TSTP Solution File: GEO084+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO084+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 : n016.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 7.19s 1.75s
% Output : Proof 9.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO084+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n016.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 21:53:01 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.62/0.60 ________ _____
% 0.62/0.60 ___ __ \_________(_)________________________________
% 0.62/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.62/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.62/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.62/0.60
% 0.62/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.62/0.60 (2023-06-19)
% 0.62/0.60
% 0.62/0.60 (c) Philipp Rümmer, 2009-2023
% 0.62/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.62/0.60 Amanda Stjerna.
% 0.62/0.60 Free software under BSD-3-Clause.
% 0.62/0.60
% 0.62/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.62/0.60
% 0.62/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.65/0.61 Running up to 7 provers in parallel.
% 0.65/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.65/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.65/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.65/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.65/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.65/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.65/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.71/1.11 Prover 4: Preprocessing ...
% 2.71/1.12 Prover 1: Preprocessing ...
% 3.28/1.17 Prover 6: Preprocessing ...
% 3.28/1.17 Prover 0: Preprocessing ...
% 3.28/1.18 Prover 5: Preprocessing ...
% 3.28/1.18 Prover 2: Preprocessing ...
% 3.28/1.18 Prover 3: Preprocessing ...
% 5.99/1.54 Prover 2: Proving ...
% 5.99/1.56 Prover 5: Proving ...
% 5.99/1.56 Prover 1: Warning: ignoring some quantifiers
% 5.99/1.57 Prover 3: Warning: ignoring some quantifiers
% 5.99/1.59 Prover 6: Proving ...
% 5.99/1.59 Prover 1: Constructing countermodel ...
% 5.99/1.59 Prover 3: Constructing countermodel ...
% 7.19/1.75 Prover 3: proved (1133ms)
% 7.19/1.75
% 7.19/1.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.19/1.75
% 7.19/1.75 Prover 2: stopped
% 7.19/1.75 Prover 5: stopped
% 7.19/1.75 Prover 6: stopped
% 7.19/1.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.19/1.76 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.19/1.76 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.19/1.76 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.08/1.82 Prover 10: Preprocessing ...
% 8.10/1.83 Prover 11: Preprocessing ...
% 8.10/1.83 Prover 1: Found proof (size 39)
% 8.10/1.86 Prover 1: proved (1232ms)
% 8.10/1.87 Prover 7: Preprocessing ...
% 8.10/1.87 Prover 8: Preprocessing ...
% 8.10/1.87 Prover 10: stopped
% 8.10/1.89 Prover 7: Warning: ignoring some quantifiers
% 8.70/1.91 Prover 7: Constructing countermodel ...
% 8.70/1.91 Prover 7: stopped
% 8.70/1.92 Prover 11: stopped
% 8.70/1.95 Prover 8: Warning: ignoring some quantifiers
% 8.70/1.96 Prover 8: Constructing countermodel ...
% 8.70/1.97 Prover 8: stopped
% 9.25/2.00 Prover 4: Warning: ignoring some quantifiers
% 9.25/2.03 Prover 4: Constructing countermodel ...
% 9.25/2.04 Prover 4: stopped
% 9.73/2.08 Prover 0: Proving ...
