TSTP Solution File: ARI678_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI678_1 : TPTP v8.1.2. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n018.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 : Wed Aug 30 17:48:47 EDT 2023
% Result : Theorem 4.36s 1.38s
% Output : Proof 6.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ARI678_1 : TPTP v8.1.2. Released v6.3.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 18:18:33 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.62 ________ _____
% 0.22/0.62 ___ __ \_________(_)________________________________
% 0.22/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.62
% 0.22/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.62 (2023-06-19)
% 0.22/0.62
% 0.22/0.62 (c) Philipp Rümmer, 2009-2023
% 0.22/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.62 Amanda Stjerna.
% 0.22/0.62 Free software under BSD-3-Clause.
% 0.22/0.62
% 0.22/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.62
% 0.22/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.64 Running up to 7 provers in parallel.
% 0.22/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.16/1.00 Prover 5: Preprocessing ...
% 2.16/1.00 Prover 1: Preprocessing ...
% 2.16/1.00 Prover 0: Preprocessing ...
% 2.16/1.00 Prover 3: Preprocessing ...
% 2.16/1.00 Prover 4: Preprocessing ...
% 2.16/1.00 Prover 6: Preprocessing ...
% 2.16/1.00 Prover 2: Preprocessing ...
% 2.16/1.06 Prover 0: Constructing countermodel ...
% 2.16/1.06 Prover 1: Constructing countermodel ...
% 2.16/1.06 Prover 4: Constructing countermodel ...
% 2.16/1.06 Prover 5: Constructing countermodel ...
% 2.16/1.06 Prover 2: Constructing countermodel ...
% 2.16/1.06 Prover 6: Constructing countermodel ...
% 2.16/1.06 Prover 3: Constructing countermodel ...
% 4.36/1.38 Prover 3: proved (730ms)
% 4.36/1.38
% 4.36/1.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.36/1.38
% 4.36/1.38 Prover 5: proved (729ms)
% 4.36/1.38
% 4.36/1.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.36/1.38
% 4.36/1.39 Prover 2: stopped
% 4.36/1.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.36/1.39 Prover 6: proved (736ms)
% 4.36/1.39
% 4.36/1.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.36/1.39
% 4.36/1.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.36/1.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.36/1.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.36/1.40 Prover 0: proved (751ms)
% 4.36/1.40
% 4.36/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.36/1.40
% 4.36/1.40 Prover 10: Preprocessing ...
% 4.36/1.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.36/1.40 Prover 7: Preprocessing ...
% 4.36/1.40 Prover 11: Preprocessing ...
% 4.36/1.40 Prover 8: Preprocessing ...
% 4.36/1.40 Prover 13: Preprocessing ...
% 4.36/1.41 Prover 7: Constructing countermodel ...
% 4.36/1.41 Prover 11: Constructing countermodel ...
% 4.36/1.41 Prover 13: Constructing countermodel ...
% 4.36/1.42 Prover 8: Constructing countermodel ...
% 4.36/1.43 Prover 10: Constructing countermodel ...
% 5.13/1.48 Prover 1: Found proof (size 178)
% 5.13/1.48 Prover 1: proved (838ms)
% 5.13/1.49 Prover 8: stopped
% 5.52/1.50 Prover 4: Found proof (size 178)
% 5.52/1.50 Prover 4: proved (858ms)
% 5.52/1.54 Prover 7: Found proof (size 178)
% 5.52/1.54 Prover 7: proved (160ms)
% 5.52/1.55 Prover 11: Found proof (size 178)
% 5.52/1.55 Prover 11: proved (156ms)
% 5.52/1.55 Prover 13: Found proof (size 178)
% 5.52/1.55 Prover 13: proved (148ms)
% 5.52/1.55 Prover 10: Found proof (size 178)
% 5.52/1.55 Prover 10: proved (159ms)
% 5.52/1.55
% 5.52/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.52/1.55
% 5.91/1.56 % SZS output start Proof for theBenchmark
% 5.91/1.57 Assumptions after simplification:
% 5.91/1.57 ---------------------------------
% 5.91/1.57
% 5.91/1.57 (conj)
% 5.91/1.57 ? [v0: int] : ? [v1: int] : ($lesseq(v1, 7) & $product(v0, a) = v1 &
% 5.91/1.57 $product(a, a) = v0)
% 5.91/1.57
% 5.91/1.57 (conj_001)
% 5.91/1.57 $lesseq(0, a)
% 5.91/1.57
% 5.91/1.57 (conj_002)
% 5.91/1.57 ? [v0: int] : ? [v1: int] : ? [v2: int] : ($lesseq(2, v2) & $product(v1, a)
% 5.91/1.57 = v2 & $product(v0, a) = v1 & $product(a, a) = v0)
% 5.91/1.57
