 | | | | | | all_42_42) = 0)
% 25.88/4.34 | | | | | | (340) ! [v0: int] : ( ~ ($lesseq(1, $difference(v0, all_42_17)))
% 25.88/4.34 | | | | | | | ~ (mem(v0, all_42_38) = 0))
% 25.88/4.34 | | | | | |
% 25.88/4.34 | | | | | | GROUND_INST: instantiating (max_y) with all_42_17, all_42_39,
% 25.88/4.34 | | | | | | all_42_15, simplifying with (336) gives:
% 25.88/4.34 | | | | | | (341) all_42_15 = all_42_39 | ~ ($lesseq(all_42_17, all_42_39))
% 25.88/4.34 | | | | | |
% 25.88/4.34 | | | | | | GROUND_INST: instantiating (max_x) with all_42_17, all_42_39,
% 25.88/4.34 | | | | | | all_42_15, simplifying with (336) gives:
% 25.88/4.34 | | | | | | (342) all_42_15 = all_42_17 | ~ ($lesseq(all_42_39, all_42_17))
% 25.88/4.34 | | | | | |
% 25.88/4.34 | | | | | | GROUND_INST: instantiating (1) with all_42_17, all_42_39, all_42_15,
% 25.88/4.34 | | | | | | simplifying with (336) gives:
% 25.88/4.34 | | | | | | (343) $lesseq(all_42_17, all_42_15)
% 25.88/4.34 | | | | | |
% 25.88/4.34 | | | | | | GROUND_INST: instantiating (9) with all_42_39, empty, all_42_38,
% 25.88/4.34 | | | | | | all_42_42, all_42_14, simplifying with (17), (317),
% 25.88/4.34 | | | | | | (318) gives:
% 25.88/4.34 | | | | | | (344) all_42_14 = 0 | ~ (mem(all_42_39, all_42_42) = all_42_14)
% 25.88/4.34 | | | | | |
% 25.88/4.34 | | | | | | GROUND_INST: instantiating (10) with all_42_15, empty, all_42_39,
% 25.88/4.34 | | | | | | all_42_38, all_42_42, all_42_14, simplifying with (17),
% 25.88/4.34 | | | | | | (317), (318), (338) gives:
% 25.88/4.34 | | | | | | (345) all_42_14 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0)
% 26.32/4.34 | | | | | | & ~ (v0 = 0) & mem(all_42_15, all_42_38) = v1 &
% 26.32/4.34 | | | | | | mem(all_42_15, empty) = v0)
% 26.32/4.34 | | | | | |
% 26.32/4.34 | | | | | | BETA: splitting (339) gives:
% 26.32/4.34 | | | | | |
% 26.32/4.34 | | | | | | Case 1:
% 26.32/4.34 | | | | | | |
% 26.32/4.34 | | | | | | | (346) ~ (all_42_14 = 0)
% 26.32/4.34 | | | | | | |
% 26.32/4.34 | | | | | | | BETA: splitting (345) gives:
% 26.32/4.34 | | | | | | |
% 26.32/4.34 | | | | | | | Case 1:
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | | (347) all_42_14 = 0
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | | REDUCE: (346), (347) imply:
% 26.32/4.34 | | | | | | | | (348) $false
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | | CLOSE: (348) is inconsistent.
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | Case 2:
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | | (349) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 =
% 26.32/4.34 | | | | | | | | 0) & mem(all_42_15, all_42_38) = v1 &
% 26.32/4.34 | | | | | | | | mem(all_42_15, empty) = v0)
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | | DELTA: instantiating (349) with fresh symbols all_203_0,
% 26.32/4.34 | | | | | | | | all_203_1 gives:
% 26.32/4.34 | | | | | | | | (350) ~ (all_203_0 = 0) & ~ (all_203_1 = 0) &
% 26.32/4.34 | | | | | | | | mem(all_42_15, all_42_38) = all_203_0 & mem(all_42_15,
% 26.32/4.34 | | | | | | | | empty) = all_203_1
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | | ALPHA: (350) implies:
% 26.32/4.34 | | | | | | | | (351) ~ (all_203_0 = 0)
% 26.32/4.34 | | | | | | | | (352) mem(all_42_15, all_42_38) = all_203_0
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | | GROUND_INST: instantiating (14) with 0, all_203_0, all_42_38,
% 26.32/4.34 | | | | | | | | all_42_17, simplifying with (337) gives:
% 26.32/4.34 | | | | | | | | (353) all_203_0 = 0 | ~ (mem(all_42_17, all_42_38) =
% 26.32/4.34 | | | | | | | | all_203_0)
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | | BETA: splitting (341) gives:
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | | Case 1:
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | (354) $lesseq(1, $difference(all_42_17, all_42_39))
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | BETA: splitting (342) gives:
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | Case 1:
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | (355) $lesseq(1, $difference(all_42_39, all_42_17))
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | COMBINE_INEQS: (354), (355) imply:
% 26.32/4.34 | | | | | | | | | | (356) $false
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | CLOSE: (356) is inconsistent.
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | Case 2:
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | (357) all_42_15 = all_42_17
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | REDUCE: (352), (357) imply:
% 26.32/4.34 | | | | | | | | | | (358) mem(all_42_17, all_42_38) = all_203_0
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | BETA: splitting (353) gives:
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | Case 1:
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | | (359) ~ (mem(all_42_17, all_42_38) = all_203_0)
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | | PRED_UNIFY: (358), (359) imply:
% 26.32/4.34 | | | | | | | | | | | (360) $false
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | | CLOSE: (360) is inconsistent.
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | Case 2:
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | | (361) all_203_0 = 0
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | | REDUCE: (351), (361) imply:
% 26.32/4.34 | | | | | | | | | | | (362) $false
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | | CLOSE: (362) is inconsistent.
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | End of split
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | End of split
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | Case 2:
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | (363) all_42_15 = all_42_39
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | REDUCE: (338), (363) imply:
% 26.32/4.34 | | | | | | | | | (364) mem(all_42_39, all_42_42) = all_42_14
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | BETA: splitting (344) gives:
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | Case 1:
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | (365) ~ (mem(all_42_39, all_42_42) = all_42_14)
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | PRED_UNIFY: (364), (365) imply:
% 26.32/4.34 | | | | | | | | | | (366) $false
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | CLOSE: (366) is inconsistent.
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | Case 2:
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | (367) all_42_14 = 0
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | REDUCE: (346), (367) imply:
% 26.32/4.34 | | | | | | | | | | (368) $false
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | CLOSE: (368) is inconsistent.
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | End of split
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | End of split
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | End of split
% 26.32/4.34 | | | | | | |
% 26.32/4.34 | | | | | | Case 2:
% 26.32/4.34 | | | | | | |
% 26.32/4.34 | | | | | | | (369) all_42_12 = 0 & $lesseq(1, $difference(all_42_13,
% 26.32/4.34 | | | | | | | all_42_15)) & mem(all_42_13, all_42_42) = 0
% 26.32/4.34 | | | | | | |
% 26.32/4.34 | | | | | | | ALPHA: (369) implies:
% 26.32/4.34 | | | | | | | (370) $lesseq(1, $difference(all_42_13, all_42_15))
% 26.32/4.34 | | | | | | | (371) mem(all_42_13, all_42_42) = 0
% 26.32/4.34 | | | | | | |
% 26.32/4.34 | | | | | | | GROUND_INST: instantiating (8) with all_42_13, empty, all_42_39,
% 26.32/4.34 | | | | | | | all_42_38, all_42_42, simplifying with (17), (317),
% 26.32/4.34 | | | | | | | (318), (371) gives:
% 26.32/4.34 | | | | | | | (372) all_42_13 = all_42_39 | ? [v0: any] : ? [v1: any] :
% 26.32/4.34 | | | | | | | (mem(all_42_13, all_42_38) = v1 & mem(all_42_13, empty) =
% 26.32/4.34 | | | | | | | v0 & (v1 = 0 | v0 = 0))
% 26.32/4.34 | | | | | | |
% 26.32/4.34 | | | | | | | BETA: splitting (341) gives:
% 26.32/4.34 | | | | | | |
% 26.32/4.34 | | | | | | | Case 1:
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | | (373) $lesseq(1, $difference(all_42_17, all_42_39))
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | | BETA: splitting (342) gives:
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | | Case 1:
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | (374) $lesseq(1, $difference(all_42_39, all_42_17))
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | COMBINE_INEQS: (373), (374) imply:
% 26.32/4.34 | | | | | | | | | (375) $false
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | CLOSE: (375) is inconsistent.
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | Case 2:
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | (376) all_42_15 = all_42_17
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | REDUCE: (370), (376) imply:
% 26.32/4.34 | | | | | | | | | (377) $lesseq(1, $difference(all_42_13, all_42_17))
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | BETA: splitting (372) gives:
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | Case 1:
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | (378) all_42_13 = all_42_39
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | REDUCE: (377), (378) imply:
% 26.32/4.34 | | | | | | | | | | (379) $lesseq(1, $difference(all_42_39, all_42_17))
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | COMBINE_INEQS: (373), (379) imply:
% 26.32/4.34 | | | | | | | | | | (380) $false
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | CLOSE: (380) is inconsistent.
