TSTP Solution File: ARI643_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI643_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 17:48:40 EDT 2023
% Result : Theorem 4.57s 1.55s
% Output : Proof 5.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : ARI643_1 : TPTP v8.1.2. Released v6.3.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 18:27:18 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.44/0.62 ________ _____
% 0.44/0.62 ___ __ \_________(_)________________________________
% 0.44/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.44/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.44/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.44/0.62
% 0.44/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.44/0.62 (2023-06-19)
% 0.44/0.62
% 0.44/0.62 (c) Philipp Rümmer, 2009-2023
% 0.44/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.44/0.62 Amanda Stjerna.
% 0.44/0.62 Free software under BSD-3-Clause.
% 0.44/0.62
% 0.44/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.44/0.62
% 0.44/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.44/0.64 Running up to 7 provers in parallel.
% 0.44/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.44/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.44/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.44/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.44/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.44/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.44/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.15/1.13 Prover 5: Preprocessing ...
% 2.15/1.13 Prover 4: Preprocessing ...
% 2.15/1.13 Prover 2: Preprocessing ...
% 2.15/1.13 Prover 6: Preprocessing ...
% 2.15/1.13 Prover 3: Preprocessing ...
% 2.15/1.13 Prover 0: Preprocessing ...
% 2.15/1.13 Prover 1: Preprocessing ...
% 2.26/1.27 Prover 0: Constructing countermodel ...
% 2.26/1.27 Prover 1: Constructing countermodel ...
% 2.26/1.27 Prover 6: Constructing countermodel ...
% 2.26/1.27 Prover 3: Constructing countermodel ...
% 2.26/1.27 Prover 4: Constructing countermodel ...
% 2.26/1.27 Prover 5: Constructing countermodel ...
% 2.26/1.27 Prover 2: Constructing countermodel ...
% 4.57/1.54 Prover 2: proved (896ms)
% 4.57/1.54 Prover 3: proved (894ms)
% 4.57/1.55
% 4.57/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.57/1.55
% 4.57/1.55
% 4.57/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.57/1.55
% 4.57/1.55 Prover 0: proved (897ms)
% 4.57/1.55
% 4.57/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.57/1.55
% 4.57/1.55 Prover 6: proved (891ms)
% 4.57/1.55
% 4.57/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.57/1.55
% 4.57/1.55 Prover 5: proved (890ms)
% 4.57/1.55
% 4.57/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.57/1.55
% 4.57/1.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.57/1.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.57/1.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.57/1.56 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.57/1.56 Prover 1: Found proof (size 52)
% 4.57/1.56 Prover 1: proved (908ms)
% 4.57/1.56 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.57/1.57 Prover 7: Preprocessing ...
% 4.57/1.58 Prover 10: Preprocessing ...
% 4.57/1.58 Prover 11: Preprocessing ...
% 4.57/1.58 Prover 8: Preprocessing ...
% 5.03/1.59 Prover 13: Preprocessing ...
% 5.03/1.60 Prover 4: Found proof (size 49)
% 5.03/1.60 Prover 4: proved (949ms)
% 5.03/1.60 Prover 10: Constructing countermodel ...
% 5.03/1.60 Prover 7: Constructing countermodel ...
% 5.03/1.60 Prover 8: Constructing countermodel ...
% 5.03/1.60 Prover 10: stopped
% 5.03/1.60 Prover 7: stopped
% 5.03/1.60 Prover 8: stopped
% 5.03/1.61 Prover 11: Constructing countermodel ...
% 5.03/1.61 Prover 11: stopped
% 5.03/1.62 Prover 13: Constructing countermodel ...
