TSTP Solution File: GEO223+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO223+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n001.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 23:22:32 EDT 2023
% Result : Theorem 18.77s 3.34s
% Output : Proof 46.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GEO223+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.35 % Computer : n001.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue Aug 29 22:24:23 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.95/1.11 Prover 1: Preprocessing ...
% 2.95/1.11 Prover 4: Preprocessing ...
% 2.98/1.15 Prover 5: Preprocessing ...
% 2.98/1.15 Prover 2: Preprocessing ...
% 2.98/1.15 Prover 3: Preprocessing ...
% 2.98/1.15 Prover 0: Preprocessing ...
% 2.98/1.16 Prover 6: Preprocessing ...
% 4.94/1.45 Prover 5: Proving ...
% 4.94/1.46 Prover 2: Proving ...
% 4.94/1.50 Prover 1: Constructing countermodel ...
% 4.94/1.51 Prover 3: Constructing countermodel ...
% 4.94/1.53 Prover 6: Constructing countermodel ...
% 6.35/1.60 Prover 3: gave up
% 6.35/1.60 Prover 1: gave up
% 6.35/1.60 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.35/1.61 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.35/1.62 Prover 6: gave up
% 6.35/1.62 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 6.53/1.66 Prover 9: Preprocessing ...
% 6.53/1.67 Prover 7: Preprocessing ...
% 6.53/1.67 Prover 8: Preprocessing ...
% 6.53/1.72 Prover 7: Warning: ignoring some quantifiers
% 7.21/1.73 Prover 4: Constructing countermodel ...
% 7.21/1.76 Prover 7: Constructing countermodel ...
% 7.21/1.79 Prover 0: Proving ...
% 7.72/1.80 Prover 8: Warning: ignoring some quantifiers
% 7.72/1.82 Prover 8: Constructing countermodel ...
% 8.37/1.88 Prover 8: gave up
% 8.52/1.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.65/1.94 Prover 10: Preprocessing ...
% 8.65/1.98 Prover 10: Warning: ignoring some quantifiers
% 8.65/1.99 Prover 9: Constructing countermodel ...
% 8.65/2.00 Prover 10: Constructing countermodel ...
% 8.65/2.06 Prover 7: gave up
% 8.65/2.06 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.65/2.08 Prover 10: gave up
% 8.65/2.08 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 8.65/2.10 Prover 12: Preprocessing ...
% 8.65/2.12 Prover 11: Preprocessing ...
% 10.85/2.24 Prover 12: Proving ...
% 11.50/2.35 Prover 11: Constructing countermodel ...
% 18.77/3.34 Prover 0: proved (2707ms)
% 18.77/3.34
% 18.77/3.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.77/3.34
% 18.77/3.34 Prover 12: stopped
% 18.77/3.34 Prover 9: stopped
% 18.77/3.35 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 18.77/3.35 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 18.77/3.35 Prover 5: stopped
% 18.77/3.35 Prover 2: stopped
% 18.77/3.36 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 19.07/3.36 Prover 16: Preprocessing ...
% 19.07/3.37 Prover 13: Preprocessing ...
% 19.07/3.38 Prover 19: Preprocessing ...
% 19.07/3.39 Prover 16: Warning: ignoring some quantifiers
% 19.07/3.39 Prover 13: Warning: ignoring some quantifiers
% 19.07/3.40 Prover 16: Constructing countermodel ...
% 19.07/3.40 Prover 13: Constructing countermodel ...
% 19.07/3.46 Prover 13: gave up
% 19.07/3.48 Prover 19: Warning: ignoring some quantifiers
% 19.07/3.49 Prover 19: Constructing countermodel ...
% 19.07/3.49 Prover 16: gave up
% 19.07/3.53 Prover 19: gave up
% 45.58/8.44 Prover 11: Found proof (size 177)
% 45.58/8.44 Prover 11: proved (6386ms)
% 45.58/8.44 Prover 4: stopped
% 45.58/8.44
% 45.58/8.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.58/8.44
% 45.58/8.46 % SZS output start Proof for theBenchmark
% 45.58/8.46 Assumptions after simplification:
% 45.58/8.46 ---------------------------------
% 45.58/8.46
% 45.58/8.46 (apart3)
% 46.02/8.48 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0))
% 46.02/8.48
% 46.02/8.48 (apart6)
% 46.02/8.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 46.02/8.49 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0,
% 46.02/8.49 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 =
% 46.02/8.49 0) & convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : !
% 46.02/8.49 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~
% 46.02/8.49 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 46.02/8.49 convergent_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 46.02/8.49 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~
% 46.02/8.49 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 46.02/8.49 convergent_lines(v1, v2) = 0)
% 46.02/8.49
% 46.02/8.49 (ceq3)
% 46.02/8.49 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (distinct_lines(v0,
% 46.02/8.49 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 46.02/8.49 convergent_lines(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 46.02/8.49 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v0,
% 46.02/8.49 v1) = 0)
% 46.02/8.49
% 46.02/8.49 (con)
% 46.02/8.49 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 46.02/8.49 (orthogonal_through_point(v3, v0) = v4 & orthogonal_through_point(v1, v0) = v3
% 46.02/8.49 & parallel_through_point(v1, v0) = v2 & distinct_lines(v2, v4) = 0 & $i(v4)
% 46.02/8.49 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 46.02/8.49
% 46.02/8.49 (cp1)
% 46.02/8.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (parallel_through_point(v1, v0)
% 46.02/8.50 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 46.02/8.50 convergent_lines(v2, v1) = v3))
% 46.02/8.50
% 46.02/8.50 (cp2)
% 46.02/8.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (parallel_through_point(v1, v0)
% 46.02/8.50 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 46.02/8.50 apart_point_and_line(v0, v2) = v3))
% 46.02/8.50
% 46.02/8.50 (cu1)
% 46.15/8.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 46.15/8.51 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 46.15/8.51 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 46.15/8.51 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 46.15/8.51 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 &
% 46.15/8.51 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2,
% 46.15/8.51 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 46.15/8.51 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1,
% 46.15/8.51 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~
% 46.15/8.51 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 46.15/8.51 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 46.15/8.51 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0,
% 46.15/8.51 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 46.15/8.51 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 46.15/8.51 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 46.15/8.51 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 46.15/8.51 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 =
% 46.15/8.51 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 &
% 46.15/8.51 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2,
% 46.15/8.51 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 46.15/8.51 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 46.15/8.51 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~
% 46.15/8.51 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 46.15/8.51 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 =
% 46.15/8.51 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 &
% 46.15/8.51 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2,
% 46.15/8.51 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 46.15/8.51 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 46.15/8.51 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~
% 46.15/8.51 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~
% 46.15/8.51 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 46.15/8.51 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 &
% 46.15/8.51 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0,
% 46.15/8.51 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 46.15/8.51 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0,
% 46.15/8.51 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~
% 46.15/8.51 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 46.15/8.51 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 46.15/8.51 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1,
% 46.15/8.51 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i]
% 46.15/8.51 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) |
% 46.15/8.51 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 46.15/8.51 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 =
% 46.15/8.51 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 &
% 46.15/8.51 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0,
% 46.15/8.51 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 46.15/8.51
% 46.15/8.51 (cup1)
% 46.15/8.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 46.15/8.52 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~
% 46.15/8.52 (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 46.15/8.52 [v5: int] : ? [v6: int] : ((v6 = 0 & convergent_lines(v1, v2) = 0) | ( ~
% 46.15/8.52 (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0: $i] : ! [v1: $i] :
% 46.15/8.52 ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~
% 46.15/8.52 (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) |
% 46.15/8.52 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ((v6 = 0 &
% 46.15/8.52 apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1,
% 46.15/8.52 v2) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] :
% 46.15/8.52 ! [v4: int] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~
% 46.15/8.52 (convergent_lines(v1, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 46.15/8.52 [v5: int] : ? [v6: int] : ((v6 = 0 & apart_point_and_line(v0, v2) = 0) | (
% 46.15/8.52 ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0: $i] : ! [v1: $i]
% 46.15/8.52 : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) =
% 46.15/8.52 v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 46.15/8.52 | ? [v4: int] : ? [v5: int] : ((v5 = 0 & convergent_lines(v1, v2) = 0) |
% 46.15/8.52 (v4 = 0 & apart_point_and_line(v0, v1) = 0))) & ! [v0: $i] : ! [v1: $i]
% 46.15/8.52 : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) =
% 46.15/8.52 v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 46.15/8.52 | ? [v4: int] : ? [v5: int] : ((v5 = 0 & convergent_lines(v1, v2) = 0) |