% 5.91/1.57 Those formulas are unsatisfiable:
% 5.91/1.57 ---------------------------------
% 5.91/1.57
% 5.91/1.57 Begin of proof
% 5.91/1.58 |
% 5.91/1.58 | DELTA: instantiating (conj) with fresh symbols all_3_0, all_3_1 gives:
% 5.91/1.58 | (1) $lesseq(all_3_0, 7) & $product(all_3_1, a) = all_3_0 & $product(a, a) =
% 5.91/1.58 | all_3_1
% 5.91/1.58 |
% 5.91/1.58 | ALPHA: (1) implies:
% 5.91/1.58 | (2) $lesseq(all_3_0, 7)
% 5.91/1.58 | (3) $product(a, a) = all_3_1
% 5.91/1.58 | (4) $product(all_3_1, a) = all_3_0
% 5.91/1.58 |
% 5.91/1.58 | DELTA: instantiating (conj_002) with fresh symbols all_6_0, all_6_1, all_6_2
% 5.91/1.58 | gives:
% 5.91/1.58 | (5) $lesseq(2, all_6_0) & $product(all_6_1, a) = all_6_0 &
% 5.91/1.58 | $product(all_6_2, a) = all_6_1 & $product(a, a) = all_6_2
% 5.91/1.58 |
% 5.91/1.58 | ALPHA: (5) implies:
% 5.91/1.58 | (6) $lesseq(2, all_6_0)
% 5.91/1.59 | (7) $product(a, a) = all_6_2
% 5.91/1.59 | (8) $product(all_6_2, a) = all_6_1
% 5.91/1.59 | (9) $product(all_6_1, a) = all_6_0
% 5.91/1.59 |
% 5.91/1.59 | THEORY_AXIOM GroebnerMultiplication:
% 5.91/1.59 | (10) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~
% 5.91/1.59 | ($product(v0, v0) = v2) | ~ ($product(v0, v0) = v1))
% 5.91/1.59 |
% 5.91/1.59 | GROUND_INST: instantiating (10) with a, all_3_1, all_6_2, simplifying with
% 5.91/1.59 | (3), (7) gives:
% 5.91/1.59 | (11) all_6_2 = all_3_1
% 5.91/1.59 |
% 5.91/1.59 | THEORY_AXIOM GroebnerMultiplication:
% 5.91/1.59 | (12) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 5.91/1.59 | int] : (v4 = v2 | ~ ($product(v3, v0) = v4) | ~ ($product(v1, v0)
% 5.91/1.59 | = v2) | ~ ($product(v0, v0) = v3) | ~ ($product(v0, v0) = v1))
% 5.91/1.59 |
% 5.91/1.59 | GROUND_INST: instantiating (12) with a, all_3_1, all_3_0, all_6_2, all_6_1,
% 5.91/1.59 | simplifying with (3), (4), (7), (8) gives:
% 5.91/1.59 | (13) all_6_1 = all_3_0
% 5.91/1.59 |
% 5.91/1.59 | REDUCE: (9), (13) imply:
% 5.91/1.59 | (14) $product(all_3_0, a) = all_6_0
% 5.91/1.59 |
% 5.91/1.59 | THEORY_AXIOM GroebnerMultiplication:
% 5.91/1.59 | (15) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(2, v2)) | ~
% 5.91/1.59 | ($lesseq(v1, -1)) | ~ ($lesseq(0, v0)) | ~ ($product(v1, v0) =
% 5.91/1.59 | v2))
% 5.91/1.59 |
% 5.91/1.59 | GROUND_INST: instantiating (15) with a, all_3_0, all_6_0, simplifying with
% 5.91/1.59 | (14) gives:
% 5.91/1.59 | (16) ~ ($lesseq(2, all_6_0)) | ~ ($lesseq(all_3_0, -1)) | ~ ($lesseq(0,
% 5.91/1.59 | a))
% 5.91/1.59 |
% 5.91/1.59 | BETA: splitting (16) gives:
% 5.91/1.59 |
% 5.91/1.59 | Case 1:
% 5.91/1.59 | |
% 5.91/1.59 | | (17) $lesseq(all_6_0, 1)
% 5.91/1.59 | |
% 5.91/1.59 | | COMBINE_INEQS: (6), (17) imply:
% 5.91/1.59 | | (18) $false
% 5.91/1.60 | |
% 5.91/1.60 | | CLOSE: (18) is inconsistent.
% 5.91/1.60 | |
% 5.91/1.60 | Case 2:
% 5.91/1.60 | |
% 5.91/1.60 | | (19) ~ ($lesseq(all_3_0, -1)) | ~ ($lesseq(0, a))
% 5.91/1.60 | |
% 5.91/1.60 | | BETA: splitting (19) gives:
% 5.91/1.60 | |
% 5.91/1.60 | | Case 1:
% 5.91/1.60 | | |
% 5.91/1.60 | | | (20) $lesseq(a, -1)
% 5.91/1.60 | | |
% 5.91/1.60 | | | COMBINE_INEQS: (20), (conj_001) imply:
% 5.91/1.60 | | | (21) $false
% 5.91/1.60 | | |
% 5.91/1.60 | | | CLOSE: (21) is inconsistent.
% 5.91/1.60 | | |
% 5.91/1.60 | | Case 2:
% 5.91/1.60 | | |
% 5.91/1.60 | | | (22) $lesseq(0, all_3_0)
% 5.91/1.60 | | |
% 5.91/1.60 | | | THEORY_AXIOM GroebnerMultiplication:
% 5.91/1.60 | | | (23) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1,
% 5.91/1.60 | | | $difference(v2, $product(7, v0)))) | ~ ($lesseq(v1, 7)) |
% 5.91/1.60 | | | ~ ($lesseq(0, v0)) | ~ ($product(v1, v0) = v2))
% 5.91/1.60 | | |
% 5.91/1.60 | | | GROUND_INST: instantiating (23) with a, all_3_0, all_6_0, simplifying with
% 5.91/1.60 | | | (14) gives:
% 5.91/1.60 | | | (24) ~ ($lesseq(1, $difference(all_6_0, $product(7, a)))) | ~
% 5.91/1.60 | | | ($lesseq(all_3_0, 7)) | ~ ($lesseq(0, a))
% 5.91/1.60 | | |
% 5.91/1.60 | | | BETA: splitting (24) gives:
% 5.91/1.60 | | |
% 5.91/1.60 | | | Case 1:
% 5.91/1.60 | | | |
% 5.91/1.60 | | | | (25) $lesseq(8, all_3_0)
% 5.91/1.60 | | | |
% 5.91/1.60 | | | | COMBINE_INEQS: (2), (25) imply:
% 5.91/1.60 | | | | (26) $false
% 5.91/1.60 | | | |
% 5.91/1.60 | | | | CLOSE: (26) is inconsistent.