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | Case 2:
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | (381) ? [v0: any] : ? [v1: any] : (mem(all_42_13,
% 26.32/4.34 | | | | | | | | | | all_42_38) = v1 & mem(all_42_13, empty) = v0 &
% 26.32/4.34 | | | | | | | | | | (v1 = 0 | v0 = 0))
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | DELTA: instantiating (381) with fresh symbols all_280_0,
% 26.32/4.34 | | | | | | | | | | all_280_1 gives:
% 26.32/4.34 | | | | | | | | | | (382) mem(all_42_13, all_42_38) = all_280_0 &
% 26.32/4.34 | | | | | | | | | | mem(all_42_13, empty) = all_280_1 & (all_280_0 = 0
% 26.32/4.34 | | | | | | | | | | | all_280_1 = 0)
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | ALPHA: (382) implies:
% 26.32/4.34 | | | | | | | | | | (383) mem(all_42_13, empty) = all_280_1
% 26.32/4.34 | | | | | | | | | | (384) mem(all_42_13, all_42_38) = all_280_0
% 26.32/4.34 | | | | | | | | | | (385) all_280_0 = 0 | all_280_1 = 0
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | BETA: splitting (385) gives:
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | Case 1:
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | | (386) all_280_0 = 0
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | | REDUCE: (384), (386) imply:
% 26.32/4.34 | | | | | | | | | | | (387) mem(all_42_13, all_42_38) = 0
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | | GROUND_INST: instantiating (340) with all_42_13, simplifying
% 26.32/4.34 | | | | | | | | | | | with (387) gives:
% 26.32/4.34 | | | | | | | | | | | (388) $lesseq(all_42_13, all_42_17)
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | | COMBINE_INEQS: (377), (388) imply:
% 26.32/4.34 | | | | | | | | | | | (389) $false
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | | CLOSE: (389) is inconsistent.
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | Case 2:
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | | (390) all_280_1 = 0
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | | REDUCE: (383), (390) imply:
% 26.32/4.34 | | | | | | | | | | | (391) mem(all_42_13, empty) = 0
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_42_13, simplifying with
% 26.32/4.34 | | | | | | | | | | | (391) gives:
% 26.32/4.34 | | | | | | | | | | | (392) $false
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | | CLOSE: (392) is inconsistent.
% 26.32/4.34 | | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | End of split
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | End of split
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | End of split
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | Case 2:
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | | (393) all_42_15 = all_42_39
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | | REDUCE: (370), (393) imply:
% 26.32/4.34 | | | | | | | | (394) $lesseq(1, $difference(all_42_13, all_42_39))
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | | REDUCE: (343), (393) imply:
% 26.32/4.34 | | | | | | | | (395) $lesseq(all_42_17, all_42_39)
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | | BETA: splitting (372) gives:
% 26.32/4.34 | | | | | | | |
% 26.32/4.34 | | | | | | | | Case 1:
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | (396) all_42_13 = all_42_39
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | REDUCE: (394), (396) imply:
% 26.32/4.34 | | | | | | | | | (397) $false
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | CLOSE: (397) is inconsistent.
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | Case 2:
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | (398) ? [v0: any] : ? [v1: any] : (mem(all_42_13,
% 26.32/4.34 | | | | | | | | | all_42_38) = v1 & mem(all_42_13, empty) = v0 &
% 26.32/4.34 | | | | | | | | | (v1 = 0 | v0 = 0))
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | DELTA: instantiating (398) with fresh symbols all_216_0,
% 26.32/4.34 | | | | | | | | | all_216_1 gives:
% 26.32/4.34 | | | | | | | | | (399) mem(all_42_13, all_42_38) = all_216_0 &
% 26.32/4.34 | | | | | | | | | mem(all_42_13, empty) = all_216_1 & (all_216_0 = 0 |
% 26.32/4.34 | | | | | | | | | all_216_1 = 0)
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | ALPHA: (399) implies:
% 26.32/4.34 | | | | | | | | | (400) mem(all_42_13, empty) = all_216_1
% 26.32/4.34 | | | | | | | | | (401) mem(all_42_13, all_42_38) = all_216_0
% 26.32/4.34 | | | | | | | | | (402) all_216_0 = 0 | all_216_1 = 0
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | BETA: splitting (402) gives:
% 26.32/4.34 | | | | | | | | |
% 26.32/4.34 | | | | | | | | | Case 1:
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | (403) all_216_0 = 0
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | REDUCE: (401), (403) imply:
% 26.32/4.34 | | | | | | | | | | (404) mem(all_42_13, all_42_38) = 0
% 26.32/4.34 | | | | | | | | | |
% 26.32/4.34 | | | | | | | | | | GROUND_INST: instantiating (340) with all_42_13, simplifying
% 26.32/4.35 | | | | | | | | | | with (404) gives:
% 26.32/4.35 | | | | | | | | | | (405) $lesseq(all_42_13, all_42_17)
% 26.32/4.35 | | | | | | | | | |
% 26.32/4.35 | | | | | | | | | | COMBINE_INEQS: (394), (405) imply:
% 26.32/4.35 | | | | | | | | | | (406) $lesseq(1, $difference(all_42_17, all_42_39))
% 26.32/4.35 | | | | | | | | | |
% 26.32/4.35 | | | | | | | | | | COMBINE_INEQS: (395), (406) imply:
% 26.32/4.35 | | | | | | | | | | (407) $false
% 26.32/4.35 | | | | | | | | | |
% 26.32/4.35 | | | | | | | | | | CLOSE: (407) is inconsistent.
% 26.32/4.35 | | | | | | | | | |
% 26.32/4.35 | | | | | | | | | Case 2:
% 26.32/4.35 | | | | | | | | | |
% 26.32/4.35 | | | | | | | | | | (408) all_216_1 = 0
% 26.32/4.35 | | | | | | | | | |
% 26.32/4.35 | | | | | | | | | | REDUCE: (400), (408) imply:
% 26.32/4.35 | | | | | | | | | | (409) mem(all_42_13, empty) = 0
% 26.32/4.35 | | | | | | | | | |
% 26.32/4.35 | | | | | | | | | | GROUND_INST: instantiating (7) with all_42_13, simplifying with
% 26.32/4.35 | | | | | | | | | | (409) gives:
% 26.32/4.35 | | | | | | | | | | (410) $false
% 26.32/4.35 | | | | | | | | | |
% 26.32/4.35 | | | | | | | | | | CLOSE: (410) is inconsistent.
