TSTP Solution File: GEO227+3 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO227+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 : n016.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 23:22:34 EDT 2023
% Result : Theorem 12.66s 2.39s
% Output : Proof 14.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GEO227+3 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 23:50:31 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.61/0.60 ________ _____
% 0.61/0.60 ___ __ \_________(_)________________________________
% 0.61/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.61/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.61/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.61/0.60
% 0.61/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.61/0.60 (2023-06-19)
% 0.61/0.60
% 0.61/0.60 (c) Philipp Rümmer, 2009-2023
% 0.61/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.61/0.60 Amanda Stjerna.
% 0.61/0.60 Free software under BSD-3-Clause.
% 0.61/0.60
% 0.61/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.61/0.60
% 0.61/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.64/0.61 Running up to 7 provers in parallel.
% 0.64/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.64/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.64/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.64/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.64/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.64/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.64/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.59/1.18 Prover 1: Preprocessing ...
% 3.59/1.19 Prover 4: Preprocessing ...
% 3.90/1.23 Prover 6: Preprocessing ...
% 3.90/1.23 Prover 2: Preprocessing ...
% 3.90/1.23 Prover 0: Preprocessing ...
% 3.90/1.23 Prover 5: Preprocessing ...
% 3.90/1.23 Prover 3: Preprocessing ...
% 7.37/1.77 Prover 5: Proving ...
% 8.19/1.80 Prover 2: Proving ...
% 8.35/1.82 Prover 6: Constructing countermodel ...
% 8.37/1.83 Prover 3: Constructing countermodel ...
% 8.37/1.83 Prover 1: Constructing countermodel ...
% 8.97/1.98 Prover 6: gave up
% 8.97/1.98 Prover 1: gave up
% 9.53/1.98 Prover 3: gave up
% 9.53/1.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.53/2.00 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.53/2.01 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 10.25/2.09 Prover 8: Preprocessing ...
% 10.39/2.11 Prover 9: Preprocessing ...
% 10.58/2.13 Prover 7: Preprocessing ...
% 10.58/2.19 Prover 4: Constructing countermodel ...
% 11.28/2.23 Prover 7: Warning: ignoring some quantifiers
% 11.28/2.26 Prover 0: Proving ...
% 11.28/2.27 Prover 7: Constructing countermodel ...
% 11.91/2.29 Prover 8: Warning: ignoring some quantifiers
% 11.91/2.31 Prover 8: Constructing countermodel ...
% 12.66/2.39 Prover 0: proved (1775ms)
% 12.66/2.39
% 12.66/2.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.66/2.39
% 12.66/2.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.72/2.40 Prover 5: stopped
% 12.81/2.41 Prover 2: stopped
% 12.83/2.41 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.83/2.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.83/2.42 Prover 7: gave up
% 12.83/2.42 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 12.83/2.45 Prover 8: gave up
% 12.83/2.45 Prover 4: Found proof (size 39)
% 12.83/2.45 Prover 4: proved (1835ms)
% 12.83/2.46 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 12.83/2.46 Prover 10: Preprocessing ...
% 12.83/2.46 Prover 16: Preprocessing ...
% 12.83/2.47 Prover 13: Preprocessing ...
% 12.83/2.48 Prover 11: Preprocessing ...
% 12.83/2.50 Prover 19: Preprocessing ...
% 12.83/2.50 Prover 16: stopped
% 13.54/2.50 Prover 10: stopped
% 13.54/2.51 Prover 13: stopped
% 13.54/2.58 Prover 9: Constructing countermodel ...
% 13.54/2.58 Prover 11: stopped
% 14.13/2.59 Prover 9: stopped
% 14.13/2.62 Prover 19: Warning: ignoring some quantifiers
% 14.13/2.64 Prover 19: Constructing countermodel ...