% 5.91/1.60 | | | |
% 5.91/1.60 | | | Case 2:
% 5.91/1.60 | | | |
% 5.91/1.60 | | | | (27) ~ ($lesseq(1, $difference(all_6_0, $product(7, a)))) | ~
% 5.91/1.60 | | | | ($lesseq(0, a))
% 5.91/1.60 | | | |
% 5.91/1.60 | | | | BETA: splitting (27) gives:
% 5.91/1.60 | | | |
% 5.91/1.60 | | | | Case 1:
% 5.91/1.60 | | | | |
% 5.91/1.60 | | | | | (28) $lesseq(a, -1)
% 5.91/1.60 | | | | |
% 5.91/1.60 | | | | | COMBINE_INEQS: (28), (conj_001) imply:
% 5.91/1.60 | | | | | (29) $false
% 5.91/1.60 | | | | |
% 5.91/1.60 | | | | | CLOSE: (29) is inconsistent.
% 5.91/1.60 | | | | |
% 5.91/1.60 | | | | Case 2:
% 5.91/1.60 | | | | |
% 5.91/1.60 | | | | | (30) $lesseq(all_6_0, $product(7, a))
% 5.91/1.60 | | | | |
% 5.91/1.60 | | | | | THEORY_AXIOM GroebnerMultiplication:
% 5.91/1.60 | | | | | (31) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | ~
% 5.91/1.60 | | | | | ($lesseq(0, v0)) | ~ ($product(v0, v0) = v1))
% 5.91/1.60 | | | | |
% 5.91/1.60 | | | | | GROUND_INST: instantiating (31) with a, all_3_1, simplifying with (3)
% 5.91/1.60 | | | | | gives:
% 5.91/1.60 | | | | | (32) ~ ($lesseq(all_3_1, -1)) | ~ ($lesseq(0, a))
% 5.91/1.60 | | | | |
% 5.91/1.60 | | | | | BETA: splitting (32) gives:
% 5.91/1.60 | | | | |
% 5.91/1.60 | | | | | Case 1:
% 5.91/1.60 | | | | | |
% 5.91/1.60 | | | | | | (33) $lesseq(a, -1)
% 5.91/1.60 | | | | | |
% 5.91/1.60 | | | | | | COMBINE_INEQS: (33), (conj_001) imply:
% 5.91/1.60 | | | | | | (34) $false
% 5.91/1.60 | | | | | |
% 5.91/1.60 | | | | | | CLOSE: (34) is inconsistent.
% 5.91/1.60 | | | | | |
% 5.91/1.60 | | | | | Case 2:
% 5.91/1.60 | | | | | |
% 5.91/1.60 | | | | | | (35) $lesseq(0, all_3_1)
% 5.91/1.60 | | | | | |
% 5.91/1.60 | | | | | | COMBINE_INEQS: (6), (30) imply:
% 5.91/1.60 | | | | | | (36) $lesseq(1, a)
% 5.91/1.60 | | | | | |
% 5.91/1.60 | | | | | | SIMP: (36) implies:
% 5.91/1.60 | | | | | | (37) $lesseq(1, a)
% 5.91/1.60 | | | | | |
% 5.91/1.60 | | | | | | THEORY_AXIOM GroebnerMultiplication:
% 5.91/1.61 | | | | | | (38) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, 0) | ~
% 5.91/1.61 | | | | | | ($lesseq(1, v0)) | ~ ($product(v0, v0) = v1))
% 5.91/1.61 | | | | | |
% 5.91/1.61 | | | | | | GROUND_INST: instantiating (38) with a, all_3_1, simplifying with
% 5.91/1.61 | | | | | | (3) gives:
% 5.91/1.61 | | | | | | (39) ~ ($lesseq(all_3_1, 0) | ~ ($lesseq(1, a))
% 5.91/1.61 | | | | | |
% 5.91/1.61 | | | | | | BETA: splitting (39) gives:
% 5.91/1.61 | | | | | |
% 5.91/1.61 | | | | | | Case 1:
% 5.91/1.61 | | | | | | |
% 5.91/1.61 | | | | | | | (40) $lesseq(a, 0)
% 5.91/1.61 | | | | | | |
% 5.91/1.61 | | | | | | | COMBINE_INEQS: (37), (40) imply:
% 5.91/1.61 | | | | | | | (41) $false
% 5.91/1.61 | | | | | | |
% 5.91/1.61 | | | | | | | CLOSE: (41) is inconsistent.
