TSTP Solution File: SWW634_2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW634_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 : n004.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 00:50:58 EDT 2023
% Result : Theorem 35.79s 5.61s
% Output : Proof 37.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW634_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Aug 27 19:15:22 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.46/1.39 Prover 2: Preprocessing ...
% 4.46/1.39 Prover 4: Preprocessing ...
% 4.46/1.40 Prover 0: Preprocessing ...
% 4.46/1.40 Prover 1: Preprocessing ...
% 4.46/1.41 Prover 3: Preprocessing ...
% 4.97/1.41 Prover 6: Preprocessing ...
% 4.97/1.42 Prover 5: Preprocessing ...
% 12.98/2.49 Prover 1: Warning: ignoring some quantifiers
% 12.98/2.53 Prover 3: Warning: ignoring some quantifiers
% 13.65/2.59 Prover 4: Warning: ignoring some quantifiers
% 13.65/2.61 Prover 3: Constructing countermodel ...
% 13.65/2.64 Prover 5: Proving ...
% 13.65/2.66 Prover 6: Proving ...
% 13.65/2.66 Prover 1: Constructing countermodel ...
% 14.76/2.74 Prover 0: Proving ...
% 14.76/2.75 Prover 4: Constructing countermodel ...
% 15.94/2.93 Prover 2: Proving ...
% 21.22/3.65 Prover 3: gave up
% 21.82/3.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 22.28/3.81 Prover 7: Preprocessing ...
% 24.96/4.11 Prover 7: Warning: ignoring some quantifiers
% 25.04/4.16 Prover 7: Constructing countermodel ...
% 28.58/4.61 Prover 1: gave up
% 28.58/4.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 29.21/4.75 Prover 8: Preprocessing ...
% 31.54/5.03 Prover 8: Warning: ignoring some quantifiers
% 32.23/5.07 Prover 8: Constructing countermodel ...
% 35.79/5.60 Prover 4: Found proof (size 194)
% 35.79/5.60 Prover 4: proved (4970ms)
% 35.79/5.60 Prover 6: stopped
% 35.79/5.60 Prover 7: stopped
% 35.79/5.60 Prover 8: stopped
% 35.79/5.60 Prover 2: stopped
% 35.79/5.61 Prover 5: stopped
% 35.79/5.61 Prover 0: stopped
% 35.79/5.61
% 35.79/5.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.79/5.61
% 36.39/5.64 % SZS output start Proof for theBenchmark
% 36.39/5.64 Assumptions after simplification:
% 36.39/5.64 ---------------------------------
% 36.39/5.64
% 36.39/5.64 (below_def)
% 36.39/5.66 ty(int) & ! [v0: int] : ! [v1: int] : ! [v2: uni] : ! [v3: set_int] : !
% 36.39/5.66 [v4: uni] : ! [v5: int] : (v5 = 0 | ~ ($lesseq(1, $difference(v1, v0))) | ~
% 36.39/5.66 ($lesseq(0, v0)) | ~ (below1(v1) = v3) | ~ (t2tb1(v0) = v2) | ~ (t2tb(v3)
% 36.39/5.66 = v4) | ~ (mem(int, v2, v4) = v5)) & ! [v0: int] : ! [v1: int] : !
% 36.39/5.66 [v2: uni] : ! [v3: set_int] : ! [v4: uni] : ( ~ ($lesseq(v1, v0)) | ~
% 36.39/5.66 (below1(v1) = v3) | ~ (t2tb1(v0) = v2) | ~ (t2tb(v3) = v4) | ~ (mem(int,
% 36.39/5.66 v2, v4) = 0)) & ! [v0: int] : ! [v1: int] : ! [v2: uni] : ! [v3:
% 36.39/5.66 set_int] : ! [v4: uni] : ( ~ ($lesseq(v0, -1)) | ~ (below1(v1) = v3) | ~
% 36.39/5.66 (t2tb1(v0) = v2) | ~ (t2tb(v3) = v4) | ~ (mem(int, v2, v4) = 0))
% 36.39/5.66
% 36.39/5.66 (cardinal_empty)
% 36.39/5.66 ! [v0: ty] : ! [v1: uni] : ! [v2: int] : (v2 = 0 | ~ (cardinal1(v0, v1) =
% 36.39/5.66 v2) | ~ ty(v0) | ~ uni(v1) | ? [v3: int] : ( ~ (v3 = 0) & is_empty(v0,
% 36.39/5.66 v1) = v3)) & ! [v0: ty] : ! [v1: uni] : ! [v2: int] : (v2 = 0 | ~
% 36.39/5.66 (is_empty(v0, v1) = v2) | ~ ty(v0) | ~ uni(v1) | ? [v3: int] : ( ~ (v3 =
% 36.39/5.66 0) & cardinal1(v0, v1) = v3)) & ! [v0: ty] : ! [v1: uni] : ( ~
% 36.39/5.66 (cardinal1(v0, v1) = 0) | ~ ty(v0) | ~ uni(v1) | is_empty(v0, v1) = 0) &
% 36.39/5.66 ! [v0: ty] : ! [v1: uni] : ( ~ (is_empty(v0, v1) = 0) | ~ ty(v0) | ~
% 36.39/5.66 uni(v1) | cardinal1(v0, v1) = 0)
% 36.39/5.66
% 36.39/5.66 (eq_prefix_def)
% 36.39/5.67 ty(int) & ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4:
% 36.39/5.67 int] : ! [v5: uni] : ( ~ ($lesseq(1, $difference(v3, v4))) | ~ ($lesseq(0,
% 36.39/5.67 v4)) | ~ (eq_prefix1(v0, v1, v2, v3) = 0) | ~ (t2tb1(v4) = v5) | ~
% 36.39/5.67 ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v6: uni] : (get(v0, int, v2, v5) = v6
% 36.39/5.67 & get(v0, int, v1, v5) = v6 & uni(v6))) & ! [v0: ty] : ! [v1: uni] : !
% 36.39/5.67 [v2: uni] : ! [v3: int] : ! [v4: int] : (v4 = 0 | ~ (eq_prefix1(v0, v1, v2,
% 36.39/5.67 v3) = v4) | ~ ty(v0) | ~ uni(v2) | ~ uni(v1) | ? [v5: int] : ? [v6:
% 36.39/5.67 uni] : ? [v7: uni] : ? [v8: uni] : ( ~ (v8 = v7) & $lesseq(1,
% 36.39/5.67 $difference(v3, v5)) & $lesseq(0, v5) & get(v0, int, v2, v6) = v8 &
% 36.39/5.67 get(v0, int, v1, v6) = v7 & t2tb1(v5) = v6 & uni(v8) & uni(v7) & uni(v6)))
% 36.39/5.67
% 36.39/5.67 (max_elt_def1)
% 36.39/5.67 ty(int) & ! [v0: set_int] : ! [v1: int] : ( ~ (max_elt1(v0) = v1) | ~
% 36.39/5.67 set_int(v0) | ? [v2: uni] : ? [v3: any] : ? [v4: uni] : ? [v5: any] :
% 36.39/5.67 (t2tb1(v1) = v4 & t2tb(v0) = v2 & is_empty(int, v2) = v3 & mem(int, v4, v2)
% 36.39/5.67 = v5 & uni(v4) & uni(v2) & (v5 = 0 | v3 = 0))) & ! [v0: set_int] : !
% 36.39/5.67 [v1: uni] : ( ~ (t2tb(v0) = v1) | ~ set_int(v0) | ? [v2: any] : ? [v3: int]
% 36.39/5.67 : ? [v4: uni] : ? [v5: any] : (max_elt1(v0) = v3 & t2tb1(v3) = v4 &
% 36.39/5.67 is_empty(int, v1) = v2 & mem(int, v4, v1) = v5 & uni(v4) & (v5 = 0 | v2 =
% 36.39/5.67 0)))
% 36.39/5.67
% 36.39/5.67 (max_elt_def2)
% 36.39/5.67 ty(int) & ! [v0: set_int] : ! [v1: int] : ( ~ (max_elt1(v0) = v1) | ~
% 36.39/5.67 set_int(v0) | ? [v2: uni] : ? [v3: any] : (t2tb(v0) = v2 & is_empty(int,
% 36.39/5.67 v2) = v3 & uni(v2) & (v3 = 0 | ! [v4: int] : ! [v5: uni] : ( ~
% 36.39/5.67 ($lesseq(1, $difference(v4, v1))) | ~ (t2tb1(v4) = v5) | ? [v6: int]
% 36.39/5.67 : ( ~ (v6 = 0) & mem(int, v5, v2) = v6))))) & ! [v0: set_int] : !
% 36.39/5.67 [v1: uni] : ( ~ (t2tb(v0) = v1) | ~ set_int(v0) | ? [v2: any] : ? [v3: int]
% 36.39/5.67 : (max_elt1(v0) = v3 & is_empty(int, v1) = v2 & (v2 = 0 | ! [v4: int] : !
% 36.39/5.67 [v5: uni] : ( ~ ($lesseq(1, $difference(v4, v3))) | ~ (t2tb1(v4) = v5)
% 36.39/5.67 | ? [v6: int] : ( ~ (v6 = 0) & mem(int, v5, v1) = v6)))))
% 36.39/5.67
% 36.39/5.67 (min_elt_def1)
% 36.39/5.68 ty(int) & ! [v0: set_int] : ! [v1: int] : ( ~ (min_elt1(v0) = v1) | ~
% 36.39/5.68 set_int(v0) | ? [v2: uni] : ? [v3: any] : ? [v4: uni] : ? [v5: any] :
% 36.39/5.68 (t2tb1(v1) = v4 & t2tb(v0) = v2 & is_empty(int, v2) = v3 & mem(int, v4, v2)
% 36.39/5.68 = v5 & uni(v4) & uni(v2) & (v5 = 0 | v3 = 0))) & ! [v0: set_int] : !
% 36.39/5.68 [v1: uni] : ( ~ (t2tb(v0) = v1) | ~ set_int(v0) | ? [v2: any] : ? [v3: int]
% 36.39/5.68 : ? [v4: uni] : ? [v5: any] : (min_elt1(v0) = v3 & t2tb1(v3) = v4 &
% 36.39/5.68 is_empty(int, v1) = v2 & mem(int, v4, v1) = v5 & uni(v4) & (v5 = 0 | v2 =
% 36.39/5.68 0)))
% 36.39/5.68
% 36.39/5.68 (min_elt_def2)
% 36.69/5.68 ty(int) & ! [v0: set_int] : ! [v1: int] : ( ~ (min_elt1(v0) = v1) | ~
% 36.69/5.68 set_int(v0) | ? [v2: uni] : ? [v3: any] : (t2tb(v0) = v2 & is_empty(int,
% 36.69/5.68 v2) = v3 & uni(v2) & (v3 = 0 | ! [v4: int] : ! [v5: uni] : ( ~
% 36.69/5.68 ($lesseq(1, $difference(v1, v4))) | ~ (t2tb1(v4) = v5) | ? [v6: int]
% 36.69/5.68 : ( ~ (v6 = 0) & mem(int, v5, v2) = v6))))) & ! [v0: set_int] : !
% 36.69/5.68 [v1: uni] : ( ~ (t2tb(v0) = v1) | ~ set_int(v0) | ? [v2: any] : ? [v3: int]
% 36.69/5.68 : (min_elt1(v0) = v3 & is_empty(int, v1) = v2 & (v2 = 0 | ! [v4: int] : !
% 36.69/5.68 [v5: uni] : ( ~ ($lesseq(1, $difference(v3, v4))) | ~ (t2tb1(v4) = v5)
% 36.69/5.68 | ? [v6: int] : ( ~ (v6 = 0) & mem(int, v5, v1) = v6)))))
% 36.69/5.68
% 36.69/5.68 (partial_solution_def)
% 36.69/5.68 ty(int) & ! [v0: int] : ! [v1: map_int_int] : ! [v2: int] : (v2 = 0 | ~
% 36.69/5.68 (partial_solution1(v0, v1) = v2) | ~ map_int_int(v1) | ? [v3: uni] : ?
% 36.69/5.68 [v4: int] : ? [v5: uni] : ? [v6: uni] : ? [v7: int] : ? [v8: int] : ?
% 36.69/5.68 [v9: uni] : ? [v10: uni] : ? [v11: int] : ($lesseq(1, $difference(v0, v4))
% 36.69/5.68 & $lesseq(0, v4) & t2tb2(v1) = v3 & get(int, int, v3, v5) = v6 & tb2t1(v6)
% 36.69/5.68 = v7 & t2tb1(v4) = v5 & uni(v6) & uni(v5) & uni(v3) & ( ~ ($lesseq(1,
% 36.69/5.68 $difference(n1, v7))) | ~ ($lesseq(0, v7)) | ($lesseq(1,
% 36.69/5.68 $difference(v4, v8)) & $lesseq(0, v8) & get(int, int, v3, v9) = v10
% 36.69/5.68 & tb2t1(v10) = v11 & t2tb1(v8) = v9 & uni(v10) & uni(v9) &
% 36.69/5.68 ($sum($difference($difference(v11, v8), v7), v4) = 0 |
% 36.69/5.68 $difference($sum(v11, v8), v7) = v4 | v11 = v7))))) & ! [v0: int] :
% 36.69/5.68 ! [v1: map_int_int] : ( ~ (partial_solution1(v0, v1) = 0) | ~
% 36.69/5.68 map_int_int(v1) | ? [v2: uni] : (t2tb2(v1) = v2 & uni(v2) & ! [v3: int] :
% 36.69/5.68 ! [v4: uni] : ( ~ ($lesseq(1, $difference(v0, v3))) | ~ ($lesseq(0, v3))
% 36.69/5.68 | ~ (t2tb1(v3) = v4) | ? [v5: uni] : ? [v6: int] : ($lesseq(1,
% 36.69/5.68 $difference(n1, v6)) & $lesseq(0, v6) & get(int, int, v2, v4) = v5 &
% 36.69/5.68 tb2t1(v5) = v6 & uni(v5) & ! [v7: int] : ! [v8: uni] : ( ~
% 36.69/5.68 ($lesseq(1, $difference(v3, v7))) | ~ ($lesseq(0, v7)) | ~
% 36.69/5.68 (t2tb1(v7) = v8) | ? [v9: uni] : ? [v10: int] : ( ~
% 36.69/5.68 ($sum($difference($difference(v10, v7), v6), v3) = 0) & ~
% 36.69/5.68 ($difference($sum(v10, v7), v6) = v3) & ~ (v10 = v6) & get(int,
% 36.69/5.68 int, v2, v8) = v9 & tb2t1(v9) = v10 & uni(v9)))))))
% 36.69/5.68
% 36.69/5.68 (t2tb_sort2)
% 36.69/5.68 ty(int) & ? [v0: ty] : (map(int, int) = v0 & ty(v0) & ! [v1: map_int_int] :
% 36.69/5.68 ! [v2: uni] : ( ~ (t2tb2(v1) = v2) | ~ map_int_int(v1) | sort1(v0, v2) =
% 36.69/5.68 0))
% 36.69/5.68
% 36.69/5.68 (wP_parameter_queens3)
% 36.69/5.69 ty(int) & ? [v0: uni] : ? [v1: ty] : ? [v2: map_int_lpmap_int_intrp] : ?
% 36.69/5.69 [v3: map_int_int] : ? [v4: set_int] : ? [v5: uni] : ? [v6: uni] : ? [v7:
% 36.69/5.69 uni] : ? [v8: int] : ? [v9: map_int_lpmap_int_intrp] : ? [v10:
% 36.69/5.69 map_int_int] : ? [v11: uni] : ? [v12: uni] : ? [v13: map_int_int] : ?
