TSTP Solution File: DAT046_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT046_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 22:19:00 EDT 2023
% Result : Theorem 9.47s 2.27s
% Output : Proof 13.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT046_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 14:18:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.67 ________ _____
% 0.19/0.67 ___ __ \_________(_)________________________________
% 0.19/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.67
% 0.19/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.67 (2023-06-19)
% 0.19/0.67
% 0.19/0.67 (c) Philipp Rümmer, 2009-2023
% 0.19/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.67 Amanda Stjerna.
% 0.19/0.67 Free software under BSD-3-Clause.
% 0.19/0.67
% 0.19/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.67
% 0.19/0.67 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.69 Running up to 7 provers in parallel.
% 0.19/0.71 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.72 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.72 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.72 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.72 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.72 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 2.70/1.30 Prover 1: Preprocessing ...
% 2.70/1.32 Prover 4: Preprocessing ...
% 2.70/1.37 Prover 2: Preprocessing ...
% 2.70/1.37 Prover 3: Preprocessing ...
% 2.70/1.37 Prover 0: Preprocessing ...
% 2.70/1.37 Prover 6: Preprocessing ...
% 2.70/1.37 Prover 5: Preprocessing ...
% 6.40/1.82 Prover 1: Constructing countermodel ...
% 6.40/1.82 Prover 3: Constructing countermodel ...
% 6.78/1.83 Prover 6: Constructing countermodel ...
% 6.78/1.84 Prover 5: Proving ...
% 6.78/1.85 Prover 4: Constructing countermodel ...
% 6.95/1.88 Prover 2: Proving ...
% 6.95/1.91 Prover 0: Proving ...
% 9.47/2.27 Prover 3: proved (1554ms)
% 9.47/2.27
% 9.47/2.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.47/2.27
% 9.47/2.27 Prover 0: stopped
% 9.47/2.27 Prover 2: stopped
% 9.47/2.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.47/2.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.47/2.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.47/2.28 Prover 6: stopped
% 9.47/2.30 Prover 5: proved (1589ms)
% 9.47/2.30
% 9.47/2.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.47/2.30
% 9.47/2.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.47/2.30 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.10/2.33 Prover 8: Preprocessing ...
% 10.10/2.33 Prover 10: Preprocessing ...
% 10.10/2.34 Prover 7: Preprocessing ...
% 10.10/2.35 Prover 11: Preprocessing ...
% 10.10/2.36 Prover 13: Preprocessing ...
% 10.64/2.43 Prover 8: Warning: ignoring some quantifiers
% 10.64/2.43 Prover 10: Constructing countermodel ...
% 10.64/2.44 Prover 8: Constructing countermodel ...
% 10.64/2.46 Prover 13: Warning: ignoring some quantifiers
% 11.17/2.47 Prover 13: Constructing countermodel ...
% 11.21/2.48 Prover 7: Constructing countermodel ...
% 11.64/2.54 Prover 11: Constructing countermodel ...
% 12.34/2.75 Prover 1: Found proof (size 110)
% 12.34/2.75 Prover 1: proved (2045ms)
% 12.34/2.75 Prover 7: stopped
% 12.34/2.75 Prover 8: stopped
% 12.34/2.75 Prover 13: stopped
% 12.34/2.75 Prover 11: stopped
% 12.34/2.75 Prover 4: stopped
% 12.34/2.76 Prover 10: Found proof (size 41)
% 12.34/2.76 Prover 10: proved (482ms)
% 12.34/2.76
% 12.34/2.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.34/2.76
% 12.34/2.81 % SZS output start Proof for theBenchmark
% 12.34/2.81 Assumptions after simplification:
% 12.34/2.81 ---------------------------------
% 12.34/2.81
% 12.34/2.82 (ax1)
% 13.22/2.85 collection(empty) & ! [v0: collection] : ! [v1: int] : ( ~ ($lesseq(v1, -1))
% 13.22/2.85 | ~ (count(v0) = v1) | ~ collection(v0)) & ! [v0: int] : ~ (in(v0,
% 13.22/2.85 empty) = 0)
% 13.22/2.85
% 13.22/2.85 (ax2)
% 13.22/2.85 collection(empty) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] :
% 13.22/2.85 ! [v3: int] : (v3 = 0 | ~ (add(v0, v1) = v2) | ~ (in(v0, v2) = v3) | ~
% 13.22/2.85 collection(v1)) & ! [v0: collection] : (v0 = empty | ~ (count(v0) = 0) |
% 13.22/2.85 ~ collection(v0)) & ! [v0: int] : (v0 = 0 | ~ (count(empty) = v0))
% 13.22/2.85
% 13.22/2.85 (ax3)
% 13.22/2.86 ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1)
% 13.22/2.86 = v2) | ~ (in(v0, v2) = 0) | ~ collection(v1)) & ! [v0: int] : ! [v1:
% 13.22/2.86 collection] : ! [v2: collection] : ( ~ (add(v0, v1) = v2) | ~
% 13.22/2.86 collection(v1) | ? [v3: any] : ? [v4: int] : ? [v5: int] : (count(v2) =
% 13.22/2.86 v4 & count(v1) = v5 & in(v0, v1) = v3 & ($difference(v5, v4) = -1 | v3 =
% 13.22/2.86 0))) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~
% 13.22/2.86 (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ?
