TSTP Solution File: GEO112+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO112+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 : n012.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 23:21:29 EDT 2023
% Result : Theorem 7.25s 1.77s
% Output : Proof 10.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO112+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 20:24:09 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.65 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.81/1.16 Prover 4: Preprocessing ...
% 2.81/1.16 Prover 1: Preprocessing ...
% 3.37/1.20 Prover 3: Preprocessing ...
% 3.37/1.20 Prover 0: Preprocessing ...
% 3.37/1.20 Prover 2: Preprocessing ...
% 3.37/1.20 Prover 5: Preprocessing ...
% 3.37/1.20 Prover 6: Preprocessing ...
% 6.33/1.62 Prover 2: Proving ...
% 6.33/1.62 Prover 5: Proving ...
% 6.33/1.64 Prover 1: Warning: ignoring some quantifiers
% 6.33/1.65 Prover 3: Warning: ignoring some quantifiers
% 6.33/1.67 Prover 6: Proving ...
% 6.33/1.67 Prover 1: Constructing countermodel ...
% 6.33/1.67 Prover 3: Constructing countermodel ...
% 7.25/1.77 Prover 3: proved (1109ms)
% 7.25/1.77
% 7.25/1.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.25/1.77
% 7.25/1.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.25/1.77 Prover 5: stopped
% 7.25/1.77 Prover 6: stopped
% 7.25/1.77 Prover 2: stopped
% 7.25/1.79 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.25/1.79 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.25/1.79 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.25/1.83 Prover 7: Preprocessing ...
% 7.25/1.84 Prover 10: Preprocessing ...
% 7.25/1.84 Prover 11: Preprocessing ...
% 7.25/1.85 Prover 8: Preprocessing ...
% 8.12/1.90 Prover 1: Found proof (size 29)
% 8.12/1.90 Prover 1: proved (1242ms)
% 8.12/1.91 Prover 7: Warning: ignoring some quantifiers
% 8.12/1.92 Prover 10: Warning: ignoring some quantifiers
% 8.12/1.92 Prover 7: Constructing countermodel ...
% 8.12/1.93 Prover 7: stopped
% 8.12/1.94 Prover 10: Constructing countermodel ...
% 8.12/1.94 Prover 11: stopped
% 8.12/1.95 Prover 10: stopped
% 9.04/1.98 Prover 8: Warning: ignoring some quantifiers
% 9.04/1.99 Prover 8: Constructing countermodel ...
% 9.04/2.00 Prover 8: stopped
% 9.58/2.07 Prover 4: Warning: ignoring some quantifiers
% 9.77/2.10 Prover 4: Constructing countermodel ...
% 9.77/2.11 Prover 4: stopped
% 10.12/2.17 Prover 0: Proving ...
% 10.12/2.18 Prover 0: stopped
% 10.12/2.18
% 10.12/2.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.12/2.18
% 10.12/2.20 % SZS output start Proof for theBenchmark
% 10.12/2.20 Assumptions after simplification:
% 10.12/2.20 ---------------------------------
% 10.12/2.20
% 10.12/2.20 (between_c_defn)
% 10.44/2.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 10.44/2.24 | v3 = v1 | ~ (between_c(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 10.44/2.25 $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (inner_point(v2, v5) = 0) | ~ $i(v5)
% 10.44/2.25 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (end_point(v3, v5) = v8 &
% 10.44/2.25 end_point(v1, v5) = v7 & part_of(v5, v0) = v6 & ( ~ (v8 = 0) | ~ (v7 =
% 10.44/2.25 0) | ~ (v6 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 10.44/2.25 [v3: $i] : ( ~ (between_c(v0, v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~
% 10.44/2.25 $i(v1) | ~ $i(v0) | ( ~ (v3 = v1) & ? [v4: $i] : (inner_point(v2, v4) = 0
% 10.44/2.25 & end_point(v3, v4) = 0 & end_point(v1, v4) = 0 & part_of(v4, v0) = 0 &
% 10.44/2.25 $i(v4))))
% 10.44/2.25
% 10.44/2.25 (theorem_3_8_2)
% 10.44/2.25 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 10.44/2.25 = 0) & between_c(v0, v3, v2, v1) = v4 & between_c(v0, v1, v2, v3) = 0 &
% 10.44/2.25 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 10.44/2.25
% 10.44/2.25 (function-axioms)
% 10.44/2.25 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.44/2.25 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_c(v5, v4, v3,
% 10.44/2.25 v2) = v1) | ~ (between_c(v5, v4, v3, v2) = v0)) & ! [v0:
% 10.44/2.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.44/2.25 : ! [v4: $i] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) =
% 10.44/2.25 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.44/2.26 $i] : ! [v3: $i] : (v1 = v0 | ~ (inner_point(v3, v2) = v1) | ~
% 10.44/2.26 (inner_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.44/2.26 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.44/2.26 (end_point(v3, v2) = v1) | ~ (end_point(v3, v2) = v0)) & ! [v0: $i] : !
