TSTP Solution File: GEO189+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO189+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 : n013.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 23:22:02 EDT 2023
% Result : Theorem 10.07s 2.13s
% Output : Proof 17.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO189+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 21:26:01 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.55/0.62 ________ _____
% 0.55/0.62 ___ __ \_________(_)________________________________
% 0.55/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.55/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.55/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.55/0.62
% 0.55/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.55/0.62 (2023-06-19)
% 0.55/0.62
% 0.55/0.62 (c) Philipp Rümmer, 2009-2023
% 0.55/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.55/0.62 Amanda Stjerna.
% 0.55/0.62 Free software under BSD-3-Clause.
% 0.55/0.62
% 0.55/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.55/0.62
% 0.55/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.55/0.63 Running up to 7 provers in parallel.
% 0.55/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.55/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.55/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.55/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.55/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.55/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.55/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.33/1.02 Prover 4: Preprocessing ...
% 2.33/1.02 Prover 1: Preprocessing ...
% 2.33/1.06 Prover 5: Preprocessing ...
% 2.33/1.06 Prover 6: Preprocessing ...
% 2.33/1.06 Prover 2: Preprocessing ...
% 2.33/1.06 Prover 3: Preprocessing ...
% 2.33/1.06 Prover 0: Preprocessing ...
% 4.24/1.29 Prover 2: Proving ...
% 4.24/1.30 Prover 5: Proving ...
% 4.24/1.32 Prover 1: Constructing countermodel ...
% 4.24/1.32 Prover 6: Constructing countermodel ...
% 4.24/1.33 Prover 3: Constructing countermodel ...
% 5.18/1.43 Prover 3: gave up
% 5.51/1.44 Prover 1: gave up
% 5.51/1.44 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.51/1.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.59/1.45 Prover 4: Constructing countermodel ...
% 5.59/1.47 Prover 6: gave up
% 5.59/1.48 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 5.59/1.48 Prover 7: Preprocessing ...
% 5.59/1.49 Prover 8: Preprocessing ...
% 6.08/1.51 Prover 9: Preprocessing ...
% 6.08/1.52 Prover 0: Proving ...
% 6.08/1.53 Prover 7: Warning: ignoring some quantifiers
% 6.08/1.54 Prover 7: Constructing countermodel ...
% 6.51/1.58 Prover 8: Warning: ignoring some quantifiers
% 6.51/1.59 Prover 8: Constructing countermodel ...
% 6.51/1.63 Prover 8: gave up
% 6.51/1.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.18/1.67 Prover 9: Constructing countermodel ...
% 7.18/1.68 Prover 10: Preprocessing ...
% 7.44/1.70 Prover 10: Warning: ignoring some quantifiers
% 7.44/1.70 Prover 7: gave up
% 7.44/1.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.44/1.71 Prover 10: Constructing countermodel ...
% 7.75/1.74 Prover 11: Preprocessing ...
% 7.75/1.75 Prover 10: gave up
% 7.75/1.77 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 7.75/1.77 Prover 12: Preprocessing ...
% 8.85/1.90 Prover 12: Proving ...
% 8.85/1.94 Prover 11: Constructing countermodel ...
% 10.07/2.13 Prover 0: proved (1490ms)
% 10.07/2.13
% 10.07/2.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.07/2.13
% 10.07/2.13 Prover 9: stopped
% 10.07/2.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.07/2.13 Prover 2: stopped
% 10.74/2.15 Prover 12: stopped
% 10.74/2.15 Prover 5: stopped
% 10.74/2.15 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 10.74/2.15 Prover 16: Preprocessing ...
% 10.74/2.15 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 10.74/2.16 Prover 13: Preprocessing ...
% 10.74/2.16 Prover 19: Preprocessing ...
% 10.74/2.17 Prover 16: Warning: ignoring some quantifiers
% 10.74/2.18 Prover 16: Constructing countermodel ...
% 11.08/2.21 Prover 13: Warning: ignoring some quantifiers
% 11.08/2.21 Prover 13: Constructing countermodel ...
% 11.08/2.22 Prover 19: Warning: ignoring some quantifiers
% 11.08/2.22 Prover 19: Constructing countermodel ...
% 11.59/2.26 Prover 19: gave up
% 11.99/2.34 Prover 13: gave up
% 12.66/2.45 Prover 16: gave up
% 15.85/3.00 Prover 4: Found proof (size 220)
% 15.85/3.00 Prover 4: proved (2364ms)
% 15.85/3.01 Prover 11: stopped
% 15.85/3.01
% 15.85/3.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.85/3.01
% 15.85/3.04 % SZS output start Proof for theBenchmark
% 16.34/3.05 Assumptions after simplification:
% 16.34/3.05 ---------------------------------
% 16.34/3.05
% 16.34/3.05 (ceq2)
% 16.58/3.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 16.58/3.09 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1,
% 16.58/3.09 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 =
% 16.58/3.09 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 16.58/3.09 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) |
% 16.58/3.09 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 16.58/3.09 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 16.58/3.10 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~
% 16.58/3.10 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 16.58/3.10 apart_point_and_line(v0, v2) = 0)
% 16.58/3.10
% 16.58/3.10 (ci1)
% 16.58/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 16.58/3.10 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 16.58/3.10 (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4
% 16.58/3.10 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 16.58/3.10 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 16.58/3.10 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 &
% 16.58/3.10 apart_point_and_line(v0, v2) = v3 & $i(v2)))
% 16.58/3.10
% 16.58/3.10 (ci2)
% 16.58/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 16.58/3.10 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 16.58/3.10 (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4
% 16.58/3.10 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 16.58/3.10 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 16.58/3.10 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 &
% 16.58/3.10 apart_point_and_line(v1, v2) = v3 & $i(v2)))
% 16.58/3.10
% 16.58/3.10 (con)
% 16.58/3.11 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5:
% 16.58/3.11 $i] : ( ~ (v4 = 0) & line_connecting(v0, v2) = v5 & line_connecting(v0, v1)
% 16.58/3.11 = v3 & apart_point_and_line(v2, v3) = v4 & apart_point_and_line(v1, v5) = 0
% 16.58/3.11 & distinct_points(v1, v2) = 0 & distinct_points(v0, v2) = 0 &
% 16.58/3.11 distinct_points(v0, v1) = 0 & $i(v5) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 16.58/3.11
% 16.58/3.11 (cu1)
% 16.58/3.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 16.58/3.12 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 16.58/3.12 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 16.58/3.12 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 16.58/3.12 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0,
% 16.58/3.12 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 16.58/3.12 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 16.58/3.12 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) =
% 16.58/3.12 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3)
% 16.58/3.12 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 16.58/3.12 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 &
% 16.58/3.12 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6
% 16.58/3.12 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 16.58/3.12 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 16.58/3.12 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4)
% 16.58/3.12 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 16.58/3.12 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 16.58/3.12 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 16.58/3.12 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 =
% 16.58/3.12 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 16.58/3.12 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) =
% 16.58/3.12 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 16.58/3.12 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9:
% 16.58/3.12 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) =
% 16.58/3.12 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7
% 16.58/3.12 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 16.58/3.12 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 16.58/3.12 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4)
% 16.58/3.12 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 16.58/3.12 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 16.58/3.12 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 &
% 16.58/3.12 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0:
% 16.58/3.12 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 16.58/3.12 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~
% 16.58/3.12 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 16.58/3.12 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 16.58/3.12 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1,
% 16.58/3.12 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 16.58/3.12 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 16.58/3.12 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3)
% 16.58/3.12 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 16.58/3.12 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 16.58/3.12 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 16.58/3.12 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 16.58/3.12
% 16.58/3.12 (function-axioms)
% 16.58/3.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.58/3.12 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) &
% 16.58/3.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.58/3.12 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 16.58/3.12 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 16.58/3.12 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 16.58/3.12 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.58/3.12 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.58/3.12 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & !
% 16.58/3.12 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 16.58/3.12 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3,
% 16.58/3.12 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 16.58/3.12 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 16.58/3.12 (distinct_points(v3, v2) = v0))
% 16.58/3.12
% 16.58/3.12 Further assumptions not needed in the proof:
% 16.58/3.12 --------------------------------------------
% 16.58/3.12 apart1, apart2, apart3, apart4, apart5, ax6, ceq1, ceq3, ci3, ci4
% 16.58/3.12
% 16.58/3.12 Those formulas are unsatisfiable:
% 16.58/3.12 ---------------------------------
% 16.58/3.12
% 16.58/3.12 Begin of proof
% 16.58/3.13 |
% 16.58/3.13 | ALPHA: (ci1) implies:
% 16.58/3.13 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~
% 16.58/3.13 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 16.58/3.13 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 &
% 16.58/3.13 | $i(v2)))
% 16.58/3.13 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1)
% 16.58/3.13 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 16.58/3.13 | (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & (
% 16.58/3.13 | ~ (v4 = 0) | ~ (v3 = 0))))
% 16.58/3.13 |
% 16.58/3.13 | ALPHA: (ci2) implies:
% 16.58/3.13 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~
% 16.58/3.13 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 16.58/3.13 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 &
% 16.58/3.13 | $i(v2)))
% 16.58/3.13 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1)
% 16.58/3.13 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 16.58/3.13 | (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & (
% 16.58/3.13 | ~ (v4 = 0) | ~ (v3 = 0))))
% 16.58/3.13 |
% 16.58/3.13 | ALPHA: (cu1) implies:
% 16.58/3.13 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 16.58/3.13 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5)
% 16.58/3.13 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0,
% 16.58/3.13 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 16.58/3.13 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v1,
% 16.58/3.13 | v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2,
% 16.58/3.13 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 16.58/3.13 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 16.58/3.13 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5)
% 16.58/3.13 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 16.58/3.13 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ?