% 14.13/2.64 Prover 19: stopped
% 14.13/2.64
% 14.13/2.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.13/2.65
% 14.13/2.65 % SZS output start Proof for theBenchmark
% 14.13/2.65 Assumptions after simplification:
% 14.13/2.65 ---------------------------------
% 14.13/2.65
% 14.13/2.65 (a1_defns)
% 14.13/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 14.13/2.68 (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ~
% 14.13/2.68 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) &
% 14.13/2.68 unequally_directed_opposite_lines(v0, v1) = v4)) & ! [v0: $i] : ! [v1:
% 14.13/2.68 $i] : ! [v2: int] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1)
% 14.13/2.68 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0)
% 14.13/2.68 & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4 & $i(v3)))
% 14.13/2.68 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (reverse_line(v1) = v2) | ~
% 14.13/2.68 (unequally_directed_lines(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) |
% 14.13/2.68 unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] :
% 14.13/2.68 ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 14.13/2.68 ? [v2: $i] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0 &
% 14.13/2.68 $i(v2)))
% 14.13/2.68
% 14.13/2.68 (a4_defns)
% 14.60/2.69 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 14.60/2.69 (equally_directed_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 14.60/2.69 unequally_directed_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 14.60/2.69 int] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | ~ $i(v1) | ~
% 14.60/2.69 $i(v0) | equally_directed_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : (
% 14.60/2.69 ~ (equally_directed_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 14.60/2.69 int] : ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2)) & ! [v0:
% 14.60/2.69 $i] : ! [v1: $i] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v1) |
% 14.60/2.69 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & equally_directed_lines(v0, v1) =
% 14.60/2.69 v2))
% 14.60/2.69
% 14.60/2.69 (a5_defns)
% 14.60/2.69 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 14.60/2.69 (equally_directed_opposite_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 14.60/2.69 unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] :
% 14.60/2.69 ! [v2: int] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) |
% 14.60/2.69 ~ $i(v1) | ~ $i(v0) | equally_directed_opposite_lines(v0, v1) = 0) & !
% 14.60/2.69 [v0: $i] : ! [v1: $i] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) |
% 14.60/2.69 ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 14.60/2.69 unequally_directed_opposite_lines(v0, v1) = v2)) & ! [v0: $i] : ! [v1:
% 14.60/2.69 $i] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ~ $i(v1) | ~
% 14.60/2.69 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & equally_directed_opposite_lines(v0,
% 14.60/2.69 v1) = v2))
% 14.60/2.69
% 14.60/2.69 (ax7_basics)
% 14.70/2.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 14.70/2.71 any] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~
% 14.70/2.71 (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0,
% 14.70/2.71 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 14.70/2.71 any] : ? [v8: any] : ? [v9: any] : (unequally_directed_lines(v1, v2) =
% 14.70/2.71 v9 & unequally_directed_lines(v0, v4) = v8 & unequally_directed_lines(v0,
% 14.70/2.71 v2) = v7 & unequally_directed_lines(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 =
% 14.70/2.71 0 & v5 = 0) | (v8 = 0 & v7 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 14.70/2.71 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (reverse_line(v2) =
% 14.70/2.71 v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v4) =
% 14.70/2.71 v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) |
% 14.70/2.71 ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: any] :
% 14.70/2.71 (unequally_directed_lines(v1, v4) = v9 & unequally_directed_lines(v1, v2) =
% 14.70/2.71 v8 & unequally_directed_lines(v0, v2) = v7 & unequally_directed_lines(v0,
% 14.70/2.71 v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v8 = 0) | (v7 = 0 & v5 = 0)))) & !
% 14.70/2.71 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: $i] : ! [v5:
% 14.70/2.71 any] : ( ~ (reverse_line(v2) = v4) | ~ (unequally_directed_lines(v1, v4) =
% 14.70/2.71 v5) | ~ (unequally_directed_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 14.70/2.71 ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : ?
% 14.70/2.71 [v10: any] : (reverse_line(v1) = v7 & unequally_directed_lines(v1, v2) = v10
% 14.70/2.71 & unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v4)
% 14.70/2.71 = v9 & unequally_directed_lines(v0, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~
% 14.70/2.71 (v6 = 0) | (v10 = 0 & v5 = 0) | (v9 = 0 & v3 = 0)))) & ! [v0: $i] : !