% 10.44/2.26 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~
% 10.44/2.26 (sum(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.44/2.26 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (part_of(v3,
% 10.44/2.26 v2) = v1) | ~ (part_of(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 10.44/2.26 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.44/2.26 (incident_c(v3, v2) = v1) | ~ (incident_c(v3, v2) = v0)) & ! [v0:
% 10.44/2.26 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 10.44/2.26 ~ (open(v2) = v1) | ~ (open(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 10.44/2.26 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (closed(v2) = v1) | ~
% 10.44/2.26 (closed(v2) = v0))
% 10.44/2.26
% 10.44/2.26 Further assumptions not needed in the proof:
% 10.44/2.26 --------------------------------------------
% 10.44/2.26 c1, c2, c3, c4, c5, c6, c7, c8, c9, closed_defn, end_point_defn,
% 10.44/2.26 inner_point_defn, meet_defn, open_defn, part_of_defn, sum_defn
% 10.44/2.26
% 10.44/2.26 Those formulas are unsatisfiable:
% 10.44/2.26 ---------------------------------
% 10.44/2.26
% 10.44/2.26 Begin of proof
% 10.44/2.26 |
% 10.44/2.26 | ALPHA: (between_c_defn) implies:
% 10.44/2.26 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 10.44/2.26 | (between_c(v0, v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 10.44/2.26 | ~ $i(v0) | ( ~ (v3 = v1) & ? [v4: $i] : (inner_point(v2, v4) = 0 &
% 10.44/2.26 | end_point(v3, v4) = 0 & end_point(v1, v4) = 0 & part_of(v4, v0) =
% 10.44/2.26 | 0 & $i(v4))))
% 10.70/2.26 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 10.70/2.26 | (v4 = 0 | v3 = v1 | ~ (between_c(v0, v1, v2, v3) = v4) | ~ $i(v3) |
% 10.70/2.26 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v5: $i] : ( ~ (inner_point(v2,
% 10.70/2.26 | v5) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: any] : ? [v8:
% 10.70/2.26 | any] : (end_point(v3, v5) = v8 & end_point(v1, v5) = v7 &
% 10.70/2.26 | part_of(v5, v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 =
% 10.70/2.26 | 0)))))
% 10.70/2.26 |
% 10.70/2.26 | ALPHA: (function-axioms) implies:
% 10.70/2.27 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.70/2.27 | ! [v3: $i] : (v1 = v0 | ~ (part_of(v3, v2) = v1) | ~ (part_of(v3,
% 10.70/2.27 | v2) = v0))
% 10.70/2.27 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.70/2.27 | ! [v3: $i] : (v1 = v0 | ~ (end_point(v3, v2) = v1) | ~
% 10.70/2.27 | (end_point(v3, v2) = v0))
% 10.70/2.27 |
% 10.70/2.27 | DELTA: instantiating (theorem_3_8_2) with fresh symbols all_19_0, all_19_1,
% 10.70/2.27 | all_19_2, all_19_3, all_19_4 gives:
% 10.70/2.27 | (5) ~ (all_19_0 = 0) & between_c(all_19_4, all_19_1, all_19_2, all_19_3) =
% 10.70/2.27 | all_19_0 & between_c(all_19_4, all_19_3, all_19_2, all_19_1) = 0 &
% 10.70/2.27 | $i(all_19_1) & $i(all_19_2) & $i(all_19_3) & $i(all_19_4)
% 10.70/2.27 |
% 10.70/2.27 | ALPHA: (5) implies:
% 10.70/2.27 | (6) ~ (all_19_0 = 0)
% 10.70/2.27 | (7) $i(all_19_4)
% 10.70/2.27 | (8) $i(all_19_3)
% 10.70/2.27 | (9) $i(all_19_2)
% 10.70/2.27 | (10) $i(all_19_1)
% 10.70/2.27 | (11) between_c(all_19_4, all_19_3, all_19_2, all_19_1) = 0