% 5.91/1.61 | | | | | | |
% 5.91/1.61 | | | | | | Case 2:
% 5.91/1.61 | | | | | | |
% 5.91/1.61 | | | | | | | (42) $lesseq(1, all_3_1)
% 5.91/1.61 | | | | | | |
% 5.91/1.61 | | | | | | | THEORY_AXIOM GroebnerMultiplication:
% 5.91/1.61 | | | | | | | (43) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~
% 5.91/1.61 | | | | | | | ($lesseq(v2, 7)) | ~ ($lesseq(0, v2)) | ~ ($lesseq(5,
% 5.91/1.61 | | | | | | | v1)) | ~ ($lesseq(1, v0)) | ~ ($product(v1, v0) =
% 5.91/1.61 | | | | | | | v2) | ~ ($product(v0, v0) = v1))
% 5.91/1.61 | | | | | | |
% 5.91/1.61 | | | | | | | GROUND_INST: instantiating (43) with a, all_3_1, all_3_0,
% 5.91/1.61 | | | | | | | simplifying with (3), (4) gives:
% 5.91/1.61 | | | | | | | (44) ~ ($lesseq(all_3_0, 7)) | ~ ($lesseq(0, all_3_0)) | ~
% 5.91/1.61 | | | | | | | ($lesseq(5, all_3_1)) | ~ ($lesseq(1, a))
% 5.91/1.61 | | | | | | |
% 5.91/1.61 | | | | | | | BETA: splitting (44) gives:
% 5.91/1.61 | | | | | | |
% 5.91/1.61 | | | | | | | Case 1:
% 5.91/1.61 | | | | | | | |
% 5.91/1.61 | | | | | | | | (45) ~ ($lesseq(all_3_0, 7)) | ~ ($lesseq(0, all_3_0))
% 5.91/1.61 | | | | | | | |
% 5.91/1.61 | | | | | | | | BETA: splitting (45) gives:
% 5.91/1.61 | | | | | | | |
% 5.91/1.61 | | | | | | | | Case 1:
% 5.91/1.61 | | | | | | | | |
% 5.91/1.61 | | | | | | | | | (46) $lesseq(8, all_3_0)
% 5.91/1.61 | | | | | | | | |
% 5.91/1.61 | | | | | | | | | COMBINE_INEQS: (2), (46) imply:
% 5.91/1.61 | | | | | | | | | (47) $false
% 5.91/1.61 | | | | | | | | |
% 5.91/1.61 | | | | | | | | | CLOSE: (47) is inconsistent.
% 5.91/1.61 | | | | | | | | |
% 5.91/1.61 | | | | | | | | Case 2:
% 5.91/1.61 | | | | | | | | |
% 5.91/1.61 | | | | | | | | | (48) $lesseq(all_3_0, -1)
% 5.91/1.61 | | | | | | | | |
% 5.91/1.61 | | | | | | | | | COMBINE_INEQS: (22), (48) imply:
% 5.91/1.61 | | | | | | | | | (49) $false
% 5.91/1.61 | | | | | | | | |
% 5.91/1.61 | | | | | | | | | CLOSE: (49) is inconsistent.
% 5.91/1.61 | | | | | | | | |
% 5.91/1.61 | | | | | | | | End of split
% 5.91/1.61 | | | | | | | |
% 5.91/1.61 | | | | | | | Case 2:
% 5.91/1.61 | | | | | | | |
% 5.91/1.61 | | | | | | | | (50) ~ ($lesseq(5, all_3_1)) | ~ ($lesseq(1, a))
% 5.91/1.61 | | | | | | | |
% 5.91/1.61 | | | | | | | | BETA: splitting (50) gives:
% 5.91/1.61 | | | | | | | |
% 5.91/1.61 | | | | | | | | Case 1:
% 5.91/1.61 | | | | | | | | |
% 5.91/1.61 | | | | | | | | | (51) $lesseq(a, 0)
% 5.91/1.61 | | | | | | | | |
% 5.91/1.61 | | | | | | | | | COMBINE_INEQS: (37), (51) imply:
% 5.91/1.61 | | | | | | | | | (52) $false
% 5.91/1.61 | | | | | | | | |
% 5.91/1.61 | | | | | | | | | CLOSE: (52) is inconsistent.
% 5.91/1.61 | | | | | | | | |
% 5.91/1.61 | | | | | | | | Case 2:
% 5.91/1.61 | | | | | | | | |
% 5.91/1.61 | | | | | | | | | (53) $lesseq(all_3_1, 4)
% 5.91/1.61 | | | | | | | | |
% 5.91/1.61 | | | | | | | | | THEORY_AXIOM GroebnerMultiplication:
% 5.91/1.61 | | | | | | | | | (54) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~
% 5.91/1.61 | | | | | | | | | ($lesseq(1, $difference(v1, v2))) | ~ ($lesseq(0,
% 5.91/1.61 | | | | | | | | | v1)) | ~ ($lesseq(1, v0)) | ~ ($product(v1,
% 5.91/1.61 | | | | | | | | | v0) = v2))
% 5.91/1.61 | | | | | | | | |
% 5.91/1.61 | | | | | | | | | GROUND_INST: instantiating (54) with a, all_3_0, all_6_0,
% 5.91/1.61 | | | | | | | | | simplifying with (14) gives:
% 5.91/1.61 | | | | | | | | | (55) ~ ($lesseq(1, $difference(all_3_0, all_6_0))) | ~
% 5.91/1.61 | | | | | | | | | ($lesseq(0, all_3_0)) | ~ ($lesseq(1, a))
% 5.91/1.61 | | | | | | | | |
% 5.91/1.61 | | | | | | | | | BETA: splitting (55) gives:
% 5.91/1.61 | | | | | | | | |
% 5.91/1.61 | | | | | | | | | Case 1:
% 5.91/1.61 | | | | | | | | | |
% 5.91/1.61 | | | | | | | | | | (56) $lesseq(all_3_0, -1)
% 5.91/1.61 | | | | | | | | | |
% 5.91/1.61 | | | | | | | | | | COMBINE_INEQS: (22), (56) imply:
% 5.91/1.61 | | | | | | | | | | (57) $false
% 5.91/1.61 | | | | | | | | | |
% 5.91/1.61 | | | | | | | | | | CLOSE: (57) is inconsistent.