% 36.69/5.69 [v14: any] : ? [v15: uni] : ? [v16: int] : ? [v17: uni] : ? [v18: uni] :
% 36.69/5.69 ? [v19: int] : ($lesseq(0, v8) & $lesseq(0, n1) & sorted1(v9, 0, v8) = 0 &
% 36.69/5.69 t2tb3(v9) = v12 & t2tb3(v2) = v7 & partial_solution1(n1, v13) = v14 &
% 36.69/5.69 partial_solution1(0, v3) = 0 & t2tb2(v13) = v15 & t2tb2(v10) = v11 &
% 36.69/5.69 t2tb2(v3) = v6 & eq_prefix1(v1, v7, v12, 0) = 0 & eq_prefix1(int, v6, v11,
% 36.69/5.69 0) = 0 & map(int, int) = v1 & below1(n1) = v4 & t2tb(v4) = v5 &
% 36.69/5.69 cardinal1(int, v5) = n1 & empty(int) = v0 & map_int_lpmap_int_intrp(v9) &
% 36.69/5.69 map_int_lpmap_int_intrp(v2) & map_int_int(v13) & map_int_int(v10) &
% 36.69/5.69 map_int_int(v3) & set_int(v4) & ty(v1) & uni(v15) & uni(v12) & uni(v11) &
% 36.69/5.69 uni(v7) & uni(v6) & uni(v5) & uni(v0) & ! [v20: map_int_int] : ! [v21:
% 36.69/5.69 uni] : ! [v22: int] : ! [v23: uni] : ( ~ ($lesseq(1, $difference(v8,
% 36.69/5.69 v22))) | ~ ($lesseq(0, v22)) | ~ (t2tb2(v20) = v21) | ~
% 36.69/5.69 (t2tb1(v22) = v23) | ~ map_int_int(v20) | ? [v24: any] : ? [v25: int] :
% 36.69/5.69 ((v25 = 0 & v24 = 0 & partial_solution1(n1, v20) = 0 & eq_prefix1(int,
% 36.69/5.69 v11, v21, 0) = 0) | ( ~ (v25 = 0) & eq_prefix1(int, v21, v24, n1) =
% 36.69/5.69 v25 & get(v1, int, v12, v23) = v24 & uni(v24)))) & ! [v20: int] : !
% 36.69/5.69 [v21: uni] : ( ~ ($lesseq(1, $difference(n1, v20))) | ~ ($lesseq(0, v20)) |
% 36.69/5.69 ~ (t2tb1(v20) = v21) | mem(int, v21, v5) = 0) & ! [v20: int] : ! [v21:
% 36.69/5.69 uni] : ( ~ ($lesseq(v20, -1)) | ~ (t2tb1(v20) = v21) | ? [v22: int] : (
% 36.69/5.69 ~ (v22 = 0) & mem(int, v21, v5) = v22)) & ! [v20: int] : ! [v21: uni]
% 36.69/5.69 : ( ~ ($lesseq(n1, v20)) | ~ (t2tb1(v20) = v21) | ? [v22: int] : ( ~ (v22
% 36.69/5.69 = 0) & mem(int, v21, v5) = v22)) & ! [v20: int] : ! [v21: uni] : ( ~
% 36.69/5.69 ($lesseq(0, v20)) | ~ (t2tb1(v20) = v21) | ? [v22: int] : ( ~ (v22 = 0)
% 36.69/5.69 & mem(int, v21, v0) = v22)) & ! [v20: map_int_int] : ! [v21: any] : (
% 36.69/5.69 ~ (partial_solution1(n1, v20) = v21) | ~ map_int_int(v20) | ? [v22: uni]
% 36.69/5.69 : ? [v23: any] : (t2tb2(v20) = v22 & eq_prefix1(int, v11, v22, 0) = v23 &
% 36.69/5.69 uni(v22) & ( ! [v24: int] : ! [v25: uni] : ( ~ ($lesseq(1,
% 36.69/5.69 $difference(v8, v24))) | ~ ($lesseq(0, v24)) | ~ (t2tb1(v24) =
% 36.69/5.69 v25) | ? [v26: uni] : ? [v27: int] : ( ~ (v27 = 0) &
% 36.69/5.69 eq_prefix1(int, v22, v26, n1) = v27 & get(v1, int, v12, v25) = v26
% 36.69/5.69 & uni(v26))) | (v23 = 0 & v21 = 0)))) & ! [v20: map_int_int] : !
% 36.69/5.69 [v21: uni] : ( ~ (t2tb2(v20) = v21) | ~ map_int_int(v20) | ? [v22: int] :
% 36.69/5.69 ? [v23: any] : ? [v24: uni] : ? [v25: int] : ((v25 = 0 & $lesseq(1,
% 36.69/5.69 $difference(v8, v22)) & $lesseq(0, v22) & eq_prefix1(int, v21, v24,
% 36.69/5.69 n1) = 0 & get(v1, int, v12, v23) = v24 & t2tb1(v22) = v23 & uni(v24)
% 36.69/5.69 & uni(v23)) | (partial_solution1(n1, v20) = v22 & eq_prefix1(int, v11,
% 36.69/5.69 v21, 0) = v23 & ( ~ (v23 = 0) | ~ (v22 = 0))))) & ! [v20:
% 36.69/5.69 map_int_int] : ( ~ (partial_solution1(n1, v20) = 0) | ~ map_int_int(v20)
% 36.69/5.69 | ? [v21: uni] : ? [v22: any] : ? [v23: int] : ? [v24: uni] : ? [v25:
% 36.69/5.69 uni] : ? [v26: int] : (t2tb2(v20) = v21 & eq_prefix1(int, v11, v21, 0)
% 36.69/5.69 = v22 & uni(v21) & ( ~ (v22 = 0) | (v26 = 0 & $lesseq(1, $difference(v8,
% 36.69/5.69 v23)) & $lesseq(0, v23) & eq_prefix1(int, v21, v25, n1) = 0 &
% 36.69/5.69 get(v1, int, v12, v24) = v25 & t2tb1(v23) = v24 & uni(v25) &
% 36.69/5.69 uni(v24))))) & ((v19 = 0 & ~ (v14 = 0) & $lesseq(1, $difference(v8,
% 36.69/5.69 v16)) & $lesseq(0, v16) & eq_prefix1(int, v15, v18, n1) = 0 &
% 36.69/5.69 get(v1, int, v12, v17) = v18 & t2tb1(v16) = v17 & uni(v18) & uni(v17)) |
% 36.69/5.69 (v14 = 0 & ! [v20: int] : ! [v21: uni] : ( ~ ($lesseq(1, $difference(v8,
% 36.69/5.69 v20))) | ~ ($lesseq(0, v20)) | ~ (t2tb1(v20) = v21) | ? [v22:
% 36.69/5.69 uni] : ? [v23: int] : ( ~ (v23 = 0) & eq_prefix1(int, v15, v22, n1)
% 36.69/5.69 = v23 & get(v1, int, v12, v21) = v22 & uni(v22))))))
% 36.69/5.69
% 36.69/5.69 (function-axioms)
% 36.69/5.70 ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4: uni] : !
% 36.69/5.70 [v5: ty] : ! [v6: ty] : (v1 = v0 | ~ (set1(v6, v5, v4, v3, v2) = v1) | ~
% 36.69/5.70 (set1(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 36.69/5.70 MultipleValueBool] : ! [v2: int] : ! [v3: uni] : ! [v4: uni] : ! [v5:
% 36.69/5.70 ty] : (v1 = v0 | ~ (eq_prefix1(v5, v4, v3, v2) = v1) | ~ (eq_prefix1(v5,
% 36.69/5.70 v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : !
% 36.69/5.70 [v3: uni] : ! [v4: ty] : ! [v5: ty] : (v1 = v0 | ~ (get(v5, v4, v3, v2) =
% 36.69/5.70 v1) | ~ (get(v5, v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : !
% 36.69/5.70 [v2: uni] : ! [v3: uni] : ! [v4: bool1] : ! [v5: ty] : (v1 = v0 | ~
% 36.69/5.70 (match_bool1(v5, v4, v3, v2) = v1) | ~ (match_bool1(v5, v4, v3, v2) = v0))
% 36.69/5.70 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int] : !
% 36.69/5.70 [v3: int] : ! [v4: map_int_lpmap_int_intrp] : (v1 = v0 | ~ (sorted1(v4, v3,
% 36.69/5.70 v2) = v1) | ~ (sorted1(v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni]
% 36.69/5.70 : ! [v2: uni] : ! [v3: ty] : ! [v4: ty] : (v1 = v0 | ~ (const(v4, v3, v2)
% 36.69/5.70 = v1) | ~ (const(v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : !
% 36.69/5.70 [v2: uni] : ! [v3: uni] : ! [v4: ty] : (v1 = v0 | ~ (diff(v4, v3, v2) = v1)
% 36.69/5.70 | ~ (diff(v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] :
% 36.69/5.70 ! [v3: uni] : ! [v4: ty] : (v1 = v0 | ~ (inter(v4, v3, v2) = v1) | ~
% 36.69/5.70 (inter(v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : !
% 36.69/5.70 [v3: uni] : ! [v4: ty] : (v1 = v0 | ~ (union(v4, v3, v2) = v1) | ~
% 36.69/5.70 (union(v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : !
% 36.69/5.70 [v3: uni] : ! [v4: ty] : (v1 = v0 | ~ (remove(v4, v3, v2) = v1) | ~
% 36.69/5.70 (remove(v4, v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : !
% 36.69/5.70 [v3: uni] : ! [v4: ty] : (v1 = v0 | ~ (add(v4, v3, v2) = v1) | ~ (add(v4,
% 36.69/5.70 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 36.69/5.70 : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] : (v1 = v0 | ~ (subset(v4, v3,
% 36.69/5.70 v2) = v1) | ~ (subset(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 36.69/5.70 ! [v1: MultipleValueBool] : ! [v2: uni] : ! [v3: uni] : ! [v4: ty] : (v1 =
% 36.69/5.70 v0 | ~ (infix_eqeq(v4, v3, v2) = v1) | ~ (infix_eqeq(v4, v3, v2) = v0)) &
% 36.69/5.70 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: uni] : !
% 36.69/5.70 [v3: uni] : ! [v4: ty] : (v1 = v0 | ~ (mem(v4, v3, v2) = v1) | ~ (mem(v4,
% 36.69/5.70 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 36.69/5.70 : ! [v2: map_int_int] : ! [v3: map_int_int] : (v1 = v0 | ~ (lt_sol1(v3, v2)
% 36.69/5.70 = v1) | ~ (lt_sol1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 36.69/5.70 MultipleValueBool] : ! [v2: map_int_int] : ! [v3: int] : (v1 = v0 | ~
% 36.69/5.70 (partial_solution1(v3, v2) = v1) | ~ (partial_solution1(v3, v2) = v0)) & !
% 36.69/5.70 [v0: ty] : ! [v1: ty] : ! [v2: ty] : ! [v3: ty] : (v1 = v0 | ~ (map(v3,
% 36.69/5.70 v2) = v1) | ~ (map(v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : !
% 36.69/5.70 [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (contents(v3, v2) = v1) | ~
% 36.69/5.70 (contents(v3, v2) = v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : !
% 36.69/5.70 [v3: ty] : (v1 = v0 | ~ (mk_ref(v3, v2) = v1) | ~ (mk_ref(v3, v2) = v0)) &
% 36.69/5.70 ! [v0: int] : ! [v1: int] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~
% 36.69/5.70 (cardinal1(v3, v2) = v1) | ~ (cardinal1(v3, v2) = v0)) & ! [v0: uni] : !
% 36.69/5.70 [v1: uni] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~ (choose(v3, v2) = v1) |
% 36.69/5.70 ~ (choose(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 36.69/5.70 MultipleValueBool] : ! [v2: uni] : ! [v3: ty] : (v1 = v0 | ~
% 36.69/5.70 (is_empty(v3, v2) = v1) | ~ (is_empty(v3, v2) = v0)) & ! [v0:
% 36.69/5.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: uni] : ! [v3: ty]
% 36.69/5.70 : (v1 = v0 | ~ (sort1(v3, v2) = v1) | ~ (sort1(v3, v2) = v0)) & ! [v0:
% 36.69/5.70 map_int_lpmap_int_intrp] : ! [v1: map_int_lpmap_int_intrp] : ! [v2: uni] :
% 36.69/5.70 (v1 = v0 | ~ (tb2t3(v2) = v1) | ~ (tb2t3(v2) = v0)) & ! [v0: uni] : ! [v1:
% 36.69/5.70 uni] : ! [v2: map_int_lpmap_int_intrp] : (v1 = v0 | ~ (t2tb3(v2) = v1) |
% 36.69/5.70 ~ (t2tb3(v2) = v0)) & ! [v0: map_int_int] : ! [v1: map_int_int] : ! [v2:
% 36.69/5.70 uni] : (v1 = v0 | ~ (tb2t2(v2) = v1) | ~ (tb2t2(v2) = v0)) & ! [v0: uni]
% 36.69/5.70 : ! [v1: uni] : ! [v2: map_int_int] : (v1 = v0 | ~ (t2tb2(v2) = v1) | ~
% 36.69/5.70 (t2tb2(v2) = v0)) & ! [v0: ty] : ! [v1: ty] : ! [v2: ty] : (v1 = v0 | ~
% 36.69/5.70 (ref(v2) = v1) | ~ (ref(v2) = v0)) & ! [v0: set_int] : ! [v1: set_int] :
% 36.69/5.70 ! [v2: set_int] : (v1 = v0 | ~ (pred1(v2) = v1) | ~ (pred1(v2) = v0)) & !
% 36.69/5.70 [v0: set_int] : ! [v1: set_int] : ! [v2: set_int] : (v1 = v0 | ~ (succ1(v2)
% 36.69/5.70 = v1) | ~ (succ1(v2) = v0)) & ! [v0: set_int] : ! [v1: set_int] : !
% 36.69/5.70 [v2: int] : (v1 = v0 | ~ (below1(v2) = v1) | ~ (below1(v2) = v0)) & ! [v0:
% 36.69/5.70 int] : ! [v1: int] : ! [v2: set_int] : (v1 = v0 | ~ (max_elt1(v2) = v1) |
% 36.69/5.70 ~ (max_elt1(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: set_int] :
% 36.69/5.70 (v1 = v0 | ~ (min_elt1(v2) = v1) | ~ (min_elt1(v2) = v0)) & ! [v0: int] :
% 36.69/5.70 ! [v1: int] : ! [v2: uni] : (v1 = v0 | ~ (tb2t1(v2) = v1) | ~ (tb2t1(v2) =
% 36.69/5.70 v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: int] : (v1 = v0 | ~
% 36.69/5.70 (t2tb1(v2) = v1) | ~ (t2tb1(v2) = v0)) & ! [v0: set_int] : ! [v1:
% 36.69/5.70 set_int] : ! [v2: uni] : (v1 = v0 | ~ (tb2t(v2) = v1) | ~ (tb2t(v2) =
% 36.69/5.70 v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: set_int] : (v1 = v0 | ~
% 36.69/5.70 (t2tb(v2) = v1) | ~ (t2tb(v2) = v0)) & ! [v0: uni] : ! [v1: uni] : !
