TSTP Solution File: GEO083+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO083+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n025.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 23:21:19 EDT 2023
% Result : Theorem 7.73s 1.76s
% Output : Proof 10.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO083+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n025.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
% 0.20/0.34 % CPULimit : 300
% 0.20/0.34 % WCLimit : 300
% 0.20/0.34 % DateTime : Wed Aug 30 00:22:55 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.05/1.09 Prover 4: Preprocessing ...
% 3.05/1.09 Prover 1: Preprocessing ...
% 3.05/1.12 Prover 5: Preprocessing ...
% 3.05/1.12 Prover 3: Preprocessing ...
% 3.05/1.12 Prover 2: Preprocessing ...
% 3.05/1.12 Prover 6: Preprocessing ...
% 3.05/1.12 Prover 0: Preprocessing ...
% 5.98/1.50 Prover 2: Proving ...
% 5.98/1.51 Prover 5: Proving ...
% 5.98/1.53 Prover 3: Warning: ignoring some quantifiers
% 5.98/1.55 Prover 6: Proving ...
% 5.98/1.55 Prover 3: Constructing countermodel ...
% 6.63/1.57 Prover 1: Warning: ignoring some quantifiers
% 6.80/1.59 Prover 1: Constructing countermodel ...
% 7.73/1.76 Prover 3: proved (1111ms)
% 7.73/1.76
% 7.73/1.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.73/1.76
% 7.73/1.76 Prover 2: stopped
% 7.73/1.76 Prover 5: stopped
% 8.20/1.78 Prover 6: stopped
% 8.20/1.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.20/1.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.20/1.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.20/1.81 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.20/1.83 Prover 8: Preprocessing ...
% 8.20/1.83 Prover 7: Preprocessing ...
% 8.20/1.86 Prover 10: Preprocessing ...
% 8.20/1.86 Prover 11: Preprocessing ...
% 8.96/1.90 Prover 1: Found proof (size 41)
% 8.96/1.90 Prover 1: proved (1266ms)
% 8.96/1.91 Prover 10: Warning: ignoring some quantifiers
% 8.96/1.92 Prover 7: Warning: ignoring some quantifiers
% 8.96/1.92 Prover 10: Constructing countermodel ...
% 9.24/1.92 Prover 10: stopped
% 9.24/1.93 Prover 7: Constructing countermodel ...
% 9.24/1.93 Prover 11: stopped
% 9.24/1.93 Prover 7: stopped
% 9.24/1.95 Prover 8: Warning: ignoring some quantifiers
% 9.24/1.97 Prover 8: Constructing countermodel ...
% 9.24/1.97 Prover 8: stopped
% 9.24/1.98 Prover 4: Warning: ignoring some quantifiers
% 9.24/2.02 Prover 4: Constructing countermodel ...
% 9.79/2.03 Prover 4: stopped
% 9.79/2.07 Prover 0: Proving ...
