TSTP Solution File: GEO222+3 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO222+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 : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 23:22:31 EDT 2023
% Result : Theorem 13.65s 2.51s
% Output : Proof 34.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO222+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 22:56:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.55/0.58 ________ _____
% 0.55/0.58 ___ __ \_________(_)________________________________
% 0.55/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.55/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.55/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.55/0.58
% 0.55/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.55/0.58 (2023-06-19)
% 0.55/0.58
% 0.55/0.58 (c) Philipp Rümmer, 2009-2023
% 0.55/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.55/0.58 Amanda Stjerna.
% 0.55/0.58 Free software under BSD-3-Clause.
% 0.55/0.58
% 0.55/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.55/0.58
% 0.55/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.59/0.60 Running up to 7 provers in parallel.
% 0.59/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.59/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.59/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.59/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.59/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.59/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.59/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.04/1.11 Prover 1: Preprocessing ...
% 3.04/1.11 Prover 4: Preprocessing ...
% 3.04/1.15 Prover 5: Preprocessing ...
% 3.04/1.15 Prover 3: Preprocessing ...
% 3.04/1.15 Prover 2: Preprocessing ...
% 3.04/1.15 Prover 6: Preprocessing ...
% 3.04/1.15 Prover 0: Preprocessing ...
% 5.88/1.50 Prover 5: Proving ...
% 6.16/1.50 Prover 2: Proving ...
% 6.44/1.57 Prover 6: Constructing countermodel ...
% 6.44/1.58 Prover 3: Constructing countermodel ...
% 6.44/1.61 Prover 1: Constructing countermodel ...
% 7.16/1.68 Prover 3: gave up
% 7.16/1.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.66/1.74 Prover 7: Preprocessing ...
% 7.66/1.76 Prover 6: gave up
% 7.66/1.76 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.35/1.81 Prover 7: Warning: ignoring some quantifiers
% 8.35/1.82 Prover 8: Preprocessing ...
% 8.52/1.84 Prover 1: gave up
% 8.52/1.84 Prover 7: Constructing countermodel ...
% 8.52/1.84 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 8.52/1.84 Prover 4: Constructing countermodel ...
% 8.52/1.87 Prover 9: Preprocessing ...
% 8.52/1.91 Prover 0: Proving ...
% 9.30/1.99 Prover 8: Warning: ignoring some quantifiers
% 9.90/2.03 Prover 8: Constructing countermodel ...
% 10.86/2.16 Prover 8: gave up
% 10.86/2.18 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.86/2.20 Prover 9: Constructing countermodel ...
% 11.71/2.24 Prover 10: Preprocessing ...
% 12.27/2.33 Prover 10: Warning: ignoring some quantifiers
% 12.27/2.34 Prover 10: Constructing countermodel ...
% 12.89/2.47 Prover 10: gave up
% 13.55/2.48 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.65/2.51 Prover 0: proved (1902ms)
% 13.65/2.51
% 13.65/2.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.65/2.51
% 13.65/2.51 Prover 9: stopped
% 13.65/2.51 Prover 11: Preprocessing ...
% 13.65/2.51 Prover 5: stopped
% 13.65/2.51 Prover 2: stopped
% 13.65/2.51 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.65/2.51 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 13.65/2.51 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 13.88/2.53 Prover 13: Preprocessing ...
% 13.88/2.53 Prover 16: Preprocessing ...
% 13.88/2.56 Prover 19: Preprocessing ...
% 13.88/2.57 Prover 7: gave up
% 13.88/2.59 Prover 16: Warning: ignoring some quantifiers
% 13.88/2.59 Prover 13: Warning: ignoring some quantifiers
% 13.88/2.60 Prover 16: Constructing countermodel ...
% 13.88/2.60 Prover 13: Constructing countermodel ...
% 14.56/2.68 Prover 19: Warning: ignoring some quantifiers
% 15.15/2.69 Prover 19: Constructing countermodel ...
% 15.15/2.70 Prover 13: gave up
% 15.15/2.73 Prover 11: Constructing countermodel ...
% 15.96/2.80 Prover 19: gave up
% 16.88/2.93 Prover 16: gave up
% 32.69/5.95 Prover 11: Found proof (size 483)
% 32.69/5.95 Prover 11: proved (3467ms)
% 32.69/5.95 Prover 4: stopped
% 32.69/5.95
% 32.69/5.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.69/5.95
% 32.69/5.98 % SZS output start Proof for theBenchmark
% 32.69/5.99 Assumptions after simplification:
% 32.69/5.99 ---------------------------------
% 32.69/5.99
% 32.69/5.99 (a3)
% 33.12/6.04 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (parallel_lines(v0,
% 33.12/6.04 v1) = v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v1) = 0) & !
% 33.12/6.04 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (convergent_lines(v0, v1)
% 33.12/6.04 = v2) | ~ $i(v1) | ~ $i(v0) | parallel_lines(v0, v1) = 0) & ! [v0: $i]
% 33.12/6.04 : ! [v1: $i] : ( ~ (parallel_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 33.12/6.04 [v2: int] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) & ! [v0: $i] :
% 33.12/6.04 ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 33.12/6.04 [v2: int] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 33.12/6.04
% 33.12/6.04 (ax6)
% 33.12/6.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 33.12/6.05 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0,
% 33.12/6.05 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 =
% 33.12/6.05 0) & convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : !
% 33.12/6.05 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~
% 33.12/6.05 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 33.12/6.05 convergent_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 33.12/6.05 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~
% 33.12/6.05 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 33.12/6.05 convergent_lines(v1, v2) = 0)
% 33.12/6.05
% 33.12/6.05 (coipo1)
% 33.12/6.05 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 33.12/6.05 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 33.12/6.05 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] :
% 33.12/6.05 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 33.12/6.05 unorthogonal_lines(v0, v1) = 0)
% 33.12/6.05
% 33.12/6.05 (con)
% 33.12/6.05 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 33.12/6.05 = 0) & parallel_lines(v1, v3) = v4 & orthogonal_through_point(v2, v0) = v3
% 33.12/6.05 & orthogonal_through_point(v1, v0) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 33.12/6.05
% 33.12/6.05 (cotno1)
% 33.12/6.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 33.12/6.08 (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) |
% 33.12/6.08 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7:
% 33.12/6.08 int] : ? [v8: int] : ((v6 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) |
% 33.12/6.08 (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) &
% 33.12/6.08 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1,
% 33.12/6.08 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] :
% 33.12/6.08 ! [v4: any] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~
% 33.12/6.08 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 33.12/6.08 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 &
% 33.12/6.08 convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 &
% 33.12/6.08 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1,
% 33.12/6.08 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0:
% 33.12/6.08 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 33.12/6.08 (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ~
% 33.12/6.08 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int]
% 33.12/6.08 : ? [v8: int] : ((v6 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 =
% 33.12/6.08 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) &
% 33.12/6.08 unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1,
% 33.12/6.08 v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] :
% 33.12/6.08 ! [v4: any] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0,
% 33.12/6.08 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 33.12/6.08 int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 &
% 33.12/6.08 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 &
% 33.12/6.08 unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v1,
% 33.12/6.08 v2) = v8) | ( ~ (v7 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0:
% 33.12/6.08 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1,
% 33.12/6.08 v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 33.12/6.08 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] :
% 33.12/6.08 ((v6 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 &
% 33.12/6.08 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7
% 33.12/6.08 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] :
% 33.12/6.08 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~
% 33.12/6.08 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 33.12/6.08 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 &
% 33.12/6.08 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0
% 33.12/6.08 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) &
% 33.12/6.08 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 33.12/6.08 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~
% 33.12/6.08 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 33.12/6.08 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 &
% 33.12/6.08 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 &
% 33.12/6.08 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7
% 33.12/6.08 = 0) & convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] :
% 33.12/6.08 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~
% 33.12/6.08 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 33.12/6.08 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 &
% 33.12/6.08 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0
% 33.12/6.08 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) &
% 33.12/6.08 convergent_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 33.12/6.08 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~
% 33.12/6.08 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 33.12/6.08 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 &
% 33.12/6.08 convergent_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 &
% 33.12/6.08 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7
% 33.12/6.08 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i]
% 33.12/6.08 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~
% 33.12/6.08 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 33.12/6.08 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 &
% 33.12/6.08 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0
% 33.12/6.08 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) &
% 33.12/6.08 unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 33.12/6.08 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~
% 33.12/6.08 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 33.12/6.08 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 &
% 33.12/6.08 unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 &
% 33.12/6.08 unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7
% 33.12/6.08 = 0) & unorthogonal_lines(v1, v2) = v7))) & ! [v0: $i] : ! [v1: $i]
% 33.12/6.08 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = 0) | ~
% 33.12/6.08 (convergent_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 33.12/6.08 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 &
% 33.12/6.08 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0
% 33.12/6.08 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) &
% 33.12/6.08 unorthogonal_lines(v1, v2) = v7)))
% 33.12/6.08
% 33.12/6.08 (couo1)
% 33.57/6.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 33.57/6.08 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~
% 33.57/6.08 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 33.57/6.08 [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0: $i] :
% 33.57/6.08 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0,
% 33.57/6.08 v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) |
% 33.57/6.08 ~ $i(v0) | unorthogonal_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : !
% 33.57/6.08 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~
% 33.57/6.08 (convergent_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 33.57/6.08 unorthogonal_lines(v0, v2) = 0)
% 33.57/6.08
% 33.57/6.08 (oac1)
% 33.60/6.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 33.60/6.10 (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) |
% 33.60/6.10 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7:
% 33.60/6.10 int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) |
% 33.60/6.10 (v7 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 33.60/6.10 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0,
% 33.60/6.10 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] :
% 33.60/6.10 ! [v4: any] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~
% 33.60/6.10 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 33.60/6.10 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 33.60/6.10 convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 33.60/6.10 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0,
% 33.60/6.10 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0:
% 33.60/6.10 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~
% 33.60/6.10 (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ~
% 33.60/6.10 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int]
% 33.60/6.10 : ? [v8: int] : ((v8 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v7 =
% 33.60/6.10 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 33.60/6.10 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0,
% 33.60/6.10 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] :
% 33.60/6.10 ! [v4: any] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0,
% 33.60/6.10 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 33.60/6.10 int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 33.60/6.10 unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 33.60/6.10 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0,
% 33.60/6.10 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0:
% 33.60/6.10 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1,
% 33.60/6.10 v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1)
% 33.60/6.10 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] :
% 33.60/6.10 ((v7 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 33.60/6.10 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 33.60/6.10 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] :
% 33.60/6.10 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~
% 33.60/6.10 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 33.60/6.10 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 33.60/6.10 convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 33.60/6.10 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 33.60/6.10 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i]
% 33.60/6.10 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~
% 33.60/6.10 (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 33.60/6.10 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 33.60/6.10 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 33.60/6.10 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 33.60/6.10 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 33.60/6.10 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~
% 33.60/6.10 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 33.60/6.10 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 33.60/6.10 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 33.60/6.10 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 33.60/6.10 unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 33.60/6.10 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~
% 33.60/6.10 (convergent_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 33.60/6.10 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 33.60/6.10 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 33.60/6.10 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 33.60/6.10 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] :
% 33.60/6.10 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~
% 33.60/6.10 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 33.60/6.10 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 33.60/6.10 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 33.60/6.10 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 33.60/6.10 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 33.60/6.10 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = v3) | ~
% 33.60/6.10 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 33.60/6.10 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 33.60/6.10 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 33.60/6.10 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4
% 33.60/6.10 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i]
% 33.60/6.10 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v0, v2) = v3) | ~
% 33.60/6.10 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 33.60/6.10 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 33.60/6.10 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0
% 33.60/6.10 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 33.60/6.10 unorthogonal_lines(v0, v1) = v4)))
% 33.60/6.10
% 33.60/6.10 (occu1)
% 33.60/6.10 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 33.60/6.10 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 33.60/6.10 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] :
% 33.60/6.10 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 33.60/6.10 unorthogonal_lines(v0, v1) = 0)
% 33.60/6.10
% 33.60/6.10 (ooc1)
% 33.66/6.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (orthogonal_through_point(v1,
% 33.66/6.10 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 33.66/6.10 unorthogonal_lines(v2, v1) = v3))
% 33.66/6.10
% 33.66/6.10 (ooc2)
% 33.66/6.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (orthogonal_through_point(v1,
% 33.66/6.10 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 33.66/6.10 apart_point_and_line(v0, v2) = v3))
% 33.66/6.10
% 33.66/6.10 (ouo1)
% 33.66/6.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 33.66/6.11 int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~
% 33.66/6.11 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ~
% 33.66/6.11 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 33.66/6.11 ((v7 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 &
% 33.66/6.11 apart_point_and_line(v0, v1) = 0))) & ! [v0: $i] : ! [v1: $i] : !