% 5.03/1.62 Prover 13: stopped
% 5.03/1.62
% 5.03/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.03/1.62
% 5.03/1.64 % SZS output start Proof for theBenchmark
% 5.03/1.64 Assumptions after simplification:
% 5.03/1.64 ---------------------------------
% 5.03/1.64
% 5.03/1.64 (conj)
% 5.03/1.65 ~ (a = 0) & ? [v0: int] : ( ~ (v0 = 0) & ? [v1: int] : ($lesseq(v1,
% 5.03/1.65 0)$product(v0, a) = v1 & (($lesseq(1, $difference(v1, a)) & $lesseq(a,
% 5.03/1.65 -1)) | ($lesseq(1, $sum(v1, a)) & $lesseq(1, a)))))
% 5.03/1.65
% 5.03/1.65 Those formulas are unsatisfiable:
% 5.03/1.65 ---------------------------------
% 5.03/1.65
% 5.03/1.65 Begin of proof
% 5.03/1.65 |
% 5.03/1.65 | ALPHA: (conj) implies:
% 5.03/1.66 | (1) ? [v0: int] : ( ~ (v0 = 0) & ? [v1: int] : ($lesseq(v1,
% 5.03/1.66 | 0)$product(v0, a) = v1 & (($lesseq(1, $difference(v1, a)) &
% 5.03/1.66 | $lesseq(a, -1)) | ($lesseq(1, $sum(v1, a)) & $lesseq(1, a)))))
% 5.03/1.66 |
% 5.03/1.66 | DELTA: instantiating (1) with fresh symbol all_3_0 gives:
% 5.03/1.66 | (2) ~ (all_3_0 = 0) & ? [v0: int] : ($lesseq(v0, 0)$product(all_3_0, a) =
% 5.03/1.66 | v0 & (($lesseq(1, $difference(v0, a)) & $lesseq(a, -1)) | ($lesseq(1,
% 5.03/1.66 | $sum(v0, a)) & $lesseq(1, a))))
% 5.03/1.66 |
% 5.03/1.66 | ALPHA: (2) implies:
% 5.03/1.66 | (3) ~ (all_3_0 = 0)
% 5.03/1.66 | (4) ? [v0: int] : ($lesseq(v0, 0)$product(all_3_0, a) = v0 & (($lesseq(1,
% 5.03/1.66 | $difference(v0, a)) & $lesseq(a, -1)) | ($lesseq(1, $sum(v0,
% 5.03/1.66 | a)) & $lesseq(1, a))))
% 5.03/1.66 |
% 5.03/1.66 | DELTA: instantiating (4) with fresh symbol all_5_0 gives:
% 5.03/1.67 | (5) $lesseq(all_5_0, 0)$product(all_3_0, a) = all_5_0 & (($lesseq(1,
% 5.30/1.67 | $difference(all_5_0, a)) & $lesseq(a, -1)) | ($lesseq(1,
% 5.30/1.67 | $sum(all_5_0, a)) & $lesseq(1, a)))
% 5.30/1.67 |
% 5.30/1.67 | ALPHA: (5) implies:
% 5.30/1.67 | (6) $lesseq(all_5_0, 0)
% 5.30/1.67 | (7) $product(all_3_0, a) = all_5_0
% 5.30/1.67 | (8) ($lesseq(1, $difference(all_5_0, a)) & $lesseq(a, -1)) | ($lesseq(1,
% 5.30/1.67 | $sum(all_5_0, a)) & $lesseq(1, a))
% 5.30/1.67 |
% 5.30/1.67 | BETA: splitting (8) gives:
% 5.30/1.67 |
% 5.30/1.67 | Case 1:
% 5.30/1.67 | |
% 5.30/1.67 | | (9) $lesseq(1, $difference(all_5_0, a)) & $lesseq(a, -1)
% 5.30/1.67 | |
% 5.30/1.67 | | ALPHA: (9) implies:
% 5.30/1.67 | | (10) $lesseq(1, $difference(all_5_0, a))
% 5.30/1.67 | |
% 5.30/1.67 | | COMBINE_INEQS: (6), (10) imply:
% 5.31/1.67 | | (11) $lesseq(a, -1)
% 5.31/1.67 | |
% 5.31/1.67 | | THEORY_AXIOM GroebnerMultiplication:
% 5.31/1.67 | | (12) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(v2, 0) |
% 5.31/1.67 | | ~ ($lesseq(v1, -1)) | ~ ($lesseq(v0, -1)) | ~ ($product(v1,
% 5.31/1.67 | | v0) = v2))
% 5.31/1.68 | |
% 5.31/1.68 | | GROUND_INST: instantiating (12) with a, all_3_0, all_5_0, simplifying with
% 5.31/1.68 | | (7) gives:
% 5.31/1.68 | | (13) ~ ($lesseq(all_5_0, 0) | ~ ($lesseq(all_3_0, -1)) | ~ ($lesseq(a,
% 5.31/1.68 | | -1))
% 5.31/1.68 | |
% 5.31/1.68 | | BETA: splitting (13) gives:
% 5.31/1.68 | |
% 5.31/1.68 | | Case 1:
% 5.31/1.68 | | |
% 5.31/1.68 | | | (14) $lesseq(1, all_5_0)
% 5.31/1.68 | | |
% 5.31/1.68 | | | COMBINE_INEQS: (6), (14) imply:
% 5.31/1.68 | | | (15) $false
% 5.31/1.68 | | |
% 5.31/1.68 | | | CLOSE: (15) is inconsistent.