% 46.15/8.52 (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 46.15/8.52
% 46.15/8.52 (oac1)
% 46.23/8.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 46.23/8.53 (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) |
% 46.23/8.53 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7:
% 46.23/8.53 int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) |
% 46.23/8.53 (v7 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 46.23/8.53 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0,
% 46.23/8.53 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] :
% 46.23/8.53 ! [v4: any] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~
% 46.23/8.53 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 46.23/8.53 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 46.23/8.53 convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 46.23/8.53 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0,
% 46.23/8.53 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0:
% 46.23/8.53 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 46.23/8.53 (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ~
% 46.23/8.53 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int]
% 46.23/8.53 : ? [v8: int] : ((v8 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v7 =
% 46.23/8.53 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 46.23/8.53 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0,
% 46.23/8.53 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] :
% 46.23/8.53 ! [v4: any] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0,
% 46.23/8.53 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 46.23/8.53 int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 46.23/8.53 unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 46.23/8.53 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0,
% 46.23/8.53 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0:
% 46.23/8.53 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1,
% 46.23/8.53 v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1)
% 46.23/8.53 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] :
% 46.23/8.53 ((v7 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 46.23/8.53 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 46.23/8.53 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] :
% 46.23/8.53 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~
% 46.23/8.53 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 46.23/8.53 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 46.23/8.53 convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 46.23/8.53 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 46.23/8.53 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i]
% 46.23/8.53 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~
% 46.23/8.53 (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 46.23/8.53 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 46.23/8.53 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 46.23/8.53 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 46.23/8.53 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 46.23/8.53 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~
% 46.23/8.53 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 46.23/8.53 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 46.23/8.53 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 46.23/8.53 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 46.23/8.53 unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 46.23/8.53 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~
% 46.23/8.53 (convergent_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 46.23/8.53 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 46.23/8.53 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 46.23/8.54 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 46.23/8.54 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] :
% 46.23/8.54 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~
% 46.23/8.54 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 46.23/8.54 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 46.23/8.54 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 46.23/8.54 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 46.23/8.54 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 46.23/8.54 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = v3) | ~
% 46.23/8.54 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 46.23/8.54 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 46.23/8.54 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 46.23/8.54 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 46.23/8.54 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i]
% 46.23/8.54 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v0, v2) = v3) | ~
% 46.23/8.54 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 46.23/8.54 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 46.23/8.54 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 46.23/8.54 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 46.23/8.54 unorthogonal_lines(v0, v1) = v4)))
% 46.23/8.54
% 46.23/8.54 (occu1)
% 46.23/8.54 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 46.23/8.54 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 46.23/8.54 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] :
% 46.23/8.54 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 46.23/8.54 unorthogonal_lines(v0, v1) = 0)
% 46.23/8.54
% 46.23/8.54 (ooc1)
% 46.23/8.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (orthogonal_through_point(v1,
% 46.23/8.54 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 46.23/8.54 unorthogonal_lines(v2, v1) = v3))
% 46.23/8.54
% 46.23/8.54 (ooc2)
% 46.23/8.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (orthogonal_through_point(v1,
% 46.23/8.54 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 46.23/8.54 apart_point_and_line(v0, v2) = v3))
% 46.23/8.54
% 46.23/8.54 (ouo1)
% 46.23/8.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 46.23/8.54 int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~
% 46.23/8.54 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ~
% 46.23/8.54 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 46.23/8.54 ((v7 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 &
% 46.23/8.54 apart_point_and_line(v0, v1) = 0))) & ! [v0: $i] : ! [v1: $i] : !
% 46.23/8.54 [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 46.23/8.54 (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) |
% 46.23/8.54 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int]
% 46.23/8.54 : ? [v8: int] : ((v8 = 0 & unorthogonal_lines(v1, v3) = 0) | (v7 = 0 &
% 46.23/8.54 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1,
% 46.23/8.54 v2) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 46.23/8.54 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3)
% 46.23/8.54 = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) |
% 46.23/8.54 ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0
% 46.23/8.54 & unorthogonal_lines(v2, v3) = 0) | (v7 = 0 & apart_point_and_line(v0,
% 46.23/8.54 v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0: $i]
% 46.23/8.54 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5
% 46.23/8.54 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~
% 46.23/8.54 (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ~
% 46.23/8.54 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 46.23/8.54 ((v7 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 &
% 46.23/8.54 apart_point_and_line(v0, v2) = 0)))
% 46.23/8.54
% 46.23/8.54 (function-axioms)
% 46.23/8.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 46.23/8.55 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 46.23/8.55 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 46.23/8.55 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 46.23/8.55 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 46.23/8.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 46.23/8.55 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 46.23/8.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 46.23/8.55 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 46.23/8.55 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 46.23/8.55 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 46.23/8.55 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 46.23/8.55 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 46.23/8.55 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 46.23/8.55 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 46.23/8.55 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 46.23/8.55 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 46.23/8.55 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 46.23/8.55 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 46.23/8.55 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 46.23/8.55 v0))
% 46.23/8.55
% 46.23/8.55 Further assumptions not needed in the proof:
% 46.23/8.55 --------------------------------------------
% 46.23/8.55 apart1, apart2, apart4, apart5, ceq1, ceq2, con1, con2
% 46.23/8.55
% 46.23/8.55 Those formulas are unsatisfiable:
% 46.23/8.55 ---------------------------------
% 46.23/8.55
% 46.23/8.55 Begin of proof
% 46.23/8.55 |
% 46.23/8.55 | ALPHA: (apart6) implies:
% 46.23/8.55 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 46.23/8.55 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) |
% 46.23/8.55 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v1, v2) = 0)
% 46.23/8.55 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 46.23/8.55 | (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) |
% 46.23/8.55 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0)
% 46.23/8.55 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] :
% 46.23/8.55 | (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~
% 46.23/8.55 | (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 46.23/8.55 | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 46.23/8.55 |
% 46.23/8.55 | ALPHA: (cu1) implies:
% 46.23/8.55 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 46.23/8.55 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5)
% 46.23/8.56 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 46.23/8.56 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ?
