TSTP Solution File: GEO177+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO177+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n003.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 23:21:53 EDT 2023
% Result : Theorem 9.68s 2.02s
% Output : Proof 17.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO177+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 20:32:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.51/0.60 ________ _____
% 0.51/0.60 ___ __ \_________(_)________________________________
% 0.51/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.51/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.51/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.51/0.60
% 0.51/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.51/0.60 (2023-06-19)
% 0.51/0.60
% 0.51/0.60 (c) Philipp Rümmer, 2009-2023
% 0.51/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.51/0.60 Amanda Stjerna.
% 0.51/0.60 Free software under BSD-3-Clause.
% 0.51/0.60
% 0.51/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.51/0.60
% 0.51/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.51/0.62 Running up to 7 provers in parallel.
% 0.51/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.51/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.51/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.51/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.51/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.51/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.51/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.64/1.05 Prover 4: Preprocessing ...
% 2.64/1.05 Prover 1: Preprocessing ...
% 2.96/1.09 Prover 2: Preprocessing ...
% 2.96/1.09 Prover 3: Preprocessing ...
% 2.96/1.09 Prover 5: Preprocessing ...
% 2.96/1.09 Prover 0: Preprocessing ...
% 2.96/1.09 Prover 6: Preprocessing ...
% 4.53/1.31 Prover 6: Constructing countermodel ...
% 4.53/1.31 Prover 5: Proving ...
% 4.53/1.32 Prover 2: Proving ...
% 4.53/1.33 Prover 1: Constructing countermodel ...
% 4.53/1.34 Prover 3: Constructing countermodel ...
% 5.48/1.47 Prover 4: Constructing countermodel ...
% 5.48/1.48 Prover 0: Proving ...
% 5.48/1.48 Prover 3: gave up
% 5.48/1.48 Prover 6: gave up
% 5.48/1.48 Prover 1: gave up
% 5.48/1.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.48/1.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.48/1.49 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 5.89/1.53 Prover 9: Preprocessing ...
% 5.89/1.53 Prover 8: Preprocessing ...
% 6.37/1.57 Prover 7: Preprocessing ...
% 6.37/1.60 Prover 7: Warning: ignoring some quantifiers
% 6.73/1.60 Prover 7: Constructing countermodel ...
% 7.04/1.64 Prover 8: Warning: ignoring some quantifiers
% 7.04/1.65 Prover 8: Constructing countermodel ...
% 7.04/1.71 Prover 9: Constructing countermodel ...
% 7.04/1.72 Prover 8: gave up
% 7.04/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.78/1.75 Prover 10: Preprocessing ...
% 7.78/1.78 Prover 7: gave up
% 7.78/1.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.78/1.80 Prover 11: Preprocessing ...
% 7.78/1.82 Prover 10: Warning: ignoring some quantifiers
% 7.78/1.83 Prover 10: Constructing countermodel ...
% 8.34/1.87 Prover 10: gave up
% 8.34/1.88 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 8.92/1.92 Prover 12: Preprocessing ...
% 8.92/1.98 Prover 11: Constructing countermodel ...
% 8.92/1.99 Prover 12: Proving ...
% 9.68/2.02 Prover 0: proved (1395ms)
% 9.68/2.02
% 9.68/2.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.68/2.02
% 9.68/2.02 Prover 9: stopped
% 9.68/2.02 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.68/2.02 Prover 12: stopped
% 9.68/2.02 Prover 5: stopped
% 9.68/2.02 Prover 2: stopped
% 9.68/2.02 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 9.68/2.02 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.68/2.04 Prover 16: Preprocessing ...
% 9.68/2.04 Prover 19: Preprocessing ...
% 9.68/2.04 Prover 13: Preprocessing ...
% 9.68/2.07 Prover 13: Warning: ignoring some quantifiers
% 9.68/2.07 Prover 16: Warning: ignoring some quantifiers
% 9.68/2.07 Prover 13: Constructing countermodel ...
% 9.68/2.07 Prover 16: Constructing countermodel ...
% 9.68/2.09 Prover 19: Warning: ignoring some quantifiers
% 9.68/2.10 Prover 19: Constructing countermodel ...
% 10.40/2.14 Prover 19: gave up
% 11.15/2.20 Prover 13: gave up
% 11.15/2.26 Prover 16: gave up
% 16.72/3.19 Prover 11: Found proof (size 234)
% 16.72/3.19 Prover 11: proved (1411ms)
% 16.72/3.19 Prover 4: stopped
% 16.72/3.19
% 16.72/3.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.72/3.19
% 16.72/3.21 % SZS output start Proof for theBenchmark
% 16.72/3.21 Assumptions after simplification:
% 16.72/3.21 ---------------------------------
% 16.72/3.21
% 16.72/3.21 (ceq2)
% 16.72/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 16.72/3.24 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1,
% 16.72/3.24 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 =
% 16.72/3.24 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 16.72/3.24 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) |
% 16.72/3.24 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 16.72/3.24 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 16.72/3.24 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~
% 16.72/3.24 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 16.72/3.24 apart_point_and_line(v0, v2) = 0)
% 16.72/3.24
% 16.72/3.24 (ci1)
% 16.72/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 16.72/3.24 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) &
% 16.72/3.24 apart_point_and_line(v0, v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0,
% 16.72/3.24 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1)
% 16.72/3.24 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 16.72/3.24 line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 &
% 16.72/3.24 $i(v2)))
% 16.72/3.24
% 16.72/3.24 (ci2)
% 16.72/3.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 16.72/3.25 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) &
% 16.72/3.25 apart_point_and_line(v1, v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0,
% 16.72/3.25 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1)
% 16.72/3.25 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 16.72/3.25 line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 &
% 16.72/3.25 $i(v2)))
% 16.72/3.25
% 16.72/3.25 (con)
% 16.72/3.25 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 16.72/3.25 int] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: int] : ( ~ (v9 =
% 16.72/3.25 0) & ~ (v8 = 0) & line_connecting(v2, v3) = v4 & line_connecting(v0, v1)
% 16.72/3.25 = v7 & apart_point_and_line(v3, v7) = v9 & apart_point_and_line(v2, v7) = v8
% 16.72/3.25 & distinct_points(v2, v3) = 0 & distinct_points(v0, v1) = 0 & $i(v7) &
% 16.72/3.25 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v6 = 0 &
% 16.72/3.25 apart_point_and_line(v1, v4) = 0) | (v5 = 0 & apart_point_and_line(v0,
% 16.72/3.25 v4) = 0)))
% 16.72/3.25
% 16.72/3.25 (cu1)
% 16.72/3.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 16.72/3.27 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 16.72/3.27 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 16.72/3.27 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 16.72/3.27 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 &
% 16.72/3.27 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2,
% 16.72/3.27 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 16.72/3.27 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1,
% 16.72/3.27 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~
% 16.72/3.27 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 16.72/3.27 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 16.72/3.27 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0,
% 16.72/3.27 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 16.72/3.27 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 16.72/3.27 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 16.72/3.27 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 16.72/3.27 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 =
% 16.72/3.27 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 &
% 16.72/3.27 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2,
% 16.72/3.27 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 16.72/3.27 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 16.72/3.27 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~
% 16.72/3.27 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 16.72/3.27 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 =
% 16.72/3.27 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 &
% 16.72/3.27 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2,
% 16.72/3.27 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 16.72/3.27 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 16.72/3.27 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~
% 16.72/3.27 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~
% 16.72/3.27 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 16.72/3.27 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 &
% 16.72/3.27 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0,
% 16.72/3.27 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 16.72/3.27 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0,
% 16.72/3.27 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~
% 16.72/3.27 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 16.72/3.27 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 16.72/3.27 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1,
% 16.72/3.27 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i]
% 16.72/3.27 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) |
% 16.72/3.27 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 16.72/3.27 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 =
% 16.72/3.27 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 &
% 16.72/3.27 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0,
% 16.72/3.27 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 16.72/3.27
% 16.72/3.27 (function-axioms)
% 16.72/3.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.72/3.28 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) &
% 16.72/3.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.72/3.28 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 16.72/3.28 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 16.72/3.28 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 16.72/3.28 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.72/3.28 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.72/3.28 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & !
% 16.72/3.28 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 16.72/3.28 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3,
% 16.72/3.28 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 16.72/3.28 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 16.72/3.28 (distinct_points(v3, v2) = v0))
% 16.72/3.28
% 16.72/3.28 Further assumptions not needed in the proof:
% 16.72/3.28 --------------------------------------------
% 16.72/3.28 apart1, apart2, apart3, apart4, apart5, ax6, ceq1, ceq3, ci3, ci4
% 16.72/3.28
% 16.72/3.28 Those formulas are unsatisfiable:
% 16.72/3.28 ---------------------------------
% 16.72/3.28
% 16.72/3.28 Begin of proof
% 16.72/3.28 |
% 16.72/3.28 | ALPHA: (ci1) implies:
% 16.72/3.28 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~
% 16.72/3.28 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 16.72/3.28 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 &
% 16.72/3.28 | $i(v2)))
% 16.72/3.28 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1)
% 16.72/3.28 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~
% 16.72/3.28 | (v4 = 0) & apart_point_and_line(v0, v2) = v4) | ( ~ (v3 = 0) &
% 16.72/3.28 | distinct_points(v0, v1) = v3)))
% 16.72/3.28 |
% 16.72/3.28 | ALPHA: (ci2) implies:
% 16.72/3.28 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~
% 16.72/3.28 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 16.72/3.28 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 &
% 16.72/3.28 | $i(v2)))
% 16.72/3.28 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1)
% 16.72/3.28 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~
% 16.72/3.28 | (v4 = 0) & apart_point_and_line(v1, v2) = v4) | ( ~ (v3 = 0) &
% 16.72/3.28 | distinct_points(v0, v1) = v3)))
% 16.72/3.28 |
% 16.72/3.28 | ALPHA: (cu1) implies:
% 16.72/3.29 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 16.72/3.29 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5)
% 16.72/3.29 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0,
% 16.72/3.29 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 16.72/3.29 | [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 16.72/3.29 | apart_point_and_line(v1, v3) = 0) | (v7 = 0 &
% 16.72/3.29 | apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) &
% 16.72/3.29 | distinct_lines(v2, v3) = v6)))
% 16.72/3.29 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 16.72/3.29 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5)
% 16.72/3.29 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 16.72/3.29 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ?
