TSTP Solution File: DAT032_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT032_1 : TPTP v8.1.2. Released v5.0.0.
% 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 : Wed Aug 30 22:18:57 EDT 2023
% Result : Theorem 6.63s 1.67s
% Output : Proof 10.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : DAT032_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.35 % Computer : n004.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Thu Aug 24 14:29:23 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.59 ________ _____
% 0.20/0.59 ___ __ \_________(_)________________________________
% 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.59 (2023-06-19)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2023
% 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.59 Amanda Stjerna.
% 0.20/0.59 Free software under BSD-3-Clause.
% 0.20/0.59
% 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.59
% 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.60 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.40/1.08 Prover 4: Preprocessing ...
% 2.40/1.08 Prover 1: Preprocessing ...
% 2.91/1.12 Prover 5: Preprocessing ...
% 2.91/1.12 Prover 6: Preprocessing ...
% 2.91/1.12 Prover 3: Preprocessing ...
% 2.91/1.12 Prover 0: Preprocessing ...
% 2.91/1.12 Prover 2: Preprocessing ...
% 5.09/1.45 Prover 1: Constructing countermodel ...
% 5.09/1.45 Prover 6: Constructing countermodel ...
% 5.09/1.45 Prover 3: Constructing countermodel ...
% 5.09/1.46 Prover 5: Proving ...
% 5.09/1.46 Prover 2: Proving ...
% 5.09/1.48 Prover 4: Constructing countermodel ...
% 5.60/1.49 Prover 0: Proving ...
% 6.63/1.67 Prover 6: proved (1048ms)
% 6.63/1.67
% 6.63/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.63/1.67
% 6.63/1.67 Prover 2: stopped
% 6.63/1.67 Prover 5: stopped
% 6.63/1.68 Prover 0: stopped
% 6.63/1.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.63/1.68 Prover 3: stopped
% 6.63/1.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.63/1.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.63/1.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.63/1.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.63/1.71 Prover 7: Preprocessing ...
% 6.63/1.71 Prover 8: Preprocessing ...
% 6.63/1.72 Prover 11: Preprocessing ...
% 7.31/1.72 Prover 10: Preprocessing ...
% 7.31/1.73 Prover 13: Preprocessing ...
% 7.83/1.80 Prover 8: Warning: ignoring some quantifiers
% 7.83/1.81 Prover 7: Constructing countermodel ...
% 7.83/1.82 Prover 8: Constructing countermodel ...
% 7.83/1.83 Prover 10: Constructing countermodel ...
% 7.83/1.83 Prover 13: Warning: ignoring some quantifiers
% 7.83/1.85 Prover 13: Constructing countermodel ...
% 7.83/1.85 Prover 11: Constructing countermodel ...
% 9.47/2.07 Prover 10: Found proof (size 102)
% 9.47/2.07 Prover 10: proved (379ms)
% 9.47/2.07 Prover 7: stopped
% 9.47/2.07 Prover 11: stopped
% 9.47/2.07 Prover 8: stopped
% 9.47/2.07 Prover 4: stopped
% 9.47/2.07 Prover 13: Found proof (size 97)
% 9.47/2.07 Prover 13: proved (383ms)
% 9.47/2.08 Prover 1: Found proof (size 135)
% 9.47/2.08 Prover 1: proved (1467ms)
% 9.47/2.08
% 9.47/2.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.47/2.08
% 9.47/2.09 % SZS output start Proof for theBenchmark
% 9.47/2.09 Assumptions after simplification:
% 9.47/2.09 ---------------------------------
% 9.47/2.09
% 9.47/2.09 (ax5)
% 10.07/2.11 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : (v2