% 9.79/2.07 Prover 0: stopped
% 9.79/2.07
% 9.79/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.79/2.07
% 9.79/2.08 % SZS output start Proof for theBenchmark
% 9.79/2.08 Assumptions after simplification:
% 9.79/2.08 ---------------------------------
% 9.79/2.08
% 9.79/2.08 (corollary_2_6_1)
% 10.31/2.11 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 10.31/2.11 $i] : ? [v6: int] : ( ~ (v6 = 0) & meet(v3, v0, v2) = 0 & meet(v3, v0, v1)
% 10.31/2.11 = 0 & sum(v0, v2) = v5 & sum(v0, v1) = v4 & part_of(v4, v5) = v6 &
% 10.31/2.11 part_of(v1, v2) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.31/2.11
% 10.31/2.11 (part_of_defn)
% 10.31/2.11 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (part_of(v1, v0) = v2)
% 10.31/2.11 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 10.31/2.11 incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4 & $i(v3))) & ! [v0: $i]
% 10.31/2.11 : ! [v1: $i] : ( ~ (part_of(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2:
% 10.31/2.11 $i] : ! [v3: int] : (v3 = 0 | ~ (incident_c(v2, v0) = v3) | ~ $i(v2) |
% 10.31/2.11 ? [v4: int] : ( ~ (v4 = 0) & incident_c(v2, v1) = v4)))
% 10.31/2.11
% 10.31/2.11 (sum_defn)
% 10.31/2.12 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (sum(v1,
% 10.31/2.12 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5:
% 10.31/2.12 any] : ? [v6: any] : ? [v7: any] : (incident_c(v4, v2) = v7 &
% 10.31/2.12 incident_c(v4, v1) = v6 & incident_c(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0)
% 10.31/2.12 | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) & ! [v0:
% 10.31/2.12 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sum(v1, v2) = v0) | ~ $i(v2) | ~
% 10.31/2.12 $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 10.31/2.12 (incident_c(v3, v0) = v4) | ~ $i(v3) | ? [v5: int] : ? [v6: int] : (
% 10.31/2.12 ~ (v6 = 0) & ~ (v5 = 0) & incident_c(v3, v2) = v6 & incident_c(v3,
% 10.31/2.12 v1) = v5)) & ! [v3: $i] : ( ~ (incident_c(v3, v0) = 0) | ~ $i(v3)
% 10.31/2.12 | ? [v4: any] : ? [v5: any] : (incident_c(v3, v2) = v5 &
% 10.31/2.12 incident_c(v3, v1) = v4 & (v5 = 0 | v4 = 0)))))
% 10.31/2.12
% 10.31/2.12 (function-axioms)
% 10.31/2.13 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.31/2.13 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4,
% 10.31/2.13 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 10.31/2.13 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~
% 10.31/2.13 (inner_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.31/2.13 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.31/2.13 (end_point(v3, v2) = v1) | ~ (end_point(v3, v2) = v0)) & ! [v0: $i] : !
% 10.31/2.13 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~
% 10.31/2.13 (sum(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.31/2.13 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (part_of(v3,
% 10.31/2.13 v2) = v1) | ~ (part_of(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 10.31/2.13 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.31/2.13 (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0)) & ! [v0:
% 10.31/2.13 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 10.31/2.13 ~ (open(v2) = v1) | ~ (open(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 10.31/2.13 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (closed(v2) = v1) | ~
% 10.31/2.13 (closed(v2) = v0))
% 10.31/2.13
% 10.31/2.13 Further assumptions not needed in the proof:
% 10.31/2.13 --------------------------------------------
% 10.31/2.13 c1, c2, c3, c4, c5, c6, c7, c8, c9, closed_defn, end_point_defn,
% 10.31/2.13 inner_point_defn, meet_defn, open_defn
% 10.31/2.13
% 10.31/2.13 Those formulas are unsatisfiable:
% 10.31/2.13 ---------------------------------
% 10.31/2.13
% 10.31/2.13 Begin of proof
% 10.31/2.13 |
% 10.31/2.13 | ALPHA: (part_of_defn) implies:
% 10.31/2.13 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (part_of(v1, v0) = 0) | ~ $i(v1) | ~
% 10.31/2.13 | $i(v0) | ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (incident_c(v2,
% 10.31/2.13 | v0) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) &
% 10.31/2.13 | incident_c(v2, v1) = v4)))
% 10.31/2.14 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (part_of(v1,
% 10.31/2.14 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] :
% 10.31/2.14 | ( ~ (v4 = 0) & incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4 &
% 10.31/2.14 | $i(v3)))
% 10.31/2.14 |
% 10.31/2.14 | ALPHA: (sum_defn) implies:
% 10.31/2.14 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sum(v1, v2) = v0) | ~
% 10.31/2.14 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: int] : (v4 =
% 10.31/2.14 | 0 | ~ (incident_c(v3, v0) = v4) | ~ $i(v3) | ? [v5: int] : ?