% 14.70/2.71 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ! [v5: any] : ( ~
% 14.70/2.71 (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v3) = v5) | ~
% 14.70/2.71 (unequally_directed_lines(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 14.70/2.71 | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : ? [v10: any] :
% 14.70/2.71 (reverse_line(v1) = v7 & unequally_directed_lines(v1, v2) = v10 &
% 14.70/2.71 unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v2) =
% 14.70/2.71 v9 & unequally_directed_lines(v0, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~
% 14.70/2.71 (v6 = 0) | (v10 = 0 & v5 = 0) | (v9 = 0 & v4 = 0)))) & ! [v0: $i] : !
% 14.70/2.71 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ! [v5: any] : ( ~
% 14.70/2.71 (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = v5) | ~
% 14.70/2.71 (unequally_directed_lines(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 14.70/2.71 | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : ? [v10: any] :
% 14.70/2.71 (reverse_line(v1) = v7 & unequally_directed_lines(v1, v3) = v10 &
% 14.70/2.71 unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v2) =
% 14.70/2.71 v9 & unequally_directed_lines(v0, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~
% 14.70/2.71 (v6 = 0) | (v10 = 0 & v5 = 0) | (v9 = 0 & v4 = 0)))) & ! [v0: $i] : !
% 14.70/2.71 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ (reverse_line(v2) =
% 14.70/2.71 v3) | ~ (unequally_directed_lines(v1, v3) = v4) | ~
% 14.70/2.71 (unequally_directed_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 14.70/2.71 ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: any] :
% 14.70/2.71 (reverse_line(v1) = v5 & unequally_directed_lines(v1, v2) = v9 &
% 14.70/2.71 unequally_directed_lines(v0, v5) = v6 & unequally_directed_lines(v0, v3) =
% 14.70/2.71 v8 & unequally_directed_lines(v0, v2) = v7 & $i(v5) & ( ~ (v6 = 0) | (v9 =
% 14.70/2.71 0 & v4 = 0) | (v8 = 0 & v7 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 14.70/2.71 [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ (reverse_line(v2) = v3) | ~
% 14.70/2.71 (unequally_directed_lines(v0, v3) = v4) | ~ (unequally_directed_lines(v0,
% 14.70/2.71 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6:
% 14.70/2.71 any] : ? [v7: any] : ? [v8: any] : ? [v9: any] : (reverse_line(v1) = v5
% 14.70/2.71 & unequally_directed_lines(v1, v3) = v9 & unequally_directed_lines(v1, v2)
% 14.70/2.71 = v8 & unequally_directed_lines(v0, v5) = v6 &
% 14.70/2.71 unequally_directed_lines(v0, v2) = v7 & $i(v5) & ( ~ (v6 = 0) | (v9 = 0 &
% 14.70/2.71 v8 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 14.70/2.71 $i] : ! [v3: $i] : ! [v4: any] : ( ~ (reverse_line(v1) = v3) | ~
% 14.70/2.71 (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0,
% 14.70/2.71 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 14.70/2.71 any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : (reverse_line(v2) = v7
% 14.70/2.71 & unequally_directed_lines(v1, v7) = v9 & unequally_directed_lines(v0, v7)
% 14.70/2.71 = v8 & unequally_directed_lines(v0, v2) = v6 &
% 14.70/2.71 unequally_directed_lines(v0, v1) = v5 & $i(v7) & ( ~ (v5 = 0) | (v9 = 0 &
% 14.70/2.71 v4 = 0) | (v8 = 0 & v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 14.70/2.71 $i] : ! [v3: $i] : ! [v4: any] : ( ~ (reverse_line(v1) = v3) | ~
% 14.70/2.71 (unequally_directed_lines(v0, v3) = 0) | ~ (unequally_directed_lines(v0,
% 14.70/2.71 v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 14.70/2.71 $i] : ? [v7: any] : ? [v8: any] : ? [v9: any] : (reverse_line(v2) = v6
% 14.70/2.71 & unequally_directed_lines(v1, v6) = v9 & unequally_directed_lines(v1, v2)
% 14.70/2.71 = v8 & unequally_directed_lines(v0, v6) = v7 &
% 14.70/2.71 unequally_directed_lines(v0, v1) = v5 & $i(v6) & ( ~ (v5 = 0) | (v9 = 0 &
% 14.70/2.71 v8 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 14.70/2.71 $i] : ! [v3: any] : ! [v4: any] : ( ~ (unequally_directed_lines(v1, v2) =
% 14.70/2.71 v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 14.70/2.71 ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ?