% 13.22/2.86 [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~ (v5 =
% 13.22/2.86 0) | ~ ($difference(v4, v3) = -1))))
% 13.22/2.86
% 13.22/2.86 (ax4)
% 13.22/2.87 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : !
% 13.22/2.87 [v4: int] : (v4 = 0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~
% 13.22/2.87 collection(v1) | ( ~ (v2 = v0) & ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) =
% 13.22/2.87 v5))) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3:
% 13.22/2.87 collection] : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~
% 13.22/2.87 collection(v1) | in(v0, v1) = 0) & ! [v0: int] : ! [v1: collection] : !
% 13.22/2.87 [v2: collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: any] :
% 13.22/2.87 ? [v4: int] : ? [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1)
% 13.22/2.87 = v3 & ( ~ (v3 = 0) | v5 = v4))) & ! [v0: int] : ! [v1: collection] : !
% 13.22/2.87 [v2: collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: int] :
% 13.22/2.87 ? [v4: int] : ? [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1)
% 13.22/2.87 = v5 & ( ~ (v4 = v3) | v5 = 0)))
% 13.22/2.87
% 13.22/2.87 (co1)
% 13.22/2.88 collection(empty) & ? [v0: collection] : ? [v1: collection] : ? [v2: int] :
% 13.22/2.88 ( ~ (v2 = 2) & add(3, empty) = v0 & add(1, v0) = v1 & count(v1) = v2 &
% 13.22/2.88 collection(v1) & collection(v0))
% 13.22/2.88
% 13.22/2.88 (function-axioms)
% 13.22/2.88 ! [v0: collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int]
% 13.22/2.88 : (v1 = v0 | ~ (remove(v3, v2) = v1) | ~ (remove(v3, v2) = v0)) & ! [v0:
% 13.22/2.88 collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v1
% 13.22/2.88 = v0 | ~ (add(v3, v2) = v1) | ~ (add(v3, v2) = v0)) & ! [v0:
% 13.22/2.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: collection] : !
% 13.22/2.88 [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 13.22/2.88 int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~ (count(v2) = v1) |
% 13.22/2.88 ~ (count(v2) = v0))
% 13.22/2.88
% 13.22/2.88 Further assumptions not needed in the proof:
% 13.22/2.88 --------------------------------------------
% 13.22/2.88 ax5, ax6, ax7
% 13.22/2.88
% 13.22/2.88 Those formulas are unsatisfiable:
% 13.22/2.88 ---------------------------------
% 13.22/2.88
% 13.22/2.88 Begin of proof
% 13.22/2.89 |
% 13.22/2.89 | ALPHA: (ax1) implies:
% 13.22/2.89 | (1) ! [v0: int] : ~ (in(v0, empty) = 0)
% 13.22/2.89 |
% 13.22/2.89 | ALPHA: (ax2) implies:
% 13.22/2.89 | (2) ! [v0: int] : (v0 = 0 | ~ (count(empty) = v0))
% 13.22/2.89 |
% 13.22/2.89 | ALPHA: (ax3) implies:
% 13.22/2.89 | (3) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0,
% 13.22/2.89 | v1) = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ?
% 13.22/2.89 | [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~
% 13.22/2.89 | (v5 = 0) | ~ ($difference(v4, v3) = -1))))
% 13.76/2.90 | (4) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0,
% 13.76/2.90 | v1) = v2) | ~ collection(v1) | ? [v3: any] : ? [v4: int] : ?
% 13.76/2.90 | [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 &
% 13.76/2.90 | ($difference(v5, v4) = -1 | v3 = 0)))
% 13.76/2.90 |
% 13.76/2.90 | ALPHA: (ax4) implies:
% 13.79/2.90 | (5) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0,
% 13.79/2.90 | v1) = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ?
% 13.79/2.90 | [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~
% 13.79/2.90 | (v4 = v3) | v5 = 0)))
% 13.80/2.90 | (6) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0,
% 13.80/2.90 | v1) = v2) | ~ collection(v1) | ? [v3: any] : ? [v4: int] : ?