% 10.31/2.14 | [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & incident_c(v3, v2) = v6
% 10.31/2.14 | & incident_c(v3, v1) = v5)) & ! [v3: $i] : ( ~ (incident_c(v3,
% 10.31/2.14 | v0) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] :
% 10.31/2.14 | (incident_c(v3, v2) = v5 & incident_c(v3, v1) = v4 & (v5 = 0 | v4
% 10.31/2.14 | = 0)))))
% 10.31/2.14 |
% 10.31/2.14 | ALPHA: (function-axioms) implies:
% 10.31/2.14 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.31/2.14 | ! [v3: $i] : (v1 = v0 | ~ (incident_c(v3, v2) = v1) | ~
% 10.31/2.14 | (incident_c(v3, v2) = v0))
% 10.31/2.14 |
% 10.31/2.14 | DELTA: instantiating (corollary_2_6_1) with fresh symbols all_19_0, all_19_1,
% 10.31/2.14 | all_19_2, all_19_3, all_19_4, all_19_5, all_19_6 gives:
% 10.31/2.14 | (5) ~ (all_19_0 = 0) & meet(all_19_3, all_19_6, all_19_4) = 0 &
% 10.31/2.14 | meet(all_19_3, all_19_6, all_19_5) = 0 & sum(all_19_6, all_19_4) =
% 10.31/2.14 | all_19_1 & sum(all_19_6, all_19_5) = all_19_2 & part_of(all_19_2,
% 10.31/2.14 | all_19_1) = all_19_0 & part_of(all_19_5, all_19_4) = 0 & $i(all_19_1)
% 10.31/2.14 | & $i(all_19_2) & $i(all_19_3) & $i(all_19_4) & $i(all_19_5) &
% 10.31/2.14 | $i(all_19_6)
% 10.31/2.14 |
% 10.31/2.14 | ALPHA: (5) implies:
% 10.31/2.14 | (6) ~ (all_19_0 = 0)
% 10.31/2.14 | (7) $i(all_19_6)
% 10.31/2.14 | (8) $i(all_19_5)
% 10.31/2.14 | (9) $i(all_19_4)
% 10.31/2.15 | (10) $i(all_19_2)
% 10.31/2.15 | (11) $i(all_19_1)
% 10.31/2.15 | (12) part_of(all_19_5, all_19_4) = 0
% 10.31/2.15 | (13) part_of(all_19_2, all_19_1) = all_19_0
% 10.31/2.15 | (14) sum(all_19_6, all_19_5) = all_19_2
% 10.31/2.15 | (15) sum(all_19_6, all_19_4) = all_19_1
% 10.31/2.15 |
% 10.31/2.15 | GROUND_INST: instantiating (1) with all_19_4, all_19_5, simplifying with (8),
% 10.31/2.15 | (9), (12) gives:
% 10.31/2.15 | (16) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (incident_c(v0, all_19_4) =
% 10.31/2.15 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & incident_c(v0,
% 10.31/2.15 | all_19_5) = v2))
% 10.31/2.15 |
% 10.31/2.15 | GROUND_INST: instantiating (2) with all_19_1, all_19_2, all_19_0, simplifying
% 10.31/2.15 | with (10), (11), (13) gives:
% 10.31/2.15 | (17) all_19_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 10.31/2.15 | incident_c(v0, all_19_1) = v1 & incident_c(v0, all_19_2) = 0 &
% 10.31/2.15 | $i(v0))
% 10.31/2.15 |
% 10.31/2.15 | GROUND_INST: instantiating (3) with all_19_2, all_19_6, all_19_5, simplifying
% 10.31/2.15 | with (7), (8), (10), (14) gives:
% 10.31/2.15 | (18) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (incident_c(v0, all_19_2) =