% 16.58/3.13 | [v9: any] : (apart_point_and_line(v1, v3) = v9 &
% 16.58/3.13 | apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 &
% 16.58/3.13 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0
% 16.58/3.13 | | v8 = 0)))
% 16.58/3.13 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 16.58/3.13 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5)
% 16.58/3.13 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 16.58/3.13 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ?
% 16.58/3.13 | [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 16.58/3.13 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 16.58/3.13 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0
% 16.58/3.13 | | v8 = 0)))
% 16.58/3.14 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 16.58/3.14 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5)
% 16.58/3.14 | | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0,
% 16.58/3.14 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 16.58/3.14 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v0,
% 16.58/3.14 | v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2,
% 16.58/3.14 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 16.58/3.14 |
% 16.58/3.14 | ALPHA: (ceq2) implies:
% 16.58/3.14 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 16.58/3.14 | (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0,
% 16.58/3.14 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v1,
% 16.58/3.14 | v2) = 0)
% 16.58/3.14 |
% 16.58/3.14 | ALPHA: (function-axioms) implies:
% 16.58/3.14 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 16.58/3.14 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 16.58/3.14 | (distinct_points(v3, v2) = v0))
% 16.58/3.14 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 16.58/3.14 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~
% 16.58/3.14 | (distinct_lines(v3, v2) = v0))
% 16.58/3.14 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 16.58/3.14 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 16.58/3.14 | (apart_point_and_line(v3, v2) = v0))
% 16.58/3.14 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.58/3.14 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 16.58/3.14 |
% 16.58/3.14 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2,
% 16.58/3.14 | all_17_3, all_17_4, all_17_5 gives:
% 16.58/3.14 | (14) ~ (all_17_1 = 0) & line_connecting(all_17_5, all_17_3) = all_17_0 &
% 16.58/3.14 | line_connecting(all_17_5, all_17_4) = all_17_2 &
% 16.58/3.14 | apart_point_and_line(all_17_3, all_17_2) = all_17_1 &
% 16.58/3.14 | apart_point_and_line(all_17_4, all_17_0) = 0 &
% 16.58/3.14 | distinct_points(all_17_4, all_17_3) = 0 & distinct_points(all_17_5,
% 16.58/3.14 | all_17_3) = 0 & distinct_points(all_17_5, all_17_4) = 0 &
% 16.58/3.14 | $i(all_17_0) & $i(all_17_2) & $i(all_17_3) & $i(all_17_4) &
% 16.58/3.14 | $i(all_17_5)
% 16.58/3.14 |
% 16.58/3.14 | ALPHA: (14) implies:
% 16.58/3.14 | (15) ~ (all_17_1 = 0)
% 16.58/3.14 | (16) $i(all_17_5)
% 16.58/3.14 | (17) $i(all_17_4)
% 16.58/3.14 | (18) $i(all_17_3)
% 16.58/3.14 | (19) $i(all_17_2)
% 16.58/3.14 | (20) distinct_points(all_17_5, all_17_4) = 0
% 16.58/3.14 | (21) distinct_points(all_17_5, all_17_3) = 0
% 16.58/3.14 | (22) distinct_points(all_17_4, all_17_3) = 0
% 16.58/3.14 | (23) apart_point_and_line(all_17_4, all_17_0) = 0
% 16.58/3.14 | (24) apart_point_and_line(all_17_3, all_17_2) = all_17_1
% 16.58/3.14 | (25) line_connecting(all_17_5, all_17_4) = all_17_2
% 16.58/3.14 | (26) line_connecting(all_17_5, all_17_3) = all_17_0
% 16.58/3.14 |
% 16.58/3.14 | GROUND_INST: instantiating (3) with all_17_5, all_17_4, simplifying with (16),
% 16.58/3.14 | (17), (20) gives:
% 16.58/3.14 | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5,
% 16.58/3.14 | all_17_4) = v0 & apart_point_and_line(all_17_4, v0) = v1 & $i(v0))
% 16.58/3.14 |
% 16.58/3.14 | GROUND_INST: instantiating (1) with all_17_5, all_17_4, simplifying with (16),
% 16.58/3.14 | (17), (20) gives:
% 16.58/3.14 | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5,
% 16.58/3.14 | all_17_4) = v0 & apart_point_and_line(all_17_5, v0) = v1 & $i(v0))
% 16.58/3.14 |
% 16.58/3.14 | GROUND_INST: instantiating (3) with all_17_5, all_17_3, simplifying with (16),
% 16.58/3.14 | (18), (21) gives:
% 16.58/3.14 | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5,
% 16.58/3.14 | all_17_3) = v0 & apart_point_and_line(all_17_3, v0) = v1 & $i(v0))
% 16.58/3.15 |
% 16.58/3.15 | GROUND_INST: instantiating (1) with all_17_5, all_17_3, simplifying with (16),
% 16.58/3.15 | (18), (21) gives:
% 16.58/3.15 | (30) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5,
% 16.58/3.15 | all_17_3) = v0 & apart_point_and_line(all_17_5, v0) = v1 & $i(v0))
% 16.58/3.15 |
% 16.58/3.15 | GROUND_INST: instantiating (3) with all_17_4, all_17_3, simplifying with (17),
% 16.58/3.15 | (18), (22) gives:
% 16.58/3.15 | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_4,
% 16.58/3.15 | all_17_3) = v0 & apart_point_and_line(all_17_3, v0) = v1 & $i(v0))
% 16.58/3.16 |
% 16.58/3.16 | GROUND_INST: instantiating (1) with all_17_4, all_17_3, simplifying with (17),
% 16.58/3.16 | (18), (22) gives:
% 16.58/3.16 | (32) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_4,
% 16.58/3.16 | all_17_3) = v0 & apart_point_and_line(all_17_4, v0) = v1 & $i(v0))
% 16.58/3.16 |
% 16.58/3.16 | GROUND_INST: instantiating (8) with all_17_4, all_17_3, all_17_2, all_17_2,
% 16.58/3.16 | all_17_1, all_17_1, simplifying with (17), (18), (19), (22), (24)
% 16.58/3.16 | gives:
% 16.58/3.16 | (33) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 16.58/3.17 | (apart_point_and_line(all_17_4, all_17_2) = v2 &
% 16.58/3.17 | apart_point_and_line(all_17_4, all_17_2) = v1 &
% 16.58/3.17 | distinct_lines(all_17_2, all_17_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1
% 16.58/3.17 | = 0))
% 16.58/3.17 |
% 16.58/3.17 | GROUND_INST: instantiating (8) with all_17_5, all_17_3, all_17_2, all_17_2,
% 16.58/3.17 | all_17_1, all_17_1, simplifying with (16), (18), (19), (21), (24)
% 16.58/3.17 | gives:
% 16.58/3.17 | (34) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 16.58/3.17 | (apart_point_and_line(all_17_5, all_17_2) = v2 &
% 16.58/3.17 | apart_point_and_line(all_17_5, all_17_2) = v1 &
% 16.58/3.17 | distinct_lines(all_17_2, all_17_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1
% 16.58/3.17 | = 0))
% 16.58/3.17 |
% 16.58/3.17 | GROUND_INST: instantiating (7) with all_17_3, all_17_3, all_17_2, all_17_2,
% 16.58/3.17 | all_17_1, all_17_1, simplifying with (18), (19), (24) gives:
% 16.58/3.17 | (35) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 16.58/3.17 | any] : (apart_point_and_line(all_17_3, all_17_2) = v3 &
% 16.58/3.17 | apart_point_and_line(all_17_3, all_17_2) = v2 &
% 16.58/3.17 | distinct_lines(all_17_2, all_17_2) = v1 & distinct_points(all_17_3,
% 16.58/3.17 | all_17_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 16.58/3.17 |
% 16.58/3.17 | GROUND_INST: instantiating (4) with all_17_5, all_17_4, all_17_2, simplifying
% 16.58/3.17 | with (16), (17), (25) gives:
% 16.58/3.18 | (36) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_4,
% 16.58/3.18 | all_17_2) = v1 & distinct_points(all_17_5, all_17_4) = v0 & ( ~
% 16.58/3.18 | (v1 = 0) | ~ (v0 = 0)))
% 16.58/3.18 |
% 16.58/3.18 | GROUND_INST: instantiating (2) with all_17_5, all_17_4, all_17_2, simplifying