% 16.72/3.29 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 &
% 16.72/3.29 | apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) &
% 16.72/3.29 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0,
% 16.72/3.29 | v1) = v6)))
% 16.72/3.29 |
% 16.72/3.29 | ALPHA: (ceq2) implies:
% 16.72/3.29 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 16.72/3.29 | (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3)
% 16.72/3.29 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v0, v2) =
% 16.72/3.29 | 0)
% 16.72/3.29 |
% 16.72/3.29 | ALPHA: (function-axioms) implies:
% 16.72/3.29 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 16.72/3.29 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 16.72/3.29 | (distinct_points(v3, v2) = v0))
% 16.72/3.29 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 16.72/3.29 | ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~
% 16.72/3.29 | (distinct_lines(v3, v2) = v0))
% 16.72/3.29 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 16.72/3.29 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 16.72/3.29 | (apart_point_and_line(v3, v2) = v0))
% 16.72/3.29 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.72/3.29 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 16.72/3.29 |
% 16.72/3.29 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2,
% 16.72/3.29 | all_17_3, all_17_4, all_17_5, all_17_6, all_17_7, all_17_8, all_17_9
% 16.72/3.29 | gives:
% 16.72/3.29 | (12) ~ (all_17_0 = 0) & ~ (all_17_1 = 0) & line_connecting(all_17_7,
% 16.72/3.29 | all_17_6) = all_17_5 & line_connecting(all_17_9, all_17_8) =
% 16.72/3.29 | all_17_2 & apart_point_and_line(all_17_6, all_17_2) = all_17_0 &
% 16.72/3.29 | apart_point_and_line(all_17_7, all_17_2) = all_17_1 &
% 16.72/3.29 | distinct_points(all_17_7, all_17_6) = 0 & distinct_points(all_17_9,
% 16.72/3.29 | all_17_8) = 0 & $i(all_17_2) & $i(all_17_5) & $i(all_17_6) &
% 16.72/3.29 | $i(all_17_7) & $i(all_17_8) & $i(all_17_9) & ((all_17_3 = 0 &
% 16.72/3.29 | apart_point_and_line(all_17_8, all_17_5) = 0) | (all_17_4 = 0 &
% 16.72/3.29 | apart_point_and_line(all_17_9, all_17_5) = 0))
% 16.72/3.29 |
% 16.72/3.29 | ALPHA: (12) implies:
% 16.72/3.30 | (13) ~ (all_17_1 = 0)
% 16.72/3.30 | (14) ~ (all_17_0 = 0)
% 16.72/3.30 | (15) $i(all_17_9)
% 16.72/3.30 | (16) $i(all_17_8)
% 16.72/3.30 | (17) $i(all_17_7)
% 16.72/3.30 | (18) $i(all_17_6)
% 16.72/3.30 | (19) distinct_points(all_17_9, all_17_8) = 0
% 16.72/3.30 | (20) distinct_points(all_17_7, all_17_6) = 0
% 16.72/3.30 | (21) apart_point_and_line(all_17_7, all_17_2) = all_17_1
% 16.72/3.30 | (22) apart_point_and_line(all_17_6, all_17_2) = all_17_0
% 16.72/3.30 | (23) line_connecting(all_17_9, all_17_8) = all_17_2
% 16.72/3.30 | (24) line_connecting(all_17_7, all_17_6) = all_17_5
% 17.27/3.30 | (25) (all_17_3 = 0 & apart_point_and_line(all_17_8, all_17_5) = 0) |
% 17.27/3.30 | (all_17_4 = 0 & apart_point_and_line(all_17_9, all_17_5) = 0)
% 17.27/3.30 |
% 17.27/3.30 | GROUND_INST: instantiating (3) with all_17_9, all_17_8, simplifying with (15),
% 17.27/3.30 | (16), (19) gives:
% 17.27/3.30 | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_9,
% 17.27/3.30 | all_17_8) = v0 & apart_point_and_line(all_17_8, v0) = v1 & $i(v0))
% 17.27/3.30 |
% 17.27/3.30 | GROUND_INST: instantiating (1) with all_17_9, all_17_8, simplifying with (15),
% 17.27/3.30 | (16), (19) gives:
% 17.27/3.30 | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_9,
% 17.27/3.30 | all_17_8) = v0 & apart_point_and_line(all_17_9, v0) = v1 & $i(v0))
% 17.27/3.30 |
% 17.27/3.30 | GROUND_INST: instantiating (3) with all_17_7, all_17_6, simplifying with (17),
% 17.27/3.30 | (18), (20) gives:
% 17.27/3.30 | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_7,
% 17.27/3.30 | all_17_6) = v0 & apart_point_and_line(all_17_6, v0) = v1 & $i(v0))
% 17.27/3.30 |
% 17.27/3.30 | GROUND_INST: instantiating (1) with all_17_7, all_17_6, simplifying with (17),
% 17.27/3.30 | (18), (20) gives:
% 17.27/3.30 | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_7,
% 17.27/3.30 | all_17_6) = v0 & apart_point_and_line(all_17_7, v0) = v1 & $i(v0))
% 17.27/3.30 |
% 17.27/3.30 | GROUND_INST: instantiating (4) with all_17_9, all_17_8, all_17_2, simplifying
% 17.27/3.30 | with (15), (16), (23) gives:
% 17.27/3.30 | (30) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) &
% 17.27/3.30 | apart_point_and_line(all_17_8, all_17_2) = v1) | ( ~ (v0 = 0) &
% 17.27/3.30 | distinct_points(all_17_9, all_17_8) = v0))
% 17.27/3.30 |
% 17.27/3.30 | GROUND_INST: instantiating (2) with all_17_9, all_17_8, all_17_2, simplifying
% 17.27/3.30 | with (15), (16), (23) gives:
% 17.27/3.30 | (31) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) &
% 17.27/3.30 | apart_point_and_line(all_17_9, all_17_2) = v1) | ( ~ (v0 = 0) &
% 17.27/3.30 | distinct_points(all_17_9, all_17_8) = v0))
% 17.27/3.30 |
% 17.27/3.30 | GROUND_INST: instantiating (4) with all_17_7, all_17_6, all_17_5, simplifying
% 17.27/3.30 | with (17), (18), (24) gives:
% 17.27/3.30 | (32) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) &
% 17.27/3.30 | apart_point_and_line(all_17_6, all_17_5) = v1) | ( ~ (v0 = 0) &
% 17.27/3.30 | distinct_points(all_17_7, all_17_6) = v0))
% 17.27/3.31 |
% 17.27/3.31 | GROUND_INST: instantiating (2) with all_17_7, all_17_6, all_17_5, simplifying
% 17.27/3.31 | with (17), (18), (24) gives:
% 17.27/3.31 | (33) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) &
% 17.27/3.31 | apart_point_and_line(all_17_7, all_17_5) = v1) | ( ~ (v0 = 0) &
% 17.27/3.31 | distinct_points(all_17_7, all_17_6) = v0))
% 17.27/3.31 |
% 17.27/3.31 | DELTA: instantiating (33) with fresh symbols all_24_0, all_24_1 gives:
% 17.27/3.31 | (34) ( ~ (all_24_0 = 0) & apart_point_and_line(all_17_7, all_17_5) =
% 17.27/3.31 | all_24_0) | ( ~ (all_24_1 = 0) & distinct_points(all_17_7, all_17_6)
% 17.27/3.31 | = all_24_1)
% 17.27/3.31 |
% 17.27/3.31 | DELTA: instantiating (32) with fresh symbols all_25_0, all_25_1 gives:
% 17.27/3.31 | (35) ( ~ (all_25_0 = 0) & apart_point_and_line(all_17_6, all_17_5) =
% 17.27/3.31 | all_25_0) | ( ~ (all_25_1 = 0) & distinct_points(all_17_7, all_17_6)
% 17.27/3.31 | = all_25_1)
% 17.27/3.31 |
% 17.27/3.31 | DELTA: instantiating (31) with fresh symbols all_26_0, all_26_1 gives:
% 17.27/3.31 | (36) ( ~ (all_26_0 = 0) & apart_point_and_line(all_17_9, all_17_2) =
% 17.27/3.31 | all_26_0) | ( ~ (all_26_1 = 0) & distinct_points(all_17_9, all_17_8)
% 17.27/3.31 | = all_26_1)
% 17.27/3.31 |
% 17.27/3.31 | DELTA: instantiating (29) with fresh symbols all_27_0, all_27_1 gives:
% 17.27/3.31 | (37) ~ (all_27_0 = 0) & line_connecting(all_17_7, all_17_6) = all_27_1 &
% 17.27/3.31 | apart_point_and_line(all_17_7, all_27_1) = all_27_0 & $i(all_27_1)
% 17.27/3.31 |
% 17.27/3.31 | ALPHA: (37) implies:
% 17.27/3.31 | (38) ~ (all_27_0 = 0)
% 17.27/3.31 | (39) $i(all_27_1)
% 17.27/3.31 | (40) apart_point_and_line(all_17_7, all_27_1) = all_27_0
% 17.27/3.31 | (41) line_connecting(all_17_7, all_17_6) = all_27_1
% 17.27/3.31 |
% 17.27/3.31 | DELTA: instantiating (28) with fresh symbols all_29_0, all_29_1 gives:
% 17.27/3.31 | (42) ~ (all_29_0 = 0) & line_connecting(all_17_7, all_17_6) = all_29_1 &
% 17.27/3.31 | apart_point_and_line(all_17_6, all_29_1) = all_29_0 & $i(all_29_1)