% 10.31/2.15 | v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ( ~ (v3 = 0) & ~
% 10.31/2.15 | (v2 = 0) & incident_c(v0, all_19_5) = v3 & incident_c(v0,
% 10.31/2.15 | all_19_6) = v2)) & ! [v0: $i] : ( ~ (incident_c(v0, all_19_2) =
% 10.31/2.15 | 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (incident_c(v0,
% 10.31/2.15 | all_19_5) = v2 & incident_c(v0, all_19_6) = v1 & (v2 = 0 | v1 =
% 10.31/2.15 | 0)))
% 10.31/2.15 |
% 10.31/2.15 | ALPHA: (18) implies:
% 10.31/2.15 | (19) ! [v0: $i] : ( ~ (incident_c(v0, all_19_2) = 0) | ~ $i(v0) | ? [v1:
% 10.31/2.15 | any] : ? [v2: any] : (incident_c(v0, all_19_5) = v2 &
% 10.31/2.15 | incident_c(v0, all_19_6) = v1 & (v2 = 0 | v1 = 0)))
% 10.31/2.15 |
% 10.31/2.15 | GROUND_INST: instantiating (3) with all_19_1, all_19_6, all_19_4, simplifying
% 10.31/2.15 | with (7), (9), (11), (15) gives:
% 10.31/2.15 | (20) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (incident_c(v0, all_19_1) =
% 10.31/2.15 | v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ( ~ (v3 = 0) & ~
% 10.31/2.15 | (v2 = 0) & incident_c(v0, all_19_4) = v3 & incident_c(v0,
% 10.31/2.15 | all_19_6) = v2)) & ! [v0: $i] : ( ~ (incident_c(v0, all_19_1) =
% 10.31/2.15 | 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (incident_c(v0,
% 10.31/2.15 | all_19_4) = v2 & incident_c(v0, all_19_6) = v1 & (v2 = 0 | v1 =
% 10.31/2.15 | 0)))
% 10.31/2.15 |
% 10.31/2.15 | ALPHA: (20) implies:
% 10.31/2.16 | (21) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (incident_c(v0, all_19_1) =
% 10.31/2.16 | v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ( ~ (v3 = 0) & ~
% 10.31/2.16 | (v2 = 0) & incident_c(v0, all_19_4) = v3 & incident_c(v0,
% 10.31/2.16 | all_19_6) = v2))
% 10.31/2.16 |
% 10.31/2.16 | BETA: splitting (17) gives:
% 10.31/2.16 |
% 10.31/2.16 | Case 1:
% 10.31/2.16 | |
% 10.31/2.16 | | (22) all_19_0 = 0
% 10.31/2.16 | |
% 10.31/2.16 | | REDUCE: (6), (22) imply:
% 10.31/2.16 | | (23) $false
% 10.31/2.16 | |
% 10.31/2.16 | | CLOSE: (23) is inconsistent.
% 10.31/2.16 | |
% 10.31/2.16 | Case 2:
% 10.31/2.16 | |
% 10.31/2.16 | | (24) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & incident_c(v0, all_19_1)
% 10.31/2.16 | | = v1 & incident_c(v0, all_19_2) = 0 & $i(v0))
% 10.31/2.16 | |
% 10.31/2.16 | | DELTA: instantiating (24) with fresh symbols all_38_0, all_38_1 gives:
% 10.31/2.16 | | (25) ~ (all_38_0 = 0) & incident_c(all_38_1, all_19_1) = all_38_0 &
% 10.31/2.16 | | incident_c(all_38_1, all_19_2) = 0 & $i(all_38_1)
% 10.31/2.16 | |
% 10.31/2.16 | | ALPHA: (25) implies:
% 10.31/2.16 | | (26) ~ (all_38_0 = 0)
% 10.31/2.16 | | (27) $i(all_38_1)
% 10.31/2.16 | | (28) incident_c(all_38_1, all_19_2) = 0