% 5.91/1.61 | | | | | | | | | |
% 5.91/1.61 | | | | | | | | | Case 2:
% 5.91/1.61 | | | | | | | | | |
% 5.91/1.61 | | | | | | | | | | (58) ~ ($lesseq(1, $difference(all_3_0, all_6_0))) | ~
% 5.91/1.61 | | | | | | | | | | ($lesseq(1, a))
% 5.91/1.61 | | | | | | | | | |
% 5.91/1.61 | | | | | | | | | | BETA: splitting (58) gives:
% 5.91/1.61 | | | | | | | | | |
% 5.91/1.61 | | | | | | | | | | Case 1:
% 5.91/1.61 | | | | | | | | | | |
% 5.91/1.61 | | | | | | | | | | | (59) $lesseq(a, 0)
% 5.91/1.61 | | | | | | | | | | |
% 5.91/1.61 | | | | | | | | | | | COMBINE_INEQS: (37), (59) imply:
% 5.91/1.61 | | | | | | | | | | | (60) $false
% 5.91/1.61 | | | | | | | | | | |
% 5.91/1.61 | | | | | | | | | | | CLOSE: (60) is inconsistent.
% 5.91/1.61 | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | Case 2:
% 5.91/1.62 | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | (61) $lesseq(all_3_0, all_6_0)
% 5.91/1.62 | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | GROUND_INST: instantiating (54) with a, all_3_1, all_3_0,
% 5.91/1.62 | | | | | | | | | | | simplifying with (4) gives:
% 5.91/1.62 | | | | | | | | | | | (62) ~ ($lesseq(1, $difference(all_3_1, all_3_0))) |
% 5.91/1.62 | | | | | | | | | | | ~ ($lesseq(0, all_3_1)) | ~ ($lesseq(1, a))
% 5.91/1.62 | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | BETA: splitting (62) gives:
% 5.91/1.62 | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | Case 1:
% 5.91/1.62 | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | (63) $lesseq(all_3_1, -1)
% 5.91/1.62 | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | COMBINE_INEQS: (35), (63) imply:
% 5.91/1.62 | | | | | | | | | | | | (64) $false
% 5.91/1.62 | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | CLOSE: (64) is inconsistent.
% 5.91/1.62 | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | Case 2:
% 5.91/1.62 | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | (65) ~ ($lesseq(1, $difference(all_3_1, all_3_0))) |
% 5.91/1.62 | | | | | | | | | | | | ~ ($lesseq(1, a))
% 5.91/1.62 | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | BETA: splitting (65) gives:
% 5.91/1.62 | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | Case 1:
% 5.91/1.62 | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | (66) $lesseq(a, 0)
% 5.91/1.62 | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | COMBINE_INEQS: (37), (66) imply:
% 5.91/1.62 | | | | | | | | | | | | | (67) $false
% 5.91/1.62 | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | CLOSE: (67) is inconsistent.
% 5.91/1.62 | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | Case 2:
% 5.91/1.62 | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | (68) $lesseq(all_3_1, all_3_0)
% 5.91/1.62 | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication:
% 5.91/1.62 | | | | | | | | | | | | | (69) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(2,
% 5.91/1.62 | | | | | | | | | | | | | $difference($product(2, v0), v1))) | ~
% 5.91/1.62 | | | | | | | | | | | | | ($lesseq(1, v0)) | ~ ($product(v0, v0) = v1))
% 5.91/1.62 | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | GROUND_INST: instantiating (69) with a, all_3_1, simplifying
% 5.91/1.62 | | | | | | | | | | | | | with (3) gives:
% 5.91/1.62 | | | | | | | | | | | | | (70) ~ ($lesseq(2, $difference($product(2, a),
% 5.91/1.62 | | | | | | | | | | | | | all_3_1))) | ~ ($lesseq(1, a))
% 5.91/1.62 | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | BETA: splitting (70) gives:
% 5.91/1.62 | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | Case 1:
% 5.91/1.62 | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | (71) $lesseq(a, 0)
% 5.91/1.62 | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | COMBINE_INEQS: (37), (71) imply:
% 5.91/1.62 | | | | | | | | | | | | | | (72) $false
% 5.91/1.62 | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | CLOSE: (72) is inconsistent.
% 5.91/1.62 | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | Case 2:
% 5.91/1.62 | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | (73) $lesseq(-1, $difference(all_3_1, $product(2, a)))
% 5.91/1.62 | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | COMBINE_INEQS: (30), (61) imply:
% 5.91/1.62 | | | | | | | | | | | | | | (74) $lesseq(all_3_0, $product(7, a))
% 5.91/1.62 | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | COMBINE_INEQS: (68), (74) imply:
% 5.91/1.62 | | | | | | | | | | | | | | (75) $lesseq(all_3_1, $product(7, a))
% 5.91/1.62 | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | COMBINE_INEQS: (42), (68) imply:
% 5.91/1.62 | | | | | | | | | | | | | | (76) $lesseq(1, all_3_0)
% 5.91/1.62 | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | COMBINE_INEQS: (53), (73) imply:
% 5.91/1.62 | | | | | | | | | | | | | | (77) $lesseq(a, 2)
% 5.91/1.62 | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | SIMP: (77) implies:
% 5.91/1.62 | | | | | | | | | | | | | | (78) $lesseq(a, 2)
% 5.91/1.62 | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | COMBINE_INEQS: (42), (75) imply:
% 5.91/1.62 | | | | | | | | | | | | | | (79) $lesseq(1, a)
% 5.91/1.62 | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication:
% 5.91/1.62 | | | | | | | | | | | | | | (80) ! [v0: int] : ! [v1: int] : ! [v2: int] : !