% 36.69/5.70 [v2: ty] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: ty]
% 36.69/5.70 : ! [v1: ty] : ! [v2: ty] : (v1 = v0 | ~ (set(v2) = v1) | ~ (set(v2) =
% 36.69/5.70 v0)) & ! [v0: uni] : ! [v1: uni] : ! [v2: ty] : (v1 = v0 | ~
% 36.69/5.70 (witness1(v2) = v1) | ~ (witness1(v2) = v0))
% 36.69/5.70
% 36.69/5.70 Further assumptions not needed in the proof:
% 36.69/5.70 --------------------------------------------
% 36.69/5.70 add_def1, add_remove, add_sort1, bool_inversion, bridgeL, bridgeL1, bridgeL2,
% 36.69/5.70 bridgeL3, bridgeR, bridgeR1, bridgeR2, bridgeR3, cardinal1, cardinal_add,
% 36.69/5.70 cardinal_below, cardinal_nonneg, cardinal_remove, cardinal_subset, choose_def,
% 36.69/5.70 choose_sort1, compatOrderMult, const, const_sort1, contents_def1,
% 36.69/5.70 contents_sort1, diff_def1, diff_sort1, empty_def1, empty_sort1, extensionality,
% 36.69/5.70 get_sort1, infix_eqeq_def, inter_def1, inter_sort1, is_empty_def, lt_sol_def,
% 36.69/5.70 match_bool_False, match_bool_True, match_bool_sort1, mem_empty, mk_ref_sort1,
% 36.69/5.70 no_duplicate, partial_solution_eq_prefix, pred_def, ref_inversion1, remove_add,
% 36.69/5.70 remove_def1, remove_sort1, select_eq, select_neq, set_sort1, sorted_def,
% 36.69/5.70 subset_def, subset_diff, subset_refl, subset_remove, subset_trans, succ_def,
% 36.69/5.70 t2tb_sort, t2tb_sort1, t2tb_sort3, true_False, tuple0_inversion, union_def1,
% 36.69/5.70 union_sort1, witness_sort1
% 36.69/5.70
% 36.69/5.70 Those formulas are unsatisfiable:
% 36.69/5.70 ---------------------------------
% 36.69/5.70
% 36.69/5.70 Begin of proof
% 36.69/5.70 |
% 36.69/5.70 | ALPHA: (cardinal_empty) implies:
% 36.69/5.70 | (1) ! [v0: ty] : ! [v1: uni] : ! [v2: int] : (v2 = 0 | ~ (cardinal1(v0,
% 36.69/5.70 | v1) = v2) | ~ ty(v0) | ~ uni(v1) | ? [v3: int] : ( ~ (v3 = 0)
% 36.69/5.70 | & is_empty(v0, v1) = v3))
% 36.69/5.70 |
% 36.69/5.70 | ALPHA: (min_elt_def1) implies:
% 36.69/5.71 | (2) ! [v0: set_int] : ! [v1: uni] : ( ~ (t2tb(v0) = v1) | ~ set_int(v0)
% 36.69/5.71 | | ? [v2: any] : ? [v3: int] : ? [v4: uni] : ? [v5: any] :
% 36.69/5.71 | (min_elt1(v0) = v3 & t2tb1(v3) = v4 & is_empty(int, v1) = v2 &
% 36.69/5.71 | mem(int, v4, v1) = v5 & uni(v4) & (v5 = 0 | v2 = 0)))
% 36.69/5.71 | (3) ! [v0: set_int] : ! [v1: int] : ( ~ (min_elt1(v0) = v1) | ~
% 36.69/5.71 | set_int(v0) | ? [v2: uni] : ? [v3: any] : ? [v4: uni] : ? [v5:
% 36.69/5.71 | any] : (t2tb1(v1) = v4 & t2tb(v0) = v2 & is_empty(int, v2) = v3 &
% 36.69/5.71 | mem(int, v4, v2) = v5 & uni(v4) & uni(v2) & (v5 = 0 | v3 = 0)))
% 36.69/5.71 |
% 36.69/5.71 | ALPHA: (min_elt_def2) implies:
% 36.69/5.71 | (4) ! [v0: set_int] : ! [v1: uni] : ( ~ (t2tb(v0) = v1) | ~ set_int(v0)
% 36.69/5.71 | | ? [v2: any] : ? [v3: int] : (min_elt1(v0) = v3 & is_empty(int,
% 36.69/5.71 | v1) = v2 & (v2 = 0 | ! [v4: int] : ! [v5: uni] : ( ~
% 36.69/5.71 | ($lesseq(1, $difference(v3, v4))) | ~ (t2tb1(v4) = v5) | ?
% 36.69/5.71 | [v6: int] : ( ~ (v6 = 0) & mem(int, v5, v1) = v6)))))
% 36.69/5.71 | (5) ! [v0: set_int] : ! [v1: int] : ( ~ (min_elt1(v0) = v1) | ~
% 36.69/5.71 | set_int(v0) | ? [v2: uni] : ? [v3: any] : (t2tb(v0) = v2 &
% 36.69/5.71 | is_empty(int, v2) = v3 & uni(v2) & (v3 = 0 | ! [v4: int] : ! [v5:
% 36.69/5.71 | uni] : ( ~ ($lesseq(1, $difference(v1, v4))) | ~ (t2tb1(v4) =
% 36.69/5.71 | v5) | ? [v6: int] : ( ~ (v6 = 0) & mem(int, v5, v2) =
% 36.69/5.71 | v6)))))
% 36.69/5.71 |
% 36.69/5.71 | ALPHA: (max_elt_def1) implies:
% 36.69/5.71 | (6) ! [v0: set_int] : ! [v1: uni] : ( ~ (t2tb(v0) = v1) | ~ set_int(v0)
% 36.69/5.71 | | ? [v2: any] : ? [v3: int] : ? [v4: uni] : ? [v5: any] :
% 36.69/5.71 | (max_elt1(v0) = v3 & t2tb1(v3) = v4 & is_empty(int, v1) = v2 &
% 36.69/5.71 | mem(int, v4, v1) = v5 & uni(v4) & (v5 = 0 | v2 = 0)))
% 36.69/5.71 | (7) ! [v0: set_int] : ! [v1: int] : ( ~ (max_elt1(v0) = v1) | ~
% 36.69/5.71 | set_int(v0) | ? [v2: uni] : ? [v3: any] : ? [v4: uni] : ? [v5:
% 36.69/5.71 | any] : (t2tb1(v1) = v4 & t2tb(v0) = v2 & is_empty(int, v2) = v3 &
% 36.69/5.71 | mem(int, v4, v2) = v5 & uni(v4) & uni(v2) & (v5 = 0 | v3 = 0)))
% 36.69/5.71 |
% 36.69/5.71 | ALPHA: (max_elt_def2) implies:
% 36.69/5.71 | (8) ! [v0: set_int] : ! [v1: uni] : ( ~ (t2tb(v0) = v1) | ~ set_int(v0)
% 36.69/5.71 | | ? [v2: any] : ? [v3: int] : (max_elt1(v0) = v3 & is_empty(int,
% 36.69/5.71 | v1) = v2 & (v2 = 0 | ! [v4: int] : ! [v5: uni] : ( ~
% 36.69/5.71 | ($lesseq(1, $difference(v4, v3))) | ~ (t2tb1(v4) = v5) | ?
% 36.69/5.71 | [v6: int] : ( ~ (v6 = 0) & mem(int, v5, v1) = v6)))))
% 36.69/5.71 | (9) ! [v0: set_int] : ! [v1: int] : ( ~ (max_elt1(v0) = v1) | ~
% 36.69/5.71 | set_int(v0) | ? [v2: uni] : ? [v3: any] : (t2tb(v0) = v2 &
% 36.69/5.71 | is_empty(int, v2) = v3 & uni(v2) & (v3 = 0 | ! [v4: int] : ! [v5:
% 36.69/5.71 | uni] : ( ~ ($lesseq(1, $difference(v4, v1))) | ~ (t2tb1(v4) =
% 36.69/5.71 | v5) | ? [v6: int] : ( ~ (v6 = 0) & mem(int, v5, v2) =
% 36.69/5.71 | v6)))))
% 36.69/5.71 |
% 36.69/5.71 | ALPHA: (below_def) implies:
% 36.69/5.71 | (10) ! [v0: int] : ! [v1: int] : ! [v2: uni] : ! [v3: set_int] : !
% 36.69/5.71 | [v4: uni] : ( ~ ($lesseq(v0, -1)) | ~ (below1(v1) = v3) | ~
% 36.69/5.71 | (t2tb1(v0) = v2) | ~ (t2tb(v3) = v4) | ~ (mem(int, v2, v4) = 0))
% 36.69/5.71 |
% 36.69/5.71 | ALPHA: (eq_prefix_def) implies:
% 36.69/5.71 | (11) ! [v0: ty] : ! [v1: uni] : ! [v2: uni] : ! [v3: int] : ! [v4:
% 36.69/5.71 | int] : (v4 = 0 | ~ (eq_prefix1(v0, v1, v2, v3) = v4) | ~ ty(v0) |
% 36.69/5.71 | ~ uni(v2) | ~ uni(v1) | ? [v5: int] : ? [v6: uni] : ? [v7: uni]
% 36.69/5.71 | : ? [v8: uni] : ( ~ (v8 = v7) & $lesseq(1, $difference(v3, v5)) &
% 36.69/5.71 | $lesseq(0, v5) & get(v0, int, v2, v6) = v8 & get(v0, int, v1, v6)
% 36.69/5.71 | = v7 & t2tb1(v5) = v6 & uni(v8) & uni(v7) & uni(v6)))
% 36.69/5.71 |
% 36.69/5.71 | ALPHA: (t2tb_sort2) implies:
% 36.69/5.71 | (12) ? [v0: ty] : (map(int, int) = v0 & ty(v0) & ! [v1: map_int_int] : !
% 36.69/5.71 | [v2: uni] : ( ~ (t2tb2(v1) = v2) | ~ map_int_int(v1) | sort1(v0,
% 36.69/5.71 | v2) = 0))
% 36.69/5.71 |
% 36.69/5.71 | ALPHA: (partial_solution_def) implies:
% 36.69/5.72 | (13) ! [v0: int] : ! [v1: map_int_int] : ! [v2: int] : (v2 = 0 | ~
% 36.69/5.72 | (partial_solution1(v0, v1) = v2) | ~ map_int_int(v1) | ? [v3: uni]
% 36.69/5.72 | : ? [v4: int] : ? [v5: uni] : ? [v6: uni] : ? [v7: int] : ?
% 36.69/5.72 | [v8: int] : ? [v9: uni] : ? [v10: uni] : ? [v11: int] :
% 36.69/5.72 | ($lesseq(1, $difference(v0, v4)) & $lesseq(0, v4) & t2tb2(v1) = v3 &
% 36.69/5.72 | get(int, int, v3, v5) = v6 & tb2t1(v6) = v7 & t2tb1(v4) = v5 &
% 36.69/5.72 | uni(v6) & uni(v5) & uni(v3) & ( ~ ($lesseq(1, $difference(n1,
% 36.69/5.72 | v7))) | ~ ($lesseq(0, v7)) | ($lesseq(1, $difference(v4,
% 36.69/5.72 | v8)) & $lesseq(0, v8) & get(int, int, v3, v9) = v10 &
% 36.69/5.72 | tb2t1(v10) = v11 & t2tb1(v8) = v9 & uni(v10) & uni(v9) &
% 36.69/5.72 | ($sum($difference($difference(v11, v8), v7), v4) = 0 |
% 36.69/5.72 | $difference($sum(v11, v8), v7) = v4 | v11 = v7)))))
% 36.69/5.72 |
% 36.69/5.72 | ALPHA: (wP_parameter_queens3) implies:
% 36.69/5.72 | (14) ty(int)
% 36.69/5.72 | (15) ? [v0: uni] : ? [v1: ty] : ? [v2: map_int_lpmap_int_intrp] : ?
% 36.69/5.72 | [v3: map_int_int] : ? [v4: set_int] : ? [v5: uni] : ? [v6: uni] :
% 36.69/5.72 | ? [v7: uni] : ? [v8: int] : ? [v9: map_int_lpmap_int_intrp] : ?
% 36.69/5.72 | [v10: map_int_int] : ? [v11: uni] : ? [v12: uni] : ? [v13:
% 36.69/5.72 | map_int_int] : ? [v14: any] : ? [v15: uni] : ? [v16: int] : ?
% 36.69/5.72 | [v17: uni] : ? [v18: uni] : ? [v19: int] : ($lesseq(0, v8) &
% 36.69/5.72 | $lesseq(0, n1) & sorted1(v9, 0, v8) = 0 & t2tb3(v9) = v12 &
% 36.69/5.72 | t2tb3(v2) = v7 & partial_solution1(n1, v13) = v14 &
% 36.69/5.72 | partial_solution1(0, v3) = 0 & t2tb2(v13) = v15 & t2tb2(v10) = v11 &
% 36.69/5.72 | t2tb2(v3) = v6 & eq_prefix1(v1, v7, v12, 0) = 0 & eq_prefix1(int,
% 36.69/5.72 | v6, v11, 0) = 0 & map(int, int) = v1 & below1(n1) = v4 & t2tb(v4)
% 36.69/5.72 | = v5 & cardinal1(int, v5) = n1 & empty(int) = v0 &
% 36.69/5.72 | map_int_lpmap_int_intrp(v9) & map_int_lpmap_int_intrp(v2) &
% 36.69/5.72 | map_int_int(v13) & map_int_int(v10) & map_int_int(v3) & set_int(v4)
% 36.69/5.72 | & ty(v1) & uni(v15) & uni(v12) & uni(v11) & uni(v7) & uni(v6) &
% 36.69/5.72 | uni(v5) & uni(v0) & ! [v20: map_int_int] : ! [v21: uni] : ! [v22:
% 36.69/5.72 | int] : ! [v23: uni] : ( ~ ($lesseq(1, $difference(v8, v22))) | ~
% 36.69/5.72 | ($lesseq(0, v22)) | ~ (t2tb2(v20) = v21) | ~ (t2tb1(v22) = v23)
% 36.69/5.72 | | ~ map_int_int(v20) | ? [v24: any] : ? [v25: int] : ((v25 = 0
% 36.69/5.72 | & v24 = 0 & partial_solution1(n1, v20) = 0 & eq_prefix1(int,
% 36.69/5.72 | v11, v21, 0) = 0) | ( ~ (v25 = 0) & eq_prefix1(int, v21,
% 36.69/5.72 | v24, n1) = v25 & get(v1, int, v12, v23) = v24 & uni(v24))))
% 36.69/5.72 | & ! [v20: int] : ! [v21: uni] : ( ~ ($lesseq(1, $difference(n1,
% 36.69/5.72 | v20))) | ~ ($lesseq(0, v20)) | ~ (t2tb1(v20) = v21) |
% 36.69/5.72 | mem(int, v21, v5) = 0) & ! [v20: int] : ! [v21: uni] : ( ~
% 36.69/5.72 | ($lesseq(v20, -1)) | ~ (t2tb1(v20) = v21) | ? [v22: int] : ( ~
% 36.69/5.72 | (v22 = 0) & mem(int, v21, v5) = v22)) & ! [v20: int] : ! [v21:
% 36.69/5.72 | uni] : ( ~ ($lesseq(n1, v20)) | ~ (t2tb1(v20) = v21) | ? [v22:
% 36.69/5.72 | int] : ( ~ (v22 = 0) & mem(int, v21, v5) = v22)) & ! [v20: int]
% 36.69/5.72 | : ! [v21: uni] : ( ~ ($lesseq(0, v20)) | ~ (t2tb1(v20) = v21) | ?
% 36.69/5.72 | [v22: int] : ( ~ (v22 = 0) & mem(int, v21, v0) = v22)) & ! [v20:
% 36.69/5.72 | map_int_int] : ! [v21: any] : ( ~ (partial_solution1(n1, v20) =
% 36.69/5.72 | v21) | ~ map_int_int(v20) | ? [v22: uni] : ? [v23: any] :
% 36.69/5.72 | (t2tb2(v20) = v22 & eq_prefix1(int, v11, v22, 0) = v23 & uni(v22)
% 36.69/5.72 | & ( ! [v24: int] : ! [v25: uni] : ( ~ ($lesseq(1,
% 36.69/5.72 | $difference(v8, v24))) | ~ ($lesseq(0, v24)) | ~
% 36.69/5.72 | (t2tb1(v24) = v25) | ? [v26: uni] : ? [v27: int] : ( ~
% 36.69/5.72 | (v27 = 0) & eq_prefix1(int, v22, v26, n1) = v27 & get(v1,
% 36.69/5.72 | int, v12, v25) = v26 & uni(v26))) | (v23 = 0 & v21 =
% 36.69/5.72 | 0)))) & ! [v20: map_int_int] : ! [v21: uni] : ( ~
% 36.69/5.72 | (t2tb2(v20) = v21) | ~ map_int_int(v20) | ? [v22: int] : ?