% 17.27/3.31 |
% 17.27/3.31 | ALPHA: (42) implies:
% 17.27/3.31 | (43) ~ (all_29_0 = 0)
% 17.27/3.31 | (44) apart_point_and_line(all_17_6, all_29_1) = all_29_0
% 17.27/3.31 | (45) line_connecting(all_17_7, all_17_6) = all_29_1
% 17.27/3.31 |
% 17.27/3.31 | DELTA: instantiating (26) with fresh symbols all_31_0, all_31_1 gives:
% 17.27/3.31 | (46) ~ (all_31_0 = 0) & line_connecting(all_17_9, all_17_8) = all_31_1 &
% 17.27/3.31 | apart_point_and_line(all_17_8, all_31_1) = all_31_0 & $i(all_31_1)
% 17.27/3.31 |
% 17.27/3.31 | ALPHA: (46) implies:
% 17.27/3.31 | (47) $i(all_31_1)
% 17.27/3.31 | (48) apart_point_and_line(all_17_8, all_31_1) = all_31_0
% 17.27/3.31 | (49) line_connecting(all_17_9, all_17_8) = all_31_1
% 17.27/3.31 |
% 17.27/3.31 | DELTA: instantiating (27) with fresh symbols all_33_0, all_33_1 gives:
% 17.27/3.31 | (50) ~ (all_33_0 = 0) & line_connecting(all_17_9, all_17_8) = all_33_1 &
% 17.27/3.31 | apart_point_and_line(all_17_9, all_33_1) = all_33_0 & $i(all_33_1)
% 17.27/3.31 |
% 17.27/3.31 | ALPHA: (50) implies:
% 17.27/3.31 | (51) ~ (all_33_0 = 0)
% 17.27/3.31 | (52) apart_point_and_line(all_17_9, all_33_1) = all_33_0
% 17.27/3.31 | (53) line_connecting(all_17_9, all_17_8) = all_33_1
% 17.27/3.31 |
% 17.27/3.31 | DELTA: instantiating (30) with fresh symbols all_35_0, all_35_1 gives:
% 17.27/3.31 | (54) ( ~ (all_35_0 = 0) & apart_point_and_line(all_17_8, all_17_2) =
% 17.27/3.31 | all_35_0) | ( ~ (all_35_1 = 0) & distinct_points(all_17_9, all_17_8)
% 17.27/3.31 | = all_35_1)
% 17.27/3.31 |
% 17.27/3.31 | BETA: splitting (54) gives:
% 17.27/3.31 |
% 17.27/3.31 | Case 1:
% 17.27/3.31 | |
% 17.27/3.31 | | (55) ~ (all_35_0 = 0) & apart_point_and_line(all_17_8, all_17_2) =
% 17.27/3.31 | | all_35_0
% 17.27/3.31 | |
% 17.27/3.31 | | ALPHA: (55) implies:
% 17.27/3.31 | | (56) ~ (all_35_0 = 0)
% 17.27/3.31 | | (57) apart_point_and_line(all_17_8, all_17_2) = all_35_0
% 17.27/3.31 | |
% 17.27/3.31 | | BETA: splitting (34) gives:
% 17.27/3.31 | |
% 17.27/3.31 | | Case 1:
% 17.27/3.31 | | |
% 17.27/3.31 | | | (58) ~ (all_24_0 = 0) & apart_point_and_line(all_17_7, all_17_5) =
% 17.27/3.31 | | | all_24_0
% 17.27/3.31 | | |
% 17.27/3.31 | | | ALPHA: (58) implies:
% 17.27/3.31 | | | (59) apart_point_and_line(all_17_7, all_17_5) = all_24_0
% 17.27/3.31 | | |
% 17.27/3.31 | | | BETA: splitting (36) gives:
% 17.27/3.31 | | |
% 17.27/3.31 | | | Case 1:
% 17.27/3.31 | | | |
% 17.27/3.32 | | | | (60) ~ (all_26_0 = 0) & apart_point_and_line(all_17_9, all_17_2) =
% 17.27/3.32 | | | | all_26_0
% 17.27/3.32 | | | |
% 17.27/3.32 | | | | ALPHA: (60) implies:
% 17.27/3.32 | | | | (61) apart_point_and_line(all_17_9, all_17_2) = all_26_0
% 17.27/3.32 | | | |
% 17.27/3.32 | | | | BETA: splitting (35) gives:
% 17.27/3.32 | | | |
% 17.27/3.32 | | | | Case 1:
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | (62) ~ (all_25_0 = 0) & apart_point_and_line(all_17_6, all_17_5) =
% 17.27/3.32 | | | | | all_25_0
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | ALPHA: (62) implies:
% 17.27/3.32 | | | | | (63) apart_point_and_line(all_17_6, all_17_5) = all_25_0
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | GROUND_INST: instantiating (11) with all_17_2, all_33_1, all_17_8,
% 17.27/3.32 | | | | | all_17_9, simplifying with (23), (53) gives:
% 17.27/3.32 | | | | | (64) all_33_1 = all_17_2
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | GROUND_INST: instantiating (11) with all_31_1, all_33_1, all_17_8,
% 17.27/3.32 | | | | | all_17_9, simplifying with (49), (53) gives:
% 17.27/3.32 | | | | | (65) all_33_1 = all_31_1
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | GROUND_INST: instantiating (11) with all_17_5, all_29_1, all_17_6,
% 17.27/3.32 | | | | | all_17_7, simplifying with (24), (45) gives:
% 17.27/3.32 | | | | | (66) all_29_1 = all_17_5
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | GROUND_INST: instantiating (11) with all_27_1, all_29_1, all_17_6,
% 17.27/3.32 | | | | | all_17_7, simplifying with (41), (45) gives:
% 17.27/3.32 | | | | | (67) all_29_1 = all_27_1
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | COMBINE_EQS: (64), (65) imply:
% 17.27/3.32 | | | | | (68) all_31_1 = all_17_2
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | SIMP: (68) implies:
% 17.27/3.32 | | | | | (69) all_31_1 = all_17_2
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | COMBINE_EQS: (66), (67) imply:
% 17.27/3.32 | | | | | (70) all_27_1 = all_17_5
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | SIMP: (70) implies:
% 17.27/3.32 | | | | | (71) all_27_1 = all_17_5
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | REDUCE: (44), (66) imply:
% 17.27/3.32 | | | | | (72) apart_point_and_line(all_17_6, all_17_5) = all_29_0
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | REDUCE: (40), (71) imply:
% 17.27/3.32 | | | | | (73) apart_point_and_line(all_17_7, all_17_5) = all_27_0
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | REDUCE: (48), (69) imply:
% 17.27/3.32 | | | | | (74) apart_point_and_line(all_17_8, all_17_2) = all_31_0
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | REDUCE: (52), (64) imply:
% 17.27/3.32 | | | | | (75) apart_point_and_line(all_17_9, all_17_2) = all_33_0
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | REDUCE: (47), (69) imply:
% 17.27/3.32 | | | | | (76) $i(all_17_2)
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | REDUCE: (39), (71) imply:
% 17.27/3.32 | | | | | (77) $i(all_17_5)
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | GROUND_INST: instantiating (10) with all_26_0, all_33_0, all_17_2,
% 17.27/3.32 | | | | | all_17_9, simplifying with (61), (75) gives:
% 17.27/3.32 | | | | | (78) all_33_0 = all_26_0
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | GROUND_INST: instantiating (10) with all_35_0, all_31_0, all_17_2,
% 17.27/3.32 | | | | | all_17_8, simplifying with (57), (74) gives:
% 17.27/3.32 | | | | | (79) all_35_0 = all_31_0
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | GROUND_INST: instantiating (10) with all_24_0, all_27_0, all_17_5,
% 17.27/3.32 | | | | | all_17_7, simplifying with (59), (73) gives:
% 17.27/3.32 | | | | | (80) all_27_0 = all_24_0
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | GROUND_INST: instantiating (10) with all_25_0, all_29_0, all_17_5,
% 17.27/3.32 | | | | | all_17_6, simplifying with (63), (72) gives:
% 17.27/3.32 | | | | | (81) all_29_0 = all_25_0
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | REDUCE: (56), (79) imply:
% 17.27/3.32 | | | | | (82) ~ (all_31_0 = 0)
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | REDUCE: (51), (78) imply:
% 17.27/3.32 | | | | | (83) ~ (all_26_0 = 0)
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | REDUCE: (43), (81) imply:
% 17.27/3.32 | | | | | (84) ~ (all_25_0 = 0)
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | REDUCE: (38), (80) imply:
% 17.27/3.32 | | | | | (85) ~ (all_24_0 = 0)
% 17.27/3.32 | | | | |
% 17.27/3.32 | | | | | GROUND_INST: instantiating (6) with all_17_7, all_17_6, all_17_5,
% 17.27/3.32 | | | | | all_17_2, all_24_0, all_17_0, simplifying with (17),
% 17.27/3.32 | | | | | (18), (22), (59), (76), (77) gives:
% 17.27/3.33 | | | | | (86) all_24_0 = 0 | all_17_0 = 0 | ? [v0: int] : ? [v1: int] : ?