% 14.70/2.71 [v9: any] : ? [v10: any] : (reverse_line(v2) = v8 & reverse_line(v1) = v6 &
% 14.70/2.71 unequally_directed_lines(v1, v8) = v10 & unequally_directed_lines(v0, v8)
% 14.70/2.71 = v9 & unequally_directed_lines(v0, v6) = v7 &
% 14.70/2.71 unequally_directed_lines(v0, v1) = v5 & $i(v8) & $i(v6) & ( ~ (v7 = 0) |
% 14.70/2.71 ~ (v5 = 0) | (v10 = 0 & v4 = 0) | (v9 = 0 & v3 = 0)))) & ! [v0: $i] :
% 14.70/2.71 ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unequally_directed_lines(v1,
% 14.70/2.72 v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v2) | ~
% 14.70/2.72 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: $i]
% 14.70/2.72 : ? [v8: any] : ? [v9: any] : (reverse_line(v2) = v7 & reverse_line(v1) =
% 14.70/2.72 v4 & unequally_directed_lines(v1, v7) = v9 & unequally_directed_lines(v0,
% 14.70/2.72 v7) = v8 & unequally_directed_lines(v0, v4) = v5 &
% 14.70/2.72 unequally_directed_lines(v0, v2) = v6 & $i(v7) & $i(v4) & ( ~ (v5 = 0) |
% 14.70/2.72 (v9 = 0 & v3 = 0) | (v8 = 0 & v6 = 0)))) & ! [v0: $i] : ! [v1: $i] :
% 14.70/2.72 ! [v2: $i] : ! [v3: any] : ( ~ (unequally_directed_lines(v0, v2) = v3) | ~
% 14.70/2.72 (unequally_directed_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 14.70/2.72 ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : ?
% 14.70/2.72 [v9: any] : (reverse_line(v2) = v6 & reverse_line(v1) = v4 &
% 14.70/2.72 unequally_directed_lines(v1, v6) = v9 & unequally_directed_lines(v1, v2) =
% 14.70/2.72 v8 & unequally_directed_lines(v0, v6) = v7 & unequally_directed_lines(v0,
% 14.70/2.72 v4) = v5 & $i(v6) & $i(v4) & ( ~ (v5 = 0) | (v9 = 0 & v8 = 0) | (v7 = 0
% 14.70/2.72 & v3 = 0))))
% 14.70/2.72
% 14.70/2.72 (ax8_basics)
% 14.75/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 14.75/2.72 (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ~
% 14.75/2.72 $i(v1) | ~ $i(v0) | unequally_directed_lines(v0, v1) = 0) & ! [v0: $i] :
% 14.75/2.72 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) =
% 14.75/2.72 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (reverse_line(v1) = v3 &
% 14.75/2.72 unequally_directed_lines(v0, v3) = 0 & $i(v3)))
% 14.75/2.72
% 14.75/2.72 (con)
% 14.75/2.72 ? [v0: $i] : ? [v1: $i] : (equally_directed_opposite_lines(v0, v1) = 0 &
% 14.75/2.72 equally_directed_lines(v0, v1) = 0 & $i(v1) & $i(v0))
% 14.75/2.72
% 14.75/2.72 (function-axioms)
% 14.75/2.73 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.75/2.73 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_on_line(v5, v4,
% 14.75/2.73 v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0:
% 14.75/2.73 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.75/2.73 : ! [v4: $i] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~
% 14.75/2.73 (before_on_line(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.75/2.73 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 14.75/2.73 (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) &
% 14.75/2.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.75/2.73 (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) =
% 14.75/2.73 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 14.75/2.73 ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 14.75/2.73 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.75/2.73 [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~
% 14.75/2.73 (distinct_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.75/2.73 ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 14.75/2.73 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.75/2.73 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.75/2.73 (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & !
% 14.75/2.73 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 14.75/2.73 $i] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~
% 14.75/2.73 (incident_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 14.75/2.73 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.75/2.73 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & !
% 14.75/2.73 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 14.75/2.73 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 14.75/2.73 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.75/2.73 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.75/2.73 (equally_directed_opposite_lines(v3, v2) = v1) | ~
% 14.75/2.73 (equally_directed_opposite_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool]
% 14.75/2.73 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.75/2.73 (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) =
% 14.75/2.73 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.75/2.73 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~
% 14.75/2.73 (left_convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.75/2.73 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.75/2.73 (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) =
% 14.75/2.73 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.75/2.73 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~
% 14.75/2.73 (left_apart_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.75/2.73 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.75/2.73 (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0)) & !
% 14.75/2.73 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 14.75/2.73 $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~
% 14.75/2.73 (unequally_directed_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 14.75/2.73 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.75/2.73 (unequally_directed_opposite_lines(v3, v2) = v1) | ~
% 14.75/2.73 (unequally_directed_opposite_lines(v3, v2) = v0)) & ! [v0:
% 14.75/2.73 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 14.75/2.73 ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 14.75/2.73 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (line(v2) = v1) | ~
% 14.75/2.73 (line(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 14.75/2.73 (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 14.75/2.73
% 14.75/2.73 Further assumptions not needed in the proof:
% 14.75/2.73 --------------------------------------------
% 14.75/2.73 a2_defns, a3_defns, a6_defns, a7_defns, a8_defns, a9_defns, ax10_basics,
% 14.75/2.73 ax10_cons_objs, ax11_basics, ax1_basics, ax1_cons_objs, ax1_subs, ax1_uniq_cons,
% 14.75/2.73 ax2_basics, ax2_cons_objs, ax2_subs, ax2_uniq_cons, ax3_basics, ax3_cons_objs,
% 14.75/2.73 ax3_subs, ax4_basics, ax4_cons_objs, ax4_defns, ax5_basics, ax5_cons_objs,
% 14.75/2.73 ax6_basics, ax6_cons_objs, ax7_cons_objs, ax8_cons_objs, ax9_basics,
% 14.75/2.73 ax9_cons_objs
% 14.75/2.73
% 14.75/2.73 Those formulas are unsatisfiable:
% 14.75/2.73 ---------------------------------
% 14.75/2.73
% 14.75/2.73 Begin of proof
% 14.75/2.73 |
% 14.75/2.73 | ALPHA: (a1_defns) implies:
% 14.75/2.73 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 14.75/2.73 | (unequally_directed_opposite_lines(v0, v1) = v2) | ~ $i(v1) | ~
% 14.75/2.73 | $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & reverse_line(v1)
% 14.75/2.73 | = v3 & unequally_directed_lines(v0, v3) = v4 & $i(v3)))
% 14.75/2.73 |
% 14.75/2.73 | ALPHA: (a4_defns) implies:
% 14.75/2.73 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (equally_directed_lines(v0, v1) = 0) |
% 14.75/2.73 | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 14.75/2.73 | unequally_directed_lines(v0, v1) = v2))
% 14.75/2.73 |
% 14.75/2.73 | ALPHA: (a5_defns) implies:
% 14.75/2.73 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (equally_directed_opposite_lines(v0,
% 14.75/2.73 | v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 14.75/2.73 | unequally_directed_opposite_lines(v0, v1) = v2))
% 14.75/2.73 |
% 14.75/2.73 | ALPHA: (ax7_basics) implies:
% 14.75/2.73 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] :
% 14.75/2.73 | ( ~ (unequally_directed_lines(v1, v2) = v4) | ~
% 14.75/2.73 | (unequally_directed_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 14.75/2.73 | $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ?