% 46.23/8.56 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 &
% 46.23/8.56 | apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) &
% 46.23/8.56 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0,
% 46.23/8.56 | v1) = v6)))
% 46.23/8.56 |
% 46.23/8.56 | ALPHA: (ceq3) implies:
% 46.23/8.56 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~
% 46.23/8.56 | $i(v1) | ~ $i(v0) | distinct_lines(v0, v1) = 0)
% 46.23/8.56 |
% 46.23/8.56 | ALPHA: (cup1) implies:
% 46.23/8.56 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 46.23/8.56 | (apart_point_and_line(v0, v2) = v3) | ~ (distinct_lines(v1, v2) = 0)
% 46.23/8.56 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] :
% 46.23/8.56 | ((v5 = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 &
% 46.23/8.56 | apart_point_and_line(v0, v1) = 0)))
% 46.23/8.56 |
% 46.23/8.56 | ALPHA: (occu1) implies:
% 46.23/8.56 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 46.23/8.56 | (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 46.23/8.56 | convergent_lines(v0, v1) = 0)
% 46.23/8.56 |
% 46.23/8.56 | ALPHA: (oac1) implies:
% 46.23/8.56 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] :
% 46.23/8.56 | ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) =
% 46.23/8.56 | v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 46.23/8.56 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 46.23/8.56 | unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 46.23/8.56 | convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 46.23/8.56 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) &
% 46.23/8.56 | convergent_lines(v0, v1) = v5)))
% 46.23/8.56 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] :
% 46.23/8.56 | ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) =
% 46.23/8.56 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 46.23/8.56 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 46.23/8.56 | convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 46.23/8.56 | unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 46.23/8.56 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) &
% 46.23/8.56 | convergent_lines(v0, v1) = v5)))
% 46.23/8.56 |
% 46.23/8.56 | ALPHA: (ouo1) implies:
% 46.23/8.56 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 46.23/8.56 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5)
% 46.23/8.56 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1,
% 46.23/8.56 | v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 46.23/8.56 | [v6: int] : ? [v7: int] : ((v7 = 0 & unorthogonal_lines(v1, v3) =
% 46.23/8.56 | 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0)))
% 46.23/8.56 |
% 46.23/8.56 | ALPHA: (function-axioms) implies:
% 46.23/8.56 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 46.23/8.56 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 46.23/8.56 | (convergent_lines(v3, v2) = v0))
% 46.23/8.56 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 46.23/8.56 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 46.23/8.56 | (apart_point_and_line(v3, v2) = v0))
% 46.23/8.56 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 46.23/8.56 | : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 46.23/8.56 | (unorthogonal_lines(v3, v2) = v0))
% 46.23/8.56 |
% 46.23/8.56 | DELTA: instantiating (con) with fresh symbols all_23_0, all_23_1, all_23_2,
% 46.23/8.56 | all_23_3, all_23_4 gives:
% 46.23/8.57 | (14) orthogonal_through_point(all_23_1, all_23_4) = all_23_0 &
% 46.23/8.57 | orthogonal_through_point(all_23_3, all_23_4) = all_23_1 &
% 46.23/8.57 | parallel_through_point(all_23_3, all_23_4) = all_23_2 &
% 46.23/8.57 | distinct_lines(all_23_2, all_23_0) = 0 & $i(all_23_0) & $i(all_23_1) &
% 46.23/8.57 | $i(all_23_2) & $i(all_23_3) & $i(all_23_4)
% 46.23/8.57 |
% 46.23/8.57 | ALPHA: (14) implies:
% 46.23/8.57 | (15) $i(all_23_4)
% 46.23/8.57 | (16) $i(all_23_3)
% 46.23/8.57 | (17) $i(all_23_2)
% 46.23/8.57 | (18) $i(all_23_1)
% 46.23/8.57 | (19) $i(all_23_0)
% 46.23/8.57 | (20) distinct_lines(all_23_2, all_23_0) = 0
% 46.23/8.57 | (21) parallel_through_point(all_23_3, all_23_4) = all_23_2
% 46.23/8.57 | (22) orthogonal_through_point(all_23_3, all_23_4) = all_23_1
% 46.23/8.57 | (23) orthogonal_through_point(all_23_1, all_23_4) = all_23_0
% 46.23/8.57 |
% 46.23/8.57 | GROUND_INST: instantiating (cp2) with all_23_4, all_23_3, all_23_2,
% 46.23/8.57 | simplifying with (15), (16), (21) gives:
% 46.23/8.57 | (24) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_23_4, all_23_2)
% 46.23/8.57 | = v0)
% 46.23/8.57 |
% 46.23/8.57 | GROUND_INST: instantiating (cp1) with all_23_4, all_23_3, all_23_2,
% 46.23/8.57 | simplifying with (15), (16), (21) gives:
% 46.23/8.57 | (25) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_23_2, all_23_3) =
% 46.23/8.57 | v0)
% 46.23/8.57 |
% 46.23/8.57 | GROUND_INST: instantiating (ooc1) with all_23_4, all_23_3, all_23_1,
% 46.23/8.57 | simplifying with (15), (16), (22) gives:
% 46.23/8.57 | (26) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_23_1, all_23_3) =
% 46.23/8.57 | v0)
% 46.23/8.57 |
% 46.23/8.57 | GROUND_INST: instantiating (ooc2) with all_23_4, all_23_3, all_23_1,
% 46.23/8.57 | simplifying with (15), (16), (22) gives:
% 46.23/8.57 | (27) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_23_4, all_23_1)
% 46.23/8.57 | = v0)
% 46.23/8.57 |
% 46.23/8.57 | GROUND_INST: instantiating (ooc1) with all_23_4, all_23_1, all_23_0,
% 46.23/8.57 | simplifying with (15), (18), (23) gives:
% 46.23/8.57 | (28) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_23_0, all_23_1) =
% 46.23/8.57 | v0)
% 46.23/8.57 |
% 46.23/8.57 | GROUND_INST: instantiating (ooc2) with all_23_4, all_23_1, all_23_0,
% 46.23/8.57 | simplifying with (15), (18), (23) gives:
% 46.23/8.57 | (29) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_23_4, all_23_0)
% 46.23/8.57 | = v0)
% 46.23/8.57 |
% 46.23/8.57 | DELTA: instantiating (29) with fresh symbol all_30_0 gives:
% 46.23/8.57 | (30) ~ (all_30_0 = 0) & apart_point_and_line(all_23_4, all_23_0) =
% 46.23/8.57 | all_30_0
% 46.23/8.57 |
% 46.23/8.57 | ALPHA: (30) implies:
% 46.23/8.57 | (31) ~ (all_30_0 = 0)
% 46.23/8.57 | (32) apart_point_and_line(all_23_4, all_23_0) = all_30_0
% 46.23/8.57 |
% 46.23/8.57 | DELTA: instantiating (27) with fresh symbol all_32_0 gives:
% 46.23/8.57 | (33) ~ (all_32_0 = 0) & apart_point_and_line(all_23_4, all_23_1) =
% 46.23/8.57 | all_32_0
% 46.23/8.57 |
% 46.23/8.57 | ALPHA: (33) implies:
% 46.23/8.57 | (34) ~ (all_32_0 = 0)