% 17.27/3.33 | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 &
% 17.27/3.33 | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) | (v2 = 0 &
% 17.27/3.33 | | | | | apart_point_and_line(all_17_7, all_17_2) = 0) | ( ~ (v1 =
% 17.27/3.33 | | | | | 0) & distinct_lines(all_17_5, all_17_2) = v1) | ( ~ (v0
% 17.27/3.33 | | | | | = 0) & distinct_points(all_17_7, all_17_6) = v0))
% 17.27/3.33 | | | | |
% 17.27/3.33 | | | | | GROUND_INST: instantiating (5) with all_17_7, all_17_6, all_17_5,
% 17.27/3.33 | | | | | all_17_2, all_24_0, all_17_1, simplifying with (17),
% 17.27/3.33 | | | | | (18), (20), (21), (59), (76), (77) gives:
% 17.27/3.33 | | | | | (87) all_24_0 = 0 | all_17_1 = 0 | ? [v0: int] : ? [v1: int] : ?
% 17.27/3.33 | | | | | [v2: int] : ((v2 = 0 & apart_point_and_line(all_17_6,
% 17.27/3.33 | | | | | all_17_2) = 0) | (v1 = 0 &
% 17.27/3.33 | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) | ( ~ (v0 =
% 17.27/3.33 | | | | | 0) & distinct_lines(all_17_5, all_17_2) = v0))
% 17.27/3.33 | | | | |
% 17.27/3.33 | | | | | GROUND_INST: instantiating (6) with all_17_6, all_17_9, all_17_5,
% 17.27/3.33 | | | | | all_17_2, all_25_0, all_26_0, simplifying with (15),
% 17.27/3.33 | | | | | (18), (61), (63), (76), (77) gives:
% 17.27/3.33 | | | | | (88) all_26_0 = 0 | all_25_0 = 0 | ? [v0: int] : ? [v1: int] : ?
% 17.27/3.33 | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 &
% 17.27/3.33 | | | | | apart_point_and_line(all_17_9, all_17_5) = 0) | (v2 = 0 &
% 17.27/3.33 | | | | | apart_point_and_line(all_17_6, all_17_2) = 0) | ( ~ (v1 =
% 17.27/3.33 | | | | | 0) & distinct_lines(all_17_5, all_17_2) = v1) | ( ~ (v0
% 17.27/3.33 | | | | | = 0) & distinct_points(all_17_6, all_17_9) = v0))
% 17.27/3.33 | | | | |
% 17.27/3.33 | | | | | BETA: splitting (25) gives:
% 17.27/3.33 | | | | |
% 17.27/3.33 | | | | | Case 1:
% 17.27/3.33 | | | | | |
% 17.27/3.33 | | | | | | (89) all_17_3 = 0 & apart_point_and_line(all_17_8, all_17_5) = 0
% 17.27/3.33 | | | | | |
% 17.27/3.33 | | | | | | ALPHA: (89) implies:
% 17.27/3.33 | | | | | | (90) apart_point_and_line(all_17_8, all_17_5) = 0
% 17.27/3.33 | | | | | |
% 17.27/3.33 | | | | | | BETA: splitting (86) gives:
% 17.27/3.33 | | | | | |
% 17.27/3.33 | | | | | | Case 1:
% 17.27/3.33 | | | | | | |
% 17.27/3.33 | | | | | | | (91) all_24_0 = 0
% 17.27/3.33 | | | | | | |
% 17.27/3.33 | | | | | | | REDUCE: (85), (91) imply:
% 17.27/3.33 | | | | | | | (92) $false
% 17.27/3.33 | | | | | | |
% 17.27/3.33 | | | | | | | CLOSE: (92) is inconsistent.
% 17.27/3.33 | | | | | | |
% 17.52/3.33 | | | | | | Case 2:
% 17.52/3.33 | | | | | | |
% 17.52/3.33 | | | | | | | (93) all_17_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int]
% 17.52/3.33 | | | | | | | : ? [v3: int] : ((v3 = 0 & apart_point_and_line(all_17_6,
% 17.52/3.33 | | | | | | | all_17_5) = 0) | (v2 = 0 &
% 17.52/3.33 | | | | | | | apart_point_and_line(all_17_7, all_17_2) = 0) | ( ~
% 17.52/3.33 | | | | | | | (v1 = 0) & distinct_lines(all_17_5, all_17_2) = v1) |
% 17.52/3.33 | | | | | | | ( ~ (v0 = 0) & distinct_points(all_17_7, all_17_6) =
% 17.52/3.33 | | | | | | | v0))
% 17.52/3.33 | | | | | | |
% 17.52/3.33 | | | | | | | BETA: splitting (87) gives:
% 17.52/3.33 | | | | | | |
% 17.52/3.33 | | | | | | | Case 1:
% 17.52/3.33 | | | | | | | |
% 17.52/3.33 | | | | | | | | (94) all_24_0 = 0
% 17.52/3.33 | | | | | | | |
% 17.52/3.33 | | | | | | | | REDUCE: (85), (94) imply:
% 17.52/3.33 | | | | | | | | (95) $false
% 17.52/3.33 | | | | | | | |
% 17.52/3.33 | | | | | | | | CLOSE: (95) is inconsistent.
% 17.52/3.33 | | | | | | | |
% 17.52/3.33 | | | | | | | Case 2:
% 17.52/3.33 | | | | | | | |
% 17.52/3.33 | | | | | | | | (96) all_17_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2:
% 17.52/3.33 | | | | | | | | int] : ((v2 = 0 & apart_point_and_line(all_17_6,
% 17.52/3.33 | | | | | | | | all_17_2) = 0) | (v1 = 0 &
% 17.52/3.33 | | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) | ( ~
% 17.52/3.33 | | | | | | | | (v0 = 0) & distinct_lines(all_17_5, all_17_2) = v0))
% 17.52/3.33 | | | | | | | |
% 17.52/3.33 | | | | | | | | BETA: splitting (88) gives:
% 17.52/3.33 | | | | | | | |
% 17.52/3.33 | | | | | | | | Case 1:
% 17.52/3.33 | | | | | | | | |
% 17.52/3.33 | | | | | | | | | (97) all_26_0 = 0
% 17.52/3.33 | | | | | | | | |
% 17.52/3.33 | | | | | | | | | REDUCE: (83), (97) imply:
% 17.52/3.33 | | | | | | | | | (98) $false
% 17.52/3.33 | | | | | | | | |
% 17.52/3.33 | | | | | | | | | CLOSE: (98) is inconsistent.
% 17.52/3.33 | | | | | | | | |
% 17.52/3.33 | | | | | | | | Case 2:
% 17.52/3.34 | | | | | | | | |
% 17.52/3.34 | | | | | | | | | (99) all_25_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2:
% 17.52/3.34 | | | | | | | | | int] : ? [v3: int] : ((v3 = 0 &
% 17.52/3.34 | | | | | | | | | apart_point_and_line(all_17_9, all_17_5) = 0) |
% 17.52/3.34 | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_6, all_17_2) =
% 17.52/3.34 | | | | | | | | | 0) | ( ~ (v1 = 0) & distinct_lines(all_17_5,
% 17.52/3.34 | | | | | | | | | all_17_2) = v1) | ( ~ (v0 = 0) &
% 17.52/3.34 | | | | | | | | | distinct_points(all_17_6, all_17_9) = v0))
% 17.52/3.34 | | | | | | | | |
% 17.52/3.34 | | | | | | | | | BETA: splitting (93) gives:
% 17.52/3.34 | | | | | | | | |
% 17.52/3.34 | | | | | | | | | Case 1:
% 17.52/3.34 | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | (100) all_17_0 = 0
% 17.52/3.34 | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | REDUCE: (14), (100) imply:
% 17.52/3.34 | | | | | | | | | | (101) $false
% 17.52/3.34 | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | CLOSE: (101) is inconsistent.
% 17.52/3.34 | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | Case 2:
% 17.52/3.34 | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | (102) ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 17.52/3.34 | | | | | | | | | | [v3: int] : ((v3 = 0 &
% 17.52/3.34 | | | | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) |
% 17.52/3.34 | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_7,
% 17.52/3.34 | | | | | | | | | | all_17_2) = 0) | ( ~ (v1 = 0) &
% 17.52/3.34 | | | | | | | | | | distinct_lines(all_17_5, all_17_2) = v1) | ( ~
% 17.52/3.34 | | | | | | | | | | (v0 = 0) & distinct_points(all_17_7, all_17_6)
% 17.52/3.34 | | | | | | | | | | = v0))
% 17.52/3.34 | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | DELTA: instantiating (102) with fresh symbols all_286_0,
% 17.52/3.34 | | | | | | | | | | all_286_1, all_286_2, all_286_3 gives:
% 17.52/3.34 | | | | | | | | | | (103) (all_286_0 = 0 & apart_point_and_line(all_17_6,
% 17.52/3.34 | | | | | | | | | | all_17_5) = 0) | (all_286_1 = 0 &
% 17.52/3.34 | | | | | | | | | | apart_point_and_line(all_17_7, all_17_2) = 0) | (
% 17.52/3.34 | | | | | | | | | | ~ (all_286_2 = 0) & distinct_lines(all_17_5,
% 17.52/3.34 | | | | | | | | | | all_17_2) = all_286_2) | ( ~ (all_286_3 = 0) &
% 17.52/3.34 | | | | | | | | | | distinct_points(all_17_7, all_17_6) = all_286_3)
% 17.52/3.34 | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | BETA: splitting (96) gives:
% 17.52/3.34 | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | Case 1:
% 17.52/3.34 | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | (104) all_17_1 = 0
% 17.52/3.34 | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | REDUCE: (13), (104) imply:
% 17.52/3.34 | | | | | | | | | | | (105) $false
% 17.52/3.34 | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | CLOSE: (105) is inconsistent.