% 9.73/2.09 Prover 0: stopped
% 9.80/2.09
% 9.80/2.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.80/2.09
% 9.80/2.10 % SZS output start Proof for theBenchmark
% 9.80/2.11 Assumptions after simplification:
% 9.80/2.11 ---------------------------------
% 9.80/2.11
% 9.80/2.11 (corollary_2_6_2)
% 9.90/2.15 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 9.90/2.15 int] : ( ~ (v5 = 0) & meet(v3, v0, v1) = 0 & sum(v0, v1) = v4 & part_of(v4,
% 9.90/2.15 v2) = v5 & part_of(v1, v2) = 0 & part_of(v0, v2) = 0 & $i(v4) & $i(v3) &
% 9.90/2.15 $i(v2) & $i(v1) & $i(v0))
% 9.90/2.15
% 9.90/2.15 (part_of_defn)
% 9.90/2.15 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (part_of(v1, v0) = v2)
% 9.90/2.16 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 9.90/2.16 incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4 & $i(v3))) & ! [v0: $i]
% 9.90/2.16 : ! [v1: $i] : ( ~ (part_of(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2:
% 9.90/2.16 $i] : ! [v3: int] : (v3 = 0 | ~ (incident_c(v2, v0) = v3) | ~ $i(v2) |
% 9.90/2.16 ? [v4: int] : ( ~ (v4 = 0) & incident_c(v2, v1) = v4)))
% 9.90/2.16
% 9.90/2.16 (sum_defn)
% 9.90/2.16 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (sum(v1,
% 9.90/2.16 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5:
% 9.90/2.16 any] : ? [v6: any] : ? [v7: any] : (incident_c(v4, v2) = v7 &
% 9.90/2.16 incident_c(v4, v1) = v6 & incident_c(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0)
% 9.90/2.16 | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) & ! [v0:
% 9.90/2.16 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sum(v1, v2) = v0) | ~ $i(v2) | ~
% 9.90/2.16 $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 9.90/2.16 (incident_c(v3, v0) = v4) | ~ $i(v3) | ? [v5: int] : ? [v6: int] : (
% 9.90/2.17 ~ (v6 = 0) & ~ (v5 = 0) & incident_c(v3, v2) = v6 & incident_c(v3,
% 9.90/2.17 v1) = v5)) & ! [v3: $i] : ( ~ (incident_c(v3, v0) = 0) | ~ $i(v3)
% 9.90/2.17 | ? [v4: any] : ? [v5: any] : (incident_c(v3, v2) = v5 &
% 9.90/2.17 incident_c(v3, v1) = v4 & (v5 = 0 | v4 = 0)))))
% 9.90/2.17
% 9.90/2.17 (function-axioms)
% 9.90/2.17 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 9.90/2.17 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4,
% 9.90/2.17 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 9.90/2.17 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~
% 9.90/2.17 (inner_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.90/2.17 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.90/2.17 (end_point(v3, v2) = v1) | ~ (end_point(v3, v2) = v0)) & ! [v0: $i] : !
% 9.90/2.17 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~
% 9.90/2.17 (sum(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.90/2.17 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (part_of(v3,
% 9.90/2.17 v2) = v1) | ~ (part_of(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 9.90/2.17 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.90/2.17 (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0)) & ! [v0:
% 9.90/2.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.90/2.17 ~ (open(v2) = v1) | ~ (open(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 9.90/2.17 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (closed(v2) = v1) | ~
% 9.90/2.17 (closed(v2) = v0))
% 9.90/2.17
% 9.90/2.17 Further assumptions not needed in the proof:
% 9.90/2.17 --------------------------------------------
% 9.90/2.17 c1, c2, c3, c4, c5, c6, c7, c8, c9, closed_defn, end_point_defn,
% 9.90/2.17 inner_point_defn, meet_defn, open_defn
% 9.90/2.17
% 9.90/2.17 Those formulas are unsatisfiable:
% 9.90/2.17 ---------------------------------
% 9.90/2.17
% 9.90/2.17 Begin of proof
% 9.90/2.17 |
% 9.90/2.17 | ALPHA: (part_of_defn) implies:
% 9.90/2.18 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (part_of(v1, v0) = 0) | ~ $i(v1) | ~
% 9.90/2.18 | $i(v0) | ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (incident_c(v2,
% 9.90/2.18 | v0) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) &
% 9.90/2.18 | incident_c(v2, v1) = v4)))
% 9.90/2.18 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (part_of(v1,
% 9.90/2.18 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] :
% 9.90/2.18 | ( ~ (v4 = 0) & incident_c(v3, v1) = 0 & incident_c(v3, v0) = v4 &
% 9.90/2.18 | $i(v3)))
% 9.90/2.18 |
% 9.90/2.18 | ALPHA: (sum_defn) implies:
% 9.90/2.18 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sum(v1, v2) = v0) | ~
% 9.90/2.18 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: int] : (v4 =
% 9.90/2.18 | 0 | ~ (incident_c(v3, v0) = v4) | ~ $i(v3) | ? [v5: int] : ?