% 10.07/2.11 = v0 | ~ (remove(v2, v1) = v3) | ~ collection(v1) | ~ in(v0, v1) | in(v0,
% 10.07/2.11 v3)) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3:
% 10.07/2.11 collection] : ( ~ (remove(v2, v1) = v3) | ~ collection(v1) | ~ in(v0, v3)
% 10.07/2.11 | in(v0, v1)) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : (
% 10.07/2.11 ~ (remove(v0, v1) = v2) | ~ collection(v1) | ~ in(v0, v2)) & ! [v0: int]
% 10.07/2.11 : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) = v2) | ~
% 10.07/2.11 collection(v1) | ~ in(v0, v1) | ? [v3: int] : (count(v2) = v3 & count(v1)
% 10.07/2.11 = $sum(v3, 1))) & ! [v0: int] : ! [v1: collection] : ! [v2: collection]
% 10.07/2.11 : ( ~ (remove(v0, v1) = v2) | ~ collection(v1) | in(v0, v1) | ? [v3: int] :
% 10.07/2.12 ? [v4: int] : ( ~ ($difference(v4, v3) = 1) & count(v2) = v3 & count(v1) =
% 10.07/2.12 v4))
% 10.07/2.12
% 10.07/2.12 (ax6)
% 10.07/2.12 ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1)
% 10.07/2.12 = v2) | ~ collection(v1) | ~ in(v0, v1) | ? [v3: int] : ? [v4: int] :
% 10.07/2.12 ( ~ (v4 = v3) & count(v2) = v3 & count(v1) = v4)) & ! [v0: int] : ! [v1:
% 10.07/2.12 collection] : ! [v2: collection] : ( ~ (remove(v0, v1) = v2) | ~
% 10.07/2.12 collection(v1) | in(v0, v1) | ? [v3: int] : (count(v2) = v3 & count(v1) =
% 10.07/2.12 v3))
% 10.07/2.12
% 10.07/2.12 (co1)
% 10.07/2.12 ? [v0: collection] : ? [v1: collection] : ? [v2: int] : ? [v3: collection]
% 10.07/2.12 : ? [v4: int] : ($lesseq(v4, 5) & $lesseq(7, v2) & remove(5, v0) = v1 &
% 10.07/2.12 remove(4, v0) = v3 & count(v3) = v4 & count(v1) = v2 & collection(v3) &
% 10.07/2.12 collection(v1) & collection(v0))
% 10.07/2.12
% 10.07/2.12 (function-axioms)
% 10.07/2.12 ! [v0: collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int]
% 10.07/2.12 : (v1 = v0 | ~ (remove(v3, v2) = v1) | ~ (remove(v3, v2) = v0)) & ! [v0:
% 10.07/2.12 collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v1
% 10.07/2.12 = v0 | ~ (add(v3, v2) = v1) | ~ (add(v3, v2) = v0)) & ! [v0: int] : !
% 10.07/2.12 [v1: int] : ! [v2: collection] : (v1 = v0 | ~ (count(v2) = v1) | ~
% 10.07/2.12 (count(v2) = v0))
% 10.07/2.12
% 10.07/2.12 Further assumptions not needed in the proof:
% 10.07/2.12 --------------------------------------------
% 10.07/2.12 ax1, ax2, ax3, ax4, ax7
% 10.07/2.12
% 10.07/2.12 Those formulas are unsatisfiable:
% 10.07/2.12 ---------------------------------
% 10.07/2.12
% 10.07/2.12 Begin of proof
% 10.07/2.12 |
% 10.07/2.12 | ALPHA: (ax5) implies:
% 10.07/2.13 | (1) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~
% 10.07/2.13 | (remove(v0, v1) = v2) | ~ collection(v1) | in(v0, v1) | ? [v3: int]
% 10.07/2.13 | : ? [v4: int] : ( ~ ($difference(v4, v3) = 1) & count(v2) = v3 &
% 10.07/2.13 | count(v1) = v4))
% 10.07/2.13 | (2) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~
% 10.07/2.13 | (remove(v0, v1) = v2) | ~ collection(v1) | ~ in(v0, v1) | ? [v3:
% 10.07/2.13 | int] : (count(v2) = v3 & count(v1) = $sum(v3, 1)))
% 10.07/2.13 |
% 10.07/2.13 | ALPHA: (ax6) implies:
% 10.07/2.13 | (3) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~
% 10.07/2.13 | (remove(v0, v1) = v2) | ~ collection(v1) | in(v0, v1) | ? [v3: int]
% 10.07/2.13 | : (count(v2) = v3 & count(v1) = v3))
% 10.07/2.13 | (4) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~
% 10.07/2.13 | (remove(v0, v1) = v2) | ~ collection(v1) | ~ in(v0, v1) | ? [v3:
% 10.07/2.13 | int] : ? [v4: int] : ( ~ (v4 = v3) & count(v2) = v3 & count(v1) =
% 10.07/2.13 | v4))
% 10.07/2.13 |