% 26.32/4.35 | | | | | | | | | |
% 26.32/4.35 | | | | | | | | | End of split
% 26.32/4.35 | | | | | | | | |
% 26.32/4.35 | | | | | | | | End of split
% 26.32/4.35 | | | | | | | |
% 26.32/4.35 | | | | | | | End of split
% 26.32/4.35 | | | | | | |
% 26.32/4.35 | | | | | | End of split
% 26.32/4.35 | | | | | |
% 26.32/4.35 | | | | | End of split
% 26.32/4.35 | | | | |
% 26.32/4.35 | | | | End of split
% 26.32/4.35 | | | |
% 26.32/4.35 | | | End of split
% 26.32/4.35 | | |
% 26.32/4.35 | | End of split
% 26.32/4.35 | |
% 26.32/4.35 | Case 2:
% 26.32/4.35 | |
% 26.32/4.35 | | (411) all_42_38 = empty & ((all_42_8 = all_42_40 & node(all_42_11,
% 26.32/4.35 | | all_42_10, all_42_9) = all_42_40 & (all_42_40 = empty | ~
% 26.32/4.35 | | ($lesseq(1, $difference(all_42_41, all_42_36))) | ~
% 26.32/4.35 | | ($lesseq(0, all_42_41)) | (all_42_6 = 0 & mem(all_42_5,
% 26.32/4.35 | | all_42_42) = all_42_4 & mem(all_42_7, all_42_40) = 0 &
% 26.32/4.35 | | max(all_42_7, all_42_39) = all_42_5 & ! [v0: int] : ( ~
% 26.32/4.35 | | ($lesseq(1, $difference(v0, all_42_7))) | ~ (mem(v0,
% 26.32/4.35 | | all_42_40) = 0)) & ( ~ (all_42_4 = 0) | (all_42_2 = 0
% 26.32/4.35 | | & $lesseq(1, $difference(all_42_3, all_42_5)) &
% 26.32/4.35 | | mem(all_42_3, all_42_42) = 0))))) | (all_42_40 = empty
% 26.32/4.35 | | & ( ~ (all_42_37 = 0) | (all_42_0 = 0 & $lesseq(1,
% 26.32/4.35 | | $difference(all_42_1, all_42_39)) & mem(all_42_1,
% 26.32/4.35 | | all_42_42) = 0))))
% 26.32/4.35 | |
% 26.32/4.35 | | ALPHA: (411) implies:
% 26.32/4.35 | | (412) all_42_38 = empty
% 26.32/4.35 | | (413) (all_42_8 = all_42_40 & node(all_42_11, all_42_10, all_42_9) =
% 26.32/4.35 | | all_42_40 & (all_42_40 = empty | ~ ($lesseq(1,
% 26.32/4.35 | | $difference(all_42_41, all_42_36))) | ~ ($lesseq(0,
% 26.32/4.35 | | all_42_41)) | (all_42_6 = 0 & mem(all_42_5, all_42_42) =
% 26.32/4.35 | | all_42_4 & mem(all_42_7, all_42_40) = 0 & max(all_42_7,
% 26.32/4.35 | | all_42_39) = all_42_5 & ! [v0: int] : ( ~ ($lesseq(1,
% 26.32/4.35 | | $difference(v0, all_42_7))) | ~ (mem(v0, all_42_40) =
% 26.32/4.35 | | 0)) & ( ~ (all_42_4 = 0) | (all_42_2 = 0 & $lesseq(1,
% 26.32/4.35 | | $difference(all_42_3, all_42_5)) & mem(all_42_3,
% 26.32/4.35 | | all_42_42) = 0))))) | (all_42_40 = empty & ( ~
% 26.32/4.35 | | (all_42_37 = 0) | (all_42_0 = 0 & $lesseq(1,
% 26.32/4.35 | | $difference(all_42_1, all_42_39)) & mem(all_42_1,
% 26.32/4.35 | | all_42_42) = 0)))
% 26.32/4.35 | |
% 26.32/4.35 | | REDUCE: (42), (412) imply:
% 26.32/4.35 | | (414) size(empty) = $sum($difference(all_42_41, all_42_36), -1)
% 26.32/4.35 | |
% 26.32/4.35 | | REDUCE: (24), (412) imply:
% 26.32/4.35 | | (415) node(all_42_40, all_42_39, empty) = all_42_42
% 26.32/4.35 | |
% 26.32/4.35 | | REDUCE: (17), (412) imply:
% 26.32/4.35 | | (416) tree(empty)
% 26.32/4.35 | |
% 26.32/4.35 | | GROUND_INST: instantiating (12) with 0, $sum($difference(all_42_41,
% 26.32/4.35 | | all_42_36), -1), empty, simplifying with (5), (414) gives:
% 26.32/4.35 | | (417) $difference(all_42_36, all_42_41) = -1
% 26.32/4.35 | |
% 26.32/4.35 | | REDUCE: (26), (417) imply:
% 26.32/4.35 | | (418) size(all_42_40) = $sum(all_42_41, -1)
% 26.32/4.35 | |
% 26.32/4.35 | | BETA: splitting (413) gives:
% 26.32/4.35 | |
% 26.32/4.35 | | Case 1:
% 26.32/4.35 | | |
% 26.32/4.35 | | | (419) all_42_8 = all_42_40 & node(all_42_11, all_42_10, all_42_9) =
% 26.32/4.35 | | | all_42_40 & (all_42_40 = empty | ~ ($lesseq(1,
% 26.32/4.35 | | | $difference(all_42_41, all_42_36))) | ~ ($lesseq(0,
% 26.32/4.35 | | | all_42_41)) | (all_42_6 = 0 & mem(all_42_5, all_42_42) =
% 26.32/4.35 | | | all_42_4 & mem(all_42_7, all_42_40) = 0 & max(all_42_7,
% 26.32/4.35 | | | all_42_39) = all_42_5 & ! [v0: int] : ( ~ ($lesseq(1,
% 26.32/4.35 | | | $difference(v0, all_42_7))) | ~ (mem(v0, all_42_40) =
% 26.32/4.35 | | | 0)) & ( ~ (all_42_4 = 0) | (all_42_2 = 0 & $lesseq(1,
% 26.32/4.35 | | | $difference(all_42_3, all_42_5)) & mem(all_42_3,
% 26.32/4.35 | | | all_42_42) = 0))))
% 26.32/4.35 | | |
% 26.32/4.35 | | | ALPHA: (419) implies:
% 26.32/4.35 | | | (420) node(all_42_11, all_42_10, all_42_9) = all_42_40
% 26.32/4.35 | | | (421) all_42_40 = empty | ~ ($lesseq(1, $difference(all_42_41,
% 26.32/4.35 | | | all_42_36))) | ~ ($lesseq(0, all_42_41)) | (all_42_6 = 0 &
% 26.32/4.35 | | | mem(all_42_5, all_42_42) = all_42_4 & mem(all_42_7, all_42_40)
% 26.32/4.35 | | | = 0 & max(all_42_7, all_42_39) = all_42_5 & ! [v0: int] : ( ~
% 26.32/4.35 | | | ($lesseq(1, $difference(v0, all_42_7))) | ~ (mem(v0,
% 26.32/4.35 | | | all_42_40) = 0)) & ( ~ (all_42_4 = 0) | (all_42_2 = 0 &
% 26.32/4.35 | | | $lesseq(1, $difference(all_42_3, all_42_5)) & mem(all_42_3,
% 26.32/4.35 | | | all_42_42) = 0)))
% 26.32/4.35 | | |
% 26.32/4.35 | | | GROUND_INST: instantiating (6) with all_42_11, all_42_10, all_42_9,
% 26.32/4.35 | | | all_42_40, simplifying with (22), (23), (420) gives:
% 26.32/4.35 | | | (422) ? [v0: int] : ? [v1: int] : (size(all_42_9) =
% 26.32/4.35 | | | $sum($difference(v0, v1), -1) & size(all_42_11) = v1 &
% 26.32/4.35 | | | size(all_42_40) = v0)
% 26.32/4.35 | | |
% 26.32/4.35 | | | DELTA: instantiating (422) with fresh symbols all_119_0, all_119_1 gives:
% 26.32/4.35 | | | (423) size(all_42_9) = $sum($difference(all_119_1, all_119_0), -1) &
% 26.32/4.35 | | | size(all_42_11) = all_119_0 & size(all_42_40) = all_119_1
% 26.32/4.35 | | |
% 26.32/4.35 | | | ALPHA: (423) implies:
% 26.32/4.35 | | | (424) size(all_42_40) = all_119_1
% 26.32/4.35 | | | (425) size(all_42_11) = all_119_0
% 26.32/4.35 | | | (426) size(all_42_9) = $sum($difference(all_119_1, all_119_0), -1)
% 26.32/4.35 | | |
% 26.32/4.35 | | | GROUND_INST: instantiating (12) with $sum(all_42_41, -1), all_119_1,
% 26.32/4.35 | | | all_42_40, simplifying with (418), (424) gives:
% 26.32/4.35 | | | (427) $difference(all_119_1, all_42_41) = -1
% 26.32/4.35 | | |
% 26.32/4.35 | | | REDUCE: (426), (427) imply:
% 26.32/4.35 | | | (428) size(all_42_9) = $sum($difference(all_42_41, all_119_0), -2)
% 26.32/4.35 | | |
% 26.32/4.35 | | | GROUND_INST: instantiating (size_nonneg) with all_42_11, all_119_0,
% 26.32/4.35 | | | simplifying with (22), (425) gives:
% 26.32/4.35 | | | (429) $lesseq(0, all_119_0)
% 26.32/4.35 | | |
% 26.32/4.35 | | | GROUND_INST: instantiating (size_nonneg) with all_42_9,
% 26.32/4.35 | | | $sum($difference(all_42_41, all_119_0), -2), simplifying with
% 26.32/4.35 | | | (23), (428) gives:
% 26.32/4.35 | | | (430) $lesseq(2, $difference(all_42_41, all_119_0))
% 26.32/4.35 | | |
% 26.32/4.35 | | | COMBINE_INEQS: (429), (430) imply:
% 26.32/4.35 | | | (431) $lesseq(2, all_42_41)
% 26.32/4.35 | | |
% 26.32/4.35 | | | BETA: splitting (421) gives:
% 26.32/4.35 | | |
% 26.32/4.35 | | | Case 1:
% 26.32/4.35 | | | |
% 26.32/4.35 | | | | (432) $lesseq(all_42_41, -1)
% 26.32/4.35 | | | |
% 26.32/4.35 | | | | COMBINE_INEQS: (431), (432) imply:
% 26.32/4.35 | | | | (433) $false
% 26.32/4.35 | | | |
% 26.32/4.35 | | | | CLOSE: (433) is inconsistent.