% 16.58/3.18 | with (16), (17), (25) gives:
% 16.58/3.18 | (37) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_5,
% 16.58/3.18 | all_17_2) = v1 & distinct_points(all_17_5, all_17_4) = v0 & ( ~
% 16.58/3.18 | (v1 = 0) | ~ (v0 = 0)))
% 16.58/3.18 |
% 16.58/3.18 | GROUND_INST: instantiating (4) with all_17_5, all_17_3, all_17_0, simplifying
% 16.58/3.18 | with (16), (18), (26) gives:
% 16.58/3.18 | (38) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_3,
% 16.58/3.18 | all_17_0) = v1 & distinct_points(all_17_5, all_17_3) = v0 & ( ~
% 16.58/3.18 | (v1 = 0) | ~ (v0 = 0)))
% 16.58/3.18 |
% 16.58/3.18 | GROUND_INST: instantiating (2) with all_17_5, all_17_3, all_17_0, simplifying
% 16.58/3.18 | with (16), (18), (26) gives:
% 16.58/3.18 | (39) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_5,
% 16.58/3.18 | all_17_0) = v1 & distinct_points(all_17_5, all_17_3) = v0 & ( ~
% 16.58/3.18 | (v1 = 0) | ~ (v0 = 0)))
% 16.58/3.18 |
% 16.58/3.18 | DELTA: instantiating (39) with fresh symbols all_24_0, all_24_1 gives:
% 16.58/3.18 | (40) apart_point_and_line(all_17_5, all_17_0) = all_24_0 &
% 16.58/3.18 | distinct_points(all_17_5, all_17_3) = all_24_1 & ( ~ (all_24_0 = 0) |
% 16.58/3.18 | ~ (all_24_1 = 0))
% 16.58/3.18 |
% 16.58/3.18 | ALPHA: (40) implies:
% 16.58/3.18 | (41) distinct_points(all_17_5, all_17_3) = all_24_1
% 16.58/3.18 | (42) apart_point_and_line(all_17_5, all_17_0) = all_24_0
% 16.58/3.18 |
% 16.58/3.18 | DELTA: instantiating (32) with fresh symbols all_26_0, all_26_1 gives:
% 16.58/3.18 | (43) ~ (all_26_0 = 0) & line_connecting(all_17_4, all_17_3) = all_26_1 &
% 16.58/3.18 | apart_point_and_line(all_17_4, all_26_1) = all_26_0 & $i(all_26_1)
% 16.58/3.19 |
% 16.58/3.19 | ALPHA: (43) implies:
% 16.58/3.19 | (44) line_connecting(all_17_4, all_17_3) = all_26_1
% 16.58/3.19 |
% 16.58/3.19 | DELTA: instantiating (38) with fresh symbols all_28_0, all_28_1 gives:
% 16.58/3.19 | (45) apart_point_and_line(all_17_3, all_17_0) = all_28_0 &
% 16.58/3.19 | distinct_points(all_17_5, all_17_3) = all_28_1 & ( ~ (all_28_0 = 0) |
% 16.58/3.19 | ~ (all_28_1 = 0))
% 16.58/3.19 |
% 16.58/3.19 | ALPHA: (45) implies:
% 16.58/3.19 | (46) distinct_points(all_17_5, all_17_3) = all_28_1
% 16.58/3.19 | (47) apart_point_and_line(all_17_3, all_17_0) = all_28_0
% 16.58/3.19 | (48) ~ (all_28_0 = 0) | ~ (all_28_1 = 0)
% 16.58/3.19 |
% 16.58/3.19 | DELTA: instantiating (37) with fresh symbols all_30_0, all_30_1 gives:
% 16.58/3.19 | (49) apart_point_and_line(all_17_5, all_17_2) = all_30_0 &
% 16.58/3.19 | distinct_points(all_17_5, all_17_4) = all_30_1 & ( ~ (all_30_0 = 0) |
% 16.58/3.19 | ~ (all_30_1 = 0))
% 16.58/3.19 |
% 16.58/3.19 | ALPHA: (49) implies:
% 16.58/3.19 | (50) apart_point_and_line(all_17_5, all_17_2) = all_30_0
% 16.58/3.19 |
% 16.58/3.19 | DELTA: instantiating (31) with fresh symbols all_32_0, all_32_1 gives:
% 16.58/3.19 | (51) ~ (all_32_0 = 0) & line_connecting(all_17_4, all_17_3) = all_32_1 &
% 16.58/3.19 | apart_point_and_line(all_17_3, all_32_1) = all_32_0 & $i(all_32_1)
% 16.58/3.19 |
% 16.58/3.19 | ALPHA: (51) implies:
% 16.58/3.19 | (52) ~ (all_32_0 = 0)
% 16.58/3.19 | (53) $i(all_32_1)
% 16.58/3.19 | (54) apart_point_and_line(all_17_3, all_32_1) = all_32_0
% 16.58/3.19 | (55) line_connecting(all_17_4, all_17_3) = all_32_1
% 16.58/3.19 |
% 16.58/3.19 | DELTA: instantiating (30) with fresh symbols all_34_0, all_34_1 gives:
% 16.58/3.19 | (56) ~ (all_34_0 = 0) & line_connecting(all_17_5, all_17_3) = all_34_1 &
% 16.58/3.19 | apart_point_and_line(all_17_5, all_34_1) = all_34_0 & $i(all_34_1)
% 16.58/3.19 |
% 16.58/3.19 | ALPHA: (56) implies:
% 16.58/3.19 | (57) ~ (all_34_0 = 0)
% 16.58/3.19 | (58) $i(all_34_1)
% 16.58/3.19 | (59) apart_point_and_line(all_17_5, all_34_1) = all_34_0
% 16.58/3.19 | (60) line_connecting(all_17_5, all_17_3) = all_34_1
% 16.58/3.19 |
% 16.58/3.19 | DELTA: instantiating (28) with fresh symbols all_36_0, all_36_1 gives:
% 16.58/3.19 | (61) ~ (all_36_0 = 0) & line_connecting(all_17_5, all_17_4) = all_36_1 &
% 16.58/3.19 | apart_point_and_line(all_17_5, all_36_1) = all_36_0 & $i(all_36_1)
% 16.58/3.19 |
% 16.58/3.19 | ALPHA: (61) implies:
% 16.58/3.19 | (62) ~ (all_36_0 = 0)
% 16.58/3.19 | (63) $i(all_36_1)
% 16.58/3.19 | (64) apart_point_and_line(all_17_5, all_36_1) = all_36_0
% 16.58/3.19 | (65) line_connecting(all_17_5, all_17_4) = all_36_1
% 16.58/3.19 |
% 16.58/3.19 | DELTA: instantiating (36) with fresh symbols all_38_0, all_38_1 gives:
% 16.58/3.19 | (66) apart_point_and_line(all_17_4, all_17_2) = all_38_0 &
% 16.58/3.19 | distinct_points(all_17_5, all_17_4) = all_38_1 & ( ~ (all_38_0 = 0) |
% 16.58/3.19 | ~ (all_38_1 = 0))
% 16.58/3.19 |
% 16.58/3.19 | ALPHA: (66) implies:
% 16.58/3.19 | (67) apart_point_and_line(all_17_4, all_17_2) = all_38_0
% 16.58/3.19 |
% 16.58/3.19 | DELTA: instantiating (27) with fresh symbols all_40_0, all_40_1 gives:
% 16.58/3.20 | (68) ~ (all_40_0 = 0) & line_connecting(all_17_5, all_17_4) = all_40_1 &
% 16.58/3.20 | apart_point_and_line(all_17_4, all_40_1) = all_40_0 & $i(all_40_1)
% 16.58/3.20 |
% 16.58/3.20 | ALPHA: (68) implies:
% 16.58/3.20 | (69) ~ (all_40_0 = 0)
% 16.58/3.20 | (70) apart_point_and_line(all_17_4, all_40_1) = all_40_0
% 16.58/3.20 | (71) line_connecting(all_17_5, all_17_4) = all_40_1
% 16.58/3.20 |
% 16.58/3.20 | DELTA: instantiating (29) with fresh symbols all_42_0, all_42_1 gives:
% 16.58/3.20 | (72) ~ (all_42_0 = 0) & line_connecting(all_17_5, all_17_3) = all_42_1 &
% 16.58/3.20 | apart_point_and_line(all_17_3, all_42_1) = all_42_0 & $i(all_42_1)
% 16.58/3.20 |
% 16.58/3.20 | ALPHA: (72) implies:
% 16.58/3.20 | (73) ~ (all_42_0 = 0)
% 16.58/3.20 | (74) apart_point_and_line(all_17_3, all_42_1) = all_42_0
% 16.58/3.20 | (75) line_connecting(all_17_5, all_17_3) = all_42_1
% 16.58/3.20 |
% 16.58/3.20 | BETA: splitting (34) gives:
% 16.58/3.20 |
% 16.58/3.20 | Case 1:
% 16.58/3.20 | |
% 16.58/3.20 | | (76) all_17_1 = 0
% 16.58/3.20 | |
% 16.58/3.20 | | REDUCE: (15), (76) imply:
% 16.58/3.20 | | (77) $false
% 16.58/3.20 | |
% 16.58/3.20 | | CLOSE: (77) is inconsistent.
% 16.58/3.20 | |
% 16.58/3.20 | Case 2:
% 16.58/3.20 | |
% 16.58/3.20 | | (78) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 16.58/3.20 | | (apart_point_and_line(all_17_5, all_17_2) = v2 &
% 16.58/3.20 | | apart_point_and_line(all_17_5, all_17_2) = v1 &
% 16.58/3.20 | | distinct_lines(all_17_2, all_17_2) = v0 & ( ~ (v0 = 0) | v2 = 0 |
% 16.58/3.20 | | v1 = 0))
% 16.58/3.20 | |
% 16.58/3.20 | | DELTA: instantiating (78) with fresh symbols all_48_0, all_48_1, all_48_2
% 16.58/3.20 | | gives:
% 16.58/3.20 | | (79) apart_point_and_line(all_17_5, all_17_2) = all_48_0 &
% 16.58/3.20 | | apart_point_and_line(all_17_5, all_17_2) = all_48_1 &
% 16.58/3.20 | | distinct_lines(all_17_2, all_17_2) = all_48_2 & ( ~ (all_48_2 = 0) |
% 16.58/3.20 | | all_48_0 = 0 | all_48_1 = 0)
% 16.58/3.20 | |
% 16.58/3.20 | | ALPHA: (79) implies:
% 16.58/3.20 | | (80) apart_point_and_line(all_17_5, all_17_2) = all_48_1
% 16.58/3.20 | | (81) apart_point_and_line(all_17_5, all_17_2) = all_48_0
% 16.58/3.20 | |
% 16.58/3.20 | | BETA: splitting (33) gives:
% 16.58/3.20 | |
% 16.58/3.20 | | Case 1:
% 16.58/3.20 | | |
% 16.58/3.20 | | | (82) all_17_1 = 0
% 16.58/3.20 | | |
% 16.58/3.20 | | | REDUCE: (15), (82) imply:
% 16.58/3.20 | | | (83) $false
% 16.58/3.20 | | |
% 16.58/3.20 | | | CLOSE: (83) is inconsistent.