% 5.31/1.68 | | |
% 5.31/1.68 | | Case 2:
% 5.31/1.68 | | |
% 5.31/1.68 | | | (16) ~ ($lesseq(all_3_0, -1)) | ~ ($lesseq(a, -1))
% 5.31/1.68 | | |
% 5.31/1.68 | | | BETA: splitting (16) gives:
% 5.31/1.68 | | |
% 5.31/1.68 | | | Case 1:
% 5.31/1.68 | | | |
% 5.31/1.68 | | | | (17) $lesseq(0, a)
% 5.31/1.68 | | | |
% 5.31/1.68 | | | | COMBINE_INEQS: (11), (17) imply:
% 5.31/1.68 | | | | (18) $false
% 5.31/1.68 | | | |
% 5.31/1.68 | | | | CLOSE: (18) is inconsistent.
% 5.31/1.68 | | | |
% 5.31/1.68 | | | Case 2:
% 5.31/1.68 | | | |
% 5.31/1.68 | | | | (19) $lesseq(0, all_3_0)
% 5.31/1.68 | | | |
% 5.31/1.68 | | | | STRENGTHEN: (3), (19) imply:
% 5.31/1.68 | | | | (20) $lesseq(1, all_3_0)
% 5.31/1.68 | | | |
% 5.31/1.68 | | | | THEORY_AXIOM GroebnerMultiplication:
% 5.31/1.69 | | | | (21) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(2,
% 5.31/1.69 | | | | $difference($sum(v2, v1), v0))) | ~ ($lesseq(1, v1)) | ~
% 5.31/1.69 | | | | ($lesseq(v0, -1)) | ~ ($product(v1, v0) = v2))
% 5.31/1.69 | | | |
% 5.31/1.69 | | | | GROUND_INST: instantiating (21) with a, all_3_0, all_5_0, simplifying
% 5.31/1.69 | | | | with (7) gives:
% 5.31/1.69 | | | | (22) ~ ($lesseq(2, $difference($sum(all_5_0, all_3_0), a))) | ~
% 5.31/1.69 | | | | ($lesseq(1, all_3_0)) | ~ ($lesseq(a, -1))
% 5.31/1.69 | | | |
% 5.31/1.69 | | | | BETA: splitting (22) gives:
% 5.31/1.69 | | | |
% 5.31/1.69 | | | | Case 1:
% 5.31/1.69 | | | | |
% 5.31/1.69 | | | | | (23) $lesseq(all_3_0, 0)
% 5.31/1.69 | | | | |
% 5.31/1.69 | | | | | COMBINE_INEQS: (20), (23) imply:
% 5.31/1.69 | | | | | (24) $false
% 5.31/1.69 | | | | |
% 5.31/1.69 | | | | | CLOSE: (24) is inconsistent.
% 5.31/1.69 | | | | |
% 5.31/1.69 | | | | Case 2:
% 5.31/1.69 | | | | |
% 5.31/1.69 | | | | | (25) ~ ($lesseq(2, $difference($sum(all_5_0, all_3_0), a))) | ~
% 5.31/1.69 | | | | | ($lesseq(a, -1))
% 5.31/1.69 | | | | |
% 5.31/1.69 | | | | | BETA: splitting (25) gives:
% 5.31/1.69 | | | | |
% 5.31/1.69 | | | | | Case 1:
% 5.31/1.69 | | | | | |
% 5.31/1.69 | | | | | | (26) $lesseq(0, a)
% 5.31/1.69 | | | | | |
% 5.31/1.69 | | | | | | COMBINE_INEQS: (11), (26) imply:
% 5.31/1.69 | | | | | | (27) $false
% 5.31/1.69 | | | | | |
% 5.31/1.69 | | | | | | CLOSE: (27) is inconsistent.