% 17.52/3.34 | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | Case 2:
% 17.52/3.34 | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | (106) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2
% 17.52/3.34 | | | | | | | | | | | = 0 & apart_point_and_line(all_17_6, all_17_2)
% 17.52/3.34 | | | | | | | | | | | = 0) | (v1 = 0 &
% 17.52/3.34 | | | | | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0)
% 17.52/3.34 | | | | | | | | | | | | ( ~ (v0 = 0) & distinct_lines(all_17_5,
% 17.52/3.34 | | | | | | | | | | | all_17_2) = v0))
% 17.52/3.34 | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | DELTA: instantiating (106) with fresh symbols all_294_0,
% 17.52/3.34 | | | | | | | | | | | all_294_1, all_294_2 gives:
% 17.52/3.34 | | | | | | | | | | | (107) (all_294_0 = 0 & apart_point_and_line(all_17_6,
% 17.52/3.34 | | | | | | | | | | | all_17_2) = 0) | (all_294_1 = 0 &
% 17.52/3.34 | | | | | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) |
% 17.52/3.34 | | | | | | | | | | | ( ~ (all_294_2 = 0) & distinct_lines(all_17_5,
% 17.52/3.34 | | | | | | | | | | | all_17_2) = all_294_2)
% 17.52/3.34 | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | BETA: splitting (107) gives:
% 17.52/3.34 | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | Case 1:
% 17.52/3.34 | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | | (108) all_294_0 = 0 & apart_point_and_line(all_17_6,
% 17.52/3.34 | | | | | | | | | | | | all_17_2) = 0
% 17.52/3.34 | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | | ALPHA: (108) implies:
% 17.52/3.34 | | | | | | | | | | | | (109) apart_point_and_line(all_17_6, all_17_2) = 0
% 17.52/3.34 | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | | REF_CLOSE: (10), (14), (22), (109) are inconsistent by
% 17.52/3.34 | | | | | | | | | | | | sub-proof #3.
% 17.52/3.34 | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | Case 2:
% 17.52/3.34 | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | | (110) (all_294_1 = 0 & apart_point_and_line(all_17_6,
% 17.52/3.34 | | | | | | | | | | | | all_17_5) = 0) | ( ~ (all_294_2 = 0) &
% 17.52/3.34 | | | | | | | | | | | | distinct_lines(all_17_5, all_17_2) = all_294_2)
% 17.52/3.34 | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | | BETA: splitting (110) gives:
% 17.52/3.34 | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | | Case 1:
% 17.52/3.34 | | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | | | (111) all_294_1 = 0 & apart_point_and_line(all_17_6,
% 17.52/3.34 | | | | | | | | | | | | | all_17_5) = 0
% 17.52/3.34 | | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | | | ALPHA: (111) implies:
% 17.52/3.34 | | | | | | | | | | | | | (112) apart_point_and_line(all_17_6, all_17_5) = 0
% 17.52/3.34 | | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | | | REF_CLOSE: (10), (63), (84), (112) are inconsistent by
% 17.52/3.34 | | | | | | | | | | | | | sub-proof #2.
% 17.52/3.34 | | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | | Case 2:
% 17.52/3.34 | | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | | | (113) ~ (all_294_2 = 0) & distinct_lines(all_17_5,
% 17.52/3.34 | | | | | | | | | | | | | all_17_2) = all_294_2
% 17.52/3.34 | | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | | | ALPHA: (113) implies:
% 17.52/3.34 | | | | | | | | | | | | | (114) ~ (all_294_2 = 0)
% 17.52/3.34 | | | | | | | | | | | | | (115) distinct_lines(all_17_5, all_17_2) = all_294_2
% 17.52/3.34 | | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | | | BETA: splitting (103) gives:
% 17.52/3.34 | | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | | | Case 1:
% 17.52/3.34 | | | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | | | | (116) (all_286_0 = 0 & apart_point_and_line(all_17_6,
% 17.52/3.34 | | | | | | | | | | | | | | all_17_5) = 0) | (all_286_1 = 0 &
% 17.52/3.34 | | | | | | | | | | | | | | apart_point_and_line(all_17_7, all_17_2) = 0)
% 17.52/3.34 | | | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 17.52/3.34 | | | | | | | | | | | | | |
% 17.52/3.34 | | | | | | | | | | | | | | Case 1:
% 17.52/3.34 | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | (117) all_286_0 = 0 & apart_point_and_line(all_17_6,
% 17.52/3.35 | | | | | | | | | | | | | | | all_17_5) = 0
% 17.52/3.35 | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 17.52/3.35 | | | | | | | | | | | | | | | (118) apart_point_and_line(all_17_6, all_17_5) = 0
% 17.52/3.35 | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | REF_CLOSE: (10), (63), (84), (118) are inconsistent by
% 17.52/3.35 | | | | | | | | | | | | | | | sub-proof #2.
% 17.52/3.35 | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | Case 2:
% 17.52/3.35 | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | (119) all_286_1 = 0 & apart_point_and_line(all_17_7,
% 17.52/3.35 | | | | | | | | | | | | | | | all_17_2) = 0
% 17.52/3.35 | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 17.52/3.35 | | | | | | | | | | | | | | | (120) apart_point_and_line(all_17_7, all_17_2) = 0
% 17.52/3.35 | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (21), (120) are inconsistent by
% 17.52/3.35 | | | | | | | | | | | | | | | sub-proof #1.
% 17.52/3.35 | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | End of split
% 17.52/3.35 | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | Case 2:
% 17.52/3.35 | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | (121) ( ~ (all_286_2 = 0) & distinct_lines(all_17_5,
% 17.52/3.35 | | | | | | | | | | | | | | all_17_2) = all_286_2) | ( ~ (all_286_3 = 0) &
% 17.52/3.35 | | | | | | | | | | | | | | distinct_points(all_17_7, all_17_6) = all_286_3)
% 17.52/3.35 | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 17.52/3.35 | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | Case 1:
% 17.52/3.35 | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | (122) ~ (all_286_2 = 0) & distinct_lines(all_17_5,
% 17.52/3.35 | | | | | | | | | | | | | | | all_17_2) = all_286_2
% 17.52/3.35 | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 17.52/3.35 | | | | | | | | | | | | | | | (123) distinct_lines(all_17_5, all_17_2) = all_286_2
% 17.52/3.35 | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 17.52/3.35 | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | Case 1:
% 17.52/3.35 | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | | (124) all_25_0 = 0
% 17.52/3.35 | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | | REDUCE: (84), (124) imply:
% 17.52/3.35 | | | | | | | | | | | | | | | | (125) $false
% 17.52/3.35 | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | | CLOSE: (125) is inconsistent.
% 17.52/3.35 | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | Case 2:
% 17.52/3.35 | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_286_2, all_294_2,
% 17.52/3.35 | | | | | | | | | | | | | | | | all_17_2, all_17_5, simplifying with (115), (123)
% 17.52/3.35 | | | | | | | | | | | | | | | | gives:
% 17.52/3.35 | | | | | | | | | | | | | | | | (126) all_294_2 = all_286_2
% 17.52/3.35 | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | | REDUCE: (114), (126) imply:
% 17.52/3.35 | | | | | | | | | | | | | | | | (127) ~ (all_286_2 = 0)
% 17.52/3.35 | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_17_8, all_17_5,
% 17.52/3.35 | | | | | | | | | | | | | | | | all_17_2, all_286_2, simplifying with (16), (76),
% 17.52/3.35 | | | | | | | | | | | | | | | | (77), (90), (123) gives:
% 17.52/3.35 | | | | | | | | | | | | | | | | (128) all_286_2 = 0 | apart_point_and_line(all_17_8,
% 17.52/3.35 | | | | | | | | | | | | | | | | all_17_2) = 0
% 17.52/3.35 | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 17.52/3.35 | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | | Case 1:
% 17.52/3.35 | | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | | | (129) apart_point_and_line(all_17_8, all_17_2) = 0
% 17.52/3.35 | | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_31_0, 0, all_17_2,
% 17.52/3.35 | | | | | | | | | | | | | | | | | all_17_8, simplifying with (74), (129) gives:
% 17.52/3.35 | | | | | | | | | | | | | | | | | (130) all_31_0 = 0
% 17.52/3.35 | | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | | | REDUCE: (82), (130) imply:
% 17.52/3.35 | | | | | | | | | | | | | | | | | (131) $false
% 17.52/3.35 | | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | | | CLOSE: (131) is inconsistent.
% 17.52/3.35 | | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | | Case 2:
% 17.52/3.35 | | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | | | (132) all_286_2 = 0
% 17.52/3.35 | | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | | | REDUCE: (127), (132) imply:
% 17.52/3.35 | | | | | | | | | | | | | | | | | (133) $false
% 17.52/3.35 | | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | | | CLOSE: (133) is inconsistent.
% 17.52/3.35 | | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | | End of split
% 17.52/3.35 | | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | End of split
% 17.52/3.35 | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | Case 2:
% 17.52/3.35 | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | (134) ~ (all_286_3 = 0) & distinct_points(all_17_7,
% 17.52/3.35 | | | | | | | | | | | | | | | all_17_6) = all_286_3
% 17.52/3.35 | | | | | | | | | | | | | | |
% 17.52/3.35 | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 17.52/3.36 | | | | | | | | | | | | | | | (135) ~ (all_286_3 = 0)
% 17.52/3.36 | | | | | | | | | | | | | | | (136) distinct_points(all_17_7, all_17_6) = all_286_3
% 17.52/3.36 | | | | | | | | | | | | | | |
% 17.52/3.36 | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_286_3, all_17_6,
% 17.52/3.36 | | | | | | | | | | | | | | | all_17_7, simplifying with (20), (136) gives:
% 17.52/3.36 | | | | | | | | | | | | | | | (137) all_286_3 = 0
% 17.52/3.36 | | | | | | | | | | | | | | |
% 17.52/3.36 | | | | | | | | | | | | | | | REDUCE: (135), (137) imply:
% 17.52/3.36 | | | | | | | | | | | | | | | (138) $false
% 17.52/3.36 | | | | | | | | | | | | | | |
% 17.52/3.36 | | | | | | | | | | | | | | | CLOSE: (138) is inconsistent.