% 9.90/2.18 | [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & incident_c(v3, v2) = v6
% 9.90/2.18 | & incident_c(v3, v1) = v5)) & ! [v3: $i] : ( ~ (incident_c(v3,
% 9.90/2.18 | v0) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] :
% 9.90/2.18 | (incident_c(v3, v2) = v5 & incident_c(v3, v1) = v4 & (v5 = 0 | v4
% 9.90/2.18 | = 0)))))
% 9.90/2.18 |
% 9.90/2.18 | ALPHA: (function-axioms) implies:
% 9.90/2.18 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.90/2.18 | ! [v3: $i] : (v1 = v0 | ~ (incident_c(v3, v2) = v1) | ~
% 9.90/2.18 | (incident_c(v3, v2) = v0))
% 9.90/2.18 |
% 9.90/2.18 | DELTA: instantiating (corollary_2_6_2) with fresh symbols all_19_0, all_19_1,
% 9.90/2.18 | all_19_2, all_19_3, all_19_4, all_19_5 gives:
% 9.90/2.18 | (5) ~ (all_19_0 = 0) & meet(all_19_2, all_19_5, all_19_4) = 0 &
% 9.90/2.18 | sum(all_19_5, all_19_4) = all_19_1 & part_of(all_19_1, all_19_3) =
% 9.90/2.18 | all_19_0 & part_of(all_19_4, all_19_3) = 0 & part_of(all_19_5,
% 9.90/2.18 | all_19_3) = 0 & $i(all_19_1) & $i(all_19_2) & $i(all_19_3) &
% 9.90/2.18 | $i(all_19_4) & $i(all_19_5)
% 9.90/2.18 |
% 9.90/2.18 | ALPHA: (5) implies:
% 9.90/2.18 | (6) ~ (all_19_0 = 0)
% 9.90/2.18 | (7) $i(all_19_5)
% 9.90/2.18 | (8) $i(all_19_4)
% 9.90/2.18 | (9) $i(all_19_3)
% 9.90/2.18 | (10) $i(all_19_1)
% 9.90/2.18 | (11) part_of(all_19_5, all_19_3) = 0
% 9.90/2.18 | (12) part_of(all_19_4, all_19_3) = 0
% 9.90/2.19 | (13) part_of(all_19_1, all_19_3) = all_19_0
% 9.90/2.19 | (14) sum(all_19_5, all_19_4) = all_19_1
% 9.90/2.19 |
% 9.90/2.19 | GROUND_INST: instantiating (1) with all_19_3, all_19_5, simplifying with (7),
% 9.90/2.19 | (9), (11) gives:
% 9.90/2.19 | (15) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (incident_c(v0, all_19_3) =
% 9.90/2.19 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & incident_c(v0,
% 9.90/2.19 | all_19_5) = v2))
% 9.90/2.19 |
% 9.90/2.19 | GROUND_INST: instantiating (1) with all_19_3, all_19_4, simplifying with (8),
% 9.90/2.19 | (9), (12) gives:
% 9.90/2.19 | (16) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (incident_c(v0, all_19_3) =
% 9.90/2.19 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & incident_c(v0,
% 9.90/2.19 | all_19_4) = v2))
% 9.90/2.19 |
% 9.90/2.19 | GROUND_INST: instantiating (2) with all_19_3, all_19_1, all_19_0, simplifying
% 9.90/2.19 | with (9), (10), (13) gives:
% 9.90/2.19 | (17) all_19_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 9.90/2.19 | incident_c(v0, all_19_1) = 0 & incident_c(v0, all_19_3) = v1 &
% 9.90/2.19 | $i(v0))
% 9.90/2.19 |
% 9.90/2.19 | GROUND_INST: instantiating (3) with all_19_1, all_19_5, all_19_4, simplifying
% 9.90/2.19 | with (7), (8), (10), (14) gives:
% 9.90/2.19 | (18) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (incident_c(v0, all_19_1) =
% 9.90/2.19 | v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ( ~ (v3 = 0) & ~
% 9.90/2.19 | (v2 = 0) & incident_c(v0, all_19_4) = v3 & incident_c(v0,
% 9.90/2.19 | all_19_5) = v2)) & ! [v0: $i] : ( ~ (incident_c(v0, all_19_1) =
% 9.90/2.19 | 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (incident_c(v0,
% 9.90/2.19 | all_19_4) = v2 & incident_c(v0, all_19_5) = v1 & (v2 = 0 | v1 =
% 9.90/2.19 | 0)))
% 9.90/2.19 |
% 9.90/2.19 | ALPHA: (18) implies:
% 9.90/2.19 | (19) ! [v0: $i] : ( ~ (incident_c(v0, all_19_1) = 0) | ~ $i(v0) | ? [v1:
% 9.90/2.19 | any] : ? [v2: any] : (incident_c(v0, all_19_4) = v2 &
% 9.90/2.19 | incident_c(v0, all_19_5) = v1 & (v2 = 0 | v1 = 0)))
% 9.90/2.19 |
% 9.90/2.19 | BETA: splitting (17) gives:
% 9.90/2.19 |
% 9.90/2.19 | Case 1:
% 9.90/2.19 | |
% 9.90/2.19 | | (20) all_19_0 = 0
% 9.90/2.19 | |
% 9.90/2.19 | | REDUCE: (6), (20) imply:
% 9.90/2.19 | | (21) $false
% 9.90/2.19 | |
% 9.90/2.19 | | CLOSE: (21) is inconsistent.