% 5.31/1.69 | | | | | |
% 5.31/1.69 | | | | | Case 2:
% 5.31/1.69 | | | | | |
% 5.31/1.69 | | | | | | (28) $lesseq(-1, $sum($difference($product(-1, all_5_0),
% 5.31/1.69 | | | | | | all_3_0), a))
% 5.31/1.69 | | | | | |
% 5.31/1.69 | | | | | | COMBINE_INEQS: (10), (28) imply:
% 5.31/1.69 | | | | | | (29) $lesseq(all_3_0, 0)
% 5.31/1.69 | | | | | |
% 5.31/1.69 | | | | | | COMBINE_INEQS: (20), (29) imply:
% 5.31/1.69 | | | | | | (30) $false
% 5.31/1.69 | | | | | |
% 5.31/1.69 | | | | | | CLOSE: (30) is inconsistent.
% 5.31/1.69 | | | | | |
% 5.31/1.69 | | | | | End of split
% 5.31/1.69 | | | | |
% 5.31/1.69 | | | | End of split
% 5.31/1.69 | | | |
% 5.31/1.69 | | | End of split
% 5.31/1.69 | | |
% 5.31/1.69 | | End of split
% 5.31/1.69 | |
% 5.31/1.69 | Case 2:
% 5.31/1.69 | |
% 5.31/1.70 | | (31) $lesseq(1, $sum(all_5_0, a)) & $lesseq(1, a)
% 5.31/1.70 | |
% 5.31/1.70 | | ALPHA: (31) implies:
% 5.31/1.70 | | (32) $lesseq(1, $sum(all_5_0, a))
% 5.31/1.70 | |
% 5.31/1.70 | | COMBINE_INEQS: (6), (32) imply:
% 5.31/1.70 | | (33) $lesseq(1, a)
% 5.31/1.70 | |
% 5.31/1.70 | | THEORY_AXIOM GroebnerMultiplication:
% 5.31/1.70 | | (34) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(v2, 0) |
% 5.31/1.70 | | ~ ($lesseq(1, v1)) | ~ ($lesseq(1, v0)) | ~ ($product(v1, v0)
% 5.31/1.70 | | = v2))
% 5.31/1.70 | |
% 5.31/1.70 | | GROUND_INST: instantiating (34) with a, all_3_0, all_5_0, simplifying with
% 5.31/1.70 | | (7) gives:
% 5.31/1.70 | | (35) ~ ($lesseq(all_5_0, 0) | ~ ($lesseq(1, all_3_0)) | ~ ($lesseq(1,
% 5.31/1.70 | | a))
% 5.31/1.70 | |
% 5.31/1.70 | | BETA: splitting (35) gives:
% 5.31/1.70 | |
% 5.31/1.70 | | Case 1:
% 5.31/1.70 | | |
% 5.31/1.70 | | | (36) $lesseq(1, all_5_0)
% 5.31/1.70 | | |
% 5.31/1.70 | | | COMBINE_INEQS: (6), (36) imply:
% 5.31/1.70 | | | (37) $false
% 5.31/1.70 | | |
% 5.31/1.70 | | | CLOSE: (37) is inconsistent.
% 5.31/1.70 | | |
% 5.31/1.70 | | Case 2:
% 5.31/1.70 | | |
% 5.31/1.70 | | | (38) ~ ($lesseq(1, all_3_0)) | ~ ($lesseq(1, a))
% 5.31/1.70 | | |
% 5.31/1.70 | | | BETA: splitting (38) gives:
% 5.31/1.70 | | |
% 5.31/1.70 | | | Case 1:
% 5.31/1.70 | | | |
% 5.31/1.70 | | | | (39) $lesseq(a, 0)
% 5.31/1.70 | | | |
% 5.31/1.70 | | | | COMBINE_INEQS: (33), (39) imply:
% 5.38/1.70 | | | | (40) $false
% 5.38/1.70 | | | |
% 5.38/1.70 | | | | CLOSE: (40) is inconsistent.