% 17.52/3.36 | | | | | | | | | | | | | | |
% 17.52/3.36 | | | | | | | | | | | | | | End of split
% 17.52/3.36 | | | | | | | | | | | | | |
% 17.52/3.36 | | | | | | | | | | | | | End of split
% 17.52/3.36 | | | | | | | | | | | | |
% 17.52/3.36 | | | | | | | | | | | | End of split
% 17.52/3.36 | | | | | | | | | | | |
% 17.52/3.36 | | | | | | | | | | | End of split
% 17.52/3.36 | | | | | | | | | | |
% 17.52/3.36 | | | | | | | | | | End of split
% 17.52/3.36 | | | | | | | | | |
% 17.52/3.36 | | | | | | | | | End of split
% 17.52/3.36 | | | | | | | | |
% 17.52/3.36 | | | | | | | | End of split
% 17.52/3.36 | | | | | | | |
% 17.52/3.36 | | | | | | | End of split
% 17.52/3.36 | | | | | | |
% 17.52/3.36 | | | | | | End of split
% 17.52/3.36 | | | | | |
% 17.52/3.36 | | | | | Case 2:
% 17.52/3.36 | | | | | |
% 17.52/3.36 | | | | | | (139) all_17_4 = 0 & apart_point_and_line(all_17_9, all_17_5) = 0
% 17.52/3.36 | | | | | |
% 17.52/3.36 | | | | | | ALPHA: (139) implies:
% 17.52/3.36 | | | | | | (140) apart_point_and_line(all_17_9, all_17_5) = 0
% 17.52/3.36 | | | | | |
% 17.52/3.36 | | | | | | BETA: splitting (86) gives:
% 17.52/3.36 | | | | | |
% 17.52/3.36 | | | | | | Case 1:
% 17.52/3.36 | | | | | | |
% 17.52/3.36 | | | | | | | (141) all_24_0 = 0
% 17.52/3.36 | | | | | | |
% 17.52/3.36 | | | | | | | REDUCE: (85), (141) imply:
% 17.52/3.36 | | | | | | | (142) $false
% 17.52/3.36 | | | | | | |
% 17.52/3.36 | | | | | | | CLOSE: (142) is inconsistent.
% 17.52/3.36 | | | | | | |
% 17.52/3.36 | | | | | | Case 2:
% 17.52/3.36 | | | | | | |
% 17.52/3.36 | | | | | | | (143) all_17_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int]
% 17.52/3.36 | | | | | | | : ? [v3: int] : ((v3 = 0 &
% 17.52/3.36 | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) | (v2 =
% 17.52/3.36 | | | | | | | 0 & apart_point_and_line(all_17_7, all_17_2) = 0) | (
% 17.52/3.36 | | | | | | | ~ (v1 = 0) & distinct_lines(all_17_5, all_17_2) = v1)
% 17.52/3.36 | | | | | | | | ( ~ (v0 = 0) & distinct_points(all_17_7, all_17_6) =
% 17.52/3.36 | | | | | | | v0))
% 17.52/3.36 | | | | | | |
% 17.52/3.36 | | | | | | | BETA: splitting (87) gives:
% 17.52/3.36 | | | | | | |
% 17.52/3.36 | | | | | | | Case 1:
% 17.52/3.36 | | | | | | | |
% 17.52/3.36 | | | | | | | | (144) all_24_0 = 0
% 17.52/3.36 | | | | | | | |
% 17.52/3.36 | | | | | | | | REDUCE: (85), (144) imply:
% 17.52/3.36 | | | | | | | | (145) $false
% 17.52/3.36 | | | | | | | |
% 17.52/3.36 | | | | | | | | CLOSE: (145) is inconsistent.
% 17.52/3.36 | | | | | | | |
% 17.52/3.36 | | | | | | | Case 2:
% 17.52/3.36 | | | | | | | |
% 17.52/3.36 | | | | | | | | (146) all_17_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2:
% 17.52/3.36 | | | | | | | | int] : ((v2 = 0 & apart_point_and_line(all_17_6,
% 17.52/3.36 | | | | | | | | all_17_2) = 0) | (v1 = 0 &
% 17.52/3.36 | | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) | ( ~
% 17.52/3.36 | | | | | | | | (v0 = 0) & distinct_lines(all_17_5, all_17_2) =
% 17.52/3.36 | | | | | | | | v0))
% 17.52/3.36 | | | | | | | |
% 17.52/3.36 | | | | | | | | BETA: splitting (88) gives:
% 17.52/3.36 | | | | | | | |
% 17.52/3.36 | | | | | | | | Case 1:
% 17.52/3.36 | | | | | | | | |
% 17.52/3.36 | | | | | | | | | (147) all_26_0 = 0
% 17.52/3.36 | | | | | | | | |
% 17.52/3.36 | | | | | | | | | REDUCE: (83), (147) imply:
% 17.52/3.36 | | | | | | | | | (148) $false
% 17.52/3.36 | | | | | | | | |
% 17.52/3.36 | | | | | | | | | CLOSE: (148) is inconsistent.
% 17.52/3.36 | | | | | | | | |
% 17.52/3.36 | | | | | | | | Case 2:
% 17.52/3.36 | | | | | | | | |
% 17.52/3.36 | | | | | | | | | (149) all_25_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2:
% 17.52/3.36 | | | | | | | | | int] : ? [v3: int] : ((v3 = 0 &
% 17.52/3.36 | | | | | | | | | apart_point_and_line(all_17_9, all_17_5) = 0) |
% 17.52/3.36 | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_6, all_17_2)
% 17.52/3.36 | | | | | | | | | = 0) | ( ~ (v1 = 0) & distinct_lines(all_17_5,
% 17.52/3.36 | | | | | | | | | all_17_2) = v1) | ( ~ (v0 = 0) &
% 17.52/3.36 | | | | | | | | | distinct_points(all_17_6, all_17_9) = v0))
% 17.52/3.36 | | | | | | | | |
% 17.52/3.36 | | | | | | | | | BETA: splitting (143) gives:
% 17.52/3.36 | | | | | | | | |
% 17.52/3.36 | | | | | | | | | Case 1:
% 17.52/3.36 | | | | | | | | | |
% 17.52/3.36 | | | | | | | | | | (150) all_17_0 = 0
% 17.52/3.36 | | | | | | | | | |
% 17.52/3.36 | | | | | | | | | | REDUCE: (14), (150) imply:
% 17.52/3.36 | | | | | | | | | | (151) $false
% 17.52/3.36 | | | | | | | | | |
% 17.52/3.36 | | | | | | | | | | CLOSE: (151) is inconsistent.
% 17.52/3.36 | | | | | | | | | |
% 17.52/3.36 | | | | | | | | | Case 2:
% 17.52/3.36 | | | | | | | | | |
% 17.52/3.36 | | | | | | | | | | (152) ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 17.52/3.36 | | | | | | | | | | [v3: int] : ((v3 = 0 &
% 17.52/3.36 | | | | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) |
% 17.52/3.36 | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_7,
% 17.52/3.36 | | | | | | | | | | all_17_2) = 0) | ( ~ (v1 = 0) &
% 17.52/3.36 | | | | | | | | | | distinct_lines(all_17_5, all_17_2) = v1) | ( ~
% 17.52/3.36 | | | | | | | | | | (v0 = 0) & distinct_points(all_17_7, all_17_6)
% 17.52/3.36 | | | | | | | | | | = v0))
% 17.52/3.36 | | | | | | | | | |
% 17.52/3.36 | | | | | | | | | | DELTA: instantiating (152) with fresh symbols all_286_0,
% 17.52/3.36 | | | | | | | | | | all_286_1, all_286_2, all_286_3 gives:
% 17.52/3.36 | | | | | | | | | | (153) (all_286_0 = 0 & apart_point_and_line(all_17_6,
% 17.52/3.36 | | | | | | | | | | all_17_5) = 0) | (all_286_1 = 0 &
% 17.52/3.36 | | | | | | | | | | apart_point_and_line(all_17_7, all_17_2) = 0) | (
% 17.52/3.37 | | | | | | | | | | ~ (all_286_2 = 0) & distinct_lines(all_17_5,
% 17.52/3.37 | | | | | | | | | | all_17_2) = all_286_2) | ( ~ (all_286_3 = 0) &
% 17.52/3.37 | | | | | | | | | | distinct_points(all_17_7, all_17_6) = all_286_3)
% 17.52/3.37 | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | BETA: splitting (146) gives:
% 17.52/3.37 | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | Case 1:
% 17.52/3.37 | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | (154) all_17_1 = 0
% 17.52/3.37 | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | REDUCE: (13), (154) imply:
% 17.52/3.37 | | | | | | | | | | | (155) $false
% 17.52/3.37 | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | CLOSE: (155) is inconsistent.
% 17.52/3.37 | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | Case 2:
% 17.52/3.37 | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | (156) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2
% 17.52/3.37 | | | | | | | | | | | = 0 & apart_point_and_line(all_17_6, all_17_2)
% 17.52/3.37 | | | | | | | | | | | = 0) | (v1 = 0 &
% 17.52/3.37 | | | | | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0)
% 17.52/3.37 | | | | | | | | | | | | ( ~ (v0 = 0) & distinct_lines(all_17_5,
% 17.52/3.37 | | | | | | | | | | | all_17_2) = v0))
% 17.52/3.37 | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | DELTA: instantiating (156) with fresh symbols all_294_0,
% 17.52/3.37 | | | | | | | | | | | all_294_1, all_294_2 gives:
% 17.52/3.37 | | | | | | | | | | | (157) (all_294_0 = 0 & apart_point_and_line(all_17_6,
% 17.52/3.37 | | | | | | | | | | | all_17_2) = 0) | (all_294_1 = 0 &
% 17.52/3.37 | | | | | | | | | | | apart_point_and_line(all_17_6, all_17_5) = 0) |
% 17.52/3.37 | | | | | | | | | | | ( ~ (all_294_2 = 0) & distinct_lines(all_17_5,
% 17.52/3.37 | | | | | | | | | | | all_17_2) = all_294_2)
% 17.52/3.37 | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | BETA: splitting (157) gives:
% 17.52/3.37 | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | Case 1:
% 17.52/3.37 | | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | | (158) all_294_0 = 0 & apart_point_and_line(all_17_6,
% 17.52/3.37 | | | | | | | | | | | | all_17_2) = 0
% 17.52/3.37 | | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | | ALPHA: (158) implies:
% 17.52/3.37 | | | | | | | | | | | | (159) apart_point_and_line(all_17_6, all_17_2) = 0
% 17.52/3.37 | | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | | REF_CLOSE: (10), (14), (22), (159) are inconsistent by
% 17.52/3.37 | | | | | | | | | | | | sub-proof #3.