% 36.69/5.72 | [v23: any] : ? [v24: uni] : ? [v25: int] : ((v25 = 0 &
% 36.69/5.72 | $lesseq(1, $difference(v8, v22)) & $lesseq(0, v22) &
% 36.69/5.72 | eq_prefix1(int, v21, v24, n1) = 0 & get(v1, int, v12, v23) =
% 36.69/5.72 | v24 & t2tb1(v22) = v23 & uni(v24) & uni(v23)) |
% 36.69/5.72 | (partial_solution1(n1, v20) = v22 & eq_prefix1(int, v11, v21, 0)
% 36.69/5.72 | = v23 & ( ~ (v23 = 0) | ~ (v22 = 0))))) & ! [v20:
% 36.69/5.72 | map_int_int] : ( ~ (partial_solution1(n1, v20) = 0) | ~
% 36.69/5.72 | map_int_int(v20) | ? [v21: uni] : ? [v22: any] : ? [v23: int] :
% 36.69/5.72 | ? [v24: uni] : ? [v25: uni] : ? [v26: int] : (t2tb2(v20) = v21
% 36.69/5.72 | & eq_prefix1(int, v11, v21, 0) = v22 & uni(v21) & ( ~ (v22 = 0)
% 36.69/5.72 | | (v26 = 0 & $lesseq(1, $difference(v8, v23)) & $lesseq(0,
% 36.69/5.72 | v23) & eq_prefix1(int, v21, v25, n1) = 0 & get(v1, int,
% 36.69/5.72 | v12, v24) = v25 & t2tb1(v23) = v24 & uni(v25) &
% 36.69/5.72 | uni(v24))))) & ((v19 = 0 & ~ (v14 = 0) & $lesseq(1,
% 36.69/5.72 | $difference(v8, v16)) & $lesseq(0, v16) & eq_prefix1(int, v15,
% 36.69/5.72 | v18, n1) = 0 & get(v1, int, v12, v17) = v18 & t2tb1(v16) = v17
% 36.69/5.72 | & uni(v18) & uni(v17)) | (v14 = 0 & ! [v20: int] : ! [v21:
% 36.69/5.72 | uni] : ( ~ ($lesseq(1, $difference(v8, v20))) | ~ ($lesseq(0,
% 36.69/5.72 | v20)) | ~ (t2tb1(v20) = v21) | ? [v22: uni] : ? [v23:
% 36.69/5.72 | int] : ( ~ (v23 = 0) & eq_prefix1(int, v15, v22, n1) = v23 &
% 36.69/5.72 | get(v1, int, v12, v21) = v22 & uni(v22))))))
% 36.69/5.72 |
% 36.69/5.72 | ALPHA: (function-axioms) implies:
% 36.69/5.72 | (16) ! [v0: uni] : ! [v1: uni] : ! [v2: set_int] : (v1 = v0 | ~
% 36.69/5.72 | (t2tb(v2) = v1) | ~ (t2tb(v2) = v0))
% 36.69/5.72 | (17) ! [v0: uni] : ! [v1: uni] : ! [v2: int] : (v1 = v0 | ~ (t2tb1(v2)
% 36.69/5.72 | = v1) | ~ (t2tb1(v2) = v0))
% 36.69/5.72 | (18) ! [v0: int] : ! [v1: int] : ! [v2: set_int] : (v1 = v0 | ~
% 36.69/5.72 | (min_elt1(v2) = v1) | ~ (min_elt1(v2) = v0))
% 36.69/5.72 | (19) ! [v0: int] : ! [v1: int] : ! [v2: set_int] : (v1 = v0 | ~
% 36.69/5.72 | (max_elt1(v2) = v1) | ~ (max_elt1(v2) = v0))
% 36.69/5.72 | (20) ! [v0: uni] : ! [v1: uni] : ! [v2: map_int_int] : (v1 = v0 | ~
% 36.69/5.73 | (t2tb2(v2) = v1) | ~ (t2tb2(v2) = v0))
% 36.69/5.73 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: uni]
% 36.69/5.73 | : ! [v3: ty] : (v1 = v0 | ~ (is_empty(v3, v2) = v1) | ~
% 36.69/5.73 | (is_empty(v3, v2) = v0))
% 36.69/5.73 | (22) ! [v0: ty] : ! [v1: ty] : ! [v2: ty] : ! [v3: ty] : (v1 = v0 | ~
% 36.69/5.73 | (map(v3, v2) = v1) | ~ (map(v3, v2) = v0))
% 36.69/5.73 | (23) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 36.69/5.73 | map_int_int] : ! [v3: int] : (v1 = v0 | ~ (partial_solution1(v3,
% 36.69/5.73 | v2) = v1) | ~ (partial_solution1(v3, v2) = v0))
% 36.69/5.73 | (24) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: uni]
% 36.69/5.73 | : ! [v3: uni] : ! [v4: ty] : (v1 = v0 | ~ (mem(v4, v3, v2) = v1) |
% 36.69/5.73 | ~ (mem(v4, v3, v2) = v0))
% 36.69/5.73 | (25) ! [v0: uni] : ! [v1: uni] : ! [v2: uni] : ! [v3: uni] : ! [v4:
% 36.69/5.73 | ty] : ! [v5: ty] : (v1 = v0 | ~ (get(v5, v4, v3, v2) = v1) | ~
% 36.69/5.73 | (get(v5, v4, v3, v2) = v0))
% 36.69/5.73 | (26) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: int]
% 36.69/5.73 | : ! [v3: uni] : ! [v4: uni] : ! [v5: ty] : (v1 = v0 | ~
% 36.69/5.73 | (eq_prefix1(v5, v4, v3, v2) = v1) | ~ (eq_prefix1(v5, v4, v3, v2) =
% 36.69/5.73 | v0))
% 36.69/5.73 |
% 36.69/5.73 | DELTA: instantiating (12) with fresh symbol all_87_0 gives:
% 36.69/5.73 | (27) map(int, int) = all_87_0 & ty(all_87_0) & ! [v0: map_int_int] : !
% 36.69/5.73 | [v1: uni] : ( ~ (t2tb2(v0) = v1) | ~ map_int_int(v0) |
% 36.69/5.73 | sort1(all_87_0, v1) = 0)
% 36.69/5.73 |
% 36.69/5.73 | ALPHA: (27) implies:
% 36.69/5.73 | (28) map(int, int) = all_87_0
% 36.69/5.73 |
% 36.69/5.73 | DELTA: instantiating (15) with fresh symbols all_102_0, all_102_1, all_102_2,
% 36.69/5.73 | all_102_3, all_102_4, all_102_5, all_102_6, all_102_7, all_102_8,
% 36.69/5.73 | all_102_9, all_102_10, all_102_11, all_102_12, all_102_13, all_102_14,
% 36.69/5.73 | all_102_15, all_102_16, all_102_17, all_102_18, all_102_19 gives:
% 36.69/5.73 | (29) $lesseq(0, all_102_11) & $lesseq(0, n1) & sorted1(all_102_10, 0,
% 36.69/5.73 | all_102_11) = 0 & t2tb3(all_102_10) = all_102_7 & t2tb3(all_102_17)
% 36.69/5.73 | = all_102_12 & partial_solution1(n1, all_102_6) = all_102_5 &
% 36.69/5.73 | partial_solution1(0, all_102_16) = 0 & t2tb2(all_102_6) = all_102_4 &
% 36.69/5.73 | t2tb2(all_102_9) = all_102_8 & t2tb2(all_102_16) = all_102_13 &
% 36.69/5.73 | eq_prefix1(all_102_18, all_102_12, all_102_7, 0) = 0 & eq_prefix1(int,
% 36.69/5.73 | all_102_13, all_102_8, 0) = 0 & map(int, int) = all_102_18 &
% 36.69/5.73 | below1(n1) = all_102_15 & t2tb(all_102_15) = all_102_14 &
% 36.69/5.73 | cardinal1(int, all_102_14) = n1 & empty(int) = all_102_19 &
% 36.69/5.73 | map_int_lpmap_int_intrp(all_102_10) &
% 36.69/5.73 | map_int_lpmap_int_intrp(all_102_17) & map_int_int(all_102_6) &
% 36.69/5.73 | map_int_int(all_102_9) & map_int_int(all_102_16) & set_int(all_102_15)
% 36.69/5.73 | & ty(all_102_18) & uni(all_102_4) & uni(all_102_7) & uni(all_102_8) &
% 36.69/5.73 | uni(all_102_12) & uni(all_102_13) & uni(all_102_14) & uni(all_102_19)
% 36.69/5.73 | & ! [v0: map_int_int] : ! [v1: uni] : ! [v2: int] : ! [v3: uni] :
% 36.69/5.73 | ( ~ ($lesseq(1, $difference(all_102_11, v2))) | ~ ($lesseq(0, v2)) |
% 36.69/5.73 | ~ (t2tb2(v0) = v1) | ~ (t2tb1(v2) = v3) | ~ map_int_int(v0) | ?
% 36.69/5.73 | [v4: any] : ? [v5: int] : ((v5 = 0 & v4 = 0 & partial_solution1(n1,
% 36.69/5.73 | v0) = 0 & eq_prefix1(int, all_102_8, v1, 0) = 0) | ( ~ (v5 =
% 36.69/5.73 | 0) & eq_prefix1(int, v1, v4, n1) = v5 & get(all_102_18, int,
% 36.69/5.73 | all_102_7, v3) = v4 & uni(v4)))) & ! [v0: int] : ! [v1: uni]
% 36.69/5.73 | : ( ~ ($lesseq(1, $difference(n1, v0))) | ~ ($lesseq(0, v0)) | ~
% 36.69/5.73 | (t2tb1(v0) = v1) | mem(int, v1, all_102_14) = 0) & ! [v0: int] : !
% 36.69/5.73 | [v1: uni] : ( ~ ($lesseq(v0, -1)) | ~ (t2tb1(v0) = v1) | ? [v2: int]
% 36.69/5.73 | : ( ~ (v2 = 0) & mem(int, v1, all_102_14) = v2)) & ! [v0: int] : !
% 36.69/5.73 | [v1: uni] : ( ~ ($lesseq(n1, v0)) | ~ (t2tb1(v0) = v1) | ? [v2: int]
% 36.69/5.73 | : ( ~ (v2 = 0) & mem(int, v1, all_102_14) = v2)) & ! [v0: int] : !
% 36.69/5.73 | [v1: uni] : ( ~ ($lesseq(0, v0)) | ~ (t2tb1(v0) = v1) | ? [v2: int]
% 36.69/5.73 | : ( ~ (v2 = 0) & mem(int, v1, all_102_19) = v2)) & ! [v0:
% 36.69/5.73 | map_int_int] : ! [v1: any] : ( ~ (partial_solution1(n1, v0) = v1) |
% 36.69/5.73 | ~ map_int_int(v0) | ? [v2: uni] : ? [v3: any] : (t2tb2(v0) = v2 &
% 36.69/5.73 | eq_prefix1(int, all_102_8, v2, 0) = v3 & uni(v2) & ( ! [v4: int] :
% 36.69/5.73 | ! [v5: uni] : ( ~ ($lesseq(1, $difference(all_102_11, v4))) |
% 36.69/5.73 | ~ ($lesseq(0, v4)) | ~ (t2tb1(v4) = v5) | ? [v6: uni] : ?
% 36.69/5.73 | [v7: int] : ( ~ (v7 = 0) & eq_prefix1(int, v2, v6, n1) = v7 &
% 36.69/5.73 | get(all_102_18, int, all_102_7, v5) = v6 & uni(v6))) | (v3 =
% 36.69/5.73 | 0 & v1 = 0)))) & ! [v0: map_int_int] : ! [v1: uni] : ( ~
% 36.69/5.74 | (t2tb2(v0) = v1) | ~ map_int_int(v0) | ? [v2: int] : ? [v3: any]
% 36.69/5.74 | : ? [v4: uni] : ? [v5: int] : ((v5 = 0 & $lesseq(1,
% 36.69/5.74 | $difference(all_102_11, v2)) & $lesseq(0, v2) &
% 36.69/5.74 | eq_prefix1(int, v1, v4, n1) = 0 & get(all_102_18, int,
% 36.69/5.74 | all_102_7, v3) = v4 & t2tb1(v2) = v3 & uni(v4) & uni(v3)) |
% 36.69/5.74 | (partial_solution1(n1, v0) = v2 & eq_prefix1(int, all_102_8, v1,
% 36.69/5.74 | 0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ! [v0:
% 36.69/5.74 | map_int_int] : ( ~ (partial_solution1(n1, v0) = 0) | ~
% 36.69/5.74 | map_int_int(v0) | ? [v1: uni] : ? [v2: any] : ? [v3: int] : ?
% 36.69/5.74 | [v4: uni] : ? [v5: uni] : ? [v6: int] : (t2tb2(v0) = v1 &
% 36.69/5.74 | eq_prefix1(int, all_102_8, v1, 0) = v2 & uni(v1) & ( ~ (v2 = 0) |
% 36.69/5.74 | (v6 = 0 & $lesseq(1, $difference(all_102_11, v3)) & $lesseq(0,
% 36.69/5.74 | v3) & eq_prefix1(int, v1, v5, n1) = 0 & get(all_102_18, int,
% 36.69/5.74 | all_102_7, v4) = v5 & t2tb1(v3) = v4 & uni(v5) & uni(v4)))))
% 36.69/5.74 | & ((all_102_0 = 0 & ~ (all_102_5 = 0) & $lesseq(1,
% 36.69/5.74 | $difference(all_102_11, all_102_3)) & $lesseq(0, all_102_3) &
% 36.69/5.74 | eq_prefix1(int, all_102_4, all_102_1, n1) = 0 & get(all_102_18,
% 36.69/5.74 | int, all_102_7, all_102_2) = all_102_1 & t2tb1(all_102_3) =
% 36.69/5.74 | all_102_2 & uni(all_102_1) & uni(all_102_2)) | (all_102_5 = 0 & !
% 36.69/5.74 | [v0: int] : ! [v1: uni] : ( ~ ($lesseq(1, $difference(all_102_11,
% 36.69/5.74 | v0))) | ~ ($lesseq(0, v0)) | ~ (t2tb1(v0) = v1) | ?
% 36.69/5.74 | [v2: uni] : ? [v3: int] : ( ~ (v3 = 0) & eq_prefix1(int,
% 36.69/5.74 | all_102_4, v2, n1) = v3 & get(all_102_18, int, all_102_7,
% 36.69/5.74 | v1) = v2 & uni(v2)))))
% 36.69/5.74 |
% 36.69/5.74 | ALPHA: (29) implies:
% 36.69/5.74 | (30) uni(all_102_14)
% 36.69/5.74 | (31) uni(all_102_8)
% 36.69/5.74 | (32) set_int(all_102_15)
% 36.69/5.74 | (33) map_int_int(all_102_9)
% 36.69/5.74 | (34) map_int_int(all_102_6)
% 36.69/5.74 | (35) cardinal1(int, all_102_14) = n1
% 36.69/5.74 | (36) t2tb(all_102_15) = all_102_14
% 36.69/5.74 | (37) below1(n1) = all_102_15
% 36.69/5.74 | (38) map(int, int) = all_102_18
% 36.69/5.74 | (39) t2tb2(all_102_9) = all_102_8
% 36.69/5.74 | (40) t2tb2(all_102_6) = all_102_4
% 36.69/5.74 | (41) partial_solution1(n1, all_102_6) = all_102_5
% 36.69/5.74 | (42) (all_102_0 = 0 & ~ (all_102_5 = 0) & $lesseq(1,
% 36.69/5.74 | $difference(all_102_11, all_102_3)) & $lesseq(0, all_102_3) &
% 36.69/5.74 | eq_prefix1(int, all_102_4, all_102_1, n1) = 0 & get(all_102_18, int,
% 36.69/5.74 | all_102_7, all_102_2) = all_102_1 & t2tb1(all_102_3) = all_102_2 &
% 36.69/5.74 | uni(all_102_1) & uni(all_102_2)) | (all_102_5 = 0 & ! [v0: int] :
% 36.69/5.74 | ! [v1: uni] : ( ~ ($lesseq(1, $difference(all_102_11, v0))) | ~
% 36.69/5.74 | ($lesseq(0, v0)) | ~ (t2tb1(v0) = v1) | ? [v2: uni] : ? [v3:
% 36.69/5.74 | int] : ( ~ (v3 = 0) & eq_prefix1(int, all_102_4, v2, n1) = v3 &
% 36.69/5.74 | get(all_102_18, int, all_102_7, v1) = v2 & uni(v2))))
% 36.69/5.74 | (43) ! [v0: map_int_int] : ! [v1: uni] : ( ~ (t2tb2(v0) = v1) | ~
% 36.69/5.74 | map_int_int(v0) | ? [v2: int] : ? [v3: any] : ? [v4: uni] : ?