% 9.90/2.19 | |
% 9.90/2.20 | Case 2:
% 9.90/2.20 | |
% 9.90/2.20 | | (22) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & incident_c(v0, all_19_1)
% 9.90/2.20 | | = 0 & incident_c(v0, all_19_3) = v1 & $i(v0))
% 9.90/2.20 | |
% 9.90/2.20 | | DELTA: instantiating (22) with fresh symbols all_37_0, all_37_1 gives:
% 9.90/2.20 | | (23) ~ (all_37_0 = 0) & incident_c(all_37_1, all_19_1) = 0 &
% 9.90/2.20 | | incident_c(all_37_1, all_19_3) = all_37_0 & $i(all_37_1)
% 9.90/2.20 | |
% 9.90/2.20 | | ALPHA: (23) implies:
% 9.90/2.20 | | (24) ~ (all_37_0 = 0)
% 9.90/2.20 | | (25) $i(all_37_1)
% 9.90/2.20 | | (26) incident_c(all_37_1, all_19_3) = all_37_0
% 9.90/2.20 | | (27) incident_c(all_37_1, all_19_1) = 0
% 9.90/2.20 | |
% 9.90/2.20 | | GROUND_INST: instantiating (16) with all_37_1, all_37_0, simplifying with
% 9.90/2.20 | | (25), (26) gives:
% 9.90/2.20 | | (28) all_37_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & incident_c(all_37_1,
% 9.90/2.20 | | all_19_4) = v0)
% 9.90/2.20 | |
% 9.90/2.20 | | GROUND_INST: instantiating (15) with all_37_1, all_37_0, simplifying with
% 9.90/2.20 | | (25), (26) gives:
% 9.90/2.20 | | (29) all_37_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & incident_c(all_37_1,
% 9.90/2.20 | | all_19_5) = v0)
% 9.90/2.20 | |
% 9.90/2.20 | | GROUND_INST: instantiating (19) with all_37_1, simplifying with (25), (27)
% 9.90/2.20 | | gives:
% 9.90/2.20 | | (30) ? [v0: any] : ? [v1: any] : (incident_c(all_37_1, all_19_4) = v1 &
% 9.90/2.20 | | incident_c(all_37_1, all_19_5) = v0 & (v1 = 0 | v0 = 0))
% 9.90/2.20 | |
% 9.90/2.20 | | DELTA: instantiating (30) with fresh symbols all_44_0, all_44_1 gives:
% 9.90/2.20 | | (31) incident_c(all_37_1, all_19_4) = all_44_0 & incident_c(all_37_1,
% 9.90/2.20 | | all_19_5) = all_44_1 & (all_44_0 = 0 | all_44_1 = 0)
% 9.90/2.20 | |
% 9.90/2.20 | | ALPHA: (31) implies:
% 9.90/2.20 | | (32) incident_c(all_37_1, all_19_5) = all_44_1
% 9.90/2.20 | | (33) incident_c(all_37_1, all_19_4) = all_44_0
% 9.90/2.20 | | (34) all_44_0 = 0 | all_44_1 = 0
% 9.90/2.20 | |
% 9.90/2.20 | | BETA: splitting (29) gives:
% 9.90/2.20 | |
% 9.90/2.20 | | Case 1:
% 9.90/2.20 | | |
% 9.90/2.20 | | | (35) all_37_0 = 0
% 9.90/2.20 | | |
% 9.90/2.20 | | | REDUCE: (24), (35) imply:
% 9.90/2.20 | | | (36) $false
% 9.90/2.20 | | |
% 9.90/2.20 | | | CLOSE: (36) is inconsistent.
