TSTP Solution File: GEO171+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO171+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 23:21:49 EDT 2023
% Result : Theorem 17.14s 3.11s
% Output : Proof 25.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO171+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 30 00:19:25 EDT 2023
% 0.13/0.34 % 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 ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.16/1.14 Prover 1: Preprocessing ...
% 3.16/1.15 Prover 4: Preprocessing ...
% 3.43/1.18 Prover 5: Preprocessing ...
% 3.43/1.18 Prover 3: Preprocessing ...
% 3.43/1.18 Prover 0: Preprocessing ...
% 3.43/1.18 Prover 6: Preprocessing ...
% 3.43/1.18 Prover 2: Preprocessing ...
% 6.32/1.60 Prover 5: Proving ...
% 6.32/1.60 Prover 2: Proving ...
% 6.32/1.64 Prover 6: Constructing countermodel ...
% 7.11/1.68 Prover 3: Constructing countermodel ...
% 7.11/1.70 Prover 1: Constructing countermodel ...
% 7.11/1.73 Prover 6: gave up
% 7.11/1.73 Prover 3: gave up
% 7.55/1.73 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.55/1.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.72/1.78 Prover 7: Preprocessing ...
% 7.72/1.80 Prover 1: gave up
% 7.72/1.81 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 8.20/1.82 Prover 8: Preprocessing ...
% 8.53/1.87 Prover 9: Preprocessing ...
% 8.53/1.91 Prover 7: Warning: ignoring some quantifiers
% 9.11/1.95 Prover 7: Constructing countermodel ...
% 9.33/1.99 Prover 4: Constructing countermodel ...
% 9.33/2.01 Prover 8: Warning: ignoring some quantifiers
% 9.33/2.01 Prover 0: Proving ...
% 9.33/2.03 Prover 8: Constructing countermodel ...
% 10.82/2.20 Prover 8: gave up
% 10.82/2.20 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.36/2.26 Prover 9: Constructing countermodel ...
% 11.44/2.27 Prover 10: Preprocessing ...
% 11.96/2.35 Prover 10: Warning: ignoring some quantifiers
% 11.96/2.36 Prover 10: Constructing countermodel ...
% 13.06/2.50 Prover 7: gave up
% 13.06/2.51 Prover 10: gave up
% 13.06/2.51 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.06/2.51 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 13.06/2.55 Prover 11: Preprocessing ...
% 13.57/2.56 Prover 12: Preprocessing ...
% 13.96/2.68 Prover 12: Proving ...
% 14.77/2.88 Prover 11: Constructing countermodel ...
% 17.14/3.11 Prover 9: proved (1293ms)
% 17.14/3.11
% 17.14/3.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.14/3.11
% 17.14/3.12 Prover 5: stopped
% 17.14/3.12 Prover 2: stopped
% 17.14/3.14 Prover 12: stopped
% 17.14/3.14 Prover 0: stopped
% 17.14/3.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 17.14/3.14 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 17.14/3.14 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 17.81/3.15 Prover 13: Preprocessing ...
% 17.81/3.16 Prover 19: Preprocessing ...
% 17.81/3.16 Prover 16: Preprocessing ...
% 17.81/3.18 Prover 13: Warning: ignoring some quantifiers
% 18.14/3.21 Prover 13: Constructing countermodel ...
% 18.14/3.21 Prover 16: Warning: ignoring some quantifiers
% 18.14/3.22 Prover 16: Constructing countermodel ...
% 18.58/3.25 Prover 19: Warning: ignoring some quantifiers
% 18.58/3.25 Prover 19: Constructing countermodel ...
% 19.05/3.35 Prover 13: gave up
% 19.05/3.41 Prover 19: gave up
% 20.92/3.64 Prover 16: gave up
% 22.92/4.06 Prover 4: Found proof (size 583)
% 22.92/4.06 Prover 4: proved (3438ms)
% 22.92/4.07 Prover 11: stopped
% 22.92/4.07
% 22.92/4.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.92/4.07
% 24.29/4.28 % SZS output start Proof for theBenchmark
% 24.29/4.29 Assumptions after simplification:
% 24.29/4.29 ---------------------------------
% 24.29/4.29
% 24.29/4.29 (apart3)
% 24.36/4.31 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0))
% 24.36/4.31
% 24.36/4.31 (ax2)
% 24.46/4.32 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_lines(v0, v1) =
% 24.46/4.32 v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v0, v1) = 0) & ! [v0: $i] :
% 24.46/4.32 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ~
% 24.46/4.32 $i(v1) | ~ $i(v0) | equal_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] :
% 24.46/4.32 ( ~ (equal_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2
% 24.46/4.32 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 24.46/4.32 (distinct_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~
% 24.46/4.32 (v2 = 0) & equal_lines(v0, v1) = v2))
% 24.46/4.32
% 24.46/4.32 (ceq3)
% 24.50/4.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 24.50/4.32 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2)
% 24.50/4.32 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 24.50/4.32 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 24.50/4.32 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~
% 24.50/4.32 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 24.50/4.32 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 24.50/4.32 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~
% 24.50/4.32 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 24.50/4.32 convergent_lines(v0, v2) = 0)
% 24.50/4.32
% 24.50/4.32 (ci3)
% 24.50/4.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 24.50/4.32 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 24.50/4.32 (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4
% 24.50/4.32 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 24.50/4.32 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 24.50/4.32 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 &
% 24.50/4.32 apart_point_and_line(v2, v0) = v3 & $i(v2)))
% 24.50/4.32
% 24.50/4.32 (ci4)
% 24.50/4.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 24.50/4.33 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 24.50/4.33 (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4
% 24.50/4.33 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 24.50/4.33 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 24.50/4.33 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 &
% 24.50/4.33 apart_point_and_line(v2, v1) = v3 & $i(v2)))
% 24.50/4.33
% 24.50/4.33 (coipo1)
% 24.50/4.33 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 24.50/4.33 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 24.50/4.33 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] :
% 24.50/4.33 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 24.50/4.33 unorthogonal_lines(v0, v1) = 0)
% 24.50/4.33
% 24.50/4.33 (con)
% 24.50/4.33 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & convergent_lines(v0,
% 24.50/4.33 v1) = 0 & distinct_lines(v0, v1) = v2 & $i(v1) & $i(v0))
% 24.50/4.33
% 24.50/4.33 (cotno1)
% 24.50/4.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 24.50/4.35 (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) |
% 24.50/4.35 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7:
% 24.50/4.35 any] : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 &
% 24.50/4.35 convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 &
% 24.50/4.35 convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4
% 24.50/4.35 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 24.50/4.35 : ! [v3: any] : ! [v4: any] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~
% 24.50/4.35 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.50/4.35 [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 24.50/4.35 (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v1) = v5 &
% 24.50/4.35 convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & ( ~ (v8 =
% 24.50/4.35 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0:
% 24.50/4.35 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 24.50/4.35 (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ~
% 24.50/4.35 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any]
% 24.50/4.35 : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0,
% 24.50/4.35 v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v1) = v5
% 24.50/4.35 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) &
% 24.50/4.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 24.50/4.35 (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ~
% 24.50/4.35 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any]
% 24.50/4.35 : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0,
% 24.50/4.35 v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) =
% 24.50/4.35 v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0))))
% 24.50/4.35 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 24.50/4.35 (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ~
% 24.50/4.35 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any]
% 24.50/4.35 : ? [v7: any] : (unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2)
% 24.50/4.35 = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~
% 24.50/4.35 (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0: $i] : !
% 24.50/4.35 [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) |
% 24.50/4.35 ~ (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 24.50/4.35 ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 24.50/4.35 (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 &
% 24.50/4.35 convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 =
% 24.50/4.35 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1:
% 24.50/4.35 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~
% 24.50/4.35 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.50/4.35 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 24.50/4.35 (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 &
% 24.50/4.35 convergent_lines(v1, v2) = v7 & convergent_lines(v0, v1) = v4 & ( ~ (v7 =
% 24.50/4.35 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0: $i] : ! [v1:
% 24.50/4.35 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~
% 24.50/4.35 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.50/4.35 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 24.50/4.35 (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 &
% 24.50/4.35 convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v7 =
% 24.50/4.35 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1:
% 24.50/4.35 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) |
% 24.50/4.35 ~ (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.50/4.35 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 24.50/4.35 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v5 &
% 24.50/4.35 convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v7 =
% 24.50/4.35 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0: $i] : ! [v1:
% 24.50/4.35 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = v3) |
% 24.50/4.35 ~ (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.50/4.35 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 24.50/4.35 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 &
% 24.50/4.35 convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 =
% 24.50/4.35 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1:
% 24.50/4.35 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~
% 24.50/4.35 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.50/4.35 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 24.50/4.35 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 &
% 24.50/4.35 unorthogonal_lines(v0, v1) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7
% 24.50/4.35 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0: $i] : !
% 24.50/4.35 [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) |
% 24.50/4.35 ~ (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.50/4.35 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 24.50/4.35 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 &
% 24.50/4.35 unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v7
% 24.50/4.35 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0))))
% 24.50/4.35
% 24.50/4.35 (couo1)
% 24.50/4.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 24.50/4.35 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~
% 24.50/4.35 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.50/4.35 [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0: $i] :
% 24.50/4.35 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0,
% 24.50/4.35 v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) |
% 24.50/4.35 ~ $i(v0) | unorthogonal_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : !
% 24.50/4.35 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~
% 24.50/4.35 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 24.50/4.35 unorthogonal_lines(v0, v2) = 0)
% 24.50/4.35
% 24.50/4.35 (cup1)
% 24.50/4.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 24.50/4.36 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~
% 24.50/4.36 (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.50/4.36 [v5: any] : ? [v6: any] : (convergent_lines(v1, v2) = v6 &
% 24.50/4.36 distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : !
% 24.50/4.36 [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~
% 24.50/4.36 (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) |
% 24.50/4.36 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 24.50/4.36 (apart_point_and_line(v0, v1) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 =
% 24.50/4.36 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 24.50/4.36 int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) =
% 24.50/4.36 v3) | ~ (convergent_lines(v1, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 24.50/4.36 $i(v0) | ? [v5: any] : ? [v6: any] : (apart_point_and_line(v0, v2) = v6 &
% 24.50/4.36 distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : !
% 24.50/4.36 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0,
% 24.50/4.36 v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 24.50/4.36 $i(v0) | ? [v4: any] : ? [v5: any] : (apart_point_and_line(v0, v1) = v4 &
% 24.50/4.36 convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0))) & ! [v0: $i] : !
% 24.50/4.36 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0,
% 24.50/4.36 v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 24.50/4.36 $i(v0) | ? [v4: any] : ? [v5: any] : (apart_point_and_line(v0, v2) = v4 &
% 24.50/4.36 convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0)))
% 24.50/4.36
% 24.50/4.36 (int1)
% 24.50/4.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 24.50/4.36 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 24.50/4.36 ? [v6: any] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 &
% 24.50/4.36 convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) |
% 24.50/4.36 v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) =
% 24.50/4.36 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] :
% 24.50/4.36 ? [v5: any] : (point(v4) = v5 & line(v1) = v3 & line(v0) = v2 &
% 24.50/4.36 intersection_point(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5
% 24.50/4.36 = 0)))
% 24.50/4.36
% 24.50/4.36 (oac1)
% 24.50/4.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 24.50/4.37 (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) |
% 24.50/4.37 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7:
% 24.50/4.37 any] : ? [v8: any] : (unorthogonal_lines(v0, v1) = v6 &
% 24.50/4.37 convergent_lines(v1, v2) = v8 & convergent_lines(v0, v2) = v7 &
% 24.50/4.37 convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4
% 24.50/4.37 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 24.50/4.37 : ! [v3: any] : ! [v4: any] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~
% 24.50/4.37 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.50/4.37 [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 24.50/4.37 (unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = v6 &
% 24.50/4.37 convergent_lines(v1, v2) = v8 & convergent_lines(v0, v1) = v5 & ( ~ (v6 =
% 24.50/4.37 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) & ! [v0:
% 24.50/4.37 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 24.50/4.37 (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ~
% 24.50/4.37 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any]
% 24.50/4.37 : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0,
% 24.50/4.37 v1) = v6 & convergent_lines(v0, v2) = v7 & convergent_lines(v0, v1) = v5
% 24.50/4.37 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) &
% 24.50/4.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 24.50/4.37 (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ~
% 24.50/4.37 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any]
% 24.50/4.37 : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0,
% 24.50/4.37 v2) = v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v1) =
% 24.50/4.38 v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0))))
% 24.50/4.38 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 24.50/4.38 (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ~
% 24.50/4.38 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any]
% 24.50/4.38 : ? [v7: any] : (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2)
% 24.50/4.38 = v7 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~
% 24.50/4.38 (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : !
% 24.50/4.38 [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = v3)
% 24.50/4.38 | ~ (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.50/4.38 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 24.50/4.38 (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 &
% 24.50/4.38 convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v4 =
% 24.50/4.38 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1:
% 24.50/4.38 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) |
% 24.50/4.38 ~ (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.50/4.38 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 24.50/4.38 (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 &
% 24.50/4.38 convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 =
% 24.50/4.38 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1:
% 24.50/4.38 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) |
% 24.50/4.38 ~ (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.50/4.38 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 24.50/4.38 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v4 &
% 24.50/4.38 convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & ( ~ (v4 =
% 24.50/4.38 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1:
% 24.50/4.38 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~
% 24.50/4.38 (convergent_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.50/4.38 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 24.50/4.38 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 &
% 24.50/4.38 convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 =
% 24.50/4.38 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : ! [v1:
% 24.50/4.38 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~
% 24.50/4.38 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.50/4.38 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 24.50/4.38 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 &
% 24.50/4.38 convergent_lines(v1, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v4 =
% 24.50/4.38 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1:
% 24.50/4.38 $i] : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = v3) | ~
% 24.50/4.38 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 24.50/4.38 any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 24.50/4.38 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 &
% 24.50/4.38 unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v4
% 24.50/4.38 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0: $i] : !
% 24.50/4.38 [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v0, v2) = v3) |
% 24.50/4.38 ~ (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 24.50/4.38 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 24.50/4.38 (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 &
% 24.50/4.38 unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & ( ~ (v4
% 24.50/4.38 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0))))
% 24.50/4.38
% 24.50/4.38 (occu1)
% 24.50/4.38 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 24.50/4.38 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 24.50/4.38 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] :
% 24.50/4.38 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 24.50/4.38 unorthogonal_lines(v0, v1) = 0)
% 24.50/4.38
% 24.50/4.38 (p1)
% 24.50/4.38 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (convergent_lines(v0,
% 24.50/4.38 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 24.50/4.38 distinct_lines(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 24.50/4.38 (distinct_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0,
% 24.50/4.38 v1) = 0)
% 24.50/4.38
% 24.50/4.38 (function-axioms)
% 24.50/4.38 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 24.50/4.38 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~
% 24.50/4.38 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.50/4.38 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.50/4.38 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2)
% 24.50/4.38 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 24.50/4.38 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~
% 24.50/4.38 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.50/4.39 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.50/4.39 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0:
% 24.50/4.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.50/4.39 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 24.50/4.39 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.50/4.39 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 24.50/4.39 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 24.50/4.39 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 24.50/4.39 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 24.50/4.39 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 24.50/4.39 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 24.50/4.39 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 24.50/4.39 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 24.50/4.39 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 24.50/4.39 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.50/4.39 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.50/4.39 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 24.50/4.39 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 24.50/4.39 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 24.50/4.39 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 24.50/4.39 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.50/4.39 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 24.50/4.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.50/4.39 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 24.50/4.39 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 24.50/4.39 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0:
% 24.50/4.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 24.50/4.39 ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 24.50/4.39
% 24.50/4.39 Further assumptions not needed in the proof:
% 24.50/4.39 --------------------------------------------
% 24.50/4.39 a3, a4, a5, apart1, apart2, apart4, apart5, ax1, ax6, ceq1, ceq2, ci1, ci2,
% 24.50/4.39 con1, cp1, cp2, cu1, ooc1, ooc2, orth1, ouo1, par1
% 24.50/4.39
% 24.50/4.39 Those formulas are unsatisfiable:
% 24.50/4.39 ---------------------------------
% 24.50/4.39
% 24.50/4.39 Begin of proof
% 24.50/4.39 |
% 24.50/4.39 | ALPHA: (ci3) implies:
% 24.50/4.39 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~
% 24.50/4.39 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 24.50/4.39 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3
% 24.50/4.39 | & $i(v2)))
% 24.50/4.39 |
% 24.50/4.39 | ALPHA: (ci4) implies:
% 24.50/4.39 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~
% 24.50/4.39 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 24.50/4.39 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3
% 24.50/4.39 | & $i(v2)))
% 24.50/4.39 |
% 24.50/4.39 | ALPHA: (ceq3) implies:
% 24.50/4.39 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 24.50/4.39 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) |
% 24.50/4.39 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v1, v2) = 0)
% 24.50/4.39 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] :
% 24.50/4.39 | (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~
% 24.50/4.39 | (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 24.50/4.39 | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 24.50/4.39 |
% 24.50/4.39 | ALPHA: (p1) implies:
% 24.50/4.39 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 24.50/4.39 | (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 24.50/4.39 | int] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 24.50/4.39 |
% 24.50/4.39 | ALPHA: (cup1) implies:
% 24.50/4.40 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] :
% 24.50/4.40 | (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~
% 24.50/4.40 | (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 24.50/4.40 | $i(v0) | ? [v5: any] : ? [v6: any] : (convergent_lines(v1, v2) = v6
% 24.50/4.40 | & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 24.50/4.40 |
% 24.50/4.40 | ALPHA: (oac1) implies:
% 24.50/4.40 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 24.50/4.40 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) |
% 24.50/4.40 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ?
% 24.50/4.40 | [v6: any] : ? [v7: any] : (unorthogonal_lines(v1, v2) = v7 &
% 24.50/4.40 | unorthogonal_lines(v0, v2) = v5 & unorthogonal_lines(v0, v1) = v4 &
% 24.50/4.40 | convergent_lines(v1, v2) = v6 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) |
% 24.50/4.40 | (v5 = 0 & v3 = 0))))
% 24.50/4.40 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 24.50/4.40 | (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) |
% 24.50/4.40 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ?
% 24.50/4.40 | [v6: any] : ? [v7: any] : (unorthogonal_lines(v1, v2) = v7 &
% 24.50/4.40 | unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 &
% 24.50/4.40 | convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) |
% 24.50/4.40 | (v6 = 0 & v5 = 0))))
% 24.50/4.40 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 24.50/4.40 | (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0)
% 24.50/4.40 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 24.50/4.40 | ? [v6: any] : ? [v7: any] : (unorthogonal_lines(v1, v2) = v7 &
% 24.50/4.40 | unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 &
% 24.50/4.40 | convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) |
% 24.50/4.40 | (v5 = 0 & v3 = 0))))
% 24.50/4.40 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 24.50/4.40 | (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) =
% 24.50/4.40 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 24.50/4.40 | any] : ? [v6: any] : ? [v7: any] : (unorthogonal_lines(v0, v2) =
% 24.50/4.40 | v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) =
% 24.50/4.40 | v7 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v3 =
% 24.50/4.40 | 0) | (v6 = 0 & v5 = 0))))
% 24.50/4.40 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any]
% 24.50/4.40 | : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) =
% 24.50/4.40 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 24.50/4.40 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v1, v2) =
% 24.91/4.41 | v8 & unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1)
% 24.91/4.41 | = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)
% 24.91/4.41 | | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0))))
% 24.91/4.41 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any]
% 24.91/4.41 | : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2)
% 24.91/4.41 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 24.91/4.41 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v1, v2) =
% 24.91/4.41 | v8 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v2) =
% 24.91/4.41 | v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) |
% 24.91/4.41 | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0))))
% 24.91/4.41 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any]
% 24.91/4.41 | : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2)
% 24.91/4.41 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 24.91/4.41 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v0, v2) =
% 24.91/4.41 | v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v1, v2) =
% 24.91/4.41 | v8 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) |
% 24.91/4.41 | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0))))
% 24.91/4.41 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any]
% 24.91/4.41 | : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0,
% 24.91/4.41 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] :
% 24.91/4.41 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v0,
% 24.91/4.41 | v1) = v6 & convergent_lines(v1, v2) = v8 & convergent_lines(v0,
% 24.91/4.41 | v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5
% 24.91/4.41 | = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0))))
% 24.91/4.41 |
% 24.91/4.41 | ALPHA: (occu1) implies:
% 24.91/4.41 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 24.91/4.41 | (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 24.91/4.41 | convergent_lines(v0, v1) = 0)
% 24.91/4.41 |
% 24.91/4.41 | ALPHA: (cotno1) implies:
% 24.91/4.41 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 24.91/4.41 | (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3)
% 24.91/4.41 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 24.91/4.41 | ? [v6: any] : ? [v7: any] : (unorthogonal_lines(v1, v2) = v7 &
% 24.91/4.41 | unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4
% 24.91/4.41 | & convergent_lines(v0, v2) = v5 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0)
% 24.91/4.41 | | (v4 = 0 & v3 = 0))))
% 24.91/4.41 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 24.91/4.41 | (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3)
% 24.91/4.41 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 24.91/4.41 | ? [v6: any] : ? [v7: any] : (unorthogonal_lines(v1, v2) = v7 &
% 24.91/4.41 | unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5
% 24.91/4.41 | & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0)
% 24.91/4.41 | | (v5 = 0 & v4 = 0))))
% 24.91/4.42 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 24.91/4.42 | (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) =
% 24.91/4.42 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 24.91/4.42 | any] : ? [v6: any] : ? [v7: any] : (unorthogonal_lines(v1, v2) =
% 24.91/4.42 | v7 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v0, v2) =
% 24.91/4.42 | v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v5 =
% 24.91/4.42 | 0) | (v4 = 0 & v3 = 0))))
% 24.91/4.42 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 24.91/4.42 | (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) =
% 24.91/4.42 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 24.91/4.42 | any] : ? [v6: any] : ? [v7: any] : (unorthogonal_lines(v1, v2) =
% 24.91/4.42 | v7 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v0, v2) =
% 24.91/4.42 | v6 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 =
% 24.91/4.42 | 0) | (v5 = 0 & v4 = 0))))
% 24.91/4.42 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any]
% 24.91/4.42 | : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) =
% 24.91/4.42 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 24.91/4.42 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v1, v2) =
% 24.91/4.42 | v8 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1)
% 24.91/4.42 | = v5 & convergent_lines(v1, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)
% 24.91/4.42 | | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0))))
% 24.91/4.42 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any]
% 24.91/4.42 | : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2)
% 24.91/4.42 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 24.91/4.42 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v1, v2) =
% 24.91/4.42 | v8 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) =
% 24.91/4.42 | v7 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) |
% 24.91/4.42 | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0))))
% 24.91/4.42 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any]
% 24.91/4.42 | : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1)
% 24.91/4.42 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 24.91/4.42 | any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v1, v2) =
% 24.91/4.42 | v8 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) =
% 24.91/4.42 | v7 & convergent_lines(v0, v2) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) |
% 24.91/4.42 | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0))))
% 24.91/4.42 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any]
% 24.91/4.42 | : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0,
% 24.91/4.42 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] :
% 24.91/4.42 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (unorthogonal_lines(v1,
% 24.91/4.42 | v2) = v8 & convergent_lines(v1, v2) = v7 & convergent_lines(v0,
% 24.91/4.42 | v2) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7
% 24.91/4.42 | = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0))))
% 24.91/4.42 |
% 24.91/4.42 | ALPHA: (couo1) implies:
% 24.91/4.42 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int]
% 24.91/4.42 | : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~
% 24.91/4.42 | (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 24.91/4.42 | $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) =
% 24.91/4.42 | v5))
% 24.91/4.42 |
% 24.91/4.42 | ALPHA: (int1) implies:
% 24.91/4.42 | (25) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~
% 24.91/4.42 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ?