% 10.70/2.27 | (12) between_c(all_19_4, all_19_1, all_19_2, all_19_3) = all_19_0
% 10.70/2.27 |
% 10.70/2.27 | GROUND_INST: instantiating (1) with all_19_4, all_19_3, all_19_2, all_19_1,
% 10.70/2.27 | simplifying with (7), (8), (9), (10), (11) gives:
% 10.70/2.27 | (13) ~ (all_19_1 = all_19_3) & ? [v0: $i] : (inner_point(all_19_2, v0) =
% 10.70/2.27 | 0 & end_point(all_19_1, v0) = 0 & end_point(all_19_3, v0) = 0 &
% 10.70/2.27 | part_of(v0, all_19_4) = 0 & $i(v0))
% 10.70/2.27 |
% 10.70/2.27 | ALPHA: (13) implies:
% 10.70/2.27 | (14) ~ (all_19_1 = all_19_3)
% 10.70/2.27 | (15) ? [v0: $i] : (inner_point(all_19_2, v0) = 0 & end_point(all_19_1, v0)
% 10.70/2.27 | = 0 & end_point(all_19_3, v0) = 0 & part_of(v0, all_19_4) = 0 &
% 10.70/2.27 | $i(v0))
% 10.70/2.27 |
% 10.70/2.27 | GROUND_INST: instantiating (2) with all_19_4, all_19_1, all_19_2, all_19_3,
% 10.70/2.27 | all_19_0, simplifying with (7), (8), (9), (10), (12) gives:
% 10.70/2.27 | (16) all_19_0 = 0 | all_19_1 = all_19_3 | ! [v0: $i] : ( ~
% 10.70/2.27 | (inner_point(all_19_2, v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 10.70/2.27 | any] : ? [v3: any] : (end_point(all_19_1, v0) = v2 &
% 10.70/2.27 | end_point(all_19_3, v0) = v3 & part_of(v0, all_19_4) = v1 & ( ~
% 10.70/2.27 | (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0))))
% 10.70/2.27 |
% 10.70/2.27 | DELTA: instantiating (15) with fresh symbol all_30_0 gives:
% 10.70/2.28 | (17) inner_point(all_19_2, all_30_0) = 0 & end_point(all_19_1, all_30_0) =
% 10.70/2.28 | 0 & end_point(all_19_3, all_30_0) = 0 & part_of(all_30_0, all_19_4) =
% 10.70/2.28 | 0 & $i(all_30_0)
% 10.70/2.28 |
% 10.70/2.28 | ALPHA: (17) implies:
% 10.70/2.28 | (18) $i(all_30_0)
% 10.70/2.28 | (19) part_of(all_30_0, all_19_4) = 0
% 10.70/2.28 | (20) end_point(all_19_3, all_30_0) = 0
% 10.70/2.28 | (21) end_point(all_19_1, all_30_0) = 0
% 10.70/2.28 | (22) inner_point(all_19_2, all_30_0) = 0
% 10.70/2.28 |
% 10.70/2.28 | BETA: splitting (16) gives:
% 10.70/2.28 |
% 10.70/2.28 | Case 1:
% 10.70/2.28 | |
% 10.70/2.28 | | (23) all_19_0 = 0
% 10.70/2.28 | |
% 10.70/2.28 | | REDUCE: (6), (23) imply:
% 10.70/2.28 | | (24) $false
% 10.70/2.28 | |
% 10.70/2.28 | | CLOSE: (24) is inconsistent.
% 10.70/2.28 | |
% 10.70/2.28 | Case 2:
% 10.70/2.28 | |
% 10.70/2.28 | | (25) all_19_1 = all_19_3 | ! [v0: $i] : ( ~ (inner_point(all_19_2, v0) =
% 10.70/2.28 | | 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 10.70/2.28 | | (end_point(all_19_1, v0) = v2 & end_point(all_19_3, v0) = v3 &
% 10.70/2.28 | | part_of(v0, all_19_4) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1
% 10.70/2.28 | | = 0))))
% 10.70/2.28 | |
% 10.70/2.28 | | BETA: splitting (25) gives:
% 10.70/2.28 | |
% 10.70/2.28 | | Case 1:
% 10.70/2.28 | | |
% 10.70/2.28 | | | (26) all_19_1 = all_19_3
% 10.70/2.28 | | |
% 10.70/2.28 | | | REDUCE: (14), (26) imply:
% 10.70/2.28 | | | (27) $false
% 10.70/2.28 | | |
% 10.70/2.28 | | | CLOSE: (27) is inconsistent.
% 10.70/2.28 | | |
% 10.70/2.28 | | Case 2:
% 10.70/2.28 | | |
% 10.70/2.28 | | | (28) ! [v0: $i] : ( ~ (inner_point(all_19_2, v0) = 0) | ~ $i(v0) | ?