% 17.52/3.37 | | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | Case 2:
% 17.52/3.37 | | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | | (160) (all_294_1 = 0 & apart_point_and_line(all_17_6,
% 17.52/3.37 | | | | | | | | | | | | all_17_5) = 0) | ( ~ (all_294_2 = 0) &
% 17.52/3.37 | | | | | | | | | | | | distinct_lines(all_17_5, all_17_2) = all_294_2)
% 17.52/3.37 | | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | | BETA: splitting (160) gives:
% 17.52/3.37 | | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | | Case 1:
% 17.52/3.37 | | | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | | | (161) all_294_1 = 0 & apart_point_and_line(all_17_6,
% 17.52/3.37 | | | | | | | | | | | | | all_17_5) = 0
% 17.52/3.37 | | | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | | | ALPHA: (161) implies:
% 17.52/3.37 | | | | | | | | | | | | | (162) apart_point_and_line(all_17_6, all_17_5) = 0
% 17.52/3.37 | | | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | | | REF_CLOSE: (10), (63), (84), (162) are inconsistent by
% 17.52/3.37 | | | | | | | | | | | | | sub-proof #2.
% 17.52/3.37 | | | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | | Case 2:
% 17.52/3.37 | | | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | | | (163) ~ (all_294_2 = 0) & distinct_lines(all_17_5,
% 17.52/3.37 | | | | | | | | | | | | | all_17_2) = all_294_2
% 17.52/3.37 | | | | | | | | | | | | |
% 17.52/3.37 | | | | | | | | | | | | | ALPHA: (163) implies:
% 17.52/3.37 | | | | | | | | | | | | | (164) ~ (all_294_2 = 0)
% 17.71/3.37 | | | | | | | | | | | | | (165) distinct_lines(all_17_5, all_17_2) = all_294_2
% 17.71/3.37 | | | | | | | | | | | | |
% 17.71/3.37 | | | | | | | | | | | | | BETA: splitting (153) gives:
% 17.71/3.37 | | | | | | | | | | | | |
% 17.71/3.37 | | | | | | | | | | | | | Case 1:
% 17.71/3.37 | | | | | | | | | | | | | |
% 17.71/3.37 | | | | | | | | | | | | | | (166) (all_286_0 = 0 & apart_point_and_line(all_17_6,
% 17.71/3.37 | | | | | | | | | | | | | | all_17_5) = 0) | (all_286_1 = 0 &
% 17.71/3.37 | | | | | | | | | | | | | | apart_point_and_line(all_17_7, all_17_2) = 0)
% 17.71/3.37 | | | | | | | | | | | | | |
% 17.71/3.37 | | | | | | | | | | | | | | BETA: splitting (166) gives:
% 17.71/3.37 | | | | | | | | | | | | | |
% 17.71/3.37 | | | | | | | | | | | | | | Case 1:
% 17.71/3.37 | | | | | | | | | | | | | | |
% 17.71/3.37 | | | | | | | | | | | | | | | (167) all_286_0 = 0 & apart_point_and_line(all_17_6,
% 17.71/3.37 | | | | | | | | | | | | | | | all_17_5) = 0
% 17.71/3.37 | | | | | | | | | | | | | | |
% 17.71/3.37 | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 17.71/3.37 | | | | | | | | | | | | | | | (168) apart_point_and_line(all_17_6, all_17_5) = 0
% 17.71/3.37 | | | | | | | | | | | | | | |
% 17.71/3.37 | | | | | | | | | | | | | | | REF_CLOSE: (10), (63), (84), (168) are inconsistent by
% 17.71/3.37 | | | | | | | | | | | | | | | sub-proof #2.
% 17.71/3.37 | | | | | | | | | | | | | | |
% 17.71/3.37 | | | | | | | | | | | | | | Case 2:
% 17.71/3.37 | | | | | | | | | | | | | | |
% 17.71/3.37 | | | | | | | | | | | | | | | (169) all_286_1 = 0 & apart_point_and_line(all_17_7,
% 17.71/3.37 | | | | | | | | | | | | | | | all_17_2) = 0
% 17.71/3.37 | | | | | | | | | | | | | | |
% 17.71/3.37 | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 17.71/3.37 | | | | | | | | | | | | | | | (170) apart_point_and_line(all_17_7, all_17_2) = 0
% 17.71/3.37 | | | | | | | | | | | | | | |
% 17.71/3.37 | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (21), (170) are inconsistent by
% 17.71/3.37 | | | | | | | | | | | | | | | sub-proof #1.
% 17.71/3.37 | | | | | | | | | | | | | | |
% 17.71/3.37 | | | | | | | | | | | | | | End of split
% 17.71/3.37 | | | | | | | | | | | | | |
% 17.71/3.37 | | | | | | | | | | | | | Case 2:
% 17.71/3.37 | | | | | | | | | | | | | |
% 17.71/3.37 | | | | | | | | | | | | | | (171) ( ~ (all_286_2 = 0) & distinct_lines(all_17_5,
% 17.71/3.37 | | | | | | | | | | | | | | all_17_2) = all_286_2) | ( ~ (all_286_3 = 0) &
% 17.71/3.37 | | | | | | | | | | | | | | distinct_points(all_17_7, all_17_6) = all_286_3)
% 17.71/3.37 | | | | | | | | | | | | | |
% 17.71/3.37 | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 17.71/3.37 | | | | | | | | | | | | | |
% 17.71/3.37 | | | | | | | | | | | | | | Case 1:
% 17.71/3.38 | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | (172) ~ (all_286_2 = 0) & distinct_lines(all_17_5,
% 17.71/3.38 | | | | | | | | | | | | | | | all_17_2) = all_286_2
% 17.71/3.38 | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 17.71/3.38 | | | | | | | | | | | | | | | (173) distinct_lines(all_17_5, all_17_2) = all_286_2
% 17.71/3.38 | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 17.71/3.38 | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | Case 1:
% 17.71/3.38 | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | | (174) all_25_0 = 0
% 17.71/3.38 | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | | REDUCE: (84), (174) imply:
% 17.71/3.38 | | | | | | | | | | | | | | | | (175) $false
% 17.71/3.38 | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | | CLOSE: (175) is inconsistent.
% 17.71/3.38 | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | Case 2:
% 17.71/3.38 | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_286_2, all_294_2,
% 17.71/3.38 | | | | | | | | | | | | | | | | all_17_2, all_17_5, simplifying with (165), (173)
% 17.71/3.38 | | | | | | | | | | | | | | | | gives:
% 17.71/3.38 | | | | | | | | | | | | | | | | (176) all_294_2 = all_286_2
% 17.71/3.38 | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | | REDUCE: (164), (176) imply:
% 17.71/3.38 | | | | | | | | | | | | | | | | (177) ~ (all_286_2 = 0)
% 17.71/3.38 | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_17_9, all_17_5,
% 17.71/3.38 | | | | | | | | | | | | | | | | all_17_2, all_286_2, simplifying with (15), (76),
% 17.71/3.38 | | | | | | | | | | | | | | | | (77), (140), (173) gives:
% 17.71/3.38 | | | | | | | | | | | | | | | | (178) all_286_2 = 0 | apart_point_and_line(all_17_9,
% 17.71/3.38 | | | | | | | | | | | | | | | | all_17_2) = 0
% 17.71/3.38 | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 17.71/3.38 | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | | Case 1:
% 17.71/3.38 | | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | | | (179) apart_point_and_line(all_17_9, all_17_2) = 0
% 17.71/3.38 | | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_26_0, 0, all_17_2,
% 17.71/3.38 | | | | | | | | | | | | | | | | | all_17_9, simplifying with (61), (179) gives:
% 17.71/3.38 | | | | | | | | | | | | | | | | | (180) all_26_0 = 0
% 17.71/3.38 | | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | | | REDUCE: (83), (180) imply:
% 17.71/3.38 | | | | | | | | | | | | | | | | | (181) $false
% 17.71/3.38 | | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | | | CLOSE: (181) is inconsistent.
% 17.71/3.38 | | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | | Case 2:
% 17.71/3.38 | | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | | | (182) all_286_2 = 0
% 17.71/3.38 | | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | | | REDUCE: (177), (182) imply:
% 17.71/3.38 | | | | | | | | | | | | | | | | | (183) $false
% 17.71/3.38 | | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | | | CLOSE: (183) is inconsistent.
% 17.71/3.38 | | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | | End of split
% 17.71/3.38 | | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | End of split
% 17.71/3.38 | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | Case 2:
% 17.71/3.38 | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | (184) ~ (all_286_3 = 0) & distinct_points(all_17_7,
% 17.71/3.38 | | | | | | | | | | | | | | | all_17_6) = all_286_3
% 17.71/3.38 | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 17.71/3.38 | | | | | | | | | | | | | | | (185) ~ (all_286_3 = 0)
% 17.71/3.38 | | | | | | | | | | | | | | | (186) distinct_points(all_17_7, all_17_6) = all_286_3
% 17.71/3.38 | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_286_3, all_17_6,
% 17.71/3.38 | | | | | | | | | | | | | | | all_17_7, simplifying with (20), (186) gives:
% 17.71/3.38 | | | | | | | | | | | | | | | (187) all_286_3 = 0
% 17.71/3.38 | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | REDUCE: (185), (187) imply:
% 17.71/3.38 | | | | | | | | | | | | | | | (188) $false
% 17.71/3.38 | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent.