% 24.91/4.42 | [v5: any] : (point(v4) = v5 & line(v1) = v3 & line(v0) = v2 &
% 24.91/4.42 | intersection_point(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 =
% 24.91/4.42 | 0) | v5 = 0)))
% 24.91/4.43 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0,
% 24.91/4.43 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any]
% 24.91/4.43 | : ? [v5: any] : ? [v6: any] : (point(v2) = v6 & line(v1) = v4 &
% 24.91/4.43 | line(v0) = v3 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~
% 24.91/4.43 | (v4 = 0) | ~ (v3 = 0) | v6 = 0)))
% 24.91/4.43 |
% 24.91/4.43 | ALPHA: (ax2) implies:
% 24.91/4.43 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 24.91/4.43 | (distinct_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 24.91/4.43 | equal_lines(v0, v1) = 0)
% 24.91/4.43 |
% 24.91/4.43 | ALPHA: (function-axioms) implies:
% 24.91/4.43 | (28) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.91/4.43 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~
% 24.91/4.43 | (distinct_lines(v3, v2) = v0))
% 24.91/4.43 | (29) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.91/4.43 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 24.91/4.43 | (convergent_lines(v3, v2) = v0))
% 24.91/4.43 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.91/4.43 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) =
% 24.91/4.43 | v0))
% 24.91/4.43 | (31) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 24.91/4.43 | : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 24.91/4.43 | (unorthogonal_lines(v3, v2) = v0))
% 24.91/4.43 |
% 24.91/4.43 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2
% 24.91/4.43 | gives:
% 24.91/4.43 | (32) ~ (all_38_0 = 0) & convergent_lines(all_38_2, all_38_1) = 0 &
% 24.91/4.43 | distinct_lines(all_38_2, all_38_1) = all_38_0 & $i(all_38_1) &
% 24.91/4.43 | $i(all_38_2)
% 24.91/4.43 |
% 24.91/4.43 | ALPHA: (32) implies:
% 24.91/4.43 | (33) ~ (all_38_0 = 0)
% 24.91/4.43 | (34) $i(all_38_2)
% 24.91/4.43 | (35) $i(all_38_1)
% 24.91/4.43 | (36) distinct_lines(all_38_2, all_38_1) = all_38_0
% 24.91/4.43 | (37) convergent_lines(all_38_2, all_38_1) = 0
% 24.91/4.43 |
% 24.91/4.43 | GROUND_INST: instantiating (27) with all_38_2, all_38_1, all_38_0, simplifying
% 24.91/4.43 | with (34), (35), (36) gives:
% 24.91/4.43 | (38) all_38_0 = 0 | equal_lines(all_38_2, all_38_1) = 0
% 24.91/4.43 |
% 24.91/4.43 | GROUND_INST: instantiating (7) with all_38_2, all_38_1, all_38_1, 0,
% 24.91/4.43 | simplifying with (34), (35), (37) gives:
% 24.91/4.43 | (39) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.43 | (unorthogonal_lines(all_38_1, all_38_1) = v3 &
% 24.91/4.43 | unorthogonal_lines(all_38_2, all_38_1) = v1 &
% 24.91/4.43 | unorthogonal_lines(all_38_2, all_38_1) = v0 &
% 24.91/4.43 | convergent_lines(all_38_1, all_38_1) = v2 & ( ~ (v0 = 0) | v1 = 0 |
% 24.91/4.43 | (v3 = 0 & v2 = 0)))
% 24.91/4.43 |
% 24.91/4.43 | GROUND_INST: instantiating (17) with all_38_2, all_38_2, all_38_1, 0,
% 24.91/4.43 | simplifying with (34), (35), (37) gives:
% 24.91/4.43 | (40) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.43 | (unorthogonal_lines(all_38_2, all_38_1) = v3 &
% 24.91/4.43 | unorthogonal_lines(all_38_2, all_38_1) = v2 &
% 24.91/4.43 | unorthogonal_lines(all_38_2, all_38_2) = v1 &
% 24.91/4.43 | convergent_lines(all_38_2, all_38_2) = v0 & ( ~ (v3 = 0) | v2 = 0 |
% 24.91/4.43 | (v1 = 0 & v0 = 0)))
% 24.91/4.43 |
% 24.91/4.43 | GROUND_INST: instantiating (11) with all_38_2, all_38_2, all_38_1, 0, 0,
% 24.91/4.43 | simplifying with (34), (35), (37) gives:
% 24.91/4.43 | (41) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.43 | (unorthogonal_lines(all_38_2, all_38_1) = v3 &
% 24.91/4.43 | unorthogonal_lines(all_38_2, all_38_1) = v2 &
% 24.91/4.43 | unorthogonal_lines(all_38_2, all_38_2) = v1 &
% 24.91/4.43 | convergent_lines(all_38_2, all_38_2) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 24.91/4.43 | 0) | v3 = 0 | v2 = 0))
% 24.91/4.43 |
% 24.91/4.43 | GROUND_INST: instantiating (20) with all_38_2, all_38_1, all_38_1, 0, 0,
% 24.91/4.43 | simplifying with (34), (35), (37) gives:
% 24.91/4.44 | (42) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.44 | (unorthogonal_lines(all_38_1, all_38_1) = v3 &
% 24.91/4.44 | unorthogonal_lines(all_38_2, all_38_1) = v1 &
% 24.91/4.44 | unorthogonal_lines(all_38_2, all_38_1) = v0 &
% 24.91/4.44 | convergent_lines(all_38_1, all_38_1) = v2 & ( ~ (v3 = 0) | ~ (v2 =
% 24.91/4.44 | 0) | v1 = 0 | v0 = 0))
% 24.91/4.44 |
% 24.91/4.44 | GROUND_INST: instantiating (25) with all_38_2, all_38_1, simplifying with
% 24.91/4.44 | (34), (35), (37) gives:
% 24.91/4.44 | (43) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : (point(v2)
% 24.91/4.44 | = v3 & line(all_38_1) = v1 & line(all_38_2) = v0 &
% 24.91/4.44 | intersection_point(all_38_2, all_38_1) = v2 & $i(v2) & ( ~ (v1 = 0)
% 24.91/4.44 | | ~ (v0 = 0) | v3 = 0))
% 24.91/4.44 |
% 24.91/4.44 | GROUND_INST: instantiating (2) with all_38_2, all_38_1, simplifying with (34),
% 24.91/4.44 | (35), (37) gives:
% 24.91/4.44 | (44) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 24.91/4.44 | intersection_point(all_38_2, all_38_1) = v0 &
% 24.91/4.44 | apart_point_and_line(v0, all_38_1) = v1 & $i(v0))
% 24.91/4.44 |
% 24.91/4.44 | GROUND_INST: instantiating (1) with all_38_2, all_38_1, simplifying with (34),
% 24.91/4.44 | (35), (37) gives:
% 24.91/4.44 | (45) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 24.91/4.44 | intersection_point(all_38_2, all_38_1) = v0 &
% 24.91/4.44 | apart_point_and_line(v0, all_38_2) = v1 & $i(v0))
% 24.91/4.44 |
% 24.91/4.44 | DELTA: instantiating (44) with fresh symbols all_47_0, all_47_1 gives:
% 24.91/4.44 | (46) ~ (all_47_0 = 0) & intersection_point(all_38_2, all_38_1) = all_47_1
% 24.91/4.44 | & apart_point_and_line(all_47_1, all_38_1) = all_47_0 & $i(all_47_1)
% 24.91/4.44 |
% 24.91/4.44 | ALPHA: (46) implies:
% 24.91/4.44 | (47) ~ (all_47_0 = 0)
% 24.91/4.44 | (48) apart_point_and_line(all_47_1, all_38_1) = all_47_0
% 24.91/4.44 | (49) intersection_point(all_38_2, all_38_1) = all_47_1
% 24.91/4.44 |
% 24.91/4.44 | DELTA: instantiating (45) with fresh symbols all_49_0, all_49_1 gives:
% 24.91/4.44 | (50) ~ (all_49_0 = 0) & intersection_point(all_38_2, all_38_1) = all_49_1
% 24.91/4.44 | & apart_point_and_line(all_49_1, all_38_2) = all_49_0 & $i(all_49_1)
% 24.91/4.44 |
% 24.91/4.44 | ALPHA: (50) implies:
% 24.91/4.44 | (51) ~ (all_49_0 = 0)
% 24.91/4.44 | (52) $i(all_49_1)
% 24.91/4.44 | (53) apart_point_and_line(all_49_1, all_38_2) = all_49_0
% 24.91/4.44 | (54) intersection_point(all_38_2, all_38_1) = all_49_1
% 24.91/4.44 |
% 24.91/4.44 | DELTA: instantiating (43) with fresh symbols all_51_0, all_51_1, all_51_2,
% 24.91/4.44 | all_51_3 gives:
% 24.91/4.44 | (55) point(all_51_1) = all_51_0 & line(all_38_1) = all_51_2 &
% 24.91/4.44 | line(all_38_2) = all_51_3 & intersection_point(all_38_2, all_38_1) =
% 24.91/4.44 | all_51_1 & $i(all_51_1) & ( ~ (all_51_2 = 0) | ~ (all_51_3 = 0) |
% 24.91/4.44 | all_51_0 = 0)
% 24.91/4.44 |
% 24.91/4.44 | ALPHA: (55) implies:
% 24.91/4.44 | (56) intersection_point(all_38_2, all_38_1) = all_51_1
% 24.91/4.44 |
% 24.91/4.44 | DELTA: instantiating (42) with fresh symbols all_53_0, all_53_1, all_53_2,
% 24.91/4.44 | all_53_3 gives:
% 24.91/4.44 | (57) unorthogonal_lines(all_38_1, all_38_1) = all_53_0 &
% 24.91/4.44 | unorthogonal_lines(all_38_2, all_38_1) = all_53_2 &
% 24.91/4.44 | unorthogonal_lines(all_38_2, all_38_1) = all_53_3 &
% 24.91/4.44 | convergent_lines(all_38_1, all_38_1) = all_53_1 & ( ~ (all_53_0 = 0) |
% 24.91/4.44 | ~ (all_53_1 = 0) | all_53_2 = 0 | all_53_3 = 0)
% 24.91/4.44 |
% 24.91/4.44 | ALPHA: (57) implies:
% 24.91/4.44 | (58) convergent_lines(all_38_1, all_38_1) = all_53_1
% 24.91/4.44 | (59) unorthogonal_lines(all_38_2, all_38_1) = all_53_3
% 24.91/4.44 | (60) unorthogonal_lines(all_38_2, all_38_1) = all_53_2
% 24.91/4.44 | (61) unorthogonal_lines(all_38_1, all_38_1) = all_53_0
% 24.91/4.44 |
% 24.91/4.44 | DELTA: instantiating (41) with fresh symbols all_55_0, all_55_1, all_55_2,
% 24.91/4.44 | all_55_3 gives:
% 24.91/4.44 | (62) unorthogonal_lines(all_38_2, all_38_1) = all_55_0 &
% 24.91/4.44 | unorthogonal_lines(all_38_2, all_38_1) = all_55_1 &
% 24.91/4.44 | unorthogonal_lines(all_38_2, all_38_2) = all_55_2 &
% 24.91/4.44 | convergent_lines(all_38_2, all_38_2) = all_55_3 & ( ~ (all_55_2 = 0) |
% 24.91/4.44 | ~ (all_55_3 = 0) | all_55_0 = 0 | all_55_1 = 0)
% 24.91/4.44 |
% 24.91/4.44 | ALPHA: (62) implies:
% 24.91/4.44 | (63) convergent_lines(all_38_2, all_38_2) = all_55_3
% 24.91/4.44 | (64) unorthogonal_lines(all_38_2, all_38_2) = all_55_2
% 24.91/4.44 | (65) unorthogonal_lines(all_38_2, all_38_1) = all_55_1
% 24.91/4.44 | (66) unorthogonal_lines(all_38_2, all_38_1) = all_55_0
% 24.91/4.44 | (67) ~ (all_55_2 = 0) | ~ (all_55_3 = 0) | all_55_0 = 0 | all_55_1 = 0
% 24.91/4.44 |
% 24.91/4.44 | DELTA: instantiating (40) with fresh symbols all_57_0, all_57_1, all_57_2,
% 24.91/4.44 | all_57_3 gives:
% 24.91/4.44 | (68) unorthogonal_lines(all_38_2, all_38_1) = all_57_0 &
% 24.91/4.44 | unorthogonal_lines(all_38_2, all_38_1) = all_57_1 &
% 24.91/4.44 | unorthogonal_lines(all_38_2, all_38_2) = all_57_2 &
% 24.91/4.44 | convergent_lines(all_38_2, all_38_2) = all_57_3 & ( ~ (all_57_0 = 0) |
% 24.91/4.44 | all_57_1 = 0 | (all_57_2 = 0 & all_57_3 = 0))
% 24.91/4.44 |
% 24.91/4.44 | ALPHA: (68) implies:
% 24.91/4.44 | (69) convergent_lines(all_38_2, all_38_2) = all_57_3
% 24.91/4.44 | (70) unorthogonal_lines(all_38_2, all_38_2) = all_57_2
% 24.91/4.44 | (71) unorthogonal_lines(all_38_2, all_38_1) = all_57_1
% 24.91/4.44 | (72) unorthogonal_lines(all_38_2, all_38_1) = all_57_0
% 24.91/4.44 |
% 24.91/4.44 | DELTA: instantiating (39) with fresh symbols all_59_0, all_59_1, all_59_2,
% 24.91/4.44 | all_59_3 gives:
% 24.91/4.44 | (73) unorthogonal_lines(all_38_1, all_38_1) = all_59_0 &
% 24.91/4.44 | unorthogonal_lines(all_38_2, all_38_1) = all_59_2 &
% 24.91/4.44 | unorthogonal_lines(all_38_2, all_38_1) = all_59_3 &
% 24.91/4.44 | convergent_lines(all_38_1, all_38_1) = all_59_1 & ( ~ (all_59_3 = 0) |
% 24.91/4.44 | all_59_2 = 0 | (all_59_0 = 0 & all_59_1 = 0))
% 24.91/4.44 |
% 24.91/4.44 | ALPHA: (73) implies:
% 24.91/4.44 | (74) convergent_lines(all_38_1, all_38_1) = all_59_1
% 24.91/4.44 | (75) unorthogonal_lines(all_38_2, all_38_1) = all_59_3
% 24.91/4.44 | (76) unorthogonal_lines(all_38_2, all_38_1) = all_59_2
% 24.91/4.44 | (77) unorthogonal_lines(all_38_1, all_38_1) = all_59_0
% 24.91/4.44 |
% 24.91/4.44 | BETA: splitting (38) gives:
% 24.91/4.44 |
% 24.91/4.45 | Case 1:
% 24.91/4.45 | |
% 24.91/4.45 | |
% 24.91/4.45 | | GROUND_INST: instantiating (29) with all_55_3, all_57_3, all_38_2, all_38_2,
% 24.91/4.45 | | simplifying with (63), (69) gives:
% 24.91/4.45 | | (78) all_57_3 = all_55_3
% 24.91/4.45 | |
% 24.91/4.45 | | GROUND_INST: instantiating (29) with all_53_1, all_59_1, all_38_1, all_38_1,
% 24.91/4.45 | | simplifying with (58), (74) gives:
% 24.91/4.45 | | (79) all_59_1 = all_53_1
% 24.91/4.45 | |
% 24.91/4.45 | | GROUND_INST: instantiating (30) with all_49_1, all_51_1, all_38_1, all_38_2,
% 24.91/4.45 | | simplifying with (54), (56) gives:
% 24.91/4.45 | | (80) all_51_1 = all_49_1
% 24.91/4.45 | |
% 24.91/4.45 | | GROUND_INST: instantiating (30) with all_47_1, all_51_1, all_38_1, all_38_2,
% 24.91/4.45 | | simplifying with (49), (56) gives:
% 24.91/4.45 | | (81) all_51_1 = all_47_1
% 24.91/4.45 | |
% 24.91/4.45 | | GROUND_INST: instantiating (31) with all_55_2, all_57_2, all_38_2, all_38_2,
% 24.91/4.45 | | simplifying with (64), (70) gives:
% 24.91/4.45 | | (82) all_57_2 = all_55_2
% 24.91/4.45 | |
% 24.91/4.45 | | GROUND_INST: instantiating (31) with all_53_2, all_55_1, all_38_1, all_38_2,
% 24.91/4.45 | | simplifying with (60), (65) gives:
% 24.91/4.45 | | (83) all_55_1 = all_53_2
% 24.91/4.45 | |
% 24.91/4.45 | | GROUND_INST: instantiating (31) with all_55_1, all_55_0, all_38_1, all_38_2,
% 24.91/4.45 | | simplifying with (65), (66) gives:
% 24.91/4.45 | | (84) all_55_0 = all_55_1
% 24.91/4.45 | |
% 24.91/4.45 | | GROUND_INST: instantiating (31) with all_55_0, all_57_0, all_38_1, all_38_2,
% 24.91/4.45 | | simplifying with (66), (72) gives:
% 24.91/4.45 | | (85) all_57_0 = all_55_0
% 24.91/4.45 | |
% 24.91/4.45 | | GROUND_INST: instantiating (31) with all_57_0, all_59_3, all_38_1, all_38_2,
% 24.91/4.45 | | simplifying with (72), (75) gives:
% 24.91/4.45 | | (86) all_59_3 = all_57_0
% 24.91/4.45 | |
% 24.91/4.45 | | GROUND_INST: instantiating (31) with all_57_1, all_59_3, all_38_1, all_38_2,
% 24.91/4.45 | | simplifying with (71), (75) gives:
% 24.91/4.45 | | (87) all_59_3 = all_57_1
% 24.91/4.45 | |
% 24.91/4.45 | | GROUND_INST: instantiating (31) with all_57_0, all_59_2, all_38_1, all_38_2,
% 24.91/4.45 | | simplifying with (72), (76) gives:
% 24.91/4.45 | | (88) all_59_2 = all_57_0
% 24.91/4.45 | |
% 24.91/4.45 | | GROUND_INST: instantiating (31) with all_53_3, all_59_2, all_38_1, all_38_2,
% 24.91/4.45 | | simplifying with (59), (76) gives:
% 24.91/4.45 | | (89) all_59_2 = all_53_3
% 24.91/4.45 | |
% 24.91/4.45 | | GROUND_INST: instantiating (31) with all_53_0, all_59_0, all_38_1, all_38_1,
% 24.91/4.45 | | simplifying with (61), (77) gives:
% 24.91/4.45 | | (90) all_59_0 = all_53_0
% 24.91/4.45 | |
% 24.91/4.45 | | COMBINE_EQS: (88), (89) imply:
% 24.91/4.45 | | (91) all_57_0 = all_53_3
% 24.91/4.45 | |
% 24.91/4.45 | | SIMP: (91) implies:
% 24.91/4.45 | | (92) all_57_0 = all_53_3
% 24.91/4.45 | |
% 24.91/4.45 | | COMBINE_EQS: (86), (87) imply:
% 24.91/4.45 | | (93) all_57_0 = all_57_1
% 24.91/4.45 | |
% 24.91/4.45 | | SIMP: (93) implies:
% 24.91/4.45 | | (94) all_57_0 = all_57_1
% 24.91/4.45 | |
% 24.91/4.45 | | COMBINE_EQS: (85), (94) imply:
% 24.91/4.45 | | (95) all_57_1 = all_55_0
% 24.91/4.45 | |
% 24.91/4.45 | | COMBINE_EQS: (92), (94) imply:
% 24.91/4.45 | | (96) all_57_1 = all_53_3
% 24.91/4.45 | |
% 24.91/4.45 | | COMBINE_EQS: (95), (96) imply:
% 24.91/4.45 | | (97) all_55_0 = all_53_3
% 24.91/4.45 | |
% 24.91/4.45 | | SIMP: (97) implies:
% 24.91/4.45 | | (98) all_55_0 = all_53_3
% 24.91/4.45 | |
% 24.91/4.45 | | COMBINE_EQS: (84), (98) imply:
% 24.91/4.45 | | (99) all_55_1 = all_53_3
% 24.91/4.45 | |
% 24.91/4.45 | | SIMP: (99) implies:
% 24.91/4.45 | | (100) all_55_1 = all_53_3
% 24.91/4.45 | |
% 24.91/4.45 | | COMBINE_EQS: (83), (100) imply:
% 24.91/4.45 | | (101) all_53_2 = all_53_3
% 24.91/4.45 | |
% 24.91/4.45 | | SIMP: (101) implies:
% 24.91/4.45 | | (102) all_53_2 = all_53_3
% 24.91/4.45 | |
% 24.91/4.45 | | COMBINE_EQS: (80), (81) imply:
% 24.91/4.45 | | (103) all_49_1 = all_47_1
% 24.91/4.45 | |
% 24.91/4.45 | | SIMP: (103) implies:
% 24.91/4.45 | | (104) all_49_1 = all_47_1
% 24.91/4.45 | |
% 24.91/4.45 | | REDUCE: (53), (104) imply:
% 24.91/4.45 | | (105) apart_point_and_line(all_47_1, all_38_2) = all_49_0
% 24.91/4.45 | |
% 24.91/4.45 | | REDUCE: (52), (104) imply:
% 24.91/4.45 | | (106) $i(all_47_1)
% 24.91/4.45 | |
% 24.91/4.45 | | GROUND_INST: instantiating (3) with all_38_2, all_38_1, all_38_2, all_55_3,
% 24.91/4.45 | | simplifying with (34), (35), (37), (63) gives:
% 24.91/4.45 | | (107) all_55_3 = 0 | distinct_lines(all_38_1, all_38_2) = 0
% 24.91/4.45 | |