% 26.32/4.35 | | | |
% 26.32/4.35 | | | Case 2:
% 26.32/4.35 | | | |
% 26.32/4.35 | | | | (434) all_42_40 = empty | ~ ($lesseq(1, $difference(all_42_41,
% 26.32/4.35 | | | | all_42_36))) | (all_42_6 = 0 & mem(all_42_5, all_42_42) =
% 26.32/4.35 | | | | all_42_4 & mem(all_42_7, all_42_40) = 0 & max(all_42_7,
% 26.32/4.35 | | | | all_42_39) = all_42_5 & ! [v0: int] : ( ~ ($lesseq(1,
% 26.32/4.35 | | | | $difference(v0, all_42_7))) | ~ (mem(v0, all_42_40) =
% 26.32/4.35 | | | | 0)) & ( ~ (all_42_4 = 0) | (all_42_2 = 0 & $lesseq(1,
% 26.32/4.35 | | | | $difference(all_42_3, all_42_5)) & mem(all_42_3,
% 26.32/4.35 | | | | all_42_42) = 0)))
% 26.32/4.35 | | | |
% 26.32/4.35 | | | | BETA: splitting (434) gives:
% 26.32/4.35 | | | |
% 26.32/4.35 | | | | Case 1:
% 26.32/4.35 | | | | |
% 26.32/4.35 | | | | | (435) $lesseq(all_42_41, all_42_36)
% 26.32/4.35 | | | | |
% 26.32/4.35 | | | | | REDUCE: (417), (435) imply:
% 26.32/4.35 | | | | | (436) $false
% 26.32/4.35 | | | | |
% 26.32/4.35 | | | | | CLOSE: (436) is inconsistent.
% 26.32/4.35 | | | | |
% 26.32/4.35 | | | | Case 2:
% 26.32/4.35 | | | | |
% 26.32/4.35 | | | | | (437) all_42_40 = empty | (all_42_6 = 0 & mem(all_42_5, all_42_42)
% 26.32/4.35 | | | | | = all_42_4 & mem(all_42_7, all_42_40) = 0 & max(all_42_7,
% 26.32/4.35 | | | | | all_42_39) = all_42_5 & ! [v0: int] : ( ~ ($lesseq(1,
% 26.32/4.35 | | | | | $difference(v0, all_42_7))) | ~ (mem(v0, all_42_40)
% 26.32/4.35 | | | | | = 0)) & ( ~ (all_42_4 = 0) | (all_42_2 = 0 & $lesseq(1,
% 26.32/4.35 | | | | | $difference(all_42_3, all_42_5)) & mem(all_42_3,
% 26.32/4.35 | | | | | all_42_42) = 0)))
% 26.32/4.35 | | | | |
% 26.32/4.35 | | | | | BETA: splitting (437) gives:
% 26.32/4.35 | | | | |
% 26.32/4.35 | | | | | Case 1:
% 26.32/4.35 | | | | | |
% 26.32/4.35 | | | | | | (438) all_42_40 = empty
% 26.32/4.35 | | | | | |
% 26.32/4.35 | | | | | | REDUCE: (418), (438) imply:
% 26.32/4.35 | | | | | | (439) size(empty) = $sum(all_42_41, -1)
% 26.32/4.35 | | | | | |
% 26.32/4.35 | | | | | | GROUND_INST: instantiating (12) with 0, $sum(all_42_41, -1), empty,
% 26.32/4.35 | | | | | | simplifying with (5), (439) gives:
% 26.32/4.35 | | | | | | (440) all_42_41 = 1
% 26.32/4.35 | | | | | |
% 26.32/4.35 | | | | | | REDUCE: (430), (440) imply:
% 26.32/4.35 | | | | | | (441) $lesseq(all_119_0, -1)
% 26.32/4.35 | | | | | |
% 26.32/4.35 | | | | | | COMBINE_INEQS: (429), (441) imply:
% 26.32/4.35 | | | | | | (442) $false
% 26.32/4.35 | | | | | |
% 26.32/4.35 | | | | | | CLOSE: (442) is inconsistent.
% 26.32/4.35 | | | | | |
% 26.32/4.35 | | | | | Case 2:
% 26.32/4.35 | | | | | |
% 26.32/4.35 | | | | | | (443) all_42_6 = 0 & mem(all_42_5, all_42_42) = all_42_4 &
% 26.32/4.35 | | | | | | mem(all_42_7, all_42_40) = 0 & max(all_42_7, all_42_39) =
% 26.32/4.35 | | | | | | all_42_5 & ! [v0: int] : ( ~ ($lesseq(1, $difference(v0,
% 26.32/4.35 | | | | | | all_42_7))) | ~ (mem(v0, all_42_40) = 0)) & ( ~
% 26.32/4.35 | | | | | | (all_42_4 = 0) | (all_42_2 = 0 & $lesseq(1,
% 26.32/4.35 | | | | | | $difference(all_42_3, all_42_5)) & mem(all_42_3,
% 26.32/4.35 | | | | | | all_42_42) = 0))
% 26.32/4.35 | | | | | |
% 26.32/4.35 | | | | | | ALPHA: (443) implies:
% 26.32/4.35 | | | | | | (444) max(all_42_7, all_42_39) = all_42_5
% 26.32/4.35 | | | | | | (445) mem(all_42_7, all_42_40) = 0
% 26.32/4.35 | | | | | | (446) mem(all_42_5, all_42_42) = all_42_4
% 26.32/4.35 | | | | | | (447) ~ (all_42_4 = 0) | (all_42_2 = 0 & $lesseq(1,
% 26.32/4.35 | | | | | | $difference(all_42_3, all_42_5)) & mem(all_42_3,
% 26.32/4.35 | | | | | | all_42_42) = 0)
% 26.32/4.35 | | | | | | (448) ! [v0: int] : ( ~ ($lesseq(1, $difference(v0, all_42_7)))
% 26.32/4.35 | | | | | | | ~ (mem(v0, all_42_40) = 0))
% 26.32/4.35 | | | | | |
% 26.32/4.35 | | | | | | GROUND_INST: instantiating (max_y) with all_42_7, all_42_39,
% 26.32/4.35 | | | | | | all_42_5, simplifying with (444) gives:
% 26.32/4.35 | | | | | | (449) all_42_5 = all_42_39 | ~ ($lesseq(all_42_7, all_42_39))
% 26.32/4.35 | | | | | |
% 26.32/4.35 | | | | | | GROUND_INST: instantiating (max_x) with all_42_7, all_42_39,
% 26.32/4.35 | | | | | | all_42_5, simplifying with (444) gives:
% 26.32/4.35 | | | | | | (450) all_42_5 = all_42_7 | ~ ($lesseq(all_42_39, all_42_7))
% 26.32/4.35 | | | | | |
% 26.32/4.35 | | | | | | GROUND_INST: instantiating (1) with all_42_7, all_42_39, all_42_5,
% 26.32/4.35 | | | | | | simplifying with (444) gives:
% 26.32/4.35 | | | | | | (451) $lesseq(all_42_7, all_42_5)
% 26.32/4.35 | | | | | |
% 26.32/4.35 | | | | | | GROUND_INST: instantiating (9) with all_42_39, all_42_40, empty,
% 26.32/4.35 | | | | | | all_42_42, all_42_4, simplifying with (16), (415),
% 26.32/4.35 | | | | | | (416) gives:
% 26.32/4.35 | | | | | | (452) all_42_4 = 0 | ~ (mem(all_42_39, all_42_42) = all_42_4)
% 26.32/4.35 | | | | | |
% 26.32/4.35 | | | | | | GROUND_INST: instantiating (10) with all_42_5, all_42_40, all_42_39,
% 26.32/4.35 | | | | | | empty, all_42_42, all_42_4, simplifying with (16),
% 26.32/4.35 | | | | | | (415), (416), (446) gives:
% 26.32/4.35 | | | | | | (453) all_42_4 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) &
% 26.32/4.35 | | | | | | ~ (v0 = 0) & mem(all_42_5, all_42_40) = v0 &
% 26.32/4.35 | | | | | | mem(all_42_5, empty) = v1)
% 26.32/4.35 | | | | | |
% 26.32/4.35 | | | | | | BETA: splitting (447) gives:
% 26.32/4.35 | | | | | |
% 26.32/4.35 | | | | | | Case 1:
% 26.32/4.35 | | | | | | |
% 26.32/4.35 | | | | | | | (454) ~ (all_42_4 = 0)
% 26.32/4.35 | | | | | | |
% 26.32/4.35 | | | | | | | BETA: splitting (453) gives:
% 26.32/4.35 | | | | | | |
% 26.32/4.35 | | | | | | | Case 1:
% 26.32/4.35 | | | | | | | |
% 26.32/4.35 | | | | | | | | (455) all_42_4 = 0
% 26.32/4.35 | | | | | | | |
% 26.32/4.35 | | | | | | | | REDUCE: (454), (455) imply:
% 26.32/4.35 | | | | | | | | (456) $false
% 26.32/4.35 | | | | | | | |
% 26.32/4.35 | | | | | | | | CLOSE: (456) is inconsistent.