% 14.75/2.73 | [v9: any] : ? [v10: any] : (reverse_line(v2) = v8 & reverse_line(v1)
% 14.75/2.73 | = v6 & unequally_directed_lines(v1, v8) = v10 &
% 14.75/2.73 | unequally_directed_lines(v0, v8) = v9 &
% 14.75/2.73 | unequally_directed_lines(v0, v6) = v7 &
% 14.75/2.73 | unequally_directed_lines(v0, v1) = v5 & $i(v8) & $i(v6) & ( ~ (v7 =
% 14.75/2.73 | 0) | ~ (v5 = 0) | (v10 = 0 & v4 = 0) | (v9 = 0 & v3 = 0))))
% 14.75/2.73 |
% 14.75/2.73 | ALPHA: (ax8_basics) implies:
% 14.75/2.74 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 14.75/2.74 | (unequally_directed_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 14.75/2.74 | [v3: $i] : (reverse_line(v1) = v3 & unequally_directed_lines(v0, v3)
% 14.75/2.74 | = 0 & $i(v3)))
% 14.75/2.74 |
% 14.75/2.74 | ALPHA: (function-axioms) implies:
% 14.75/2.74 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 14.75/2.74 | (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 14.75/2.74 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.75/2.74 | ! [v3: $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) |
% 14.75/2.74 | ~ (unequally_directed_lines(v3, v2) = v0))
% 14.75/2.74 |
% 14.75/2.74 | DELTA: instantiating (con) with fresh symbols all_39_0, all_39_1 gives:
% 14.75/2.74 | (8) equally_directed_opposite_lines(all_39_1, all_39_0) = 0 &
% 14.75/2.74 | equally_directed_lines(all_39_1, all_39_0) = 0 & $i(all_39_0) &
% 14.75/2.74 | $i(all_39_1)
% 14.75/2.74 |
% 14.75/2.74 | ALPHA: (8) implies:
% 14.75/2.74 | (9) $i(all_39_1)
% 14.75/2.74 | (10) $i(all_39_0)
% 14.75/2.74 | (11) equally_directed_lines(all_39_1, all_39_0) = 0
% 14.75/2.74 | (12) equally_directed_opposite_lines(all_39_1, all_39_0) = 0
% 14.75/2.74 |
% 14.75/2.74 | GROUND_INST: instantiating (2) with all_39_1, all_39_0, simplifying with (9),
% 14.75/2.74 | (10), (11) gives:
% 14.75/2.74 | (13) ? [v0: int] : ( ~ (v0 = 0) & unequally_directed_lines(all_39_1,
% 14.75/2.74 | all_39_0) = v0)
% 14.75/2.74 |
% 14.75/2.74 | GROUND_INST: instantiating (3) with all_39_1, all_39_0, simplifying with (9),
% 14.75/2.74 | (10), (12) gives:
% 14.75/2.74 | (14) ? [v0: int] : ( ~ (v0 = 0) &
% 14.75/2.74 | unequally_directed_opposite_lines(all_39_1, all_39_0) = v0)
% 14.75/2.74 |
% 14.75/2.74 | DELTA: instantiating (14) with fresh symbol all_46_0 gives:
% 14.75/2.74 | (15) ~ (all_46_0 = 0) & unequally_directed_opposite_lines(all_39_1,
% 14.75/2.74 | all_39_0) = all_46_0
% 14.75/2.74 |
% 14.75/2.74 | ALPHA: (15) implies:
% 14.75/2.74 | (16) ~ (all_46_0 = 0)
% 14.75/2.74 | (17) unequally_directed_opposite_lines(all_39_1, all_39_0) = all_46_0
% 14.75/2.74 |
% 14.75/2.74 | DELTA: instantiating (13) with fresh symbol all_48_0 gives:
% 14.75/2.74 | (18) ~ (all_48_0 = 0) & unequally_directed_lines(all_39_1, all_39_0) =
% 14.75/2.74 | all_48_0
% 14.75/2.74 |
% 14.75/2.74 | ALPHA: (18) implies:
% 14.75/2.74 | (19) ~ (all_48_0 = 0)
% 14.75/2.74 | (20) unequally_directed_lines(all_39_1, all_39_0) = all_48_0
% 14.75/2.74 |
% 14.75/2.74 | GROUND_INST: instantiating (1) with all_39_1, all_39_0, all_46_0, simplifying
% 14.75/2.74 | with (9), (10), (17) gives:
% 14.75/2.75 | (21) all_46_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 14.75/2.75 | reverse_line(all_39_0) = v0 & unequally_directed_lines(all_39_1, v0)