% 16.58/3.20 | | |
% 16.58/3.20 | | Case 2:
% 16.58/3.20 | | |
% 16.58/3.20 | | | (84) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 16.58/3.20 | | | (apart_point_and_line(all_17_4, all_17_2) = v2 &
% 16.58/3.20 | | | apart_point_and_line(all_17_4, all_17_2) = v1 &
% 16.58/3.20 | | | distinct_lines(all_17_2, all_17_2) = v0 & ( ~ (v0 = 0) | v2 = 0
% 16.58/3.20 | | | | v1 = 0))
% 16.58/3.20 | | |
% 16.58/3.20 | | | DELTA: instantiating (84) with fresh symbols all_53_0, all_53_1, all_53_2
% 16.58/3.20 | | | gives:
% 16.58/3.21 | | | (85) apart_point_and_line(all_17_4, all_17_2) = all_53_0 &
% 16.58/3.21 | | | apart_point_and_line(all_17_4, all_17_2) = all_53_1 &
% 16.58/3.21 | | | distinct_lines(all_17_2, all_17_2) = all_53_2 & ( ~ (all_53_2 = 0)
% 16.58/3.21 | | | | all_53_0 = 0 | all_53_1 = 0)
% 16.58/3.21 | | |
% 16.58/3.21 | | | ALPHA: (85) implies:
% 16.58/3.21 | | | (86) apart_point_and_line(all_17_4, all_17_2) = all_53_1
% 16.58/3.21 | | | (87) apart_point_and_line(all_17_4, all_17_2) = all_53_0
% 16.58/3.21 | | |
% 16.58/3.21 | | | BETA: splitting (35) gives:
% 16.58/3.21 | | |
% 16.58/3.21 | | | Case 1:
% 16.58/3.21 | | | |
% 16.58/3.21 | | | | (88) all_17_1 = 0
% 16.58/3.21 | | | |
% 16.58/3.21 | | | | REDUCE: (15), (88) imply:
% 16.58/3.21 | | | | (89) $false
% 16.58/3.21 | | | |
% 16.58/3.21 | | | | CLOSE: (89) is inconsistent.
% 16.58/3.21 | | | |
% 16.58/3.21 | | | Case 2:
% 16.58/3.21 | | | |
% 16.58/3.21 | | | | (90) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 16.58/3.21 | | | | (apart_point_and_line(all_17_3, all_17_2) = v3 &
% 16.58/3.21 | | | | apart_point_and_line(all_17_3, all_17_2) = v2 &
% 16.58/3.21 | | | | distinct_lines(all_17_2, all_17_2) = v1 &
% 16.58/3.21 | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~ (v1 = 0) | ~
% 16.58/3.21 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 16.58/3.21 | | | |
% 16.58/3.21 | | | | DELTA: instantiating (90) with fresh symbols all_58_0, all_58_1,
% 16.58/3.21 | | | | all_58_2, all_58_3 gives:
% 16.58/3.21 | | | | (91) apart_point_and_line(all_17_3, all_17_2) = all_58_0 &
% 16.58/3.21 | | | | apart_point_and_line(all_17_3, all_17_2) = all_58_1 &
% 16.58/3.21 | | | | distinct_lines(all_17_2, all_17_2) = all_58_2 &
% 16.58/3.21 | | | | distinct_points(all_17_3, all_17_3) = all_58_3 & ( ~ (all_58_2 =
% 16.58/3.21 | | | | 0) | ~ (all_58_3 = 0) | all_58_0 = 0 | all_58_1 = 0)
% 16.58/3.21 | | | |
% 16.58/3.21 | | | | ALPHA: (91) implies:
% 16.58/3.21 | | | | (92) apart_point_and_line(all_17_3, all_17_2) = all_58_1
% 16.58/3.21 | | | | (93) apart_point_and_line(all_17_3, all_17_2) = all_58_0
% 16.58/3.21 | | | |
% 16.58/3.21 | | | | GROUND_INST: instantiating (10) with 0, all_28_1, all_17_3, all_17_5,
% 16.58/3.21 | | | | simplifying with (21), (46) gives:
% 16.58/3.21 | | | | (94) all_28_1 = 0
% 16.58/3.21 | | | |
% 17.10/3.21 | | | | GROUND_INST: instantiating (10) with all_24_1, all_28_1, all_17_3,
% 17.10/3.21 | | | | all_17_5, simplifying with (41), (46) gives:
% 17.10/3.21 | | | | (95) all_28_1 = all_24_1
% 17.10/3.21 | | | |
% 17.10/3.21 | | | | GROUND_INST: instantiating (12) with all_48_1, all_48_0, all_17_2,
% 17.10/3.21 | | | | all_17_5, simplifying with (80), (81) gives:
% 17.10/3.21 | | | | (96) all_48_0 = all_48_1
% 17.10/3.21 | | | |
% 17.10/3.21 | | | | GROUND_INST: instantiating (12) with all_30_0, all_48_0, all_17_2,
% 17.10/3.21 | | | | all_17_5, simplifying with (50), (81) gives:
% 17.10/3.21 | | | | (97) all_48_0 = all_30_0
% 17.10/3.21 | | | |
% 17.10/3.21 | | | | GROUND_INST: instantiating (12) with all_53_1, all_53_0, all_17_2,
% 17.10/3.21 | | | | all_17_4, simplifying with (86), (87) gives:
% 17.10/3.21 | | | | (98) all_53_0 = all_53_1
% 17.10/3.21 | | | |
% 17.10/3.21 | | | | GROUND_INST: instantiating (12) with all_38_0, all_53_0, all_17_2,
% 17.10/3.21 | | | | all_17_4, simplifying with (67), (87) gives:
% 17.10/3.21 | | | | (99) all_53_0 = all_38_0
% 17.10/3.21 | | | |
% 17.10/3.21 | | | | GROUND_INST: instantiating (12) with all_17_1, all_58_0, all_17_2,
% 17.10/3.21 | | | | all_17_3, simplifying with (24), (93) gives:
% 17.10/3.21 | | | | (100) all_58_0 = all_17_1
% 17.10/3.21 | | | |
% 17.10/3.21 | | | | GROUND_INST: instantiating (12) with all_58_1, all_58_0, all_17_2,
% 17.10/3.21 | | | | all_17_3, simplifying with (92), (93) gives:
% 17.10/3.21 | | | | (101) all_58_0 = all_58_1
% 17.10/3.21 | | | |
% 17.10/3.21 | | | | GROUND_INST: instantiating (13) with all_17_2, all_40_1, all_17_4,
% 17.10/3.21 | | | | all_17_5, simplifying with (25), (71) gives:
% 17.10/3.21 | | | | (102) all_40_1 = all_17_2
% 17.10/3.21 | | | |
% 17.10/3.22 | | | | GROUND_INST: instantiating (13) with all_36_1, all_40_1, all_17_4,
% 17.10/3.22 | | | | all_17_5, simplifying with (65), (71) gives:
% 17.10/3.22 | | | | (103) all_40_1 = all_36_1
% 17.10/3.22 | | | |
% 17.10/3.22 | | | | GROUND_INST: instantiating (13) with all_17_0, all_42_1, all_17_3,
% 17.10/3.22 | | | | all_17_5, simplifying with (26), (75) gives:
% 17.10/3.22 | | | | (104) all_42_1 = all_17_0
% 17.10/3.22 | | | |
% 17.10/3.22 | | | | GROUND_INST: instantiating (13) with all_34_1, all_42_1, all_17_3,
% 17.10/3.22 | | | | all_17_5, simplifying with (60), (75) gives:
% 17.10/3.22 | | | | (105) all_42_1 = all_34_1
% 17.10/3.22 | | | |
% 17.17/3.22 | | | | GROUND_INST: instantiating (13) with all_26_1, all_32_1, all_17_3,
% 17.17/3.22 | | | | all_17_4, simplifying with (44), (55) gives:
% 17.17/3.22 | | | | (106) all_32_1 = all_26_1
% 17.17/3.22 | | | |
% 17.17/3.22 | | | | COMBINE_EQS: (100), (101) imply:
% 17.17/3.22 | | | | (107) all_58_1 = all_17_1
% 17.17/3.22 | | | |
% 17.17/3.22 | | | | COMBINE_EQS: (98), (99) imply:
% 17.17/3.22 | | | | (108) all_53_1 = all_38_0
% 17.17/3.22 | | | |
% 17.17/3.22 | | | | COMBINE_EQS: (96), (97) imply:
% 17.17/3.22 | | | | (109) all_48_1 = all_30_0
% 17.17/3.22 | | | |
% 17.17/3.22 | | | | COMBINE_EQS: (104), (105) imply:
% 17.17/3.22 | | | | (110) all_34_1 = all_17_0
% 17.17/3.22 | | | |
% 17.17/3.22 | | | | COMBINE_EQS: (102), (103) imply:
% 17.17/3.22 | | | | (111) all_36_1 = all_17_2
% 17.17/3.22 | | | |
% 17.17/3.22 | | | | COMBINE_EQS: (94), (95) imply:
% 17.17/3.22 | | | | (112) all_24_1 = 0
% 17.17/3.22 | | | |
% 17.17/3.22 | | | | SIMP: (112) implies:
% 17.17/3.22 | | | | (113) all_24_1 = 0
% 17.17/3.22 | | | |
% 17.17/3.22 | | | | REDUCE: (74), (104) imply:
% 17.17/3.22 | | | | (114) apart_point_and_line(all_17_3, all_17_0) = all_42_0
% 17.17/3.22 | | | |
% 17.17/3.22 | | | | REDUCE: (54), (106) imply:
% 17.17/3.22 | | | | (115) apart_point_and_line(all_17_3, all_26_1) = all_32_0
% 17.17/3.22 | | | |
% 17.17/3.22 | | | | REDUCE: (70), (102) imply:
% 17.17/3.22 | | | | (116) apart_point_and_line(all_17_4, all_17_2) = all_40_0
% 17.17/3.22 | | | |
% 17.17/3.22 | | | | REDUCE: (64), (111) imply:
% 17.17/3.22 | | | | (117) apart_point_and_line(all_17_5, all_17_2) = all_36_0
% 17.17/3.22 | | | |