% 13.80/2.90 | [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 & ( ~
% 13.80/2.90 | (v3 = 0) | v5 = v4)))
% 13.80/2.90 | (7) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection]
% 13.80/2.90 | : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~
% 13.80/2.90 | collection(v1) | in(v0, v1) = 0)
% 13.80/2.91 |
% 13.80/2.91 | ALPHA: (co1) implies:
% 13.80/2.91 | (8) collection(empty)
% 13.80/2.91 | (9) ? [v0: collection] : ? [v1: collection] : ? [v2: int] : ( ~ (v2 = 2)
% 13.80/2.91 | & add(3, empty) = v0 & add(1, v0) = v1 & count(v1) = v2 &
% 13.80/2.91 | collection(v1) & collection(v0))
% 13.80/2.91 |
% 13.80/2.91 | ALPHA: (function-axioms) implies:
% 13.80/2.91 | (10) ! [v0: int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~
% 13.80/2.91 | (count(v2) = v1) | ~ (count(v2) = v0))
% 13.80/2.91 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.80/2.91 | collection] : ! [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~
% 13.80/2.91 | (in(v3, v2) = v0))
% 13.80/2.91 |
% 13.80/2.91 | DELTA: instantiating (9) with fresh symbols all_13_0, all_13_1, all_13_2
% 13.80/2.91 | gives:
% 13.80/2.91 | (12) ~ (all_13_0 = 2) & add(3, empty) = all_13_2 & add(1, all_13_2) =
% 13.80/2.91 | all_13_1 & count(all_13_1) = all_13_0 & collection(all_13_1) &
% 13.80/2.91 | collection(all_13_2)
% 13.80/2.91 |
% 13.80/2.91 | ALPHA: (12) implies:
% 13.80/2.91 | (13) ~ (all_13_0 = 2)
% 13.80/2.91 | (14) collection(all_13_2)
% 13.80/2.91 | (15) count(all_13_1) = all_13_0
% 13.80/2.91 | (16) add(1, all_13_2) = all_13_1
% 13.80/2.91 | (17) add(3, empty) = all_13_2
% 13.80/2.91 |
% 13.80/2.92 | GROUND_INST: instantiating (6) with 1, all_13_2, all_13_1, simplifying with
% 13.80/2.92 | (14), (16) gives:
% 13.80/2.92 | (18) ? [v0: any] : ? [v1: int] : ? [v2: int] : (count(all_13_1) = v1 &
% 13.80/2.92 | count(all_13_2) = v2 & in(1, all_13_2) = v0 & ( ~ (v0 = 0) | v2 =
% 13.80/2.92 | v1))
% 13.80/2.92 |
% 13.80/2.92 | GROUND_INST: instantiating (4) with 1, all_13_2, all_13_1, simplifying with
% 13.80/2.92 | (14), (16) gives:
% 13.80/2.92 | (19) ? [v0: any] : ? [v1: int] : ? [v2: int] : (count(all_13_1) = v1 &
% 13.80/2.92 | count(all_13_2) = v2 & in(1, all_13_2) = v0 & ($difference(v2, v1) =
% 13.80/2.92 | -1 | v0 = 0))
% 13.80/2.92 |
% 13.80/2.92 | GROUND_INST: instantiating (3) with 1, all_13_2, all_13_1, simplifying with
% 13.80/2.92 | (14), (16) gives:
% 13.80/2.92 | (20) ? [v0: int] : ? [v1: int] : ? [v2: any] : (count(all_13_1) = v0 &
% 13.80/2.92 | count(all_13_2) = v1 & in(1, all_13_2) = v2 & ( ~ (v2 = 0) | ~
% 13.80/2.92 | ($difference(v1, v0) = -1)))
% 13.80/2.92 |
% 13.80/2.92 | GROUND_INST: instantiating (5) with 1, all_13_2, all_13_1, simplifying with
% 13.80/2.92 | (14), (16) gives:
% 13.80/2.92 | (21) ? [v0: int] : ? [v1: int] : ? [v2: any] : (count(all_13_1) = v0 &
% 13.80/2.92 | count(all_13_2) = v1 & in(1, all_13_2) = v2 & ( ~ (v1 = v0) | v2 =
% 13.80/2.92 | 0))
% 13.80/2.92 |
% 13.80/2.92 | GROUND_INST: instantiating (6) with 3, empty, all_13_2, simplifying with (8),