% 46.23/8.57 | (35) apart_point_and_line(all_23_4, all_23_1) = all_32_0
% 46.23/8.57 |
% 46.23/8.57 | DELTA: instantiating (25) with fresh symbol all_34_0 gives:
% 46.23/8.57 | (36) ~ (all_34_0 = 0) & convergent_lines(all_23_2, all_23_3) = all_34_0
% 46.23/8.57 |
% 46.23/8.57 | ALPHA: (36) implies:
% 46.23/8.57 | (37) ~ (all_34_0 = 0)
% 46.23/8.57 | (38) convergent_lines(all_23_2, all_23_3) = all_34_0
% 46.23/8.57 |
% 46.23/8.57 | DELTA: instantiating (24) with fresh symbol all_36_0 gives:
% 46.23/8.57 | (39) ~ (all_36_0 = 0) & apart_point_and_line(all_23_4, all_23_2) =
% 46.23/8.57 | all_36_0
% 46.23/8.57 |
% 46.23/8.57 | ALPHA: (39) implies:
% 46.23/8.57 | (40) ~ (all_36_0 = 0)
% 46.23/8.57 | (41) apart_point_and_line(all_23_4, all_23_2) = all_36_0
% 46.23/8.57 |
% 46.23/8.57 | DELTA: instantiating (26) with fresh symbol all_38_0 gives:
% 46.23/8.57 | (42) ~ (all_38_0 = 0) & unorthogonal_lines(all_23_1, all_23_3) = all_38_0
% 46.23/8.57 |
% 46.23/8.57 | ALPHA: (42) implies:
% 46.23/8.57 | (43) ~ (all_38_0 = 0)
% 46.23/8.57 | (44) unorthogonal_lines(all_23_1, all_23_3) = all_38_0
% 46.23/8.57 |
% 46.23/8.57 | DELTA: instantiating (28) with fresh symbol all_40_0 gives:
% 46.23/8.57 | (45) ~ (all_40_0 = 0) & unorthogonal_lines(all_23_0, all_23_1) = all_40_0
% 46.23/8.57 |
% 46.23/8.57 | ALPHA: (45) implies:
% 46.23/8.57 | (46) ~ (all_40_0 = 0)
% 46.23/8.57 | (47) unorthogonal_lines(all_23_0, all_23_1) = all_40_0
% 46.23/8.57 |
% 46.23/8.57 | GROUND_INST: instantiating (3) with all_23_2, all_23_2, all_23_3, all_34_0,
% 46.23/8.57 | all_34_0, simplifying with (16), (17), (38) gives:
% 46.23/8.57 | (48) all_34_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 46.23/8.57 | convergent_lines(all_23_2, all_23_2) = v0)
% 46.23/8.57 |
% 46.23/8.58 | GROUND_INST: instantiating (4) with all_23_4, all_23_4, all_23_1, all_23_2,
% 46.23/8.58 | all_36_0, all_32_0, simplifying with (15), (17), (18), (35), (41)
% 46.23/8.58 | gives:
% 46.23/8.58 | (49) all_36_0 = 0 | all_32_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2:
% 46.23/8.58 | int] : ? [v3: int] : ((v3 = 0 & apart_point_and_line(all_23_4,
% 46.23/8.58 | all_23_2) = 0) | (v2 = 0 & apart_point_and_line(all_23_4,
% 46.23/8.58 | all_23_1) = 0) | ( ~ (v1 = 0) & distinct_lines(all_23_1,
% 46.23/8.58 | all_23_2) = v1) | ( ~ (v0 = 0) & distinct_points(all_23_4,
% 46.23/8.58 | all_23_4) = v0))
% 46.23/8.58 |
% 46.23/8.58 | GROUND_INST: instantiating (6) with all_23_4, all_23_2, all_23_0, all_30_0,
% 46.23/8.58 | simplifying with (15), (17), (19), (20), (32) gives:
% 46.23/8.58 | (50) all_30_0 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 46.23/8.58 | convergent_lines(all_23_2, all_23_0) = 0) | (v0 = 0 &
% 46.23/8.58 | apart_point_and_line(all_23_4, all_23_2) = 0))
% 46.23/8.58 |
% 46.23/8.58 | GROUND_INST: instantiating (9) with all_23_2, all_23_1, all_23_3, all_34_0,
% 46.23/8.58 | all_38_0, simplifying with (16), (17), (18), (38), (44) gives:
% 46.23/8.58 | (51) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 &
% 46.23/8.58 | all_38_0 = 0 & convergent_lines(all_23_1, all_23_3) = 0) | (v2 = 0
% 46.23/8.58 | & all_34_0 = 0 & unorthogonal_lines(all_23_2, all_23_3) = 0) | ( ~
% 46.23/8.58 | (v1 = 0) & unorthogonal_lines(all_23_2, all_23_1) = v1) | ( ~ (v0
% 46.23/8.58 | = 0) & convergent_lines(all_23_2, all_23_1) = v0))
% 46.23/8.58 |
% 46.23/8.58 | GROUND_INST: instantiating (8) with all_23_1, all_23_2, all_23_3, all_38_0,
% 46.23/8.58 | all_34_0, simplifying with (16), (17), (18), (38), (44) gives:
% 46.23/8.58 | (52) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 &
% 46.23/8.58 | all_34_0 = 0 & unorthogonal_lines(all_23_2, all_23_3) = 0) | (v2 =
% 46.23/8.58 | 0 & all_38_0 = 0 & convergent_lines(all_23_1, all_23_3) = 0) | ( ~
% 46.23/8.58 | (v1 = 0) & unorthogonal_lines(all_23_1, all_23_2) = v1) | ( ~ (v0
% 46.23/8.58 | = 0) & convergent_lines(all_23_1, all_23_2) = v0))
% 46.23/8.58 |
% 46.23/8.58 | GROUND_INST: instantiating (7) with all_23_1, all_23_3, all_38_0, simplifying
% 46.23/8.58 | with (16), (18), (44) gives:
% 46.23/8.58 | (53) all_38_0 = 0 | convergent_lines(all_23_1, all_23_3) = 0
% 46.23/8.58 |
% 46.23/8.58 | GROUND_INST: instantiating (10) with all_23_4, all_23_2, all_23_0, all_23_1,
% 46.23/8.58 | all_30_0, all_40_0, simplifying with (15), (17), (18), (19),
% 46.23/8.58 | (20), (32), (47) gives:
% 46.23/8.58 | (54) all_40_0 = 0 | all_30_0 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 46.23/8.58 | unorthogonal_lines(all_23_2, all_23_1) = 0) | (v0 = 0 &
% 46.23/8.58 | apart_point_and_line(all_23_4, all_23_2) = 0))
% 46.23/8.58 |
% 46.23/8.58 | GROUND_INST: instantiating (7) with all_23_0, all_23_1, all_40_0, simplifying
% 46.23/8.58 | with (18), (19), (47) gives:
% 46.23/8.58 | (55) all_40_0 = 0 | convergent_lines(all_23_0, all_23_1) = 0
% 46.23/8.58 |
% 46.23/8.58 | DELTA: instantiating (52) with fresh symbols all_49_0, all_49_1, all_49_2,
% 46.23/8.58 | all_49_3 gives:
% 46.23/8.58 | (56) (all_49_0 = 0 & all_34_0 = 0 & unorthogonal_lines(all_23_2, all_23_3)
% 46.23/8.58 | = 0) | (all_49_1 = 0 & all_38_0 = 0 & convergent_lines(all_23_1,
% 46.23/8.58 | all_23_3) = 0) | ( ~ (all_49_2 = 0) & unorthogonal_lines(all_23_1,
% 46.23/8.58 | all_23_2) = all_49_2) | ( ~ (all_49_3 = 0) &
% 46.23/8.58 | convergent_lines(all_23_1, all_23_2) = all_49_3)
% 46.23/8.58 |
% 46.23/8.58 | DELTA: instantiating (51) with fresh symbols all_51_0, all_51_1, all_51_2,
% 46.23/8.58 | all_51_3 gives:
% 46.23/8.58 | (57) (all_51_0 = 0 & all_38_0 = 0 & convergent_lines(all_23_1, all_23_3) =
% 46.23/8.58 | 0) | (all_51_1 = 0 & all_34_0 = 0 & unorthogonal_lines(all_23_2,
% 46.23/8.58 | all_23_3) = 0) | ( ~ (all_51_2 = 0) & unorthogonal_lines(all_23_2,
% 46.23/8.58 | all_23_1) = all_51_2) | ( ~ (all_51_3 = 0) &
% 46.23/8.58 | convergent_lines(all_23_2, all_23_1) = all_51_3)
% 46.23/8.58 |
% 46.23/8.58 | BETA: splitting (55) gives:
% 46.23/8.58 |
% 46.23/8.58 | Case 1:
% 46.23/8.58 | |
% 46.23/8.58 | | (58) convergent_lines(all_23_0, all_23_1) = 0
% 46.23/8.58 | |
% 46.23/8.58 | | BETA: splitting (53) gives:
% 46.23/8.58 | |
% 46.23/8.58 | | Case 1:
% 46.23/8.58 | | |
% 46.23/8.58 | | | (59) convergent_lines(all_23_1, all_23_3) = 0
% 46.23/8.58 | | |
% 46.23/8.58 | | | BETA: splitting (50) gives:
% 46.23/8.58 | | |
% 46.23/8.58 | | | Case 1:
% 46.23/8.58 | | | |
% 46.23/8.58 | | | | (60) all_30_0 = 0
% 46.23/8.58 | | | |
% 46.23/8.58 | | | | REDUCE: (31), (60) imply:
% 46.23/8.58 | | | | (61) $false
% 46.23/8.58 | | | |
% 46.23/8.58 | | | | CLOSE: (61) is inconsistent.