% 5.38/1.70 | | | |
% 5.38/1.70 | | | Case 2:
% 5.38/1.70 | | | |
% 5.38/1.70 | | | | (41) $lesseq(all_3_0, 0)
% 5.38/1.70 | | | |
% 5.38/1.70 | | | | STRENGTHEN: (3), (41) imply:
% 5.38/1.70 | | | | (42) $lesseq(all_3_0, -1)
% 5.38/1.70 | | | |
% 5.38/1.70 | | | | THEORY_AXIOM GroebnerMultiplication:
% 5.38/1.70 | | | | (43) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(2,
% 5.38/1.70 | | | | $sum($difference(v2, v1), v0))) | ~ ($lesseq(v1, -1)) |
% 5.38/1.70 | | | | ~ ($lesseq(1, v0)) | ~ ($product(v1, v0) = v2))
% 5.38/1.70 | | | |
% 5.38/1.71 | | | | GROUND_INST: instantiating (43) with a, all_3_0, all_5_0, simplifying
% 5.38/1.71 | | | | with (7) gives:
% 5.38/1.71 | | | | (44) ~ ($lesseq(2, $sum($difference(all_5_0, all_3_0), a))) | ~
% 5.38/1.71 | | | | ($lesseq(all_3_0, -1)) | ~ ($lesseq(1, a))
% 5.38/1.71 | | | |
% 5.38/1.71 | | | | BETA: splitting (44) gives:
% 5.38/1.71 | | | |
% 5.38/1.71 | | | | Case 1:
% 5.38/1.71 | | | | |
% 5.38/1.71 | | | | | (45) $lesseq(0, all_3_0)
% 5.38/1.71 | | | | |
% 5.38/1.71 | | | | | COMBINE_INEQS: (42), (45) imply:
% 5.38/1.71 | | | | | (46) $false
% 5.38/1.71 | | | | |
% 5.38/1.71 | | | | | CLOSE: (46) is inconsistent.
% 5.38/1.71 | | | | |
% 5.38/1.71 | | | | Case 2:
% 5.38/1.71 | | | | |
% 5.38/1.71 | | | | | (47) ~ ($lesseq(2, $sum($difference(all_5_0, all_3_0), a))) | ~
% 5.38/1.71 | | | | | ($lesseq(1, a))
% 5.38/1.71 | | | | |
% 5.38/1.71 | | | | | BETA: splitting (47) gives:
% 5.38/1.71 | | | | |
% 5.38/1.71 | | | | | Case 1:
% 5.38/1.71 | | | | | |
% 5.38/1.71 | | | | | | (48) $lesseq(a, 0)
% 5.38/1.71 | | | | | |
% 5.38/1.71 | | | | | | COMBINE_INEQS: (33), (48) imply:
% 5.38/1.71 | | | | | | (49) $false
% 5.38/1.71 | | | | | |
% 5.38/1.71 | | | | | | CLOSE: (49) is inconsistent.
% 5.38/1.71 | | | | | |
% 5.38/1.71 | | | | | Case 2:
% 5.38/1.71 | | | | | |
% 5.38/1.71 | | | | | | (50) $lesseq(-1, $difference($difference(all_3_0, all_5_0), a))
% 5.38/1.71 | | | | | |
% 5.38/1.71 | | | | | | COMBINE_INEQS: (32), (50) imply:
% 5.38/1.71 | | | | | | (51) $lesseq(0, all_3_0)
% 5.38/1.71 | | | | | |
% 5.38/1.71 | | | | | | COMBINE_INEQS: (42), (51) imply:
% 5.38/1.71 | | | | | | (52) $false
% 5.38/1.71 | | | | | |
% 5.38/1.71 | | | | | | CLOSE: (52) is inconsistent.
% 5.38/1.71 | | | | | |
% 5.38/1.71 | | | | | End of split
% 5.38/1.71 | | | | |
% 5.38/1.71 | | | | End of split
% 5.38/1.71 | | | |
% 5.38/1.71 | | | End of split
% 5.38/1.71 | | |
% 5.38/1.71 | | End of split
% 5.38/1.71 | |
% 5.38/1.71 | End of split
% 5.38/1.71 |
% 5.38/1.71 End of proof
% 5.38/1.71 % SZS output end Proof for theBenchmark
% 5.38/1.71
% 5.38/1.71 1085ms
%------------------------------------------------------------------------------