% 10.31/2.16 | | (29) incident_c(all_38_1, all_19_1) = all_38_0
% 10.31/2.16 | |
% 10.31/2.16 | | GROUND_INST: instantiating (19) with all_38_1, simplifying with (27), (28)
% 10.31/2.16 | | gives:
% 10.31/2.16 | | (30) ? [v0: any] : ? [v1: any] : (incident_c(all_38_1, all_19_5) = v1 &
% 10.31/2.16 | | incident_c(all_38_1, all_19_6) = v0 & (v1 = 0 | v0 = 0))
% 10.31/2.16 | |
% 10.31/2.16 | | GROUND_INST: instantiating (21) with all_38_1, all_38_0, simplifying with
% 10.31/2.16 | | (27), (29) gives:
% 10.31/2.16 | | (31) all_38_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 =
% 10.31/2.16 | | 0) & incident_c(all_38_1, all_19_4) = v1 & incident_c(all_38_1,
% 10.31/2.16 | | all_19_6) = v0)
% 10.31/2.16 | |
% 10.31/2.16 | | DELTA: instantiating (30) with fresh symbols all_45_0, all_45_1 gives:
% 10.31/2.16 | | (32) incident_c(all_38_1, all_19_5) = all_45_0 & incident_c(all_38_1,
% 10.31/2.16 | | all_19_6) = all_45_1 & (all_45_0 = 0 | all_45_1 = 0)
% 10.31/2.16 | |
% 10.31/2.16 | | ALPHA: (32) implies:
% 10.31/2.16 | | (33) incident_c(all_38_1, all_19_6) = all_45_1
% 10.31/2.16 | | (34) incident_c(all_38_1, all_19_5) = all_45_0
% 10.31/2.16 | | (35) all_45_0 = 0 | all_45_1 = 0
% 10.31/2.16 | |
% 10.31/2.16 | | BETA: splitting (31) gives:
% 10.31/2.16 | |
% 10.31/2.16 | | Case 1:
% 10.31/2.16 | | |
% 10.31/2.16 | | | (36) all_38_0 = 0
% 10.31/2.16 | | |
% 10.31/2.16 | | | REDUCE: (26), (36) imply:
% 10.31/2.16 | | | (37) $false
% 10.31/2.16 | | |
% 10.31/2.16 | | | CLOSE: (37) is inconsistent.
% 10.31/2.16 | | |
% 10.31/2.16 | | Case 2:
% 10.31/2.16 | | |
% 10.31/2.16 | | | (38) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 10.31/2.16 | | | incident_c(all_38_1, all_19_4) = v1 & incident_c(all_38_1,
% 10.31/2.16 | | | all_19_6) = v0)
% 10.31/2.16 | | |
% 10.31/2.16 | | | DELTA: instantiating (38) with fresh symbols all_51_0, all_51_1 gives:
% 10.31/2.17 | | | (39) ~ (all_51_0 = 0) & ~ (all_51_1 = 0) & incident_c(all_38_1,
% 10.31/2.17 | | | all_19_4) = all_51_0 & incident_c(all_38_1, all_19_6) = all_51_1
% 10.31/2.17 | | |
% 10.31/2.17 | | | ALPHA: (39) implies:
% 10.31/2.17 | | | (40) ~ (all_51_1 = 0)
% 10.31/2.17 | | | (41) ~ (all_51_0 = 0)
% 10.31/2.17 | | | (42) incident_c(all_38_1, all_19_6) = all_51_1
% 10.31/2.17 | | | (43) incident_c(all_38_1, all_19_4) = all_51_0
% 10.31/2.17 | | |
% 10.31/2.17 | | | GROUND_INST: instantiating (4) with all_45_1, all_51_1, all_19_6,
% 10.31/2.17 | | | all_38_1, simplifying with (33), (42) gives:
% 10.31/2.17 | | | (44) all_51_1 = all_45_1
% 10.31/2.17 | | |
% 10.31/2.17 | | | REDUCE: (40), (44) imply:
% 10.31/2.17 | | | (45) ~ (all_45_1 = 0)