% 46.23/8.58 | | | |
% 46.23/8.58 | | | Case 2:
% 46.23/8.58 | | | |
% 46.23/8.58 | | | | (62) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 46.23/8.58 | | | | convergent_lines(all_23_2, all_23_0) = 0) | (v0 = 0 &
% 46.23/8.58 | | | | apart_point_and_line(all_23_4, all_23_2) = 0))
% 46.23/8.58 | | | |
% 46.23/8.58 | | | | DELTA: instantiating (62) with fresh symbols all_66_0, all_66_1 gives:
% 46.23/8.58 | | | | (63) (all_66_0 = 0 & convergent_lines(all_23_2, all_23_0) = 0) |
% 46.23/8.58 | | | | (all_66_1 = 0 & apart_point_and_line(all_23_4, all_23_2) = 0)
% 46.23/8.58 | | | |
% 46.23/8.58 | | | | BETA: splitting (63) gives:
% 46.23/8.58 | | | |
% 46.23/8.58 | | | | Case 1:
% 46.23/8.58 | | | | |
% 46.23/8.59 | | | | | (64) all_66_0 = 0 & convergent_lines(all_23_2, all_23_0) = 0
% 46.23/8.59 | | | | |
% 46.23/8.59 | | | | | ALPHA: (64) implies:
% 46.23/8.59 | | | | | (65) convergent_lines(all_23_2, all_23_0) = 0
% 46.23/8.59 | | | | |
% 46.23/8.59 | | | | | BETA: splitting (54) gives:
% 46.23/8.59 | | | | |
% 46.23/8.59 | | | | | Case 1:
% 46.23/8.59 | | | | | |
% 46.23/8.59 | | | | | | (66) all_40_0 = 0
% 46.23/8.59 | | | | | |
% 46.23/8.59 | | | | | | REDUCE: (46), (66) imply:
% 46.23/8.59 | | | | | | (67) $false
% 46.23/8.59 | | | | | |
% 46.23/8.59 | | | | | | CLOSE: (67) is inconsistent.
% 46.23/8.59 | | | | | |
% 46.23/8.59 | | | | | Case 2:
% 46.23/8.59 | | | | | |
% 46.23/8.59 | | | | | | (68) all_30_0 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 46.23/8.59 | | | | | | unorthogonal_lines(all_23_2, all_23_1) = 0) | (v0 = 0 &
% 46.23/8.59 | | | | | | apart_point_and_line(all_23_4, all_23_2) = 0))
% 46.23/8.59 | | | | | |
% 46.23/8.59 | | | | | | BETA: splitting (48) gives:
% 46.23/8.59 | | | | | |
% 46.23/8.59 | | | | | | Case 1:
% 46.23/8.59 | | | | | | |
% 46.23/8.59 | | | | | | | (69) all_34_0 = 0
% 46.23/8.59 | | | | | | |
% 46.23/8.59 | | | | | | | REDUCE: (37), (69) imply:
% 46.23/8.59 | | | | | | | (70) $false
% 46.23/8.59 | | | | | | |
% 46.23/8.59 | | | | | | | CLOSE: (70) is inconsistent.
% 46.23/8.59 | | | | | | |
% 46.23/8.59 | | | | | | Case 2:
% 46.23/8.59 | | | | | | |
% 46.23/8.59 | | | | | | | (71) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_23_2,
% 46.23/8.59 | | | | | | | all_23_2) = v0)
% 46.23/8.59 | | | | | | |
% 46.23/8.59 | | | | | | | DELTA: instantiating (71) with fresh symbol all_90_0 gives:
% 46.23/8.59 | | | | | | | (72) ~ (all_90_0 = 0) & convergent_lines(all_23_2, all_23_2) =
% 46.23/8.59 | | | | | | | all_90_0
% 46.23/8.59 | | | | | | |
% 46.23/8.59 | | | | | | | ALPHA: (72) implies:
% 46.23/8.59 | | | | | | | (73) ~ (all_90_0 = 0)
% 46.23/8.59 | | | | | | | (74) convergent_lines(all_23_2, all_23_2) = all_90_0
% 46.23/8.59 | | | | | | |
% 46.23/8.59 | | | | | | | BETA: splitting (49) gives:
% 46.23/8.59 | | | | | | |
% 46.23/8.59 | | | | | | | Case 1:
% 46.23/8.59 | | | | | | | |
% 46.23/8.59 | | | | | | | | (75) all_36_0 = 0
% 46.23/8.59 | | | | | | | |
% 46.23/8.59 | | | | | | | | REDUCE: (40), (75) imply:
% 46.23/8.59 | | | | | | | | (76) $false
% 46.23/8.59 | | | | | | | |
% 46.23/8.59 | | | | | | | | CLOSE: (76) is inconsistent.
% 46.23/8.59 | | | | | | | |
% 46.23/8.59 | | | | | | | Case 2:
% 46.23/8.59 | | | | | | | |
% 46.23/8.59 | | | | | | | | (77) all_32_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2:
% 46.23/8.59 | | | | | | | | int] : ? [v3: int] : ((v3 = 0 &
% 46.23/8.59 | | | | | | | | apart_point_and_line(all_23_4, all_23_2) = 0) | (v2
% 46.23/8.59 | | | | | | | | = 0 & apart_point_and_line(all_23_4, all_23_1) = 0)
% 46.23/8.59 | | | | | | | | | ( ~ (v1 = 0) & distinct_lines(all_23_1, all_23_2) =
% 46.23/8.59 | | | | | | | | v1) | ( ~ (v0 = 0) & distinct_points(all_23_4,
% 46.23/8.59 | | | | | | | | all_23_4) = v0))
% 46.23/8.59 | | | | | | | |
% 46.23/8.59 | | | | | | | | BETA: splitting (68) gives:
% 46.23/8.59 | | | | | | | |
% 46.23/8.59 | | | | | | | | Case 1:
% 46.23/8.59 | | | | | | | | |
% 46.23/8.59 | | | | | | | | | (78) all_30_0 = 0
% 46.23/8.59 | | | | | | | | |
% 46.23/8.59 | | | | | | | | | REDUCE: (31), (78) imply:
% 46.23/8.59 | | | | | | | | | (79) $false
% 46.23/8.59 | | | | | | | | |
% 46.23/8.59 | | | | | | | | | CLOSE: (79) is inconsistent.
% 46.23/8.59 | | | | | | | | |
% 46.23/8.59 | | | | | | | | Case 2:
% 46.23/8.59 | | | | | | | | |
% 46.23/8.59 | | | | | | | | | (80) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 46.23/8.59 | | | | | | | | | unorthogonal_lines(all_23_2, all_23_1) = 0) | (v0
% 46.23/8.59 | | | | | | | | | = 0 & apart_point_and_line(all_23_4, all_23_2) =
% 46.23/8.59 | | | | | | | | | 0))
% 46.23/8.59 | | | | | | | | |
% 46.23/8.59 | | | | | | | | | DELTA: instantiating (80) with fresh symbols all_164_0,
% 46.23/8.59 | | | | | | | | | all_164_1 gives:
% 46.23/8.59 | | | | | | | | | (81) (all_164_0 = 0 & unorthogonal_lines(all_23_2,
% 46.23/8.59 | | | | | | | | | all_23_1) = 0) | (all_164_1 = 0 &
% 46.23/8.59 | | | | | | | | | apart_point_and_line(all_23_4, all_23_2) = 0)
% 46.23/8.59 | | | | | | | | |
% 46.23/8.59 | | | | | | | | | BETA: splitting (81) gives:
% 46.23/8.59 | | | | | | | | |
% 46.23/8.59 | | | | | | | | | Case 1:
% 46.23/8.59 | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | (82) all_164_0 = 0 & unorthogonal_lines(all_23_2,
% 46.23/8.59 | | | | | | | | | | all_23_1) = 0
% 46.23/8.59 | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | ALPHA: (82) implies:
% 46.23/8.59 | | | | | | | | | | (83) unorthogonal_lines(all_23_2, all_23_1) = 0
% 46.23/8.59 | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | BETA: splitting (57) gives:
% 46.23/8.59 | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | Case 1:
% 46.23/8.59 | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | (84) (all_51_0 = 0 & all_38_0 = 0 &
% 46.23/8.59 | | | | | | | | | | | convergent_lines(all_23_1, all_23_3) = 0) |
% 46.23/8.59 | | | | | | | | | | | (all_51_1 = 0 & all_34_0 = 0 &
% 46.23/8.59 | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0)
% 46.23/8.59 | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | BETA: splitting (84) gives:
% 46.23/8.59 | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | Case 1:
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | (85) all_51_0 = 0 & all_38_0 = 0 &
% 46.23/8.59 | | | | | | | | | | | | convergent_lines(all_23_1, all_23_3) = 0
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | ALPHA: (85) implies:
% 46.23/8.59 | | | | | | | | | | | | (86) all_38_0 = 0
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | REDUCE: (43), (86) imply:
% 46.23/8.59 | | | | | | | | | | | | (87) $false
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | CLOSE: (87) is inconsistent.