% 26.32/4.35 | | | | | | | |
% 26.32/4.35 | | | | | | | Case 2:
% 26.32/4.35 | | | | | | | |
% 26.32/4.36 | | | | | | | | (457) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 =
% 26.32/4.36 | | | | | | | | 0) & mem(all_42_5, all_42_40) = v0 & mem(all_42_5,
% 26.32/4.36 | | | | | | | | empty) = v1)
% 26.32/4.36 | | | | | | | |
% 26.32/4.36 | | | | | | | | DELTA: instantiating (457) with fresh symbols all_203_0,
% 26.32/4.36 | | | | | | | | all_203_1 gives:
% 26.32/4.36 | | | | | | | | (458) ~ (all_203_0 = 0) & ~ (all_203_1 = 0) & mem(all_42_5,
% 26.32/4.36 | | | | | | | | all_42_40) = all_203_1 & mem(all_42_5, empty) =
% 26.32/4.36 | | | | | | | | all_203_0
% 26.32/4.36 | | | | | | | |
% 26.32/4.36 | | | | | | | | ALPHA: (458) implies:
% 26.32/4.36 | | | | | | | | (459) ~ (all_203_1 = 0)
% 26.32/4.36 | | | | | | | | (460) mem(all_42_5, all_42_40) = all_203_1
% 26.32/4.36 | | | | | | | |
% 26.32/4.36 | | | | | | | | GROUND_INST: instantiating (14) with 0, all_203_1, all_42_40,
% 26.32/4.36 | | | | | | | | all_42_7, simplifying with (445) gives:
% 26.32/4.36 | | | | | | | | (461) all_203_1 = 0 | ~ (mem(all_42_7, all_42_40) =
% 26.32/4.36 | | | | | | | | all_203_1)
% 26.32/4.36 | | | | | | | |
% 26.32/4.36 | | | | | | | | BETA: splitting (449) gives:
% 26.32/4.36 | | | | | | | |
% 26.32/4.36 | | | | | | | | Case 1:
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | (462) $lesseq(1, $difference(all_42_7, all_42_39))
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | BETA: splitting (450) gives:
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | Case 1:
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | (463) $lesseq(1, $difference(all_42_39, all_42_7))
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | COMBINE_INEQS: (462), (463) imply:
% 26.32/4.36 | | | | | | | | | | (464) $false
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | CLOSE: (464) is inconsistent.
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | Case 2:
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | (465) all_42_5 = all_42_7
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | REDUCE: (460), (465) imply:
% 26.32/4.36 | | | | | | | | | | (466) mem(all_42_7, all_42_40) = all_203_1
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | BETA: splitting (461) gives:
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | Case 1:
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | | (467) ~ (mem(all_42_7, all_42_40) = all_203_1)
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | | PRED_UNIFY: (466), (467) imply:
% 26.32/4.36 | | | | | | | | | | | (468) $false
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | | CLOSE: (468) is inconsistent.
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | Case 2:
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | | (469) all_203_1 = 0
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | | REDUCE: (459), (469) imply:
% 26.32/4.36 | | | | | | | | | | | (470) $false
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | | CLOSE: (470) is inconsistent.
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | End of split
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | End of split
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | Case 2:
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | (471) all_42_5 = all_42_39
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | REDUCE: (446), (471) imply:
% 26.32/4.36 | | | | | | | | | (472) mem(all_42_39, all_42_42) = all_42_4
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | BETA: splitting (452) gives:
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | Case 1:
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | (473) ~ (mem(all_42_39, all_42_42) = all_42_4)
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | PRED_UNIFY: (472), (473) imply:
% 26.32/4.36 | | | | | | | | | | (474) $false
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | CLOSE: (474) is inconsistent.
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | Case 2:
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | (475) all_42_4 = 0
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | REDUCE: (454), (475) imply:
% 26.32/4.36 | | | | | | | | | | (476) $false
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | CLOSE: (476) is inconsistent.
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | End of split
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | End of split
% 26.32/4.36 | | | | | | | |
% 26.32/4.36 | | | | | | | End of split
% 26.32/4.36 | | | | | | |
% 26.32/4.36 | | | | | | Case 2:
% 26.32/4.36 | | | | | | |
% 26.32/4.36 | | | | | | | (477) all_42_2 = 0 & $lesseq(1, $difference(all_42_3,
% 26.32/4.36 | | | | | | | all_42_5)) & mem(all_42_3, all_42_42) = 0
% 26.32/4.36 | | | | | | |
% 26.32/4.36 | | | | | | | ALPHA: (477) implies:
% 26.32/4.36 | | | | | | | (478) $lesseq(1, $difference(all_42_3, all_42_5))
% 26.32/4.36 | | | | | | | (479) mem(all_42_3, all_42_42) = 0
% 26.32/4.36 | | | | | | |
% 26.32/4.36 | | | | | | | GROUND_INST: instantiating (8) with all_42_3, all_42_40,
% 26.32/4.36 | | | | | | | all_42_39, empty, all_42_42, simplifying with (16),
% 26.32/4.36 | | | | | | | (415), (416), (479) gives:
% 26.32/4.36 | | | | | | | (480) all_42_3 = all_42_39 | ? [v0: any] : ? [v1: any] :
% 26.32/4.36 | | | | | | | (mem(all_42_3, all_42_40) = v0 & mem(all_42_3, empty) =
% 26.32/4.36 | | | | | | | v1 & (v1 = 0 | v0 = 0))
% 26.32/4.36 | | | | | | |
% 26.32/4.36 | | | | | | | BETA: splitting (449) gives:
% 26.32/4.36 | | | | | | |
% 26.32/4.36 | | | | | | | Case 1:
% 26.32/4.36 | | | | | | | |
% 26.32/4.36 | | | | | | | | (481) $lesseq(1, $difference(all_42_7, all_42_39))
% 26.32/4.36 | | | | | | | |
% 26.32/4.36 | | | | | | | | BETA: splitting (450) gives:
% 26.32/4.36 | | | | | | | |
% 26.32/4.36 | | | | | | | | Case 1:
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | (482) $lesseq(1, $difference(all_42_39, all_42_7))
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | COMBINE_INEQS: (481), (482) imply:
% 26.32/4.36 | | | | | | | | | (483) $false
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | CLOSE: (483) is inconsistent.
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | Case 2:
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | (484) all_42_5 = all_42_7
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | REDUCE: (478), (484) imply:
% 26.32/4.36 | | | | | | | | | (485) $lesseq(1, $difference(all_42_3, all_42_7))
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | BETA: splitting (480) gives:
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | Case 1:
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | (486) all_42_3 = all_42_39
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | REDUCE: (485), (486) imply:
% 26.32/4.36 | | | | | | | | | | (487) $lesseq(1, $difference(all_42_39, all_42_7))
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | COMBINE_INEQS: (481), (487) imply:
% 26.32/4.36 | | | | | | | | | | (488) $false
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | CLOSE: (488) is inconsistent.
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | Case 2:
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | (489) ? [v0: any] : ? [v1: any] : (mem(all_42_3,
% 26.32/4.36 | | | | | | | | | | all_42_40) = v0 & mem(all_42_3, empty) = v1 &
% 26.32/4.36 | | | | | | | | | | (v1 = 0 | v0 = 0))
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | DELTA: instantiating (489) with fresh symbols all_280_0,
% 26.32/4.36 | | | | | | | | | | all_280_1 gives:
% 26.32/4.36 | | | | | | | | | | (490) mem(all_42_3, all_42_40) = all_280_1 &
% 26.32/4.36 | | | | | | | | | | mem(all_42_3, empty) = all_280_0 & (all_280_0 = 0 |
% 26.32/4.36 | | | | | | | | | | all_280_1 = 0)
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | ALPHA: (490) implies:
% 26.32/4.36 | | | | | | | | | | (491) mem(all_42_3, empty) = all_280_0
% 26.32/4.36 | | | | | | | | | | (492) mem(all_42_3, all_42_40) = all_280_1
% 26.32/4.36 | | | | | | | | | | (493) all_280_0 = 0 | all_280_1 = 0
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | BETA: splitting (493) gives:
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | Case 1:
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | | (494) all_280_0 = 0
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | | REDUCE: (491), (494) imply:
% 26.32/4.36 | | | | | | | | | | | (495) mem(all_42_3, empty) = 0
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_42_3, simplifying with
% 26.32/4.36 | | | | | | | | | | | (495) gives:
% 26.32/4.36 | | | | | | | | | | | (496) $false
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | | CLOSE: (496) is inconsistent.
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | Case 2:
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | | (497) all_280_1 = 0
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | | REDUCE: (492), (497) imply:
% 26.32/4.36 | | | | | | | | | | | (498) mem(all_42_3, all_42_40) = 0
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | | GROUND_INST: instantiating (448) with all_42_3, simplifying
% 26.32/4.36 | | | | | | | | | | | with (498) gives:
% 26.32/4.36 | | | | | | | | | | | (499) $lesseq(all_42_3, all_42_7)
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | | COMBINE_INEQS: (485), (499) imply:
% 26.32/4.36 | | | | | | | | | | | (500) $false
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | | CLOSE: (500) is inconsistent.