% 36.69/5.74 | [v5: int] : ((v5 = 0 & $lesseq(1, $difference(all_102_11, v2)) &
% 36.69/5.74 | $lesseq(0, v2) & eq_prefix1(int, v1, v4, n1) = 0 &
% 36.69/5.74 | get(all_102_18, int, all_102_7, v3) = v4 & t2tb1(v2) = v3 &
% 36.69/5.74 | uni(v4) & uni(v3)) | (partial_solution1(n1, v0) = v2 &
% 36.69/5.74 | eq_prefix1(int, all_102_8, v1, 0) = v3 & ( ~ (v3 = 0) | ~ (v2 =
% 36.69/5.74 | 0)))))
% 36.69/5.74 | (44) ! [v0: map_int_int] : ! [v1: any] : ( ~ (partial_solution1(n1, v0) =
% 36.69/5.74 | v1) | ~ map_int_int(v0) | ? [v2: uni] : ? [v3: any] :
% 36.69/5.74 | (t2tb2(v0) = v2 & eq_prefix1(int, all_102_8, v2, 0) = v3 & uni(v2) &
% 36.69/5.74 | ( ! [v4: int] : ! [v5: uni] : ( ~ ($lesseq(1,
% 36.69/5.74 | $difference(all_102_11, v4))) | ~ ($lesseq(0, v4)) | ~
% 36.69/5.74 | (t2tb1(v4) = v5) | ? [v6: uni] : ? [v7: int] : ( ~ (v7 = 0)
% 36.69/5.74 | & eq_prefix1(int, v2, v6, n1) = v7 & get(all_102_18, int,
% 36.69/5.74 | all_102_7, v5) = v6 & uni(v6))) | (v3 = 0 & v1 = 0))))
% 36.69/5.74 | (45) ! [v0: int] : ! [v1: uni] : ( ~ ($lesseq(0, v0)) | ~ (t2tb1(v0) =
% 36.69/5.74 | v1) | ? [v2: int] : ( ~ (v2 = 0) & mem(int, v1, all_102_19) =
% 36.69/5.74 | v2))
% 36.69/5.74 | (46) ! [v0: map_int_int] : ! [v1: uni] : ! [v2: int] : ! [v3: uni] : (
% 36.69/5.74 | ~ ($lesseq(1, $difference(all_102_11, v2))) | ~ ($lesseq(0, v2)) |
% 36.69/5.74 | ~ (t2tb2(v0) = v1) | ~ (t2tb1(v2) = v3) | ~ map_int_int(v0) | ?
% 36.69/5.74 | [v4: any] : ? [v5: int] : ((v5 = 0 & v4 = 0 & partial_solution1(n1,
% 36.69/5.74 | v0) = 0 & eq_prefix1(int, all_102_8, v1, 0) = 0) | ( ~ (v5 =
% 36.69/5.74 | 0) & eq_prefix1(int, v1, v4, n1) = v5 & get(all_102_18, int,
% 36.69/5.74 | all_102_7, v3) = v4 & uni(v4))))
% 36.69/5.74 |
% 36.69/5.74 | GROUND_INST: instantiating (22) with all_87_0, all_102_18, int, int,
% 36.69/5.74 | simplifying with (28), (38) gives:
% 36.69/5.74 | (47) all_102_18 = all_87_0
% 36.69/5.74 |
% 36.69/5.74 | GROUND_INST: instantiating (1) with int, all_102_14, n1, simplifying with
% 36.69/5.74 | (14), (30), (35) gives:
% 36.69/5.74 | (48) n1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & is_empty(int, all_102_14) = v0)
% 36.69/5.74 |
% 36.69/5.74 | GROUND_INST: instantiating (6) with all_102_15, all_102_14, simplifying with
% 36.69/5.74 | (32), (36) gives:
% 36.69/5.74 | (49) ? [v0: any] : ? [v1: int] : ? [v2: uni] : ? [v3: any] :
% 36.69/5.74 | (max_elt1(all_102_15) = v1 & t2tb1(v1) = v2 & is_empty(int,
% 36.69/5.74 | all_102_14) = v0 & mem(int, v2, all_102_14) = v3 & uni(v2) & (v3 =
% 36.69/5.74 | 0 | v0 = 0))
% 36.69/5.74 |
% 36.69/5.75 | GROUND_INST: instantiating (2) with all_102_15, all_102_14, simplifying with
% 36.69/5.75 | (32), (36) gives:
% 36.69/5.75 | (50) ? [v0: any] : ? [v1: int] : ? [v2: uni] : ? [v3: any] :
% 36.69/5.75 | (min_elt1(all_102_15) = v1 & t2tb1(v1) = v2 & is_empty(int,
% 36.69/5.75 | all_102_14) = v0 & mem(int, v2, all_102_14) = v3 & uni(v2) & (v3 =
% 36.69/5.75 | 0 | v0 = 0))
% 36.69/5.75 |
% 36.69/5.75 | GROUND_INST: instantiating (8) with all_102_15, all_102_14, simplifying with
% 36.69/5.75 | (32), (36) gives:
% 36.69/5.75 | (51) ? [v0: any] : ? [v1: int] : (max_elt1(all_102_15) = v1 &
% 36.69/5.75 | is_empty(int, all_102_14) = v0 & (v0 = 0 | ! [v2: int] : ! [v3:
% 36.69/5.75 | uni] : ( ~ ($lesseq(1, $difference(v2, v1))) | ~ (t2tb1(v2) =
% 36.69/5.75 | v3) | ? [v4: int] : ( ~ (v4 = 0) & mem(int, v3, all_102_14) =
% 36.69/5.75 | v4))))
% 36.69/5.75 |
% 36.69/5.75 | GROUND_INST: instantiating (4) with all_102_15, all_102_14, simplifying with
% 36.69/5.75 | (32), (36) gives:
% 36.69/5.75 | (52) ? [v0: any] : ? [v1: int] : (min_elt1(all_102_15) = v1 &
% 36.69/5.75 | is_empty(int, all_102_14) = v0 & (v0 = 0 | ! [v2: int] : ! [v3:
% 36.69/5.75 | uni] : ( ~ ($lesseq(1, $difference(v1, v2))) | ~ (t2tb1(v2) =
% 36.69/5.75 | v3) | ? [v4: int] : ( ~ (v4 = 0) & mem(int, v3, all_102_14) =
% 36.69/5.75 | v4))))
% 36.69/5.75 |
% 36.69/5.75 | GROUND_INST: instantiating (43) with all_102_6, all_102_4, simplifying with
% 36.69/5.75 | (34), (40) gives:
% 36.69/5.75 | (53) ? [v0: int] : ? [v1: any] : ? [v2: uni] : ? [v3: int] : ((v3 = 0 &
% 36.69/5.75 | $lesseq(1, $difference(all_102_11, v0)) & $lesseq(0, v0) &
% 36.69/5.75 | eq_prefix1(int, all_102_4, v2, n1) = 0 & get(all_102_18, int,
% 36.69/5.75 | all_102_7, v1) = v2 & t2tb1(v0) = v1 & uni(v2) & uni(v1)) |
% 36.69/5.75 | (partial_solution1(n1, all_102_6) = v0 & eq_prefix1(int, all_102_8,
% 36.69/5.75 | all_102_4, 0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 36.69/5.75 |
% 36.69/5.75 | GROUND_INST: instantiating (44) with all_102_6, all_102_5, simplifying with
% 36.69/5.75 | (34), (41) gives:
% 36.69/5.75 | (54) ? [v0: uni] : ? [v1: any] : (t2tb2(all_102_6) = v0 & eq_prefix1(int,
% 36.69/5.75 | all_102_8, v0, 0) = v1 & uni(v0) & ( ! [v2: int] : ! [v3: uni] :
% 36.69/5.75 | ( ~ ($lesseq(1, $difference(all_102_11, v2))) | ~ ($lesseq(0,
% 36.69/5.75 | v2)) | ~ (t2tb1(v2) = v3) | ? [v4: uni] : ? [v5: int] : (
% 36.69/5.75 | ~ (v5 = 0) & eq_prefix1(int, v0, v4, n1) = v5 &
% 36.69/5.75 | get(all_102_18, int, all_102_7, v3) = v4 & uni(v4))) | (v1 = 0
% 36.69/5.75 | & all_102_5 = 0)))
% 36.69/5.75 |
% 36.69/5.75 | GROUND_INST: instantiating (13) with n1, all_102_6, all_102_5, simplifying
% 36.69/5.75 | with (34), (41) gives:
% 36.69/5.75 | (55) all_102_5 = 0 | ? [v0: uni] : ? [v1: int] : ? [v2: uni] : ? [v3:
% 36.69/5.75 | uni] : ? [v4: int] : ? [v5: int] : ? [v6: uni] : ? [v7: uni] :
% 36.69/5.75 | ? [v8: int] : ($lesseq(1, $difference(n1, v1)) & $lesseq(0, v1) &
% 36.69/5.75 | t2tb2(all_102_6) = v0 & get(int, int, v0, v2) = v3 & tb2t1(v3) = v4
% 36.69/5.75 | & t2tb1(v1) = v2 & uni(v3) & uni(v2) & uni(v0) & ( ~ ($lesseq(1,
% 36.69/5.75 | $difference(n1, v4))) | ~ ($lesseq(0, v4)) | ($lesseq(1,
% 36.69/5.75 | $difference(v1, v5)) & $lesseq(0, v5) & get(int, int, v0, v6)
% 36.69/5.75 | = v7 & tb2t1(v7) = v8 & t2tb1(v5) = v6 & uni(v7) & uni(v6) &
% 36.69/5.75 | ($sum($difference($difference(v8, v5), v4), v1) = 0 |
% 36.69/5.75 | $difference($sum(v8, v5), v4) = v1 | v8 = v4))))
% 36.69/5.75 |
% 36.69/5.75 | DELTA: instantiating (52) with fresh symbols all_130_0, all_130_1 gives:
% 36.69/5.75 | (56) min_elt1(all_102_15) = all_130_0 & is_empty(int, all_102_14) =
% 36.69/5.75 | all_130_1 & (all_130_1 = 0 | ! [v0: int] : ! [v1: uni] : ( ~
% 36.69/5.75 | ($lesseq(1, $difference(all_130_0, v0))) | ~ (t2tb1(v0) = v1) |
% 36.69/5.75 | ? [v2: int] : ( ~ (v2 = 0) & mem(int, v1, all_102_14) = v2)))
% 36.69/5.75 |
% 36.69/5.75 | ALPHA: (56) implies:
% 36.69/5.75 | (57) is_empty(int, all_102_14) = all_130_1
% 36.69/5.75 | (58) min_elt1(all_102_15) = all_130_0
% 36.69/5.75 |
% 36.69/5.75 | DELTA: instantiating (50) with fresh symbols all_132_0, all_132_1, all_132_2,
% 36.69/5.75 | all_132_3 gives:
% 36.69/5.75 | (59) min_elt1(all_102_15) = all_132_2 & t2tb1(all_132_2) = all_132_1 &
% 36.69/5.75 | is_empty(int, all_102_14) = all_132_3 & mem(int, all_132_1,
% 36.69/5.75 | all_102_14) = all_132_0 & uni(all_132_1) & (all_132_0 = 0 |
% 36.69/5.75 | all_132_3 = 0)
% 36.69/5.75 |
% 36.69/5.75 | ALPHA: (59) implies:
% 36.69/5.75 | (60) is_empty(int, all_102_14) = all_132_3
% 36.69/5.75 | (61) min_elt1(all_102_15) = all_132_2
% 36.69/5.75 |
% 36.69/5.75 | DELTA: instantiating (49) with fresh symbols all_134_0, all_134_1, all_134_2,
% 36.69/5.75 | all_134_3 gives:
% 36.69/5.75 | (62) max_elt1(all_102_15) = all_134_2 & t2tb1(all_134_2) = all_134_1 &
% 36.69/5.75 | is_empty(int, all_102_14) = all_134_3 & mem(int, all_134_1,
% 36.69/5.75 | all_102_14) = all_134_0 & uni(all_134_1) & (all_134_0 = 0 |
% 36.69/5.75 | all_134_3 = 0)
% 36.69/5.75 |
% 36.69/5.75 | ALPHA: (62) implies:
% 36.69/5.75 | (63) mem(int, all_134_1, all_102_14) = all_134_0
% 36.69/5.75 | (64) is_empty(int, all_102_14) = all_134_3
% 36.69/5.75 | (65) t2tb1(all_134_2) = all_134_1
% 36.69/5.75 | (66) max_elt1(all_102_15) = all_134_2
% 36.69/5.75 |
% 36.69/5.75 | DELTA: instantiating (51) with fresh symbols all_136_0, all_136_1 gives:
% 36.69/5.76 | (67) max_elt1(all_102_15) = all_136_0 & is_empty(int, all_102_14) =
% 36.69/5.76 | all_136_1 & (all_136_1 = 0 | ! [v0: int] : ! [v1: uni] : ( ~
% 36.69/5.76 | ($lesseq(1, $difference(v0, all_136_0))) | ~ (t2tb1(v0) = v1) |
% 36.69/5.76 | ? [v2: int] : ( ~ (v2 = 0) & mem(int, v1, all_102_14) = v2)))
% 36.69/5.76 |
% 36.69/5.76 | ALPHA: (67) implies:
% 36.69/5.76 | (68) is_empty(int, all_102_14) = all_136_1
% 36.69/5.76 | (69) max_elt1(all_102_15) = all_136_0
% 36.69/5.76 |
% 36.69/5.76 | DELTA: instantiating (53) with fresh symbols all_143_0, all_143_1, all_143_2,
% 36.69/5.76 | all_143_3 gives:
% 36.69/5.76 | (70) (all_143_0 = 0 & $lesseq(1, $difference(all_102_11, all_143_3)) &
% 36.69/5.76 | $lesseq(0, all_143_3) & eq_prefix1(int, all_102_4, all_143_1, n1) =
% 36.69/5.76 | 0 & get(all_102_18, int, all_102_7, all_143_2) = all_143_1 &
% 36.69/5.76 | t2tb1(all_143_3) = all_143_2 & uni(all_143_1) & uni(all_143_2)) |
% 36.69/5.76 | (partial_solution1(n1, all_102_6) = all_143_3 & eq_prefix1(int,
% 36.69/5.76 | all_102_8, all_102_4, 0) = all_143_2 & ( ~ (all_143_2 = 0) | ~
% 36.69/5.76 | (all_143_3 = 0)))
% 36.69/5.76 |
% 36.69/5.76 | DELTA: instantiating (54) with fresh symbols all_144_0, all_144_1 gives:
% 36.69/5.76 | (71) t2tb2(all_102_6) = all_144_1 & eq_prefix1(int, all_102_8, all_144_1,
% 36.69/5.76 | 0) = all_144_0 & uni(all_144_1) & ( ! [v0: int] : ! [v1: uni] : ( ~
% 36.69/5.76 | ($lesseq(1, $difference(all_102_11, v0))) | ~ ($lesseq(0, v0)) |
% 36.69/5.76 | ~ (t2tb1(v0) = v1) | ? [v2: uni] : ? [v3: int] : ( ~ (v3 = 0) &
% 36.69/5.76 | eq_prefix1(int, all_144_1, v2, n1) = v3 & get(all_102_18, int,
% 36.69/5.76 | all_102_7, v1) = v2 & uni(v2))) | (all_144_0 = 0 & all_102_5 =
% 36.69/5.76 | 0))
% 36.69/5.76 |
% 36.69/5.76 | ALPHA: (71) implies:
% 36.69/5.76 | (72) uni(all_144_1)
% 36.69/5.76 | (73) eq_prefix1(int, all_102_8, all_144_1, 0) = all_144_0
% 36.69/5.76 | (74) t2tb2(all_102_6) = all_144_1
% 36.69/5.76 |
% 36.69/5.76 | GROUND_INST: instantiating (21) with all_134_3, all_136_1, all_102_14, int,
% 36.69/5.76 | simplifying with (64), (68) gives:
% 36.69/5.76 | (75) all_136_1 = all_134_3
% 36.69/5.76 |
% 36.69/5.76 | GROUND_INST: instantiating (21) with all_132_3, all_136_1, all_102_14, int,
% 36.69/5.76 | simplifying with (60), (68) gives:
% 36.69/5.76 | (76) all_136_1 = all_132_3
% 36.69/5.76 |
% 36.69/5.76 | GROUND_INST: instantiating (21) with all_130_1, all_136_1, all_102_14, int,
% 36.69/5.76 | simplifying with (57), (68) gives:
% 36.69/5.76 | (77) all_136_1 = all_130_1
% 36.69/5.76 |
% 36.69/5.76 | GROUND_INST: instantiating (18) with all_130_0, all_132_2, all_102_15,
% 36.69/5.76 | simplifying with (58), (61) gives:
% 36.69/5.76 | (78) all_132_2 = all_130_0
% 36.69/5.76 |
% 36.69/5.76 | GROUND_INST: instantiating (19) with all_134_2, all_136_0, all_102_15,
% 36.69/5.76 | simplifying with (66), (69) gives:
% 36.69/5.76 | (79) all_136_0 = all_134_2
% 36.69/5.76 |