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | Case 2:
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | (88) all_51_1 = 0 & all_34_0 = 0 &
% 46.23/8.59 | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | ALPHA: (88) implies:
% 46.23/8.59 | | | | | | | | | | | | (89) all_34_0 = 0
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | REDUCE: (37), (89) imply:
% 46.23/8.59 | | | | | | | | | | | | (90) $false
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | CLOSE: (90) is inconsistent.
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | End of split
% 46.23/8.59 | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | Case 2:
% 46.23/8.59 | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | (91) ( ~ (all_51_2 = 0) & unorthogonal_lines(all_23_2,
% 46.23/8.59 | | | | | | | | | | | all_23_1) = all_51_2) | ( ~ (all_51_3 = 0) &
% 46.23/8.59 | | | | | | | | | | | convergent_lines(all_23_2, all_23_1) = all_51_3)
% 46.23/8.59 | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | BETA: splitting (91) gives:
% 46.23/8.59 | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | Case 1:
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | (92) ~ (all_51_2 = 0) & unorthogonal_lines(all_23_2,
% 46.23/8.59 | | | | | | | | | | | | all_23_1) = all_51_2
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | ALPHA: (92) implies:
% 46.23/8.59 | | | | | | | | | | | | (93) ~ (all_51_2 = 0)
% 46.23/8.59 | | | | | | | | | | | | (94) unorthogonal_lines(all_23_2, all_23_1) = all_51_2
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_51_2, all_23_1,
% 46.23/8.59 | | | | | | | | | | | | all_23_2, simplifying with (83), (94) gives:
% 46.23/8.59 | | | | | | | | | | | | (95) all_51_2 = 0
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | REDUCE: (93), (95) imply:
% 46.23/8.59 | | | | | | | | | | | | (96) $false
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | CLOSE: (96) is inconsistent.
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | Case 2:
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | (97) ~ (all_51_3 = 0) & convergent_lines(all_23_2,
% 46.23/8.59 | | | | | | | | | | | | all_23_1) = all_51_3
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | ALPHA: (97) implies:
% 46.23/8.59 | | | | | | | | | | | | (98) ~ (all_51_3 = 0)
% 46.23/8.59 | | | | | | | | | | | | (99) convergent_lines(all_23_2, all_23_1) = all_51_3
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | BETA: splitting (77) gives:
% 46.23/8.59 | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | Case 1:
% 46.23/8.59 | | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | | (100) all_32_0 = 0
% 46.23/8.59 | | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | | REDUCE: (34), (100) imply:
% 46.23/8.59 | | | | | | | | | | | | | (101) $false
% 46.23/8.59 | | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | | CLOSE: (101) is inconsistent.
% 46.23/8.59 | | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | Case 2:
% 46.23/8.59 | | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_23_2, all_23_0,
% 46.23/8.59 | | | | | | | | | | | | | all_23_2, all_90_0, simplifying with (17), (19),
% 46.23/8.59 | | | | | | | | | | | | | (65), (74) gives:
% 46.23/8.59 | | | | | | | | | | | | | (102) all_90_0 = 0 | convergent_lines(all_23_0,
% 46.23/8.59 | | | | | | | | | | | | | all_23_2) = 0
% 46.23/8.59 | | | | | | | | | | | | |
% 46.23/8.59 | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_23_0, all_23_1,
% 46.23/8.59 | | | | | | | | | | | | | simplifying with (18), (19), (58) gives:
% 46.23/8.59 | | | | | | | | | | | | | (103) distinct_lines(all_23_0, all_23_1) = 0
% 46.23/8.59 | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_23_0, all_23_2,
% 46.23/8.60 | | | | | | | | | | | | | all_23_1, 0, 0, simplifying with (17), (18), (19),
% 46.23/8.60 | | | | | | | | | | | | | (58), (83) gives:
% 46.23/8.60 | | | | | | | | | | | | | (104) ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 46.23/8.60 | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & convergent_lines(all_23_2,
% 46.23/8.60 | | | | | | | | | | | | | all_23_1) = 0) | (v2 = 0 &
% 46.23/8.60 | | | | | | | | | | | | | unorthogonal_lines(all_23_0, all_23_1) = 0) |
% 46.23/8.60 | | | | | | | | | | | | | ( ~ (v1 = 0) & unorthogonal_lines(all_23_0,
% 46.23/8.60 | | | | | | | | | | | | | all_23_2) = v1) | ( ~ (v0 = 0) &
% 46.23/8.60 | | | | | | | | | | | | | convergent_lines(all_23_0, all_23_2) = v0))
% 46.23/8.60 | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | DELTA: instantiating (104) with fresh symbols all_376_0,
% 46.23/8.60 | | | | | | | | | | | | | all_376_1, all_376_2, all_376_3 gives:
% 46.23/8.60 | | | | | | | | | | | | | (105) (all_376_0 = 0 & convergent_lines(all_23_2,
% 46.23/8.60 | | | | | | | | | | | | | all_23_1) = 0) | (all_376_1 = 0 &
% 46.23/8.60 | | | | | | | | | | | | | unorthogonal_lines(all_23_0, all_23_1) = 0) | (
% 46.23/8.60 | | | | | | | | | | | | | ~ (all_376_2 = 0) & unorthogonal_lines(all_23_0,
% 46.23/8.60 | | | | | | | | | | | | | all_23_2) = all_376_2) | ( ~ (all_376_3 = 0) &
% 46.23/8.60 | | | | | | | | | | | | | convergent_lines(all_23_0, all_23_2) =
% 46.23/8.60 | | | | | | | | | | | | | all_376_3)
% 46.23/8.60 | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | BETA: splitting (102) gives:
% 46.23/8.60 | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | Case 1:
% 46.23/8.60 | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | (106) convergent_lines(all_23_0, all_23_2) = 0
% 46.23/8.60 | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 46.23/8.60 | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | Case 1:
% 46.23/8.60 | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | (107) (all_376_0 = 0 & convergent_lines(all_23_2,
% 46.23/8.60 | | | | | | | | | | | | | | | all_23_1) = 0) | (all_376_1 = 0 &
% 46.23/8.60 | | | | | | | | | | | | | | | unorthogonal_lines(all_23_0, all_23_1) = 0)
% 46.23/8.60 | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 46.23/8.60 | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | Case 1:
% 46.23/8.60 | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | (108) all_376_0 = 0 & convergent_lines(all_23_2,
% 46.23/8.60 | | | | | | | | | | | | | | | | all_23_1) = 0
% 46.23/8.60 | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | ALPHA: (108) implies:
% 46.23/8.60 | | | | | | | | | | | | | | | | (109) convergent_lines(all_23_2, all_23_1) = 0
% 46.23/8.60 | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_51_3, all_23_1,
% 46.23/8.60 | | | | | | | | | | | | | | | | all_23_2, simplifying with (99), (109) gives:
% 46.23/8.60 | | | | | | | | | | | | | | | | (110) all_51_3 = 0
% 46.23/8.60 | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | REDUCE: (98), (110) imply:
% 46.23/8.60 | | | | | | | | | | | | | | | | (111) $false
% 46.23/8.60 | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | CLOSE: (111) is inconsistent.