% 5.91/1.62 | | | | | | | | | | | | | | [v3: int] : ( ~ ($lesseq(1, $sum($difference(v3,
% 5.91/1.62 | | | | | | | | | | | | | | $product(3, v2)), $product(2, v1)))) |
% 5.91/1.62 | | | | | | | | | | | | | | ~ ($lesseq(v1, v2)) | ~ ($lesseq(v0, 2)) | ~
% 5.91/1.62 | | | | | | | | | | | | | | ($product(v2, v0) = v3) | ~ ($product(v1, v0) =
% 5.91/1.62 | | | | | | | | | | | | | | v2))
% 5.91/1.62 | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | GROUND_INST: instantiating (80) with a, all_3_1, all_3_0,
% 5.91/1.62 | | | | | | | | | | | | | | all_6_0, simplifying with (4), (14) gives:
% 5.91/1.62 | | | | | | | | | | | | | | (81) ~ ($lesseq(1, $sum($difference(all_6_0,
% 5.91/1.62 | | | | | | | | | | | | | | $product(3, all_3_0)), $product(2,
% 5.91/1.62 | | | | | | | | | | | | | | all_3_1)))) | ~ ($lesseq(all_3_1,
% 5.91/1.62 | | | | | | | | | | | | | | all_3_0)) | ~ ($lesseq(a, 2))
% 5.91/1.62 | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 5.91/1.62 | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | Case 1:
% 5.91/1.62 | | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | | (82) $lesseq(1, $difference(all_3_1, all_3_0))
% 5.91/1.62 | | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | | COMBINE_INEQS: (68), (82) imply:
% 5.91/1.62 | | | | | | | | | | | | | | | (83) $false
% 5.91/1.62 | | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | | CLOSE: (83) is inconsistent.
% 5.91/1.62 | | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | Case 2:
% 5.91/1.62 | | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | | (84) ~ ($lesseq(1, $sum($difference(all_6_0,
% 5.91/1.62 | | | | | | | | | | | | | | | $product(3, all_3_0)), $product(2,
% 5.91/1.62 | | | | | | | | | | | | | | | all_3_1)))) | ~ ($lesseq(a, 2))
% 5.91/1.62 | | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 5.91/1.62 | | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | | Case 1:
% 5.91/1.62 | | | | | | | | | | | | | | | |
% 5.91/1.62 | | | | | | | | | | | | | | | | (85) $lesseq(3, a)
% 5.91/1.63 | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | COMBINE_INEQS: (78), (85) imply:
% 5.91/1.63 | | | | | | | | | | | | | | | | (86) $false
% 5.91/1.63 | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | CLOSE: (86) is inconsistent.
% 5.91/1.63 | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | Case 2:
% 5.91/1.63 | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | (87) $lesseq(0, $difference($difference($product(3,
% 5.91/1.63 | | | | | | | | | | | | | | | | all_3_0), all_6_0), $product(2, all_3_1)))
% 5.91/1.63 | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication:
% 5.91/1.63 | | | | | | | | | | | | | | | | (88) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~
% 5.91/1.63 | | | | | | | | | | | | | | | | ($lesseq(-1, $difference($difference(v2,
% 5.91/1.63 | | | | | | | | | | | | | | | | $product(2, v1)), v0))) | ~ ($lesseq(1,
% 5.91/1.63 | | | | | | | | | | | | | | | | v1)) | ~ ($lesseq(v0, 2)) | ~
% 5.91/1.63 | | | | | | | | | | | | | | | | ($product(v1, v0) = v2))
% 5.91/1.63 | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (88) with a, all_3_0, all_6_0,
% 5.91/1.63 | | | | | | | | | | | | | | | | simplifying with (14) gives:
% 5.91/1.63 | | | | | | | | | | | | | | | | (89) ~ ($lesseq(-1, $difference($difference(all_6_0,
% 5.91/1.63 | | | | | | | | | | | | | | | | $product(2, all_3_0)), a))) | ~
% 5.91/1.63 | | | | | | | | | | | | | | | | ($lesseq(1, all_3_0)) | ~ ($lesseq(a, 2))
% 5.91/1.63 | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 5.91/1.63 | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | Case 1:
% 5.91/1.63 | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | (90) $lesseq(all_3_0, 0)
% 5.91/1.63 | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | COMBINE_INEQS: (76), (90) imply:
% 5.91/1.63 | | | | | | | | | | | | | | | | | (91) $false
% 5.91/1.63 | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | CLOSE: (91) is inconsistent.
% 5.91/1.63 | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | Case 2:
% 5.91/1.63 | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | (92) ~ ($lesseq(-1, $difference($difference(all_6_0,
% 5.91/1.63 | | | | | | | | | | | | | | | | | $product(2, all_3_0)), a))) | ~
% 5.91/1.63 | | | | | | | | | | | | | | | | | ($lesseq(a, 2))
% 5.91/1.63 | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 5.91/1.63 | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | Case 1:
% 5.91/1.63 | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | (93) $lesseq(3, a)
% 5.91/1.63 | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (78), (93) imply:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | (94) $false
% 5.91/1.63 | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | CLOSE: (94) is inconsistent.