% 17.17/3.22 | | | | REDUCE: (59), (110) imply:
% 17.17/3.22 | | | | (118) apart_point_and_line(all_17_5, all_17_0) = all_34_0
% 17.17/3.22 | | | |
% 17.17/3.22 | | | | REDUCE: (58), (110) imply:
% 17.17/3.22 | | | | (119) $i(all_17_0)
% 17.17/3.22 | | | |
% 17.17/3.22 | | | | REDUCE: (53), (106) imply:
% 17.17/3.22 | | | | (120) $i(all_26_1)
% 17.17/3.22 | | | |
% 17.17/3.22 | | | | BETA: splitting (48) gives:
% 17.17/3.22 | | | |
% 17.17/3.22 | | | | Case 1:
% 17.17/3.22 | | | | |
% 17.17/3.22 | | | | |
% 17.17/3.22 | | | | | GROUND_INST: instantiating (12) with all_30_0, all_36_0, all_17_2,
% 17.17/3.22 | | | | | all_17_5, simplifying with (50), (117) gives:
% 17.17/3.22 | | | | | (121) all_36_0 = all_30_0
% 17.17/3.22 | | | | |
% 17.17/3.22 | | | | | GROUND_INST: instantiating (12) with all_24_0, all_34_0, all_17_0,
% 17.17/3.22 | | | | | all_17_5, simplifying with (42), (118) gives:
% 17.17/3.22 | | | | | (122) all_34_0 = all_24_0
% 17.17/3.22 | | | | |
% 17.17/3.22 | | | | | GROUND_INST: instantiating (12) with all_38_0, all_40_0, all_17_2,
% 17.17/3.22 | | | | | all_17_4, simplifying with (67), (116) gives:
% 17.17/3.22 | | | | | (123) all_40_0 = all_38_0
% 17.17/3.22 | | | | |
% 17.17/3.22 | | | | | GROUND_INST: instantiating (12) with all_28_0, all_42_0, all_17_0,
% 17.17/3.22 | | | | | all_17_3, simplifying with (47), (114) gives:
% 17.17/3.22 | | | | | (124) all_42_0 = all_28_0
% 17.17/3.22 | | | | |
% 17.17/3.22 | | | | | REDUCE: (73), (124) imply:
% 17.17/3.22 | | | | | (125) ~ (all_28_0 = 0)
% 17.17/3.22 | | | | |
% 17.17/3.22 | | | | | REDUCE: (69), (123) imply:
% 17.17/3.22 | | | | | (126) ~ (all_38_0 = 0)
% 17.17/3.22 | | | | |
% 17.17/3.22 | | | | | REDUCE: (62), (121) imply:
% 17.17/3.22 | | | | | (127) ~ (all_30_0 = 0)
% 17.17/3.22 | | | | |
% 17.17/3.22 | | | | | REDUCE: (57), (122) imply:
% 17.17/3.22 | | | | | (128) ~ (all_24_0 = 0)
% 17.17/3.22 | | | | |
% 17.17/3.23 | | | | | GROUND_INST: instantiating (7) with all_17_5, all_17_3, all_17_0,
% 17.17/3.23 | | | | | all_17_2, all_24_0, all_17_1, simplifying with (16),
% 17.17/3.23 | | | | | (18), (19), (24), (42), (119) gives:
% 17.17/3.23 | | | | | (129) all_24_0 = 0 | all_17_1 = 0 | ? [v0: any] : ? [v1: any] :
% 17.17/3.23 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3,
% 17.17/3.23 | | | | | all_17_0) = v3 & apart_point_and_line(all_17_5, all_17_2)
% 17.17/3.23 | | | | | = v2 & distinct_lines(all_17_0, all_17_2) = v1 &
% 17.17/3.23 | | | | | distinct_points(all_17_5, all_17_3) = v0 & ( ~ (v1 = 0) |
% 17.17/3.23 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.17/3.23 | | | | |
% 17.17/3.23 | | | | | GROUND_INST: instantiating (6) with all_17_3, all_17_5, all_17_0,
% 17.17/3.23 | | | | | all_17_2, all_17_1, all_24_0, simplifying with (16),
% 17.17/3.23 | | | | | (18), (19), (24), (42), (119) gives:
% 17.17/3.23 | | | | | (130) all_24_0 = 0 | all_17_1 = 0 | ? [v0: any] : ? [v1: any] :
% 17.17/3.23 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3,
% 17.17/3.23 | | | | | all_17_0) = v2 & apart_point_and_line(all_17_5, all_17_2)
% 17.17/3.23 | | | | | = v3 & distinct_lines(all_17_0, all_17_2) = v1 &
% 17.17/3.23 | | | | | distinct_points(all_17_3, all_17_5) = v0 & ( ~ (v1 = 0) |
% 17.17/3.23 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.17/3.23 | | | | |
% 17.17/3.23 | | | | | GROUND_INST: instantiating (5) with all_17_5, all_17_3, all_17_0,
% 17.17/3.23 | | | | | all_17_0, all_24_0, all_24_0, simplifying with (16),
% 17.17/3.23 | | | | | (18), (21), (42), (119) gives:
% 17.17/3.23 | | | | | (131) all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.17/3.23 | | | | | (apart_point_and_line(all_17_3, all_17_0) = v2 &
% 17.17/3.23 | | | | | apart_point_and_line(all_17_3, all_17_0) = v1 &
% 17.17/3.23 | | | | | distinct_lines(all_17_0, all_17_0) = v0 & ( ~ (v0 = 0) | v2
% 17.17/3.23 | | | | | = 0 | v1 = 0))
% 17.17/3.23 | | | | |
% 17.17/3.23 | | | | | GROUND_INST: instantiating (9) with all_17_4, all_17_0, all_17_2,
% 17.17/3.23 | | | | | all_38_0, simplifying with (17), (19), (23), (67), (119)
% 17.17/3.23 | | | | | gives:
% 17.17/3.23 | | | | | (132) all_38_0 = 0 | distinct_lines(all_17_0, all_17_2) = 0
% 17.17/3.23 | | | | |
% 17.17/3.23 | | | | | GROUND_INST: instantiating (6) with all_17_3, all_17_3, all_17_0,
% 17.17/3.23 | | | | | all_17_2, all_17_1, all_28_0, simplifying with (18),
% 17.17/3.23 | | | | | (19), (24), (47), (119) gives:
% 17.17/3.23 | | | | | (133) all_28_0 = 0 | all_17_1 = 0 | ? [v0: any] : ? [v1: any] :
% 17.17/3.23 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3,
% 17.17/3.23 | | | | | all_17_0) = v2 & apart_point_and_line(all_17_3, all_17_2)
% 17.17/3.23 | | | | | = v3 & distinct_lines(all_17_0, all_17_2) = v1 &
% 17.17/3.23 | | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~ (v1 = 0) |
% 17.17/3.23 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.17/3.23 | | | | |
% 17.17/3.23 | | | | | GROUND_INST: instantiating (7) with all_17_3, all_17_5, all_17_0,
% 17.17/3.23 | | | | | all_17_2, all_28_0, all_30_0, simplifying with (16),
% 17.17/3.23 | | | | | (18), (19), (47), (50), (119) gives:
% 17.17/3.23 | | | | | (134) all_30_0 = 0 | all_28_0 = 0 | ? [v0: any] : ? [v1: any] :
% 17.17/3.23 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3,
% 17.17/3.23 | | | | | all_17_2) = v2 & apart_point_and_line(all_17_5, all_17_0)
% 17.17/3.23 | | | | | = v3 & distinct_lines(all_17_0, all_17_2) = v1 &
% 17.17/3.23 | | | | | distinct_points(all_17_3, all_17_5) = v0 & ( ~ (v1 = 0) |
% 17.17/3.23 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.17/3.23 | | | | |
% 17.17/3.23 | | | | | GROUND_INST: instantiating (6) with all_17_3, all_17_3, all_17_0,
% 17.17/3.23 | | | | | all_26_1, all_32_0, all_28_0, simplifying with (18),
% 17.17/3.23 | | | | | (47), (115), (119), (120) gives:
% 17.17/3.23 | | | | | (135) all_32_0 = 0 | all_28_0 = 0 | ? [v0: any] : ? [v1: any] :
% 17.17/3.23 | | | | | ? [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_3,
% 17.17/3.23 | | | | | all_26_1) = v3 & apart_point_and_line(all_17_3, all_17_0)
% 17.17/3.23 | | | | | = v2 & distinct_lines(all_17_0, all_26_1) = v1 &
% 17.17/3.23 | | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~ (v1 = 0) |
% 17.17/3.23 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.17/3.23 | | | | |
% 17.17/3.23 | | | | | BETA: splitting (132) gives:
% 17.17/3.23 | | | | |
% 17.17/3.23 | | | | | Case 1:
% 17.17/3.23 | | | | | |
% 17.17/3.23 | | | | | | (136) distinct_lines(all_17_0, all_17_2) = 0
% 17.17/3.23 | | | | | |
% 17.17/3.23 | | | | | | BETA: splitting (135) gives:
% 17.17/3.23 | | | | | |
% 17.17/3.23 | | | | | | Case 1:
% 17.17/3.23 | | | | | | |
% 17.17/3.23 | | | | | | | (137) all_32_0 = 0
% 17.17/3.23 | | | | | | |
% 17.17/3.23 | | | | | | | REDUCE: (52), (137) imply:
% 17.17/3.23 | | | | | | | (138) $false
% 17.17/3.23 | | | | | | |
% 17.17/3.23 | | | | | | | CLOSE: (138) is inconsistent.