% 13.80/2.92 | (17) gives:
% 13.80/2.93 | (22) ? [v0: any] : ? [v1: int] : ? [v2: int] : (count(all_13_2) = v1 &
% 13.80/2.93 | count(empty) = v2 & in(3, empty) = v0 & ( ~ (v0 = 0) | v2 = v1))
% 13.80/2.93 |
% 13.80/2.93 | GROUND_INST: instantiating (4) with 3, empty, all_13_2, simplifying with (8),
% 13.80/2.93 | (17) gives:
% 13.80/2.93 | (23) ? [v0: any] : ? [v1: int] : ? [v2: int] : (count(all_13_2) = v1 &
% 13.80/2.93 | count(empty) = v2 & in(3, empty) = v0 & ($difference(v2, v1) = -1 |
% 13.80/2.93 | v0 = 0))
% 13.80/2.93 |
% 13.80/2.93 | GROUND_INST: instantiating (3) with 3, empty, all_13_2, simplifying with (8),
% 13.80/2.93 | (17) gives:
% 13.80/2.93 | (24) ? [v0: int] : ? [v1: int] : ? [v2: any] : (count(all_13_2) = v0 &
% 13.80/2.93 | count(empty) = v1 & in(3, empty) = v2 & ( ~ (v2 = 0) | ~
% 13.80/2.93 | ($difference(v1, v0) = -1)))
% 13.80/2.93 |
% 13.80/2.93 | GROUND_INST: instantiating (5) with 3, empty, all_13_2, simplifying with (8),
% 13.80/2.93 | (17) gives:
% 13.80/2.93 | (25) ? [v0: int] : ? [v1: int] : ? [v2: any] : (count(all_13_2) = v0 &
% 13.80/2.93 | count(empty) = v1 & in(3, empty) = v2 & ( ~ (v1 = v0) | v2 = 0))
% 13.80/2.93 |
% 13.80/2.93 | DELTA: instantiating (24) with fresh symbols all_22_0, all_22_1, all_22_2
% 13.80/2.93 | gives:
% 13.80/2.93 | (26) count(all_13_2) = all_22_2 & count(empty) = all_22_1 & in(3, empty) =
% 13.80/2.93 | all_22_0 & ( ~ (all_22_0 = 0) | ~ ($difference(all_22_1, all_22_2) =
% 13.80/2.93 | -1))
% 13.80/2.93 |
% 13.80/2.93 | ALPHA: (26) implies:
% 13.80/2.93 | (27) in(3, empty) = all_22_0
% 13.80/2.93 | (28) count(all_13_2) = all_22_2
% 13.80/2.93 | (29) ~ (all_22_0 = 0) | ~ ($difference(all_22_1, all_22_2) = -1)
% 13.80/2.93 |
% 13.80/2.93 | DELTA: instantiating (23) with fresh symbols all_24_0, all_24_1, all_24_2
% 13.80/2.93 | gives:
% 13.80/2.94 | (30) count(all_13_2) = all_24_1 & count(empty) = all_24_0 & in(3, empty) =
% 13.80/2.94 | all_24_2 & ($difference(all_24_0, all_24_1) = -1 | all_24_2 = 0)
% 13.80/2.94 |
% 13.80/2.94 | ALPHA: (30) implies:
% 13.80/2.94 | (31) in(3, empty) = all_24_2
% 13.80/2.94 | (32) count(empty) = all_24_0
% 13.80/2.94 | (33) count(all_13_2) = all_24_1
% 13.80/2.94 | (34) $difference(all_24_0, all_24_1) = -1 | all_24_2 = 0
% 13.80/2.94 |
% 13.80/2.94 | DELTA: instantiating (18) with fresh symbols all_26_0, all_26_1, all_26_2
% 13.80/2.94 | gives:
% 13.80/2.94 | (35) count(all_13_1) = all_26_1 & count(all_13_2) = all_26_0 & in(1,
% 13.80/2.94 | all_13_2) = all_26_2 & ( ~ (all_26_2 = 0) | all_26_0 = all_26_1)
% 13.80/2.94 |
% 13.80/2.94 | ALPHA: (35) implies:
% 13.80/2.94 | (36) in(1, all_13_2) = all_26_2
% 13.80/2.94 | (37) count(all_13_2) = all_26_0
% 13.80/2.94 |
% 13.80/2.94 | DELTA: instantiating (22) with fresh symbols all_28_0, all_28_1, all_28_2
% 13.80/2.94 | gives:
% 13.80/2.94 | (38) count(all_13_2) = all_28_1 & count(empty) = all_28_0 & in(3, empty) =
% 13.80/2.94 | all_28_2 & ( ~ (all_28_2 = 0) | all_28_0 = all_28_1)
% 13.80/2.94 |