% 36.69/5.76 | GROUND_INST: instantiating (20) with all_102_4, all_144_1, all_102_6,
% 36.69/5.76 | simplifying with (40), (74) gives:
% 36.69/5.76 | (80) all_144_1 = all_102_4
% 36.69/5.76 |
% 36.69/5.76 | COMBINE_EQS: (75), (77) imply:
% 36.69/5.76 | (81) all_134_3 = all_130_1
% 36.69/5.76 |
% 36.69/5.76 | COMBINE_EQS: (75), (76) imply:
% 36.69/5.76 | (82) all_134_3 = all_132_3
% 36.69/5.76 |
% 36.69/5.76 | COMBINE_EQS: (81), (82) imply:
% 36.69/5.76 | (83) all_132_3 = all_130_1
% 36.69/5.76 |
% 36.69/5.76 | SIMP: (83) implies:
% 36.69/5.76 | (84) all_132_3 = all_130_1
% 36.69/5.76 |
% 36.69/5.76 | REDUCE: (73), (80) imply:
% 36.69/5.76 | (85) eq_prefix1(int, all_102_8, all_102_4, 0) = all_144_0
% 36.69/5.76 |
% 36.69/5.76 | REDUCE: (72), (80) imply:
% 36.69/5.76 | (86) uni(all_102_4)
% 37.10/5.76 |
% 37.10/5.76 | GROUND_INST: instantiating (45) with all_134_2, all_134_1, simplifying with
% 37.10/5.76 | (65) gives:
% 37.10/5.76 | (87) ~ ($lesseq(0, all_134_2)) | ? [v0: int] : ( ~ (v0 = 0) & mem(int,
% 37.10/5.76 | all_134_1, all_102_19) = v0)
% 37.10/5.76 |
% 37.10/5.76 | GROUND_INST: instantiating (3) with all_102_15, all_130_0, simplifying with
% 37.10/5.76 | (32), (58) gives:
% 37.10/5.76 | (88) ? [v0: uni] : ? [v1: any] : ? [v2: uni] : ? [v3: any] :
% 37.10/5.76 | (t2tb1(all_130_0) = v2 & t2tb(all_102_15) = v0 & is_empty(int, v0) =
% 37.10/5.76 | v1 & mem(int, v2, v0) = v3 & uni(v2) & uni(v0) & (v3 = 0 | v1 = 0))
% 37.10/5.76 |
% 37.10/5.76 | GROUND_INST: instantiating (5) with all_102_15, all_130_0, simplifying with
% 37.10/5.76 | (32), (58) gives:
% 37.10/5.76 | (89) ? [v0: uni] : ? [v1: any] : (t2tb(all_102_15) = v0 & is_empty(int,
% 37.10/5.76 | v0) = v1 & uni(v0) & (v1 = 0 | ! [v2: int] : ! [v3: uni] : ( ~
% 37.10/5.76 | ($lesseq(1, $difference(all_130_0, v2))) | ~ (t2tb1(v2) = v3) |
% 37.10/5.76 | ? [v4: int] : ( ~ (v4 = 0) & mem(int, v3, v0) = v4))))
% 37.10/5.76 |
% 37.10/5.76 | GROUND_INST: instantiating (7) with all_102_15, all_134_2, simplifying with
% 37.10/5.76 | (32), (66) gives:
% 37.10/5.76 | (90) ? [v0: uni] : ? [v1: any] : ? [v2: uni] : ? [v3: any] :
% 37.10/5.76 | (t2tb1(all_134_2) = v2 & t2tb(all_102_15) = v0 & is_empty(int, v0) =
% 37.10/5.76 | v1 & mem(int, v2, v0) = v3 & uni(v2) & uni(v0) & (v3 = 0 | v1 = 0))
% 37.10/5.76 |
% 37.10/5.76 | GROUND_INST: instantiating (9) with all_102_15, all_134_2, simplifying with
% 37.10/5.76 | (32), (66) gives:
% 37.10/5.76 | (91) ? [v0: uni] : ? [v1: any] : (t2tb(all_102_15) = v0 & is_empty(int,
% 37.10/5.76 | v0) = v1 & uni(v0) & (v1 = 0 | ! [v2: int] : ! [v3: uni] : ( ~
% 37.10/5.76 | ($lesseq(1, $difference(v2, all_134_2))) | ~ (t2tb1(v2) = v3) |
% 37.10/5.76 | ? [v4: int] : ( ~ (v4 = 0) & mem(int, v3, v0) = v4))))
% 37.10/5.76 |
% 37.10/5.76 | GROUND_INST: instantiating (11) with int, all_102_8, all_102_4, 0, all_144_0,
% 37.10/5.76 | simplifying with (14), (31), (85), (86) gives:
% 37.10/5.76 | (92) all_144_0 = 0
% 37.10/5.76 |
% 37.10/5.76 | DELTA: instantiating (88) with fresh symbols all_180_0, all_180_1, all_180_2,
% 37.10/5.76 | all_180_3 gives:
% 37.10/5.76 | (93) t2tb1(all_130_0) = all_180_1 & t2tb(all_102_15) = all_180_3 &
% 37.10/5.76 | is_empty(int, all_180_3) = all_180_2 & mem(int, all_180_1, all_180_3)
% 37.10/5.76 | = all_180_0 & uni(all_180_1) & uni(all_180_3) & (all_180_0 = 0 |
% 37.10/5.76 | all_180_2 = 0)
% 37.10/5.76 |
% 37.10/5.76 | ALPHA: (93) implies:
% 37.10/5.76 | (94) is_empty(int, all_180_3) = all_180_2
% 37.10/5.76 | (95) t2tb(all_102_15) = all_180_3
% 37.10/5.76 |
% 37.10/5.76 | DELTA: instantiating (91) with fresh symbols all_182_0, all_182_1 gives:
% 37.10/5.76 | (96) t2tb(all_102_15) = all_182_1 & is_empty(int, all_182_1) = all_182_0 &
% 37.10/5.76 | uni(all_182_1) & (all_182_0 = 0 | ! [v0: int] : ! [v1: uni] : ( ~
% 37.10/5.76 | ($lesseq(1, $difference(v0, all_134_2))) | ~ (t2tb1(v0) = v1) |
% 37.10/5.76 | ? [v2: int] : ( ~ (v2 = 0) & mem(int, v1, all_182_1) = v2)))
% 37.10/5.77 |
% 37.10/5.77 | ALPHA: (96) implies:
% 37.10/5.77 | (97) is_empty(int, all_182_1) = all_182_0
% 37.10/5.77 | (98) t2tb(all_102_15) = all_182_1
% 37.10/5.77 |
% 37.10/5.77 | DELTA: instantiating (90) with fresh symbols all_184_0, all_184_1, all_184_2,
% 37.10/5.77 | all_184_3 gives:
% 37.10/5.77 | (99) t2tb1(all_134_2) = all_184_1 & t2tb(all_102_15) = all_184_3 &
% 37.10/5.77 | is_empty(int, all_184_3) = all_184_2 & mem(int, all_184_1, all_184_3)
% 37.10/5.77 | = all_184_0 & uni(all_184_1) & uni(all_184_3) & (all_184_0 = 0 |
% 37.10/5.77 | all_184_2 = 0)
% 37.10/5.77 |
% 37.10/5.77 | ALPHA: (99) implies:
% 37.10/5.77 | (100) mem(int, all_184_1, all_184_3) = all_184_0
% 37.10/5.77 | (101) is_empty(int, all_184_3) = all_184_2
% 37.10/5.77 | (102) t2tb(all_102_15) = all_184_3
% 37.10/5.77 | (103) t2tb1(all_134_2) = all_184_1
% 37.10/5.77 | (104) all_184_0 = 0 | all_184_2 = 0
% 37.10/5.77 |
% 37.10/5.77 | DELTA: instantiating (89) with fresh symbols all_186_0, all_186_1 gives:
% 37.10/5.77 | (105) t2tb(all_102_15) = all_186_1 & is_empty(int, all_186_1) = all_186_0 &
% 37.10/5.77 | uni(all_186_1) & (all_186_0 = 0 | ! [v0: int] : ! [v1: uni] : ( ~
% 37.10/5.77 | ($lesseq(1, $difference(all_130_0, v0))) | ~ (t2tb1(v0) = v1) |
% 37.10/5.77 | ? [v2: int] : ( ~ (v2 = 0) & mem(int, v1, all_186_1) = v2)))
% 37.10/5.77 |
% 37.10/5.77 | ALPHA: (105) implies:
% 37.10/5.77 | (106) is_empty(int, all_186_1) = all_186_0
% 37.10/5.77 | (107) t2tb(all_102_15) = all_186_1
% 37.10/5.77 |
% 37.10/5.77 | REDUCE: (85), (92) imply:
% 37.10/5.77 | (108) eq_prefix1(int, all_102_8, all_102_4, 0) = 0
% 37.10/5.77 |
% 37.10/5.77 | GROUND_INST: instantiating (16) with all_102_14, all_184_3, all_102_15,
% 37.10/5.77 | simplifying with (36), (102) gives:
% 37.10/5.77 | (109) all_184_3 = all_102_14
% 37.10/5.77 |
% 37.10/5.77 | GROUND_INST: instantiating (16) with all_182_1, all_184_3, all_102_15,
% 37.10/5.77 | simplifying with (98), (102) gives:
% 37.10/5.77 | (110) all_184_3 = all_182_1
% 37.10/5.77 |
% 37.10/5.77 | GROUND_INST: instantiating (16) with all_182_1, all_186_1, all_102_15,
% 37.10/5.77 | simplifying with (98), (107) gives:
% 37.10/5.77 | (111) all_186_1 = all_182_1
% 37.10/5.77 |
% 37.10/5.77 | GROUND_INST: instantiating (16) with all_180_3, all_186_1, all_102_15,
% 37.10/5.77 | simplifying with (95), (107) gives:
% 37.10/5.77 | (112) all_186_1 = all_180_3
% 37.10/5.77 |
% 37.10/5.77 | GROUND_INST: instantiating (17) with all_134_1, all_184_1, all_134_2,
% 37.10/5.77 | simplifying with (65), (103) gives:
% 37.10/5.77 | (113) all_184_1 = all_134_1
% 37.10/5.77 |
% 37.10/5.77 | COMBINE_EQS: (111), (112) imply:
% 37.10/5.77 | (114) all_182_1 = all_180_3
% 37.10/5.77 |
% 37.10/5.77 | SIMP: (114) implies:
% 37.10/5.77 | (115) all_182_1 = all_180_3
% 37.10/5.77 |
% 37.10/5.77 | COMBINE_EQS: (109), (110) imply:
% 37.10/5.77 | (116) all_182_1 = all_102_14
% 37.10/5.77 |
% 37.10/5.77 | SIMP: (116) implies:
% 37.10/5.77 | (117) all_182_1 = all_102_14
% 37.10/5.77 |
% 37.10/5.77 | COMBINE_EQS: (115), (117) imply:
% 37.10/5.77 | (118) all_180_3 = all_102_14
% 37.10/5.77 |
% 37.10/5.77 | SIMP: (118) implies:
% 37.10/5.77 | (119) all_180_3 = all_102_14
% 37.10/5.77 |
% 37.10/5.77 | COMBINE_EQS: (112), (119) imply:
% 37.10/5.77 | (120) all_186_1 = all_102_14
% 37.10/5.77 |
% 37.10/5.77 | REDUCE: (106), (120) imply:
% 37.10/5.77 | (121) is_empty(int, all_102_14) = all_186_0
% 37.10/5.77 |
% 37.10/5.77 | REDUCE: (101), (109) imply:
% 37.10/5.77 | (122) is_empty(int, all_102_14) = all_184_2
% 37.10/5.77 |
% 37.10/5.77 | REDUCE: (97), (117) imply:
% 37.10/5.77 | (123) is_empty(int, all_102_14) = all_182_0
% 37.10/5.77 |
% 37.10/5.77 | REDUCE: (94), (119) imply:
% 37.10/5.77 | (124) is_empty(int, all_102_14) = all_180_2
% 37.10/5.77 |
% 37.10/5.77 | REDUCE: (100), (109), (113) imply:
% 37.10/5.77 | (125) mem(int, all_134_1, all_102_14) = all_184_0
% 37.10/5.77 |
% 37.10/5.77 | GROUND_INST: instantiating (24) with all_134_0, all_184_0, all_102_14,
% 37.10/5.77 | all_134_1, int, simplifying with (63), (125) gives:
% 37.10/5.77 | (126) all_184_0 = all_134_0
% 37.10/5.77 |
% 37.10/5.77 | GROUND_INST: instantiating (21) with all_130_1, all_182_0, all_102_14, int,
% 37.10/5.77 | simplifying with (57), (123) gives:
% 37.10/5.77 | (127) all_182_0 = all_130_1
% 37.10/5.77 |
% 37.10/5.77 | GROUND_INST: instantiating (21) with all_182_0, all_184_2, all_102_14, int,
% 37.10/5.77 | simplifying with (122), (123) gives:
% 37.10/5.77 | (128) all_184_2 = all_182_0
% 37.10/5.77 |
% 37.10/5.77 | GROUND_INST: instantiating (21) with all_184_2, all_186_0, all_102_14, int,
% 37.10/5.77 | simplifying with (121), (122) gives:
% 37.10/5.77 | (129) all_186_0 = all_184_2
% 37.10/5.77 |
% 37.10/5.77 | GROUND_INST: instantiating (21) with all_180_2, all_186_0, all_102_14, int,
% 37.10/5.77 | simplifying with (121), (124) gives:
% 37.10/5.77 | (130) all_186_0 = all_180_2
% 37.10/5.77 |
% 37.10/5.77 | COMBINE_EQS: (129), (130) imply:
% 37.10/5.77 | (131) all_184_2 = all_180_2
% 37.10/5.77 |
% 37.10/5.77 | SIMP: (131) implies:
% 37.10/5.77 | (132) all_184_2 = all_180_2
% 37.10/5.77 |
% 37.10/5.77 | COMBINE_EQS: (128), (132) imply:
% 37.10/5.77 | (133) all_182_0 = all_180_2
% 37.10/5.77 |
% 37.10/5.77 | SIMP: (133) implies:
% 37.10/5.77 | (134) all_182_0 = all_180_2
% 37.10/5.77 |
% 37.10/5.77 | COMBINE_EQS: (127), (134) imply:
% 37.10/5.77 | (135) all_180_2 = all_130_1
% 37.10/5.77 |
% 37.10/5.77 | SIMP: (135) implies:
% 37.10/5.77 | (136) all_180_2 = all_130_1
% 37.10/5.77 |
% 37.10/5.77 | COMBINE_EQS: (132), (136) imply:
% 37.10/5.77 | (137) all_184_2 = all_130_1
% 37.10/5.77 |
% 37.10/5.77 | BETA: splitting (42) gives:
% 37.10/5.77 |
% 37.10/5.77 | Case 1:
% 37.10/5.77 | |
% 37.10/5.77 | | (138) all_102_0 = 0 & ~ (all_102_5 = 0) & $lesseq(1,
% 37.10/5.77 | | $difference(all_102_11, all_102_3)) & $lesseq(0, all_102_3) &
% 37.10/5.77 | | eq_prefix1(int, all_102_4, all_102_1, n1) = 0 & get(all_102_18,
% 37.10/5.77 | | int, all_102_7, all_102_2) = all_102_1 & t2tb1(all_102_3) =
% 37.10/5.77 | | all_102_2 & uni(all_102_1) & uni(all_102_2)
% 37.10/5.77 | |
% 37.10/5.77 | | ALPHA: (138) implies:
% 37.10/5.77 | | (139) ~ (all_102_5 = 0)
% 37.10/5.77 | | (140) $lesseq(0, all_102_3)
% 37.10/5.77 | | (141) $lesseq(1, $difference(all_102_11, all_102_3))
% 37.10/5.77 | | (142) t2tb1(all_102_3) = all_102_2
% 37.10/5.77 | | (143) get(all_102_18, int, all_102_7, all_102_2) = all_102_1
% 37.10/5.77 | | (144) eq_prefix1(int, all_102_4, all_102_1, n1) = 0
% 37.10/5.77 | |
% 37.10/5.77 | | REDUCE: (47), (143) imply:
% 37.10/5.77 | | (145) get(all_87_0, int, all_102_7, all_102_2) = all_102_1
% 37.10/5.77 | |
% 37.10/5.77 | | BETA: splitting (55) gives:
% 37.10/5.77 | |
% 37.10/5.77 | | Case 1:
% 37.10/5.77 | | |
% 37.10/5.77 | | | (146) all_102_5 = 0
% 37.10/5.77 | | |
% 37.10/5.77 | | | REDUCE: (139), (146) imply:
% 37.10/5.77 | | | (147) $false
% 37.10/5.78 | | |
% 37.10/5.78 | | | CLOSE: (147) is inconsistent.