% 17.17/3.23 | | | | | | |
% 17.17/3.23 | | | | | | Case 2:
% 17.17/3.23 | | | | | | |
% 17.17/3.23 | | | | | | | (139) all_28_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any]
% 17.17/3.23 | | | | | | | : ? [v3: any] : (apart_point_and_line(all_17_3,
% 17.17/3.23 | | | | | | | all_26_1) = v3 & apart_point_and_line(all_17_3,
% 17.17/3.23 | | | | | | | all_17_0) = v2 & distinct_lines(all_17_0, all_26_1) =
% 17.17/3.23 | | | | | | | v1 & distinct_points(all_17_3, all_17_3) = v0 & ( ~ (v1
% 17.17/3.23 | | | | | | | = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.17/3.23 | | | | | | |
% 17.17/3.23 | | | | | | | BETA: splitting (133) gives:
% 17.17/3.23 | | | | | | |
% 17.17/3.23 | | | | | | | Case 1:
% 17.17/3.23 | | | | | | | |
% 17.17/3.23 | | | | | | | | (140) all_28_0 = 0
% 17.17/3.23 | | | | | | | |
% 17.17/3.23 | | | | | | | | REDUCE: (125), (140) imply:
% 17.17/3.23 | | | | | | | | (141) $false
% 17.17/3.23 | | | | | | | |
% 17.17/3.24 | | | | | | | | CLOSE: (141) is inconsistent.
% 17.17/3.24 | | | | | | | |
% 17.17/3.24 | | | | | | | Case 2:
% 17.17/3.24 | | | | | | | |
% 17.17/3.24 | | | | | | | | (142) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 17.17/3.24 | | | | | | | | any] : ? [v3: any] : (apart_point_and_line(all_17_3,
% 17.17/3.24 | | | | | | | | all_17_0) = v2 & apart_point_and_line(all_17_3,
% 17.17/3.24 | | | | | | | | all_17_2) = v3 & distinct_lines(all_17_0, all_17_2)
% 17.17/3.24 | | | | | | | | = v1 & distinct_points(all_17_3, all_17_3) = v0 & ( ~
% 17.17/3.24 | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.17/3.24 | | | | | | | |
% 17.17/3.24 | | | | | | | | BETA: splitting (129) gives:
% 17.17/3.24 | | | | | | | |
% 17.17/3.24 | | | | | | | | Case 1:
% 17.17/3.24 | | | | | | | | |
% 17.17/3.24 | | | | | | | | | (143) all_24_0 = 0
% 17.17/3.24 | | | | | | | | |
% 17.17/3.24 | | | | | | | | | REDUCE: (128), (143) imply:
% 17.17/3.24 | | | | | | | | | (144) $false
% 17.17/3.24 | | | | | | | | |
% 17.17/3.24 | | | | | | | | | CLOSE: (144) is inconsistent.
% 17.17/3.24 | | | | | | | | |
% 17.17/3.24 | | | | | | | | Case 2:
% 17.17/3.24 | | | | | | | | |
% 17.17/3.24 | | | | | | | | | (145) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 17.17/3.24 | | | | | | | | | any] : ? [v3: any] :
% 17.17/3.24 | | | | | | | | | (apart_point_and_line(all_17_3, all_17_0) = v3 &
% 17.17/3.24 | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = v2 &
% 17.17/3.24 | | | | | | | | | distinct_lines(all_17_0, all_17_2) = v1 &
% 17.17/3.24 | | | | | | | | | distinct_points(all_17_5, all_17_3) = v0 & ( ~ (v1
% 17.17/3.24 | | | | | | | | | = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.17/3.24 | | | | | | | | |
% 17.17/3.24 | | | | | | | | | BETA: splitting (130) gives:
% 17.17/3.24 | | | | | | | | |
% 17.17/3.24 | | | | | | | | | Case 1:
% 17.17/3.24 | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | (146) all_24_0 = 0
% 17.17/3.24 | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | REDUCE: (128), (146) imply:
% 17.17/3.24 | | | | | | | | | | (147) $false
% 17.17/3.24 | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | CLOSE: (147) is inconsistent.
% 17.17/3.24 | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | Case 2:
% 17.17/3.24 | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | (148) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ?
% 17.17/3.24 | | | | | | | | | | [v2: any] : ? [v3: any] :
% 17.17/3.24 | | | | | | | | | | (apart_point_and_line(all_17_3, all_17_0) = v2 &
% 17.17/3.24 | | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = v3 &
% 17.17/3.24 | | | | | | | | | | distinct_lines(all_17_0, all_17_2) = v1 &
% 17.17/3.24 | | | | | | | | | | distinct_points(all_17_3, all_17_5) = v0 & ( ~
% 17.17/3.24 | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.17/3.24 | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | BETA: splitting (134) gives:
% 17.17/3.24 | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | Case 1:
% 17.17/3.24 | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | (149) all_30_0 = 0
% 17.17/3.24 | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | REDUCE: (127), (149) imply:
% 17.17/3.24 | | | | | | | | | | | (150) $false
% 17.17/3.24 | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | CLOSE: (150) is inconsistent.
% 17.17/3.24 | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | Case 2:
% 17.17/3.24 | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | (151) all_28_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 17.17/3.24 | | | | | | | | | | | [v2: any] : ? [v3: any] :
% 17.17/3.24 | | | | | | | | | | | (apart_point_and_line(all_17_3, all_17_2) = v2 &
% 17.17/3.24 | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_0) = v3 &
% 17.17/3.24 | | | | | | | | | | | distinct_lines(all_17_0, all_17_2) = v1 &
% 17.17/3.24 | | | | | | | | | | | distinct_points(all_17_3, all_17_5) = v0 & ( ~
% 17.17/3.24 | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.17/3.24 | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | BETA: splitting (131) gives:
% 17.17/3.24 | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | Case 1:
% 17.17/3.24 | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | (152) all_24_0 = 0
% 17.17/3.24 | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | REDUCE: (128), (152) imply:
% 17.17/3.24 | | | | | | | | | | | | (153) $false
% 17.17/3.24 | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | CLOSE: (153) is inconsistent.