% 13.80/2.94 | ALPHA: (38) implies:
% 13.80/2.94 | (39) in(3, empty) = all_28_2
% 13.80/2.94 | (40) count(empty) = all_28_0
% 13.80/2.94 | (41) count(all_13_2) = all_28_1
% 13.80/2.94 |
% 13.80/2.94 | DELTA: instantiating (25) with fresh symbols all_30_0, all_30_1, all_30_2
% 13.80/2.94 | gives:
% 13.80/2.94 | (42) count(all_13_2) = all_30_2 & count(empty) = all_30_1 & in(3, empty) =
% 13.80/2.94 | all_30_0 & ( ~ (all_30_1 = all_30_2) | all_30_0 = 0)
% 13.80/2.94 |
% 13.80/2.94 | ALPHA: (42) implies:
% 13.80/2.94 | (43) in(3, empty) = all_30_0
% 13.80/2.94 | (44) count(empty) = all_30_1
% 13.80/2.94 | (45) count(all_13_2) = all_30_2
% 13.80/2.94 |
% 13.80/2.94 | DELTA: instantiating (20) with fresh symbols all_32_0, all_32_1, all_32_2
% 13.80/2.94 | gives:
% 13.80/2.95 | (46) count(all_13_1) = all_32_2 & count(all_13_2) = all_32_1 & in(1,
% 13.80/2.95 | all_13_2) = all_32_0 & ( ~ (all_32_0 = 0) | ~
% 13.80/2.95 | ($difference(all_32_1, all_32_2) = -1))
% 13.80/2.95 |
% 13.80/2.95 | ALPHA: (46) implies:
% 13.80/2.95 | (47) in(1, all_13_2) = all_32_0
% 13.80/2.95 | (48) count(all_13_2) = all_32_1
% 13.80/2.95 | (49) count(all_13_1) = all_32_2
% 13.80/2.95 |
% 13.80/2.95 | DELTA: instantiating (21) with fresh symbols all_34_0, all_34_1, all_34_2
% 13.80/2.95 | gives:
% 13.80/2.95 | (50) count(all_13_1) = all_34_2 & count(all_13_2) = all_34_1 & in(1,
% 13.80/2.95 | all_13_2) = all_34_0 & ( ~ (all_34_1 = all_34_2) | all_34_0 = 0)
% 13.80/2.95 |
% 13.80/2.95 | ALPHA: (50) implies:
% 13.80/2.95 | (51) in(1, all_13_2) = all_34_0
% 13.80/2.95 | (52) count(all_13_2) = all_34_1
% 13.80/2.95 | (53) count(all_13_1) = all_34_2
% 13.80/2.95 |
% 13.80/2.95 | DELTA: instantiating (19) with fresh symbols all_36_0, all_36_1, all_36_2
% 13.80/2.95 | gives:
% 13.80/2.95 | (54) count(all_13_1) = all_36_1 & count(all_13_2) = all_36_0 & in(1,
% 13.80/2.95 | all_13_2) = all_36_2 & ($difference(all_36_0, all_36_1) = -1 |
% 13.80/2.95 | all_36_2 = 0)
% 13.80/2.95 |
% 13.80/2.95 | ALPHA: (54) implies:
% 13.80/2.95 | (55) in(1, all_13_2) = all_36_2
% 13.80/2.95 | (56) count(all_13_2) = all_36_0
% 13.80/2.95 | (57) count(all_13_1) = all_36_1
% 13.80/2.95 | (58) $difference(all_36_0, all_36_1) = -1 | all_36_2 = 0
% 13.80/2.95 |
% 13.80/2.95 | GROUND_INST: instantiating (11) with all_32_0, all_34_0, all_13_2, 1,
% 13.80/2.95 | simplifying with (47), (51) gives:
% 13.80/2.95 | (59) all_34_0 = all_32_0
% 13.80/2.95 |
% 13.80/2.95 | GROUND_INST: instantiating (11) with all_34_0, all_36_2, all_13_2, 1,
% 13.80/2.95 | simplifying with (51), (55) gives:
% 13.80/2.95 | (60) all_36_2 = all_34_0
% 13.80/2.95 |
% 13.80/2.95 | GROUND_INST: instantiating (11) with all_26_2, all_36_2, all_13_2, 1,
% 13.80/2.95 | simplifying with (36), (55) gives:
% 13.80/2.95 | (61) all_36_2 = all_26_2
% 13.80/2.95 |
% 13.80/2.96 | GROUND_INST: instantiating (11) with all_24_2, all_28_2, empty, 3, simplifying
% 13.80/2.96 | with (31), (39) gives:
% 13.80/2.96 | (62) all_28_2 = all_24_2
% 13.80/2.96 |