% 9.90/2.20 | | |
% 9.90/2.20 | | Case 2:
% 9.90/2.20 | | |
% 9.90/2.20 | | | (37) ? [v0: int] : ( ~ (v0 = 0) & incident_c(all_37_1, all_19_5) = v0)
% 9.90/2.20 | | |
% 9.90/2.20 | | | DELTA: instantiating (37) with fresh symbol all_50_0 gives:
% 9.90/2.20 | | | (38) ~ (all_50_0 = 0) & incident_c(all_37_1, all_19_5) = all_50_0
% 9.90/2.20 | | |
% 9.90/2.20 | | | ALPHA: (38) implies:
% 9.90/2.20 | | | (39) ~ (all_50_0 = 0)
% 9.90/2.20 | | | (40) incident_c(all_37_1, all_19_5) = all_50_0
% 9.90/2.20 | | |
% 9.90/2.20 | | | BETA: splitting (28) gives:
% 9.90/2.20 | | |
% 9.90/2.20 | | | Case 1:
% 9.90/2.20 | | | |
% 9.90/2.20 | | | | (41) all_37_0 = 0
% 9.90/2.20 | | | |
% 9.90/2.20 | | | | REDUCE: (24), (41) imply:
% 9.90/2.20 | | | | (42) $false
% 9.90/2.20 | | | |
% 9.90/2.20 | | | | CLOSE: (42) is inconsistent.
% 9.90/2.20 | | | |
% 9.90/2.20 | | | Case 2:
% 9.90/2.20 | | | |
% 9.90/2.20 | | | | (43) ? [v0: int] : ( ~ (v0 = 0) & incident_c(all_37_1, all_19_4) =
% 9.90/2.20 | | | | v0)
% 9.90/2.20 | | | |
% 9.90/2.20 | | | | DELTA: instantiating (43) with fresh symbol all_56_0 gives:
% 9.90/2.21 | | | | (44) ~ (all_56_0 = 0) & incident_c(all_37_1, all_19_4) = all_56_0
% 9.90/2.21 | | | |
% 9.90/2.21 | | | | ALPHA: (44) implies:
% 9.90/2.21 | | | | (45) ~ (all_56_0 = 0)
% 9.90/2.21 | | | | (46) incident_c(all_37_1, all_19_4) = all_56_0
% 9.90/2.21 | | | |
% 9.90/2.21 | | | | GROUND_INST: instantiating (4) with all_44_1, all_50_0, all_19_5,
% 9.90/2.21 | | | | all_37_1, simplifying with (32), (40) gives:
% 9.90/2.21 | | | | (47) all_50_0 = all_44_1
% 9.90/2.21 | | | |
% 9.90/2.21 | | | | GROUND_INST: instantiating (4) with all_44_0, all_56_0, all_19_4,
% 9.90/2.21 | | | | all_37_1, simplifying with (33), (46) gives:
% 9.90/2.21 | | | | (48) all_56_0 = all_44_0
% 9.90/2.21 | | | |
% 9.90/2.21 | | | | REDUCE: (45), (48) imply:
% 9.90/2.21 | | | | (49) ~ (all_44_0 = 0)
% 9.90/2.21 | | | |
% 9.90/2.21 | | | | REDUCE: (39), (47) imply:
% 9.90/2.21 | | | | (50) ~ (all_44_1 = 0)
% 9.90/2.21 | | | |
% 9.90/2.21 | | | | BETA: splitting (34) gives:
% 9.90/2.21 | | | |
% 9.90/2.21 | | | | Case 1:
% 9.90/2.21 | | | | |
% 9.90/2.21 | | | | | (51) all_44_0 = 0
% 9.90/2.21 | | | | |
% 9.90/2.21 | | | | | REDUCE: (49), (51) imply:
% 9.90/2.21 | | | | | (52) $false
% 9.90/2.21 | | | | |
% 9.90/2.21 | | | | | CLOSE: (52) is inconsistent.
% 9.90/2.21 | | | | |
% 9.90/2.21 | | | | Case 2:
% 9.90/2.21 | | | | |
% 9.90/2.21 | | | | | (53) all_44_1 = 0
% 9.90/2.21 | | | | |
% 9.90/2.21 | | | | | REDUCE: (50), (53) imply:
% 9.90/2.21 | | | | | (54) $false
% 9.90/2.21 | | | | |
% 9.90/2.21 | | | | | CLOSE: (54) is inconsistent.
% 9.90/2.21 | | | | |
% 9.90/2.21 | | | | End of split
% 9.90/2.21 | | | |
% 9.90/2.21 | | | End of split
% 9.90/2.21 | | |
% 9.90/2.21 | | End of split
% 9.90/2.21 | |
% 9.90/2.21 | End of split
% 9.90/2.21 |
% 9.90/2.21 End of proof
% 9.90/2.21 % SZS output end Proof for theBenchmark
% 9.90/2.21
% 9.90/2.21 1613ms
%------------------------------------------------------------------------------