% 37.10/5.78 | | |
% 37.10/5.78 | | Case 2:
% 37.10/5.78 | | |
% 37.10/5.78 | | | (148) ? [v0: uni] : ? [v1: int] : ? [v2: uni] : ? [v3: uni] : ?
% 37.10/5.78 | | | [v4: int] : ? [v5: int] : ? [v6: uni] : ? [v7: uni] : ? [v8:
% 37.10/5.78 | | | int] : ($lesseq(1, $difference(n1, v1)) & $lesseq(0, v1) &
% 37.10/5.78 | | | t2tb2(all_102_6) = v0 & get(int, int, v0, v2) = v3 & tb2t1(v3)
% 37.10/5.78 | | | = v4 & t2tb1(v1) = v2 & uni(v3) & uni(v2) & uni(v0) & ( ~
% 37.10/5.78 | | | ($lesseq(1, $difference(n1, v4))) | ~ ($lesseq(0, v4)) |
% 37.10/5.78 | | | ($lesseq(1, $difference(v1, v5)) & $lesseq(0, v5) & get(int,
% 37.10/5.78 | | | int, v0, v6) = v7 & tb2t1(v7) = v8 & t2tb1(v5) = v6 &
% 37.10/5.78 | | | uni(v7) & uni(v6) & ($sum($difference($difference(v8, v5),
% 37.10/5.78 | | | v4), v1) = 0 | $difference($sum(v8, v5), v4) = v1 |
% 37.10/5.78 | | | v8 = v4))))
% 37.10/5.78 | | |
% 37.10/5.78 | | | DELTA: instantiating (148) with fresh symbols all_295_0, all_295_1,
% 37.10/5.78 | | | all_295_2, all_295_3, all_295_4, all_295_5, all_295_6, all_295_7,
% 37.10/5.78 | | | all_295_8 gives:
% 37.10/5.78 | | | (149) $lesseq(1, $difference(n1, all_295_7)) & $lesseq(0, all_295_7) &
% 37.10/5.78 | | | t2tb2(all_102_6) = all_295_8 & get(int, int, all_295_8,
% 37.10/5.78 | | | all_295_6) = all_295_5 & tb2t1(all_295_5) = all_295_4 &
% 37.10/5.78 | | | t2tb1(all_295_7) = all_295_6 & uni(all_295_5) & uni(all_295_6) &
% 37.10/5.78 | | | uni(all_295_8) & ( ~ ($lesseq(1, $difference(n1, all_295_4))) |
% 37.10/5.78 | | | ~ ($lesseq(0, all_295_4)) | ($lesseq(1, $difference(all_295_7,
% 37.10/5.78 | | | all_295_3)) & $lesseq(0, all_295_3) & get(int, int,
% 37.10/5.78 | | | all_295_8, all_295_2) = all_295_1 & tb2t1(all_295_1) =
% 37.10/5.78 | | | all_295_0 & t2tb1(all_295_3) = all_295_2 & uni(all_295_1) &
% 37.10/5.78 | | | uni(all_295_2) & ($sum($difference($difference(all_295_0,
% 37.10/5.78 | | | all_295_3), all_295_4), all_295_7) = 0 |
% 37.10/5.78 | | | $difference($sum(all_295_0, all_295_3), all_295_4) =
% 37.10/5.78 | | | all_295_7 | all_295_0 = all_295_4)))
% 37.10/5.78 | | |
% 37.10/5.78 | | | ALPHA: (149) implies:
% 37.10/5.78 | | | (150) $lesseq(0, all_295_7)
% 37.10/5.78 | | | (151) $lesseq(1, $difference(n1, all_295_7))
% 37.10/5.78 | | | (152) t2tb2(all_102_6) = all_295_8
% 37.10/5.78 | | |
% 37.10/5.78 | | | BETA: splitting (48) gives:
% 37.10/5.78 | | |
% 37.10/5.78 | | | Case 1:
% 37.10/5.78 | | | |
% 37.10/5.78 | | | | (153) n1 = 0
% 37.10/5.78 | | | |
% 37.10/5.78 | | | | REDUCE: (151), (153) imply:
% 37.10/5.78 | | | | (154) $lesseq(all_295_7, -1)
% 37.10/5.78 | | | |
% 37.10/5.78 | | | | COMBINE_INEQS: (150), (154) imply:
% 37.10/5.78 | | | | (155) $false
% 37.10/5.78 | | | |
% 37.10/5.78 | | | | CLOSE: (155) is inconsistent.
% 37.10/5.78 | | | |
% 37.10/5.78 | | | Case 2:
% 37.10/5.78 | | | |
% 37.10/5.78 | | | | (156) ? [v0: int] : ( ~ (v0 = 0) & is_empty(int, all_102_14) = v0)
% 37.10/5.78 | | | |
% 37.10/5.78 | | | | DELTA: instantiating (156) with fresh symbol all_303_0 gives:
% 37.10/5.78 | | | | (157) ~ (all_303_0 = 0) & is_empty(int, all_102_14) = all_303_0
% 37.10/5.78 | | | |
% 37.10/5.78 | | | | ALPHA: (157) implies:
% 37.10/5.78 | | | | (158) ~ (all_303_0 = 0)
% 37.19/5.78 | | | | (159) is_empty(int, all_102_14) = all_303_0
% 37.19/5.78 | | | |
% 37.19/5.78 | | | | GROUND_INST: instantiating (21) with all_130_1, all_303_0, all_102_14,
% 37.19/5.78 | | | | int, simplifying with (57), (159) gives:
% 37.19/5.78 | | | | (160) all_303_0 = all_130_1
% 37.19/5.78 | | | |
% 37.19/5.78 | | | | GROUND_INST: instantiating (20) with all_102_4, all_295_8, all_102_6,
% 37.19/5.78 | | | | simplifying with (40), (152) gives:
% 37.19/5.78 | | | | (161) all_295_8 = all_102_4
% 37.19/5.78 | | | |
% 37.19/5.78 | | | | REDUCE: (158), (160) imply:
% 37.19/5.78 | | | | (162) ~ (all_130_1 = 0)
% 37.19/5.78 | | | |
% 37.19/5.78 | | | | BETA: splitting (104) gives:
% 37.19/5.78 | | | |
% 37.19/5.78 | | | | Case 1:
% 37.19/5.78 | | | | |
% 37.19/5.78 | | | | | (163) all_184_0 = 0
% 37.19/5.78 | | | | |
% 37.19/5.78 | | | | | COMBINE_EQS: (126), (163) imply:
% 37.19/5.78 | | | | | (164) all_134_0 = 0
% 37.19/5.78 | | | | |
% 37.19/5.78 | | | | | REDUCE: (63), (164) imply:
% 37.19/5.78 | | | | | (165) mem(int, all_134_1, all_102_14) = 0
% 37.19/5.78 | | | | |
% 37.19/5.78 | | | | | BETA: splitting (87) gives:
% 37.19/5.78 | | | | |
% 37.19/5.78 | | | | | Case 1:
% 37.19/5.78 | | | | | |
% 37.19/5.78 | | | | | | (166) $lesseq(all_134_2, -1)
% 37.19/5.78 | | | | | |
% 37.19/5.78 | | | | | | GROUND_INST: instantiating (10) with all_134_2, n1, all_134_1,
% 37.19/5.78 | | | | | | all_102_15, all_102_14, simplifying with (36), (37),
% 37.19/5.78 | | | | | | (65), (165) gives:
% 37.19/5.78 | | | | | | (167) $lesseq(0, all_134_2)
% 37.19/5.78 | | | | | |
% 37.19/5.78 | | | | | | COMBINE_INEQS: (166), (167) imply:
% 37.19/5.78 | | | | | | (168) $false
% 37.19/5.78 | | | | | |
% 37.19/5.78 | | | | | | CLOSE: (168) is inconsistent.
% 37.19/5.78 | | | | | |
% 37.19/5.78 | | | | | Case 2:
% 37.19/5.78 | | | | | |
% 37.19/5.78 | | | | | |
% 37.19/5.78 | | | | | | GROUND_INST: instantiating (46) with all_102_6, all_102_4,
% 37.19/5.78 | | | | | | all_102_3, all_102_2, simplifying with (34), (40),
% 37.19/5.78 | | | | | | (142) gives:
% 37.19/5.78 | | | | | | (169) ~ ($lesseq(1, $difference(all_102_11, all_102_3))) | ~
% 37.19/5.78 | | | | | | ($lesseq(0, all_102_3)) | ? [v0: any] : ? [v1: int] :
% 37.19/5.78 | | | | | | ((v1 = 0 & v0 = 0 & partial_solution1(n1, all_102_6) = 0 &
% 37.19/5.78 | | | | | | eq_prefix1(int, all_102_8, all_102_4, 0) = 0) | ( ~ (v1
% 37.19/5.78 | | | | | | = 0) & eq_prefix1(int, all_102_4, v0, n1) = v1 &
% 37.19/5.78 | | | | | | get(all_102_18, int, all_102_7, all_102_2) = v0 &
% 37.19/5.78 | | | | | | uni(v0)))
% 37.19/5.78 | | | | | |
% 37.19/5.78 | | | | | | GROUND_INST: instantiating (46) with all_102_9, all_102_8,
% 37.19/5.78 | | | | | | all_102_3, all_102_2, simplifying with (33), (39),
% 37.19/5.78 | | | | | | (142) gives:
% 37.19/5.78 | | | | | | (170) ~ ($lesseq(1, $difference(all_102_11, all_102_3))) | ~
% 37.19/5.78 | | | | | | ($lesseq(0, all_102_3)) | ? [v0: any] : ? [v1: int] :
% 37.19/5.78 | | | | | | ((v1 = 0 & v0 = 0 & partial_solution1(n1, all_102_9) = 0 &
% 37.19/5.78 | | | | | | eq_prefix1(int, all_102_8, all_102_8, 0) = 0) | ( ~ (v1
% 37.19/5.78 | | | | | | = 0) & eq_prefix1(int, all_102_8, v0, n1) = v1 &
% 37.19/5.78 | | | | | | get(all_102_18, int, all_102_7, all_102_2) = v0 &
% 37.19/5.78 | | | | | | uni(v0)))
% 37.19/5.78 | | | | | |
% 37.19/5.78 | | | | | | BETA: splitting (169) gives:
% 37.19/5.78 | | | | | |
% 37.19/5.78 | | | | | | Case 1:
% 37.19/5.78 | | | | | | |
% 37.19/5.78 | | | | | | | (171) $lesseq(all_102_3, -1)
% 37.19/5.78 | | | | | | |
% 37.19/5.78 | | | | | | | COMBINE_INEQS: (140), (171) imply:
% 37.19/5.78 | | | | | | | (172) $false
% 37.19/5.78 | | | | | | |
% 37.19/5.78 | | | | | | | CLOSE: (172) is inconsistent.
% 37.19/5.78 | | | | | | |
% 37.19/5.78 | | | | | | Case 2:
% 37.19/5.78 | | | | | | |
% 37.19/5.78 | | | | | | | (173) ~ ($lesseq(1, $difference(all_102_11, all_102_3))) | ?
% 37.19/5.78 | | | | | | | [v0: any] : ? [v1: int] : ((v1 = 0 & v0 = 0 &
% 37.19/5.78 | | | | | | | partial_solution1(n1, all_102_6) = 0 &
% 37.19/5.78 | | | | | | | eq_prefix1(int, all_102_8, all_102_4, 0) = 0) | ( ~
% 37.19/5.78 | | | | | | | (v1 = 0) & eq_prefix1(int, all_102_4, v0, n1) = v1 &
% 37.19/5.78 | | | | | | | get(all_102_18, int, all_102_7, all_102_2) = v0 &
% 37.19/5.78 | | | | | | | uni(v0)))
% 37.19/5.78 | | | | | | |
% 37.19/5.78 | | | | | | | BETA: splitting (170) gives:
% 37.19/5.78 | | | | | | |
% 37.19/5.78 | | | | | | | Case 1:
% 37.19/5.78 | | | | | | | |
% 37.19/5.78 | | | | | | | | (174) $lesseq(all_102_3, -1)
% 37.19/5.78 | | | | | | | |
% 37.19/5.78 | | | | | | | | COMBINE_INEQS: (140), (174) imply:
% 37.19/5.78 | | | | | | | | (175) $false
% 37.19/5.78 | | | | | | | |
% 37.19/5.78 | | | | | | | | CLOSE: (175) is inconsistent.
% 37.19/5.78 | | | | | | | |
% 37.19/5.78 | | | | | | | Case 2:
% 37.19/5.78 | | | | | | | |
% 37.19/5.78 | | | | | | | | (176) ~ ($lesseq(1, $difference(all_102_11, all_102_3))) |
% 37.19/5.78 | | | | | | | | ? [v0: any] : ? [v1: int] : ((v1 = 0 & v0 = 0 &
% 37.19/5.78 | | | | | | | | partial_solution1(n1, all_102_9) = 0 &
% 37.19/5.78 | | | | | | | | eq_prefix1(int, all_102_8, all_102_8, 0) = 0) | ( ~
% 37.19/5.78 | | | | | | | | (v1 = 0) & eq_prefix1(int, all_102_8, v0, n1) = v1
% 37.19/5.78 | | | | | | | | & get(all_102_18, int, all_102_7, all_102_2) = v0 &
% 37.19/5.78 | | | | | | | | uni(v0)))
% 37.19/5.78 | | | | | | | |
% 37.19/5.78 | | | | | | | | BETA: splitting (173) gives:
% 37.19/5.78 | | | | | | | |
% 37.19/5.78 | | | | | | | | Case 1:
% 37.19/5.78 | | | | | | | | |
% 37.19/5.78 | | | | | | | | | (177) $lesseq(all_102_11, all_102_3)
% 37.19/5.78 | | | | | | | | |
% 37.19/5.78 | | | | | | | | | COMBINE_INEQS: (141), (177) imply:
% 37.19/5.78 | | | | | | | | | (178) $false
% 37.19/5.78 | | | | | | | | |
% 37.19/5.78 | | | | | | | | | CLOSE: (178) is inconsistent.
% 37.19/5.78 | | | | | | | | |
% 37.19/5.78 | | | | | | | | Case 2:
% 37.19/5.78 | | | | | | | | |
% 37.19/5.78 | | | | | | | | | (179) ? [v0: any] : ? [v1: int] : ((v1 = 0 & v0 = 0 &
% 37.19/5.78 | | | | | | | | | partial_solution1(n1, all_102_6) = 0 &
% 37.19/5.78 | | | | | | | | | eq_prefix1(int, all_102_8, all_102_4, 0) = 0) | (
% 37.19/5.78 | | | | | | | | | ~ (v1 = 0) & eq_prefix1(int, all_102_4, v0, n1) =
% 37.19/5.78 | | | | | | | | | v1 & get(all_102_18, int, all_102_7, all_102_2) =
% 37.19/5.78 | | | | | | | | | v0 & uni(v0)))
% 37.19/5.78 | | | | | | | | |
% 37.19/5.78 | | | | | | | | | DELTA: instantiating (179) with fresh symbols all_579_0,
% 37.19/5.78 | | | | | | | | | all_579_1 gives:
% 37.19/5.78 | | | | | | | | | (180) (all_579_0 = 0 & all_579_1 = 0 &
% 37.19/5.78 | | | | | | | | | partial_solution1(n1, all_102_6) = 0 &
% 37.19/5.78 | | | | | | | | | eq_prefix1(int, all_102_8, all_102_4, 0) = 0) | ( ~
% 37.19/5.78 | | | | | | | | | (all_579_0 = 0) & eq_prefix1(int, all_102_4,
% 37.19/5.78 | | | | | | | | | all_579_1, n1) = all_579_0 & get(all_102_18, int,
% 37.19/5.78 | | | | | | | | | all_102_7, all_102_2) = all_579_1 &
% 37.19/5.78 | | | | | | | | | uni(all_579_1))
% 37.19/5.78 | | | | | | | | |
% 37.19/5.79 | | | | | | | | | BETA: splitting (180) gives:
% 37.19/5.79 | | | | | | | | |
% 37.19/5.79 | | | | | | | | | Case 1:
% 37.19/5.79 | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | (181) all_579_0 = 0 & all_579_1 = 0 &
% 37.19/5.79 | | | | | | | | | | partial_solution1(n1, all_102_6) = 0 &
% 37.19/5.79 | | | | | | | | | | eq_prefix1(int, all_102_8, all_102_4, 0) = 0
% 37.19/5.79 | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | ALPHA: (181) implies:
% 37.19/5.79 | | | | | | | | | | (182) partial_solution1(n1, all_102_6) = 0
% 37.19/5.79 | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | GROUND_INST: instantiating (23) with all_102_5, 0, all_102_6,
% 37.19/5.79 | | | | | | | | | | n1, simplifying with (41), (182) gives:
% 37.19/5.79 | | | | | | | | | | (183) all_102_5 = 0
% 37.19/5.79 | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | REDUCE: (139), (183) imply:
% 37.19/5.79 | | | | | | | | | | (184) $false
% 37.19/5.79 | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | CLOSE: (184) is inconsistent.