% 13.80/2.96 | GROUND_INST: instantiating (11) with all_28_2, all_30_0, empty, 3, simplifying
% 13.80/2.96 | with (39), (43) gives:
% 13.80/2.96 | (63) all_30_0 = all_28_2
% 13.80/2.96 |
% 13.80/2.96 | GROUND_INST: instantiating (11) with all_22_0, all_30_0, empty, 3, simplifying
% 13.80/2.96 | with (27), (43) gives:
% 13.80/2.96 | (64) all_30_0 = all_22_0
% 13.80/2.96 |
% 13.80/2.96 | GROUND_INST: instantiating (10) with all_28_0, all_30_1, empty, simplifying
% 13.80/2.96 | with (40), (44) gives:
% 13.80/2.96 | (65) all_30_1 = all_28_0
% 13.80/2.96 |
% 13.80/2.96 | GROUND_INST: instantiating (10) with all_24_0, all_30_1, empty, simplifying
% 13.80/2.96 | with (32), (44) gives:
% 13.80/2.96 | (66) all_30_1 = all_24_0
% 13.80/2.96 |
% 13.80/2.96 | GROUND_INST: instantiating (2) with all_30_1, simplifying with (44) gives:
% 13.80/2.96 | (67) all_30_1 = 0
% 13.80/2.96 |
% 13.80/2.96 | GROUND_INST: instantiating (10) with all_22_2, all_28_1, all_13_2, simplifying
% 13.80/2.96 | with (28), (41) gives:
% 13.80/2.96 | (68) all_28_1 = all_22_2
% 13.80/2.96 |
% 13.80/2.96 | GROUND_INST: instantiating (10) with all_32_1, all_34_1, all_13_2, simplifying
% 13.80/2.96 | with (48), (52) gives:
% 13.80/2.96 | (69) all_34_1 = all_32_1
% 13.80/2.96 |
% 13.80/2.96 | GROUND_INST: instantiating (10) with all_30_2, all_34_1, all_13_2, simplifying
% 13.80/2.96 | with (45), (52) gives:
% 13.80/2.96 | (70) all_34_1 = all_30_2
% 13.80/2.96 |
% 13.80/2.96 | GROUND_INST: instantiating (10) with all_28_1, all_34_1, all_13_2, simplifying
% 13.80/2.96 | with (41), (52) gives:
% 13.80/2.96 | (71) all_34_1 = all_28_1
% 13.80/2.96 |
% 13.80/2.96 | GROUND_INST: instantiating (10) with all_24_1, all_34_1, all_13_2, simplifying
% 13.80/2.96 | with (33), (52) gives:
% 13.80/2.96 | (72) all_34_1 = all_24_1
% 13.80/2.96 |
% 13.80/2.96 | GROUND_INST: instantiating (10) with all_28_1, all_36_0, all_13_2, simplifying
% 13.80/2.96 | with (41), (56) gives:
% 13.80/2.96 | (73) all_36_0 = all_28_1
% 13.80/2.96 |
% 13.80/2.96 | GROUND_INST: instantiating (10) with all_26_0, all_36_0, all_13_2, simplifying
% 13.80/2.96 | with (37), (56) gives:
% 13.80/2.96 | (74) all_36_0 = all_26_0
% 13.80/2.96 |
% 13.80/2.96 | GROUND_INST: instantiating (10) with all_34_2, all_36_1, all_13_1, simplifying
% 13.80/2.96 | with (53), (57) gives:
% 13.80/2.96 | (75) all_36_1 = all_34_2
% 13.80/2.96 |
% 13.80/2.96 | GROUND_INST: instantiating (10) with all_32_2, all_36_1, all_13_1, simplifying
% 13.80/2.97 | with (49), (57) gives:
% 13.80/2.97 | (76) all_36_1 = all_32_2
% 13.80/2.97 |
% 13.80/2.97 | GROUND_INST: instantiating (10) with all_13_0, all_36_1, all_13_1, simplifying
% 13.80/2.97 | with (15), (57) gives:
% 13.80/2.97 | (77) all_36_1 = all_13_0
% 13.80/2.97 |
% 13.80/2.97 | COMBINE_EQS: (73), (74) imply:
% 13.80/2.97 | (78) all_28_1 = all_26_0
% 13.80/2.97 |
% 13.80/2.97 | SIMP: (78) implies:
% 13.80/2.97 | (79) all_28_1 = all_26_0
% 13.80/2.97 |
% 13.80/2.97 | COMBINE_EQS: (75), (76) imply:
% 13.80/2.97 | (80) all_34_2 = all_32_2
% 13.80/2.97 |