% 17.71/3.38 | | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | | End of split
% 17.71/3.38 | | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | | End of split
% 17.71/3.38 | | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | | End of split
% 17.71/3.38 | | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | | End of split
% 17.71/3.38 | | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | | End of split
% 17.71/3.38 | | | | | | | | | |
% 17.71/3.38 | | | | | | | | | End of split
% 17.71/3.38 | | | | | | | | |
% 17.71/3.38 | | | | | | | | End of split
% 17.71/3.38 | | | | | | | |
% 17.71/3.38 | | | | | | | End of split
% 17.71/3.38 | | | | | | |
% 17.71/3.38 | | | | | | End of split
% 17.71/3.38 | | | | | |
% 17.71/3.38 | | | | | End of split
% 17.71/3.38 | | | | |
% 17.71/3.38 | | | | Case 2:
% 17.71/3.38 | | | | |
% 17.71/3.38 | | | | | (189) ~ (all_25_1 = 0) & distinct_points(all_17_7, all_17_6) =
% 17.71/3.38 | | | | | all_25_1
% 17.71/3.38 | | | | |
% 17.71/3.38 | | | | | ALPHA: (189) implies:
% 17.71/3.38 | | | | | (190) ~ (all_25_1 = 0)
% 17.71/3.38 | | | | | (191) distinct_points(all_17_7, all_17_6) = all_25_1
% 17.71/3.38 | | | | |
% 17.71/3.38 | | | | | GROUND_INST: instantiating (8) with 0, all_25_1, all_17_6, all_17_7,
% 17.71/3.38 | | | | | simplifying with (20), (191) gives:
% 17.71/3.38 | | | | | (192) all_25_1 = 0
% 17.71/3.38 | | | | |
% 17.71/3.38 | | | | | REDUCE: (190), (192) imply:
% 17.71/3.38 | | | | | (193) $false
% 17.71/3.38 | | | | |
% 17.71/3.38 | | | | | CLOSE: (193) is inconsistent.
% 17.71/3.38 | | | | |
% 17.71/3.38 | | | | End of split
% 17.71/3.38 | | | |
% 17.71/3.38 | | | Case 2:
% 17.71/3.38 | | | |
% 17.71/3.38 | | | | (194) ~ (all_26_1 = 0) & distinct_points(all_17_9, all_17_8) =
% 17.71/3.38 | | | | all_26_1
% 17.71/3.38 | | | |
% 17.71/3.38 | | | | ALPHA: (194) implies:
% 17.71/3.38 | | | | (195) ~ (all_26_1 = 0)
% 17.71/3.38 | | | | (196) distinct_points(all_17_9, all_17_8) = all_26_1
% 17.71/3.38 | | | |
% 17.71/3.39 | | | | GROUND_INST: instantiating (8) with 0, all_26_1, all_17_8, all_17_9,
% 17.71/3.39 | | | | simplifying with (19), (196) gives:
% 17.71/3.39 | | | | (197) all_26_1 = 0
% 17.71/3.39 | | | |
% 17.71/3.39 | | | | REDUCE: (195), (197) imply:
% 17.71/3.39 | | | | (198) $false
% 17.71/3.39 | | | |
% 17.71/3.39 | | | | CLOSE: (198) is inconsistent.
% 17.71/3.39 | | | |
% 17.71/3.39 | | | End of split
% 17.71/3.39 | | |
% 17.71/3.39 | | Case 2:
% 17.71/3.39 | | |
% 17.71/3.39 | | | (199) ~ (all_24_1 = 0) & distinct_points(all_17_7, all_17_6) =
% 17.71/3.39 | | | all_24_1
% 17.71/3.39 | | |
% 17.71/3.39 | | | ALPHA: (199) implies:
% 17.71/3.39 | | | (200) ~ (all_24_1 = 0)
% 17.71/3.39 | | | (201) distinct_points(all_17_7, all_17_6) = all_24_1
% 17.71/3.39 | | |
% 17.71/3.39 | | | GROUND_INST: instantiating (8) with 0, all_24_1, all_17_6, all_17_7,
% 17.71/3.39 | | | simplifying with (20), (201) gives:
% 17.71/3.39 | | | (202) all_24_1 = 0
% 17.71/3.39 | | |
% 17.71/3.39 | | | REDUCE: (200), (202) imply:
% 17.71/3.39 | | | (203) $false
% 17.71/3.39 | | |
% 17.71/3.39 | | | CLOSE: (203) is inconsistent.
% 17.71/3.39 | | |
% 17.71/3.39 | | End of split
% 17.71/3.39 | |
% 17.71/3.39 | Case 2:
% 17.71/3.39 | |
% 17.71/3.39 | | (204) ~ (all_35_1 = 0) & distinct_points(all_17_9, all_17_8) = all_35_1
% 17.71/3.39 | |
% 17.71/3.39 | | ALPHA: (204) implies:
% 17.71/3.39 | | (205) ~ (all_35_1 = 0)
% 17.71/3.39 | | (206) distinct_points(all_17_9, all_17_8) = all_35_1
% 17.71/3.39 | |
% 17.71/3.39 | | GROUND_INST: instantiating (8) with 0, all_35_1, all_17_8, all_17_9,
% 17.71/3.39 | | simplifying with (19), (206) gives:
% 17.71/3.39 | | (207) all_35_1 = 0
% 17.71/3.39 | |
% 17.71/3.39 | | REDUCE: (205), (207) imply:
% 17.71/3.39 | | (208) $false
% 17.71/3.39 | |
% 17.71/3.39 | | CLOSE: (208) is inconsistent.
% 17.71/3.39 | |
% 17.71/3.39 | End of split
% 17.71/3.39 |
% 17.71/3.39 End of proof
% 17.71/3.39
% 17.71/3.39 Sub-proof #1 shows that the following formulas are inconsistent:
% 17.71/3.39 ----------------------------------------------------------------
% 17.71/3.39 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.71/3.39 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 17.71/3.39 (apart_point_and_line(v3, v2) = v0))
% 17.71/3.39 (2) apart_point_and_line(all_17_7, all_17_2) = all_17_1
% 17.71/3.39 (3) apart_point_and_line(all_17_7, all_17_2) = 0
% 17.71/3.39 (4) ~ (all_17_1 = 0)
% 17.71/3.39
% 17.71/3.39 Begin of proof
% 17.71/3.39 |
% 17.71/3.39 | GROUND_INST: instantiating (1) with all_17_1, 0, all_17_2, all_17_7,
% 17.71/3.39 | simplifying with (2), (3) gives:
% 17.71/3.39 | (5) all_17_1 = 0
% 17.71/3.39 |
% 17.71/3.39 | REDUCE: (4), (5) imply:
% 17.71/3.39 | (6) $false
% 17.71/3.39 |
% 17.71/3.39 | CLOSE: (6) is inconsistent.
% 17.71/3.39 |
% 17.71/3.39 End of proof
% 17.71/3.39
% 17.71/3.39 Sub-proof #2 shows that the following formulas are inconsistent:
% 17.71/3.39 ----------------------------------------------------------------
% 17.71/3.39 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.71/3.39 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 17.71/3.39 (apart_point_and_line(v3, v2) = v0))
% 17.71/3.39 (2) apart_point_and_line(all_17_6, all_17_5) = all_25_0
% 17.71/3.39 (3) apart_point_and_line(all_17_6, all_17_5) = 0
% 17.71/3.39 (4) ~ (all_25_0 = 0)
% 17.71/3.39
% 17.71/3.39 Begin of proof
% 17.71/3.39 |
% 17.71/3.39 | GROUND_INST: instantiating (1) with all_25_0, 0, all_17_5, all_17_6,
% 17.71/3.39 | simplifying with (2), (3) gives:
% 17.71/3.39 | (5) all_25_0 = 0
% 17.71/3.39 |
% 17.71/3.39 | REDUCE: (4), (5) imply:
% 17.71/3.39 | (6) $false
% 17.71/3.39 |
% 17.71/3.39 | CLOSE: (6) is inconsistent.
% 17.71/3.39 |
% 17.71/3.39 End of proof
% 17.71/3.39
% 17.71/3.39 Sub-proof #3 shows that the following formulas are inconsistent:
% 17.71/3.39 ----------------------------------------------------------------
% 17.71/3.39 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.71/3.39 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 17.71/3.39 (apart_point_and_line(v3, v2) = v0))
% 17.71/3.39 (2) apart_point_and_line(all_17_6, all_17_2) = all_17_0
% 17.71/3.39 (3) apart_point_and_line(all_17_6, all_17_2) = 0
% 17.71/3.40 (4) ~ (all_17_0 = 0)
% 17.71/3.40
% 17.71/3.40 Begin of proof
% 17.71/3.40 |
% 17.71/3.40 | GROUND_INST: instantiating (1) with all_17_0, 0, all_17_2, all_17_6,
% 17.71/3.40 | simplifying with (2), (3) gives:
% 17.71/3.40 | (5) all_17_0 = 0
% 17.71/3.40 |
% 17.71/3.40 | REDUCE: (4), (5) imply:
% 17.71/3.40 | (6) $false
% 17.71/3.40 |
% 17.71/3.40 | CLOSE: (6) is inconsistent.
% 17.71/3.40 |
% 17.71/3.40 End of proof
% 17.71/3.40 % SZS output end Proof for theBenchmark
% 17.71/3.40
% 17.71/3.40 2792ms
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