% 24.91/4.45 | | GROUND_INST: instantiating (7) with all_38_2, all_38_1, all_38_2, all_55_3,
% 24.91/4.45 | | simplifying with (34), (35), (37), (63) gives:
% 24.91/4.45 | | (108) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.45 | | (unorthogonal_lines(all_38_1, all_38_2) = v3 &
% 24.91/4.45 | | unorthogonal_lines(all_38_2, all_38_1) = v0 &
% 24.91/4.45 | | unorthogonal_lines(all_38_2, all_38_2) = v1 &
% 24.91/4.45 | | convergent_lines(all_38_1, all_38_2) = v2 & ( ~ (v0 = 0) | (v3 =
% 24.91/4.45 | | 0 & v2 = 0) | (v1 = 0 & all_55_3 = 0)))
% 24.91/4.45 | |
% 24.91/4.45 | | GROUND_INST: instantiating (20) with all_38_2, all_38_1, all_38_2, 0,
% 24.91/4.45 | | all_55_3, simplifying with (34), (35), (37), (63) gives:
% 24.91/4.45 | | (109) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.45 | | (unorthogonal_lines(all_38_1, all_38_2) = v3 &
% 24.91/4.45 | | unorthogonal_lines(all_38_2, all_38_1) = v0 &
% 24.91/4.45 | | unorthogonal_lines(all_38_2, all_38_2) = v1 &
% 24.91/4.45 | | convergent_lines(all_38_1, all_38_2) = v2 & ( ~ (v3 = 0) | ~ (v2
% 24.91/4.45 | | = 0) | v0 = 0 | (v1 = 0 & all_55_3 = 0)))
% 24.91/4.45 | |
% 24.91/4.46 | | GROUND_INST: instantiating (17) with all_38_1, all_38_2, all_38_1, all_53_1,
% 24.91/4.46 | | simplifying with (34), (35), (37), (58) gives:
% 24.91/4.46 | | (110) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.46 | | (unorthogonal_lines(all_38_1, all_38_1) = v2 &
% 24.91/4.46 | | unorthogonal_lines(all_38_1, all_38_2) = v1 &
% 24.91/4.46 | | unorthogonal_lines(all_38_2, all_38_1) = v3 &
% 24.91/4.46 | | convergent_lines(all_38_1, all_38_2) = v0 & ( ~ (v3 = 0) | (v2 =
% 24.91/4.46 | | 0 & all_53_1 = 0) | (v1 = 0 & v0 = 0)))
% 24.91/4.46 | |
% 24.91/4.46 | | GROUND_INST: instantiating (11) with all_38_1, all_38_2, all_38_1, all_53_1,
% 24.91/4.46 | | 0, simplifying with (34), (35), (37), (58) gives:
% 24.91/4.46 | | (111) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.46 | | (unorthogonal_lines(all_38_1, all_38_1) = v2 &
% 24.91/4.46 | | unorthogonal_lines(all_38_1, all_38_2) = v1 &
% 24.91/4.46 | | unorthogonal_lines(all_38_2, all_38_1) = v3 &
% 24.91/4.46 | | convergent_lines(all_38_1, all_38_2) = v0 & ( ~ (v1 = 0) | ~ (v0
% 24.91/4.46 | | = 0) | v3 = 0 | (v2 = 0 & all_53_1 = 0)))
% 24.91/4.46 | |
% 24.91/4.46 | | GROUND_INST: instantiating (4) with all_38_1, all_38_2, all_38_1, all_38_0,
% 24.91/4.46 | | all_53_1, simplifying with (34), (35), (36), (58) gives:
% 24.91/4.46 | | (112) all_53_1 = 0 | all_38_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 24.91/4.46 | | convergent_lines(all_38_1, all_38_2) = v0)
% 24.91/4.46 | |
% 24.91/4.46 | | GROUND_INST: instantiating (6) with all_47_1, all_38_1, all_38_1, all_47_0,
% 24.91/4.46 | | all_47_0, simplifying with (35), (48), (106) gives:
% 24.91/4.46 | | (113) all_47_0 = 0 | ? [v0: any] : ? [v1: any] :
% 24.91/4.46 | | (convergent_lines(all_38_1, all_38_1) = v1 &
% 24.91/4.46 | | distinct_lines(all_38_1, all_38_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 24.91/4.46 | |
% 24.91/4.46 | | GROUND_INST: instantiating (6) with all_47_1, all_38_1, all_38_2, all_47_0,
% 24.91/4.46 | | all_49_0, simplifying with (34), (35), (48), (105), (106)
% 24.91/4.46 | | gives:
% 24.91/4.46 | | (114) all_49_0 = 0 | all_47_0 = 0 | ? [v0: any] : ? [v1: any] :
% 24.91/4.46 | | (convergent_lines(all_38_1, all_38_2) = v1 &
% 24.91/4.46 | | distinct_lines(all_38_1, all_38_2) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 24.91/4.46 | |
% 24.91/4.46 | | GROUND_INST: instantiating (26) with all_38_2, all_38_1, all_47_1,
% 24.91/4.46 | | simplifying with (34), (35), (49) gives:
% 24.91/4.46 | | (115) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.46 | | (point(all_47_1) = v3 & line(all_38_1) = v1 & line(all_38_2) = v0 &
% 24.91/4.46 | | convergent_lines(all_38_2, all_38_1) = v2 & ( ~ (v2 = 0) | ~ (v1
% 24.91/4.46 | | = 0) | ~ (v0 = 0) | v3 = 0))
% 24.91/4.46 | |
% 24.91/4.46 | | GROUND_INST: instantiating (24) with all_38_2, all_38_2, all_38_2, all_55_2,
% 24.91/4.46 | | all_55_2, simplifying with (34), (64) gives:
% 24.91/4.46 | | (116) all_55_2 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 24.91/4.46 | | convergent_lines(all_38_2, all_38_2) = v0)
% 24.91/4.46 | |
% 24.91/4.46 | | GROUND_INST: instantiating (9) with all_38_2, all_38_1, all_38_2, all_55_2,
% 24.91/4.46 | | simplifying with (34), (35), (37), (64) gives:
% 24.91/4.46 | | (117) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.46 | | (unorthogonal_lines(all_38_1, all_38_2) = v3 &
% 24.91/4.46 | | unorthogonal_lines(all_38_2, all_38_1) = v0 &
% 24.91/4.46 | | convergent_lines(all_38_1, all_38_2) = v2 &
% 24.91/4.46 | | convergent_lines(all_38_2, all_38_2) = v1 & ( ~ (v0 = 0) | (v3 =
% 24.91/4.46 | | 0 & v2 = 0) | (v1 = 0 & all_55_2 = 0)))
% 24.91/4.46 | |
% 24.91/4.46 | | GROUND_INST: instantiating (22) with all_38_2, all_38_1, all_38_2, 0,
% 24.91/4.46 | | all_55_2, simplifying with (34), (35), (37), (64) gives:
% 24.91/4.46 | | (118) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.46 | | (unorthogonal_lines(all_38_1, all_38_2) = v3 &
% 24.91/4.46 | | unorthogonal_lines(all_38_2, all_38_1) = v0 &
% 24.91/4.46 | | convergent_lines(all_38_1, all_38_2) = v2 &
% 24.91/4.46 | | convergent_lines(all_38_2, all_38_2) = v1 & ( ~ (v3 = 0) | ~ (v2
% 24.91/4.46 | | = 0) | v0 = 0 | (v1 = 0 & all_55_2 = 0)))
% 24.91/4.46 | |
% 24.91/4.46 | | GROUND_INST: instantiating (15) with all_38_2, all_38_2, all_55_2,
% 24.91/4.46 | | simplifying with (34), (64) gives:
% 24.91/4.46 | | (119) all_55_2 = 0 | convergent_lines(all_38_2, all_38_2) = 0
% 24.91/4.46 | |
% 24.91/4.46 | | GROUND_INST: instantiating (23) with all_38_2, all_38_1, all_38_1, all_53_3,
% 24.91/4.46 | | all_53_3, simplifying with (34), (35), (59) gives:
% 24.91/4.46 | | (120) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.46 | | (unorthogonal_lines(all_38_1, all_38_1) = v3 &
% 24.91/4.46 | | convergent_lines(all_38_1, all_38_1) = v2 &
% 24.91/4.46 | | convergent_lines(all_38_2, all_38_1) = v1 &
% 24.91/4.46 | | convergent_lines(all_38_2, all_38_1) = v0 & ( ~ (v3 = 0) | ~ (v2
% 24.91/4.46 | | = 0) | (v1 = 0 & all_53_3 = 0) | (v0 = 0 & all_53_3 = 0)))
% 24.91/4.46 | |
% 24.91/4.46 | | GROUND_INST: instantiating (14) with all_38_2, all_38_2, all_38_1, all_53_3,
% 24.91/4.46 | | all_53_3, simplifying with (34), (35), (59) gives:
% 24.91/4.47 | | (121) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.47 | | (unorthogonal_lines(all_38_2, all_38_2) = v1 &
% 24.91/4.47 | | convergent_lines(all_38_2, all_38_1) = v3 &
% 24.91/4.47 | | convergent_lines(all_38_2, all_38_1) = v2 &
% 24.91/4.47 | | convergent_lines(all_38_2, all_38_2) = v0 & ( ~ (v1 = 0) | ~ (v0
% 24.91/4.47 | | = 0) | (v3 = 0 & all_53_3 = 0) | (v2 = 0 & all_53_3 = 0)))
% 24.91/4.47 | |
% 24.91/4.47 | | GROUND_INST: instantiating (23) with all_38_2, all_38_1, all_38_2, all_53_3,
% 24.91/4.47 | | all_55_2, simplifying with (34), (35), (59), (64) gives:
% 24.91/4.47 | | (122) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.47 | | (unorthogonal_lines(all_38_1, all_38_2) = v3 &
% 24.91/4.47 | | convergent_lines(all_38_1, all_38_2) = v2 &
% 24.91/4.47 | | convergent_lines(all_38_2, all_38_1) = v0 &
% 24.91/4.47 | | convergent_lines(all_38_2, all_38_2) = v1 & ( ~ (v3 = 0) | ~ (v2
% 24.91/4.47 | | = 0) | (v1 = 0 & all_55_2 = 0) | (v0 = 0 & all_53_3 = 0)))
% 24.91/4.47 | |
% 24.91/4.47 | | GROUND_INST: instantiating (13) with all_38_2, all_38_2, all_38_1, 0,
% 24.91/4.47 | | all_53_3, simplifying with (34), (35), (37), (59) gives:
% 24.91/4.47 | | (123) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.47 | | (unorthogonal_lines(all_38_2, all_38_1) = v2 &
% 24.91/4.47 | | unorthogonal_lines(all_38_2, all_38_2) = v1 &
% 24.91/4.47 | | convergent_lines(all_38_2, all_38_1) = v3 &
% 24.91/4.47 | | convergent_lines(all_38_2, all_38_2) = v0 & ( ~ (v1 = 0) | ~ (v0
% 24.91/4.47 | | = 0) | v2 = 0 | (v3 = 0 & all_53_3 = 0)))
% 24.91/4.47 | |
% 24.91/4.47 | | GROUND_INST: instantiating (12) with all_38_2, all_38_2, all_38_1, all_53_3,
% 24.91/4.47 | | 0, simplifying with (34), (35), (37), (59) gives:
% 24.91/4.47 | | (124) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.47 | | (unorthogonal_lines(all_38_2, all_38_1) = v3 &
% 24.91/4.47 | | unorthogonal_lines(all_38_2, all_38_2) = v1 &
% 24.91/4.47 | | convergent_lines(all_38_2, all_38_1) = v2 &
% 24.91/4.47 | | convergent_lines(all_38_2, all_38_2) = v0 & ( ~ (v1 = 0) | ~ (v0
% 24.91/4.47 | | = 0) | v3 = 0 | (v2 = 0 & all_53_3 = 0)))
% 24.91/4.47 | |
% 24.91/4.47 | | GROUND_INST: instantiating (22) with all_38_2, all_38_1, all_38_1, 0,
% 24.91/4.47 | | all_53_3, simplifying with (34), (35), (37), (59) gives:
% 24.91/4.47 | | (125) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.47 | | (unorthogonal_lines(all_38_1, all_38_1) = v3 &
% 24.91/4.47 | | unorthogonal_lines(all_38_2, all_38_1) = v0 &
% 24.91/4.47 | | convergent_lines(all_38_1, all_38_1) = v2 &
% 24.91/4.47 | | convergent_lines(all_38_2, all_38_1) = v1 & ( ~ (v3 = 0) | ~ (v2
% 24.91/4.47 | | = 0) | v0 = 0 | (v1 = 0 & all_53_3 = 0)))
% 24.91/4.47 | |
% 24.91/4.47 | | GROUND_INST: instantiating (21) with all_38_2, all_38_1, all_38_1, all_53_3,
% 24.91/4.47 | | 0, simplifying with (34), (35), (37), (59) gives:
% 24.91/4.47 | | (126) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.47 | | (unorthogonal_lines(all_38_1, all_38_1) = v3 &
% 24.91/4.47 | | unorthogonal_lines(all_38_2, all_38_1) = v1 &
% 24.91/4.47 | | convergent_lines(all_38_1, all_38_1) = v2 &
% 24.91/4.47 | | convergent_lines(all_38_2, all_38_1) = v0 & ( ~ (v3 = 0) | ~ (v2
% 24.91/4.47 | | = 0) | v1 = 0 | (v0 = 0 & all_53_3 = 0)))
% 24.91/4.47 | |
% 24.91/4.47 | | GROUND_INST: instantiating (13) with all_38_1, all_38_2, all_38_1, all_53_1,
% 24.91/4.47 | | all_53_3, simplifying with (34), (35), (58), (59) gives:
% 24.91/4.47 | | (127) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.47 | | (unorthogonal_lines(all_38_1, all_38_1) = v2 &
% 24.91/4.47 | | unorthogonal_lines(all_38_1, all_38_2) = v1 &
% 24.91/4.47 | | convergent_lines(all_38_1, all_38_2) = v0 &
% 24.91/4.47 | | convergent_lines(all_38_2, all_38_1) = v3 & ( ~ (v1 = 0) | ~ (v0
% 24.91/4.47 | | = 0) | (v3 = 0 & all_53_3 = 0) | (v2 = 0 & all_53_1 = 0)))
% 24.91/4.47 | |
% 24.91/4.47 | | GROUND_INST: instantiating (21) with all_38_2, all_38_1, all_38_2, all_53_3,
% 24.91/4.47 | | all_55_3, simplifying with (34), (35), (59), (63) gives:
% 24.91/4.47 | | (128) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.47 | | (unorthogonal_lines(all_38_1, all_38_2) = v3 &
% 24.91/4.47 | | unorthogonal_lines(all_38_2, all_38_2) = v1 &
% 24.91/4.47 | | convergent_lines(all_38_1, all_38_2) = v2 &
% 24.91/4.47 | | convergent_lines(all_38_2, all_38_1) = v0 & ( ~ (v3 = 0) | ~ (v2
% 24.91/4.47 | | = 0) | (v1 = 0 & all_55_3 = 0) | (v0 = 0 & all_53_3 = 0)))
% 24.91/4.47 | |
% 24.91/4.47 | | GROUND_INST: instantiating (14) with all_38_1, all_38_2, all_38_1, all_53_0,
% 24.91/4.47 | | all_53_3, simplifying with (34), (35), (59), (61) gives:
% 24.91/4.47 | | (129) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.47 | | (unorthogonal_lines(all_38_1, all_38_2) = v1 &
% 24.91/4.47 | | convergent_lines(all_38_1, all_38_1) = v2 &
% 24.91/4.47 | | convergent_lines(all_38_1, all_38_2) = v0 &
% 24.91/4.47 | | convergent_lines(all_38_2, all_38_1) = v3 & ( ~ (v1 = 0) | ~ (v0
% 24.91/4.47 | | = 0) | (v3 = 0 & all_53_3 = 0) | (v2 = 0 & all_53_0 = 0)))
% 24.91/4.47 | |
% 24.91/4.47 | | GROUND_INST: instantiating (19) with all_38_1, all_38_2, all_38_1, all_53_0,
% 24.91/4.47 | | simplifying with (34), (35), (37), (61) gives:
% 24.91/4.47 | | (130) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.47 | | (unorthogonal_lines(all_38_1, all_38_2) = v1 &
% 24.91/4.47 | | unorthogonal_lines(all_38_2, all_38_1) = v3 &
% 24.91/4.47 | | convergent_lines(all_38_1, all_38_1) = v2 &
% 24.91/4.47 | | convergent_lines(all_38_1, all_38_2) = v0 & ( ~ (v3 = 0) | (v2 =
% 24.91/4.47 | | 0 & all_53_0 = 0) | (v1 = 0 & v0 = 0)))
% 24.91/4.47 | |
% 24.91/4.47 | | GROUND_INST: instantiating (12) with all_38_1, all_38_2, all_38_1, all_53_0,
% 24.91/4.47 | | 0, simplifying with (34), (35), (37), (61) gives:
% 24.91/4.47 | | (131) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 24.91/4.47 | | (unorthogonal_lines(all_38_1, all_38_2) = v1 &
% 24.91/4.47 | | unorthogonal_lines(all_38_2, all_38_1) = v3 &
% 24.91/4.47 | | convergent_lines(all_38_1, all_38_1) = v2 &
% 24.91/4.47 | | convergent_lines(all_38_1, all_38_2) = v0 & ( ~ (v1 = 0) | ~ (v0
% 24.91/4.47 | | = 0) | v3 = 0 | (v2 = 0 & all_53_0 = 0)))
% 24.91/4.47 | |
% 24.91/4.47 | | DELTA: instantiating (115) with fresh symbols all_80_0, all_80_1, all_80_2,
% 24.91/4.47 | | all_80_3 gives:
% 24.91/4.47 | | (132) point(all_47_1) = all_80_0 & line(all_38_1) = all_80_2 &
% 24.91/4.47 | | line(all_38_2) = all_80_3 & convergent_lines(all_38_2, all_38_1) =
% 24.91/4.47 | | all_80_1 & ( ~ (all_80_1 = 0) | ~ (all_80_2 = 0) | ~ (all_80_3 =
% 24.91/4.47 | | 0) | all_80_0 = 0)
% 24.91/4.47 | |
% 24.91/4.47 | | ALPHA: (132) implies:
% 24.91/4.47 | | (133) convergent_lines(all_38_2, all_38_1) = all_80_1
% 24.91/4.47 | |
% 24.91/4.47 | | DELTA: instantiating (131) with fresh symbols all_82_0, all_82_1, all_82_2,
% 24.91/4.47 | | all_82_3 gives:
% 24.91/4.47 | | (134) unorthogonal_lines(all_38_1, all_38_2) = all_82_2 &
% 24.91/4.47 | | unorthogonal_lines(all_38_2, all_38_1) = all_82_0 &
% 24.91/4.47 | | convergent_lines(all_38_1, all_38_1) = all_82_1 &
% 24.91/4.47 | | convergent_lines(all_38_1, all_38_2) = all_82_3 & ( ~ (all_82_2 =
% 24.91/4.47 | | 0) | ~ (all_82_3 = 0) | all_82_0 = 0 | (all_82_1 = 0 &
% 24.91/4.47 | | all_53_0 = 0))
% 24.91/4.47 | |
% 24.91/4.47 | | ALPHA: (134) implies:
% 24.91/4.48 | | (135) convergent_lines(all_38_1, all_38_2) = all_82_3
% 24.91/4.48 | | (136) convergent_lines(all_38_1, all_38_1) = all_82_1
% 24.91/4.48 | | (137) unorthogonal_lines(all_38_1, all_38_2) = all_82_2
% 24.91/4.48 | |
% 24.91/4.48 | | DELTA: instantiating (130) with fresh symbols all_84_0, all_84_1, all_84_2,
% 24.91/4.48 | | all_84_3 gives:
% 24.91/4.48 | | (138) unorthogonal_lines(all_38_1, all_38_2) = all_84_2 &
% 24.91/4.48 | | unorthogonal_lines(all_38_2, all_38_1) = all_84_0 &
% 24.91/4.48 | | convergent_lines(all_38_1, all_38_1) = all_84_1 &
% 24.91/4.48 | | convergent_lines(all_38_1, all_38_2) = all_84_3 & ( ~ (all_84_0 =
% 24.91/4.48 | | 0) | (all_84_1 = 0 & all_53_0 = 0) | (all_84_2 = 0 & all_84_3 =
% 24.91/4.48 | | 0))
% 24.91/4.48 | |
% 24.91/4.48 | | ALPHA: (138) implies:
% 24.91/4.48 | | (139) convergent_lines(all_38_1, all_38_2) = all_84_3
% 24.91/4.48 | | (140) convergent_lines(all_38_1, all_38_1) = all_84_1
% 24.91/4.48 | | (141) unorthogonal_lines(all_38_1, all_38_2) = all_84_2
% 24.91/4.48 | |
% 24.91/4.48 | | DELTA: instantiating (111) with fresh symbols all_86_0, all_86_1, all_86_2,
% 24.91/4.48 | | all_86_3 gives:
% 24.91/4.48 | | (142) unorthogonal_lines(all_38_1, all_38_1) = all_86_1 &
% 24.91/4.48 | | unorthogonal_lines(all_38_1, all_38_2) = all_86_2 &
% 24.91/4.48 | | unorthogonal_lines(all_38_2, all_38_1) = all_86_0 &
% 24.91/4.48 | | convergent_lines(all_38_1, all_38_2) = all_86_3 & ( ~ (all_86_2 =
% 24.91/4.48 | | 0) | ~ (all_86_3 = 0) | all_86_0 = 0 | (all_86_1 = 0 &