% 26.32/4.36 | | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | End of split
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | End of split
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | End of split
% 26.32/4.36 | | | | | | | |
% 26.32/4.36 | | | | | | | Case 2:
% 26.32/4.36 | | | | | | | |
% 26.32/4.36 | | | | | | | | (501) all_42_5 = all_42_39
% 26.32/4.36 | | | | | | | |
% 26.32/4.36 | | | | | | | | REDUCE: (478), (501) imply:
% 26.32/4.36 | | | | | | | | (502) $lesseq(1, $difference(all_42_3, all_42_39))
% 26.32/4.36 | | | | | | | |
% 26.32/4.36 | | | | | | | | REDUCE: (451), (501) imply:
% 26.32/4.36 | | | | | | | | (503) $lesseq(all_42_7, all_42_39)
% 26.32/4.36 | | | | | | | |
% 26.32/4.36 | | | | | | | | BETA: splitting (480) gives:
% 26.32/4.36 | | | | | | | |
% 26.32/4.36 | | | | | | | | Case 1:
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | (504) all_42_3 = all_42_39
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | REDUCE: (502), (504) imply:
% 26.32/4.36 | | | | | | | | | (505) $false
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | CLOSE: (505) is inconsistent.
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | Case 2:
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | (506) ? [v0: any] : ? [v1: any] : (mem(all_42_3,
% 26.32/4.36 | | | | | | | | | all_42_40) = v0 & mem(all_42_3, empty) = v1 & (v1
% 26.32/4.36 | | | | | | | | | = 0 | v0 = 0))
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | DELTA: instantiating (506) with fresh symbols all_216_0,
% 26.32/4.36 | | | | | | | | | all_216_1 gives:
% 26.32/4.36 | | | | | | | | | (507) mem(all_42_3, all_42_40) = all_216_1 & mem(all_42_3,
% 26.32/4.36 | | | | | | | | | empty) = all_216_0 & (all_216_0 = 0 | all_216_1 =
% 26.32/4.36 | | | | | | | | | 0)
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | ALPHA: (507) implies:
% 26.32/4.36 | | | | | | | | | (508) mem(all_42_3, empty) = all_216_0
% 26.32/4.36 | | | | | | | | | (509) mem(all_42_3, all_42_40) = all_216_1
% 26.32/4.36 | | | | | | | | | (510) all_216_0 = 0 | all_216_1 = 0
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | BETA: splitting (510) gives:
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | | Case 1:
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | (511) all_216_0 = 0
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | REDUCE: (508), (511) imply:
% 26.32/4.36 | | | | | | | | | | (512) mem(all_42_3, empty) = 0
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | GROUND_INST: instantiating (7) with all_42_3, simplifying with
% 26.32/4.36 | | | | | | | | | | (512) gives:
% 26.32/4.36 | | | | | | | | | | (513) $false
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | CLOSE: (513) is inconsistent.
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | Case 2:
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | (514) all_216_1 = 0
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | REDUCE: (509), (514) imply:
% 26.32/4.36 | | | | | | | | | | (515) mem(all_42_3, all_42_40) = 0
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | GROUND_INST: instantiating (448) with all_42_3, simplifying
% 26.32/4.36 | | | | | | | | | | with (515) gives:
% 26.32/4.36 | | | | | | | | | | (516) $lesseq(all_42_3, all_42_7)
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | COMBINE_INEQS: (502), (516) imply:
% 26.32/4.36 | | | | | | | | | | (517) $lesseq(1, $difference(all_42_7, all_42_39))
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | COMBINE_INEQS: (503), (517) imply:
% 26.32/4.36 | | | | | | | | | | (518) $false
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | | CLOSE: (518) is inconsistent.
% 26.32/4.36 | | | | | | | | | |
% 26.32/4.36 | | | | | | | | | End of split
% 26.32/4.36 | | | | | | | | |
% 26.32/4.36 | | | | | | | | End of split
% 26.32/4.36 | | | | | | | |
% 26.32/4.36 | | | | | | | End of split
% 26.32/4.36 | | | | | | |
% 26.32/4.36 | | | | | | End of split
% 26.32/4.36 | | | | | |
% 26.32/4.36 | | | | | End of split
% 26.32/4.36 | | | | |
% 26.32/4.36 | | | | End of split
% 26.32/4.36 | | | |
% 26.32/4.36 | | | End of split
% 26.32/4.36 | | |
% 26.32/4.36 | | Case 2:
% 26.32/4.36 | | |
% 26.32/4.36 | | | (519) all_42_40 = empty & ( ~ (all_42_37 = 0) | (all_42_0 = 0 &
% 26.32/4.36 | | | $lesseq(1, $difference(all_42_1, all_42_39)) & mem(all_42_1,
% 26.32/4.36 | | | all_42_42) = 0))
% 26.32/4.36 | | |
% 26.32/4.36 | | | ALPHA: (519) implies:
% 26.32/4.36 | | | (520) all_42_40 = empty
% 26.32/4.36 | | | (521) ~ (all_42_37 = 0) | (all_42_0 = 0 & $lesseq(1,
% 26.32/4.36 | | | $difference(all_42_1, all_42_39)) & mem(all_42_1, all_42_42)
% 26.32/4.36 | | | = 0)
% 26.32/4.36 | | |
% 26.32/4.36 | | | REDUCE: (415), (520) imply:
% 26.32/4.36 | | | (522) node(empty, all_42_39, empty) = all_42_42
% 26.32/4.36 | | |
% 26.32/4.36 | | | BETA: splitting (521) gives:
% 26.32/4.36 | | |
% 26.32/4.36 | | | Case 1:
% 26.32/4.36 | | | |
% 26.32/4.36 | | | | (523) ~ (all_42_37 = 0)
% 26.32/4.36 | | | |
% 26.32/4.36 | | | | REDUCE: (31), (523) imply:
% 26.32/4.36 | | | | (524) $false
% 26.32/4.36 | | | |
% 26.32/4.36 | | | | CLOSE: (524) is inconsistent.
% 26.32/4.36 | | | |
% 26.32/4.36 | | | Case 2:
% 26.32/4.36 | | | |
% 26.32/4.36 | | | | (525) all_42_0 = 0 & $lesseq(1, $difference(all_42_1, all_42_39)) &
% 26.32/4.36 | | | | mem(all_42_1, all_42_42) = 0
% 26.32/4.36 | | | |
% 26.32/4.36 | | | | ALPHA: (525) implies:
% 26.32/4.36 | | | | (526) $lesseq(1, $difference(all_42_1, all_42_39))
% 26.32/4.36 | | | | (527) mem(all_42_1, all_42_42) = 0
% 26.32/4.36 | | | |
% 26.32/4.36 | | | | GROUND_INST: instantiating (8) with all_42_1, empty, all_42_39, empty,
% 26.32/4.36 | | | | all_42_42, simplifying with (416), (522), (527) gives:
% 26.32/4.36 | | | | (528) all_42_1 = all_42_39 | ? [v0: any] : ? [v1: any] :
% 26.32/4.36 | | | | (mem(all_42_1, empty) = v1 & mem(all_42_1, empty) = v0 & (v1 =
% 26.32/4.36 | | | | 0 | v0 = 0))
% 26.32/4.36 | | | |
% 26.32/4.36 | | | | BETA: splitting (528) gives:
% 26.32/4.36 | | | |
% 26.32/4.36 | | | | Case 1:
% 26.32/4.36 | | | | |
% 26.32/4.36 | | | | | (529) all_42_1 = all_42_39
% 26.32/4.36 | | | | |
% 26.32/4.36 | | | | | REDUCE: (526), (529) imply:
% 26.32/4.36 | | | | | (530) $false
% 26.32/4.36 | | | | |
% 26.32/4.36 | | | | | CLOSE: (530) is inconsistent.
% 26.32/4.36 | | | | |
% 26.32/4.36 | | | | Case 2:
% 26.32/4.36 | | | | |
% 26.32/4.36 | | | | | (531) ? [v0: any] : ? [v1: any] : (mem(all_42_1, empty) = v1 &
% 26.32/4.36 | | | | | mem(all_42_1, empty) = v0 & (v1 = 0 | v0 = 0))
% 26.32/4.36 | | | | |
% 26.32/4.36 | | | | | DELTA: instantiating (531) with fresh symbols all_136_0, all_136_1
% 26.32/4.36 | | | | | gives:
% 26.32/4.36 | | | | | (532) mem(all_42_1, empty) = all_136_0 & mem(all_42_1, empty) =
% 26.32/4.36 | | | | | all_136_1 & (all_136_0 = 0 | all_136_1 = 0)
% 26.32/4.36 | | | | |
% 26.32/4.36 | | | | | ALPHA: (532) implies:
% 26.32/4.36 | | | | | (533) mem(all_42_1, empty) = all_136_1
% 26.32/4.36 | | | | | (534) mem(all_42_1, empty) = all_136_0
% 26.32/4.36 | | | | | (535) all_136_0 = 0 | all_136_1 = 0
% 26.32/4.36 | | | | |
% 26.32/4.36 | | | | | GROUND_INST: instantiating (14) with all_136_1, all_136_0, empty,
% 26.32/4.36 | | | | | all_42_1, simplifying with (533), (534) gives:
% 26.32/4.36 | | | | | (536) all_136_0 = all_136_1
% 26.32/4.36 | | | | |
% 26.32/4.36 | | | | | BETA: splitting (535) gives:
% 26.32/4.36 | | | | |
% 26.32/4.36 | | | | | Case 1:
% 26.32/4.36 | | | | | |
% 26.32/4.36 | | | | | | (537) all_136_0 = 0
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | | COMBINE_EQS: (536), (537) imply:
% 26.32/4.37 | | | | | | (538) all_136_1 = 0
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | | REDUCE: (533), (538) imply:
% 26.32/4.37 | | | | | | (539) mem(all_42_1, empty) = 0
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | | GROUND_INST: instantiating (7) with all_42_1, simplifying with (539)
% 26.32/4.37 | | | | | | gives:
% 26.32/4.37 | | | | | | (540) $false
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | | CLOSE: (540) is inconsistent.