% 5.91/1.63 | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | Case 2:
% 5.91/1.63 | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | (95) $lesseq(2, $sum($difference($product(2, all_3_0),
% 5.91/1.63 | | | | | | | | | | | | | | | | | | all_6_0), a))
% 5.91/1.63 | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | (96) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~
% 5.91/1.63 | | | | | | | | | | | | | | | | | | ($lesseq(9, $sum($difference($product(2, v1),
% 5.91/1.63 | | | | | | | | | | | | | | | | | | v2), $product(4, v0)))) | ~
% 5.91/1.63 | | | | | | | | | | | | | | | | | | ($lesseq(v1, 4)) | ~ ($lesseq(v0, 2)) | ~
% 5.91/1.63 | | | | | | | | | | | | | | | | | | ($product(v1, v0) = v2))
% 5.91/1.63 | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (96) with a, all_3_1, all_3_0,
% 5.91/1.63 | | | | | | | | | | | | | | | | | | simplifying with (4) gives:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | (97) ~ ($lesseq(9, $sum($difference($product(2,
% 5.91/1.63 | | | | | | | | | | | | | | | | | | all_3_1), all_3_0), $product(4, a)))) |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | ~ ($lesseq(all_3_1, 4)) | ~ ($lesseq(a, 2))
% 5.91/1.63 | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 5.91/1.63 | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | Case 1:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | (98) $lesseq(5, all_3_1)
% 5.91/1.63 | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (53), (98) imply:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | (99) $false
% 5.91/1.63 | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | CLOSE: (99) is inconsistent.
% 5.91/1.63 | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | Case 2:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | (100) ~ ($lesseq(9, $sum($difference($product(2,
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | all_3_1), all_3_0), $product(4, a)))) |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | ~ ($lesseq(a, 2))
% 5.91/1.63 | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | Case 1:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | (101) $lesseq(3, a)
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (78), (101) imply:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | (102) $false
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | CLOSE: (102) is inconsistent.
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | Case 2:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | (103) $lesseq(-8, $difference($difference(all_3_0,
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | $product(2, all_3_1)), $product(4, a)))
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | (104) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | ($lesseq(-3, $difference($difference(v2, v1),
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | $product(4, v0)))) | ~ ($lesseq(v1, 4)) |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(1, v0)) | ~ ($product(v1, v0) =
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | v2))
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (104) with a, all_3_1, all_3_0,
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | simplifying with (4) gives:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | (105) ~ ($lesseq(-3, $difference($difference(all_3_0,
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | all_3_1), $product(4, a)))) | ~
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | ($lesseq(all_3_1, 4)) | ~ ($lesseq(1, a))
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | Case 1:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | (106) $lesseq(5, all_3_1)
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (53), (106) imply:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | (107) $false
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | CLOSE: (107) is inconsistent.
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | Case 2:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | (108) ~ ($lesseq(-3, $difference($difference(all_3_0,
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | all_3_1), $product(4, a)))) | ~
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, a))
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | | (109) $lesseq(a, 0)
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (37), (109) imply:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | | (110) $false
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (110) is inconsistent.
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | | (111) $lesseq(4, $sum($difference(all_3_1, all_3_0),
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | | $product(4, a)))
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.63 | | | | | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | (112) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(3, $sum($difference(v2, $product(4,
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | v1)), $product(5, v0)))) | ~
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | ($lesseq(-1, $difference(v1, $product(2, v0))))
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(v0, 2)) | ~ ($product(v1, v0) =
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | v2) | ~ ($product(v0, v0) = v1))
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (112) with a, all_3_1, all_3_0,
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | simplifying with (3), (4) gives:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | (113) ~ ($lesseq(3, $sum($difference(all_3_0,
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | $product(4, all_3_1)), $product(5, a)))) |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(-1, $difference(all_3_1, $product(2,
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | a)))) | ~ ($lesseq(a, 2))
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | (114) $lesseq(2, $difference($product(2, a), all_3_1))
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (73), (114) imply:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | (115) $false
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (115) is inconsistent.
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | (116) ~ ($lesseq(3, $sum($difference(all_3_0,
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | $product(4, all_3_1)), $product(5, a)))) |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(a, 2))
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | (117) $lesseq(3, a)
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (78), (117) imply:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | (118) $false
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (118) is inconsistent.
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | (119) $lesseq(-2, $difference($difference($product(4,
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | all_3_1), all_3_0), $product(5, a)))
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | (120) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(0, $difference($difference($product(3,
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | v1), v2), $product(3, v0)))) | ~
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(-1, $difference(v1, $product(2, v0))))
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(1, v0)) | ~ ($product(v1, v0) =
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | v2) | ~ ($product(v0, v0) = v1))
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (120) with a, all_3_1, all_3_0,
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (3), (4) gives:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | (121) ~ ($lesseq(0, $difference($difference($product(3,
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | all_3_1), all_3_0), $product(3, a)))) |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(-1, $difference(all_3_1, $product(2,
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | a)))) | ~ ($lesseq(1, a))
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | (122) $lesseq(2, $difference($product(2, a), all_3_1))
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (73), (122) imply:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | (123) $false
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (123) is inconsistent.
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | (124) ~ ($lesseq(0, $difference($difference($product(3,
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_3_1), all_3_0), $product(3, a)))) |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | ~ ($lesseq(1, a))
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (125) $lesseq(a, 0)
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (37), (125) imply:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (126) $false
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (126) is inconsistent.