% 10.07/2.13 | ALPHA: (function-axioms) implies:
% 10.07/2.13 | (5) ! [v0: int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~
% 10.07/2.13 | (count(v2) = v1) | ~ (count(v2) = v0))
% 10.07/2.13 |
% 10.07/2.13 | DELTA: instantiating (co1) with fresh symbols all_13_0, all_13_1, all_13_2,
% 10.07/2.13 | all_13_3, all_13_4 gives:
% 10.07/2.13 | (6) $lesseq(all_13_0, 5) & $lesseq(7, all_13_2) & remove(5, all_13_4) =
% 10.07/2.13 | all_13_3 & remove(4, all_13_4) = all_13_1 & count(all_13_1) = all_13_0
% 10.07/2.13 | & count(all_13_3) = all_13_2 & collection(all_13_1) &
% 10.07/2.13 | collection(all_13_3) & collection(all_13_4)
% 10.07/2.13 |
% 10.07/2.13 | ALPHA: (6) implies:
% 10.07/2.13 | (7) $lesseq(7, all_13_2)
% 10.07/2.13 | (8) $lesseq(all_13_0, 5)
% 10.07/2.13 | (9) collection(all_13_4)
% 10.07/2.13 | (10) count(all_13_3) = all_13_2
% 10.07/2.13 | (11) count(all_13_1) = all_13_0
% 10.07/2.13 | (12) remove(4, all_13_4) = all_13_1
% 10.07/2.13 | (13) remove(5, all_13_4) = all_13_3
% 10.07/2.13 |
% 10.07/2.14 | GROUND_INST: instantiating (1) with 4, all_13_4, all_13_1, simplifying with
% 10.07/2.14 | (9), (12) gives:
% 10.07/2.14 | (14) in(4, all_13_4) | ? [v0: int] : ? [v1: int] : ( ~ ($difference(v1,
% 10.07/2.14 | v0) = 1) & count(all_13_1) = v0 & count(all_13_4) = v1)
% 10.07/2.14 |
% 10.07/2.14 | GROUND_INST: instantiating (3) with 4, all_13_4, all_13_1, simplifying with
% 10.07/2.14 | (9), (12) gives:
% 10.07/2.14 | (15) in(4, all_13_4) | ? [v0: int] : (count(all_13_1) = v0 &
% 10.07/2.14 | count(all_13_4) = v0)
% 10.07/2.14 |
% 10.07/2.14 | GROUND_INST: instantiating (3) with 5, all_13_4, all_13_3, simplifying with
% 10.07/2.14 | (9), (13) gives:
% 10.07/2.14 | (16) in(5, all_13_4) | ? [v0: int] : (count(all_13_3) = v0 &
% 10.07/2.14 | count(all_13_4) = v0)
% 10.07/2.14 |
% 10.07/2.14 | BETA: splitting (15) gives:
% 10.07/2.14 |
% 10.07/2.14 | Case 1:
% 10.07/2.14 | |
% 10.07/2.14 | | (17) in(4, all_13_4)
% 10.07/2.14 | |
% 10.07/2.14 | | GROUND_INST: instantiating (4) with 4, all_13_4, all_13_1, simplifying with
% 10.07/2.14 | | (9), (12), (17) gives:
% 10.07/2.14 | | (18) ? [v0: int] : ? [v1: int] : ( ~ (v1 = v0) & count(all_13_1) = v0 &
% 10.07/2.14 | | count(all_13_4) = v1)
% 10.07/2.14 | |
% 10.07/2.14 | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (11), (12), (13), (16), (17), (18)
% 10.07/2.14 | | are inconsistent by sub-proof #1.
% 10.07/2.14 | |
% 10.07/2.14 | Case 2:
% 10.07/2.14 | |
% 10.07/2.14 | | (19) ? [v0: int] : (count(all_13_1) = v0 & count(all_13_4) = v0)
% 10.07/2.14 | |
% 10.07/2.14 | | DELTA: instantiating (19) with fresh symbol all_32_0 gives:
% 10.07/2.14 | | (20) count(all_13_1) = all_32_0 & count(all_13_4) = all_32_0
% 10.07/2.14 | |
% 10.07/2.14 | | ALPHA: (20) implies:
% 10.07/2.14 | | (21) count(all_13_4) = all_32_0
% 10.07/2.14 | | (22) count(all_13_1) = all_32_0
% 10.07/2.14 | |
% 10.07/2.14 | | BETA: splitting (14) gives:
% 10.07/2.14 | |
% 10.07/2.14 | | Case 1:
% 10.07/2.14 | | |
% 10.07/2.14 | | | (23) in(4, all_13_4)
% 10.07/2.14 | | |
% 10.07/2.14 | | | GROUND_INST: instantiating (4) with 4, all_13_4, all_13_1, simplifying
% 10.07/2.14 | | | with (9), (12), (23) gives:
% 10.07/2.14 | | | (24) ? [v0: int] : ? [v1: int] : ( ~ (v1 = v0) & count(all_13_1) = v0
% 10.07/2.14 | | | & count(all_13_4) = v1)
% 10.07/2.14 | | |
% 10.07/2.15 | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (11), (12), (13), (16), (23),
% 10.07/2.15 | | | (24) are inconsistent by sub-proof #1.