% 24.91/4.48 | | all_53_1 = 0))
% 24.91/4.48 | |
% 24.91/4.48 | | ALPHA: (142) implies:
% 24.91/4.48 | | (143) convergent_lines(all_38_1, all_38_2) = all_86_3
% 24.91/4.48 | | (144) unorthogonal_lines(all_38_1, all_38_2) = all_86_2
% 24.91/4.48 | | (145) unorthogonal_lines(all_38_1, all_38_1) = all_86_1
% 24.91/4.48 | |
% 24.91/4.48 | | DELTA: instantiating (110) with fresh symbols all_88_0, all_88_1, all_88_2,
% 24.91/4.48 | | all_88_3 gives:
% 24.91/4.48 | | (146) unorthogonal_lines(all_38_1, all_38_1) = all_88_1 &
% 24.91/4.48 | | unorthogonal_lines(all_38_1, all_38_2) = all_88_2 &
% 24.91/4.48 | | unorthogonal_lines(all_38_2, all_38_1) = all_88_0 &
% 24.91/4.48 | | convergent_lines(all_38_1, all_38_2) = all_88_3 & ( ~ (all_88_0 =
% 24.91/4.48 | | 0) | (all_88_1 = 0 & all_53_1 = 0) | (all_88_2 = 0 & all_88_3 =
% 24.91/4.48 | | 0))
% 24.91/4.48 | |
% 24.91/4.48 | | ALPHA: (146) implies:
% 24.91/4.48 | | (147) convergent_lines(all_38_1, all_38_2) = all_88_3
% 24.91/4.48 | | (148) unorthogonal_lines(all_38_1, all_38_2) = all_88_2
% 24.91/4.48 | | (149) unorthogonal_lines(all_38_1, all_38_1) = all_88_1
% 24.91/4.48 | |
% 24.91/4.48 | | DELTA: instantiating (108) with fresh symbols all_90_0, all_90_1, all_90_2,
% 24.91/4.48 | | all_90_3 gives:
% 24.91/4.48 | | (150) unorthogonal_lines(all_38_1, all_38_2) = all_90_0 &
% 24.91/4.48 | | unorthogonal_lines(all_38_2, all_38_1) = all_90_3 &
% 24.91/4.48 | | unorthogonal_lines(all_38_2, all_38_2) = all_90_2 &
% 24.91/4.48 | | convergent_lines(all_38_1, all_38_2) = all_90_1 & ( ~ (all_90_3 =
% 24.91/4.48 | | 0) | (all_90_0 = 0 & all_90_1 = 0) | (all_90_2 = 0 & all_55_3 =
% 24.91/4.48 | | 0))
% 24.91/4.48 | |
% 24.91/4.48 | | ALPHA: (150) implies:
% 24.91/4.48 | | (151) convergent_lines(all_38_1, all_38_2) = all_90_1
% 24.91/4.48 | | (152) unorthogonal_lines(all_38_2, all_38_2) = all_90_2
% 24.91/4.48 | | (153) unorthogonal_lines(all_38_1, all_38_2) = all_90_0
% 24.91/4.48 | |
% 24.91/4.48 | | DELTA: instantiating (126) with fresh symbols all_92_0, all_92_1, all_92_2,
% 24.91/4.48 | | all_92_3 gives:
% 24.91/4.48 | | (154) unorthogonal_lines(all_38_1, all_38_1) = all_92_0 &
% 24.91/4.48 | | unorthogonal_lines(all_38_2, all_38_1) = all_92_2 &
% 24.91/4.48 | | convergent_lines(all_38_1, all_38_1) = all_92_1 &
% 24.91/4.48 | | convergent_lines(all_38_2, all_38_1) = all_92_3 & ( ~ (all_92_0 =
% 24.91/4.48 | | 0) | ~ (all_92_1 = 0) | all_92_2 = 0 | (all_92_3 = 0 &
% 24.91/4.48 | | all_53_3 = 0))
% 24.91/4.48 | |
% 24.91/4.48 | | ALPHA: (154) implies:
% 24.91/4.48 | | (155) convergent_lines(all_38_2, all_38_1) = all_92_3
% 24.91/4.48 | | (156) convergent_lines(all_38_1, all_38_1) = all_92_1
% 24.91/4.48 | | (157) unorthogonal_lines(all_38_1, all_38_1) = all_92_0
% 24.91/4.48 | |
% 24.91/4.48 | | DELTA: instantiating (125) with fresh symbols all_94_0, all_94_1, all_94_2,
% 24.91/4.48 | | all_94_3 gives:
% 24.91/4.48 | | (158) unorthogonal_lines(all_38_1, all_38_1) = all_94_0 &
% 24.91/4.48 | | unorthogonal_lines(all_38_2, all_38_1) = all_94_3 &
% 24.91/4.48 | | convergent_lines(all_38_1, all_38_1) = all_94_1 &
% 24.91/4.48 | | convergent_lines(all_38_2, all_38_1) = all_94_2 & ( ~ (all_94_0 =
% 24.91/4.48 | | 0) | ~ (all_94_1 = 0) | all_94_3 = 0 | (all_94_2 = 0 &
% 24.91/4.48 | | all_53_3 = 0))
% 24.91/4.48 | |
% 24.91/4.48 | | ALPHA: (158) implies:
% 24.91/4.48 | | (159) convergent_lines(all_38_2, all_38_1) = all_94_2
% 24.91/4.48 | | (160) convergent_lines(all_38_1, all_38_1) = all_94_1
% 24.91/4.48 | | (161) unorthogonal_lines(all_38_1, all_38_1) = all_94_0
% 24.91/4.48 | |
% 24.91/4.48 | | DELTA: instantiating (123) with fresh symbols all_96_0, all_96_1, all_96_2,
% 24.91/4.48 | | all_96_3 gives:
% 24.91/4.48 | | (162) unorthogonal_lines(all_38_2, all_38_1) = all_96_1 &
% 24.91/4.48 | | unorthogonal_lines(all_38_2, all_38_2) = all_96_2 &
% 24.91/4.48 | | convergent_lines(all_38_2, all_38_1) = all_96_0 &
% 24.91/4.48 | | convergent_lines(all_38_2, all_38_2) = all_96_3 & ( ~ (all_96_2 =
% 24.91/4.48 | | 0) | ~ (all_96_3 = 0) | all_96_1 = 0 | (all_96_0 = 0 &
% 24.91/4.48 | | all_53_3 = 0))
% 24.91/4.48 | |
% 24.91/4.48 | | ALPHA: (162) implies:
% 24.91/4.48 | | (163) convergent_lines(all_38_2, all_38_2) = all_96_3
% 25.28/4.48 | | (164) convergent_lines(all_38_2, all_38_1) = all_96_0
% 25.28/4.48 | | (165) unorthogonal_lines(all_38_2, all_38_2) = all_96_2
% 25.28/4.48 | |
% 25.28/4.48 | | DELTA: instantiating (124) with fresh symbols all_98_0, all_98_1, all_98_2,
% 25.28/4.48 | | all_98_3 gives:
% 25.28/4.48 | | (166) unorthogonal_lines(all_38_2, all_38_1) = all_98_0 &
% 25.28/4.48 | | unorthogonal_lines(all_38_2, all_38_2) = all_98_2 &
% 25.28/4.48 | | convergent_lines(all_38_2, all_38_1) = all_98_1 &
% 25.28/4.48 | | convergent_lines(all_38_2, all_38_2) = all_98_3 & ( ~ (all_98_2 =
% 25.28/4.48 | | 0) | ~ (all_98_3 = 0) | all_98_0 = 0 | (all_98_1 = 0 &
% 25.28/4.48 | | all_53_3 = 0))
% 25.28/4.48 | |
% 25.28/4.48 | | ALPHA: (166) implies:
% 25.28/4.48 | | (167) convergent_lines(all_38_2, all_38_2) = all_98_3
% 25.28/4.48 | | (168) convergent_lines(all_38_2, all_38_1) = all_98_1
% 25.28/4.48 | | (169) unorthogonal_lines(all_38_2, all_38_2) = all_98_2
% 25.28/4.48 | |
% 25.28/4.48 | | DELTA: instantiating (109) with fresh symbols all_100_0, all_100_1,
% 25.28/4.48 | | all_100_2, all_100_3 gives:
% 25.28/4.48 | | (170) unorthogonal_lines(all_38_1, all_38_2) = all_100_0 &
% 25.28/4.48 | | unorthogonal_lines(all_38_2, all_38_1) = all_100_3 &
% 25.28/4.48 | | unorthogonal_lines(all_38_2, all_38_2) = all_100_2 &
% 25.28/4.48 | | convergent_lines(all_38_1, all_38_2) = all_100_1 & ( ~ (all_100_0 =
% 25.28/4.48 | | 0) | ~ (all_100_1 = 0) | all_100_3 = 0 | (all_100_2 = 0 &
% 25.28/4.48 | | all_55_3 = 0))
% 25.28/4.48 | |
% 25.28/4.48 | | ALPHA: (170) implies:
% 25.28/4.48 | | (171) convergent_lines(all_38_1, all_38_2) = all_100_1
% 25.28/4.48 | | (172) unorthogonal_lines(all_38_2, all_38_2) = all_100_2
% 25.28/4.48 | | (173) unorthogonal_lines(all_38_1, all_38_2) = all_100_0
% 25.28/4.48 | |
% 25.28/4.48 | | DELTA: instantiating (118) with fresh symbols all_102_0, all_102_1,
% 25.28/4.48 | | all_102_2, all_102_3 gives:
% 25.28/4.48 | | (174) unorthogonal_lines(all_38_1, all_38_2) = all_102_0 &
% 25.28/4.48 | | unorthogonal_lines(all_38_2, all_38_1) = all_102_3 &
% 25.28/4.48 | | convergent_lines(all_38_1, all_38_2) = all_102_1 &
% 25.28/4.48 | | convergent_lines(all_38_2, all_38_2) = all_102_2 & ( ~ (all_102_0 =
% 25.28/4.48 | | 0) | ~ (all_102_1 = 0) | all_102_3 = 0 | (all_102_2 = 0 &
% 25.28/4.48 | | all_55_2 = 0))
% 25.28/4.48 | |
% 25.28/4.48 | | ALPHA: (174) implies:
% 25.28/4.48 | | (175) convergent_lines(all_38_2, all_38_2) = all_102_2
% 25.28/4.48 | | (176) convergent_lines(all_38_1, all_38_2) = all_102_1
% 25.28/4.48 | | (177) unorthogonal_lines(all_38_1, all_38_2) = all_102_0
% 25.28/4.48 | |
% 25.28/4.48 | | DELTA: instantiating (117) with fresh symbols all_104_0, all_104_1,
% 25.28/4.48 | | all_104_2, all_104_3 gives:
% 25.28/4.48 | | (178) unorthogonal_lines(all_38_1, all_38_2) = all_104_0 &
% 25.28/4.48 | | unorthogonal_lines(all_38_2, all_38_1) = all_104_3 &
% 25.28/4.48 | | convergent_lines(all_38_1, all_38_2) = all_104_1 &
% 25.28/4.48 | | convergent_lines(all_38_2, all_38_2) = all_104_2 & ( ~ (all_104_3 =
% 25.28/4.48 | | 0) | (all_104_0 = 0 & all_104_1 = 0) | (all_104_2 = 0 &
% 25.28/4.48 | | all_55_2 = 0))
% 25.28/4.48 | |
% 25.28/4.48 | | ALPHA: (178) implies:
% 25.28/4.48 | | (179) convergent_lines(all_38_2, all_38_2) = all_104_2
% 25.28/4.49 | | (180) convergent_lines(all_38_1, all_38_2) = all_104_1
% 25.28/4.49 | | (181) unorthogonal_lines(all_38_1, all_38_2) = all_104_0
% 25.28/4.49 | |
% 25.28/4.49 | | DELTA: instantiating (129) with fresh symbols all_106_0, all_106_1,
% 25.28/4.49 | | all_106_2, all_106_3 gives:
% 25.28/4.49 | | (182) unorthogonal_lines(all_38_1, all_38_2) = all_106_2 &
% 25.28/4.49 | | convergent_lines(all_38_1, all_38_1) = all_106_1 &
% 25.28/4.49 | | convergent_lines(all_38_1, all_38_2) = all_106_3 &
% 25.28/4.49 | | convergent_lines(all_38_2, all_38_1) = all_106_0 & ( ~ (all_106_2 =
% 25.28/4.49 | | 0) | ~ (all_106_3 = 0) | (all_106_0 = 0 & all_53_3 = 0) |
% 25.28/4.49 | | (all_106_1 = 0 & all_53_0 = 0))
% 25.28/4.49 | |
% 25.28/4.49 | | ALPHA: (182) implies:
% 25.28/4.49 | | (183) convergent_lines(all_38_2, all_38_1) = all_106_0
% 25.28/4.49 | | (184) convergent_lines(all_38_1, all_38_2) = all_106_3
% 25.28/4.49 | | (185) convergent_lines(all_38_1, all_38_1) = all_106_1
% 25.28/4.49 | | (186) unorthogonal_lines(all_38_1, all_38_2) = all_106_2
% 25.28/4.49 | |
% 25.28/4.49 | | DELTA: instantiating (127) with fresh symbols all_108_0, all_108_1,
% 25.28/4.49 | | all_108_2, all_108_3 gives:
% 25.28/4.49 | | (187) unorthogonal_lines(all_38_1, all_38_1) = all_108_1 &
% 25.28/4.49 | | unorthogonal_lines(all_38_1, all_38_2) = all_108_2 &
% 25.28/4.49 | | convergent_lines(all_38_1, all_38_2) = all_108_3 &
% 25.28/4.49 | | convergent_lines(all_38_2, all_38_1) = all_108_0 & ( ~ (all_108_2 =
% 25.28/4.49 | | 0) | ~ (all_108_3 = 0) | (all_108_0 = 0 & all_53_3 = 0) |
% 25.28/4.49 | | (all_108_1 = 0 & all_53_1 = 0))
% 25.28/4.49 | |
% 25.28/4.49 | | ALPHA: (187) implies:
% 25.28/4.49 | | (188) convergent_lines(all_38_2, all_38_1) = all_108_0
% 25.28/4.49 | | (189) convergent_lines(all_38_1, all_38_2) = all_108_3
% 25.28/4.49 | | (190) unorthogonal_lines(all_38_1, all_38_2) = all_108_2
% 25.28/4.49 | | (191) unorthogonal_lines(all_38_1, all_38_1) = all_108_1
% 25.28/4.49 | |
% 25.28/4.49 | | DELTA: instantiating (120) with fresh symbols all_110_0, all_110_1,
% 25.28/4.49 | | all_110_2, all_110_3 gives:
% 25.28/4.49 | | (192) unorthogonal_lines(all_38_1, all_38_1) = all_110_0 &
% 25.28/4.49 | | convergent_lines(all_38_1, all_38_1) = all_110_1 &
% 25.28/4.49 | | convergent_lines(all_38_2, all_38_1) = all_110_2 &
% 25.28/4.49 | | convergent_lines(all_38_2, all_38_1) = all_110_3 & ( ~ (all_110_0 =
% 25.28/4.49 | | 0) | ~ (all_110_1 = 0) | (all_110_2 = 0 & all_53_3 = 0) |
% 25.28/4.49 | | (all_110_3 = 0 & all_53_3 = 0))
% 25.28/4.49 | |
% 25.28/4.49 | | ALPHA: (192) implies:
% 25.28/4.49 | | (193) convergent_lines(all_38_2, all_38_1) = all_110_3
% 25.28/4.49 | | (194) convergent_lines(all_38_2, all_38_1) = all_110_2
% 25.28/4.49 | | (195) convergent_lines(all_38_1, all_38_1) = all_110_1
% 25.28/4.49 | | (196) unorthogonal_lines(all_38_1, all_38_1) = all_110_0
% 25.28/4.49 | |
% 25.28/4.49 | | DELTA: instantiating (122) with fresh symbols all_112_0, all_112_1,
% 25.28/4.49 | | all_112_2, all_112_3 gives:
% 25.28/4.49 | | (197) unorthogonal_lines(all_38_1, all_38_2) = all_112_0 &
% 25.28/4.49 | | convergent_lines(all_38_1, all_38_2) = all_112_1 &
% 25.28/4.49 | | convergent_lines(all_38_2, all_38_1) = all_112_3 &
% 25.28/4.49 | | convergent_lines(all_38_2, all_38_2) = all_112_2 & ( ~ (all_112_0 =
% 25.28/4.49 | | 0) | ~ (all_112_1 = 0) | (all_112_2 = 0 & all_55_2 = 0) |
% 25.28/4.49 | | (all_112_3 = 0 & all_53_3 = 0))
% 25.28/4.49 | |
% 25.28/4.49 | | ALPHA: (197) implies:
% 25.28/4.49 | | (198) convergent_lines(all_38_2, all_38_2) = all_112_2
% 25.28/4.49 | | (199) convergent_lines(all_38_2, all_38_1) = all_112_3
% 25.28/4.49 | | (200) convergent_lines(all_38_1, all_38_2) = all_112_1
% 25.28/4.49 | | (201) unorthogonal_lines(all_38_1, all_38_2) = all_112_0
% 25.28/4.49 | |
% 25.28/4.49 | | DELTA: instantiating (121) with fresh symbols all_114_0, all_114_1,
% 25.28/4.49 | | all_114_2, all_114_3 gives:
% 25.28/4.49 | | (202) unorthogonal_lines(all_38_2, all_38_2) = all_114_2 &
% 25.28/4.49 | | convergent_lines(all_38_2, all_38_1) = all_114_0 &
% 25.28/4.49 | | convergent_lines(all_38_2, all_38_1) = all_114_1 &
% 25.28/4.49 | | convergent_lines(all_38_2, all_38_2) = all_114_3 & ( ~ (all_114_2 =
% 25.28/4.49 | | 0) | ~ (all_114_3 = 0) | (all_114_0 = 0 & all_53_3 = 0) |
% 25.28/4.49 | | (all_114_1 = 0 & all_53_3 = 0))
% 25.28/4.49 | |
% 25.28/4.49 | | ALPHA: (202) implies:
% 25.28/4.49 | | (203) convergent_lines(all_38_2, all_38_2) = all_114_3
% 25.28/4.49 | | (204) convergent_lines(all_38_2, all_38_1) = all_114_1
% 25.28/4.49 | | (205) convergent_lines(all_38_2, all_38_1) = all_114_0
% 25.28/4.49 | | (206) unorthogonal_lines(all_38_2, all_38_2) = all_114_2
% 25.28/4.49 | |
% 25.28/4.49 | | DELTA: instantiating (128) with fresh symbols all_116_0, all_116_1,
% 25.28/4.49 | | all_116_2, all_116_3 gives:
% 25.28/4.49 | | (207) unorthogonal_lines(all_38_1, all_38_2) = all_116_0 &
% 25.28/4.49 | | unorthogonal_lines(all_38_2, all_38_2) = all_116_2 &
% 25.28/4.49 | | convergent_lines(all_38_1, all_38_2) = all_116_1 &
% 25.28/4.49 | | convergent_lines(all_38_2, all_38_1) = all_116_3 & ( ~ (all_116_0 =
% 25.28/4.49 | | 0) | ~ (all_116_1 = 0) | (all_116_2 = 0 & all_55_3 = 0) |
% 25.28/4.49 | | (all_116_3 = 0 & all_53_3 = 0))
% 25.28/4.49 | |
% 25.28/4.49 | | ALPHA: (207) implies:
% 25.28/4.49 | | (208) convergent_lines(all_38_2, all_38_1) = all_116_3
% 25.28/4.49 | | (209) convergent_lines(all_38_1, all_38_2) = all_116_1
% 25.28/4.49 | | (210) unorthogonal_lines(all_38_2, all_38_2) = all_116_2
% 25.28/4.49 | | (211) unorthogonal_lines(all_38_1, all_38_2) = all_116_0
% 25.28/4.49 | |
% 25.28/4.49 | | BETA: splitting (113) gives:
% 25.28/4.49 | |
% 25.28/4.49 | | Case 1:
% 25.28/4.49 | | |
% 25.28/4.49 | | | (212) all_47_0 = 0
% 25.28/4.49 | | |
% 25.28/4.49 | | | REDUCE: (47), (212) imply:
% 25.28/4.49 | | | (213) $false
% 25.28/4.49 | | |
% 25.28/4.49 | | | CLOSE: (213) is inconsistent.
% 25.28/4.49 | | |
% 25.28/4.49 | | Case 2:
% 25.28/4.49 | | |
% 25.28/4.49 | | | (214) ? [v0: any] : ? [v1: any] : (convergent_lines(all_38_1,
% 25.28/4.49 | | | all_38_1) = v1 & distinct_lines(all_38_1, all_38_1) = v0 & (
% 25.28/4.49 | | | ~ (v0 = 0) | v1 = 0))
% 25.28/4.49 | | |
% 25.28/4.49 | | | DELTA: instantiating (214) with fresh symbols all_129_0, all_129_1 gives:
% 25.28/4.49 | | | (215) convergent_lines(all_38_1, all_38_1) = all_129_0 &
% 25.28/4.49 | | | distinct_lines(all_38_1, all_38_1) = all_129_1 & ( ~ (all_129_1 =
% 25.28/4.49 | | | 0) | all_129_0 = 0)
% 25.28/4.49 | | |
% 25.28/4.49 | | | ALPHA: (215) implies:
% 25.28/4.49 | | | (216) convergent_lines(all_38_1, all_38_1) = all_129_0
% 25.28/4.49 | | |
% 25.28/4.49 | | | BETA: splitting (114) gives:
% 25.28/4.49 | | |
% 25.28/4.49 | | | Case 1:
% 25.28/4.49 | | | |
% 25.28/4.49 | | | | (217) all_49_0 = 0
% 25.28/4.49 | | | |
% 25.28/4.49 | | | | REDUCE: (51), (217) imply:
% 25.28/4.49 | | | | (218) $false
% 25.28/4.49 | | | |
% 25.28/4.49 | | | | CLOSE: (218) is inconsistent.
% 25.28/4.49 | | | |
% 25.28/4.49 | | | Case 2:
% 25.28/4.49 | | | |
% 25.28/4.49 | | | | (219) all_47_0 = 0 | ? [v0: any] : ? [v1: any] :
% 25.28/4.49 | | | | (convergent_lines(all_38_1, all_38_2) = v1 &
% 25.28/4.49 | | | | distinct_lines(all_38_1, all_38_2) = v0 & ( ~ (v0 = 0) | v1 =
% 25.28/4.49 | | | | 0))
% 25.28/4.49 | | | |
% 25.28/4.49 | | | | BETA: splitting (219) gives:
% 25.28/4.49 | | | |
% 25.28/4.49 | | | | Case 1:
% 25.28/4.49 | | | | |
% 25.28/4.49 | | | | | (220) all_47_0 = 0
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | REDUCE: (47), (220) imply:
% 25.28/4.50 | | | | | (221) $false
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | CLOSE: (221) is inconsistent.