% 33.66/6.11 [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 33.66/6.11 (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) |
% 33.66/6.11 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int]
% 33.66/6.11 : ? [v8: int] : ((v8 = 0 & unorthogonal_lines(v1, v3) = 0) | (v7 = 0 &
% 33.66/6.11 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1,
% 33.66/6.11 v2) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 33.66/6.11 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3)
% 33.66/6.11 = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) |
% 33.66/6.11 ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0
% 33.66/6.11 & unorthogonal_lines(v2, v3) = 0) | (v7 = 0 & apart_point_and_line(v0,
% 33.66/6.11 v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0: $i]
% 33.66/6.11 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5
% 33.66/6.11 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~
% 33.66/6.11 (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ~
% 33.66/6.11 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 33.66/6.11 ((v7 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 &
% 33.66/6.11 apart_point_and_line(v0, v2) = 0)))
% 33.66/6.11
% 33.66/6.11 (function-axioms)
% 33.66/6.12 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 33.66/6.12 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~
% 33.66/6.12 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.66/6.12 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 33.66/6.12 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2)
% 33.66/6.12 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 33.66/6.12 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~
% 33.66/6.12 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.66/6.12 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 33.66/6.12 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0:
% 33.66/6.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 33.66/6.12 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 33.66/6.12 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 33.66/6.12 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 33.66/6.12 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 33.66/6.12 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 33.66/6.12 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 33.66/6.12 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 33.66/6.12 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 33.66/6.12 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 33.66/6.12 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 33.66/6.12 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 33.66/6.12 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.66/6.12 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 33.66/6.12 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 33.66/6.12 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 33.66/6.12 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 33.66/6.12 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.66/6.12 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 33.66/6.12 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 33.66/6.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 33.66/6.12 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 33.66/6.12 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 33.66/6.12 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0:
% 33.66/6.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 33.66/6.12 ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 33.66/6.12
% 33.66/6.12 Further assumptions not needed in the proof:
% 33.66/6.12 --------------------------------------------
% 33.66/6.12 a4, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ceq1, ceq2, ceq3, ci1,
% 33.66/6.12 ci2, ci3, ci4, con1, cp1, cp2, cu1, cup1, int1, orth1, p1, par1
% 33.66/6.12
% 33.66/6.12 Those formulas are unsatisfiable:
% 33.66/6.12 ---------------------------------
% 33.66/6.12
% 33.66/6.12 Begin of proof
% 33.66/6.12 |
% 33.66/6.12 | ALPHA: (ax6) implies:
% 33.66/6.12 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 33.66/6.12 | (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) |
% 33.66/6.12 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v1, v2) = 0)
% 33.66/6.12 |
% 33.66/6.12 | ALPHA: (oac1) implies:
% 33.74/6.12 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 33.74/6.12 | (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3)
% 33.74/6.12 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] :
% 33.74/6.12 | ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 &
% 33.74/6.12 | unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) |
% 33.74/6.12 | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) &
% 33.74/6.12 | convergent_lines(v0, v1) = v4)))
% 33.74/6.12 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 33.74/6.12 | (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3)
% 33.74/6.12 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] :
% 33.74/6.12 | ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 33.74/6.12 | unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 33.74/6.12 | unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) |
% 33.74/6.12 | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 33.74/6.12 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 33.74/6.12 | (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) =
% 33.74/6.13 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5:
% 33.74/6.13 | int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 &
% 33.74/6.13 | convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 &
% 33.74/6.13 | unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) |
% 33.74/6.13 | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 33.74/6.13 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] :
% 33.74/6.13 | ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2)
% 33.74/6.13 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 33.74/6.13 | int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 &
% 33.74/6.13 | convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 &
% 33.74/6.13 | convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) &
% 33.74/6.13 | unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) &
% 33.74/6.13 | convergent_lines(v0, v1) = v5)))
% 33.74/6.13 |
% 33.74/6.13 | ALPHA: (ouo1) implies:
% 33.74/6.13 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 33.74/6.13 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) |
% 33.74/6.13 | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 33.74/6.13 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] :
% 33.74/6.13 | ((v8 = 0 & unorthogonal_lines(v2, v3) = 0) | (v7 = 0 &
% 33.74/6.13 | apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) &
% 33.74/6.13 | distinct_lines(v1, v2) = v6)))
% 33.74/6.13 |
% 33.74/6.13 | ALPHA: (occu1) implies:
% 33.74/6.13 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 33.74/6.13 | (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 33.74/6.13 | convergent_lines(v0, v1) = 0)
% 33.74/6.13 |
% 33.74/6.13 | ALPHA: (cotno1) implies:
% 33.74/6.13 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 33.74/6.13 | (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) |
% 33.74/6.13 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ?
% 33.74/6.13 | [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 & unorthogonal_lines(v0,
% 33.74/6.13 | v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 &
% 33.74/6.13 | unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0) &
% 33.74/6.13 | unorthogonal_lines(v1, v2) = v7)))
% 33.74/6.13 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 33.74/6.13 | (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) |
% 33.74/6.13 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ?
% 33.74/6.13 | [v6: int] : ? [v7: int] : ((v6 = 0 & v3 = 0 & unorthogonal_lines(v0,
% 33.74/6.13 | v2) = 0) | (v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 &
% 33.74/6.13 | convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) &
% 33.74/6.13 | unorthogonal_lines(v1, v2) = v7)))
% 33.74/6.13 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 33.74/6.13 | (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) =
% 33.74/6.13 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5:
% 33.74/6.13 | int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 &
% 33.74/6.13 | unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) |
% 33.74/6.13 | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) &
% 33.74/6.13 | unorthogonal_lines(v1, v2) = v7)))
% 33.74/6.13 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 33.74/6.13 | (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) =
% 33.74/6.13 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5:
% 33.74/6.13 | int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 &
% 33.74/6.13 | unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) |
% 33.74/6.13 | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v7 = 0)
% 33.74/6.13 | & convergent_lines(v1, v2) = v7)))
% 33.74/6.13 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 33.74/6.13 | (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) =
% 33.74/6.13 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5:
% 33.74/6.13 | int] : ? [v6: int] : ? [v7: int] : ((v6 = 0 & v5 = 0 &
% 33.74/6.13 | unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) |
% 33.74/6.13 | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v7 = 0) &
% 33.74/6.13 | convergent_lines(v1, v2) = v7)))
% 33.74/6.14 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any]
% 33.74/6.14 | : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) =
% 33.74/6.14 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 33.74/6.14 | int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 &
% 33.74/6.14 | unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 &
% 33.74/6.14 | unorthogonal_lines(v0, v1) = 0) | ( ~ (v8 = 0) &
% 33.74/6.14 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) &
% 33.74/6.14 | convergent_lines(v1, v2) = v7)))
% 33.74/6.14 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any]
% 33.74/6.14 | : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2)
% 33.74/6.14 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 33.74/6.14 | int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 &
% 33.74/6.14 | unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 &
% 33.74/6.14 | convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) &
% 33.74/6.14 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) &
% 33.74/6.14 | convergent_lines(v1, v2) = v7)))
% 33.74/6.14 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any]
% 33.74/6.14 | : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0,
% 33.74/6.14 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] :
% 33.74/6.14 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v6 = 0 & v4 = 0 &
% 33.74/6.14 | convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 &
% 33.74/6.14 | convergent_lines(v0, v1) = 0) | ( ~ (v8 = 0) &
% 33.74/6.14 | unorthogonal_lines(v1, v2) = v8) | ( ~ (v7 = 0) &
% 33.74/6.14 | convergent_lines(v1, v2) = v7)))
% 33.74/6.14 |
% 33.74/6.14 | ALPHA: (couo1) implies:
% 33.74/6.14 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 33.74/6.14 | (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) =
% 33.74/6.14 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | unorthogonal_lines(v0,
% 33.74/6.14 | v2) = 0)
% 33.74/6.14 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 33.74/6.14 | (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) =
% 33.74/6.14 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | unorthogonal_lines(v0,
% 33.74/6.14 | v1) = 0)
% 33.74/6.14 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int]
% 33.74/6.14 | : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~
% 33.74/6.14 | (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 33.74/6.14 | $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) =
% 33.74/6.14 | v5))
% 33.74/6.14 |
% 33.74/6.14 | ALPHA: (a3) implies:
% 33.74/6.14 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 33.74/6.14 | (parallel_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 33.74/6.14 | convergent_lines(v0, v1) = 0)
% 33.74/6.14 |
% 33.74/6.14 | ALPHA: (function-axioms) implies:
% 33.74/6.14 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 33.74/6.14 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 33.74/6.14 | (convergent_lines(v3, v2) = v0))
% 33.74/6.14 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 33.74/6.14 | : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 33.74/6.14 | (unorthogonal_lines(v3, v2) = v0))
% 33.74/6.14 |
% 33.74/6.14 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2,
% 33.74/6.14 | all_38_3, all_38_4 gives:
% 33.74/6.14 | (22) ~ (all_38_0 = 0) & parallel_lines(all_38_3, all_38_1) = all_38_0 &
% 33.74/6.14 | orthogonal_through_point(all_38_2, all_38_4) = all_38_1 &
% 33.74/6.14 | orthogonal_through_point(all_38_3, all_38_4) = all_38_2 & $i(all_38_1)
% 33.74/6.14 | & $i(all_38_2) & $i(all_38_3) & $i(all_38_4)
% 33.74/6.14 |
% 33.74/6.14 | ALPHA: (22) implies:
% 33.74/6.14 | (23) ~ (all_38_0 = 0)
% 33.74/6.14 | (24) $i(all_38_4)
% 33.74/6.14 | (25) $i(all_38_3)
% 33.74/6.14 | (26) $i(all_38_2)
% 33.74/6.14 | (27) $i(all_38_1)
% 33.74/6.14 | (28) orthogonal_through_point(all_38_3, all_38_4) = all_38_2
% 33.74/6.14 | (29) orthogonal_through_point(all_38_2, all_38_4) = all_38_1
% 33.74/6.14 | (30) parallel_lines(all_38_3, all_38_1) = all_38_0
% 33.74/6.14 |