% 10.07/2.15 | | |
% 10.07/2.15 | | Case 2:
% 10.07/2.15 | | |
% 10.07/2.15 | | | (25) ? [v0: int] : ? [v1: int] : ( ~ ($difference(v1, v0) = 1) &
% 10.07/2.15 | | | count(all_13_1) = v0 & count(all_13_4) = v1)
% 10.07/2.15 | | |
% 10.07/2.15 | | | DELTA: instantiating (25) with fresh symbols all_38_0, all_38_1 gives:
% 10.07/2.15 | | | (26) ~ ($difference(all_38_0, all_38_1) = 1) & count(all_13_1) =
% 10.07/2.15 | | | all_38_1 & count(all_13_4) = all_38_0
% 10.07/2.15 | | |
% 10.07/2.15 | | | ALPHA: (26) implies:
% 10.07/2.15 | | | (27) count(all_13_1) = all_38_1
% 10.07/2.15 | | |
% 10.07/2.15 | | | GROUND_INST: instantiating (5) with all_13_0, all_38_1, all_13_1,
% 10.07/2.15 | | | simplifying with (11), (27) gives:
% 10.07/2.15 | | | (28) all_38_1 = all_13_0
% 10.07/2.15 | | |
% 10.07/2.15 | | | GROUND_INST: instantiating (5) with all_32_0, all_38_1, all_13_1,
% 10.07/2.15 | | | simplifying with (22), (27) gives:
% 10.07/2.15 | | | (29) all_38_1 = all_32_0
% 10.07/2.15 | | |
% 10.07/2.15 | | | COMBINE_EQS: (28), (29) imply:
% 10.07/2.15 | | | (30) all_32_0 = all_13_0
% 10.07/2.15 | | |
% 10.07/2.15 | | | SIMP: (30) implies:
% 10.07/2.15 | | | (31) all_32_0 = all_13_0
% 10.07/2.15 | | |
% 10.07/2.15 | | | REDUCE: (21), (31) imply:
% 10.07/2.15 | | | (32) count(all_13_4) = all_13_0
% 10.07/2.15 | | |
% 10.07/2.15 | | | BETA: splitting (16) gives:
% 10.07/2.15 | | |
% 10.07/2.15 | | | Case 1:
% 10.07/2.15 | | | |
% 10.07/2.15 | | | | (33) in(5, all_13_4)
% 10.07/2.15 | | | |
% 10.07/2.15 | | | | GROUND_INST: instantiating (2) with 5, all_13_4, all_13_3, simplifying
% 10.07/2.15 | | | | with (9), (13), (33) gives:
% 10.07/2.15 | | | | (34) ? [v0: int] : (count(all_13_3) = v0 & count(all_13_4) =
% 10.07/2.15 | | | | $sum(v0, 1))
% 10.07/2.15 | | | |
% 10.07/2.15 | | | | DELTA: instantiating (34) with fresh symbol all_54_0 gives:
% 10.07/2.15 | | | | (35) count(all_13_3) = all_54_0 & count(all_13_4) = $sum(all_54_0, 1)
% 10.07/2.15 | | | |
% 10.07/2.15 | | | | ALPHA: (35) implies:
% 10.07/2.15 | | | | (36) count(all_13_4) = $sum(all_54_0, 1)
% 10.07/2.15 | | | | (37) count(all_13_3) = all_54_0
% 10.07/2.15 | | | |
% 10.07/2.15 | | | | GROUND_INST: instantiating (5) with all_13_0, $sum(all_54_0, 1),
% 10.07/2.15 | | | | all_13_4, simplifying with (32), (36) gives:
% 10.07/2.15 | | | | (38) $difference(all_54_0, all_13_0) = -1
% 10.07/2.15 | | | |
% 10.07/2.15 | | | | GROUND_INST: instantiating (5) with all_13_2, all_54_0, all_13_3,
% 10.07/2.15 | | | | simplifying with (10), (37) gives:
% 10.07/2.15 | | | | (39) all_54_0 = all_13_2
% 10.07/2.15 | | | |
% 10.07/2.15 | | | | COMBINE_EQS: (38), (39) imply:
% 10.07/2.15 | | | | (40) $difference(all_13_0, all_13_2) = 1
% 10.07/2.15 | | | |
% 10.07/2.15 | | | | SIMP: (40) implies:
% 10.07/2.15 | | | | (41) $difference(all_13_0, all_13_2) = 1
% 10.07/2.15 | | | |
% 10.07/2.15 | | | | REDUCE: (8), (41) imply:
% 10.07/2.15 | | | | (42) $lesseq(all_13_2, 4)
% 10.07/2.15 | | | |
% 10.07/2.15 | | | | COMBINE_INEQS: (7), (42) imply:
% 10.07/2.15 | | | | (43) $false
% 10.07/2.15 | | | |
% 10.07/2.15 | | | | CLOSE: (43) is inconsistent.
% 10.07/2.15 | | | |
% 10.07/2.15 | | | Case 2:
% 10.07/2.15 | | | |
% 10.07/2.15 | | | | (44) ? [v0: int] : (count(all_13_3) = v0 & count(all_13_4) = v0)
% 10.07/2.15 | | | |
% 10.07/2.15 | | | | DELTA: instantiating (44) with fresh symbol all_48_0 gives:
% 10.07/2.15 | | | | (45) count(all_13_3) = all_48_0 & count(all_13_4) = all_48_0
% 10.07/2.15 | | | |
% 10.07/2.15 | | | | ALPHA: (45) implies:
% 10.07/2.15 | | | | (46) count(all_13_4) = all_48_0
% 10.07/2.15 | | | | (47) count(all_13_3) = all_48_0
% 10.07/2.15 | | | |
% 10.07/2.15 | | | | GROUND_INST: instantiating (5) with all_13_0, all_48_0, all_13_4,
% 10.07/2.15 | | | | simplifying with (32), (46) gives:
% 10.07/2.15 | | | | (48) all_48_0 = all_13_0
% 10.07/2.15 | | | |
% 10.07/2.15 | | | | GROUND_INST: instantiating (5) with all_13_2, all_48_0, all_13_3,
% 10.07/2.15 | | | | simplifying with (10), (47) gives:
% 10.07/2.16 | | | | (49) all_48_0 = all_13_2
% 10.07/2.16 | | | |
% 10.07/2.16 | | | | COMBINE_EQS: (48), (49) imply:
% 10.07/2.16 | | | | (50) all_13_0 = all_13_2
% 10.07/2.16 | | | |
% 10.07/2.16 | | | | SIMP: (50) implies:
% 10.07/2.16 | | | | (51) all_13_0 = all_13_2
% 10.07/2.16 | | | |
% 10.07/2.16 | | | | REDUCE: (8), (51) imply:
% 10.07/2.16 | | | | (52) $lesseq(all_13_2, 5)
% 10.07/2.16 | | | |
% 10.07/2.16 | | | | COMBINE_INEQS: (7), (52) imply:
% 10.07/2.16 | | | | (53) $false
% 10.07/2.16 | | | |
% 10.07/2.16 | | | | CLOSE: (53) is inconsistent.