% 14.75/2.75 | = v1 & $i(v0))
% 14.75/2.75 |
% 14.75/2.75 | GROUND_INST: instantiating (4) with all_39_1, all_39_1, all_39_0, all_48_0,
% 14.75/2.75 | all_48_0, simplifying with (9), (10), (20) gives:
% 14.75/2.75 | (22) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any]
% 14.75/2.75 | : ? [v5: any] : (reverse_line(all_39_0) = v3 & reverse_line(all_39_1)
% 14.75/2.75 | = v1 & unequally_directed_lines(all_39_1, v3) = v5 &
% 14.75/2.75 | unequally_directed_lines(all_39_1, v3) = v4 &
% 14.75/2.75 | unequally_directed_lines(all_39_1, v1) = v2 &
% 14.75/2.75 | unequally_directed_lines(all_39_1, all_39_1) = v0 & $i(v3) & $i(v1)
% 14.75/2.75 | & ( ~ (v2 = 0) | ~ (v0 = 0) | (v5 = 0 & all_48_0 = 0) | (v4 = 0 &
% 14.75/2.75 | all_48_0 = 0)))
% 14.75/2.75 |
% 14.75/2.75 | GROUND_INST: instantiating (5) with all_39_1, all_39_0, all_48_0, simplifying
% 14.75/2.75 | with (9), (10), (20) gives:
% 14.75/2.75 | (23) all_48_0 = 0 | ? [v0: $i] : (reverse_line(all_39_0) = v0 &
% 14.75/2.75 | unequally_directed_lines(all_39_1, v0) = 0 & $i(v0))
% 14.75/2.75 |
% 14.75/2.75 | DELTA: instantiating (22) with fresh symbols all_59_0, all_59_1, all_59_2,
% 14.75/2.75 | all_59_3, all_59_4, all_59_5 gives:
% 14.75/2.75 | (24) reverse_line(all_39_0) = all_59_2 & reverse_line(all_39_1) = all_59_4
% 14.75/2.75 | & unequally_directed_lines(all_39_1, all_59_2) = all_59_0 &
% 14.75/2.75 | unequally_directed_lines(all_39_1, all_59_2) = all_59_1 &
% 14.75/2.75 | unequally_directed_lines(all_39_1, all_59_4) = all_59_3 &
% 14.75/2.75 | unequally_directed_lines(all_39_1, all_39_1) = all_59_5 & $i(all_59_2)
% 14.75/2.75 | & $i(all_59_4) & ( ~ (all_59_3 = 0) | ~ (all_59_5 = 0) | (all_59_0 =
% 14.75/2.75 | 0 & all_48_0 = 0) | (all_59_1 = 0 & all_48_0 = 0))
% 14.75/2.75 |
% 14.75/2.75 | ALPHA: (24) implies:
% 14.75/2.75 | (25) reverse_line(all_39_0) = all_59_2
% 14.75/2.75 |
% 14.75/2.75 | BETA: splitting (21) gives:
% 14.75/2.75 |
% 14.75/2.75 | Case 1:
% 14.75/2.75 | |
% 14.75/2.75 | | (26) all_46_0 = 0
% 14.75/2.75 | |
% 14.75/2.75 | | REDUCE: (16), (26) imply:
% 14.75/2.75 | | (27) $false
% 14.75/2.75 | |
% 14.75/2.75 | | CLOSE: (27) is inconsistent.
% 14.75/2.75 | |
% 14.75/2.75 | Case 2:
% 14.75/2.75 | |
% 14.75/2.75 | | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & reverse_line(all_39_0) =
% 14.75/2.75 | | v0 & unequally_directed_lines(all_39_1, v0) = v1 & $i(v0))
% 14.75/2.75 | |
% 14.75/2.75 | | DELTA: instantiating (28) with fresh symbols all_65_0, all_65_1 gives:
% 14.75/2.75 | | (29) ~ (all_65_0 = 0) & reverse_line(all_39_0) = all_65_1 &
% 14.75/2.75 | | unequally_directed_lines(all_39_1, all_65_1) = all_65_0 &
% 14.75/2.75 | | $i(all_65_1)
% 14.75/2.75 | |
% 14.75/2.75 | | ALPHA: (29) implies:
% 14.75/2.75 | | (30) ~ (all_65_0 = 0)
% 14.75/2.75 | | (31) unequally_directed_lines(all_39_1, all_65_1) = all_65_0
% 14.75/2.75 | | (32) reverse_line(all_39_0) = all_65_1
% 14.75/2.75 | |
% 14.75/2.75 | | BETA: splitting (23) gives:
% 14.75/2.75 | |
% 14.75/2.75 | | Case 1:
% 14.75/2.75 | | |
% 14.75/2.75 | | | (33) all_48_0 = 0
% 14.75/2.75 | | |
% 14.75/2.75 | | | REDUCE: (19), (33) imply:
% 14.75/2.75 | | | (34) $false
% 14.75/2.75 | | |
% 14.75/2.75 | | | CLOSE: (34) is inconsistent.