% 33.74/6.15 | GROUND_INST: instantiating (ooc1) with all_38_4, all_38_3, all_38_2,
% 33.74/6.15 | simplifying with (24), (25), (28) gives:
% 33.74/6.15 | (31) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_38_2, all_38_3) =
% 33.74/6.15 | v0)
% 33.74/6.15 |
% 33.74/6.15 | GROUND_INST: instantiating (ooc1) with all_38_4, all_38_2, all_38_1,
% 33.74/6.15 | simplifying with (24), (26), (29) gives:
% 33.74/6.15 | (32) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_38_1, all_38_2) =
% 33.74/6.15 | v0)
% 33.74/6.15 |
% 33.74/6.15 | GROUND_INST: instantiating (ooc2) with all_38_4, all_38_2, all_38_1,
% 33.74/6.15 | simplifying with (24), (26), (29) gives:
% 33.74/6.15 | (33) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_4, all_38_1)
% 33.74/6.15 | = v0)
% 33.74/6.15 |
% 33.74/6.15 | GROUND_INST: instantiating (19) with all_38_3, all_38_1, all_38_0, simplifying
% 33.74/6.15 | with (25), (27), (30) gives:
% 33.74/6.15 | (34) all_38_0 = 0 | convergent_lines(all_38_3, all_38_1) = 0
% 33.74/6.15 |
% 33.74/6.15 | DELTA: instantiating (33) with fresh symbol all_45_0 gives:
% 33.74/6.15 | (35) ~ (all_45_0 = 0) & apart_point_and_line(all_38_4, all_38_1) =
% 33.74/6.15 | all_45_0
% 33.74/6.15 |
% 33.74/6.15 | ALPHA: (35) implies:
% 33.74/6.15 | (36) ~ (all_45_0 = 0)
% 33.74/6.15 | (37) apart_point_and_line(all_38_4, all_38_1) = all_45_0
% 33.74/6.15 |
% 33.74/6.15 | DELTA: instantiating (32) with fresh symbol all_47_0 gives:
% 33.74/6.15 | (38) ~ (all_47_0 = 0) & unorthogonal_lines(all_38_1, all_38_2) = all_47_0
% 33.74/6.15 |
% 33.74/6.15 | ALPHA: (38) implies:
% 33.74/6.15 | (39) ~ (all_47_0 = 0)
% 33.74/6.15 | (40) unorthogonal_lines(all_38_1, all_38_2) = all_47_0
% 33.74/6.15 |
% 33.74/6.15 | DELTA: instantiating (31) with fresh symbol all_51_0 gives:
% 33.74/6.15 | (41) ~ (all_51_0 = 0) & unorthogonal_lines(all_38_2, all_38_3) = all_51_0
% 33.74/6.15 |
% 33.74/6.15 | ALPHA: (41) implies:
% 33.74/6.15 | (42) ~ (all_51_0 = 0)
% 33.74/6.15 | (43) unorthogonal_lines(all_38_2, all_38_3) = all_51_0
% 33.74/6.15 |
% 33.74/6.15 | BETA: splitting (34) gives:
% 33.74/6.15 |
% 33.74/6.15 | Case 1:
% 33.74/6.15 | |
% 33.74/6.15 | | (44) convergent_lines(all_38_3, all_38_1) = 0
% 33.74/6.15 | |
% 33.74/6.15 | | GROUND_INST: instantiating (9) with all_38_3, all_38_3, all_38_1, 0,
% 33.74/6.15 | | simplifying with (25), (27), (44) gives:
% 33.74/6.15 | | (45) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v2 = 0
% 33.74/6.15 | | & unorthogonal_lines(all_38_3, all_38_1) = 0) | (v1 = 0 & v0 = 0
% 33.74/6.15 | | & unorthogonal_lines(all_38_3, all_38_3) = 0 &
% 33.74/6.15 | | convergent_lines(all_38_3, all_38_3) = 0) | ( ~ (v3 = 0) &
% 33.74/6.15 | | unorthogonal_lines(all_38_3, all_38_1) = v3))
% 33.74/6.15 | |
% 33.74/6.15 | | GROUND_INST: instantiating (13) with all_38_3, all_38_1, all_38_1, 0, 0,
% 33.74/6.15 | | simplifying with (25), (27), (44) gives:
% 33.74/6.15 | | (46) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v1 = 0
% 33.74/6.15 | | & unorthogonal_lines(all_38_3, all_38_1) = 0) | (v0 = 0 &
% 33.74/6.15 | | unorthogonal_lines(all_38_3, all_38_1) = 0) | ( ~ (v3 = 0) &
% 33.74/6.15 | | unorthogonal_lines(all_38_1, all_38_1) = v3) | ( ~ (v2 = 0) &
% 33.74/6.15 | | convergent_lines(all_38_1, all_38_1) = v2))
% 33.74/6.15 | |
% 33.74/6.15 | | GROUND_INST: instantiating (6) with all_38_4, all_38_2, all_38_1, all_38_3,
% 33.74/6.15 | | all_45_0, all_51_0, simplifying with (24), (25), (26), (27),
% 33.74/6.15 | | (37), (43) gives:
% 33.74/6.15 | | (47) all_51_0 = 0 | all_45_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2:
% 33.74/6.15 | | int] : ((v2 = 0 & unorthogonal_lines(all_38_1, all_38_3) = 0) |
% 33.74/6.15 | | (v1 = 0 & apart_point_and_line(all_38_4, all_38_2) = 0) | ( ~ (v0
% 33.74/6.15 | | = 0) & distinct_lines(all_38_2, all_38_1) = v0))
% 33.74/6.15 | |
% 33.74/6.15 | | GROUND_INST: instantiating (18) with all_38_2, all_38_3, all_38_3, all_51_0,
% 33.74/6.15 | | all_51_0, simplifying with (25), (26), (43) gives:
% 33.74/6.15 | | (48) all_51_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 33.74/6.15 | | convergent_lines(all_38_3, all_38_3) = v0)
% 33.74/6.15 | |
% 33.74/6.15 | | GROUND_INST: instantiating (15) with all_38_2, all_38_3, all_38_3, all_51_0,
% 33.74/6.15 | | all_51_0, simplifying with (25), (26), (43) gives:
% 33.74/6.15 | | (49) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v1 = 0
% 33.74/6.15 | | & all_51_0 = 0 & convergent_lines(all_38_2, all_38_3) = 0) | (v0
% 33.74/6.15 | | = 0 & all_51_0 = 0 & convergent_lines(all_38_2, all_38_3) = 0) |
% 33.74/6.15 | | ( ~ (v3 = 0) & unorthogonal_lines(all_38_3, all_38_3) = v3) | ( ~
% 33.74/6.15 | | (v2 = 0) & convergent_lines(all_38_3, all_38_3) = v2))
% 33.74/6.15 | |
% 33.74/6.15 | | GROUND_INST: instantiating (5) with all_38_2, all_38_2, all_38_3, all_51_0,
% 33.74/6.15 | | all_51_0, simplifying with (25), (26), (43) gives:
% 33.74/6.15 | | (50) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0
% 33.74/6.15 | | & all_51_0 = 0 & convergent_lines(all_38_2, all_38_3) = 0) | (v2
% 33.74/6.15 | | = 0 & all_51_0 = 0 & convergent_lines(all_38_2, all_38_3) = 0) |
% 33.74/6.15 | | ( ~ (v1 = 0) & unorthogonal_lines(all_38_2, all_38_2) = v1) | ( ~
% 33.74/6.15 | | (v0 = 0) & convergent_lines(all_38_2, all_38_2) = v0))
% 33.74/6.15 | |
% 33.74/6.16 | | GROUND_INST: instantiating (16) with all_38_2, all_38_3, all_38_1, all_51_0,
% 33.74/6.16 | | simplifying with (25), (26), (27), (43), (44) gives:
% 33.74/6.16 | | (51) all_51_0 = 0 | unorthogonal_lines(all_38_2, all_38_1) = 0
% 33.74/6.16 | |
% 33.74/6.16 | | GROUND_INST: instantiating (10) with all_38_2, all_38_3, all_38_1, all_51_0,
% 33.74/6.16 | | simplifying with (25), (26), (27), (43), (44) gives:
% 33.74/6.16 | | (52) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v2 = 0
% 33.74/6.16 | | & v1 = 0 & unorthogonal_lines(all_38_2, all_38_1) = 0 &
% 33.74/6.16 | | convergent_lines(all_38_2, all_38_1) = 0) | (v0 = 0 & all_51_0 =
% 33.74/6.16 | | 0 & convergent_lines(all_38_2, all_38_3) = 0) | ( ~ (v3 = 0) &
% 33.74/6.16 | | unorthogonal_lines(all_38_3, all_38_1) = v3))
% 33.74/6.16 | |
% 33.74/6.16 | | GROUND_INST: instantiating (7) with all_38_2, all_38_3, all_51_0,
% 33.74/6.16 | | simplifying with (25), (26), (43) gives:
% 33.74/6.16 | | (53) all_51_0 = 0 | convergent_lines(all_38_2, all_38_3) = 0
% 33.74/6.16 | |
% 33.74/6.16 | | GROUND_INST: instantiating (18) with all_38_1, all_38_2, all_38_2, all_47_0,
% 33.74/6.16 | | all_47_0, simplifying with (26), (27), (40) gives:
% 33.74/6.16 | | (54) all_47_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 33.74/6.16 | | convergent_lines(all_38_2, all_38_2) = v0)
% 33.74/6.16 | |
% 33.74/6.16 | | GROUND_INST: instantiating (5) with all_38_1, all_38_1, all_38_2, all_47_0,
% 33.74/6.16 | | all_47_0, simplifying with (26), (27), (40) gives:
% 33.74/6.16 | | (55) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0
% 33.74/6.16 | | & all_47_0 = 0 & convergent_lines(all_38_1, all_38_2) = 0) | (v2
% 33.74/6.16 | | = 0 & all_47_0 = 0 & convergent_lines(all_38_1, all_38_2) = 0) |
% 33.74/6.16 | | ( ~ (v1 = 0) & unorthogonal_lines(all_38_1, all_38_1) = v1) | ( ~
% 33.74/6.16 | | (v0 = 0) & convergent_lines(all_38_1, all_38_1) = v0))
% 33.74/6.16 | |
% 33.74/6.16 | | GROUND_INST: instantiating (7) with all_38_1, all_38_2, all_47_0,
% 33.74/6.16 | | simplifying with (26), (27), (40) gives:
% 33.74/6.16 | | (56) all_47_0 = 0 | convergent_lines(all_38_1, all_38_2) = 0
% 33.74/6.16 | |
% 33.74/6.16 | | DELTA: instantiating (45) with fresh symbols all_69_0, all_69_1, all_69_2,
% 33.74/6.16 | | all_69_3 gives:
% 33.74/6.16 | | (57) (all_69_1 = 0 & unorthogonal_lines(all_38_3, all_38_1) = 0) |
% 33.74/6.16 | | (all_69_2 = 0 & all_69_3 = 0 & unorthogonal_lines(all_38_3,
% 33.74/6.16 | | all_38_3) = 0 & convergent_lines(all_38_3, all_38_3) = 0) | ( ~
% 33.74/6.16 | | (all_69_0 = 0) & unorthogonal_lines(all_38_3, all_38_1) =
% 33.74/6.16 | | all_69_0)
% 33.74/6.16 | |
% 33.74/6.16 | | DELTA: instantiating (46) with fresh symbols all_71_0, all_71_1, all_71_2,
% 33.74/6.16 | | all_71_3 gives:
% 33.74/6.16 | | (58) (all_71_2 = 0 & unorthogonal_lines(all_38_3, all_38_1) = 0) |
% 33.74/6.16 | | (all_71_3 = 0 & unorthogonal_lines(all_38_3, all_38_1) = 0) | ( ~
% 33.74/6.16 | | (all_71_0 = 0) & unorthogonal_lines(all_38_1, all_38_1) =
% 33.74/6.16 | | all_71_0) | ( ~ (all_71_1 = 0) & convergent_lines(all_38_1,
% 33.74/6.16 | | all_38_1) = all_71_1)
% 33.74/6.16 | |
% 33.74/6.16 | | DELTA: instantiating (52) with fresh symbols all_73_0, all_73_1, all_73_2,
% 33.74/6.16 | | all_73_3 gives:
% 33.74/6.16 | | (59) (all_73_1 = 0 & all_73_2 = 0 & unorthogonal_lines(all_38_2,
% 33.74/6.16 | | all_38_1) = 0 & convergent_lines(all_38_2, all_38_1) = 0) |
% 33.74/6.16 | | (all_73_3 = 0 & all_51_0 = 0 & convergent_lines(all_38_2, all_38_3)
% 33.74/6.16 | | = 0) | ( ~ (all_73_0 = 0) & unorthogonal_lines(all_38_3, all_38_1)
% 33.74/6.16 | | = all_73_0)
% 33.74/6.16 | |
% 33.74/6.16 | | DELTA: instantiating (50) with fresh symbols all_75_0, all_75_1, all_75_2,
% 33.74/6.16 | | all_75_3 gives:
% 33.74/6.16 | | (60) (all_75_0 = 0 & all_51_0 = 0 & convergent_lines(all_38_2, all_38_3)
% 33.74/6.16 | | = 0) | (all_75_1 = 0 & all_51_0 = 0 & convergent_lines(all_38_2,
% 33.74/6.16 | | all_38_3) = 0) | ( ~ (all_75_2 = 0) &
% 33.74/6.16 | | unorthogonal_lines(all_38_2, all_38_2) = all_75_2) | ( ~ (all_75_3
% 33.74/6.16 | | = 0) & convergent_lines(all_38_2, all_38_2) = all_75_3)
% 33.74/6.16 | |
% 33.74/6.16 | | DELTA: instantiating (49) with fresh symbols all_76_0, all_76_1, all_76_2,
% 33.74/6.16 | | all_76_3 gives:
% 33.74/6.16 | | (61) (all_76_2 = 0 & all_51_0 = 0 & convergent_lines(all_38_2, all_38_3)
% 33.74/6.16 | | = 0) | (all_76_3 = 0 & all_51_0 = 0 & convergent_lines(all_38_2,
% 33.74/6.16 | | all_38_3) = 0) | ( ~ (all_76_0 = 0) &
% 33.74/6.16 | | unorthogonal_lines(all_38_3, all_38_3) = all_76_0) | ( ~ (all_76_1
% 33.74/6.16 | | = 0) & convergent_lines(all_38_3, all_38_3) = all_76_1)
% 33.74/6.16 | |
% 33.74/6.16 | | DELTA: instantiating (55) with fresh symbols all_77_0, all_77_1, all_77_2,
% 33.74/6.16 | | all_77_3 gives:
% 33.74/6.16 | | (62) (all_77_0 = 0 & all_47_0 = 0 & convergent_lines(all_38_1, all_38_2)
% 33.74/6.16 | | = 0) | (all_77_1 = 0 & all_47_0 = 0 & convergent_lines(all_38_1,
% 33.74/6.16 | | all_38_2) = 0) | ( ~ (all_77_2 = 0) &
% 33.74/6.16 | | unorthogonal_lines(all_38_1, all_38_1) = all_77_2) | ( ~ (all_77_3
% 33.74/6.16 | | = 0) & convergent_lines(all_38_1, all_38_1) = all_77_3)
% 33.74/6.16 | |
% 33.74/6.16 | | BETA: splitting (51) gives:
% 33.74/6.16 | |
% 33.74/6.16 | | Case 1:
% 33.74/6.16 | | |
% 33.74/6.16 | | | (63) unorthogonal_lines(all_38_2, all_38_1) = 0
% 33.74/6.16 | | |
% 33.74/6.16 | | | BETA: splitting (53) gives:
% 33.74/6.16 | | |
% 33.74/6.16 | | | Case 1:
% 33.74/6.16 | | | |
% 33.74/6.16 | | | | (64) convergent_lines(all_38_2, all_38_3) = 0
% 33.74/6.16 | | | |
% 33.74/6.16 | | | | BETA: splitting (56) gives:
% 33.74/6.16 | | | |
% 33.74/6.16 | | | | Case 1:
% 33.74/6.16 | | | | |
% 33.74/6.16 | | | | | (65) convergent_lines(all_38_1, all_38_2) = 0
% 33.74/6.16 | | | | |
% 33.74/6.16 | | | | | BETA: splitting (48) gives:
% 33.74/6.16 | | | | |
% 33.74/6.16 | | | | | Case 1:
% 33.74/6.16 | | | | | |
% 33.74/6.16 | | | | | | (66) all_51_0 = 0
% 33.74/6.16 | | | | | |
% 33.74/6.16 | | | | | | REDUCE: (42), (66) imply:
% 33.74/6.16 | | | | | | (67) $false
% 33.74/6.16 | | | | | |
% 33.74/6.16 | | | | | | CLOSE: (67) is inconsistent.
% 33.74/6.16 | | | | | |
% 33.74/6.16 | | | | | Case 2:
% 33.74/6.16 | | | | | |
% 33.74/6.16 | | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_3,
% 33.74/6.16 | | | | | | all_38_3) = v0)
% 33.74/6.16 | | | | | |
% 33.74/6.16 | | | | | | DELTA: instantiating (68) with fresh symbol all_102_0 gives:
% 33.74/6.16 | | | | | | (69) ~ (all_102_0 = 0) & convergent_lines(all_38_3, all_38_3) =
% 33.74/6.16 | | | | | | all_102_0
% 33.74/6.16 | | | | | |
% 33.74/6.16 | | | | | | ALPHA: (69) implies:
% 33.74/6.17 | | | | | | (70) ~ (all_102_0 = 0)
% 33.74/6.17 | | | | | | (71) convergent_lines(all_38_3, all_38_3) = all_102_0
% 33.74/6.17 | | | | | |
% 33.74/6.17 | | | | | | BETA: splitting (54) gives:
% 33.74/6.17 | | | | | |
% 33.74/6.17 | | | | | | Case 1:
% 33.74/6.17 | | | | | | |
% 33.74/6.17 | | | | | | | (72) all_47_0 = 0
% 33.74/6.17 | | | | | | |
% 33.74/6.17 | | | | | | | REDUCE: (39), (72) imply:
% 33.74/6.17 | | | | | | | (73) $false
% 33.74/6.17 | | | | | | |
% 33.74/6.17 | | | | | | | CLOSE: (73) is inconsistent.
% 33.74/6.17 | | | | | | |
% 33.74/6.17 | | | | | | Case 2:
% 33.74/6.17 | | | | | | |
% 33.74/6.17 | | | | | | | (74) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_2,
% 33.74/6.17 | | | | | | | all_38_2) = v0)
% 33.74/6.17 | | | | | | |
% 33.74/6.17 | | | | | | | DELTA: instantiating (74) with fresh symbol all_107_0 gives:
% 33.74/6.17 | | | | | | | (75) ~ (all_107_0 = 0) & convergent_lines(all_38_2, all_38_2)
% 33.74/6.17 | | | | | | | = all_107_0
% 33.74/6.17 | | | | | | |
% 33.74/6.17 | | | | | | | ALPHA: (75) implies:
% 33.74/6.17 | | | | | | | (76) ~ (all_107_0 = 0)
% 33.74/6.17 | | | | | | | (77) convergent_lines(all_38_2, all_38_2) = all_107_0
% 33.74/6.17 | | | | | | |
% 33.74/6.17 | | | | | | | BETA: splitting (47) gives:
% 33.74/6.17 | | | | | | |
% 33.74/6.17 | | | | | | | Case 1:
% 33.74/6.17 | | | | | | | |
% 33.74/6.17 | | | | | | | | (78) all_51_0 = 0
% 33.74/6.17 | | | | | | | |
% 33.74/6.17 | | | | | | | | REDUCE: (42), (78) imply:
% 33.74/6.17 | | | | | | | | (79) $false
% 33.74/6.17 | | | | | | | |
% 33.74/6.17 | | | | | | | | CLOSE: (79) is inconsistent.