% 46.23/8.60 | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | Case 2:
% 46.23/8.60 | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | (112) all_376_1 = 0 & unorthogonal_lines(all_23_0,
% 46.23/8.60 | | | | | | | | | | | | | | | | all_23_1) = 0
% 46.23/8.60 | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 46.23/8.60 | | | | | | | | | | | | | | | | (113) unorthogonal_lines(all_23_0, all_23_1) = 0
% 46.23/8.60 | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with all_40_0, 0, all_23_1,
% 46.23/8.60 | | | | | | | | | | | | | | | | all_23_0, simplifying with (47), (113) gives:
% 46.23/8.60 | | | | | | | | | | | | | | | | (114) all_40_0 = 0
% 46.23/8.60 | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | REDUCE: (46), (114) imply:
% 46.23/8.60 | | | | | | | | | | | | | | | | (115) $false
% 46.23/8.60 | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | CLOSE: (115) is inconsistent.
% 46.23/8.60 | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | End of split
% 46.23/8.60 | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | Case 2:
% 46.23/8.60 | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | (116) ( ~ (all_376_2 = 0) & unorthogonal_lines(all_23_0,
% 46.23/8.60 | | | | | | | | | | | | | | | all_23_2) = all_376_2) | ( ~ (all_376_3 = 0) &
% 46.23/8.60 | | | | | | | | | | | | | | | convergent_lines(all_23_0, all_23_2) =
% 46.23/8.60 | | | | | | | | | | | | | | | all_376_3)
% 46.23/8.60 | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 46.23/8.60 | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | Case 1:
% 46.23/8.60 | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | (117) ~ (all_376_2 = 0) & unorthogonal_lines(all_23_0,
% 46.23/8.60 | | | | | | | | | | | | | | | | all_23_2) = all_376_2
% 46.23/8.60 | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 46.23/8.60 | | | | | | | | | | | | | | | | (118) ~ (all_376_2 = 0)
% 46.23/8.60 | | | | | | | | | | | | | | | | (119) unorthogonal_lines(all_23_0, all_23_2) = all_376_2
% 46.23/8.60 | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 46.23/8.60 | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | Case 1:
% 46.23/8.60 | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | (120) (all_49_0 = 0 & all_34_0 = 0 &
% 46.23/8.60 | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0) |
% 46.23/8.60 | | | | | | | | | | | | | | | | | (all_49_1 = 0 & all_38_0 = 0 &
% 46.23/8.60 | | | | | | | | | | | | | | | | | convergent_lines(all_23_1, all_23_3) = 0)
% 46.23/8.60 | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 46.23/8.60 | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | Case 1:
% 46.23/8.60 | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | (121) all_49_0 = 0 & all_34_0 = 0 &
% 46.23/8.60 | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_2, all_23_3) = 0
% 46.23/8.60 | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 46.23/8.60 | | | | | | | | | | | | | | | | | | (122) all_34_0 = 0
% 46.23/8.60 | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | REDUCE: (37), (122) imply:
% 46.23/8.60 | | | | | | | | | | | | | | | | | | (123) $false
% 46.23/8.60 | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | CLOSE: (123) is inconsistent.
% 46.23/8.60 | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | Case 2:
% 46.23/8.60 | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | (124) all_49_1 = 0 & all_38_0 = 0 &
% 46.23/8.60 | | | | | | | | | | | | | | | | | | convergent_lines(all_23_1, all_23_3) = 0
% 46.23/8.60 | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 46.23/8.60 | | | | | | | | | | | | | | | | | | (125) all_38_0 = 0
% 46.23/8.60 | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | REDUCE: (43), (125) imply:
% 46.23/8.60 | | | | | | | | | | | | | | | | | | (126) $false
% 46.23/8.60 | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | CLOSE: (126) is inconsistent.
% 46.23/8.60 | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | End of split
% 46.23/8.60 | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | Case 2:
% 46.23/8.60 | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | (127) ( ~ (all_49_2 = 0) & unorthogonal_lines(all_23_1,
% 46.23/8.60 | | | | | | | | | | | | | | | | | all_23_2) = all_49_2) | ( ~ (all_49_3 = 0) &
% 46.23/8.60 | | | | | | | | | | | | | | | | | convergent_lines(all_23_1, all_23_2) = all_49_3)
% 46.23/8.60 | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 46.23/8.60 | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | Case 1:
% 46.23/8.60 | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | (128) ~ (all_49_2 = 0) & unorthogonal_lines(all_23_1,
% 46.23/8.60 | | | | | | | | | | | | | | | | | | all_23_2) = all_49_2
% 46.23/8.60 | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 46.23/8.60 | | | | | | | | | | | | | | | | | | (129) ~ (all_49_2 = 0)
% 46.23/8.60 | | | | | | | | | | | | | | | | | | (130) unorthogonal_lines(all_23_1, all_23_2) = all_49_2
% 46.23/8.60 | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_23_4, all_23_0,
% 46.23/8.60 | | | | | | | | | | | | | | | | | | all_23_1, all_23_2, all_32_0, all_49_2,
% 46.23/8.60 | | | | | | | | | | | | | | | | | | simplifying with (15), (17), (18), (19), (35),
% 46.23/8.60 | | | | | | | | | | | | | | | | | | (103), (130) gives:
% 46.23/8.60 | | | | | | | | | | | | | | | | | | (131) all_49_2 = 0 | all_32_0 = 0 | ? [v0: int] : ?
% 46.23/8.60 | | | | | | | | | | | | | | | | | | [v1: int] : ((v1 = 0 &
% 46.23/8.60 | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_0, all_23_2) = 0) |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | (v0 = 0 & apart_point_and_line(all_23_4,
% 46.23/8.60 | | | | | | | | | | | | | | | | | | all_23_0) = 0))
% 46.23/8.60 | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 46.23/8.60 | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | Case 1:
% 46.23/8.60 | | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | (132) all_49_2 = 0
% 46.23/8.60 | | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | REDUCE: (129), (132) imply:
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | (133) $false
% 46.23/8.60 | | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | CLOSE: (133) is inconsistent.
% 46.23/8.60 | | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | Case 2:
% 46.23/8.60 | | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | (134) all_32_0 = 0 | ? [v0: int] : ? [v1: int] : ((v1
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | = 0 & unorthogonal_lines(all_23_0, all_23_2) =
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | 0) | (v0 = 0 & apart_point_and_line(all_23_4,
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | all_23_0) = 0))
% 46.23/8.60 | | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 46.23/8.60 | | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | Case 1:
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | | (135) all_32_0 = 0
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (135) imply:
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | | (136) $false
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | | CLOSE: (136) is inconsistent.
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | Case 2:
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | | (137) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_23_0, all_23_2) = 0) |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | | (v0 = 0 & apart_point_and_line(all_23_4,
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | | all_23_0) = 0))
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (137) with fresh symbols all_768_0,
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | | all_768_1 gives:
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | | (138) (all_768_0 = 0 & unorthogonal_lines(all_23_0,
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | | all_23_2) = 0) | (all_768_1 = 0 &
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_23_4, all_23_0) = 0)
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | |
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | | Case 1:
% 46.23/8.60 | | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | (139) all_768_0 = 0 & unorthogonal_lines(all_23_0,
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | all_23_2) = 0
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | (140) unorthogonal_lines(all_23_0, all_23_2) = 0
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_376_2, all_23_2,
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | all_23_0, simplifying with (119), (140) gives:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | (141) all_376_2 = 0
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (141) imply:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | (142) $false
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | CLOSE: (142) is inconsistent.
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | Case 2:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | (143) all_768_1 = 0 & apart_point_and_line(all_23_4,
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | all_23_0) = 0
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | (144) apart_point_and_line(all_23_4, all_23_0) = 0
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_30_0, 0, all_23_0,
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | all_23_4, simplifying with (32), (144) gives:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | (145) all_30_0 = 0
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (145) imply:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | (146) $false
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | | CLOSE: (146) is inconsistent.