% 17.17/3.24 | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | Case 2:
% 17.17/3.24 | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | (154) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.17/3.24 | | | | | | | | | | | | (apart_point_and_line(all_17_3, all_17_0) = v2 &
% 17.17/3.24 | | | | | | | | | | | | apart_point_and_line(all_17_3, all_17_0) = v1 &
% 17.17/3.24 | | | | | | | | | | | | distinct_lines(all_17_0, all_17_0) = v0 & ( ~
% 17.17/3.24 | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0))
% 17.17/3.24 | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | DELTA: instantiating (154) with fresh symbols all_444_0,
% 17.17/3.24 | | | | | | | | | | | | all_444_1, all_444_2 gives:
% 17.17/3.24 | | | | | | | | | | | | (155) apart_point_and_line(all_17_3, all_17_0) =
% 17.17/3.24 | | | | | | | | | | | | all_444_0 & apart_point_and_line(all_17_3,
% 17.17/3.24 | | | | | | | | | | | | all_17_0) = all_444_1 & distinct_lines(all_17_0,
% 17.17/3.24 | | | | | | | | | | | | all_17_0) = all_444_2 & ( ~ (all_444_2 = 0) |
% 17.17/3.24 | | | | | | | | | | | | all_444_0 = 0 | all_444_1 = 0)
% 17.17/3.24 | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | ALPHA: (155) implies:
% 17.17/3.24 | | | | | | | | | | | | (156) apart_point_and_line(all_17_3, all_17_0) =
% 17.17/3.24 | | | | | | | | | | | | all_444_1
% 17.17/3.24 | | | | | | | | | | | | (157) apart_point_and_line(all_17_3, all_17_0) =
% 17.17/3.24 | | | | | | | | | | | | all_444_0
% 17.17/3.24 | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | BETA: splitting (151) gives:
% 17.17/3.24 | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | Case 1:
% 17.17/3.24 | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | (158) all_28_0 = 0
% 17.17/3.24 | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | REDUCE: (125), (158) imply:
% 17.17/3.24 | | | | | | | | | | | | | (159) $false
% 17.17/3.24 | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 17.17/3.24 | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | Case 2:
% 17.17/3.24 | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | (160) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 17.17/3.24 | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3,
% 17.17/3.24 | | | | | | | | | | | | | all_17_2) = v2 &
% 17.17/3.24 | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_0) = v3 &
% 17.17/3.24 | | | | | | | | | | | | | distinct_lines(all_17_0, all_17_2) = v1 &
% 17.17/3.24 | | | | | | | | | | | | | distinct_points(all_17_3, all_17_5) = v0 & ( ~
% 17.17/3.24 | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.17/3.24 | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | DELTA: instantiating (160) with fresh symbols all_488_0,
% 17.17/3.24 | | | | | | | | | | | | | all_488_1, all_488_2, all_488_3 gives:
% 17.17/3.24 | | | | | | | | | | | | | (161) apart_point_and_line(all_17_3, all_17_2) =
% 17.17/3.24 | | | | | | | | | | | | | all_488_1 & apart_point_and_line(all_17_5,
% 17.17/3.24 | | | | | | | | | | | | | all_17_0) = all_488_0 & distinct_lines(all_17_0,
% 17.17/3.24 | | | | | | | | | | | | | all_17_2) = all_488_2 &
% 17.17/3.24 | | | | | | | | | | | | | distinct_points(all_17_3, all_17_5) = all_488_3 &
% 17.17/3.24 | | | | | | | | | | | | | ( ~ (all_488_2 = 0) | ~ (all_488_3 = 0) |
% 17.17/3.24 | | | | | | | | | | | | | all_488_0 = 0 | all_488_1 = 0)
% 17.17/3.24 | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | ALPHA: (161) implies:
% 17.17/3.24 | | | | | | | | | | | | | (162) distinct_lines(all_17_0, all_17_2) = all_488_2
% 17.17/3.24 | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | BETA: splitting (145) gives:
% 17.17/3.24 | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | Case 1:
% 17.17/3.24 | | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | | (163) all_17_1 = 0
% 17.17/3.24 | | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | | REDUCE: (15), (163) imply:
% 17.17/3.24 | | | | | | | | | | | | | | (164) $false
% 17.17/3.24 | | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | | CLOSE: (164) is inconsistent.
% 17.17/3.24 | | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | Case 2:
% 17.17/3.24 | | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | | (165) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 17.17/3.24 | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3,
% 17.17/3.24 | | | | | | | | | | | | | | all_17_0) = v3 &
% 17.17/3.24 | | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = v2 &
% 17.17/3.24 | | | | | | | | | | | | | | distinct_lines(all_17_0, all_17_2) = v1 &
% 17.17/3.24 | | | | | | | | | | | | | | distinct_points(all_17_5, all_17_3) = v0 & ( ~
% 17.17/3.24 | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.17/3.24 | | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | | DELTA: instantiating (165) with fresh symbols all_508_0,
% 17.17/3.24 | | | | | | | | | | | | | | all_508_1, all_508_2, all_508_3 gives:
% 17.17/3.24 | | | | | | | | | | | | | | (166) apart_point_and_line(all_17_3, all_17_0) =
% 17.17/3.24 | | | | | | | | | | | | | | all_508_0 & apart_point_and_line(all_17_5,
% 17.17/3.24 | | | | | | | | | | | | | | all_17_2) = all_508_1 & distinct_lines(all_17_0,
% 17.17/3.24 | | | | | | | | | | | | | | all_17_2) = all_508_2 &
% 17.17/3.24 | | | | | | | | | | | | | | distinct_points(all_17_5, all_17_3) = all_508_3 &
% 17.17/3.24 | | | | | | | | | | | | | | ( ~ (all_508_2 = 0) | ~ (all_508_3 = 0) |
% 17.17/3.24 | | | | | | | | | | | | | | all_508_0 = 0 | all_508_1 = 0)
% 17.17/3.24 | | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | | ALPHA: (166) implies:
% 17.17/3.24 | | | | | | | | | | | | | | (167) distinct_points(all_17_5, all_17_3) = all_508_3
% 17.17/3.24 | | | | | | | | | | | | | | (168) distinct_lines(all_17_0, all_17_2) = all_508_2
% 17.17/3.24 | | | | | | | | | | | | | | (169) apart_point_and_line(all_17_5, all_17_2) =
% 17.17/3.24 | | | | | | | | | | | | | | all_508_1
% 17.17/3.24 | | | | | | | | | | | | | | (170) apart_point_and_line(all_17_3, all_17_0) =
% 17.17/3.24 | | | | | | | | | | | | | | all_508_0
% 17.17/3.24 | | | | | | | | | | | | | | (171) ~ (all_508_2 = 0) | ~ (all_508_3 = 0) |
% 17.17/3.24 | | | | | | | | | | | | | | all_508_0 = 0 | all_508_1 = 0
% 17.17/3.24 | | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 17.17/3.24 | | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | | Case 1:
% 17.17/3.24 | | | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | | | (172) all_17_1 = 0
% 17.17/3.24 | | | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | | | REDUCE: (15), (172) imply:
% 17.17/3.24 | | | | | | | | | | | | | | | (173) $false
% 17.17/3.24 | | | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | | | CLOSE: (173) is inconsistent.
% 17.17/3.24 | | | | | | | | | | | | | | |
% 17.17/3.24 | | | | | | | | | | | | | | Case 2:
% 17.17/3.24 | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | (174) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 17.17/3.25 | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3,
% 17.17/3.25 | | | | | | | | | | | | | | | all_17_0) = v2 &
% 17.17/3.25 | | | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = v3 &
% 17.17/3.25 | | | | | | | | | | | | | | | distinct_lines(all_17_0, all_17_2) = v1 &
% 17.17/3.25 | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_5) = v0 & ( ~
% 17.17/3.25 | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.17/3.25 | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | DELTA: instantiating (174) with fresh symbols all_518_0,
% 17.17/3.25 | | | | | | | | | | | | | | | all_518_1, all_518_2, all_518_3 gives:
% 17.17/3.25 | | | | | | | | | | | | | | | (175) apart_point_and_line(all_17_3, all_17_0) =
% 17.17/3.25 | | | | | | | | | | | | | | | all_518_1 & apart_point_and_line(all_17_5,
% 17.17/3.25 | | | | | | | | | | | | | | | all_17_2) = all_518_0 & distinct_lines(all_17_0,
% 17.17/3.25 | | | | | | | | | | | | | | | all_17_2) = all_518_2 &
% 17.17/3.25 | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_5) = all_518_3 &
% 17.17/3.25 | | | | | | | | | | | | | | | ( ~ (all_518_2 = 0) | ~ (all_518_3 = 0) |
% 17.17/3.25 | | | | | | | | | | | | | | | all_518_0 = 0 | all_518_1 = 0)
% 17.17/3.25 | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 17.17/3.25 | | | | | | | | | | | | | | | (176) distinct_lines(all_17_0, all_17_2) = all_518_2
% 17.17/3.25 | | | | | | | | | | | | | | | (177) apart_point_and_line(all_17_5, all_17_2) =
% 17.17/3.25 | | | | | | | | | | | | | | | all_518_0
% 17.17/3.25 | | | | | | | | | | | | | | | (178) apart_point_and_line(all_17_3, all_17_0) =
% 17.17/3.25 | | | | | | | | | | | | | | | all_518_1
% 17.17/3.25 | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 17.17/3.25 | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | Case 1:
% 17.17/3.25 | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | (179) all_28_0 = 0
% 17.17/3.25 | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | REDUCE: (125), (179) imply:
% 17.17/3.25 | | | | | | | | | | | | | | | | (180) $false
% 17.17/3.25 | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | CLOSE: (180) is inconsistent.
% 17.17/3.25 | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | Case 2:
% 17.17/3.25 | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | (181) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 17.17/3.25 | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3,
% 17.17/3.25 | | | | | | | | | | | | | | | | all_26_1) = v3 &
% 17.17/3.25 | | | | | | | | | | | | | | | | apart_point_and_line(all_17_3, all_17_0) = v2 &
% 17.17/3.25 | | | | | | | | | | | | | | | | distinct_lines(all_17_0, all_26_1) = v1 &
% 17.17/3.25 | | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~
% 17.17/3.25 | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.17/3.25 | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | DELTA: instantiating (181) with fresh symbols all_530_0,
% 17.17/3.25 | | | | | | | | | | | | | | | | all_530_1, all_530_2, all_530_3 gives:
% 17.17/3.25 | | | | | | | | | | | | | | | | (182) apart_point_and_line(all_17_3, all_26_1) =
% 17.17/3.25 | | | | | | | | | | | | | | | | all_530_0 & apart_point_and_line(all_17_3,
% 17.17/3.25 | | | | | | | | | | | | | | | | all_17_0) = all_530_1 & distinct_lines(all_17_0,
% 17.17/3.25 | | | | | | | | | | | | | | | | all_26_1) = all_530_2 &
% 17.17/3.25 | | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_3) = all_530_3 &
% 17.17/3.25 | | | | | | | | | | | | | | | | ( ~ (all_530_2 = 0) | ~ (all_530_3 = 0) |
% 17.17/3.25 | | | | | | | | | | | | | | | | all_530_0 = 0 | all_530_1 = 0)
% 17.17/3.25 | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 17.17/3.25 | | | | | | | | | | | | | | | | (183) apart_point_and_line(all_17_3, all_17_0) =
% 17.17/3.25 | | | | | | | | | | | | | | | | all_530_1
% 17.17/3.25 | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 17.17/3.25 | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | Case 1:
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | (184) all_17_1 = 0
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | REDUCE: (15), (184) imply:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (185) $false
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | CLOSE: (185) is inconsistent.