% 13.80/2.97 | COMBINE_EQS: (75), (77) imply:
% 13.80/2.97 | (81) all_34_2 = all_13_0
% 13.80/2.97 |
% 13.80/2.97 | COMBINE_EQS: (60), (61) imply:
% 13.80/2.97 | (82) all_34_0 = all_26_2
% 13.80/2.97 |
% 13.80/2.97 | SIMP: (82) implies:
% 13.80/2.97 | (83) all_34_0 = all_26_2
% 13.80/2.97 |
% 13.80/2.97 | COMBINE_EQS: (59), (83) imply:
% 13.80/2.97 | (84) all_32_0 = all_26_2
% 13.80/2.97 |
% 13.80/2.97 | SIMP: (84) implies:
% 13.80/2.97 | (85) all_32_0 = all_26_2
% 13.80/2.97 |
% 13.80/2.97 | COMBINE_EQS: (69), (72) imply:
% 13.80/2.97 | (86) all_32_1 = all_24_1
% 13.80/2.97 |
% 13.80/2.97 | COMBINE_EQS: (69), (71) imply:
% 13.80/2.97 | (87) all_32_1 = all_28_1
% 13.80/2.97 |
% 13.80/2.97 | COMBINE_EQS: (69), (70) imply:
% 13.80/2.97 | (88) all_32_1 = all_30_2
% 13.80/2.97 |
% 13.80/2.97 | COMBINE_EQS: (80), (81) imply:
% 13.80/2.97 | (89) all_32_2 = all_13_0
% 13.80/2.97 |
% 13.80/2.97 | COMBINE_EQS: (87), (88) imply:
% 13.80/2.97 | (90) all_30_2 = all_28_1
% 13.80/2.97 |
% 13.80/2.97 | COMBINE_EQS: (86), (88) imply:
% 13.80/2.97 | (91) all_30_2 = all_24_1
% 13.80/2.97 |
% 13.80/2.97 | COMBINE_EQS: (63), (64) imply:
% 13.80/2.97 | (92) all_28_2 = all_22_0
% 13.80/2.97 |
% 13.80/2.97 | SIMP: (92) implies:
% 13.80/2.97 | (93) all_28_2 = all_22_0
% 13.80/2.97 |
% 13.80/2.97 | COMBINE_EQS: (65), (67) imply:
% 13.80/2.97 | (94) all_28_0 = 0
% 13.80/2.97 |
% 13.80/2.97 | COMBINE_EQS: (65), (66) imply:
% 13.80/2.97 | (95) all_28_0 = all_24_0
% 13.80/2.97 |
% 13.80/2.97 | COMBINE_EQS: (90), (91) imply:
% 13.80/2.97 | (96) all_28_1 = all_24_1
% 13.80/2.97 |
% 13.80/2.97 | SIMP: (96) implies:
% 13.80/2.97 | (97) all_28_1 = all_24_1
% 13.80/2.97 |
% 13.80/2.97 | COMBINE_EQS: (94), (95) imply:
% 13.80/2.97 | (98) all_24_0 = 0
% 13.80/2.97 |
% 13.80/2.97 | SIMP: (98) implies:
% 13.80/2.97 | (99) all_24_0 = 0
% 13.80/2.97 |
% 13.80/2.97 | COMBINE_EQS: (68), (79) imply:
% 13.80/2.97 | (100) all_26_0 = all_22_2
% 13.80/2.97 |
% 13.80/2.98 | COMBINE_EQS: (79), (97) imply:
% 13.80/2.98 | (101) all_26_0 = all_24_1
% 13.80/2.98 |
% 13.80/2.98 | COMBINE_EQS: (62), (93) imply:
% 13.80/2.98 | (102) all_24_2 = all_22_0
% 13.80/2.98 |
% 13.80/2.98 | SIMP: (102) implies:
% 13.80/2.98 | (103) all_24_2 = all_22_0
% 13.80/2.98 |
% 13.80/2.98 | COMBINE_EQS: (100), (101) imply:
% 13.80/2.98 | (104) all_24_1 = all_22_2
% 13.80/2.98 |
% 13.80/2.98 | COMBINE_EQS: (74), (100) imply:
% 13.80/2.98 | (105) all_36_0 = all_22_2
% 13.80/2.98 |
% 13.80/2.98 | BETA: splitting (29) gives:
% 13.80/2.98 |
% 13.80/2.98 | Case 1:
% 13.80/2.98 | |
% 13.80/2.98 | | (106) ~ (all_22_0 = 0)
% 13.80/2.98 | |
% 13.80/2.98 | | BETA: splitting (34) gives:
% 13.80/2.98 | |
% 13.80/2.98 | | Case 1:
% 13.80/2.98 | | |
% 13.80/2.98 | | | (107) all_24_2 = 0
% 13.80/2.98 | | |
% 13.80/2.98 | | | COMBINE_EQS: (103), (107) imply:
% 13.80/2.98 | | | (108) all_22_0 = 0
% 13.80/2.98 | | |
% 13.80/2.98 | | | REDUCE: (106), (108) imply:
% 13.80/2.98 | | | (109) $false
% 13.80/2.98 | | |
% 13.80/2.98 | | | CLOSE: (109) is inconsistent.