% 33.74/6.17 | | | | | | | |
% 33.74/6.17 | | | | | | | Case 2:
% 33.74/6.17 | | | | | | | |
% 33.74/6.17 | | | | | | | | (80) all_45_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2:
% 33.74/6.17 | | | | | | | | int] : ((v2 = 0 & unorthogonal_lines(all_38_1,
% 33.74/6.17 | | | | | | | | all_38_3) = 0) | (v1 = 0 &
% 33.74/6.17 | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = 0) | ( ~
% 33.74/6.17 | | | | | | | | (v0 = 0) & distinct_lines(all_38_2, all_38_1) = v0))
% 33.74/6.17 | | | | | | | |
% 33.74/6.17 | | | | | | | | BETA: splitting (80) gives:
% 33.74/6.17 | | | | | | | |
% 33.74/6.17 | | | | | | | | Case 1:
% 33.74/6.17 | | | | | | | | |
% 33.74/6.17 | | | | | | | | | (81) all_45_0 = 0
% 33.74/6.17 | | | | | | | | |
% 33.74/6.17 | | | | | | | | | REDUCE: (36), (81) imply:
% 33.74/6.17 | | | | | | | | | (82) $false
% 33.74/6.17 | | | | | | | | |
% 33.74/6.17 | | | | | | | | | CLOSE: (82) is inconsistent.
% 33.74/6.17 | | | | | | | | |
% 33.74/6.17 | | | | | | | | Case 2:
% 33.74/6.17 | | | | | | | | |
% 33.74/6.17 | | | | | | | | |
% 33.74/6.17 | | | | | | | | | GROUND_INST: instantiating (1) with all_38_3, all_38_1,
% 33.74/6.17 | | | | | | | | | all_38_3, all_102_0, simplifying with (25), (27),
% 33.74/6.17 | | | | | | | | | (44), (71) gives:
% 33.74/6.17 | | | | | | | | | (83) all_102_0 = 0 | convergent_lines(all_38_1, all_38_3) =
% 33.74/6.17 | | | | | | | | | 0
% 33.74/6.17 | | | | | | | | |
% 33.74/6.17 | | | | | | | | | GROUND_INST: instantiating (8) with all_38_2, all_38_3,
% 33.74/6.17 | | | | | | | | | all_38_1, 0, simplifying with (25), (26), (27),
% 33.74/6.17 | | | | | | | | | (44), (64) gives:
% 33.74/6.17 | | | | | | | | | (84) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3:
% 33.74/6.17 | | | | | | | | | int] : ((v2 = 0 & v1 = 0 &
% 33.74/6.17 | | | | | | | | | unorthogonal_lines(all_38_2, all_38_1) = 0 &
% 33.74/6.17 | | | | | | | | | convergent_lines(all_38_2, all_38_1) = 0) | (v0 =
% 33.74/6.17 | | | | | | | | | 0 & unorthogonal_lines(all_38_2, all_38_3) = 0) |
% 33.74/6.17 | | | | | | | | | ( ~ (v3 = 0) & unorthogonal_lines(all_38_3,
% 33.74/6.17 | | | | | | | | | all_38_1) = v3))
% 33.74/6.17 | | | | | | | | |
% 33.74/6.17 | | | | | | | | | GROUND_INST: instantiating (16) with all_38_1, all_38_2,
% 33.74/6.17 | | | | | | | | | all_38_3, all_47_0, simplifying with (25), (26),
% 33.74/6.17 | | | | | | | | | (27), (40), (64) gives:
% 33.74/6.17 | | | | | | | | | (85) all_47_0 = 0 | unorthogonal_lines(all_38_1, all_38_3)
% 33.74/6.17 | | | | | | | | | = 0
% 33.74/6.17 | | | | | | | | |
% 33.74/6.17 | | | | | | | | | GROUND_INST: instantiating (17) with all_38_2, all_38_2,
% 33.74/6.17 | | | | | | | | | all_38_3, all_51_0, simplifying with (25), (26),
% 33.74/6.17 | | | | | | | | | (43), (64) gives:
% 33.74/6.17 | | | | | | | | | (86) all_51_0 = 0 | unorthogonal_lines(all_38_2, all_38_2)
% 33.74/6.17 | | | | | | | | | = 0
% 33.74/6.17 | | | | | | | | |
% 33.74/6.17 | | | | | | | | | GROUND_INST: instantiating (17) with all_38_1, all_38_1,
% 33.74/6.17 | | | | | | | | | all_38_2, all_47_0, simplifying with (26), (27),
% 33.74/6.17 | | | | | | | | | (40), (65) gives:
% 33.74/6.17 | | | | | | | | | (87) all_47_0 = 0 | unorthogonal_lines(all_38_1, all_38_1)
% 33.74/6.17 | | | | | | | | | = 0
% 33.74/6.17 | | | | | | | | |
% 33.74/6.17 | | | | | | | | | GROUND_INST: instantiating (14) with all_38_2, all_38_1,
% 33.74/6.17 | | | | | | | | | all_38_3, 0, 0, simplifying with (25), (26), (27),
% 33.74/6.17 | | | | | | | | | (63), (64) gives:
% 33.74/6.17 | | | | | | | | | (88) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3:
% 33.74/6.17 | | | | | | | | | int] : ((v1 = 0 & unorthogonal_lines(all_38_2,
% 33.74/6.17 | | | | | | | | | all_38_3) = 0) | (v0 = 0 &
% 33.74/6.17 | | | | | | | | | convergent_lines(all_38_2, all_38_1) = 0) | ( ~
% 33.74/6.17 | | | | | | | | | (v3 = 0) & unorthogonal_lines(all_38_1, all_38_3)
% 33.74/6.17 | | | | | | | | | = v3) | ( ~ (v2 = 0) & convergent_lines(all_38_1,
% 33.74/6.17 | | | | | | | | | all_38_3) = v2))
% 33.74/6.17 | | | | | | | | |
% 33.74/6.17 | | | | | | | | | GROUND_INST: instantiating (4) with all_38_2, all_38_1,
% 33.74/6.17 | | | | | | | | | all_38_2, all_47_0, simplifying with (26), (27),
% 33.74/6.17 | | | | | | | | | (40), (63) gives:
% 33.74/6.17 | | | | | | | | | (89) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3:
% 33.74/6.17 | | | | | | | | | int] : ((v3 = 0 & all_47_0 = 0 &
% 33.74/6.17 | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0) | (v2 =
% 33.74/6.17 | | | | | | | | | 0 & v1 = 0 & unorthogonal_lines(all_38_2,
% 33.74/6.17 | | | | | | | | | all_38_2) = 0 & convergent_lines(all_38_2,
% 33.74/6.17 | | | | | | | | | all_38_2) = 0) | ( ~ (v0 = 0) &
% 33.74/6.17 | | | | | | | | | convergent_lines(all_38_2, all_38_1) = v0))
% 33.74/6.17 | | | | | | | | |
% 33.74/6.17 | | | | | | | | | GROUND_INST: instantiating (12) with all_38_1, all_38_2,
% 33.74/6.17 | | | | | | | | | all_38_1, all_47_0, simplifying with (26), (27),
% 33.74/6.17 | | | | | | | | | (40), (63) gives:
% 33.74/6.17 | | | | | | | | | (90) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3:
% 33.74/6.17 | | | | | | | | | int] : ((v2 = 0 & v1 = 0 &
% 33.74/6.17 | | | | | | | | | unorthogonal_lines(all_38_1, all_38_1) = 0 &
% 33.74/6.17 | | | | | | | | | convergent_lines(all_38_1, all_38_1) = 0) | (v0 =
% 33.74/6.17 | | | | | | | | | 0 & all_47_0 = 0 & convergent_lines(all_38_1,
% 33.74/6.17 | | | | | | | | | all_38_2) = 0) | ( ~ (v3 = 0) &
% 33.74/6.17 | | | | | | | | | convergent_lines(all_38_2, all_38_1) = v3))
% 33.74/6.17 | | | | | | | | |
% 33.74/6.17 | | | | | | | | | GROUND_INST: instantiating (11) with all_38_1, all_38_2,
% 33.74/6.17 | | | | | | | | | all_38_1, 0, simplifying with (26), (27), (63),
% 33.74/6.17 | | | | | | | | | (65) gives:
% 33.74/6.17 | | | | | | | | | (91) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3:
% 33.74/6.17 | | | | | | | | | int] : ((v2 = 0 & v1 = 0 &
% 33.74/6.17 | | | | | | | | | unorthogonal_lines(all_38_1, all_38_1) = 0 &
% 33.74/6.17 | | | | | | | | | convergent_lines(all_38_1, all_38_1) = 0) | (v0 =
% 33.74/6.17 | | | | | | | | | 0 & unorthogonal_lines(all_38_1, all_38_2) = 0) |
% 33.74/6.17 | | | | | | | | | ( ~ (v3 = 0) & convergent_lines(all_38_2, all_38_1)
% 33.74/6.17 | | | | | | | | | = v3))
% 33.74/6.17 | | | | | | | | |
% 33.74/6.17 | | | | | | | | | GROUND_INST: instantiating (3) with all_38_2, all_38_1,
% 33.74/6.17 | | | | | | | | | all_38_2, 0, simplifying with (26), (27), (63),
% 33.74/6.17 | | | | | | | | | (65) gives:
% 33.74/6.17 | | | | | | | | | (92) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3:
% 33.74/6.17 | | | | | | | | | int] : ((v3 = 0 & unorthogonal_lines(all_38_1,
% 33.74/6.17 | | | | | | | | | all_38_2) = 0) | (v2 = 0 & v1 = 0 &
% 33.74/6.17 | | | | | | | | | unorthogonal_lines(all_38_2, all_38_2) = 0 &
% 33.74/6.17 | | | | | | | | | convergent_lines(all_38_2, all_38_2) = 0) | ( ~
% 33.74/6.17 | | | | | | | | | (v0 = 0) & convergent_lines(all_38_2, all_38_1) =
% 33.74/6.17 | | | | | | | | | v0))
% 33.74/6.17 | | | | | | | | |
% 33.74/6.17 | | | | | | | | | GROUND_INST: instantiating (2) with all_38_2, all_38_1,
% 33.74/6.17 | | | | | | | | | all_38_2, all_107_0, simplifying with (26), (27),
% 33.74/6.17 | | | | | | | | | (63), (77) gives:
% 33.74/6.18 | | | | | | | | | (93) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3:
% 33.74/6.18 | | | | | | | | | int] : ((v3 = 0 & v2 = 0 &
% 33.74/6.18 | | | | | | | | | unorthogonal_lines(all_38_1, all_38_2) = 0 &
% 33.74/6.18 | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0) | (v1 =
% 33.74/6.18 | | | | | | | | | 0 & all_107_0 = 0 & unorthogonal_lines(all_38_2,
% 33.74/6.18 | | | | | | | | | all_38_2) = 0) | ( ~ (v0 = 0) &
% 33.74/6.18 | | | | | | | | | convergent_lines(all_38_2, all_38_1) = v0))
% 33.74/6.18 | | | | | | | | |
% 33.74/6.18 | | | | | | | | | DELTA: instantiating (88) with fresh symbols all_247_0,
% 33.74/6.18 | | | | | | | | | all_247_1, all_247_2, all_247_3 gives:
% 33.74/6.18 | | | | | | | | | (94) (all_247_2 = 0 & unorthogonal_lines(all_38_2,
% 33.74/6.18 | | | | | | | | | all_38_3) = 0) | (all_247_3 = 0 &
% 33.74/6.18 | | | | | | | | | convergent_lines(all_38_2, all_38_1) = 0) | ( ~
% 33.74/6.18 | | | | | | | | | (all_247_0 = 0) & unorthogonal_lines(all_38_1,
% 33.74/6.18 | | | | | | | | | all_38_3) = all_247_0) | ( ~ (all_247_1 = 0) &
% 33.74/6.18 | | | | | | | | | convergent_lines(all_38_1, all_38_3) = all_247_1)
% 33.74/6.18 | | | | | | | | |
% 33.74/6.18 | | | | | | | | | DELTA: instantiating (92) with fresh symbols all_256_0,
% 33.74/6.18 | | | | | | | | | all_256_1, all_256_2, all_256_3 gives:
% 33.74/6.18 | | | | | | | | | (95) (all_256_0 = 0 & unorthogonal_lines(all_38_1,
% 33.74/6.18 | | | | | | | | | all_38_2) = 0) | (all_256_1 = 0 & all_256_2 = 0 &
% 33.74/6.18 | | | | | | | | | unorthogonal_lines(all_38_2, all_38_2) = 0 &
% 33.74/6.18 | | | | | | | | | convergent_lines(all_38_2, all_38_2) = 0) | ( ~
% 33.74/6.18 | | | | | | | | | (all_256_3 = 0) & convergent_lines(all_38_2,
% 33.74/6.18 | | | | | | | | | all_38_1) = all_256_3)
% 33.74/6.18 | | | | | | | | |
% 33.74/6.18 | | | | | | | | | DELTA: instantiating (91) with fresh symbols all_257_0,
% 33.74/6.18 | | | | | | | | | all_257_1, all_257_2, all_257_3 gives:
% 33.74/6.18 | | | | | | | | | (96) (all_257_1 = 0 & all_257_2 = 0 &
% 33.74/6.18 | | | | | | | | | unorthogonal_lines(all_38_1, all_38_1) = 0 &
% 33.74/6.18 | | | | | | | | | convergent_lines(all_38_1, all_38_1) = 0) |
% 33.74/6.18 | | | | | | | | | (all_257_3 = 0 & unorthogonal_lines(all_38_1,
% 33.74/6.18 | | | | | | | | | all_38_2) = 0) | ( ~ (all_257_0 = 0) &
% 33.74/6.18 | | | | | | | | | convergent_lines(all_38_2, all_38_1) = all_257_0)
% 33.74/6.18 | | | | | | | | |
% 33.74/6.18 | | | | | | | | | DELTA: instantiating (84) with fresh symbols all_282_0,
% 33.74/6.18 | | | | | | | | | all_282_1, all_282_2, all_282_3 gives:
% 33.74/6.18 | | | | | | | | | (97) (all_282_1 = 0 & all_282_2 = 0 &
% 33.74/6.18 | | | | | | | | | unorthogonal_lines(all_38_2, all_38_1) = 0 &
% 33.74/6.18 | | | | | | | | | convergent_lines(all_38_2, all_38_1) = 0) |
% 33.74/6.18 | | | | | | | | | (all_282_3 = 0 & unorthogonal_lines(all_38_2,
% 33.74/6.18 | | | | | | | | | all_38_3) = 0) | ( ~ (all_282_0 = 0) &
% 33.74/6.18 | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = all_282_0)
% 33.74/6.18 | | | | | | | | |
% 33.74/6.18 | | | | | | | | | DELTA: instantiating (93) with fresh symbols all_291_0,
% 33.74/6.18 | | | | | | | | | all_291_1, all_291_2, all_291_3 gives:
% 33.74/6.18 | | | | | | | | | (98) (all_291_0 = 0 & all_291_1 = 0 &
% 33.74/6.18 | | | | | | | | | unorthogonal_lines(all_38_1, all_38_2) = 0 &
% 33.74/6.18 | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0) |
% 33.74/6.18 | | | | | | | | | (all_291_2 = 0 & all_107_0 = 0 &
% 33.74/6.18 | | | | | | | | | unorthogonal_lines(all_38_2, all_38_2) = 0) | ( ~
% 33.74/6.18 | | | | | | | | | (all_291_3 = 0) & convergent_lines(all_38_2,
% 33.74/6.18 | | | | | | | | | all_38_1) = all_291_3)
% 33.74/6.18 | | | | | | | | |
% 33.74/6.18 | | | | | | | | | DELTA: instantiating (89) with fresh symbols all_296_0,
% 33.74/6.18 | | | | | | | | | all_296_1, all_296_2, all_296_3 gives:
% 33.74/6.18 | | | | | | | | | (99) (all_296_0 = 0 & all_47_0 = 0 &
% 33.74/6.18 | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0) |
% 33.74/6.18 | | | | | | | | | (all_296_1 = 0 & all_296_2 = 0 &
% 33.74/6.18 | | | | | | | | | unorthogonal_lines(all_38_2, all_38_2) = 0 &
% 33.74/6.18 | | | | | | | | | convergent_lines(all_38_2, all_38_2) = 0) | ( ~
% 33.74/6.18 | | | | | | | | | (all_296_3 = 0) & convergent_lines(all_38_2,
% 33.74/6.18 | | | | | | | | | all_38_1) = all_296_3)
% 33.74/6.18 | | | | | | | | |
% 33.74/6.18 | | | | | | | | | DELTA: instantiating (90) with fresh symbols all_300_0,
% 33.74/6.18 | | | | | | | | | all_300_1, all_300_2, all_300_3 gives:
% 33.74/6.18 | | | | | | | | | (100) (all_300_1 = 0 & all_300_2 = 0 &
% 33.74/6.18 | | | | | | | | | unorthogonal_lines(all_38_1, all_38_1) = 0 &
% 33.74/6.18 | | | | | | | | | convergent_lines(all_38_1, all_38_1) = 0) |
% 33.74/6.18 | | | | | | | | | (all_300_3 = 0 & all_47_0 = 0 &
% 33.74/6.18 | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0) | ( ~
% 33.74/6.18 | | | | | | | | | (all_300_0 = 0) & convergent_lines(all_38_2,
% 33.74/6.18 | | | | | | | | | all_38_1) = all_300_0)
% 33.74/6.18 | | | | | | | | |
% 33.74/6.18 | | | | | | | | | BETA: splitting (86) gives:
% 33.74/6.18 | | | | | | | | |
% 33.74/6.18 | | | | | | | | | Case 1:
% 33.74/6.18 | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | (101) unorthogonal_lines(all_38_2, all_38_2) = 0
% 33.74/6.18 | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | BETA: splitting (85) gives:
% 33.74/6.18 | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | Case 1:
% 33.74/6.18 | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | (102) unorthogonal_lines(all_38_1, all_38_3) = 0
% 33.74/6.18 | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | BETA: splitting (60) gives:
% 33.74/6.18 | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | Case 1:
% 33.74/6.18 | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | (103) (all_75_0 = 0 & all_51_0 = 0 &
% 33.74/6.18 | | | | | | | | | | | | convergent_lines(all_38_2, all_38_3) = 0) |
% 33.74/6.18 | | | | | | | | | | | | (all_75_1 = 0 & all_51_0 = 0 &
% 33.74/6.18 | | | | | | | | | | | | convergent_lines(all_38_2, all_38_3) = 0)
% 33.74/6.18 | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | BETA: splitting (103) gives:
% 33.74/6.18 | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | Case 1:
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | (104) all_75_0 = 0 & all_51_0 = 0 &
% 33.74/6.18 | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_3) = 0
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | ALPHA: (104) implies:
% 33.74/6.18 | | | | | | | | | | | | | (105) all_51_0 = 0
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | REDUCE: (42), (105) imply:
% 33.74/6.18 | | | | | | | | | | | | | (106) $false
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | CLOSE: (106) is inconsistent.
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | Case 2:
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | (107) all_75_1 = 0 & all_51_0 = 0 &
% 33.74/6.18 | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_3) = 0
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | ALPHA: (107) implies:
% 33.74/6.18 | | | | | | | | | | | | | (108) all_51_0 = 0
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | REDUCE: (42), (108) imply:
% 33.74/6.18 | | | | | | | | | | | | | (109) $false
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | CLOSE: (109) is inconsistent.
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | End of split
% 33.74/6.18 | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | Case 2:
% 33.74/6.18 | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | (110) ( ~ (all_75_2 = 0) & unorthogonal_lines(all_38_2,
% 33.74/6.18 | | | | | | | | | | | | all_38_2) = all_75_2) | ( ~ (all_75_3 = 0) &
% 33.74/6.18 | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = all_75_3)
% 33.74/6.18 | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | BETA: splitting (110) gives:
% 33.74/6.18 | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | Case 1:
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | (111) ~ (all_75_2 = 0) & unorthogonal_lines(all_38_2,
% 33.74/6.18 | | | | | | | | | | | | | all_38_2) = all_75_2
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | ALPHA: (111) implies:
% 33.74/6.18 | | | | | | | | | | | | | (112) ~ (all_75_2 = 0)
% 33.74/6.18 | | | | | | | | | | | | | (113) unorthogonal_lines(all_38_2, all_38_2) = all_75_2
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_75_2, all_38_2,
% 33.74/6.18 | | | | | | | | | | | | | all_38_2, simplifying with (101), (113) gives:
% 33.74/6.18 | | | | | | | | | | | | | (114) all_75_2 = 0
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | REDUCE: (112), (114) imply:
% 33.74/6.18 | | | | | | | | | | | | | (115) $false
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | CLOSE: (115) is inconsistent.
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | Case 2:
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | (116) ~ (all_75_3 = 0) & convergent_lines(all_38_2,
% 33.74/6.18 | | | | | | | | | | | | | all_38_2) = all_75_3
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | ALPHA: (116) implies:
% 33.74/6.18 | | | | | | | | | | | | | (117) ~ (all_75_3 = 0)
% 33.74/6.18 | | | | | | | | | | | | | (118) convergent_lines(all_38_2, all_38_2) = all_75_3
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | BETA: splitting (99) gives:
% 33.74/6.18 | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | Case 1:
% 33.74/6.18 | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | (119) all_296_0 = 0 & all_47_0 = 0 &
% 33.74/6.18 | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0
% 33.74/6.18 | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | ALPHA: (119) implies:
% 33.74/6.18 | | | | | | | | | | | | | | (120) all_47_0 = 0
% 33.74/6.18 | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | REDUCE: (39), (120) imply:
% 33.74/6.18 | | | | | | | | | | | | | | (121) $false
% 33.74/6.18 | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | CLOSE: (121) is inconsistent.
% 33.74/6.18 | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | Case 2:
% 33.74/6.18 | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | (122) (all_296_1 = 0 & all_296_2 = 0 &
% 33.74/6.18 | | | | | | | | | | | | | | unorthogonal_lines(all_38_2, all_38_2) = 0 &
% 33.74/6.18 | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = 0) | ( ~
% 33.74/6.18 | | | | | | | | | | | | | | (all_296_3 = 0) & convergent_lines(all_38_2,
% 33.74/6.18 | | | | | | | | | | | | | | all_38_1) = all_296_3)
% 33.74/6.18 | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 33.74/6.18 | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | Case 1:
% 33.74/6.18 | | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | | (123) all_296_1 = 0 & all_296_2 = 0 &
% 33.74/6.18 | | | | | | | | | | | | | | | unorthogonal_lines(all_38_2, all_38_2) = 0 &
% 33.74/6.18 | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = 0
% 33.74/6.18 | | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 33.74/6.18 | | | | | | | | | | | | | | | (124) convergent_lines(all_38_2, all_38_2) = 0
% 33.74/6.18 | | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | | REF_CLOSE: (20), (77), (117), (118), (124) are inconsistent
% 33.74/6.18 | | | | | | | | | | | | | | | by sub-proof #10.
% 33.74/6.18 | | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | Case 2:
% 33.74/6.18 | | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | | (125) ~ (all_296_3 = 0) & convergent_lines(all_38_2,
% 33.74/6.18 | | | | | | | | | | | | | | | all_38_1) = all_296_3
% 33.74/6.18 | | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 33.74/6.18 | | | | | | | | | | | | | | | (126) convergent_lines(all_38_2, all_38_1) = all_296_3
% 33.74/6.18 | | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | | BETA: splitting (59) gives:
% 33.74/6.18 | | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | | Case 1:
% 33.74/6.18 | | | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | | | (127) all_73_1 = 0 & all_73_2 = 0 &
% 33.74/6.18 | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_2, all_38_1) = 0 &
% 33.74/6.18 | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) = 0
% 33.74/6.18 | | | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 33.74/6.18 | | | | | | | | | | | | | | | | (128) convergent_lines(all_38_2, all_38_1) = 0
% 33.74/6.18 | | | | | | | | | | | | | | | |
% 33.74/6.18 | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 33.74/6.19 | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.19 | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | (129) unorthogonal_lines(all_38_1, all_38_1) = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 33.74/6.19 | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.19 | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | (130) (all_77_0 = 0 & all_47_0 = 0 &
% 33.74/6.19 | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0) |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | (all_77_1 = 0 & all_47_0 = 0 &
% 33.74/6.19 | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0)
% 33.74/6.19 | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 33.74/6.19 | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | (131) all_77_0 = 0 & all_47_0 = 0 &
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | (132) all_47_0 = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | REDUCE: (39), (132) imply:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | (133) $false
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | CLOSE: (133) is inconsistent.
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | (134) all_77_1 = 0 & all_47_0 = 0 &
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | (135) all_47_0 = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | REDUCE: (39), (135) imply:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | (136) $false
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | CLOSE: (136) is inconsistent.
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.19 | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.19 | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | (137) ( ~ (all_77_2 = 0) & unorthogonal_lines(all_38_1,
% 33.74/6.19 | | | | | | | | | | | | | | | | | | all_38_1) = all_77_2) | ( ~ (all_77_3 = 0) &
% 33.74/6.19 | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = all_77_3)
% 33.74/6.19 | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 33.74/6.19 | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | (138) ~ (all_77_2 = 0) & unorthogonal_lines(all_38_1,
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | all_38_1) = all_77_2
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | (139) ~ (all_77_2 = 0)
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | (140) unorthogonal_lines(all_38_1, all_38_1) = all_77_2
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_77_2, all_38_1,
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | all_38_1, simplifying with (129), (140) gives:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | (141) all_77_2 = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | REDUCE: (139), (141) imply:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | (142) $false
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | CLOSE: (142) is inconsistent.
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | (143) ~ (all_77_3 = 0) & convergent_lines(all_38_1,
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | all_38_1) = all_77_3
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | (144) ~ (all_77_3 = 0)
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | (145) convergent_lines(all_38_1, all_38_1) = all_77_3
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | (146) all_257_1 = 0 & all_257_2 = 0 &
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_1) = 0 &
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | (147) convergent_lines(all_38_1, all_38_1) = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (144), (145), (147) are inconsistent by
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | sub-proof #9.
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | (148) (all_257_3 = 0 & unorthogonal_lines(all_38_1,
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | all_38_2) = 0) | ( ~ (all_257_0 = 0) &
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) =
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | all_257_0)
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | (149) all_257_3 = 0 & unorthogonal_lines(all_38_1,
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | (150) unorthogonal_lines(all_38_1, all_38_2) = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (39), (40), (150) are inconsistent by
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | sub-proof #8.
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | (151) ~ (all_257_0 = 0) & convergent_lines(all_38_2,
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_257_0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | (152) convergent_lines(all_38_2, all_38_1) = all_257_0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | (153) all_256_0 = 0 & unorthogonal_lines(all_38_1,
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | (154) unorthogonal_lines(all_38_1, all_38_2) = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (39), (40), (154) are inconsistent by
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | sub-proof #8.
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | (155) (all_256_1 = 0 & all_256_2 = 0 &
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_2, all_38_2) = 0 &
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = 0) | ( ~
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | (all_256_3 = 0) & convergent_lines(all_38_2,
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_256_3)
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | (156) all_256_1 = 0 & all_256_2 = 0 &
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_2, all_38_2) = 0 &
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_2) = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | (157) convergent_lines(all_38_2, all_38_2) = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (77), (117), (118), (157) are inconsistent
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #10.
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | (158) ~ (all_256_3 = 0) & convergent_lines(all_38_2,
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_256_3
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | (159) ~ (all_256_3 = 0)
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | (160) convergent_lines(all_38_2, all_38_1) = all_256_3
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | (161) all_300_1 = 0 & all_300_2 = 0 &
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_1) = 0 &
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | (162) convergent_lines(all_38_1, all_38_1) = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (144), (145), (162) are inconsistent by
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #9.