% 37.19/5.79 | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | Case 2:
% 37.19/5.79 | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | (185) ~ (all_579_0 = 0) & eq_prefix1(int, all_102_4,
% 37.19/5.79 | | | | | | | | | | all_579_1, n1) = all_579_0 & get(all_102_18, int,
% 37.19/5.79 | | | | | | | | | | all_102_7, all_102_2) = all_579_1 &
% 37.19/5.79 | | | | | | | | | | uni(all_579_1)
% 37.19/5.79 | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | ALPHA: (185) implies:
% 37.19/5.79 | | | | | | | | | | (186) ~ (all_579_0 = 0)
% 37.19/5.79 | | | | | | | | | | (187) get(all_102_18, int, all_102_7, all_102_2) =
% 37.19/5.79 | | | | | | | | | | all_579_1
% 37.19/5.79 | | | | | | | | | | (188) eq_prefix1(int, all_102_4, all_579_1, n1) =
% 37.19/5.79 | | | | | | | | | | all_579_0
% 37.19/5.79 | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | REDUCE: (47), (187) imply:
% 37.19/5.79 | | | | | | | | | | (189) get(all_87_0, int, all_102_7, all_102_2) =
% 37.19/5.79 | | | | | | | | | | all_579_1
% 37.19/5.79 | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | BETA: splitting (176) gives:
% 37.19/5.79 | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | Case 1:
% 37.19/5.79 | | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | | (190) $lesseq(all_102_11, all_102_3)
% 37.19/5.79 | | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | | COMBINE_INEQS: (141), (190) imply:
% 37.19/5.79 | | | | | | | | | | | (191) $false
% 37.19/5.79 | | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | | CLOSE: (191) is inconsistent.
% 37.19/5.79 | | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | Case 2:
% 37.19/5.79 | | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | | GROUND_INST: instantiating (25) with all_102_1, all_579_1,
% 37.19/5.79 | | | | | | | | | | | all_102_2, all_102_7, int, all_87_0, simplifying
% 37.19/5.79 | | | | | | | | | | | with (145), (189) gives:
% 37.19/5.79 | | | | | | | | | | | (192) all_579_1 = all_102_1
% 37.19/5.79 | | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | | REDUCE: (188), (192) imply:
% 37.19/5.79 | | | | | | | | | | | (193) eq_prefix1(int, all_102_4, all_102_1, n1) =
% 37.19/5.79 | | | | | | | | | | | all_579_0
% 37.19/5.79 | | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | | GROUND_INST: instantiating (26) with 0, all_579_0, n1,
% 37.19/5.79 | | | | | | | | | | | all_102_1, all_102_4, int, simplifying with (144),
% 37.19/5.79 | | | | | | | | | | | (193) gives:
% 37.19/5.79 | | | | | | | | | | | (194) all_579_0 = 0
% 37.19/5.79 | | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | | REDUCE: (186), (194) imply:
% 37.19/5.79 | | | | | | | | | | | (195) $false
% 37.19/5.79 | | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | | CLOSE: (195) is inconsistent.
% 37.19/5.79 | | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | | End of split
% 37.19/5.79 | | | | | | | | | |
% 37.19/5.79 | | | | | | | | | End of split
% 37.19/5.79 | | | | | | | | |
% 37.19/5.79 | | | | | | | | End of split
% 37.19/5.79 | | | | | | | |
% 37.19/5.79 | | | | | | | End of split
% 37.19/5.79 | | | | | | |
% 37.19/5.79 | | | | | | End of split
% 37.19/5.79 | | | | | |
% 37.19/5.79 | | | | | End of split
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | Case 2:
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | | (196) all_184_2 = 0
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | | COMBINE_EQS: (137), (196) imply:
% 37.19/5.79 | | | | | (197) all_130_1 = 0
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | | SIMP: (197) implies:
% 37.19/5.79 | | | | | (198) all_130_1 = 0
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | | REDUCE: (162), (198) imply:
% 37.19/5.79 | | | | | (199) $false
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | | CLOSE: (199) is inconsistent.
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | End of split
% 37.19/5.79 | | | |
% 37.19/5.79 | | | End of split
% 37.19/5.79 | | |
% 37.19/5.79 | | End of split
% 37.19/5.79 | |
% 37.19/5.79 | Case 2:
% 37.19/5.79 | |
% 37.19/5.79 | | (200) all_102_5 = 0 & ! [v0: int] : ! [v1: uni] : ( ~ ($lesseq(1,
% 37.19/5.79 | | $difference(all_102_11, v0))) | ~ ($lesseq(0, v0)) | ~
% 37.19/5.79 | | (t2tb1(v0) = v1) | ? [v2: uni] : ? [v3: int] : ( ~ (v3 = 0) &
% 37.19/5.79 | | eq_prefix1(int, all_102_4, v2, n1) = v3 & get(all_102_18, int,
% 37.19/5.79 | | all_102_7, v1) = v2 & uni(v2)))
% 37.19/5.79 | |
% 37.19/5.79 | | ALPHA: (200) implies:
% 37.19/5.79 | | (201) all_102_5 = 0
% 37.19/5.79 | | (202) ! [v0: int] : ! [v1: uni] : ( ~ ($lesseq(1,
% 37.19/5.79 | | $difference(all_102_11, v0))) | ~ ($lesseq(0, v0)) | ~
% 37.19/5.79 | | (t2tb1(v0) = v1) | ? [v2: uni] : ? [v3: int] : ( ~ (v3 = 0) &
% 37.19/5.79 | | eq_prefix1(int, all_102_4, v2, n1) = v3 & get(all_102_18, int,
% 37.19/5.79 | | all_102_7, v1) = v2 & uni(v2)))
% 37.19/5.79 | |
% 37.19/5.79 | | REDUCE: (41), (201) imply:
% 37.19/5.79 | | (203) partial_solution1(n1, all_102_6) = 0
% 37.19/5.79 | |
% 37.19/5.79 | | BETA: splitting (70) gives:
% 37.19/5.79 | |
% 37.19/5.79 | | Case 1:
% 37.19/5.79 | | |
% 37.19/5.79 | | | (204) all_143_0 = 0 & $lesseq(1, $difference(all_102_11, all_143_3)) &
% 37.19/5.79 | | | $lesseq(0, all_143_3) & eq_prefix1(int, all_102_4, all_143_1, n1)
% 37.19/5.79 | | | = 0 & get(all_102_18, int, all_102_7, all_143_2) = all_143_1 &
% 37.19/5.79 | | | t2tb1(all_143_3) = all_143_2 & uni(all_143_1) & uni(all_143_2)
% 37.19/5.79 | | |
% 37.19/5.79 | | | ALPHA: (204) implies:
% 37.19/5.79 | | | (205) $lesseq(0, all_143_3)
% 37.19/5.79 | | | (206) $lesseq(1, $difference(all_102_11, all_143_3))
% 37.19/5.79 | | | (207) t2tb1(all_143_3) = all_143_2
% 37.19/5.79 | | | (208) get(all_102_18, int, all_102_7, all_143_2) = all_143_1
% 37.19/5.79 | | | (209) eq_prefix1(int, all_102_4, all_143_1, n1) = 0
% 37.19/5.79 | | |
% 37.19/5.79 | | | REDUCE: (47), (208) imply:
% 37.19/5.79 | | | (210) get(all_87_0, int, all_102_7, all_143_2) = all_143_1
% 37.19/5.79 | | |
% 37.19/5.79 | | | GROUND_INST: instantiating (202) with all_143_3, all_143_2, simplifying
% 37.19/5.79 | | | with (207) gives:
% 37.19/5.79 | | | (211) ~ ($lesseq(1, $difference(all_102_11, all_143_3))) | ~
% 37.19/5.79 | | | ($lesseq(0, all_143_3)) | ? [v0: uni] : ? [v1: int] : ( ~ (v1 =
% 37.19/5.79 | | | 0) & eq_prefix1(int, all_102_4, v0, n1) = v1 &
% 37.19/5.79 | | | get(all_102_18, int, all_102_7, all_143_2) = v0 & uni(v0))
% 37.19/5.79 | | |
% 37.19/5.79 | | | BETA: splitting (211) gives:
% 37.19/5.79 | | |
% 37.19/5.79 | | | Case 1:
% 37.19/5.79 | | | |
% 37.19/5.79 | | | | (212) $lesseq(all_143_3, -1)
% 37.19/5.79 | | | |
% 37.19/5.79 | | | | COMBINE_INEQS: (205), (212) imply:
% 37.19/5.79 | | | | (213) $false
% 37.19/5.79 | | | |
% 37.19/5.79 | | | | CLOSE: (213) is inconsistent.
% 37.19/5.79 | | | |
% 37.19/5.79 | | | Case 2:
% 37.19/5.79 | | | |
% 37.19/5.79 | | | | (214) ~ ($lesseq(1, $difference(all_102_11, all_143_3))) | ? [v0:
% 37.19/5.79 | | | | uni] : ? [v1: int] : ( ~ (v1 = 0) & eq_prefix1(int,
% 37.19/5.79 | | | | all_102_4, v0, n1) = v1 & get(all_102_18, int, all_102_7,
% 37.19/5.79 | | | | all_143_2) = v0 & uni(v0))
% 37.19/5.79 | | | |
% 37.19/5.79 | | | | BETA: splitting (214) gives:
% 37.19/5.79 | | | |
% 37.19/5.79 | | | | Case 1:
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | | (215) $lesseq(all_102_11, all_143_3)
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | | COMBINE_INEQS: (206), (215) imply:
% 37.19/5.79 | | | | | (216) $false
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | | CLOSE: (216) is inconsistent.
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | Case 2:
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | | (217) ? [v0: uni] : ? [v1: int] : ( ~ (v1 = 0) & eq_prefix1(int,
% 37.19/5.79 | | | | | all_102_4, v0, n1) = v1 & get(all_102_18, int, all_102_7,
% 37.19/5.79 | | | | | all_143_2) = v0 & uni(v0))
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | | DELTA: instantiating (217) with fresh symbols all_376_0, all_376_1
% 37.19/5.79 | | | | | gives:
% 37.19/5.79 | | | | | (218) ~ (all_376_0 = 0) & eq_prefix1(int, all_102_4, all_376_1,
% 37.19/5.79 | | | | | n1) = all_376_0 & get(all_102_18, int, all_102_7,
% 37.19/5.79 | | | | | all_143_2) = all_376_1 & uni(all_376_1)
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | | ALPHA: (218) implies:
% 37.19/5.79 | | | | | (219) ~ (all_376_0 = 0)
% 37.19/5.79 | | | | | (220) get(all_102_18, int, all_102_7, all_143_2) = all_376_1
% 37.19/5.79 | | | | | (221) eq_prefix1(int, all_102_4, all_376_1, n1) = all_376_0
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | | REDUCE: (47), (220) imply:
% 37.19/5.79 | | | | | (222) get(all_87_0, int, all_102_7, all_143_2) = all_376_1
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | | GROUND_INST: instantiating (25) with all_143_1, all_376_1, all_143_2,
% 37.19/5.79 | | | | | all_102_7, int, all_87_0, simplifying with (210), (222)
% 37.19/5.79 | | | | | gives:
% 37.19/5.79 | | | | | (223) all_376_1 = all_143_1
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | | REDUCE: (221), (223) imply:
% 37.19/5.79 | | | | | (224) eq_prefix1(int, all_102_4, all_143_1, n1) = all_376_0
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | | GROUND_INST: instantiating (26) with 0, all_376_0, n1, all_143_1,
% 37.19/5.79 | | | | | all_102_4, int, simplifying with (209), (224) gives:
% 37.19/5.79 | | | | | (225) all_376_0 = 0
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | | REDUCE: (219), (225) imply:
% 37.19/5.79 | | | | | (226) $false
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | | CLOSE: (226) is inconsistent.
% 37.19/5.79 | | | | |
% 37.19/5.79 | | | | End of split
% 37.19/5.79 | | | |
% 37.19/5.79 | | | End of split
% 37.19/5.79 | | |
% 37.19/5.79 | | Case 2:
% 37.19/5.79 | | |
% 37.19/5.79 | | | (227) partial_solution1(n1, all_102_6) = all_143_3 & eq_prefix1(int,
% 37.19/5.79 | | | all_102_8, all_102_4, 0) = all_143_2 & ( ~ (all_143_2 = 0) | ~
% 37.19/5.79 | | | (all_143_3 = 0))
% 37.19/5.79 | | |
% 37.19/5.79 | | | ALPHA: (227) implies:
% 37.19/5.79 | | | (228) eq_prefix1(int, all_102_8, all_102_4, 0) = all_143_2
% 37.19/5.79 | | | (229) partial_solution1(n1, all_102_6) = all_143_3
% 37.19/5.79 | | | (230) ~ (all_143_2 = 0) | ~ (all_143_3 = 0)
% 37.19/5.79 | | |
% 37.19/5.80 | | | GROUND_INST: instantiating (26) with 0, all_143_2, 0, all_102_4,
% 37.19/5.80 | | | all_102_8, int, simplifying with (108), (228) gives:
% 37.19/5.80 | | | (231) all_143_2 = 0
% 37.19/5.80 | | |
% 37.19/5.80 | | | GROUND_INST: instantiating (23) with 0, all_143_3, all_102_6, n1,
% 37.19/5.80 | | | simplifying with (203), (229) gives:
% 37.19/5.80 | | | (232) all_143_3 = 0
% 37.19/5.80 | | |
% 37.19/5.80 | | | BETA: splitting (230) gives:
% 37.19/5.80 | | |
% 37.19/5.80 | | | Case 1:
% 37.19/5.80 | | | |
% 37.19/5.80 | | | | (233) ~ (all_143_2 = 0)
% 37.19/5.80 | | | |
% 37.19/5.80 | | | | REDUCE: (231), (233) imply:
% 37.19/5.80 | | | | (234) $false
% 37.19/5.80 | | | |
% 37.19/5.80 | | | | CLOSE: (234) is inconsistent.
% 37.19/5.80 | | | |
% 37.19/5.80 | | | Case 2:
% 37.19/5.80 | | | |
% 37.19/5.80 | | | | (235) ~ (all_143_3 = 0)
% 37.19/5.80 | | | |
% 37.19/5.80 | | | | REDUCE: (232), (235) imply:
% 37.19/5.80 | | | | (236) $false
% 37.19/5.80 | | | |
% 37.19/5.80 | | | | CLOSE: (236) is inconsistent.
% 37.19/5.80 | | | |
% 37.19/5.80 | | | End of split
% 37.19/5.80 | | |
% 37.19/5.80 | | End of split
% 37.19/5.80 | |
% 37.19/5.80 | End of split
% 37.19/5.80 |
% 37.19/5.80 End of proof
% 37.19/5.80 % SZS output end Proof for theBenchmark
% 37.19/5.80
% 37.19/5.80 5199ms
%------------------------------------------------------------------------------