% 10.31/2.17 | | |
% 10.31/2.17 | | | BETA: splitting (35) gives:
% 10.31/2.17 | | |
% 10.31/2.17 | | | Case 1:
% 10.31/2.17 | | | |
% 10.31/2.17 | | | | (46) all_45_0 = 0
% 10.31/2.17 | | | |
% 10.31/2.17 | | | | REDUCE: (34), (46) imply:
% 10.31/2.17 | | | | (47) incident_c(all_38_1, all_19_5) = 0
% 10.31/2.17 | | | |
% 10.31/2.17 | | | | GROUND_INST: instantiating (16) with all_38_1, all_51_0, simplifying
% 10.31/2.17 | | | | with (27), (43) gives:
% 10.31/2.17 | | | | (48) all_51_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 10.31/2.17 | | | | incident_c(all_38_1, all_19_5) = v0)
% 10.31/2.17 | | | |
% 10.31/2.17 | | | | BETA: splitting (48) gives:
% 10.31/2.17 | | | |
% 10.31/2.17 | | | | Case 1:
% 10.31/2.17 | | | | |
% 10.31/2.17 | | | | | (49) all_51_0 = 0
% 10.31/2.17 | | | | |
% 10.31/2.17 | | | | | REDUCE: (41), (49) imply:
% 10.31/2.17 | | | | | (50) $false
% 10.31/2.17 | | | | |
% 10.31/2.17 | | | | | CLOSE: (50) is inconsistent.
% 10.31/2.17 | | | | |
% 10.31/2.17 | | | | Case 2:
% 10.31/2.17 | | | | |
% 10.31/2.17 | | | | | (51) ? [v0: int] : ( ~ (v0 = 0) & incident_c(all_38_1, all_19_5) =
% 10.31/2.17 | | | | | v0)
% 10.31/2.17 | | | | |
% 10.31/2.17 | | | | | DELTA: instantiating (51) with fresh symbol all_74_0 gives:
% 10.31/2.17 | | | | | (52) ~ (all_74_0 = 0) & incident_c(all_38_1, all_19_5) = all_74_0
% 10.31/2.17 | | | | |
% 10.31/2.17 | | | | | ALPHA: (52) implies:
% 10.31/2.17 | | | | | (53) ~ (all_74_0 = 0)
% 10.31/2.17 | | | | | (54) incident_c(all_38_1, all_19_5) = all_74_0
% 10.31/2.17 | | | | |
% 10.31/2.17 | | | | | GROUND_INST: instantiating (4) with 0, all_74_0, all_19_5, all_38_1,
% 10.31/2.17 | | | | | simplifying with (47), (54) gives:
% 10.31/2.17 | | | | | (55) all_74_0 = 0
% 10.31/2.17 | | | | |
% 10.31/2.17 | | | | | REDUCE: (53), (55) imply:
% 10.31/2.17 | | | | | (56) $false
% 10.31/2.17 | | | | |
% 10.31/2.17 | | | | | CLOSE: (56) is inconsistent.
% 10.31/2.17 | | | | |
% 10.31/2.17 | | | | End of split
% 10.31/2.17 | | | |
% 10.31/2.17 | | | Case 2:
% 10.31/2.17 | | | |
% 10.31/2.17 | | | | (57) all_45_1 = 0
% 10.31/2.17 | | | |
% 10.31/2.17 | | | | REDUCE: (45), (57) imply:
% 10.31/2.17 | | | | (58) $false
% 10.31/2.17 | | | |
% 10.31/2.17 | | | | CLOSE: (58) is inconsistent.
% 10.31/2.17 | | | |
% 10.31/2.17 | | | End of split
% 10.31/2.17 | | |
% 10.31/2.17 | | End of split
% 10.31/2.17 | |
% 10.31/2.17 | End of split
% 10.31/2.17 |
% 10.31/2.17 End of proof
% 10.65/2.17 % SZS output end Proof for theBenchmark
% 10.65/2.17
% 10.65/2.17 1558ms
%------------------------------------------------------------------------------