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | (163) (all_300_3 = 0 & all_47_0 = 0 &
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0) | ( ~
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | (all_300_0 = 0) & convergent_lines(all_38_2,
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_300_0)
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | | (164) all_300_3 = 0 & all_47_0 = 0 &
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | | (165) all_47_0 = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (165) imply:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | | (166) $false
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (166) is inconsistent.
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | | (167) ~ (all_300_0 = 0) & convergent_lines(all_38_2,
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_300_0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | | (168) convergent_lines(all_38_2, all_38_1) = all_300_0
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (21), (39), (40), (76), (98), (126), (128),
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | | (152), (159), (160), (168) are inconsistent by
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #7.
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.19 | | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.19 | | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | End of split
% 33.74/6.19 | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.19 | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | (169) all_47_0 = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | REDUCE: (39), (169) imply:
% 33.74/6.19 | | | | | | | | | | | | | | | | | (170) $false
% 33.74/6.19 | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | CLOSE: (170) is inconsistent.
% 33.74/6.19 | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | End of split
% 33.74/6.19 | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | Case 2:
% 33.74/6.19 | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | (171) (all_73_3 = 0 & all_51_0 = 0 &
% 33.74/6.19 | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_3) = 0) | ( ~
% 33.74/6.19 | | | | | | | | | | | | | | | | (all_73_0 = 0) & unorthogonal_lines(all_38_3,
% 33.74/6.19 | | | | | | | | | | | | | | | | all_38_1) = all_73_0)
% 33.74/6.19 | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 33.74/6.19 | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.19 | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | (172) all_73_3 = 0 & all_51_0 = 0 &
% 33.74/6.19 | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_3) = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 33.74/6.19 | | | | | | | | | | | | | | | | | (173) all_51_0 = 0
% 33.74/6.19 | | | | | | | | | | | | | | | | |
% 33.74/6.19 | | | | | | | | | | | | | | | | | REDUCE: (42), (173) imply:
% 33.74/6.19 | | | | | | | | | | | | | | | | | (174) $false
% 33.74/6.19 | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | CLOSE: (174) is inconsistent.
% 33.74/6.20 | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.20 | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | (175) ~ (all_73_0 = 0) & unorthogonal_lines(all_38_3,
% 33.74/6.20 | | | | | | | | | | | | | | | | | all_38_1) = all_73_0
% 33.74/6.20 | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 33.74/6.20 | | | | | | | | | | | | | | | | | (176) ~ (all_73_0 = 0)
% 33.74/6.20 | | | | | | | | | | | | | | | | | (177) unorthogonal_lines(all_38_3, all_38_1) = all_73_0
% 33.74/6.20 | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 33.74/6.20 | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.20 | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | (178) all_69_1 = 0 & unorthogonal_lines(all_38_3,
% 33.74/6.20 | | | | | | | | | | | | | | | | | | all_38_1) = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | (179) unorthogonal_lines(all_38_3, all_38_1) = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_73_0, all_38_1,
% 33.74/6.20 | | | | | | | | | | | | | | | | | | all_38_3, simplifying with (177), (179) gives:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | (180) all_73_0 = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | REDUCE: (176), (180) imply:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | (181) $false
% 33.74/6.20 | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | CLOSE: (181) is inconsistent.
% 33.74/6.20 | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.20 | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | (182) (all_69_2 = 0 & all_69_3 = 0 &
% 33.74/6.20 | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0 &
% 33.74/6.20 | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = 0) | ( ~
% 33.74/6.20 | | | | | | | | | | | | | | | | | | (all_69_0 = 0) & unorthogonal_lines(all_38_3,
% 33.74/6.20 | | | | | | | | | | | | | | | | | | all_38_1) = all_69_0)
% 33.74/6.20 | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 33.74/6.20 | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | (183) all_69_2 = 0 & all_69_3 = 0 &
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_3) = 0 &
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | (184) convergent_lines(all_38_3, all_38_3) = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | (185) unorthogonal_lines(all_38_3, all_38_3) = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | (186) (all_76_2 = 0 & all_51_0 = 0 &
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_3) = 0) |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | (all_76_3 = 0 & all_51_0 = 0 &
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_3) = 0)
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (187) all_76_2 = 0 & all_51_0 = 0 &
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_3) = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (188) all_51_0 = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (188) imply:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (189) $false
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | CLOSE: (189) is inconsistent.
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (190) all_76_3 = 0 & all_51_0 = 0 &
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_3) = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (191) all_51_0 = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (191) imply:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (192) $false
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | CLOSE: (192) is inconsistent.
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | (193) ( ~ (all_76_0 = 0) & unorthogonal_lines(all_38_3,
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | all_38_3) = all_76_0) | ( ~ (all_76_1 = 0) &
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_3, all_38_3) = all_76_1)
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (194) ~ (all_76_0 = 0) & unorthogonal_lines(all_38_3,
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_76_0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (195) ~ (all_76_0 = 0)
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (196) unorthogonal_lines(all_38_3, all_38_3) = all_76_0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_76_0, all_38_3,
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | all_38_3, simplifying with (185), (196) gives:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (197) all_76_0 = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (195), (197) imply:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (198) $false
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | CLOSE: (198) is inconsistent.
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (199) ~ (all_76_1 = 0) & convergent_lines(all_38_3,
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_76_1
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (200) ~ (all_76_1 = 0)
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (201) convergent_lines(all_38_3, all_38_3) = all_76_1
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_102_0, 0, all_38_3,
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | all_38_3, simplifying with (71), (184) gives:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (202) all_102_0 = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_102_0, all_76_1,
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | all_38_3, all_38_3, simplifying with (71), (201)
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | gives:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (203) all_102_0 = all_76_1
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (203) imply:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (204) all_76_1 = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (200), (204) imply:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (205) $false
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent.
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.20 | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | (206) ~ (all_69_0 = 0) & unorthogonal_lines(all_38_3,
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | all_38_1) = all_69_0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | (207) ~ (all_69_0 = 0)
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | (208) unorthogonal_lines(all_38_3, all_38_1) = all_69_0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | (209) all_282_1 = 0 & all_282_2 = 0 &
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_2, all_38_1) = 0 &
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | (210) convergent_lines(all_38_2, all_38_1) = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | (211) unorthogonal_lines(all_38_1, all_38_1) = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | (212) (all_71_2 = 0 & unorthogonal_lines(all_38_3,
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0) | (all_71_3 = 0 &
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0)
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | (213) all_71_2 = 0 & unorthogonal_lines(all_38_3,
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (213) implies:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | (214) unorthogonal_lines(all_38_3, all_38_1) = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (207), (208), (214) are inconsistent by
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #6.
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | (215) all_71_3 = 0 & unorthogonal_lines(all_38_3,
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | (216) unorthogonal_lines(all_38_3, all_38_1) = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (207), (208), (216) are inconsistent by
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #6.
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | (217) ( ~ (all_71_0 = 0) & unorthogonal_lines(all_38_1,
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_71_0) | ( ~ (all_71_1 = 0) &
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = all_71_1)
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | (218) ~ (all_71_0 = 0) & unorthogonal_lines(all_38_1,
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_71_0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (218) implies:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | (219) ~ (all_71_0 = 0)
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | (220) unorthogonal_lines(all_38_1, all_38_1) = all_71_0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (211), (219), (220) are inconsistent by
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #5.
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | (221) ~ (all_71_1 = 0) & convergent_lines(all_38_1,
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_71_1
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | (222) ~ (all_71_1 = 0)
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | (223) convergent_lines(all_38_1, all_38_1) = all_71_1
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | | (224) all_257_1 = 0 & all_257_2 = 0 &
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_1) = 0 &
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = 0
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.20 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (224) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | (225) convergent_lines(all_38_1, all_38_1) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (222), (223), (225) are inconsistent by
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4.
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | (226) (all_257_3 = 0 & unorthogonal_lines(all_38_1,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0) | ( ~ (all_257_0 = 0) &
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) =
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | all_257_0)
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_257_3 = 0 & unorthogonal_lines(all_38_1,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (227) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | (228) unorthogonal_lines(all_38_1, all_38_2) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (39), (40), (228) are inconsistent by
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #8.
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | (229) ~ (all_257_0 = 0) & convergent_lines(all_38_2,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_257_0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | (230) convergent_lines(all_38_2, all_38_1) = all_257_0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (231) all_300_1 = 0 & all_300_2 = 0 &
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_1) = 0 &
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (232) convergent_lines(all_38_1, all_38_1) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (222), (223), (232) are inconsistent by
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4.
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (233) (all_300_3 = 0 & all_47_0 = 0 &
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0) | ( ~
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_300_0 = 0) & convergent_lines(all_38_2,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_300_0)
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_300_3 = 0 & all_47_0 = 0 &
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_47_0 = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (235) imply:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) $false
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (236) is inconsistent.
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) ~ (all_300_0 = 0) & convergent_lines(all_38_2,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_300_0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (237) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) convergent_lines(all_38_2, all_38_1) = all_300_0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (21), (39), (40), (76), (77), (95), (98),
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (117), (118), (126), (210), (230), (238) are
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #3.
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | (239) all_47_0 = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (239) imply:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | (240) $false
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | CLOSE: (240) is inconsistent.
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | (241) (all_282_3 = 0 & unorthogonal_lines(all_38_2,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | all_38_3) = 0) | ( ~ (all_282_0 = 0) &
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) =
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | all_282_0)
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | (242) all_282_3 = 0 & unorthogonal_lines(all_38_2,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | all_38_3) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | ALPHA: (242) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | (243) unorthogonal_lines(all_38_2, all_38_3) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (42), (43), (243) are inconsistent by
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | sub-proof #2.
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | (244) ~ (all_282_0 = 0) & unorthogonal_lines(all_38_3,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_282_0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | (245) unorthogonal_lines(all_38_3, all_38_1) = all_282_0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | (246) unorthogonal_lines(all_38_1, all_38_1) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | (247) (all_71_2 = 0 & unorthogonal_lines(all_38_3,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0) | (all_71_3 = 0 &
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_3, all_38_1) = 0)
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | (248) all_71_2 = 0 & unorthogonal_lines(all_38_3,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | (249) unorthogonal_lines(all_38_3, all_38_1) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (176), (177), (245), (249) are inconsistent
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1.
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | (250) all_71_3 = 0 & unorthogonal_lines(all_38_3,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | (251) unorthogonal_lines(all_38_3, all_38_1) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (176), (177), (245), (251) are inconsistent
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1.
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | (252) ( ~ (all_71_0 = 0) & unorthogonal_lines(all_38_1,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_71_0) | ( ~ (all_71_1 = 0) &
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = all_71_1)
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | (253) ~ (all_71_0 = 0) & unorthogonal_lines(all_38_1,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_71_0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (253) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | (254) ~ (all_71_0 = 0)
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | (255) unorthogonal_lines(all_38_1, all_38_1) = all_71_0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (246), (254), (255) are inconsistent by
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #5.
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | (256) ~ (all_71_1 = 0) & convergent_lines(all_38_1,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_71_1
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (256) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | (257) ~ (all_71_1 = 0)
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | (258) convergent_lines(all_38_1, all_38_1) = all_71_1
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | (259) all_257_1 = 0 & all_257_2 = 0 &
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_1) = 0 &
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | (260) convergent_lines(all_38_1, all_38_1) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (257), (258), (260) are inconsistent by
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4.
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | (261) (all_257_3 = 0 & unorthogonal_lines(all_38_1,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0) | ( ~ (all_257_0 = 0) &
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) =
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_257_0)
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_257_3 = 0 & unorthogonal_lines(all_38_1,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_2) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (262) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (263) unorthogonal_lines(all_38_1, all_38_2) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (39), (40), (263) are inconsistent by
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #8.
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (264) ~ (all_257_0 = 0) & convergent_lines(all_38_2,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_257_0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (264) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (265) convergent_lines(all_38_2, all_38_1) = all_257_0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) convergent_lines(all_38_1, all_38_3) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_300_1 = 0 & all_300_2 = 0 &
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | unorthogonal_lines(all_38_1, all_38_1) = 0 &
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_1) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (267) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) convergent_lines(all_38_1, all_38_1) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (257), (258), (268) are inconsistent by
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #4.
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) (all_300_3 = 0 & all_47_0 = 0 &
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0) | ( ~
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_300_0 = 0) & convergent_lines(all_38_2,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_300_0)
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_300_3 = 0 & all_47_0 = 0 &
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_2) = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (270) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_47_0 = 0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (271) imply:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) $false
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (272) is inconsistent.
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) ~ (all_300_0 = 0) & convergent_lines(all_38_2,
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_300_0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (273) implies:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) convergent_lines(all_38_2, all_38_1) = all_300_0
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 33.74/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) (all_247_2 = 0 & unorthogonal_lines(all_38_2,
% 34.18/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = 0) | (all_247_3 = 0 &
% 34.18/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_2, all_38_1) = 0)
% 34.18/6.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_247_2 = 0 & unorthogonal_lines(all_38_2,
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = 0
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (276) implies:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) unorthogonal_lines(all_38_2, all_38_3) = 0
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (42), (43), (277) are inconsistent by
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #2.
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_247_3 = 0 & convergent_lines(all_38_2,
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1) = 0
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (278) implies:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) convergent_lines(all_38_2, all_38_1) = 0
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (21), (39), (40), (76), (77), (95), (98),
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (117), (118), (126), (265), (274), (279) are
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #3.
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) ( ~ (all_247_0 = 0) & unorthogonal_lines(all_38_1,
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_247_0) | ( ~ (all_247_1 = 0) &
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | convergent_lines(all_38_1, all_38_3) =
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_247_1)
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) ~ (all_247_0 = 0) & unorthogonal_lines(all_38_1,
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_247_0
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (281) implies:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) ~ (all_247_0 = 0)
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) unorthogonal_lines(all_38_1, all_38_3) = all_247_0
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_247_0, all_38_3,
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, simplifying with (102), (283) gives:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_247_0 = 0
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (282), (284) imply:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) $false
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (285) is inconsistent.