% 10.07/2.16 | | | |
% 10.07/2.16 | | | End of split
% 10.07/2.16 | | |
% 10.07/2.16 | | End of split
% 10.07/2.16 | |
% 10.07/2.16 | End of split
% 10.07/2.16 |
% 10.07/2.16 End of proof
% 10.07/2.16
% 10.07/2.16 Sub-proof #1 shows that the following formulas are inconsistent:
% 10.07/2.16 ----------------------------------------------------------------
% 10.07/2.16 (1) count(all_13_3) = all_13_2
% 10.07/2.16 (2) remove(5, all_13_4) = all_13_3
% 10.07/2.16 (3) $lesseq(7, all_13_2)
% 10.07/2.16 (4) collection(all_13_4)
% 10.07/2.16 (5) in(4, all_13_4)
% 10.07/2.16 (6) ! [v0: int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~
% 10.07/2.16 (count(v2) = v1) | ~ (count(v2) = v0))
% 10.07/2.16 (7) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~
% 10.07/2.16 (remove(v0, v1) = v2) | ~ collection(v1) | ~ in(v0, v1) | ? [v3:
% 10.07/2.16 int] : (count(v2) = v3 & count(v1) = $sum(v3, 1)))
% 10.07/2.16 (8) in(5, all_13_4) | ? [v0: int] : (count(all_13_3) = v0 & count(all_13_4)
% 10.07/2.16 = v0)
% 10.07/2.16 (9) remove(4, all_13_4) = all_13_1
% 10.07/2.16 (10) count(all_13_1) = all_13_0
% 10.07/2.16 (11) ? [v0: int] : ? [v1: int] : ( ~ (v1 = v0) & count(all_13_1) = v0 &
% 10.07/2.16 count(all_13_4) = v1)
% 10.07/2.16 (12) $lesseq(all_13_0, 5)
% 10.07/2.16
% 10.07/2.16 Begin of proof
% 10.07/2.16 |
% 10.07/2.16 | GROUND_INST: instantiating (7) with 4, all_13_4, all_13_1, simplifying with
% 10.07/2.16 | (4), (5), (9) gives:
% 10.07/2.16 | (13) ? [v0: int] : (count(all_13_1) = v0 & count(all_13_4) = $sum(v0, 1))
% 10.07/2.16 |
% 10.07/2.16 | DELTA: instantiating (13) with fresh symbol all_38_0 gives:
% 10.07/2.16 | (14) count(all_13_1) = all_38_0 & count(all_13_4) = $sum(all_38_0, 1)
% 10.07/2.16 |
% 10.07/2.16 | ALPHA: (14) implies:
% 10.07/2.16 | (15) count(all_13_4) = $sum(all_38_0, 1)
% 10.07/2.16 | (16) count(all_13_1) = all_38_0
% 10.07/2.16 |
% 10.07/2.16 | DELTA: instantiating (11) with fresh symbols all_40_0, all_40_1 gives:
% 10.07/2.16 | (17) ~ (all_40_0 = all_40_1) & count(all_13_1) = all_40_1 &
% 10.07/2.16 | count(all_13_4) = all_40_0
% 10.07/2.16 |
% 10.07/2.16 | ALPHA: (17) implies:
% 10.07/2.16 | (18) count(all_13_1) = all_40_1
% 10.07/2.16 |
% 10.07/2.16 | GROUND_INST: instantiating (6) with all_13_0, all_40_1, all_13_1, simplifying
% 10.07/2.16 | with (10), (18) gives:
% 10.07/2.16 | (19) all_40_1 = all_13_0
% 10.07/2.16 |
% 10.07/2.16 | GROUND_INST: instantiating (6) with all_38_0, all_40_1, all_13_1, simplifying
% 10.07/2.16 | with (16), (18) gives:
% 10.07/2.16 | (20) all_40_1 = all_38_0
% 10.07/2.16 |
% 10.07/2.16 | COMBINE_EQS: (19), (20) imply:
% 10.07/2.16 | (21) all_38_0 = all_13_0
% 10.07/2.16 |
% 10.07/2.16 | SIMP: (21) implies:
% 10.07/2.16 | (22) all_38_0 = all_13_0
% 10.07/2.16 |
% 10.07/2.16 | REDUCE: (15), (22) imply:
% 10.07/2.16 | (23) count(all_13_4) = $sum(all_13_0, 1)
% 10.07/2.16 |
% 10.07/2.16 | BETA: splitting (8) gives:
% 10.07/2.16 |
% 10.07/2.16 | Case 1:
% 10.07/2.16 | |
% 10.07/2.16 | | (24) in(5, all_13_4)
% 10.07/2.16 | |