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | End of split
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | End of split
% 46.23/8.61 | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | End of split
% 46.23/8.61 | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | Case 2:
% 46.23/8.61 | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | (147) ~ (all_49_3 = 0) & convergent_lines(all_23_1,
% 46.23/8.61 | | | | | | | | | | | | | | | | | | all_23_2) = all_49_3
% 46.23/8.61 | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | (148) ~ (all_49_3 = 0)
% 46.23/8.61 | | | | | | | | | | | | | | | | | | (149) convergent_lines(all_23_1, all_23_2) = all_49_3
% 46.23/8.61 | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_23_1, all_23_3,
% 46.23/8.61 | | | | | | | | | | | | | | | | | | all_23_2, all_49_3, simplifying with (16), (17),
% 46.23/8.61 | | | | | | | | | | | | | | | | | | (18), (59), (149) gives:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | (150) all_49_3 = 0 | convergent_lines(all_23_3,
% 46.23/8.61 | | | | | | | | | | | | | | | | | | all_23_2) = 0
% 46.23/8.61 | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 46.23/8.61 | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | Case 1:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | (151) convergent_lines(all_23_3, all_23_2) = 0
% 46.23/8.61 | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_23_3, all_23_2,
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | all_23_3, all_34_0, simplifying with (16), (17),
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | (38), (151) gives:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | (152) all_34_0 = 0 | convergent_lines(all_23_3,
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | all_23_3) = 0
% 46.23/8.61 | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | Case 1:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | (153) convergent_lines(all_23_3, all_23_3) = 0
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_23_3, simplifying
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | with (16), (153) gives:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | (154) $false
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | CLOSE: (154) is inconsistent.
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | Case 2:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | (155) all_34_0 = 0
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (155) imply:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | (156) $false
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | | CLOSE: (156) is inconsistent.
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | End of split
% 46.23/8.61 | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | Case 2:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | (157) all_49_3 = 0
% 46.23/8.61 | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | REDUCE: (148), (157) imply:
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | (158) $false
% 46.23/8.61 | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | | CLOSE: (158) is inconsistent.
% 46.23/8.61 | | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | | End of split
% 46.23/8.61 | | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | | End of split
% 46.23/8.61 | | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | End of split
% 46.23/8.61 | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | Case 2:
% 46.23/8.61 | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | (159) ~ (all_376_3 = 0) & convergent_lines(all_23_0,
% 46.23/8.61 | | | | | | | | | | | | | | | | all_23_2) = all_376_3
% 46.23/8.61 | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 46.23/8.61 | | | | | | | | | | | | | | | | (160) ~ (all_376_3 = 0)
% 46.23/8.61 | | | | | | | | | | | | | | | | (161) convergent_lines(all_23_0, all_23_2) = all_376_3
% 46.23/8.61 | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_376_3, all_23_2,
% 46.23/8.61 | | | | | | | | | | | | | | | | all_23_0, simplifying with (106), (161) gives:
% 46.23/8.61 | | | | | | | | | | | | | | | | (162) all_376_3 = 0
% 46.23/8.61 | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | REDUCE: (160), (162) imply:
% 46.23/8.61 | | | | | | | | | | | | | | | | (163) $false
% 46.23/8.61 | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | | CLOSE: (163) is inconsistent.
% 46.23/8.61 | | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | | End of split
% 46.23/8.61 | | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | End of split
% 46.23/8.61 | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | Case 2:
% 46.23/8.61 | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | (164) all_90_0 = 0
% 46.23/8.61 | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | REDUCE: (73), (164) imply:
% 46.23/8.61 | | | | | | | | | | | | | | (165) $false
% 46.23/8.61 | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | | CLOSE: (165) is inconsistent.
% 46.23/8.61 | | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | | End of split
% 46.23/8.61 | | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | | End of split
% 46.23/8.61 | | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | | End of split
% 46.23/8.61 | | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | End of split
% 46.23/8.61 | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | Case 2:
% 46.23/8.61 | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | (166) all_164_1 = 0 & apart_point_and_line(all_23_4,
% 46.23/8.61 | | | | | | | | | | all_23_2) = 0
% 46.23/8.61 | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | ALPHA: (166) implies:
% 46.23/8.61 | | | | | | | | | | (167) apart_point_and_line(all_23_4, all_23_2) = 0
% 46.23/8.61 | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | | REF_CLOSE: (12), (40), (41), (167) are inconsistent by
% 46.23/8.61 | | | | | | | | | | sub-proof #1.
% 46.23/8.61 | | | | | | | | | |
% 46.23/8.61 | | | | | | | | | End of split
% 46.23/8.61 | | | | | | | | |
% 46.23/8.61 | | | | | | | | End of split
% 46.23/8.61 | | | | | | | |
% 46.23/8.61 | | | | | | | End of split
% 46.23/8.61 | | | | | | |
% 46.23/8.61 | | | | | | End of split
% 46.23/8.61 | | | | | |
% 46.23/8.61 | | | | | End of split
% 46.23/8.61 | | | | |
% 46.23/8.61 | | | | Case 2:
% 46.23/8.61 | | | | |
% 46.23/8.61 | | | | | (168) all_66_1 = 0 & apart_point_and_line(all_23_4, all_23_2) = 0
% 46.23/8.61 | | | | |
% 46.23/8.61 | | | | | ALPHA: (168) implies:
% 46.23/8.61 | | | | | (169) apart_point_and_line(all_23_4, all_23_2) = 0
% 46.23/8.61 | | | | |
% 46.66/8.61 | | | | | REF_CLOSE: (12), (40), (41), (169) are inconsistent by sub-proof #1.
% 46.66/8.61 | | | | |
% 46.66/8.61 | | | | End of split
% 46.66/8.61 | | | |
% 46.66/8.61 | | | End of split
% 46.66/8.61 | | |
% 46.66/8.61 | | Case 2:
% 46.66/8.61 | | |
% 46.66/8.61 | | | (170) all_38_0 = 0
% 46.66/8.61 | | |
% 46.66/8.61 | | | REDUCE: (43), (170) imply:
% 46.66/8.61 | | | (171) $false
% 46.66/8.61 | | |
% 46.66/8.61 | | | CLOSE: (171) is inconsistent.
% 46.66/8.61 | | |
% 46.66/8.61 | | End of split
% 46.66/8.61 | |
% 46.66/8.61 | Case 2:
% 46.66/8.61 | |
% 46.66/8.61 | | (172) all_40_0 = 0
% 46.66/8.61 | |
% 46.66/8.61 | | REDUCE: (46), (172) imply:
% 46.66/8.61 | | (173) $false
% 46.66/8.61 | |
% 46.66/8.61 | | CLOSE: (173) is inconsistent.
% 46.66/8.61 | |
% 46.66/8.61 | End of split
% 46.66/8.61 |
% 46.66/8.61 End of proof
% 46.66/8.61
% 46.66/8.61 Sub-proof #1 shows that the following formulas are inconsistent:
% 46.66/8.61 ----------------------------------------------------------------
% 46.66/8.61 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 46.66/8.61 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 46.66/8.61 (apart_point_and_line(v3, v2) = v0))
% 46.66/8.61 (2) apart_point_and_line(all_23_4, all_23_2) = all_36_0
% 46.66/8.61 (3) apart_point_and_line(all_23_4, all_23_2) = 0
% 46.66/8.61 (4) ~ (all_36_0 = 0)
% 46.66/8.61
% 46.66/8.61 Begin of proof
% 46.66/8.61 |
% 46.66/8.61 | GROUND_INST: instantiating (1) with all_36_0, 0, all_23_2, all_23_4,
% 46.66/8.61 | simplifying with (2), (3) gives:
% 46.66/8.61 | (5) all_36_0 = 0
% 46.66/8.61 |
% 46.66/8.61 | REDUCE: (4), (5) imply:
% 46.66/8.61 | (6) $false
% 46.66/8.61 |
% 46.66/8.61 | CLOSE: (6) is inconsistent.
% 46.66/8.61 |
% 46.66/8.61 End of proof
% 46.66/8.61 % SZS output end Proof for theBenchmark
% 46.66/8.61
% 46.66/8.61 8013ms
%------------------------------------------------------------------------------