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | Case 2:
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | | (541) all_136_1 = 0
% 26.32/4.37 | | | | | | (542) ~ (all_136_0 = 0)
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | | COMBINE_EQS: (536), (541) imply:
% 26.32/4.37 | | | | | | (543) all_136_0 = 0
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | | REDUCE: (542), (543) imply:
% 26.32/4.37 | | | | | | (544) $false
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | | CLOSE: (544) is inconsistent.
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | End of split
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | End of split
% 26.32/4.37 | | | |
% 26.32/4.37 | | | End of split
% 26.32/4.37 | | |
% 26.32/4.37 | | End of split
% 26.32/4.37 | |
% 26.32/4.37 | End of split
% 26.32/4.37 |
% 26.32/4.37 End of proof
% 26.32/4.37
% 26.32/4.37 Sub-proof #1 shows that the following formulas are inconsistent:
% 26.32/4.37 ----------------------------------------------------------------
% 26.32/4.37 (1) all_42_21 = all_42_26 | ~ ($lesseq(all_42_23, all_42_26))
% 26.32/4.37 (2) ! [v0: int] : ( ~ ($lesseq(1, $difference(v0, all_42_26))) | ~ (mem(v0,
% 26.32/4.37 all_42_38) = 0))
% 26.32/4.37 (3) $lesseq(1, $difference(all_42_19, all_42_21))
% 26.32/4.37 (4) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | v2 = v0 | ~
% 26.32/4.37 (max(v0, v1) = v2))
% 26.32/4.37 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: tree] :
% 26.32/4.37 ! [v3: int] : (v1 = v0 | ~ (mem(v3, v2) = v1) | ~ (mem(v3, v2) = v0))
% 26.32/4.37 (6) ! [v0: int] : ( ~ ($lesseq(1, $difference(v0, all_42_23))) | ~ (mem(v0,
% 26.32/4.37 all_42_40) = 0))
% 26.32/4.37 (7) mem(all_42_23, all_42_40) = 0
% 26.32/4.37 (8) $lesseq(1, $difference(all_42_26, all_42_23))
% 26.32/4.37 (9) max(all_42_26, all_42_39) = all_42_26
% 26.32/4.37 (10) $lesseq(all_42_39, all_42_26)
% 26.32/4.37 (11) all_42_19 = all_42_39 | ? [v0: any] : ? [v1: any] : (mem(all_42_19,
% 26.32/4.37 all_42_38) = v1 & mem(all_42_19, all_42_40) = v0 & (v1 = 0 | v0 =
% 26.32/4.37 0))
% 26.32/4.37 (12) all_42_21 = all_42_39 | ~ (max(all_42_39, all_42_39) = all_42_21) | ~
% 26.32/4.37 (max(all_42_39, all_42_39) = all_42_39)
% 26.32/4.37
% 26.32/4.37 Begin of proof
% 26.32/4.37 |
% 26.32/4.37 | BETA: splitting (1) gives:
% 26.32/4.37 |
% 26.32/4.37 | Case 1:
% 26.32/4.37 | |
% 26.32/4.37 | | (13) $lesseq(1, $difference(all_42_23, all_42_26))
% 26.32/4.37 | |
% 26.32/4.37 | | COMBINE_INEQS: (8), (13) imply:
% 26.32/4.37 | | (14) $false
% 26.32/4.37 | |
% 26.32/4.37 | | CLOSE: (14) is inconsistent.
% 26.32/4.37 | |
% 26.32/4.37 | Case 2:
% 26.32/4.37 | |
% 26.32/4.37 | | (15) all_42_21 = all_42_26
% 26.32/4.37 | |
% 26.32/4.37 | | REDUCE: (3), (15) imply:
% 26.32/4.37 | | (16) $lesseq(1, $difference(all_42_19, all_42_26))
% 26.32/4.37 | |
% 26.32/4.37 | | BETA: splitting (12) gives:
% 26.32/4.37 | |
% 26.32/4.37 | | Case 1:
% 26.32/4.37 | | |
% 26.32/4.37 | | | (17) ~ (max(all_42_39, all_42_39) = all_42_21)
% 26.32/4.37 | | |
% 26.32/4.37 | | | REDUCE: (15), (17) imply:
% 26.32/4.37 | | | (18) ~ (max(all_42_39, all_42_39) = all_42_26)
% 26.32/4.37 | | |
% 26.32/4.37 | | | PRED_UNIFY: (9), (18) imply:
% 26.32/4.37 | | | (19) ~ (all_42_26 = all_42_39)
% 26.32/4.37 | | |
% 26.32/4.37 | | | STRENGTHEN: (10), (19) imply:
% 26.32/4.37 | | | (20) $lesseq(1, $difference(all_42_26, all_42_39))
% 26.32/4.37 | | |
% 26.32/4.37 | | | BETA: splitting (11) gives:
% 26.32/4.37 | | |
% 26.32/4.37 | | | Case 1:
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | (21) all_42_19 = all_42_39
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | REDUCE: (16), (21) imply:
% 26.32/4.37 | | | | (22) $lesseq(1, $difference(all_42_39, all_42_26))
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | COMBINE_INEQS: (20), (22) imply:
% 26.32/4.37 | | | | (23) $false
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | CLOSE: (23) is inconsistent.
% 26.32/4.37 | | | |
% 26.32/4.37 | | | Case 2:
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | (24) ? [v0: any] : ? [v1: any] : (mem(all_42_19, all_42_38) = v1 &
% 26.32/4.37 | | | | mem(all_42_19, all_42_40) = v0 & (v1 = 0 | v0 = 0))
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | DELTA: instantiating (24) with fresh symbols all_387_0, all_387_1 gives:
% 26.32/4.37 | | | | (25) mem(all_42_19, all_42_38) = all_387_0 & mem(all_42_19,
% 26.32/4.37 | | | | all_42_40) = all_387_1 & (all_387_0 = 0 | all_387_1 = 0)
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | ALPHA: (25) implies:
% 26.32/4.37 | | | | (26) mem(all_42_19, all_42_40) = all_387_1
% 26.32/4.37 | | | | (27) mem(all_42_19, all_42_38) = all_387_0
% 26.32/4.37 | | | | (28) all_387_0 = 0 | all_387_1 = 0
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | GROUND_INST: instantiating (5) with 0, all_387_1, all_42_40, all_42_23,
% 26.32/4.37 | | | | simplifying with (7) gives:
% 26.32/4.37 | | | | (29) all_387_1 = 0 | ~ (mem(all_42_23, all_42_40) = all_387_1)
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | BETA: splitting (29) gives:
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | Case 1:
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | (30) ~ (mem(all_42_23, all_42_40) = all_387_1)
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | BETA: splitting (28) gives:
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | Case 1:
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | | (31) all_387_0 = 0
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | | REDUCE: (27), (31) imply:
% 26.32/4.37 | | | | | | (32) mem(all_42_19, all_42_38) = 0
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | | GROUND_INST: instantiating (2) with all_42_19, simplifying with (32)
% 26.32/4.37 | | | | | | gives:
% 26.32/4.37 | | | | | | (33) $lesseq(all_42_19, all_42_26)
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | | COMBINE_INEQS: (16), (33) imply:
% 26.32/4.37 | | | | | | (34) $false
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | | CLOSE: (34) is inconsistent.
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | Case 2:
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | | (35) all_387_1 = 0
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | | REDUCE: (30), (35) imply:
% 26.32/4.37 | | | | | | (36) ~ (mem(all_42_23, all_42_40) = 0)
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | | PRED_UNIFY: (7), (36) imply:
% 26.32/4.37 | | | | | | (37) $false
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | | CLOSE: (37) is inconsistent.