% 10.70/2.28 | | | [v1: any] : ? [v2: any] : ? [v3: any] : (end_point(all_19_1,
% 10.70/2.28 | | | v0) = v2 & end_point(all_19_3, v0) = v3 & part_of(v0,
% 10.70/2.28 | | | all_19_4) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0))))
% 10.70/2.28 | | |
% 10.70/2.28 | | | GROUND_INST: instantiating (28) with all_30_0, simplifying with (18), (22)
% 10.70/2.28 | | | gives:
% 10.70/2.28 | | | (29) ? [v0: any] : ? [v1: any] : ? [v2: any] : (end_point(all_19_1,
% 10.70/2.28 | | | all_30_0) = v1 & end_point(all_19_3, all_30_0) = v2 &
% 10.70/2.28 | | | part_of(all_30_0, all_19_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) |
% 10.70/2.28 | | | ~ (v0 = 0)))
% 10.70/2.28 | | |
% 10.70/2.28 | | | DELTA: instantiating (29) with fresh symbols all_58_0, all_58_1, all_58_2
% 10.70/2.28 | | | gives:
% 10.70/2.28 | | | (30) end_point(all_19_1, all_30_0) = all_58_1 & end_point(all_19_3,
% 10.70/2.28 | | | all_30_0) = all_58_0 & part_of(all_30_0, all_19_4) = all_58_2 &
% 10.70/2.28 | | | ( ~ (all_58_0 = 0) | ~ (all_58_1 = 0) | ~ (all_58_2 = 0))
% 10.70/2.28 | | |
% 10.70/2.28 | | | ALPHA: (30) implies:
% 10.70/2.28 | | | (31) part_of(all_30_0, all_19_4) = all_58_2
% 10.70/2.28 | | | (32) end_point(all_19_3, all_30_0) = all_58_0
% 10.70/2.28 | | | (33) end_point(all_19_1, all_30_0) = all_58_1
% 10.70/2.28 | | | (34) ~ (all_58_0 = 0) | ~ (all_58_1 = 0) | ~ (all_58_2 = 0)
% 10.70/2.28 | | |
% 10.70/2.28 | | | GROUND_INST: instantiating (3) with 0, all_58_2, all_19_4, all_30_0,
% 10.70/2.28 | | | simplifying with (19), (31) gives:
% 10.70/2.28 | | | (35) all_58_2 = 0
% 10.70/2.28 | | |
% 10.70/2.29 | | | GROUND_INST: instantiating (4) with 0, all_58_0, all_30_0, all_19_3,
% 10.70/2.29 | | | simplifying with (20), (32) gives:
% 10.70/2.29 | | | (36) all_58_0 = 0
% 10.70/2.29 | | |
% 10.70/2.29 | | | GROUND_INST: instantiating (4) with 0, all_58_1, all_30_0, all_19_1,
% 10.70/2.29 | | | simplifying with (21), (33) gives:
% 10.70/2.29 | | | (37) all_58_1 = 0
% 10.70/2.29 | | |
% 10.70/2.29 | | | BETA: splitting (34) gives:
% 10.70/2.29 | | |
% 10.70/2.29 | | | Case 1:
% 10.70/2.29 | | | |
% 10.70/2.29 | | | | (38) ~ (all_58_0 = 0)
% 10.70/2.29 | | | |
% 10.70/2.29 | | | | REDUCE: (36), (38) imply:
% 10.70/2.29 | | | | (39) $false
% 10.70/2.29 | | | |
% 10.70/2.29 | | | | CLOSE: (39) is inconsistent.
% 10.70/2.29 | | | |
% 10.70/2.29 | | | Case 2:
% 10.70/2.29 | | | |
% 10.70/2.29 | | | | (40) ~ (all_58_1 = 0) | ~ (all_58_2 = 0)
% 10.70/2.29 | | | |
% 10.70/2.29 | | | | BETA: splitting (40) gives:
% 10.70/2.29 | | | |
% 10.70/2.29 | | | | Case 1:
% 10.70/2.29 | | | | |
% 10.70/2.29 | | | | | (41) ~ (all_58_1 = 0)
% 10.70/2.29 | | | | |
% 10.70/2.29 | | | | | REDUCE: (37), (41) imply:
% 10.70/2.29 | | | | | (42) $false
% 10.70/2.29 | | | | |
% 10.70/2.29 | | | | | CLOSE: (42) is inconsistent.
% 10.70/2.29 | | | | |
% 10.70/2.29 | | | | Case 2:
% 10.70/2.29 | | | | |
% 10.70/2.29 | | | | | (43) ~ (all_58_2 = 0)
% 10.70/2.29 | | | | |
% 10.70/2.29 | | | | | REDUCE: (35), (43) imply:
% 10.70/2.29 | | | | | (44) $false
% 10.70/2.29 | | | | |
% 10.70/2.29 | | | | | CLOSE: (44) is inconsistent.
% 10.70/2.29 | | | | |
% 10.70/2.29 | | | | End of split
% 10.70/2.29 | | | |
% 10.70/2.29 | | | End of split
% 10.70/2.29 | | |
% 10.70/2.29 | | End of split
% 10.70/2.29 | |
% 10.70/2.29 | End of split
% 10.70/2.29 |
% 10.70/2.29 End of proof
% 10.70/2.29 % SZS output end Proof for theBenchmark
% 10.70/2.29
% 10.70/2.29 1651ms
%------------------------------------------------------------------------------