% 10.07/2.16 | | GROUND_INST: instantiating (7) with 5, all_13_4, all_13_3, simplifying with
% 10.07/2.16 | | (2), (4), (24) gives:
% 10.07/2.16 | | (25) ? [v0: int] : (count(all_13_3) = v0 & count(all_13_4) = $sum(v0,
% 10.07/2.16 | | 1))
% 10.07/2.16 | |
% 10.07/2.16 | | DELTA: instantiating (25) with fresh symbol all_56_0 gives:
% 10.07/2.16 | | (26) count(all_13_3) = all_56_0 & count(all_13_4) = $sum(all_56_0, 1)
% 10.07/2.16 | |
% 10.07/2.16 | | ALPHA: (26) implies:
% 10.07/2.16 | | (27) count(all_13_4) = $sum(all_56_0, 1)
% 10.07/2.17 | | (28) count(all_13_3) = all_56_0
% 10.07/2.17 | |
% 10.07/2.17 | | GROUND_INST: instantiating (6) with $sum(all_13_0, 1), $sum(all_56_0, 1),
% 10.07/2.17 | | all_13_4, simplifying with (23), (27) gives:
% 10.07/2.17 | | (29) all_56_0 = all_13_0
% 10.07/2.17 | |
% 10.07/2.17 | | GROUND_INST: instantiating (6) with all_13_2, all_56_0, all_13_3,
% 10.07/2.17 | | simplifying with (1), (28) gives:
% 10.07/2.17 | | (30) all_56_0 = all_13_2
% 10.07/2.17 | |
% 10.07/2.17 | | COMBINE_EQS: (29), (30) imply:
% 10.07/2.17 | | (31) all_13_0 = all_13_2
% 10.07/2.17 | |
% 10.07/2.17 | | SIMP: (31) implies:
% 10.07/2.17 | | (32) all_13_0 = all_13_2
% 10.07/2.17 | |
% 10.07/2.17 | | REDUCE: (12), (32) imply:
% 10.07/2.17 | | (33) $lesseq(all_13_2, 5)
% 10.07/2.17 | |
% 10.07/2.17 | | COMBINE_INEQS: (3), (33) imply:
% 10.07/2.17 | | (34) $false
% 10.07/2.17 | |
% 10.07/2.17 | | CLOSE: (34) is inconsistent.
% 10.07/2.17 | |
% 10.07/2.17 | Case 2:
% 10.07/2.17 | |
% 10.07/2.17 | | (35) ? [v0: int] : (count(all_13_3) = v0 & count(all_13_4) = v0)
% 10.07/2.17 | |
% 10.07/2.17 | | DELTA: instantiating (35) with fresh symbol all_50_0 gives:
% 10.07/2.17 | | (36) count(all_13_3) = all_50_0 & count(all_13_4) = all_50_0
% 10.07/2.17 | |
% 10.07/2.17 | | ALPHA: (36) implies:
% 10.07/2.17 | | (37) count(all_13_4) = all_50_0
% 10.07/2.17 | | (38) count(all_13_3) = all_50_0
% 10.07/2.17 | |
% 10.07/2.17 | | GROUND_INST: instantiating (6) with $sum(all_13_0, 1), all_50_0, all_13_4,
% 10.07/2.17 | | simplifying with (23), (37) gives:
% 10.07/2.17 | | (39) $difference(all_50_0, all_13_0) = 1
% 10.07/2.17 | |
% 10.07/2.17 | | GROUND_INST: instantiating (6) with all_13_2, all_50_0, all_13_3,
% 10.07/2.17 | | simplifying with (1), (38) gives:
% 10.07/2.17 | | (40) all_50_0 = all_13_2
% 10.07/2.17 | |
% 10.07/2.17 | | COMBINE_EQS: (39), (40) imply:
% 10.07/2.17 | | (41) $difference(all_13_0, all_13_2) = -1
% 10.07/2.17 | |
% 10.07/2.17 | | SIMP: (41) implies:
% 10.07/2.17 | | (42) $difference(all_13_0, all_13_2) = -1
% 10.07/2.17 | |
% 10.07/2.17 | | REDUCE: (12), (42) imply:
% 10.07/2.17 | | (43) $lesseq(all_13_2, 6)
% 10.07/2.17 | |
% 10.07/2.17 | | COMBINE_INEQS: (3), (43) imply:
% 10.07/2.17 | | (44) $false
% 10.07/2.17 | |
% 10.07/2.17 | | CLOSE: (44) is inconsistent.
% 10.07/2.17 | |
% 10.07/2.17 | End of split
% 10.07/2.17 |
% 10.07/2.17 End of proof
% 10.07/2.17 % SZS output end Proof for theBenchmark
% 10.07/2.17
% 10.07/2.17 1578ms
%------------------------------------------------------------------------------