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) ~ (all_247_1 = 0) & convergent_lines(all_38_1,
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_3) = all_247_1
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) ~ (all_247_1 = 0)
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) convergent_lines(all_38_1, all_38_3) = all_247_1
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_247_1, all_38_3,
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, simplifying with (266), (288) gives:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_247_1 = 0
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (287), (289) imply:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) $false
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (290) is inconsistent.
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_102_0 = 0
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (291) imply:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) $false
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (292) is inconsistent.
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | (293) all_47_0 = 0
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (293) imply:
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | (294) $false
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (294) is inconsistent.
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | Case 2:
% 34.18/6.22 | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | (295) all_47_0 = 0
% 34.18/6.22 | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | REDUCE: (39), (295) imply:
% 34.18/6.22 | | | | | | | | | | | (296) $false
% 34.18/6.22 | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | | CLOSE: (296) is inconsistent.
% 34.18/6.22 | | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | Case 2:
% 34.18/6.22 | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | (297) all_51_0 = 0
% 34.18/6.22 | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | REDUCE: (42), (297) imply:
% 34.18/6.22 | | | | | | | | | | (298) $false
% 34.18/6.22 | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | | CLOSE: (298) is inconsistent.
% 34.18/6.22 | | | | | | | | | |
% 34.18/6.22 | | | | | | | | | End of split
% 34.18/6.22 | | | | | | | | |
% 34.18/6.22 | | | | | | | | End of split
% 34.18/6.22 | | | | | | | |
% 34.18/6.22 | | | | | | | End of split
% 34.18/6.22 | | | | | | |
% 34.18/6.22 | | | | | | End of split
% 34.18/6.22 | | | | | |
% 34.18/6.22 | | | | | End of split
% 34.18/6.22 | | | | |
% 34.18/6.22 | | | | Case 2:
% 34.18/6.22 | | | | |
% 34.18/6.22 | | | | | (299) all_47_0 = 0
% 34.18/6.22 | | | | |
% 34.18/6.22 | | | | | REDUCE: (39), (299) imply:
% 34.18/6.22 | | | | | (300) $false
% 34.18/6.22 | | | | |
% 34.18/6.22 | | | | | CLOSE: (300) is inconsistent.
% 34.18/6.22 | | | | |
% 34.18/6.22 | | | | End of split
% 34.18/6.22 | | | |
% 34.18/6.22 | | | Case 2:
% 34.18/6.22 | | | |
% 34.18/6.22 | | | | (301) all_51_0 = 0
% 34.18/6.22 | | | |
% 34.18/6.22 | | | | REDUCE: (42), (301) imply:
% 34.18/6.22 | | | | (302) $false
% 34.18/6.22 | | | |
% 34.18/6.22 | | | | CLOSE: (302) is inconsistent.
% 34.18/6.22 | | | |
% 34.18/6.22 | | | End of split
% 34.18/6.22 | | |
% 34.18/6.22 | | Case 2:
% 34.18/6.22 | | |
% 34.18/6.22 | | | (303) all_51_0 = 0
% 34.18/6.22 | | |
% 34.18/6.22 | | | REDUCE: (42), (303) imply:
% 34.18/6.22 | | | (304) $false
% 34.18/6.22 | | |
% 34.18/6.22 | | | CLOSE: (304) is inconsistent.
% 34.18/6.22 | | |
% 34.18/6.22 | | End of split
% 34.18/6.22 | |
% 34.18/6.22 | Case 2:
% 34.18/6.22 | |
% 34.18/6.22 | | (305) all_38_0 = 0
% 34.18/6.22 | |
% 34.18/6.22 | | REDUCE: (23), (305) imply:
% 34.18/6.22 | | (306) $false
% 34.18/6.22 | |
% 34.18/6.22 | | CLOSE: (306) is inconsistent.
% 34.18/6.22 | |
% 34.18/6.22 | End of split
% 34.18/6.22 |
% 34.18/6.22 End of proof
% 34.18/6.22
% 34.18/6.22 Sub-proof #1 shows that the following formulas are inconsistent:
% 34.18/6.22 ----------------------------------------------------------------
% 34.18/6.22 (1) unorthogonal_lines(all_38_3, all_38_1) = all_73_0
% 34.18/6.22 (2) unorthogonal_lines(all_38_3, all_38_1) = all_282_0
% 34.18/6.22 (3) unorthogonal_lines(all_38_3, all_38_1) = 0
% 34.18/6.22 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 34.18/6.22 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 34.18/6.22 (unorthogonal_lines(v3, v2) = v0))
% 34.18/6.22 (5) ~ (all_73_0 = 0)
% 34.18/6.22
% 34.18/6.22 Begin of proof
% 34.18/6.22 |
% 34.18/6.22 | GROUND_INST: instantiating (4) with all_73_0, all_282_0, all_38_1, all_38_3,
% 34.18/6.22 | simplifying with (1), (2) gives:
% 34.18/6.22 | (6) all_282_0 = all_73_0
% 34.18/6.22 |
% 34.18/6.22 | GROUND_INST: instantiating (4) with 0, all_282_0, all_38_1, all_38_3,
% 34.18/6.22 | simplifying with (2), (3) gives:
% 34.18/6.22 | (7) all_282_0 = 0
% 34.18/6.22 |
% 34.18/6.22 | COMBINE_EQS: (6), (7) imply:
% 34.18/6.22 | (8) all_73_0 = 0
% 34.18/6.22 |
% 34.18/6.22 | SIMP: (8) implies:
% 34.18/6.22 | (9) all_73_0 = 0
% 34.18/6.22 |
% 34.18/6.22 | REDUCE: (5), (9) imply:
% 34.18/6.22 | (10) $false
% 34.18/6.22 |
% 34.18/6.22 | CLOSE: (10) is inconsistent.
% 34.18/6.22 |
% 34.18/6.22 End of proof
% 34.18/6.22
% 34.18/6.22 Sub-proof #2 shows that the following formulas are inconsistent:
% 34.18/6.22 ----------------------------------------------------------------
% 34.18/6.22 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 34.18/6.22 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 34.18/6.22 (unorthogonal_lines(v3, v2) = v0))
% 34.18/6.22 (2) unorthogonal_lines(all_38_2, all_38_3) = all_51_0
% 34.18/6.22 (3) unorthogonal_lines(all_38_2, all_38_3) = 0
% 34.18/6.22 (4) ~ (all_51_0 = 0)
% 34.18/6.22
% 34.18/6.22 Begin of proof
% 34.18/6.22 |
% 34.18/6.22 | GROUND_INST: instantiating (1) with all_51_0, 0, all_38_3, all_38_2,
% 34.18/6.22 | simplifying with (2), (3) gives:
% 34.18/6.22 | (5) all_51_0 = 0
% 34.18/6.22 |
% 34.18/6.22 | REDUCE: (4), (5) imply:
% 34.18/6.22 | (6) $false
% 34.18/6.22 |
% 34.18/6.22 | CLOSE: (6) is inconsistent.
% 34.18/6.22 |
% 34.18/6.22 End of proof
% 34.18/6.22
% 34.18/6.22 Sub-proof #3 shows that the following formulas are inconsistent:
% 34.18/6.22 ----------------------------------------------------------------
% 34.18/6.22 (1) ~ (all_47_0 = 0)
% 34.18/6.22 (2) convergent_lines(all_38_2, all_38_2) = all_107_0
% 34.18/6.22 (3) (all_291_0 = 0 & all_291_1 = 0 & unorthogonal_lines(all_38_1, all_38_2) =
% 34.18/6.22 0 & convergent_lines(all_38_1, all_38_2) = 0) | (all_291_2 = 0 &
% 34.18/6.22 all_107_0 = 0 & unorthogonal_lines(all_38_2, all_38_2) = 0) | ( ~
% 34.18/6.22 (all_291_3 = 0) & convergent_lines(all_38_2, all_38_1) = all_291_3)
% 34.18/6.22 (4) (all_256_0 = 0 & unorthogonal_lines(all_38_1, all_38_2) = 0) | (all_256_1
% 34.18/6.22 = 0 & all_256_2 = 0 & unorthogonal_lines(all_38_2, all_38_2) = 0 &
% 34.18/6.22 convergent_lines(all_38_2, all_38_2) = 0) | ( ~ (all_256_3 = 0) &
% 34.18/6.22 convergent_lines(all_38_2, all_38_1) = all_256_3)
% 34.18/6.22 (5) convergent_lines(all_38_2, all_38_1) = all_300_0
% 34.18/6.22 (6) convergent_lines(all_38_2, all_38_1) = all_257_0
% 34.18/6.22 (7) convergent_lines(all_38_2, all_38_1) = all_296_3
% 34.18/6.23 (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 34.18/6.23 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 34.18/6.23 (convergent_lines(v3, v2) = v0))
% 34.18/6.23 (9) unorthogonal_lines(all_38_1, all_38_2) = all_47_0
% 34.18/6.23 (10) ~ (all_107_0 = 0)
% 34.18/6.23 (11) convergent_lines(all_38_2, all_38_2) = all_75_3
% 34.18/6.23 (12) ~ (all_75_3 = 0)
% 34.18/6.23 (13) convergent_lines(all_38_2, all_38_1) = 0
% 34.18/6.23 (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 34.18/6.23 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 34.18/6.23 (unorthogonal_lines(v3, v2) = v0))
% 34.18/6.23
% 34.18/6.23 Begin of proof
% 34.18/6.23 |
% 34.18/6.23 | BETA: splitting (4) gives:
% 34.18/6.23 |
% 34.18/6.23 | Case 1:
% 34.18/6.23 | |
% 34.18/6.23 | | (15) all_256_0 = 0 & unorthogonal_lines(all_38_1, all_38_2) = 0
% 34.18/6.23 | |
% 34.18/6.23 | | ALPHA: (15) implies:
% 34.18/6.23 | | (16) unorthogonal_lines(all_38_1, all_38_2) = 0
% 34.18/6.23 | |
% 34.18/6.23 | | REF_CLOSE: (1), (9), (14), (16) are inconsistent by sub-proof #8.
% 34.18/6.23 | |
% 34.18/6.23 | Case 2:
% 34.18/6.23 | |
% 34.18/6.23 | | (17) (all_256_1 = 0 & all_256_2 = 0 & unorthogonal_lines(all_38_2,
% 34.18/6.23 | | all_38_2) = 0 & convergent_lines(all_38_2, all_38_2) = 0) | ( ~
% 34.18/6.23 | | (all_256_3 = 0) & convergent_lines(all_38_2, all_38_1) =
% 34.18/6.23 | | all_256_3)
% 34.18/6.23 | |
% 34.18/6.23 | | BETA: splitting (17) gives:
% 34.18/6.23 | |
% 34.18/6.23 | | Case 1:
% 34.18/6.23 | | |
% 34.18/6.23 | | | (18) all_256_1 = 0 & all_256_2 = 0 & unorthogonal_lines(all_38_2,
% 34.18/6.23 | | | all_38_2) = 0 & convergent_lines(all_38_2, all_38_2) = 0
% 34.18/6.23 | | |
% 34.18/6.23 | | | ALPHA: (18) implies:
% 34.18/6.23 | | | (19) convergent_lines(all_38_2, all_38_2) = 0
% 34.18/6.23 | | |
% 34.18/6.23 | | | REF_CLOSE: (2), (8), (11), (12), (19) are inconsistent by sub-proof #10.
% 34.18/6.23 | | |
% 34.18/6.23 | | Case 2:
% 34.18/6.23 | | |
% 34.18/6.23 | | | (20) ~ (all_256_3 = 0) & convergent_lines(all_38_2, all_38_1) =
% 34.18/6.23 | | | all_256_3
% 34.18/6.23 | | |
% 34.18/6.23 | | | ALPHA: (20) implies:
% 34.18/6.23 | | | (21) ~ (all_256_3 = 0)
% 34.18/6.23 | | | (22) convergent_lines(all_38_2, all_38_1) = all_256_3
% 34.18/6.23 | | |
% 34.18/6.23 | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (13), (14), (21), (22)
% 34.18/6.23 | | | are inconsistent by sub-proof #7.
% 34.18/6.23 | | |
% 34.18/6.23 | | End of split
% 34.18/6.23 | |
% 34.18/6.23 | End of split
% 34.18/6.23 |
% 34.18/6.23 End of proof
% 34.18/6.23
% 34.18/6.23 Sub-proof #4 shows that the following formulas are inconsistent:
% 34.18/6.23 ----------------------------------------------------------------
% 34.18/6.23 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 34.18/6.23 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 34.18/6.23 (convergent_lines(v3, v2) = v0))
% 34.18/6.23 (2) convergent_lines(all_38_1, all_38_1) = all_71_1
% 34.18/6.23 (3) convergent_lines(all_38_1, all_38_1) = 0
% 34.18/6.23 (4) ~ (all_71_1 = 0)
% 34.18/6.23
% 34.18/6.23 Begin of proof
% 34.18/6.23 |
% 34.18/6.23 | GROUND_INST: instantiating (1) with 0, all_71_1, all_38_1, all_38_1,
% 34.18/6.23 | simplifying with (2), (3) gives:
% 34.18/6.23 | (5) all_71_1 = 0
% 34.18/6.23 |
% 34.18/6.23 | REDUCE: (4), (5) imply:
% 34.18/6.23 | (6) $false
% 34.18/6.23 |
% 34.18/6.23 | CLOSE: (6) is inconsistent.
% 34.18/6.23 |
% 34.18/6.23 End of proof
% 34.18/6.23
% 34.18/6.23 Sub-proof #5 shows that the following formulas are inconsistent:
% 34.18/6.23 ----------------------------------------------------------------
% 34.18/6.23 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 34.18/6.23 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 34.18/6.23 (unorthogonal_lines(v3, v2) = v0))
% 34.18/6.23 (2) unorthogonal_lines(all_38_1, all_38_1) = all_71_0
% 34.18/6.23 (3) unorthogonal_lines(all_38_1, all_38_1) = 0
% 34.18/6.23 (4) ~ (all_71_0 = 0)
% 34.18/6.23
% 34.18/6.23 Begin of proof
% 34.18/6.23 |
% 34.18/6.23 | GROUND_INST: instantiating (1) with 0, all_71_0, all_38_1, all_38_1,
% 34.18/6.23 | simplifying with (2), (3) gives:
% 34.18/6.23 | (5) all_71_0 = 0
% 34.18/6.23 |
% 34.18/6.23 | REDUCE: (4), (5) imply:
% 34.18/6.23 | (6) $false
% 34.18/6.23 |
% 34.18/6.23 | CLOSE: (6) is inconsistent.