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (127) $lesseq(1, $sum($difference(all_3_0, $product(3,
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | all_3_1)), $product(3, a)))
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (88) with a, all_3_1, all_3_0,
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (4) gives:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (128) ~ ($lesseq(-1, $difference($difference(all_3_0,
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $product(2, all_3_1)), a))) | ~
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, all_3_1)) | ~ ($lesseq(a, 2))
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (129) $lesseq(all_3_1, 0)
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (42), (129) imply:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (130) $false
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (130) is inconsistent.
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (131) ~ ($lesseq(-1, $difference($difference(all_3_0,
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(2, all_3_1)), a))) | ~
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(a, 2))
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (132) $lesseq(3, a)
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (78), (132) imply:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (133) $false
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (133) is inconsistent.
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (134) $lesseq(2, $sum($difference($product(2, all_3_1),
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_3_0), a))
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication:
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(2, $sum($difference(v1, v2), v0))) | ~
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, v1)) | ~ ($lesseq(1, v0)) | ~
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($product(v1, v0) = v2))
% 5.91/1.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (135) with a, all_3_1, all_3_0,
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (4) gives:
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (136) ~ ($lesseq(2, $sum($difference(all_3_1, all_3_0),
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | a))) | ~ ($lesseq(1, all_3_1)) | ~
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, a))
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (137) $lesseq(all_3_1, 0)
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (42), (137) imply:
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (138) $false
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (138) is inconsistent.
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139) ~ ($lesseq(2, $sum($difference(all_3_1, all_3_0),
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | a))) | ~ ($lesseq(1, a))
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (140) $lesseq(a, 0)
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (37), (140) imply:
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (141) $false
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (141) is inconsistent.
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (142) $lesseq(-1, $difference($difference(all_3_0,
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_3_1), a))
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication:
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (143) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(5,
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference($product(4, v0), v1))) | ~
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(v0, 2)) | ~ ($product(v0, v0) = v1))
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (143) with a, all_3_1, simplifying
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (3) gives:
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (144) ~ ($lesseq(5, $difference($product(4, a),
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_3_1))) | ~ ($lesseq(a, 2))
% 5.91/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (144) gives:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145) $lesseq(3, a)
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (78), (145) imply:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146) $false
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (146) is inconsistent.
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (147) $lesseq(-4, $difference(all_3_1, $product(4, a)))
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | THEORY_AXIOM GroebnerMultiplication:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (148) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(-1,
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $difference(v1, $product(3, v0)))) | ~
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(v0, 2)) | ~ ($lesseq(1, v0)) | ~
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($product(v0, v0) = v1))
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (148) with a, all_3_1, simplifying
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (3) gives:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (149) ~ ($lesseq(-1, $difference(all_3_1, $product(3,
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | a)))) | ~ ($lesseq(a, 2)) | ~
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ($lesseq(1, a))
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (150) $lesseq(3, a)
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (78), (150) imply:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (151) $false
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (151) is inconsistent.
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (152) ~ ($lesseq(-1, $difference(all_3_1, $product(3,
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | a)))) | ~ ($lesseq(1, a))
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (153) $lesseq(a, 0)
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (37), (153) imply:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (154) $false
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (154) is inconsistent.
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (155) $lesseq(2, $difference($product(3, a), all_3_1))
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (6), (95) imply:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (156) $lesseq(4, $sum($product(2, all_3_0), a))
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (134), (156) imply:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157) $lesseq(8, $sum($product(4, all_3_1), $product(3,
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | a)))
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (111), (127) imply:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158) $lesseq(5, $difference($product(7, a), $product(2,
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_3_1)))
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (157), (158) imply:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (159) $lesseq(2, a)
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (159) implies:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160) $lesseq(2, a)
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (6), (87) imply:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161) $lesseq(2, $difference($product(3, all_3_0),
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(2, all_3_1)))
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (42), (161) imply:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162) $lesseq(2, all_3_0)
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (162) implies:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163) $lesseq(2, all_3_0)
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (119), (163) imply:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164) $lesseq(0, $difference($product(4, all_3_1),
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(5, a)))
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (160), (164) imply:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165) $lesseq(3, all_3_1)
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (165) implies:
% 6.39/1.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166) $lesseq(3, all_3_1)
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (2), (103) imply:
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (167) $lesseq(-7, $difference($product(-1, all_3_1),
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $product(2, a)))
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (160), (167) imply:
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168) $lesseq(all_3_1, 3)
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (168) implies:
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169) $lesseq(all_3_1, 3)
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (155), (166) imply:
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170) $lesseq(2, a)
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (147), (160) imply:
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (171) $lesseq(4, all_3_1)
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_INEQS: (169), (171) imply:
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (172) $false
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (172) is inconsistent.
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | | |
% 6.39/1.66 | | | | | | | | | End of split
% 6.39/1.66 | | | | | | | | |
% 6.39/1.66 | | | | | | | | End of split
% 6.39/1.66 | | | | | | | |
% 6.39/1.66 | | | | | | | End of split
% 6.39/1.66 | | | | | | |
% 6.39/1.66 | | | | | | End of split
% 6.39/1.66 | | | | | |
% 6.39/1.66 | | | | | End of split
% 6.39/1.66 | | | | |
% 6.39/1.66 | | | | End of split
% 6.39/1.66 | | | |
% 6.39/1.66 | | | End of split
% 6.39/1.66 | | |
% 6.39/1.66 | | End of split
% 6.39/1.66 | |
% 6.39/1.66 | End of split
% 6.39/1.66 |
% 6.39/1.66 End of proof
% 6.39/1.66 % SZS output end Proof for theBenchmark
% 6.39/1.66
% 6.39/1.66 1032ms
%------------------------------------------------------------------------------