% 14.75/2.75 | | |
% 14.75/2.75 | | Case 2:
% 14.75/2.75 | | |
% 14.75/2.75 | | | (35) ? [v0: $i] : (reverse_line(all_39_0) = v0 &
% 14.75/2.75 | | | unequally_directed_lines(all_39_1, v0) = 0 & $i(v0))
% 14.75/2.75 | | |
% 14.75/2.75 | | | DELTA: instantiating (35) with fresh symbol all_71_0 gives:
% 14.75/2.75 | | | (36) reverse_line(all_39_0) = all_71_0 &
% 14.75/2.75 | | | unequally_directed_lines(all_39_1, all_71_0) = 0 & $i(all_71_0)
% 14.75/2.75 | | |
% 14.75/2.75 | | | ALPHA: (36) implies:
% 14.75/2.75 | | | (37) unequally_directed_lines(all_39_1, all_71_0) = 0
% 14.75/2.76 | | | (38) reverse_line(all_39_0) = all_71_0
% 14.75/2.76 | | |
% 14.75/2.76 | | | GROUND_INST: instantiating (6) with all_65_1, all_71_0, all_39_0,
% 14.75/2.76 | | | simplifying with (32), (38) gives:
% 14.75/2.76 | | | (39) all_71_0 = all_65_1
% 14.75/2.76 | | |
% 14.75/2.76 | | | GROUND_INST: instantiating (6) with all_59_2, all_71_0, all_39_0,
% 14.75/2.76 | | | simplifying with (25), (38) gives:
% 14.75/2.76 | | | (40) all_71_0 = all_59_2
% 14.75/2.76 | | |
% 14.75/2.76 | | | COMBINE_EQS: (39), (40) imply:
% 14.75/2.76 | | | (41) all_65_1 = all_59_2
% 14.75/2.76 | | |
% 14.75/2.76 | | | SIMP: (41) implies:
% 14.75/2.76 | | | (42) all_65_1 = all_59_2
% 14.75/2.76 | | |
% 14.75/2.76 | | | REDUCE: (37), (40) imply:
% 14.75/2.76 | | | (43) unequally_directed_lines(all_39_1, all_59_2) = 0
% 14.75/2.76 | | |
% 14.75/2.76 | | | REDUCE: (31), (42) imply:
% 14.75/2.76 | | | (44) unequally_directed_lines(all_39_1, all_59_2) = all_65_0
% 14.75/2.76 | | |
% 14.75/2.76 | | | GROUND_INST: instantiating (7) with 0, all_65_0, all_59_2, all_39_1,
% 14.75/2.76 | | | simplifying with (43), (44) gives:
% 14.75/2.76 | | | (45) all_65_0 = 0
% 14.75/2.76 | | |
% 14.75/2.76 | | | REDUCE: (30), (45) imply:
% 14.75/2.76 | | | (46) $false
% 14.75/2.76 | | |
% 14.75/2.76 | | | CLOSE: (46) is inconsistent.
% 14.75/2.76 | | |
% 14.75/2.76 | | End of split
% 14.75/2.76 | |
% 14.75/2.76 | End of split
% 14.75/2.76 |
% 14.75/2.76 End of proof
% 14.75/2.76 % SZS output end Proof for theBenchmark
% 14.75/2.76
% 14.75/2.76 2160ms
%------------------------------------------------------------------------------