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | Case 2:
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | (222) ? [v0: any] : ? [v1: any] : (convergent_lines(all_38_1,
% 25.28/4.50 | | | | | all_38_2) = v1 & distinct_lines(all_38_1, all_38_2) = v0
% 25.28/4.50 | | | | | & ( ~ (v0 = 0) | v1 = 0))
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | DELTA: instantiating (222) with fresh symbols all_152_0, all_152_1
% 25.28/4.50 | | | | | gives:
% 25.28/4.50 | | | | | (223) convergent_lines(all_38_1, all_38_2) = all_152_0 &
% 25.28/4.50 | | | | | distinct_lines(all_38_1, all_38_2) = all_152_1 & ( ~
% 25.28/4.50 | | | | | (all_152_1 = 0) | all_152_0 = 0)
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | ALPHA: (223) implies:
% 25.28/4.50 | | | | | (224) distinct_lines(all_38_1, all_38_2) = all_152_1
% 25.28/4.50 | | | | | (225) convergent_lines(all_38_1, all_38_2) = all_152_0
% 25.28/4.50 | | | | | (226) ~ (all_152_1 = 0) | all_152_0 = 0
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_55_3, all_102_2, all_38_2,
% 25.28/4.50 | | | | | all_38_2, simplifying with (63), (175) gives:
% 25.28/4.50 | | | | | (227) all_102_2 = all_55_3
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_96_3, all_102_2, all_38_2,
% 25.28/4.50 | | | | | all_38_2, simplifying with (163), (175) gives:
% 25.28/4.50 | | | | | (228) all_102_2 = all_96_3
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_102_2, all_104_2, all_38_2,
% 25.28/4.50 | | | | | all_38_2, simplifying with (175), (179) gives:
% 25.28/4.50 | | | | | (229) all_104_2 = all_102_2
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_112_2, all_114_3, all_38_2,
% 25.28/4.50 | | | | | all_38_2, simplifying with (198), (203) gives:
% 25.28/4.50 | | | | | (230) all_114_3 = all_112_2
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_104_2, all_114_3, all_38_2,
% 25.28/4.50 | | | | | all_38_2, simplifying with (179), (203) gives:
% 25.28/4.50 | | | | | (231) all_114_3 = all_104_2
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_98_3, all_114_3, all_38_2,
% 25.28/4.50 | | | | | all_38_2, simplifying with (167), (203) gives:
% 25.28/4.50 | | | | | (232) all_114_3 = all_98_3
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with 0, all_96_0, all_38_1, all_38_2,
% 25.28/4.50 | | | | | simplifying with (37), (164) gives:
% 25.28/4.50 | | | | | (233) all_96_0 = 0
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_96_0, all_106_0, all_38_1,
% 25.28/4.50 | | | | | all_38_2, simplifying with (164), (183) gives:
% 25.28/4.50 | | | | | (234) all_106_0 = all_96_0
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_106_0, all_108_0, all_38_1,
% 25.28/4.50 | | | | | all_38_2, simplifying with (183), (188) gives:
% 25.28/4.50 | | | | | (235) all_108_0 = all_106_0
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_108_0, all_110_3, all_38_1,
% 25.28/4.50 | | | | | all_38_2, simplifying with (188), (193) gives:
% 25.28/4.50 | | | | | (236) all_110_3 = all_108_0
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_110_2, all_112_3, all_38_1,
% 25.28/4.50 | | | | | all_38_2, simplifying with (194), (199) gives:
% 25.28/4.50 | | | | | (237) all_112_3 = all_110_2
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_112_3, all_114_1, all_38_1,
% 25.28/4.50 | | | | | all_38_2, simplifying with (199), (204) gives:
% 25.28/4.50 | | | | | (238) all_114_1 = all_112_3
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_80_1, all_114_1, all_38_1,
% 25.28/4.50 | | | | | all_38_2, simplifying with (133), (204) gives:
% 25.28/4.50 | | | | | (239) all_114_1 = all_80_1
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_112_3, all_114_0, all_38_1,
% 25.28/4.50 | | | | | all_38_2, simplifying with (199), (205) gives:
% 25.28/4.50 | | | | | (240) all_114_0 = all_112_3
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_98_1, all_114_0, all_38_1,
% 25.28/4.50 | | | | | all_38_2, simplifying with (168), (205) gives:
% 25.28/4.50 | | | | | (241) all_114_0 = all_98_1
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_96_0, all_114_0, all_38_1,
% 25.28/4.50 | | | | | all_38_2, simplifying with (164), (205) gives:
% 25.28/4.50 | | | | | (242) all_114_0 = all_96_0
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_94_2, all_114_0, all_38_1,
% 25.28/4.50 | | | | | all_38_2, simplifying with (159), (205) gives:
% 25.28/4.50 | | | | | (243) all_114_0 = all_94_2
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_110_3, all_116_3, all_38_1,
% 25.28/4.50 | | | | | all_38_2, simplifying with (193), (208) gives:
% 25.28/4.50 | | | | | (244) all_116_3 = all_110_3
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_92_3, all_116_3, all_38_1,
% 25.28/4.50 | | | | | all_38_2, simplifying with (155), (208) gives:
% 25.28/4.50 | | | | | (245) all_116_3 = all_92_3
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_90_1, all_104_1, all_38_2,
% 25.28/4.50 | | | | | all_38_1, simplifying with (151), (180) gives:
% 25.28/4.50 | | | | | (246) all_104_1 = all_90_1
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_86_3, all_104_1, all_38_2,
% 25.28/4.50 | | | | | all_38_1, simplifying with (143), (180) gives:
% 25.28/4.50 | | | | | (247) all_104_1 = all_86_3
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_104_1, all_106_3, all_38_2,
% 25.28/4.50 | | | | | all_38_1, simplifying with (180), (184) gives:
% 25.28/4.50 | | | | | (248) all_106_3 = all_104_1
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_104_1, all_108_3, all_38_2,
% 25.28/4.50 | | | | | all_38_1, simplifying with (180), (189) gives:
% 25.28/4.50 | | | | | (249) all_108_3 = all_104_1
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_102_1, all_108_3, all_38_2,
% 25.28/4.50 | | | | | all_38_1, simplifying with (176), (189) gives:
% 25.28/4.50 | | | | | (250) all_108_3 = all_102_1
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_100_1, all_108_3, all_38_2,
% 25.28/4.50 | | | | | all_38_1, simplifying with (171), (189) gives:
% 25.28/4.50 | | | | | (251) all_108_3 = all_100_1
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_106_3, all_112_1, all_38_2,
% 25.28/4.50 | | | | | all_38_1, simplifying with (184), (200) gives:
% 25.28/4.50 | | | | | (252) all_112_1 = all_106_3
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_82_3, all_112_1, all_38_2,
% 25.28/4.50 | | | | | all_38_1, simplifying with (135), (200) gives:
% 25.28/4.50 | | | | | (253) all_112_1 = all_82_3
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_104_1, all_116_1, all_38_2,
% 25.28/4.50 | | | | | all_38_1, simplifying with (180), (209) gives:
% 25.28/4.50 | | | | | (254) all_116_1 = all_104_1
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_88_3, all_116_1, all_38_2,
% 25.28/4.50 | | | | | all_38_1, simplifying with (147), (209) gives:
% 25.28/4.50 | | | | | (255) all_116_1 = all_88_3
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_108_3, all_152_0, all_38_2,
% 25.28/4.50 | | | | | all_38_1, simplifying with (189), (225) gives:
% 25.28/4.50 | | | | | (256) all_152_0 = all_108_3
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_84_3, all_152_0, all_38_2,
% 25.28/4.50 | | | | | all_38_1, simplifying with (139), (225) gives:
% 25.28/4.50 | | | | | (257) all_152_0 = all_84_3
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_53_1, all_94_1, all_38_1,
% 25.28/4.50 | | | | | all_38_1, simplifying with (58), (160) gives:
% 25.28/4.50 | | | | | (258) all_94_1 = all_53_1
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_84_1, all_94_1, all_38_1,
% 25.28/4.50 | | | | | all_38_1, simplifying with (140), (160) gives:
% 25.28/4.50 | | | | | (259) all_94_1 = all_84_1
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_84_1, all_106_1, all_38_1,
% 25.28/4.50 | | | | | all_38_1, simplifying with (140), (185) gives:
% 25.28/4.50 | | | | | (260) all_106_1 = all_84_1
% 25.28/4.50 | | | | |
% 25.28/4.50 | | | | | GROUND_INST: instantiating (29) with all_82_1, all_106_1, all_38_1,
% 25.28/4.50 | | | | | all_38_1, simplifying with (136), (185) gives:
% 25.28/4.50 | | | | | (261) all_106_1 = all_82_1
% 25.28/4.50 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (29) with all_106_1, all_110_1, all_38_1,
% 25.28/4.51 | | | | | all_38_1, simplifying with (185), (195) gives:
% 25.28/4.51 | | | | | (262) all_110_1 = all_106_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (29) with all_110_1, all_129_0, all_38_1,
% 25.28/4.51 | | | | | all_38_1, simplifying with (195), (216) gives:
% 25.28/4.51 | | | | | (263) all_129_0 = all_110_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (29) with all_92_1, all_129_0, all_38_1,
% 25.28/4.51 | | | | | all_38_1, simplifying with (156), (216) gives:
% 25.28/4.51 | | | | | (264) all_129_0 = all_92_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_55_2, all_98_2, all_38_2,
% 25.28/4.51 | | | | | all_38_2, simplifying with (64), (169) gives:
% 25.28/4.51 | | | | | (265) all_98_2 = all_55_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_90_2, all_98_2, all_38_2,
% 25.28/4.51 | | | | | all_38_2, simplifying with (152), (169) gives:
% 25.28/4.51 | | | | | (266) all_98_2 = all_90_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_98_2, all_100_2, all_38_2,
% 25.28/4.51 | | | | | all_38_2, simplifying with (169), (172) gives:
% 25.28/4.51 | | | | | (267) all_100_2 = all_98_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_100_2, all_114_2, all_38_2,
% 25.28/4.51 | | | | | all_38_2, simplifying with (172), (206) gives:
% 25.28/4.51 | | | | | (268) all_114_2 = all_100_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_114_2, all_116_2, all_38_2,
% 25.28/4.51 | | | | | all_38_2, simplifying with (206), (210) gives:
% 25.28/4.51 | | | | | (269) all_116_2 = all_114_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_96_2, all_116_2, all_38_2,
% 25.28/4.51 | | | | | all_38_2, simplifying with (165), (210) gives:
% 25.28/4.51 | | | | | (270) all_116_2 = all_96_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_88_2, all_90_0, all_38_2,
% 25.28/4.51 | | | | | all_38_1, simplifying with (148), (153) gives:
% 25.28/4.51 | | | | | (271) all_90_0 = all_88_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_90_0, all_100_0, all_38_2,
% 25.28/4.51 | | | | | all_38_1, simplifying with (153), (173) gives:
% 25.28/4.51 | | | | | (272) all_100_0 = all_90_0
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_88_2, all_102_0, all_38_2,
% 25.28/4.51 | | | | | all_38_1, simplifying with (148), (177) gives:
% 25.28/4.51 | | | | | (273) all_102_0 = all_88_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_86_2, all_102_0, all_38_2,
% 25.28/4.51 | | | | | all_38_1, simplifying with (144), (177) gives:
% 25.28/4.51 | | | | | (274) all_102_0 = all_86_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_82_2, all_102_0, all_38_2,
% 25.28/4.51 | | | | | all_38_1, simplifying with (137), (177) gives:
% 25.28/4.51 | | | | | (275) all_102_0 = all_82_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_100_0, all_104_0, all_38_2,
% 25.28/4.51 | | | | | all_38_1, simplifying with (173), (181) gives:
% 25.28/4.51 | | | | | (276) all_104_0 = all_100_0
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_104_0, all_106_2, all_38_2,
% 25.28/4.51 | | | | | all_38_1, simplifying with (181), (186) gives:
% 25.28/4.51 | | | | | (277) all_106_2 = all_104_0
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_106_2, all_108_2, all_38_2,
% 25.28/4.51 | | | | | all_38_1, simplifying with (186), (190) gives:
% 25.28/4.51 | | | | | (278) all_108_2 = all_106_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_108_2, all_112_0, all_38_2,
% 25.28/4.51 | | | | | all_38_1, simplifying with (190), (201) gives:
% 25.28/4.51 | | | | | (279) all_112_0 = all_108_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_112_0, all_116_0, all_38_2,
% 25.28/4.51 | | | | | all_38_1, simplifying with (201), (211) gives:
% 25.28/4.51 | | | | | (280) all_116_0 = all_112_0
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_84_2, all_116_0, all_38_2,
% 25.28/4.51 | | | | | all_38_1, simplifying with (141), (211) gives:
% 25.28/4.51 | | | | | (281) all_116_0 = all_84_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_53_0, all_88_1, all_38_1,
% 25.28/4.51 | | | | | all_38_1, simplifying with (61), (149) gives:
% 25.28/4.51 | | | | | (282) all_88_1 = all_53_0
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_88_1, all_92_0, all_38_1,
% 25.28/4.51 | | | | | all_38_1, simplifying with (149), (157) gives:
% 25.28/4.51 | | | | | (283) all_92_0 = all_88_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_92_0, all_94_0, all_38_1,
% 25.28/4.51 | | | | | all_38_1, simplifying with (157), (161) gives:
% 25.28/4.51 | | | | | (284) all_94_0 = all_92_0
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_94_0, all_108_1, all_38_1,
% 25.28/4.51 | | | | | all_38_1, simplifying with (161), (191) gives:
% 25.28/4.51 | | | | | (285) all_108_1 = all_94_0
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_108_1, all_110_0, all_38_1,
% 25.28/4.51 | | | | | all_38_1, simplifying with (191), (196) gives:
% 25.28/4.51 | | | | | (286) all_110_0 = all_108_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | GROUND_INST: instantiating (31) with all_86_1, all_110_0, all_38_1,
% 25.28/4.51 | | | | | all_38_1, simplifying with (145), (196) gives:
% 25.28/4.51 | | | | | (287) all_110_0 = all_86_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (256), (257) imply:
% 25.28/4.51 | | | | | (288) all_108_3 = all_84_3
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (288) implies:
% 25.28/4.51 | | | | | (289) all_108_3 = all_84_3
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (263), (264) imply:
% 25.28/4.51 | | | | | (290) all_110_1 = all_92_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (290) implies:
% 25.28/4.51 | | | | | (291) all_110_1 = all_92_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (280), (281) imply:
% 25.28/4.51 | | | | | (292) all_112_0 = all_84_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (292) implies:
% 25.28/4.51 | | | | | (293) all_112_0 = all_84_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (254), (255) imply:
% 25.28/4.51 | | | | | (294) all_104_1 = all_88_3
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (294) implies:
% 25.28/4.51 | | | | | (295) all_104_1 = all_88_3
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (269), (270) imply:
% 25.28/4.51 | | | | | (296) all_114_2 = all_96_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (296) implies:
% 25.28/4.51 | | | | | (297) all_114_2 = all_96_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (244), (245) imply:
% 25.28/4.51 | | | | | (298) all_110_3 = all_92_3
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (298) implies:
% 25.28/4.51 | | | | | (299) all_110_3 = all_92_3
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (241), (243) imply:
% 25.28/4.51 | | | | | (300) all_98_1 = all_94_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (241), (242) imply:
% 25.28/4.51 | | | | | (301) all_98_1 = all_96_0
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (240), (241) imply:
% 25.28/4.51 | | | | | (302) all_112_3 = all_98_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (302) implies:
% 25.28/4.51 | | | | | (303) all_112_3 = all_98_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (238), (239) imply:
% 25.28/4.51 | | | | | (304) all_112_3 = all_80_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (304) implies:
% 25.28/4.51 | | | | | (305) all_112_3 = all_80_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (268), (297) imply:
% 25.28/4.51 | | | | | (306) all_100_2 = all_96_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (306) implies:
% 25.28/4.51 | | | | | (307) all_100_2 = all_96_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (230), (231) imply:
% 25.28/4.51 | | | | | (308) all_112_2 = all_104_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (230), (232) imply:
% 25.28/4.51 | | | | | (309) all_112_2 = all_98_3
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (279), (293) imply:
% 25.28/4.51 | | | | | (310) all_108_2 = all_84_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (310) implies:
% 25.28/4.51 | | | | | (311) all_108_2 = all_84_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (252), (253) imply:
% 25.28/4.51 | | | | | (312) all_106_3 = all_82_3
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (312) implies:
% 25.28/4.51 | | | | | (313) all_106_3 = all_82_3
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (308), (309) imply:
% 25.28/4.51 | | | | | (314) all_104_2 = all_98_3
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (314) implies:
% 25.28/4.51 | | | | | (315) all_104_2 = all_98_3
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (237), (303) imply:
% 25.28/4.51 | | | | | (316) all_110_2 = all_98_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (237), (305) imply:
% 25.28/4.51 | | | | | (317) all_110_2 = all_80_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (286), (287) imply:
% 25.28/4.51 | | | | | (318) all_108_1 = all_86_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (318) implies:
% 25.28/4.51 | | | | | (319) all_108_1 = all_86_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (262), (291) imply:
% 25.28/4.51 | | | | | (320) all_106_1 = all_92_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (320) implies:
% 25.28/4.51 | | | | | (321) all_106_1 = all_92_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (316), (317) imply:
% 25.28/4.51 | | | | | (322) all_98_1 = all_80_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (322) implies:
% 25.28/4.51 | | | | | (323) all_98_1 = all_80_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (236), (299) imply:
% 25.28/4.51 | | | | | (324) all_108_0 = all_92_3
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (324) implies:
% 25.28/4.51 | | | | | (325) all_108_0 = all_92_3
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (235), (325) imply:
% 25.28/4.51 | | | | | (326) all_106_0 = all_92_3
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (326) implies:
% 25.28/4.51 | | | | | (327) all_106_0 = all_92_3
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (285), (319) imply:
% 25.28/4.51 | | | | | (328) all_94_0 = all_86_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (328) implies:
% 25.28/4.51 | | | | | (329) all_94_0 = all_86_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (278), (311) imply:
% 25.28/4.51 | | | | | (330) all_106_2 = all_84_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (330) implies:
% 25.28/4.51 | | | | | (331) all_106_2 = all_84_2
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (249), (250) imply:
% 25.28/4.51 | | | | | (332) all_104_1 = all_102_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (332) implies:
% 25.28/4.51 | | | | | (333) all_104_1 = all_102_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (250), (289) imply:
% 25.28/4.51 | | | | | (334) all_102_1 = all_84_3
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (250), (251) imply:
% 25.28/4.51 | | | | | (335) all_102_1 = all_100_1
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | COMBINE_EQS: (234), (327) imply:
% 25.28/4.51 | | | | | (336) all_96_0 = all_92_3
% 25.28/4.51 | | | | |
% 25.28/4.51 | | | | | SIMP: (336) implies:
% 25.28/4.51 | | | | | (337) all_96_0 = all_92_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (260), (321) imply:
% 25.28/4.52 | | | | | (338) all_92_1 = all_84_1
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (261), (321) imply:
% 25.28/4.52 | | | | | (339) all_92_1 = all_82_1
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (277), (331) imply:
% 25.28/4.52 | | | | | (340) all_104_0 = all_84_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (340) implies:
% 25.28/4.52 | | | | | (341) all_104_0 = all_84_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (248), (313) imply:
% 25.28/4.52 | | | | | (342) all_104_1 = all_82_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (342) implies:
% 25.28/4.52 | | | | | (343) all_104_1 = all_82_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (276), (341) imply:
% 25.28/4.52 | | | | | (344) all_100_0 = all_84_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (344) implies:
% 25.28/4.52 | | | | | (345) all_100_0 = all_84_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (246), (247) imply:
% 25.28/4.52 | | | | | (346) all_90_1 = all_86_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (246), (295) imply:
% 25.28/4.52 | | | | | (347) all_90_1 = all_88_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (246), (343) imply:
% 25.28/4.52 | | | | | (348) all_90_1 = all_82_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (246), (333) imply:
% 25.28/4.52 | | | | | (349) all_102_1 = all_90_1
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (349) implies:
% 25.28/4.52 | | | | | (350) all_102_1 = all_90_1
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (229), (315) imply:
% 25.28/4.52 | | | | | (351) all_102_2 = all_98_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (351) implies:
% 25.28/4.52 | | | | | (352) all_102_2 = all_98_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (273), (274) imply:
% 25.28/4.52 | | | | | (353) all_88_2 = all_86_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (353) implies:
% 25.28/4.52 | | | | | (354) all_88_2 = all_86_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (274), (275) imply:
% 25.28/4.52 | | | | | (355) all_86_2 = all_82_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (335), (350) imply:
% 25.28/4.52 | | | | | (356) all_100_1 = all_90_1
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (334), (335) imply:
% 25.28/4.52 | | | | | (357) all_100_1 = all_84_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (228), (352) imply:
% 25.28/4.52 | | | | | (358) all_98_3 = all_96_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (227), (352) imply:
% 25.28/4.52 | | | | | (359) all_98_3 = all_55_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (272), (345) imply:
% 25.28/4.52 | | | | | (360) all_90_0 = all_84_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (360) implies:
% 25.28/4.52 | | | | | (361) all_90_0 = all_84_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (356), (357) imply:
% 25.28/4.52 | | | | | (362) all_90_1 = all_84_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (362) implies:
% 25.28/4.52 | | | | | (363) all_90_1 = all_84_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (267), (307) imply:
% 25.28/4.52 | | | | | (364) all_98_2 = all_96_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (364) implies:
% 25.28/4.52 | | | | | (365) all_98_2 = all_96_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (300), (323) imply:
% 25.28/4.52 | | | | | (366) all_94_2 = all_80_1
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (300), (301) imply:
% 25.28/4.52 | | | | | (367) all_96_0 = all_94_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (367) implies:
% 25.28/4.52 | | | | | (368) all_96_0 = all_94_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (266), (365) imply:
% 25.28/4.52 | | | | | (369) all_96_2 = all_90_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (265), (365) imply:
% 25.28/4.52 | | | | | (370) all_96_2 = all_55_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (358), (359) imply:
% 25.28/4.52 | | | | | (371) all_96_3 = all_55_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (337), (368) imply:
% 25.28/4.52 | | | | | (372) all_94_2 = all_92_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (372) implies:
% 25.28/4.52 | | | | | (373) all_94_2 = all_92_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (233), (337) imply:
% 25.28/4.52 | | | | | (374) all_92_3 = 0
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (369), (370) imply:
% 25.28/4.52 | | | | | (375) all_90_2 = all_55_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (375) implies:
% 25.28/4.52 | | | | | (376) all_90_2 = all_55_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (284), (329) imply:
% 25.28/4.52 | | | | | (377) all_92_0 = all_86_1
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (377) implies:
% 25.28/4.52 | | | | | (378) all_92_0 = all_86_1
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (258), (259) imply:
% 25.28/4.52 | | | | | (379) all_84_1 = all_53_1
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (379) implies:
% 25.28/4.52 | | | | | (380) all_84_1 = all_53_1
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (366), (373) imply:
% 25.28/4.52 | | | | | (381) all_92_3 = all_80_1
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (381) implies:
% 25.28/4.52 | | | | | (382) all_92_3 = all_80_1
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (283), (378) imply:
% 25.28/4.52 | | | | | (383) all_88_1 = all_86_1
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (383) implies:
% 25.28/4.52 | | | | | (384) all_88_1 = all_86_1
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (338), (339) imply:
% 25.28/4.52 | | | | | (385) all_84_1 = all_82_1
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (385) implies:
% 25.28/4.52 | | | | | (386) all_84_1 = all_82_1
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (374), (382) imply:
% 25.28/4.52 | | | | | (387) all_80_1 = 0
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (271), (361) imply:
% 25.28/4.52 | | | | | (388) all_88_2 = all_84_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (388) implies:
% 25.28/4.52 | | | | | (389) all_88_2 = all_84_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (346), (347) imply:
% 25.28/4.52 | | | | | (390) all_88_3 = all_86_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (347), (348) imply:
% 25.28/4.52 | | | | | (391) all_88_3 = all_82_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (347), (363) imply:
% 25.28/4.52 | | | | | (392) all_88_3 = all_84_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (282), (384) imply:
% 25.28/4.52 | | | | | (393) all_86_1 = all_53_0
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (354), (389) imply:
% 25.28/4.52 | | | | | (394) all_86_2 = all_84_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | SIMP: (394) implies:
% 25.28/4.52 | | | | | (395) all_86_2 = all_84_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (390), (391) imply:
% 25.28/4.52 | | | | | (396) all_86_3 = all_82_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (390), (392) imply:
% 25.28/4.52 | | | | | (397) all_86_3 = all_84_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (355), (395) imply:
% 25.28/4.52 | | | | | (398) all_84_2 = all_82_2
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (396), (397) imply:
% 25.28/4.52 | | | | | (399) all_84_3 = all_82_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (380), (386) imply:
% 25.28/4.52 | | | | | (400) all_82_1 = all_53_1
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | COMBINE_EQS: (257), (399) imply:
% 25.28/4.52 | | | | | (401) all_152_0 = all_82_3
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | GROUND_INST: instantiating (8) with all_38_2, all_38_1, all_38_2,
% 25.28/4.52 | | | | | all_82_3, simplifying with (34), (35), (37), (135) gives:
% 25.28/4.52 | | | | | (402) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.52 | | | | | (unorthogonal_lines(all_38_1, all_38_2) = v3 &
% 25.28/4.52 | | | | | unorthogonal_lines(all_38_2, all_38_1) = v0 &
% 25.28/4.52 | | | | | unorthogonal_lines(all_38_2, all_38_2) = v2 &
% 25.28/4.52 | | | | | convergent_lines(all_38_2, all_38_2) = v1 & ( ~ (v0 = 0) |
% 25.28/4.52 | | | | | (v3 = 0 & all_82_3 = 0) | (v2 = 0 & v1 = 0)))
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | GROUND_INST: instantiating (16) with all_38_1, all_38_2, all_38_1,
% 25.28/4.52 | | | | | all_82_3, simplifying with (34), (35), (37), (135) gives:
% 25.28/4.52 | | | | | (403) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.52 | | | | | (unorthogonal_lines(all_38_1, all_38_1) = v2 &
% 25.28/4.52 | | | | | unorthogonal_lines(all_38_1, all_38_2) = v0 &
% 25.28/4.52 | | | | | unorthogonal_lines(all_38_2, all_38_1) = v3 &
% 25.28/4.52 | | | | | convergent_lines(all_38_1, all_38_1) = v1 & ( ~ (v3 = 0) |
% 25.28/4.52 | | | | | (v2 = 0 & v1 = 0) | (v0 = 0 & all_82_3 = 0)))
% 25.28/4.52 | | | | |
% 25.28/4.52 | | | | | GROUND_INST: instantiating (11) with all_38_2, all_38_1, all_38_2,
% 25.28/4.52 | | | | | all_55_3, all_82_3, simplifying with (34), (35), (63),
% 25.28/4.52 | | | | | (135) gives:
% 25.28/4.53 | | | | | (404) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.53 | | | | | (unorthogonal_lines(all_38_1, all_38_2) = v3 &
% 25.28/4.53 | | | | | unorthogonal_lines(all_38_2, all_38_1) = v1 &
% 25.28/4.53 | | | | | unorthogonal_lines(all_38_2, all_38_2) = v2 &
% 25.28/4.53 | | | | | convergent_lines(all_38_2, all_38_1) = v0 & ( ~ (v1 = 0) |
% 25.28/4.53 | | | | | ~ (v0 = 0) | (v3 = 0 & all_82_3 = 0) | (v2 = 0 & all_55_3
% 25.28/4.53 | | | | | = 0)))
% 25.28/4.53 | | | | |
% 25.28/4.53 | | | | | GROUND_INST: instantiating (11) with all_38_1, all_38_1, all_38_2,
% 25.28/4.53 | | | | | all_82_3, all_82_3, simplifying with (34), (35), (135)
% 25.28/4.53 | | | | | gives:
% 25.28/4.53 | | | | | (405) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.53 | | | | | (unorthogonal_lines(all_38_1, all_38_1) = v1 &
% 25.28/4.53 | | | | | unorthogonal_lines(all_38_1, all_38_2) = v3 &
% 25.28/4.53 | | | | | unorthogonal_lines(all_38_1, all_38_2) = v2 &
% 25.28/4.53 | | | | | convergent_lines(all_38_1, all_38_1) = v0 & ( ~ (v1 = 0) |
% 25.28/4.53 | | | | | ~ (v0 = 0) | (v3 = 0 & all_82_3 = 0) | (v2 = 0 & all_82_3
% 25.28/4.53 | | | | | = 0)))
% 25.28/4.53 | | | | |
% 25.28/4.53 | | | | | GROUND_INST: instantiating (20) with all_38_1, all_38_2, all_38_2,
% 25.28/4.53 | | | | | all_82_3, all_82_3, simplifying with (34), (35), (135)
% 25.28/4.53 | | | | | gives:
% 25.28/4.53 | | | | | (406) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.53 | | | | | (unorthogonal_lines(all_38_1, all_38_2) = v1 &
% 25.28/4.53 | | | | | unorthogonal_lines(all_38_1, all_38_2) = v0 &
% 25.28/4.53 | | | | | unorthogonal_lines(all_38_2, all_38_2) = v3 &
% 25.28/4.53 | | | | | convergent_lines(all_38_2, all_38_2) = v2 & ( ~ (v3 = 0) |
% 25.28/4.53 | | | | | ~ (v2 = 0) | (v1 = 0 & all_82_3 = 0) | (v0 = 0 & all_82_3
% 25.28/4.53 | | | | | = 0)))
% 25.28/4.53 | | | | |
% 25.28/4.53 | | | | | GROUND_INST: instantiating (22) with all_38_1, all_38_2, all_38_1,
% 25.28/4.53 | | | | | all_82_3, all_53_0, simplifying with (34), (35), (61),
% 25.28/4.53 | | | | | (135) gives:
% 25.28/4.53 | | | | | (407) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.53 | | | | | (unorthogonal_lines(all_38_1, all_38_2) = v0 &
% 25.28/4.53 | | | | | unorthogonal_lines(all_38_2, all_38_1) = v3 &
% 25.28/4.53 | | | | | convergent_lines(all_38_1, all_38_1) = v1 &
% 25.28/4.53 | | | | | convergent_lines(all_38_2, all_38_1) = v2 & ( ~ (v3 = 0) |
% 25.28/4.53 | | | | | ~ (v2 = 0) | (v1 = 0 & all_53_0 = 0) | (v0 = 0 & all_82_3
% 25.28/4.53 | | | | | = 0)))
% 25.28/4.53 | | | | |
% 25.28/4.53 | | | | | GROUND_INST: instantiating (12) with all_38_2, all_38_1, all_38_2,
% 25.28/4.53 | | | | | all_55_2, all_82_3, simplifying with (34), (35), (64),
% 25.28/4.53 | | | | | (135) gives:
% 25.28/4.53 | | | | | (408) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.53 | | | | | (unorthogonal_lines(all_38_1, all_38_2) = v3 &
% 25.28/4.53 | | | | | unorthogonal_lines(all_38_2, all_38_1) = v1 &
% 25.28/4.53 | | | | | convergent_lines(all_38_2, all_38_1) = v0 &
% 25.28/4.53 | | | | | convergent_lines(all_38_2, all_38_2) = v2 & ( ~ (v1 = 0) |
% 25.28/4.53 | | | | | ~ (v0 = 0) | (v3 = 0 & all_82_3 = 0) | (v2 = 0 & all_55_2
% 25.28/4.53 | | | | | = 0)))
% 25.28/4.53 | | | | |
% 25.28/4.53 | | | | | GROUND_INST: instantiating (5) with all_38_1, all_38_2, all_82_3,
% 25.28/4.53 | | | | | simplifying with (34), (35), (135) gives:
% 25.28/4.53 | | | | | (409) all_82_3 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 25.28/4.53 | | | | | distinct_lines(all_38_1, all_38_2) = v0)
% 25.28/4.53 | | | | |
% 25.28/4.53 | | | | | GROUND_INST: instantiating (23) with all_38_1, all_38_2, all_38_1,
% 25.28/4.53 | | | | | all_82_2, all_53_0, simplifying with (34), (35), (61),
% 25.28/4.53 | | | | | (137) gives:
% 25.28/4.53 | | | | | (410) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.53 | | | | | (unorthogonal_lines(all_38_2, all_38_1) = v3 &
% 25.28/4.53 | | | | | convergent_lines(all_38_1, all_38_1) = v1 &
% 25.28/4.53 | | | | | convergent_lines(all_38_1, all_38_2) = v0 &
% 25.28/4.53 | | | | | convergent_lines(all_38_2, all_38_1) = v2 & ( ~ (v3 = 0) |
% 25.28/4.53 | | | | | ~ (v2 = 0) | (v1 = 0 & all_53_0 = 0) | (v0 = 0 & all_82_2
% 25.28/4.53 | | | | | = 0)))
% 25.28/4.53 | | | | |
% 25.28/4.53 | | | | | GROUND_INST: instantiating (14) with all_38_2, all_38_1, all_38_2,
% 25.28/4.53 | | | | | all_55_2, all_82_2, simplifying with (34), (35), (64),
% 25.28/4.53 | | | | | (137) gives:
% 25.28/4.53 | | | | | (411) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.53 | | | | | (unorthogonal_lines(all_38_2, all_38_1) = v1 &
% 25.28/4.53 | | | | | convergent_lines(all_38_1, all_38_2) = v3 &
% 25.28/4.53 | | | | | convergent_lines(all_38_2, all_38_1) = v0 &
% 25.28/4.53 | | | | | convergent_lines(all_38_2, all_38_2) = v2 & ( ~ (v1 = 0) |
% 25.28/4.53 | | | | | ~ (v0 = 0) | (v3 = 0 & all_82_2 = 0) | (v2 = 0 & all_55_2
% 25.28/4.53 | | | | | = 0)))
% 25.28/4.53 | | | | |
% 25.28/4.53 | | | | | GROUND_INST: instantiating (23) with all_38_1, all_38_2, all_38_2,
% 25.28/4.53 | | | | | all_82_2, all_82_2, simplifying with (34), (35), (137)
% 25.28/4.53 | | | | | gives:
% 25.28/4.53 | | | | | (412) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.53 | | | | | (unorthogonal_lines(all_38_2, all_38_2) = v3 &
% 25.28/4.53 | | | | | convergent_lines(all_38_1, all_38_2) = v1 &
% 25.28/4.53 | | | | | convergent_lines(all_38_1, all_38_2) = v0 &
% 25.28/4.53 | | | | | convergent_lines(all_38_2, all_38_2) = v2 & ( ~ (v3 = 0) |
% 25.28/4.53 | | | | | ~ (v2 = 0) | (v1 = 0 & all_82_2 = 0) | (v0 = 0 & all_82_2
% 25.28/4.53 | | | | | = 0)))
% 25.28/4.53 | | | | |
% 25.28/4.53 | | | | | GROUND_INST: instantiating (14) with all_38_1, all_38_1, all_38_2,
% 25.28/4.53 | | | | | all_82_2, all_82_2, simplifying with (34), (35), (137)
% 25.28/4.53 | | | | | gives:
% 25.28/4.53 | | | | | (413) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.53 | | | | | (unorthogonal_lines(all_38_1, all_38_1) = v1 &
% 25.28/4.53 | | | | | convergent_lines(all_38_1, all_38_1) = v0 &
% 25.28/4.53 | | | | | convergent_lines(all_38_1, all_38_2) = v3 &
% 25.28/4.53 | | | | | convergent_lines(all_38_1, all_38_2) = v2 & ( ~ (v1 = 0) |
% 25.28/4.53 | | | | | ~ (v0 = 0) | (v3 = 0 & all_82_2 = 0) | (v2 = 0 & all_82_2
% 25.28/4.53 | | | | | = 0)))
% 25.28/4.53 | | | | |
% 25.28/4.53 | | | | | GROUND_INST: instantiating (21) with all_38_1, all_38_2, all_38_1,
% 25.28/4.53 | | | | | all_82_2, all_53_1, simplifying with (34), (35), (58),
% 25.28/4.53 | | | | | (137) gives:
% 25.28/4.53 | | | | | (414) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.53 | | | | | (unorthogonal_lines(all_38_1, all_38_1) = v1 &
% 25.28/4.53 | | | | | unorthogonal_lines(all_38_2, all_38_1) = v3 &
% 25.28/4.53 | | | | | convergent_lines(all_38_1, all_38_2) = v0 &
% 25.28/4.53 | | | | | convergent_lines(all_38_2, all_38_1) = v2 & ( ~ (v3 = 0) |
% 25.28/4.53 | | | | | ~ (v2 = 0) | (v1 = 0 & all_53_1 = 0) | (v0 = 0 & all_82_2
% 25.28/4.53 | | | | | = 0)))
% 25.28/4.53 | | | | |
% 25.28/4.53 | | | | | GROUND_INST: instantiating (18) with all_38_1, all_38_2, all_38_1,
% 25.28/4.53 | | | | | all_82_2, simplifying with (34), (35), (37), (137) gives:
% 25.28/4.53 | | | | | (415) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.53 | | | | | (unorthogonal_lines(all_38_1, all_38_1) = v2 &
% 25.28/4.53 | | | | | unorthogonal_lines(all_38_2, all_38_1) = v3 &
% 25.28/4.53 | | | | | convergent_lines(all_38_1, all_38_1) = v1 &
% 25.28/4.53 | | | | | convergent_lines(all_38_1, all_38_2) = v0 & ( ~ (v3 = 0) |
% 25.28/4.53 | | | | | (v2 = 0 & v1 = 0) | (v0 = 0 & all_82_2 = 0)))
% 25.28/4.53 | | | | |
% 25.28/4.53 | | | | | GROUND_INST: instantiating (10) with all_38_2, all_38_1, all_38_2,
% 25.28/4.53 | | | | | all_82_2, simplifying with (34), (35), (37), (137) gives:
% 25.28/4.53 | | | | | (416) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.53 | | | | | (unorthogonal_lines(all_38_2, all_38_1) = v0 &
% 25.28/4.53 | | | | | unorthogonal_lines(all_38_2, all_38_2) = v2 &
% 25.28/4.53 | | | | | convergent_lines(all_38_1, all_38_2) = v3 &
% 25.28/4.53 | | | | | convergent_lines(all_38_2, all_38_2) = v1 & ( ~ (v0 = 0) |
% 25.28/4.53 | | | | | (v3 = 0 & all_82_2 = 0) | (v2 = 0 & v1 = 0)))
% 25.28/4.53 | | | | |
% 25.28/4.53 | | | | | GROUND_INST: instantiating (13) with all_38_2, all_38_1, all_38_2,
% 25.28/4.53 | | | | | all_55_3, all_82_2, simplifying with (34), (35), (63),
% 25.28/4.53 | | | | | (137) gives:
% 25.28/4.53 | | | | | (417) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.53 | | | | | (unorthogonal_lines(all_38_2, all_38_1) = v1 &
% 25.28/4.53 | | | | | unorthogonal_lines(all_38_2, all_38_2) = v2 &
% 25.28/4.53 | | | | | convergent_lines(all_38_1, all_38_2) = v3 &
% 25.28/4.53 | | | | | convergent_lines(all_38_2, all_38_1) = v0 & ( ~ (v1 = 0) |
% 25.28/4.53 | | | | | ~ (v0 = 0) | (v3 = 0 & all_82_2 = 0) | (v2 = 0 & all_55_3
% 25.28/4.53 | | | | | = 0)))
% 25.28/4.53 | | | | |
% 25.28/4.53 | | | | | GROUND_INST: instantiating (13) with all_38_1, all_38_1, all_38_2,
% 25.28/4.53 | | | | | all_82_3, all_82_2, simplifying with (34), (35), (135),
% 25.28/4.53 | | | | | (137) gives:
% 25.28/4.53 | | | | | (418) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.53 | | | | | (unorthogonal_lines(all_38_1, all_38_1) = v1 &
% 25.28/4.53 | | | | | unorthogonal_lines(all_38_1, all_38_2) = v2 &
% 25.28/4.53 | | | | | convergent_lines(all_38_1, all_38_1) = v0 &
% 25.28/4.53 | | | | | convergent_lines(all_38_1, all_38_2) = v3 & ( ~ (v1 = 0) |
% 25.28/4.53 | | | | | ~ (v0 = 0) | (v3 = 0 & all_82_2 = 0) | (v2 = 0 & all_82_3
% 25.28/4.53 | | | | | = 0)))
% 25.28/4.53 | | | | |
% 25.28/4.53 | | | | | GROUND_INST: instantiating (12) with all_38_1, all_38_1, all_38_2,
% 25.28/4.53 | | | | | all_82_2, all_82_3, simplifying with (34), (35), (135),
% 25.28/4.53 | | | | | (137) gives:
% 25.28/4.54 | | | | | (419) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.54 | | | | | (unorthogonal_lines(all_38_1, all_38_1) = v1 &
% 25.28/4.54 | | | | | unorthogonal_lines(all_38_1, all_38_2) = v3 &
% 25.28/4.54 | | | | | convergent_lines(all_38_1, all_38_1) = v0 &
% 25.28/4.54 | | | | | convergent_lines(all_38_1, all_38_2) = v2 & ( ~ (v1 = 0) |
% 25.28/4.54 | | | | | ~ (v0 = 0) | (v3 = 0 & all_82_3 = 0) | (v2 = 0 & all_82_2
% 25.28/4.54 | | | | | = 0)))
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | GROUND_INST: instantiating (22) with all_38_1, all_38_2, all_38_2,
% 25.28/4.54 | | | | | all_82_3, all_82_2, simplifying with (34), (35), (135),
% 25.28/4.54 | | | | | (137) gives:
% 25.28/4.54 | | | | | (420) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.54 | | | | | (unorthogonal_lines(all_38_1, all_38_2) = v0 &
% 25.28/4.54 | | | | | unorthogonal_lines(all_38_2, all_38_2) = v3 &
% 25.28/4.54 | | | | | convergent_lines(all_38_1, all_38_2) = v1 &
% 25.28/4.54 | | | | | convergent_lines(all_38_2, all_38_2) = v2 & ( ~ (v3 = 0) |
% 25.28/4.54 | | | | | ~ (v2 = 0) | (v1 = 0 & all_82_2 = 0) | (v0 = 0 & all_82_3
% 25.28/4.54 | | | | | = 0)))
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | GROUND_INST: instantiating (21) with all_38_1, all_38_2, all_38_2,
% 25.28/4.54 | | | | | all_82_2, all_82_3, simplifying with (34), (35), (135),
% 25.28/4.54 | | | | | (137) gives:
% 25.28/4.54 | | | | | (421) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 25.28/4.54 | | | | | (unorthogonal_lines(all_38_1, all_38_2) = v1 &
% 25.28/4.54 | | | | | unorthogonal_lines(all_38_2, all_38_2) = v3 &
% 25.28/4.54 | | | | | convergent_lines(all_38_1, all_38_2) = v0 &
% 25.28/4.54 | | | | | convergent_lines(all_38_2, all_38_2) = v2 & ( ~ (v3 = 0) |
% 25.28/4.54 | | | | | ~ (v2 = 0) | (v1 = 0 & all_82_3 = 0) | (v0 = 0 & all_82_2
% 25.28/4.54 | | | | | = 0)))
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | DELTA: instantiating (416) with fresh symbols all_163_0, all_163_1,
% 25.28/4.54 | | | | | all_163_2, all_163_3 gives:
% 25.28/4.54 | | | | | (422) unorthogonal_lines(all_38_2, all_38_1) = all_163_3 &
% 25.28/4.54 | | | | | unorthogonal_lines(all_38_2, all_38_2) = all_163_1 &
% 25.28/4.54 | | | | | convergent_lines(all_38_1, all_38_2) = all_163_0 &
% 25.28/4.54 | | | | | convergent_lines(all_38_2, all_38_2) = all_163_2 & ( ~
% 25.28/4.54 | | | | | (all_163_3 = 0) | (all_163_0 = 0 & all_82_2 = 0) |
% 25.28/4.54 | | | | | (all_163_1 = 0 & all_163_2 = 0))
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | ALPHA: (422) implies:
% 25.28/4.54 | | | | | (423) convergent_lines(all_38_2, all_38_2) = all_163_2
% 25.28/4.54 | | | | | (424) convergent_lines(all_38_1, all_38_2) = all_163_0
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | DELTA: instantiating (415) with fresh symbols all_165_0, all_165_1,
% 25.28/4.54 | | | | | all_165_2, all_165_3 gives:
% 25.28/4.54 | | | | | (425) unorthogonal_lines(all_38_1, all_38_1) = all_165_1 &
% 25.28/4.54 | | | | | unorthogonal_lines(all_38_2, all_38_1) = all_165_0 &