% 13.80/2.98 | | |
% 13.80/2.98 | | Case 2:
% 13.80/2.98 | | |
% 13.80/2.98 | | | (110) $difference(all_24_0, all_24_1) = -1
% 13.80/2.98 | | |
% 13.80/2.98 | | | COMBINE_EQS: (99), (110) imply:
% 13.80/2.98 | | | (111) all_24_1 = 1
% 13.80/2.98 | | |
% 13.80/2.98 | | | SIMP: (111) implies:
% 13.80/2.98 | | | (112) all_24_1 = 1
% 13.80/2.98 | | |
% 13.80/2.98 | | | COMBINE_EQS: (104), (112) imply:
% 13.80/2.98 | | | (113) all_22_2 = 1
% 13.80/2.98 | | |
% 13.80/2.98 | | | COMBINE_EQS: (105), (113) imply:
% 13.80/2.98 | | | (114) all_36_0 = 1
% 13.80/2.98 | | |
% 13.80/2.98 | | | BETA: splitting (58) gives:
% 13.80/2.98 | | |
% 13.80/2.98 | | | Case 1:
% 13.80/2.98 | | | |
% 13.80/2.98 | | | | (115) all_36_2 = 0
% 13.80/2.98 | | | |
% 13.80/2.98 | | | | COMBINE_EQS: (61), (115) imply:
% 13.80/2.98 | | | | (116) all_26_2 = 0
% 13.80/2.98 | | | |
% 13.80/2.98 | | | | SIMP: (116) implies:
% 13.80/2.98 | | | | (117) all_26_2 = 0
% 13.80/2.98 | | | |
% 13.80/2.98 | | | | REDUCE: (36), (117) imply:
% 13.80/2.98 | | | | (118) in(1, all_13_2) = 0
% 13.80/2.98 | | | |
% 13.80/2.99 | | | | GROUND_INST: instantiating (7) with 1, empty, 3, all_13_2, simplifying
% 13.80/2.99 | | | | with (8), (17), (118) gives:
% 13.80/2.99 | | | | (119) in(1, empty) = 0
% 13.80/2.99 | | | |
% 13.80/2.99 | | | | GROUND_INST: instantiating (1) with 1, simplifying with (119) gives:
% 13.80/2.99 | | | | (120) $false
% 13.80/2.99 | | | |
% 13.80/2.99 | | | | CLOSE: (120) is inconsistent.
% 13.80/2.99 | | | |
% 13.80/2.99 | | | Case 2:
% 13.80/2.99 | | | |
% 13.80/2.99 | | | | (121) $difference(all_36_0, all_36_1) = -1
% 13.80/2.99 | | | |
% 13.80/2.99 | | | | COMBINE_EQS: (114), (121) imply:
% 13.80/2.99 | | | | (122) all_36_1 = 2
% 13.80/2.99 | | | |
% 13.80/2.99 | | | | SIMP: (122) implies:
% 13.80/2.99 | | | | (123) all_36_1 = 2
% 13.80/2.99 | | | |
% 13.80/2.99 | | | | COMBINE_EQS: (77), (123) imply:
% 13.80/2.99 | | | | (124) all_13_0 = 2
% 13.80/2.99 | | | |
% 13.80/2.99 | | | | REDUCE: (13), (124) imply:
% 13.80/2.99 | | | | (125) $false
% 13.80/2.99 | | | |
% 13.80/2.99 | | | | CLOSE: (125) is inconsistent.
% 13.80/2.99 | | | |
% 13.80/2.99 | | | End of split
% 13.80/2.99 | | |
% 13.80/2.99 | | End of split
% 13.80/2.99 | |
% 13.80/2.99 | Case 2:
% 13.80/2.99 | |
% 13.80/2.99 | | (126) all_22_0 = 0
% 13.80/2.99 | |
% 13.80/2.99 | | REDUCE: (27), (126) imply:
% 13.80/2.99 | | (127) in(3, empty) = 0
% 13.80/2.99 | |
% 13.80/2.99 | | GROUND_INST: instantiating (1) with 3, simplifying with (127) gives:
% 13.80/2.99 | | (128) $false
% 13.80/2.99 | |
% 13.80/2.99 | | CLOSE: (128) is inconsistent.
% 13.80/2.99 | |
% 13.80/2.99 | End of split
% 13.80/2.99 |
% 13.80/2.99 End of proof
% 13.80/2.99 % SZS output end Proof for theBenchmark
% 13.80/2.99
% 13.80/2.99 2319ms
%------------------------------------------------------------------------------