% 34.18/6.23 |
% 34.18/6.23 End of proof
% 34.18/6.23
% 34.18/6.23 Sub-proof #6 shows that the following formulas are inconsistent:
% 34.18/6.23 ----------------------------------------------------------------
% 34.18/6.23 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 34.18/6.23 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 34.18/6.23 (unorthogonal_lines(v3, v2) = v0))
% 34.18/6.23 (2) unorthogonal_lines(all_38_3, all_38_1) = all_69_0
% 34.18/6.23 (3) unorthogonal_lines(all_38_3, all_38_1) = 0
% 34.18/6.23 (4) ~ (all_69_0 = 0)
% 34.18/6.23
% 34.18/6.23 Begin of proof
% 34.18/6.23 |
% 34.18/6.23 | GROUND_INST: instantiating (1) with 0, all_69_0, all_38_1, all_38_3,
% 34.18/6.23 | simplifying with (2), (3) gives:
% 34.18/6.23 | (5) all_69_0 = 0
% 34.18/6.23 |
% 34.18/6.23 | REDUCE: (4), (5) imply:
% 34.18/6.23 | (6) $false
% 34.18/6.23 |
% 34.18/6.23 | CLOSE: (6) is inconsistent.
% 34.18/6.23 |
% 34.18/6.23 End of proof
% 34.18/6.23
% 34.18/6.23 Sub-proof #7 shows that the following formulas are inconsistent:
% 34.18/6.23 ----------------------------------------------------------------
% 34.18/6.23 (1) ~ (all_47_0 = 0)
% 34.18/6.23 (2) (all_291_0 = 0 & all_291_1 = 0 & unorthogonal_lines(all_38_1, all_38_2) =
% 34.18/6.23 0 & convergent_lines(all_38_1, all_38_2) = 0) | (all_291_2 = 0 &
% 34.18/6.23 all_107_0 = 0 & unorthogonal_lines(all_38_2, all_38_2) = 0) | ( ~
% 34.18/6.23 (all_291_3 = 0) & convergent_lines(all_38_2, all_38_1) = all_291_3)
% 34.18/6.23 (3) convergent_lines(all_38_2, all_38_1) = all_300_0
% 34.18/6.23 (4) convergent_lines(all_38_2, all_38_1) = all_257_0
% 34.18/6.23 (5) ~ (all_256_3 = 0)
% 34.18/6.23 (6) convergent_lines(all_38_2, all_38_1) = all_296_3
% 34.18/6.23 (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 34.18/6.23 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 34.18/6.23 (convergent_lines(v3, v2) = v0))
% 34.18/6.23 (8) convergent_lines(all_38_2, all_38_1) = all_256_3
% 34.18/6.23 (9) unorthogonal_lines(all_38_1, all_38_2) = all_47_0
% 34.18/6.23 (10) ~ (all_107_0 = 0)
% 34.18/6.23 (11) convergent_lines(all_38_2, all_38_1) = 0
% 34.18/6.23 (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 34.18/6.23 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 34.18/6.23 (unorthogonal_lines(v3, v2) = v0))
% 34.18/6.23
% 34.18/6.23 Begin of proof
% 34.18/6.23 |
% 34.18/6.23 | BETA: splitting (2) gives:
% 34.18/6.23 |
% 34.18/6.23 | Case 1:
% 34.18/6.23 | |
% 34.18/6.23 | | (13) all_291_0 = 0 & all_291_1 = 0 & unorthogonal_lines(all_38_1,
% 34.18/6.23 | | all_38_2) = 0 & convergent_lines(all_38_1, all_38_2) = 0
% 34.18/6.23 | |
% 34.18/6.23 | | ALPHA: (13) implies:
% 34.18/6.23 | | (14) unorthogonal_lines(all_38_1, all_38_2) = 0
% 34.18/6.23 | |
% 34.18/6.23 | | REF_CLOSE: (1), (9), (12), (14) are inconsistent by sub-proof #8.
% 34.18/6.23 | |
% 34.18/6.23 | Case 2:
% 34.18/6.23 | |
% 34.18/6.23 | | (15) (all_291_2 = 0 & all_107_0 = 0 & unorthogonal_lines(all_38_2,
% 34.18/6.23 | | all_38_2) = 0) | ( ~ (all_291_3 = 0) &
% 34.18/6.23 | | convergent_lines(all_38_2, all_38_1) = all_291_3)
% 34.18/6.23 | |
% 34.18/6.23 | | BETA: splitting (15) gives:
% 34.18/6.23 | |
% 34.18/6.23 | | Case 1:
% 34.18/6.23 | | |
% 34.18/6.23 | | | (16) all_291_2 = 0 & all_107_0 = 0 & unorthogonal_lines(all_38_2,
% 34.18/6.23 | | | all_38_2) = 0
% 34.18/6.23 | | |
% 34.18/6.23 | | | ALPHA: (16) implies:
% 34.18/6.23 | | | (17) all_107_0 = 0
% 34.18/6.23 | | |
% 34.18/6.23 | | | REDUCE: (10), (17) imply:
% 34.18/6.23 | | | (18) $false
% 34.18/6.23 | | |
% 34.18/6.23 | | | CLOSE: (18) is inconsistent.
% 34.18/6.23 | | |
% 34.18/6.23 | | Case 2:
% 34.18/6.23 | | |
% 34.18/6.23 | | | (19) ~ (all_291_3 = 0) & convergent_lines(all_38_2, all_38_1) =
% 34.18/6.23 | | | all_291_3
% 34.18/6.23 | | |
% 34.18/6.23 | | | ALPHA: (19) implies:
% 34.18/6.23 | | | (20) convergent_lines(all_38_2, all_38_1) = all_291_3
% 34.18/6.23 | | |
% 34.18/6.23 | | | GROUND_INST: instantiating (7) with 0, all_291_3, all_38_1, all_38_2,
% 34.18/6.23 | | | simplifying with (11), (20) gives:
% 34.18/6.23 | | | (21) all_291_3 = 0
% 34.18/6.23 | | |
% 34.18/6.23 | | | GROUND_INST: instantiating (7) with all_296_3, all_300_0, all_38_1,
% 34.18/6.23 | | | all_38_2, simplifying with (3), (6) gives:
% 34.18/6.23 | | | (22) all_300_0 = all_296_3
% 34.18/6.23 | | |
% 34.18/6.23 | | | GROUND_INST: instantiating (7) with all_291_3, all_300_0, all_38_1,
% 34.18/6.23 | | | all_38_2, simplifying with (3), (20) gives:
% 34.18/6.23 | | | (23) all_300_0 = all_291_3
% 34.18/6.23 | | |
% 34.18/6.23 | | | GROUND_INST: instantiating (7) with all_257_0, all_300_0, all_38_1,
% 34.18/6.23 | | | all_38_2, simplifying with (3), (4) gives:
% 34.18/6.23 | | | (24) all_300_0 = all_257_0
% 34.18/6.23 | | |
% 34.18/6.23 | | | GROUND_INST: instantiating (7) with all_256_3, all_300_0, all_38_1,
% 34.18/6.23 | | | all_38_2, simplifying with (3), (8) gives:
% 34.18/6.23 | | | (25) all_300_0 = all_256_3
% 34.18/6.23 | | |
% 34.18/6.23 | | | COMBINE_EQS: (22), (25) imply:
% 34.18/6.23 | | | (26) all_296_3 = all_256_3
% 34.18/6.23 | | |
% 34.18/6.23 | | | COMBINE_EQS: (22), (24) imply:
% 34.18/6.23 | | | (27) all_296_3 = all_257_0
% 34.18/6.23 | | |
% 34.18/6.23 | | | COMBINE_EQS: (22), (23) imply:
% 34.18/6.23 | | | (28) all_296_3 = all_291_3
% 34.18/6.23 | | |
% 34.18/6.23 | | | COMBINE_EQS: (27), (28) imply:
% 34.18/6.24 | | | (29) all_291_3 = all_257_0
% 34.18/6.24 | | |
% 34.18/6.24 | | | SIMP: (29) implies:
% 34.18/6.24 | | | (30) all_291_3 = all_257_0
% 34.18/6.24 | | |
% 34.18/6.24 | | | COMBINE_EQS: (26), (27) imply:
% 34.18/6.24 | | | (31) all_257_0 = all_256_3
% 34.18/6.24 | | |
% 34.18/6.24 | | | COMBINE_EQS: (21), (30) imply:
% 34.18/6.24 | | | (32) all_257_0 = 0
% 34.18/6.24 | | |
% 34.18/6.24 | | | SIMP: (32) implies:
% 34.18/6.24 | | | (33) all_257_0 = 0
% 34.18/6.24 | | |
% 34.18/6.24 | | | COMBINE_EQS: (31), (33) imply:
% 34.18/6.24 | | | (34) all_256_3 = 0
% 34.18/6.24 | | |
% 34.18/6.24 | | | SIMP: (34) implies:
% 34.18/6.24 | | | (35) all_256_3 = 0
% 34.18/6.24 | | |
% 34.18/6.24 | | | REDUCE: (5), (35) imply:
% 34.18/6.24 | | | (36) $false
% 34.18/6.24 | | |
% 34.18/6.24 | | | CLOSE: (36) is inconsistent.
% 34.18/6.24 | | |
% 34.18/6.24 | | End of split
% 34.18/6.24 | |
% 34.18/6.24 | End of split
% 34.18/6.24 |
% 34.18/6.24 End of proof
% 34.18/6.24
% 34.18/6.24 Sub-proof #8 shows that the following formulas are inconsistent:
% 34.18/6.24 ----------------------------------------------------------------
% 34.18/6.24 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 34.18/6.24 ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 34.18/6.24 (unorthogonal_lines(v3, v2) = v0))
% 34.18/6.24 (2) unorthogonal_lines(all_38_1, all_38_2) = all_47_0
% 34.18/6.24 (3) unorthogonal_lines(all_38_1, all_38_2) = 0
% 34.18/6.24 (4) ~ (all_47_0 = 0)
% 34.18/6.24
% 34.18/6.24 Begin of proof
% 34.18/6.24 |
% 34.18/6.24 | GROUND_INST: instantiating (1) with all_47_0, 0, all_38_2, all_38_1,
% 34.18/6.24 | simplifying with (2), (3) gives:
% 34.18/6.24 | (5) all_47_0 = 0
% 34.18/6.24 |
% 34.18/6.24 | REDUCE: (4), (5) imply:
% 34.18/6.24 | (6) $false
% 34.18/6.24 |
% 34.18/6.24 | CLOSE: (6) is inconsistent.
% 34.18/6.24 |
% 34.18/6.24 End of proof
% 34.18/6.24
% 34.18/6.24 Sub-proof #9 shows that the following formulas are inconsistent:
% 34.18/6.24 ----------------------------------------------------------------
% 34.18/6.24 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 34.18/6.24 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 34.18/6.24 (convergent_lines(v3, v2) = v0))
% 34.18/6.24 (2) convergent_lines(all_38_1, all_38_1) = all_77_3
% 34.18/6.24 (3) convergent_lines(all_38_1, all_38_1) = 0
% 34.18/6.24 (4) ~ (all_77_3 = 0)
% 34.18/6.24
% 34.18/6.24 Begin of proof
% 34.18/6.24 |
% 34.18/6.24 | GROUND_INST: instantiating (1) with 0, all_77_3, all_38_1, all_38_1,
% 34.18/6.24 | simplifying with (2), (3) gives:
% 34.18/6.24 | (5) all_77_3 = 0
% 34.18/6.24 |
% 34.18/6.24 | REDUCE: (4), (5) imply:
% 34.18/6.24 | (6) $false
% 34.18/6.24 |
% 34.18/6.24 | CLOSE: (6) is inconsistent.
% 34.18/6.24 |
% 34.18/6.24 End of proof
% 34.18/6.24
% 34.18/6.24 Sub-proof #10 shows that the following formulas are inconsistent:
% 34.18/6.24 ----------------------------------------------------------------
% 34.18/6.24 (1) convergent_lines(all_38_2, all_38_2) = all_107_0
% 34.18/6.24 (2) convergent_lines(all_38_2, all_38_2) = 0
% 34.18/6.24 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 34.18/6.24 ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 34.18/6.24 (convergent_lines(v3, v2) = v0))
% 34.18/6.24 (4) convergent_lines(all_38_2, all_38_2) = all_75_3
% 34.18/6.24 (5) ~ (all_75_3 = 0)
% 34.18/6.24
% 34.18/6.24 Begin of proof
% 34.18/6.24 |
% 34.18/6.24 | GROUND_INST: instantiating (3) with all_107_0, 0, all_38_2, all_38_2,
% 34.18/6.24 | simplifying with (1), (2) gives:
% 34.18/6.24 | (6) all_107_0 = 0
% 34.18/6.24 |
% 34.18/6.24 | GROUND_INST: instantiating (3) with all_107_0, all_75_3, all_38_2, all_38_2,
% 34.18/6.24 | simplifying with (1), (4) gives:
% 34.18/6.24 | (7) all_107_0 = all_75_3
% 34.18/6.24 |
% 34.18/6.24 | COMBINE_EQS: (6), (7) imply:
% 34.18/6.24 | (8) all_75_3 = 0
% 34.18/6.24 |
% 34.18/6.24 | REDUCE: (5), (8) imply:
% 34.18/6.24 | (9) $false
% 34.18/6.24 |
% 34.18/6.24 | CLOSE: (9) is inconsistent.
% 34.18/6.24 |
% 34.18/6.24 End of proof
% 34.18/6.24 % SZS output end Proof for theBenchmark
% 34.18/6.24
% 34.18/6.24 5654ms
%------------------------------------------------------------------------------