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | Case 2:
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | (186) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 17.17/3.25 | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_3,
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_17_0) = v2 &
% 17.17/3.25 | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_3, all_17_2) = v3 &
% 17.17/3.25 | | | | | | | | | | | | | | | | | distinct_lines(all_17_0, all_17_2) = v1 &
% 17.17/3.25 | | | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_3) = v0 & ( ~
% 17.17/3.25 | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | DELTA: instantiating (186) with fresh symbols all_542_0,
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_542_1, all_542_2, all_542_3 gives:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (187) apart_point_and_line(all_17_3, all_17_0) =
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_542_1 & apart_point_and_line(all_17_3,
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_17_2) = all_542_0 & distinct_lines(all_17_0,
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_17_2) = all_542_2 &
% 17.17/3.25 | | | | | | | | | | | | | | | | | distinct_points(all_17_3, all_17_3) = all_542_3 &
% 17.17/3.25 | | | | | | | | | | | | | | | | | ( ~ (all_542_2 = 0) | ~ (all_542_3 = 0) |
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_542_0 = 0 | all_542_1 = 0)
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (188) distinct_lines(all_17_0, all_17_2) = all_542_2
% 17.17/3.25 | | | | | | | | | | | | | | | | | (189) apart_point_and_line(all_17_3, all_17_0) =
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_542_1
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_508_3, all_17_3,
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_17_5, simplifying with (21), (167) gives:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (190) all_508_3 = 0
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_508_2, all_17_2,
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_17_0, simplifying with (136), (168) gives:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (191) all_508_2 = 0
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_508_2, all_518_2,
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_17_2, all_17_0, simplifying with (168), (176)
% 17.17/3.25 | | | | | | | | | | | | | | | | | gives:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (192) all_518_2 = all_508_2
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_518_2, all_542_2,
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_17_2, all_17_0, simplifying with (176), (188)
% 17.17/3.25 | | | | | | | | | | | | | | | | | gives:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (193) all_542_2 = all_518_2
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_488_2, all_542_2,
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_17_2, all_17_0, simplifying with (162), (188)
% 17.17/3.25 | | | | | | | | | | | | | | | | | gives:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (194) all_542_2 = all_488_2
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_30_0, all_518_0,
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_17_2, all_17_5, simplifying with (50), (177)
% 17.17/3.25 | | | | | | | | | | | | | | | | | gives:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (195) all_518_0 = all_30_0
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_508_1, all_518_0,
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_17_2, all_17_5, simplifying with (169), (177)
% 17.17/3.25 | | | | | | | | | | | | | | | | | gives:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (196) all_518_0 = all_508_1
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_508_0, all_518_1,
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_17_0, all_17_3, simplifying with (170), (178)
% 17.17/3.25 | | | | | | | | | | | | | | | | | gives:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (197) all_518_1 = all_508_0
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_444_1, all_518_1,
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_17_0, all_17_3, simplifying with (156), (178)
% 17.17/3.25 | | | | | | | | | | | | | | | | | gives:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (198) all_518_1 = all_444_1
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_28_0, all_530_1,
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_17_0, all_17_3, simplifying with (47), (183)
% 17.17/3.25 | | | | | | | | | | | | | | | | | gives:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (199) all_530_1 = all_28_0
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_508_0, all_530_1,
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_17_0, all_17_3, simplifying with (170), (183)
% 17.17/3.25 | | | | | | | | | | | | | | | | | gives:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (200) all_530_1 = all_508_0
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_508_0, all_542_1,
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_17_0, all_17_3, simplifying with (170), (189)
% 17.17/3.25 | | | | | | | | | | | | | | | | | gives:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (201) all_542_1 = all_508_0
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_444_0, all_542_1,
% 17.17/3.25 | | | | | | | | | | | | | | | | | all_17_0, all_17_3, simplifying with (157), (189)
% 17.17/3.25 | | | | | | | | | | | | | | | | | gives:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (202) all_542_1 = all_444_0
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (201), (202) imply:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (203) all_508_0 = all_444_0
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | SIMP: (203) implies:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (204) all_508_0 = all_444_0
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (193), (194) imply:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (205) all_518_2 = all_488_2
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | SIMP: (205) implies:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (206) all_518_2 = all_488_2
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (199), (200) imply:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (207) all_508_0 = all_28_0
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | SIMP: (207) implies:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (208) all_508_0 = all_28_0
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (196) imply:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (209) all_508_1 = all_30_0
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (198) imply:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (210) all_508_0 = all_444_1
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | SIMP: (210) implies:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (211) all_508_0 = all_444_1
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (192), (206) imply:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (212) all_508_2 = all_488_2
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | SIMP: (212) implies:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (213) all_508_2 = all_488_2
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (204), (208) imply:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (214) all_444_0 = all_28_0
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (204), (211) imply:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (215) all_444_0 = all_444_1
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (191), (213) imply:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (216) all_488_2 = 0
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (214), (215) imply:
% 17.17/3.25 | | | | | | | | | | | | | | | | | (217) all_444_1 = all_28_0
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 17.17/3.25 | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | Case 1:
% 17.17/3.25 | | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | | (218) ~ (all_508_2 = 0)
% 17.17/3.25 | | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | | REDUCE: (191), (218) imply:
% 17.17/3.25 | | | | | | | | | | | | | | | | | | (219) $false
% 17.17/3.25 | | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | | CLOSE: (219) is inconsistent.
% 17.17/3.25 | | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | Case 2:
% 17.17/3.25 | | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | | (220) ~ (all_508_3 = 0) | all_508_0 = 0 | all_508_1 = 0
% 17.17/3.25 | | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 17.17/3.25 | | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | | Case 1:
% 17.17/3.25 | | | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | | | (221) ~ (all_508_3 = 0)
% 17.17/3.25 | | | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | | | REDUCE: (190), (221) imply:
% 17.17/3.25 | | | | | | | | | | | | | | | | | | | (222) $false
% 17.17/3.25 | | | | | | | | | | | | | | | | | | |
% 17.17/3.25 | | | | | | | | | | | | | | | | | | | CLOSE: (222) is inconsistent.
% 17.17/3.25 | | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | | Case 2:
% 17.17/3.26 | | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | (223) all_508_0 = 0 | all_508_1 = 0
% 17.17/3.26 | | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 17.17/3.26 | | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | Case 1:
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | | (224) all_508_0 = 0
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (208), (224) imply:
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | | (225) all_28_0 = 0
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | | SIMP: (225) implies:
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | | (226) all_28_0 = 0
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (226) imply:
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | | (227) $false
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | | CLOSE: (227) is inconsistent.
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | Case 2:
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | | (228) all_508_1 = 0
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (209), (228) imply:
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | | (229) all_30_0 = 0
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | | SIMP: (229) implies:
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | | (230) all_30_0 = 0
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (230) imply:
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | | (231) $false
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | | CLOSE: (231) is inconsistent.
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | | | End of split
% 17.17/3.26 | | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | | End of split
% 17.17/3.26 | | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | | End of split
% 17.17/3.26 | | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | | End of split
% 17.17/3.26 | | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | | End of split
% 17.17/3.26 | | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | | End of split
% 17.17/3.26 | | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | | End of split
% 17.17/3.26 | | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | | End of split
% 17.17/3.26 | | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | | End of split
% 17.17/3.26 | | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | | End of split
% 17.17/3.26 | | | | | | | | | |
% 17.17/3.26 | | | | | | | | | End of split
% 17.17/3.26 | | | | | | | | |
% 17.17/3.26 | | | | | | | | End of split
% 17.17/3.26 | | | | | | | |
% 17.17/3.26 | | | | | | | End of split
% 17.17/3.26 | | | | | | |
% 17.17/3.26 | | | | | | End of split
% 17.17/3.26 | | | | | |
% 17.17/3.26 | | | | | Case 2:
% 17.17/3.26 | | | | | |
% 17.17/3.26 | | | | | | (232) all_38_0 = 0
% 17.17/3.26 | | | | | |
% 17.17/3.26 | | | | | | REDUCE: (126), (232) imply:
% 17.17/3.26 | | | | | | (233) $false
% 17.17/3.26 | | | | | |
% 17.17/3.26 | | | | | | CLOSE: (233) is inconsistent.
% 17.17/3.26 | | | | | |
% 17.17/3.26 | | | | | End of split
% 17.17/3.26 | | | | |
% 17.17/3.26 | | | | Case 2:
% 17.17/3.26 | | | | |
% 17.17/3.26 | | | | | (234) ~ (all_28_1 = 0)
% 17.17/3.26 | | | | |
% 17.17/3.26 | | | | | REDUCE: (94), (234) imply:
% 17.17/3.26 | | | | | (235) $false
% 17.17/3.26 | | | | |
% 17.17/3.26 | | | | | CLOSE: (235) is inconsistent.
% 17.17/3.26 | | | | |
% 17.17/3.26 | | | | End of split
% 17.17/3.26 | | | |
% 17.17/3.26 | | | End of split
% 17.17/3.26 | | |
% 17.17/3.26 | | End of split
% 17.17/3.26 | |
% 17.17/3.26 | End of split
% 17.17/3.26 |
% 17.17/3.26 End of proof
% 17.17/3.26 % SZS output end Proof for theBenchmark
% 17.17/3.26
% 17.17/3.26 2641ms
%------------------------------------------------------------------------------