% 25.28/4.54 | | | | | convergent_lines(all_38_1, all_38_1) = all_165_2 &
% 25.28/4.54 | | | | | convergent_lines(all_38_1, all_38_2) = all_165_3 & ( ~
% 25.28/4.54 | | | | | (all_165_0 = 0) | (all_165_1 = 0 & all_165_2 = 0) |
% 25.28/4.54 | | | | | (all_165_3 = 0 & all_82_2 = 0))
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | ALPHA: (425) implies:
% 25.28/4.54 | | | | | (426) convergent_lines(all_38_1, all_38_2) = all_165_3
% 25.28/4.54 | | | | | (427) convergent_lines(all_38_1, all_38_1) = all_165_2
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | DELTA: instantiating (403) with fresh symbols all_167_0, all_167_1,
% 25.28/4.54 | | | | | all_167_2, all_167_3 gives:
% 25.28/4.54 | | | | | (428) unorthogonal_lines(all_38_1, all_38_1) = all_167_1 &
% 25.28/4.54 | | | | | unorthogonal_lines(all_38_1, all_38_2) = all_167_3 &
% 25.28/4.54 | | | | | unorthogonal_lines(all_38_2, all_38_1) = all_167_0 &
% 25.28/4.54 | | | | | convergent_lines(all_38_1, all_38_1) = all_167_2 & ( ~
% 25.28/4.54 | | | | | (all_167_0 = 0) | (all_167_1 = 0 & all_167_2 = 0) |
% 25.28/4.54 | | | | | (all_167_3 = 0 & all_82_3 = 0))
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | ALPHA: (428) implies:
% 25.28/4.54 | | | | | (429) convergent_lines(all_38_1, all_38_1) = all_167_2
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | DELTA: instantiating (402) with fresh symbols all_169_0, all_169_1,
% 25.28/4.54 | | | | | all_169_2, all_169_3 gives:
% 25.28/4.54 | | | | | (430) unorthogonal_lines(all_38_1, all_38_2) = all_169_0 &
% 25.28/4.54 | | | | | unorthogonal_lines(all_38_2, all_38_1) = all_169_3 &
% 25.28/4.54 | | | | | unorthogonal_lines(all_38_2, all_38_2) = all_169_1 &
% 25.28/4.54 | | | | | convergent_lines(all_38_2, all_38_2) = all_169_2 & ( ~
% 25.28/4.54 | | | | | (all_169_3 = 0) | (all_169_0 = 0 & all_82_3 = 0) |
% 25.28/4.54 | | | | | (all_169_1 = 0 & all_169_2 = 0))
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | ALPHA: (430) implies:
% 25.28/4.54 | | | | | (431) convergent_lines(all_38_2, all_38_2) = all_169_2
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | DELTA: instantiating (412) with fresh symbols all_171_0, all_171_1,
% 25.28/4.54 | | | | | all_171_2, all_171_3 gives:
% 25.28/4.54 | | | | | (432) unorthogonal_lines(all_38_2, all_38_2) = all_171_0 &
% 25.28/4.54 | | | | | convergent_lines(all_38_1, all_38_2) = all_171_2 &
% 25.28/4.54 | | | | | convergent_lines(all_38_1, all_38_2) = all_171_3 &
% 25.28/4.54 | | | | | convergent_lines(all_38_2, all_38_2) = all_171_1 & ( ~
% 25.28/4.54 | | | | | (all_171_0 = 0) | ~ (all_171_1 = 0) | (all_171_2 = 0 &
% 25.28/4.54 | | | | | all_82_2 = 0) | (all_171_3 = 0 & all_82_2 = 0))
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | ALPHA: (432) implies:
% 25.28/4.54 | | | | | (433) convergent_lines(all_38_2, all_38_2) = all_171_1
% 25.28/4.54 | | | | | (434) convergent_lines(all_38_1, all_38_2) = all_171_3
% 25.28/4.54 | | | | | (435) convergent_lines(all_38_1, all_38_2) = all_171_2
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | DELTA: instantiating (411) with fresh symbols all_173_0, all_173_1,
% 25.28/4.54 | | | | | all_173_2, all_173_3 gives:
% 25.28/4.54 | | | | | (436) unorthogonal_lines(all_38_2, all_38_1) = all_173_2 &
% 25.28/4.54 | | | | | convergent_lines(all_38_1, all_38_2) = all_173_0 &
% 25.28/4.54 | | | | | convergent_lines(all_38_2, all_38_1) = all_173_3 &
% 25.28/4.54 | | | | | convergent_lines(all_38_2, all_38_2) = all_173_1 & ( ~
% 25.28/4.54 | | | | | (all_173_2 = 0) | ~ (all_173_3 = 0) | (all_173_0 = 0 &
% 25.28/4.54 | | | | | all_82_2 = 0) | (all_173_1 = 0 & all_55_2 = 0))
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | ALPHA: (436) implies:
% 25.28/4.54 | | | | | (437) convergent_lines(all_38_2, all_38_2) = all_173_1
% 25.28/4.54 | | | | | (438) convergent_lines(all_38_1, all_38_2) = all_173_0
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | DELTA: instantiating (408) with fresh symbols all_175_0, all_175_1,
% 25.28/4.54 | | | | | all_175_2, all_175_3 gives:
% 25.28/4.54 | | | | | (439) unorthogonal_lines(all_38_1, all_38_2) = all_175_0 &
% 25.28/4.54 | | | | | unorthogonal_lines(all_38_2, all_38_1) = all_175_2 &
% 25.28/4.54 | | | | | convergent_lines(all_38_2, all_38_1) = all_175_3 &
% 25.28/4.54 | | | | | convergent_lines(all_38_2, all_38_2) = all_175_1 & ( ~
% 25.28/4.54 | | | | | (all_175_2 = 0) | ~ (all_175_3 = 0) | (all_175_0 = 0 &
% 25.28/4.54 | | | | | all_82_3 = 0) | (all_175_1 = 0 & all_55_2 = 0))
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | ALPHA: (439) implies:
% 25.28/4.54 | | | | | (440) convergent_lines(all_38_2, all_38_2) = all_175_1
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | DELTA: instantiating (407) with fresh symbols all_177_0, all_177_1,
% 25.28/4.54 | | | | | all_177_2, all_177_3 gives:
% 25.28/4.54 | | | | | (441) unorthogonal_lines(all_38_1, all_38_2) = all_177_3 &
% 25.28/4.54 | | | | | unorthogonal_lines(all_38_2, all_38_1) = all_177_0 &
% 25.28/4.54 | | | | | convergent_lines(all_38_1, all_38_1) = all_177_2 &
% 25.28/4.54 | | | | | convergent_lines(all_38_2, all_38_1) = all_177_1 & ( ~
% 25.28/4.54 | | | | | (all_177_0 = 0) | ~ (all_177_1 = 0) | (all_177_2 = 0 &
% 25.28/4.54 | | | | | all_53_0 = 0) | (all_177_3 = 0 & all_82_3 = 0))
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | ALPHA: (441) implies:
% 25.28/4.54 | | | | | (442) convergent_lines(all_38_1, all_38_1) = all_177_2
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | DELTA: instantiating (406) with fresh symbols all_179_0, all_179_1,
% 25.28/4.54 | | | | | all_179_2, all_179_3 gives:
% 25.28/4.54 | | | | | (443) unorthogonal_lines(all_38_1, all_38_2) = all_179_2 &
% 25.28/4.54 | | | | | unorthogonal_lines(all_38_1, all_38_2) = all_179_3 &
% 25.28/4.54 | | | | | unorthogonal_lines(all_38_2, all_38_2) = all_179_0 &
% 25.28/4.54 | | | | | convergent_lines(all_38_2, all_38_2) = all_179_1 & ( ~
% 25.28/4.54 | | | | | (all_179_0 = 0) | ~ (all_179_1 = 0) | (all_179_2 = 0 &
% 25.28/4.54 | | | | | all_82_3 = 0) | (all_179_3 = 0 & all_82_3 = 0))
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | ALPHA: (443) implies:
% 25.28/4.54 | | | | | (444) convergent_lines(all_38_2, all_38_2) = all_179_1
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | DELTA: instantiating (405) with fresh symbols all_181_0, all_181_1,
% 25.28/4.54 | | | | | all_181_2, all_181_3 gives:
% 25.28/4.54 | | | | | (445) unorthogonal_lines(all_38_1, all_38_1) = all_181_2 &
% 25.28/4.54 | | | | | unorthogonal_lines(all_38_1, all_38_2) = all_181_0 &
% 25.28/4.54 | | | | | unorthogonal_lines(all_38_1, all_38_2) = all_181_1 &
% 25.28/4.54 | | | | | convergent_lines(all_38_1, all_38_1) = all_181_3 & ( ~
% 25.28/4.54 | | | | | (all_181_2 = 0) | ~ (all_181_3 = 0) | (all_181_0 = 0 &
% 25.28/4.54 | | | | | all_82_3 = 0) | (all_181_1 = 0 & all_82_3 = 0))
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | ALPHA: (445) implies:
% 25.28/4.54 | | | | | (446) convergent_lines(all_38_1, all_38_1) = all_181_3
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | DELTA: instantiating (410) with fresh symbols all_183_0, all_183_1,
% 25.28/4.54 | | | | | all_183_2, all_183_3 gives:
% 25.28/4.54 | | | | | (447) unorthogonal_lines(all_38_2, all_38_1) = all_183_0 &
% 25.28/4.54 | | | | | convergent_lines(all_38_1, all_38_1) = all_183_2 &
% 25.28/4.54 | | | | | convergent_lines(all_38_1, all_38_2) = all_183_3 &
% 25.28/4.54 | | | | | convergent_lines(all_38_2, all_38_1) = all_183_1 & ( ~
% 25.28/4.54 | | | | | (all_183_0 = 0) | ~ (all_183_1 = 0) | (all_183_2 = 0 &
% 25.28/4.54 | | | | | all_53_0 = 0) | (all_183_3 = 0 & all_82_2 = 0))
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | ALPHA: (447) implies:
% 25.28/4.54 | | | | | (448) convergent_lines(all_38_1, all_38_2) = all_183_3
% 25.28/4.54 | | | | | (449) convergent_lines(all_38_1, all_38_1) = all_183_2
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | DELTA: instantiating (421) with fresh symbols all_187_0, all_187_1,
% 25.28/4.54 | | | | | all_187_2, all_187_3 gives:
% 25.28/4.54 | | | | | (450) unorthogonal_lines(all_38_1, all_38_2) = all_187_2 &
% 25.28/4.54 | | | | | unorthogonal_lines(all_38_2, all_38_2) = all_187_0 &
% 25.28/4.54 | | | | | convergent_lines(all_38_1, all_38_2) = all_187_3 &
% 25.28/4.54 | | | | | convergent_lines(all_38_2, all_38_2) = all_187_1 & ( ~
% 25.28/4.54 | | | | | (all_187_0 = 0) | ~ (all_187_1 = 0) | (all_187_2 = 0 &
% 25.28/4.54 | | | | | all_82_3 = 0) | (all_187_3 = 0 & all_82_2 = 0))
% 25.28/4.54 | | | | |
% 25.28/4.54 | | | | | ALPHA: (450) implies:
% 25.28/4.54 | | | | | (451) convergent_lines(all_38_2, all_38_2) = all_187_1
% 25.28/4.54 | | | | | (452) convergent_lines(all_38_1, all_38_2) = all_187_3
% 25.28/4.54 | | | | | (453) unorthogonal_lines(all_38_2, all_38_2) = all_187_0
% 25.28/4.55 | | | | | (454) ~ (all_187_0 = 0) | ~ (all_187_1 = 0) | (all_187_2 = 0 &
% 25.28/4.55 | | | | | all_82_3 = 0) | (all_187_3 = 0 & all_82_2 = 0)
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | DELTA: instantiating (420) with fresh symbols all_189_0, all_189_1,
% 25.28/4.55 | | | | | all_189_2, all_189_3 gives:
% 25.28/4.55 | | | | | (455) unorthogonal_lines(all_38_1, all_38_2) = all_189_3 &
% 25.28/4.55 | | | | | unorthogonal_lines(all_38_2, all_38_2) = all_189_0 &
% 25.28/4.55 | | | | | convergent_lines(all_38_1, all_38_2) = all_189_2 &
% 25.28/4.55 | | | | | convergent_lines(all_38_2, all_38_2) = all_189_1 & ( ~
% 25.28/4.55 | | | | | (all_189_0 = 0) | ~ (all_189_1 = 0) | (all_189_2 = 0 &
% 25.28/4.55 | | | | | all_82_2 = 0) | (all_189_3 = 0 & all_82_3 = 0))
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | ALPHA: (455) implies:
% 25.28/4.55 | | | | | (456) convergent_lines(all_38_2, all_38_2) = all_189_1
% 25.28/4.55 | | | | | (457) convergent_lines(all_38_1, all_38_2) = all_189_2
% 25.28/4.55 | | | | | (458) unorthogonal_lines(all_38_2, all_38_2) = all_189_0
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | DELTA: instantiating (419) with fresh symbols all_191_0, all_191_1,
% 25.28/4.55 | | | | | all_191_2, all_191_3 gives:
% 25.28/4.55 | | | | | (459) unorthogonal_lines(all_38_1, all_38_1) = all_191_2 &
% 25.28/4.55 | | | | | unorthogonal_lines(all_38_1, all_38_2) = all_191_0 &
% 25.28/4.55 | | | | | convergent_lines(all_38_1, all_38_1) = all_191_3 &
% 25.28/4.55 | | | | | convergent_lines(all_38_1, all_38_2) = all_191_1 & ( ~
% 25.28/4.55 | | | | | (all_191_2 = 0) | ~ (all_191_3 = 0) | (all_191_0 = 0 &
% 25.28/4.55 | | | | | all_82_3 = 0) | (all_191_1 = 0 & all_82_2 = 0))
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | ALPHA: (459) implies:
% 25.28/4.55 | | | | | (460) convergent_lines(all_38_1, all_38_2) = all_191_1
% 25.28/4.55 | | | | | (461) convergent_lines(all_38_1, all_38_1) = all_191_3
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | DELTA: instantiating (418) with fresh symbols all_193_0, all_193_1,
% 25.28/4.55 | | | | | all_193_2, all_193_3 gives:
% 25.28/4.55 | | | | | (462) unorthogonal_lines(all_38_1, all_38_1) = all_193_2 &
% 25.28/4.55 | | | | | unorthogonal_lines(all_38_1, all_38_2) = all_193_1 &
% 25.28/4.55 | | | | | convergent_lines(all_38_1, all_38_1) = all_193_3 &
% 25.28/4.55 | | | | | convergent_lines(all_38_1, all_38_2) = all_193_0 & ( ~
% 25.28/4.55 | | | | | (all_193_2 = 0) | ~ (all_193_3 = 0) | (all_193_0 = 0 &
% 25.28/4.55 | | | | | all_82_2 = 0) | (all_193_1 = 0 & all_82_3 = 0))
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | ALPHA: (462) implies:
% 25.28/4.55 | | | | | (463) convergent_lines(all_38_1, all_38_2) = all_193_0
% 25.28/4.55 | | | | | (464) convergent_lines(all_38_1, all_38_1) = all_193_3
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | DELTA: instantiating (414) with fresh symbols all_195_0, all_195_1,
% 25.28/4.55 | | | | | all_195_2, all_195_3 gives:
% 25.28/4.55 | | | | | (465) unorthogonal_lines(all_38_1, all_38_1) = all_195_2 &
% 25.28/4.55 | | | | | unorthogonal_lines(all_38_2, all_38_1) = all_195_0 &
% 25.28/4.55 | | | | | convergent_lines(all_38_1, all_38_2) = all_195_3 &
% 25.28/4.55 | | | | | convergent_lines(all_38_2, all_38_1) = all_195_1 & ( ~
% 25.28/4.55 | | | | | (all_195_0 = 0) | ~ (all_195_1 = 0) | (all_195_2 = 0 &
% 25.28/4.55 | | | | | all_53_1 = 0) | (all_195_3 = 0 & all_82_2 = 0))
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | ALPHA: (465) implies:
% 25.28/4.55 | | | | | (466) convergent_lines(all_38_1, all_38_2) = all_195_3
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | DELTA: instantiating (413) with fresh symbols all_197_0, all_197_1,
% 25.28/4.55 | | | | | all_197_2, all_197_3 gives:
% 25.28/4.55 | | | | | (467) unorthogonal_lines(all_38_1, all_38_1) = all_197_2 &
% 25.28/4.55 | | | | | convergent_lines(all_38_1, all_38_1) = all_197_3 &
% 25.28/4.55 | | | | | convergent_lines(all_38_1, all_38_2) = all_197_0 &
% 25.28/4.55 | | | | | convergent_lines(all_38_1, all_38_2) = all_197_1 & ( ~
% 25.28/4.55 | | | | | (all_197_2 = 0) | ~ (all_197_3 = 0) | (all_197_0 = 0 &
% 25.28/4.55 | | | | | all_82_2 = 0) | (all_197_1 = 0 & all_82_2 = 0))
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | ALPHA: (467) implies:
% 25.28/4.55 | | | | | (468) convergent_lines(all_38_1, all_38_2) = all_197_1
% 25.28/4.55 | | | | | (469) convergent_lines(all_38_1, all_38_2) = all_197_0
% 25.28/4.55 | | | | | (470) convergent_lines(all_38_1, all_38_1) = all_197_3
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | DELTA: instantiating (404) with fresh symbols all_199_0, all_199_1,
% 25.28/4.55 | | | | | all_199_2, all_199_3 gives:
% 25.28/4.55 | | | | | (471) unorthogonal_lines(all_38_1, all_38_2) = all_199_0 &
% 25.28/4.55 | | | | | unorthogonal_lines(all_38_2, all_38_1) = all_199_2 &
% 25.28/4.55 | | | | | unorthogonal_lines(all_38_2, all_38_2) = all_199_1 &
% 25.28/4.55 | | | | | convergent_lines(all_38_2, all_38_1) = all_199_3 & ( ~
% 25.28/4.55 | | | | | (all_199_2 = 0) | ~ (all_199_3 = 0) | (all_199_0 = 0 &
% 25.28/4.55 | | | | | all_82_3 = 0) | (all_199_1 = 0 & all_55_3 = 0))
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | ALPHA: (471) implies:
% 25.28/4.55 | | | | | (472) unorthogonal_lines(all_38_2, all_38_2) = all_199_1
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | DELTA: instantiating (417) with fresh symbols all_201_0, all_201_1,
% 25.28/4.55 | | | | | all_201_2, all_201_3 gives:
% 25.28/4.55 | | | | | (473) unorthogonal_lines(all_38_2, all_38_1) = all_201_2 &
% 25.28/4.55 | | | | | unorthogonal_lines(all_38_2, all_38_2) = all_201_1 &
% 25.28/4.55 | | | | | convergent_lines(all_38_1, all_38_2) = all_201_0 &
% 25.28/4.55 | | | | | convergent_lines(all_38_2, all_38_1) = all_201_3 & ( ~
% 25.28/4.55 | | | | | (all_201_2 = 0) | ~ (all_201_3 = 0) | (all_201_0 = 0 &
% 25.28/4.55 | | | | | all_82_2 = 0) | (all_201_1 = 0 & all_55_3 = 0))
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | ALPHA: (473) implies:
% 25.28/4.55 | | | | | (474) convergent_lines(all_38_1, all_38_2) = all_201_0
% 25.28/4.55 | | | | | (475) unorthogonal_lines(all_38_2, all_38_2) = all_201_1
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_55_3, all_171_1, all_38_2,
% 25.28/4.55 | | | | | all_38_2, simplifying with (63), (433) gives:
% 25.28/4.55 | | | | | (476) all_171_1 = all_55_3
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_163_2, all_173_1, all_38_2,
% 25.28/4.55 | | | | | all_38_2, simplifying with (423), (437) gives:
% 25.28/4.55 | | | | | (477) all_173_1 = all_163_2
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_173_1, all_175_1, all_38_2,
% 25.28/4.55 | | | | | all_38_2, simplifying with (437), (440) gives:
% 25.28/4.55 | | | | | (478) all_175_1 = all_173_1
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_171_1, all_175_1, all_38_2,
% 25.28/4.55 | | | | | all_38_2, simplifying with (433), (440) gives:
% 25.28/4.55 | | | | | (479) all_175_1 = all_171_1
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_175_1, all_179_1, all_38_2,
% 25.28/4.55 | | | | | all_38_2, simplifying with (440), (444) gives:
% 25.28/4.55 | | | | | (480) all_179_1 = all_175_1
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_179_1, all_187_1, all_38_2,
% 25.28/4.55 | | | | | all_38_2, simplifying with (444), (451) gives:
% 25.28/4.55 | | | | | (481) all_187_1 = all_179_1
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_187_1, all_189_1, all_38_2,
% 25.28/4.55 | | | | | all_38_2, simplifying with (451), (456) gives:
% 25.28/4.55 | | | | | (482) all_189_1 = all_187_1
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_169_2, all_189_1, all_38_2,
% 25.28/4.55 | | | | | all_38_2, simplifying with (431), (456) gives:
% 25.28/4.55 | | | | | (483) all_189_1 = all_169_2
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_82_3, all_165_3, all_38_2,
% 25.28/4.55 | | | | | all_38_1, simplifying with (135), (426) gives:
% 25.28/4.55 | | | | | (484) all_165_3 = all_82_3
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_165_3, all_171_3, all_38_2,
% 25.28/4.55 | | | | | all_38_1, simplifying with (426), (434) gives:
% 25.28/4.55 | | | | | (485) all_171_3 = all_165_3
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_171_3, all_171_2, all_38_2,
% 25.28/4.55 | | | | | all_38_1, simplifying with (434), (435) gives:
% 25.28/4.55 | | | | | (486) all_171_2 = all_171_3
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_171_2, all_173_0, all_38_2,
% 25.28/4.55 | | | | | all_38_1, simplifying with (435), (438) gives:
% 25.28/4.55 | | | | | (487) all_173_0 = all_171_2
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_173_0, all_183_3, all_38_2,
% 25.28/4.55 | | | | | all_38_1, simplifying with (438), (448) gives:
% 25.28/4.55 | | | | | (488) all_183_3 = all_173_0
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_183_3, all_187_3, all_38_2,
% 25.28/4.55 | | | | | all_38_1, simplifying with (448), (452) gives:
% 25.28/4.55 | | | | | (489) all_187_3 = all_183_3
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_187_3, all_189_2, all_38_2,
% 25.28/4.55 | | | | | all_38_1, simplifying with (452), (457) gives:
% 25.28/4.55 | | | | | (490) all_189_2 = all_187_3
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_189_2, all_191_1, all_38_2,
% 25.28/4.55 | | | | | all_38_1, simplifying with (457), (460) gives:
% 25.28/4.55 | | | | | (491) all_191_1 = all_189_2
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_191_1, all_193_0, all_38_2,
% 25.28/4.55 | | | | | all_38_1, simplifying with (460), (463) gives:
% 25.28/4.55 | | | | | (492) all_193_0 = all_191_1
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_193_0, all_195_3, all_38_2,
% 25.28/4.55 | | | | | all_38_1, simplifying with (463), (466) gives:
% 25.28/4.55 | | | | | (493) all_195_3 = all_193_0
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_195_3, all_197_1, all_38_2,
% 25.28/4.55 | | | | | all_38_1, simplifying with (466), (468) gives:
% 25.28/4.55 | | | | | (494) all_197_1 = all_195_3
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_197_1, all_197_0, all_38_2,
% 25.28/4.55 | | | | | all_38_1, simplifying with (468), (469) gives:
% 25.28/4.55 | | | | | (495) all_197_0 = all_197_1
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_197_0, all_201_0, all_38_2,
% 25.28/4.55 | | | | | all_38_1, simplifying with (469), (474) gives:
% 25.28/4.55 | | | | | (496) all_201_0 = all_197_0
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_163_0, all_201_0, all_38_2,
% 25.28/4.55 | | | | | all_38_1, simplifying with (424), (474) gives:
% 25.28/4.55 | | | | | (497) all_201_0 = all_163_0
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_53_1, all_181_3, all_38_1,
% 25.28/4.55 | | | | | all_38_1, simplifying with (58), (446) gives:
% 25.28/4.55 | | | | | (498) all_181_3 = all_53_1
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_167_2, all_181_3, all_38_1,
% 25.28/4.55 | | | | | all_38_1, simplifying with (429), (446) gives:
% 25.28/4.55 | | | | | (499) all_181_3 = all_167_2
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_165_2, all_181_3, all_38_1,
% 25.28/4.55 | | | | | all_38_1, simplifying with (427), (446) gives:
% 25.28/4.55 | | | | | (500) all_181_3 = all_165_2
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_181_3, all_183_2, all_38_1,
% 25.28/4.55 | | | | | all_38_1, simplifying with (446), (449) gives:
% 25.28/4.55 | | | | | (501) all_183_2 = all_181_3
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_183_2, all_191_3, all_38_1,
% 25.28/4.55 | | | | | all_38_1, simplifying with (449), (461) gives:
% 25.28/4.55 | | | | | (502) all_191_3 = all_183_2
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_193_3, all_197_3, all_38_1,
% 25.28/4.55 | | | | | all_38_1, simplifying with (464), (470) gives:
% 25.28/4.55 | | | | | (503) all_197_3 = all_193_3