% 26.32/4.37 | | | | | |
% 26.32/4.37 | | | | | End of split
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | Case 2:
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | (38) all_387_1 = 0
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | REDUCE: (26), (38) imply:
% 26.32/4.37 | | | | | (39) mem(all_42_19, all_42_40) = 0
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | GROUND_INST: instantiating (6) with all_42_19, simplifying with (39)
% 26.32/4.37 | | | | | gives:
% 26.32/4.37 | | | | | (40) $lesseq(all_42_19, all_42_23)
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | COMBINE_INEQS: (16), (40) imply:
% 26.32/4.37 | | | | | (41) $lesseq(1, $difference(all_42_23, all_42_26))
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | COMBINE_INEQS: (8), (41) imply:
% 26.32/4.37 | | | | | (42) $false
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | CLOSE: (42) is inconsistent.
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | End of split
% 26.32/4.37 | | | |
% 26.32/4.37 | | | End of split
% 26.32/4.37 | | |
% 26.32/4.37 | | Case 2:
% 26.32/4.37 | | |
% 26.32/4.37 | | | (43) max(all_42_39, all_42_39) = all_42_21
% 26.32/4.37 | | |
% 26.32/4.37 | | | REDUCE: (15), (43) imply:
% 26.32/4.37 | | | (44) max(all_42_39, all_42_39) = all_42_26
% 26.32/4.37 | | |
% 26.32/4.37 | | | GROUND_INST: instantiating (4) with all_42_39, all_42_39, all_42_26,
% 26.32/4.37 | | | simplifying with (44) gives:
% 26.32/4.37 | | | (45) all_42_26 = all_42_39
% 26.32/4.37 | | |
% 26.32/4.37 | | | REDUCE: (16), (45) imply:
% 26.32/4.37 | | | (46) $lesseq(1, $difference(all_42_19, all_42_39))
% 26.32/4.37 | | |
% 26.32/4.37 | | | REDUCE: (8), (45) imply:
% 26.32/4.37 | | | (47) $lesseq(1, $difference(all_42_39, all_42_23))
% 26.32/4.37 | | |
% 26.32/4.37 | | | BETA: splitting (11) gives:
% 26.32/4.37 | | |
% 26.32/4.37 | | | Case 1:
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | (48) all_42_19 = all_42_39
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | REDUCE: (46), (48) imply:
% 26.32/4.37 | | | | (49) $false
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | CLOSE: (49) is inconsistent.
% 26.32/4.37 | | | |
% 26.32/4.37 | | | Case 2:
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | (50) ? [v0: any] : ? [v1: any] : (mem(all_42_19, all_42_38) = v1 &
% 26.32/4.37 | | | | mem(all_42_19, all_42_40) = v0 & (v1 = 0 | v0 = 0))
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | DELTA: instantiating (50) with fresh symbols all_343_0, all_343_1 gives:
% 26.32/4.37 | | | | (51) mem(all_42_19, all_42_38) = all_343_0 & mem(all_42_19,
% 26.32/4.37 | | | | all_42_40) = all_343_1 & (all_343_0 = 0 | all_343_1 = 0)
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | ALPHA: (51) implies:
% 26.32/4.37 | | | | (52) mem(all_42_19, all_42_40) = all_343_1
% 26.32/4.37 | | | | (53) mem(all_42_19, all_42_38) = all_343_0
% 26.32/4.37 | | | | (54) all_343_0 = 0 | all_343_1 = 0
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | BETA: splitting (54) gives:
% 26.32/4.37 | | | |
% 26.32/4.37 | | | | Case 1:
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | (55) all_343_0 = 0
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | REDUCE: (53), (55) imply:
% 26.32/4.37 | | | | | (56) mem(all_42_19, all_42_38) = 0
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | REF_CLOSE: (2), (45), (46), (56) are inconsistent by sub-proof #2.
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | Case 2:
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | (57) all_343_1 = 0
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | REDUCE: (52), (57) imply:
% 26.32/4.37 | | | | | (58) mem(all_42_19, all_42_40) = 0
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | GROUND_INST: instantiating (6) with all_42_19, simplifying with (58)
% 26.32/4.37 | | | | | gives:
% 26.32/4.37 | | | | | (59) $lesseq(all_42_19, all_42_23)
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | COMBINE_INEQS: (46), (59) imply:
% 26.32/4.37 | | | | | (60) $lesseq(1, $difference(all_42_23, all_42_39))
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | COMBINE_INEQS: (47), (60) imply:
% 26.32/4.37 | | | | | (61) $false
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | | CLOSE: (61) is inconsistent.
% 26.32/4.37 | | | | |
% 26.32/4.37 | | | | End of split
% 26.32/4.37 | | | |
% 26.32/4.37 | | | End of split
% 26.32/4.37 | | |
% 26.32/4.37 | | End of split
% 26.32/4.37 | |
% 26.32/4.37 | End of split
% 26.32/4.37 |
% 26.32/4.37 End of proof
% 26.32/4.37
% 26.32/4.37 Sub-proof #2 shows that the following formulas are inconsistent:
% 26.32/4.37 ----------------------------------------------------------------
% 26.32/4.37 (1) ! [v0: int] : ( ~ ($lesseq(1, $difference(v0, all_42_26))) | ~ (mem(v0,
% 26.32/4.37 all_42_38) = 0))
% 26.32/4.37 (2) mem(all_42_19, all_42_38) = 0
% 26.32/4.37 (3) all_42_26 = all_42_39
% 26.32/4.37 (4) $lesseq(1, $difference(all_42_19, all_42_39))
% 26.32/4.37
% 26.32/4.37 Begin of proof
% 26.32/4.37 |
% 26.32/4.37 | GROUND_INST: instantiating (1) with all_42_19, simplifying with (2) gives:
% 26.32/4.37 | (5) $lesseq(all_42_19, all_42_26)
% 26.32/4.37 |
% 26.32/4.37 | REDUCE: (3), (5) imply:
% 26.32/4.37 | (6) $lesseq(all_42_19, all_42_39)
% 26.32/4.37 |
% 26.32/4.37 | COMBINE_INEQS: (4), (6) imply:
% 26.32/4.37 | (7) $false
% 26.32/4.37 |
% 26.32/4.37 | CLOSE: (7) is inconsistent.
% 26.32/4.37 |
% 26.32/4.37 End of proof
% 26.32/4.37
% 26.32/4.37 Sub-proof #3 shows that the following formulas are inconsistent:
% 26.32/4.37 ----------------------------------------------------------------
% 26.32/4.37 (1) ! [v0: int] : ( ~ ($lesseq(1, $difference(v0, all_42_23))) | ~ (mem(v0,
% 26.32/4.37 all_42_40) = 0))
% 26.32/4.37 (2) mem(all_42_19, all_42_40) = 0
% 26.32/4.37 (3) $lesseq(1, $difference(all_42_19, all_42_23))
% 26.32/4.37
% 26.32/4.37 Begin of proof
% 26.32/4.37 |
% 26.32/4.37 | GROUND_INST: instantiating (1) with all_42_19, simplifying with (2) gives:
% 26.32/4.37 | (4) $lesseq(all_42_19, all_42_23)
% 26.32/4.37 |
% 26.32/4.37 | COMBINE_INEQS: (3), (4) imply:
% 26.32/4.37 | (5) $false
% 26.32/4.37 |
% 26.32/4.37 | CLOSE: (5) is inconsistent.
% 26.32/4.37 |
% 26.32/4.37 End of proof
% 26.32/4.37
% 26.32/4.37 Sub-proof #4 shows that the following formulas are inconsistent:
% 26.32/4.37 ----------------------------------------------------------------
% 26.32/4.37 (1) $lesseq(1, $difference(all_42_36, all_138_0))
% 26.32/4.37 (2) $lesseq(0, all_138_0)
% 26.32/4.37 (3) size(empty) = 0
% 26.32/4.37 (4) size(empty) = all_42_36
% 26.32/4.37 (5) ! [v0: int] : ! [v1: int] : ! [v2: tree] : (v1 = v0 | ~ (size(v2) =
% 26.32/4.37 v1) | ~ (size(v2) = v0))
% 26.32/4.37
% 26.32/4.37 Begin of proof
% 26.32/4.37 |
% 26.32/4.37 | GROUND_INST: instantiating (5) with 0, all_42_36, empty, simplifying with (3),
% 26.32/4.37 | (4) gives:
% 26.32/4.37 | (6) all_42_36 = 0
% 26.32/4.37 |
% 26.32/4.37 | REDUCE: (1), (6) imply:
% 26.32/4.37 | (7) $lesseq(all_138_0, -1)
% 26.32/4.37 |
% 26.32/4.37 | COMBINE_INEQS: (2), (7) imply:
% 26.32/4.37 | (8) $false
% 26.32/4.37 |
% 26.32/4.37 | CLOSE: (8) is inconsistent.
% 26.32/4.37 |
% 26.32/4.37 End of proof
% 26.32/4.37 % SZS output end Proof for theBenchmark
% 26.32/4.37
% 26.32/4.37 3756ms
%------------------------------------------------------------------------------