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_191_3, all_197_3, all_38_1,
% 25.28/4.55 | | | | | all_38_1, simplifying with (461), (470) gives:
% 25.28/4.55 | | | | | (504) all_197_3 = all_191_3
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (29) with all_177_2, all_197_3, all_38_1,
% 25.28/4.55 | | | | | all_38_1, simplifying with (442), (470) gives:
% 25.28/4.55 | | | | | (505) all_197_3 = all_177_2
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (31) with all_55_2, all_199_1, all_38_2,
% 25.28/4.55 | | | | | all_38_2, simplifying with (64), (472) gives:
% 25.28/4.55 | | | | | (506) all_199_1 = all_55_2
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (31) with all_187_0, all_199_1, all_38_2,
% 25.28/4.55 | | | | | all_38_2, simplifying with (453), (472) gives:
% 25.28/4.55 | | | | | (507) all_199_1 = all_187_0
% 25.28/4.55 | | | | |
% 25.28/4.55 | | | | | GROUND_INST: instantiating (31) with all_199_1, all_201_1, all_38_2,
% 25.28/4.55 | | | | | all_38_2, simplifying with (472), (475) gives:
% 25.28/4.55 | | | | | (508) all_201_1 = all_199_1
% 25.28/4.55 | | | | |
% 25.28/4.56 | | | | | GROUND_INST: instantiating (31) with all_189_0, all_201_1, all_38_2,
% 25.28/4.56 | | | | | all_38_2, simplifying with (458), (475) gives:
% 25.28/4.56 | | | | | (509) all_201_1 = all_189_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (496), (497) imply:
% 25.28/4.56 | | | | | (510) all_197_0 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (510) implies:
% 25.28/4.56 | | | | | (511) all_197_0 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (508), (509) imply:
% 25.28/4.56 | | | | | (512) all_199_1 = all_189_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (512) implies:
% 25.28/4.56 | | | | | (513) all_199_1 = all_189_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (506), (513) imply:
% 25.28/4.56 | | | | | (514) all_189_0 = all_55_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (507), (513) imply:
% 25.28/4.56 | | | | | (515) all_189_0 = all_187_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (495), (511) imply:
% 25.28/4.56 | | | | | (516) all_197_1 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (516) implies:
% 25.28/4.56 | | | | | (517) all_197_1 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (494), (517) imply:
% 25.28/4.56 | | | | | (518) all_195_3 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (518) implies:
% 25.28/4.56 | | | | | (519) all_195_3 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (503), (504) imply:
% 25.28/4.56 | | | | | (520) all_193_3 = all_191_3
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (503), (505) imply:
% 25.28/4.56 | | | | | (521) all_193_3 = all_177_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (493), (519) imply:
% 25.28/4.56 | | | | | (522) all_193_0 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (522) implies:
% 25.28/4.56 | | | | | (523) all_193_0 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (492), (523) imply:
% 25.28/4.56 | | | | | (524) all_191_1 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (524) implies:
% 25.28/4.56 | | | | | (525) all_191_1 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (520), (521) imply:
% 25.28/4.56 | | | | | (526) all_191_3 = all_177_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (526) implies:
% 25.28/4.56 | | | | | (527) all_191_3 = all_177_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (491), (525) imply:
% 25.28/4.56 | | | | | (528) all_189_2 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (528) implies:
% 25.28/4.56 | | | | | (529) all_189_2 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (502), (527) imply:
% 25.28/4.56 | | | | | (530) all_183_2 = all_177_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (530) implies:
% 25.28/4.56 | | | | | (531) all_183_2 = all_177_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (514), (515) imply:
% 25.28/4.56 | | | | | (532) all_187_0 = all_55_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (532) implies:
% 25.28/4.56 | | | | | (533) all_187_0 = all_55_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (482), (483) imply:
% 25.28/4.56 | | | | | (534) all_187_1 = all_169_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (534) implies:
% 25.28/4.56 | | | | | (535) all_187_1 = all_169_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (490), (529) imply:
% 25.28/4.56 | | | | | (536) all_187_3 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (536) implies:
% 25.28/4.56 | | | | | (537) all_187_3 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (481), (535) imply:
% 25.28/4.56 | | | | | (538) all_179_1 = all_169_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (538) implies:
% 25.28/4.56 | | | | | (539) all_179_1 = all_169_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (489), (537) imply:
% 25.28/4.56 | | | | | (540) all_183_3 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (540) implies:
% 25.28/4.56 | | | | | (541) all_183_3 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (501), (531) imply:
% 25.28/4.56 | | | | | (542) all_181_3 = all_177_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (542) implies:
% 25.28/4.56 | | | | | (543) all_181_3 = all_177_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (488), (541) imply:
% 25.28/4.56 | | | | | (544) all_173_0 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (544) implies:
% 25.28/4.56 | | | | | (545) all_173_0 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (498), (543) imply:
% 25.28/4.56 | | | | | (546) all_177_2 = all_53_1
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (500), (543) imply:
% 25.28/4.56 | | | | | (547) all_177_2 = all_165_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (499), (543) imply:
% 25.28/4.56 | | | | | (548) all_177_2 = all_167_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (480), (539) imply:
% 25.28/4.56 | | | | | (549) all_175_1 = all_169_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (549) implies:
% 25.28/4.56 | | | | | (550) all_175_1 = all_169_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (547), (548) imply:
% 25.28/4.56 | | | | | (551) all_167_2 = all_165_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (546), (548) imply:
% 25.28/4.56 | | | | | (552) all_167_2 = all_53_1
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (478), (550) imply:
% 25.28/4.56 | | | | | (553) all_173_1 = all_169_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (553) implies:
% 25.28/4.56 | | | | | (554) all_173_1 = all_169_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (479), (550) imply:
% 25.28/4.56 | | | | | (555) all_171_1 = all_169_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (555) implies:
% 25.28/4.56 | | | | | (556) all_171_1 = all_169_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (487), (545) imply:
% 25.28/4.56 | | | | | (557) all_171_2 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (557) implies:
% 25.28/4.56 | | | | | (558) all_171_2 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (477), (554) imply:
% 25.28/4.56 | | | | | (559) all_169_2 = all_163_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (559) implies:
% 25.28/4.56 | | | | | (560) all_169_2 = all_163_2
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (476), (556) imply:
% 25.28/4.56 | | | | | (561) all_169_2 = all_55_3
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (561) implies:
% 25.28/4.56 | | | | | (562) all_169_2 = all_55_3
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (486), (558) imply:
% 25.28/4.56 | | | | | (563) all_171_3 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (563) implies:
% 25.28/4.56 | | | | | (564) all_171_3 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (485), (564) imply:
% 25.28/4.56 | | | | | (565) all_165_3 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | SIMP: (565) implies:
% 25.28/4.56 | | | | | (566) all_165_3 = all_163_0
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (560), (562) imply:
% 25.28/4.56 | | | | | (567) all_163_2 = all_55_3
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (551), (552) imply:
% 25.28/4.56 | | | | | (568) all_165_2 = all_53_1
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (484), (566) imply:
% 25.28/4.56 | | | | | (569) all_163_0 = all_82_3
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (537), (569) imply:
% 25.28/4.56 | | | | | (570) all_187_3 = all_82_3
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | COMBINE_EQS: (535), (562) imply:
% 25.28/4.56 | | | | | (571) all_187_1 = all_55_3
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | BETA: splitting (67) gives:
% 25.28/4.56 | | | | |
% 25.28/4.56 | | | | | Case 1:
% 25.28/4.56 | | | | | |
% 25.28/4.56 | | | | | | (572) ~ (all_55_2 = 0)
% 25.28/4.56 | | | | | |
% 25.28/4.56 | | | | | | BETA: splitting (119) gives:
% 25.28/4.56 | | | | | |
% 25.28/4.56 | | | | | | Case 1:
% 25.28/4.56 | | | | | | |
% 25.28/4.56 | | | | | | | (573) convergent_lines(all_38_2, all_38_2) = 0
% 25.28/4.56 | | | | | | |
% 25.28/4.56 | | | | | | | BETA: splitting (116) gives:
% 25.28/4.56 | | | | | | |
% 25.28/4.56 | | | | | | | Case 1:
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | | (574) all_55_2 = 0
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | | REDUCE: (572), (574) imply:
% 25.28/4.56 | | | | | | | | (575) $false
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | | CLOSE: (575) is inconsistent.
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | Case 2:
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | | (576) ? [v0: int] : ( ~ (v0 = 0) &
% 25.28/4.56 | | | | | | | | convergent_lines(all_38_2, all_38_2) = v0)
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | | DELTA: instantiating (576) with fresh symbol all_250_0 gives:
% 25.28/4.56 | | | | | | | | (577) ~ (all_250_0 = 0) & convergent_lines(all_38_2,
% 25.28/4.56 | | | | | | | | all_38_2) = all_250_0
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | | ALPHA: (577) implies:
% 25.28/4.56 | | | | | | | | (578) ~ (all_250_0 = 0)
% 25.28/4.56 | | | | | | | | (579) convergent_lines(all_38_2, all_38_2) = all_250_0
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | | GROUND_INST: instantiating (29) with 0, all_250_0, all_38_2,
% 25.28/4.56 | | | | | | | | all_38_2, simplifying with (573), (579) gives:
% 25.28/4.56 | | | | | | | | (580) all_250_0 = 0
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | | REDUCE: (578), (580) imply:
% 25.28/4.56 | | | | | | | | (581) $false
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | | CLOSE: (581) is inconsistent.
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | End of split
% 25.28/4.56 | | | | | | |
% 25.28/4.56 | | | | | | Case 2:
% 25.28/4.56 | | | | | | |
% 25.28/4.56 | | | | | | | (582) all_55_2 = 0
% 25.28/4.56 | | | | | | |
% 25.28/4.56 | | | | | | | REDUCE: (572), (582) imply:
% 25.28/4.56 | | | | | | | (583) $false
% 25.28/4.56 | | | | | | |
% 25.28/4.56 | | | | | | | CLOSE: (583) is inconsistent.
% 25.28/4.56 | | | | | | |
% 25.28/4.56 | | | | | | End of split
% 25.28/4.56 | | | | | |
% 25.28/4.56 | | | | | Case 2:
% 25.28/4.56 | | | | | |
% 25.28/4.56 | | | | | | (584) all_55_2 = 0
% 25.28/4.56 | | | | | |
% 25.28/4.56 | | | | | | COMBINE_EQS: (533), (584) imply:
% 25.28/4.56 | | | | | | (585) all_187_0 = 0
% 25.28/4.56 | | | | | |
% 25.28/4.56 | | | | | | BETA: splitting (107) gives:
% 25.28/4.56 | | | | | |
% 25.28/4.56 | | | | | | Case 1:
% 25.28/4.56 | | | | | | |
% 25.28/4.56 | | | | | | | (586) distinct_lines(all_38_1, all_38_2) = 0
% 25.28/4.56 | | | | | | |
% 25.28/4.56 | | | | | | | GROUND_INST: instantiating (28) with all_152_1, 0, all_38_2,
% 25.28/4.56 | | | | | | | all_38_1, simplifying with (224), (586) gives:
% 25.28/4.56 | | | | | | | (587) all_152_1 = 0
% 25.28/4.56 | | | | | | |
% 25.28/4.56 | | | | | | | BETA: splitting (409) gives:
% 25.28/4.56 | | | | | | |
% 25.28/4.56 | | | | | | | Case 1:
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | | (588) all_82_3 = 0
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | | REDUCE: (135), (588) imply:
% 25.28/4.56 | | | | | | | | (589) convergent_lines(all_38_1, all_38_2) = 0
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | | REF_CLOSE: (29), (33), (35), (58), (112), (589), (apart3) are
% 25.28/4.56 | | | | | | | | inconsistent by sub-proof #1.
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | Case 2:
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | | (590) ~ (all_82_3 = 0)
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | | BETA: splitting (226) gives:
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | | Case 1:
% 25.28/4.56 | | | | | | | | |
% 25.28/4.56 | | | | | | | | | (591) ~ (all_152_1 = 0)
% 25.28/4.56 | | | | | | | | |
% 25.28/4.56 | | | | | | | | | REDUCE: (587), (591) imply:
% 25.28/4.56 | | | | | | | | | (592) $false
% 25.28/4.56 | | | | | | | | |
% 25.28/4.56 | | | | | | | | | CLOSE: (592) is inconsistent.
% 25.28/4.56 | | | | | | | | |
% 25.28/4.56 | | | | | | | | Case 2:
% 25.28/4.56 | | | | | | | | |
% 25.28/4.56 | | | | | | | | | (593) all_152_0 = 0
% 25.28/4.56 | | | | | | | | |
% 25.28/4.56 | | | | | | | | | COMBINE_EQS: (401), (593) imply:
% 25.28/4.56 | | | | | | | | | (594) all_82_3 = 0
% 25.28/4.56 | | | | | | | | |
% 25.28/4.56 | | | | | | | | | REDUCE: (590), (594) imply:
% 25.28/4.56 | | | | | | | | | (595) $false
% 25.28/4.56 | | | | | | | | |
% 25.28/4.56 | | | | | | | | | CLOSE: (595) is inconsistent.
% 25.28/4.56 | | | | | | | | |
% 25.28/4.56 | | | | | | | | End of split
% 25.28/4.56 | | | | | | | |
% 25.28/4.56 | | | | | | | End of split
% 25.28/4.56 | | | | | | |
% 25.28/4.56 | | | | | | Case 2:
% 25.28/4.56 | | | | | | |
% 25.28/4.56 | | | | | | | (596) all_55_3 = 0
% 25.28/4.56 | | | | | | |
% 25.28/4.56 | | | | | | | COMBINE_EQS: (571), (596) imply:
% 25.28/4.57 | | | | | | | (597) all_187_1 = 0
% 25.28/4.57 | | | | | | |
% 25.28/4.57 | | | | | | | BETA: splitting (454) gives:
% 25.28/4.57 | | | | | | |
% 25.28/4.57 | | | | | | | Case 1:
% 25.28/4.57 | | | | | | | |
% 25.28/4.57 | | | | | | | | (598) ~ (all_187_0 = 0)
% 25.28/4.57 | | | | | | | |
% 25.28/4.57 | | | | | | | | REDUCE: (585), (598) imply:
% 25.28/4.57 | | | | | | | | (599) $false
% 25.28/4.57 | | | | | | | |
% 25.28/4.57 | | | | | | | | CLOSE: (599) is inconsistent.
% 25.28/4.57 | | | | | | | |
% 25.28/4.57 | | | | | | | Case 2:
% 25.28/4.57 | | | | | | | |
% 25.28/4.57 | | | | | | | | (600) ~ (all_187_1 = 0) | (all_187_2 = 0 & all_82_3 = 0) |
% 25.28/4.57 | | | | | | | | (all_187_3 = 0 & all_82_2 = 0)
% 25.28/4.57 | | | | | | | |
% 25.28/4.57 | | | | | | | | BETA: splitting (600) gives:
% 25.28/4.57 | | | | | | | |
% 25.28/4.57 | | | | | | | | Case 1:
% 25.28/4.57 | | | | | | | | |
% 25.28/4.57 | | | | | | | | | (601) ~ (all_187_1 = 0)
% 25.28/4.57 | | | | | | | | |
% 25.28/4.57 | | | | | | | | | REDUCE: (597), (601) imply:
% 25.28/4.57 | | | | | | | | | (602) $false
% 25.28/4.57 | | | | | | | | |
% 25.28/4.57 | | | | | | | | | CLOSE: (602) is inconsistent.
% 25.28/4.57 | | | | | | | | |
% 25.28/4.57 | | | | | | | | Case 2:
% 25.28/4.57 | | | | | | | | |
% 25.28/4.57 | | | | | | | | | (603) (all_187_2 = 0 & all_82_3 = 0) | (all_187_3 = 0 &
% 25.28/4.57 | | | | | | | | | all_82_2 = 0)
% 25.28/4.57 | | | | | | | | |
% 25.28/4.57 | | | | | | | | | BETA: splitting (603) gives:
% 25.28/4.57 | | | | | | | | |
% 25.28/4.57 | | | | | | | | | Case 1:
% 25.28/4.57 | | | | | | | | | |
% 25.28/4.57 | | | | | | | | | | (604) all_187_2 = 0 & all_82_3 = 0
% 25.28/4.57 | | | | | | | | | |
% 25.28/4.57 | | | | | | | | | | ALPHA: (604) implies:
% 25.28/4.57 | | | | | | | | | | (605) all_82_3 = 0
% 25.28/4.57 | | | | | | | | | |
% 25.28/4.57 | | | | | | | | | | REDUCE: (135), (605) imply:
% 25.28/4.57 | | | | | | | | | | (606) convergent_lines(all_38_1, all_38_2) = 0
% 25.28/4.57 | | | | | | | | | |
% 25.28/4.57 | | | | | | | | | | REF_CLOSE: (29), (33), (35), (58), (112), (606), (apart3) are
% 25.28/4.57 | | | | | | | | | | inconsistent by sub-proof #1.
% 25.28/4.57 | | | | | | | | | |
% 25.28/4.57 | | | | | | | | | Case 2:
% 25.28/4.57 | | | | | | | | | |
% 25.28/4.57 | | | | | | | | | | (607) all_187_3 = 0 & all_82_2 = 0
% 25.28/4.57 | | | | | | | | | |
% 25.28/4.57 | | | | | | | | | | ALPHA: (607) implies:
% 25.28/4.57 | | | | | | | | | | (608) all_187_3 = 0
% 25.28/4.57 | | | | | | | | | |
% 25.28/4.57 | | | | | | | | | | COMBINE_EQS: (570), (608) imply:
% 25.28/4.57 | | | | | | | | | | (609) all_82_3 = 0
% 25.28/4.57 | | | | | | | | | |
% 25.28/4.57 | | | | | | | | | | REDUCE: (135), (609) imply:
% 25.28/4.57 | | | | | | | | | | (610) convergent_lines(all_38_1, all_38_2) = 0
% 25.28/4.57 | | | | | | | | | |
% 25.28/4.57 | | | | | | | | | | REF_CLOSE: (29), (33), (35), (58), (112), (610), (apart3) are
% 25.28/4.57 | | | | | | | | | | inconsistent by sub-proof #1.
% 25.28/4.57 | | | | | | | | | |
% 25.28/4.57 | | | | | | | | | End of split
% 25.28/4.57 | | | | | | | | |
% 25.28/4.57 | | | | | | | | End of split
% 25.28/4.57 | | | | | | | |
% 25.28/4.57 | | | | | | | End of split
% 25.28/4.57 | | | | | | |
% 25.28/4.57 | | | | | | End of split
% 25.28/4.57 | | | | | |
% 25.28/4.57 | | | | | End of split
% 25.28/4.57 | | | | |
% 25.28/4.57 | | | | End of split
% 25.28/4.57 | | | |
% 25.28/4.57 | | | End of split
% 25.28/4.57 | | |
% 25.28/4.57 | | End of split
% 25.28/4.57 | |
% 25.70/4.57 | Case 2:
% 25.70/4.57 | |
% 25.70/4.57 | | (611) all_38_0 = 0
% 25.70/4.57 | |
% 25.70/4.57 | | REDUCE: (33), (611) imply:
% 25.70/4.57 | | (612) $false
% 25.70/4.57 | |
% 25.70/4.57 | | CLOSE: (612) is inconsistent.
% 25.70/4.57 | |
% 25.70/4.57 | End of split
% 25.70/4.57 |
% 25.70/4.57 End of proof
% 25.70/4.57
% 25.70/4.57 Sub-proof #1 shows that the following formulas are inconsistent:
% 25.70/4.57 ----------------------------------------------------------------
% 25.70/4.57 (1) convergent_lines(all_38_1, all_38_1) = all_53_1
% 25.70/4.57 (2) $i(all_38_1)
% 25.70/4.58 (3) ~ (all_38_0 = 0)
% 25.70/4.58 (4) convergent_lines(all_38_1, all_38_2) = 0
% 25.70/4.58 (5) ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0))
% 25.70/4.58 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 25.70/4.58 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 25.70/4.58 (convergent_lines(v3, v2) = v0))
% 25.70/4.58 (7) all_53_1 = 0 | all_38_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 25.70/4.58 convergent_lines(all_38_1, all_38_2) = v0)
% 25.70/4.58
% 25.70/4.58 Begin of proof
% 25.70/4.58 |
% 25.70/4.58 | BETA: splitting (7) gives:
% 25.70/4.58 |
% 25.70/4.58 | Case 1:
% 25.70/4.58 | |
% 25.70/4.58 | | (8) all_53_1 = 0
% 25.70/4.58 | |
% 25.70/4.58 | | REDUCE: (1), (8) imply:
% 25.70/4.58 | | (9) convergent_lines(all_38_1, all_38_1) = 0
% 25.70/4.58 | |
% 25.70/4.58 | | GROUND_INST: instantiating (5) with all_38_1, simplifying with (2), (9)
% 25.70/4.58 | | gives:
% 25.70/4.58 | | (10) $false
% 25.70/4.58 | |
% 25.70/4.58 | | CLOSE: (10) is inconsistent.
% 25.70/4.58 | |
% 25.70/4.58 | Case 2:
% 25.70/4.58 | |
% 25.70/4.58 | | (11) all_38_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 25.70/4.58 | | convergent_lines(all_38_1, all_38_2) = v0)
% 25.70/4.58 | |
% 25.70/4.58 | | BETA: splitting (11) gives:
% 25.70/4.58 | |
% 25.70/4.58 | | Case 1:
% 25.70/4.58 | | |
% 25.70/4.58 | | | (12) all_38_0 = 0
% 25.70/4.58 | | |
% 25.70/4.58 | | | REDUCE: (3), (12) imply:
% 25.70/4.58 | | | (13) $false
% 25.70/4.58 | | |
% 25.70/4.58 | | | CLOSE: (13) is inconsistent.
% 25.70/4.58 | | |
% 25.70/4.58 | | Case 2:
% 25.70/4.58 | | |
% 25.70/4.58 | | | (14) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_1, all_38_2)
% 25.70/4.58 | | | = v0)
% 25.70/4.58 | | |
% 25.70/4.58 | | | DELTA: instantiating (14) with fresh symbol all_280_0 gives:
% 25.70/4.58 | | | (15) ~ (all_280_0 = 0) & convergent_lines(all_38_1, all_38_2) =
% 25.70/4.58 | | | all_280_0
% 25.70/4.58 | | |
% 25.70/4.58 | | | ALPHA: (15) implies:
% 25.70/4.58 | | | (16) ~ (all_280_0 = 0)
% 25.70/4.58 | | | (17) convergent_lines(all_38_1, all_38_2) = all_280_0
% 25.70/4.58 | | |
% 25.70/4.58 | | | GROUND_INST: instantiating (6) with 0, all_280_0, all_38_2, all_38_1,
% 25.70/4.58 | | | simplifying with (4), (17) gives:
% 25.70/4.58 | | | (18) all_280_0 = 0
% 25.70/4.58 | | |
% 25.70/4.58 | | | REDUCE: (16), (18) imply:
% 25.70/4.58 | | | (19) $false
% 25.70/4.58 | | |
% 25.70/4.58 | | | CLOSE: (19) is inconsistent.
% 25.70/4.58 | | |
% 25.70/4.58 | | End of split
% 25.70/4.58 | |
% 25.70/4.58 | End of split
% 25.70/4.58 |
% 25.70/4.58 End of proof
% 25.70/4.58 % SZS output end Proof for theBenchmark
% 25.70/4.58
% 25.70/4.58 3979ms
%------------------------------------------------------------------------------