TSTP Solution File: GEO237+1 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO237+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n008.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 23:22:39 EDT 2023
% Result : Theorem 9.04s 1.95s
% Output : Proof 15.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO237+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 23:53:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.18/1.13 Prover 4: Preprocessing ...
% 3.36/1.15 Prover 1: Preprocessing ...
% 3.36/1.16 Prover 2: Preprocessing ...
% 3.36/1.16 Prover 5: Preprocessing ...
% 3.36/1.16 Prover 6: Preprocessing ...
% 3.36/1.17 Prover 0: Preprocessing ...
% 3.36/1.17 Prover 3: Preprocessing ...
% 6.35/1.60 Prover 5: Proving ...
% 6.93/1.66 Prover 2: Proving ...
% 6.93/1.69 Prover 6: Constructing countermodel ...
% 6.93/1.70 Prover 1: Constructing countermodel ...
% 6.93/1.70 Prover 3: Constructing countermodel ...
% 7.88/1.78 Prover 1: gave up
% 7.88/1.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.88/1.79 Prover 6: gave up
% 7.88/1.79 Prover 3: gave up
% 7.88/1.80 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.88/1.81 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 8.84/1.92 Prover 9: Preprocessing ...
% 8.84/1.93 Prover 8: Preprocessing ...
% 8.84/1.94 Prover 7: Preprocessing ...
% 9.04/1.95 Prover 5: proved (1329ms)
% 9.04/1.95
% 9.04/1.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.04/1.95
% 9.04/1.96 Prover 2: proved (1344ms)
% 9.04/1.96
% 9.04/1.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.04/1.96
% 9.04/1.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.04/1.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.04/2.05 Prover 10: Preprocessing ...
% 9.04/2.07 Prover 11: Preprocessing ...
% 9.04/2.08 Prover 7: Warning: ignoring some quantifiers
% 9.04/2.14 Prover 7: Constructing countermodel ...
% 9.04/2.14 Prover 4: Constructing countermodel ...
% 9.04/2.14 Prover 10: Warning: ignoring some quantifiers
% 10.26/2.18 Prover 8: Warning: ignoring some quantifiers
% 10.26/2.18 Prover 10: Constructing countermodel ...
% 10.26/2.21 Prover 7: gave up
% 10.94/2.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.94/2.21 Prover 8: Constructing countermodel ...
% 10.94/2.28 Prover 10: gave up
% 11.50/2.29 Prover 0: Proving ...
% 11.50/2.29 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 11.50/2.29 Prover 13: Preprocessing ...
% 11.50/2.29 Prover 0: stopped
% 11.50/2.30 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 11.50/2.34 Prover 8: gave up
% 11.50/2.34 Prover 19: Preprocessing ...
% 12.17/2.38 Prover 16: Preprocessing ...
% 12.32/2.40 Prover 13: Warning: ignoring some quantifiers
% 12.54/2.41 Prover 13: Constructing countermodel ...
% 12.61/2.47 Prover 16: Warning: ignoring some quantifiers
% 12.61/2.48 Prover 16: Constructing countermodel ...
% 12.61/2.50 Prover 19: Warning: ignoring some quantifiers
% 12.61/2.50 Prover 9: Constructing countermodel ...
% 13.24/2.51 Prover 19: Constructing countermodel ...
% 13.24/2.51 Prover 9: stopped
% 13.24/2.55 Prover 13: gave up
% 13.24/2.55 Prover 11: Constructing countermodel ...
% 13.24/2.57 Prover 16: gave up
% 14.53/2.75 Prover 19: gave up
% 14.53/2.76 Prover 11: Found proof (size 89)
% 14.53/2.76 Prover 11: proved (773ms)
% 14.53/2.76 Prover 4: stopped
% 14.53/2.76
% 14.53/2.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.53/2.76
% 14.53/2.76 % SZS output start Proof for theBenchmark
% 14.53/2.77 Assumptions after simplification:
% 14.53/2.77 ---------------------------------
% 14.53/2.77
% 14.53/2.77 (apt_def)
% 14.53/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 14.53/2.80 (reverse_line(v1) = v2) | ~ (left_apart_point(v0, v2) = v3) | ~ $i(v1) |
% 14.53/2.80 ~ $i(v0) | ? [v4: int] : ? [v5: int] : ((v5 = 0 & left_apart_point(v0, v1)
% 14.53/2.80 = 0) | ( ~ (v4 = 0) & apart_point_and_line(v0, v1) = v4))) & ! [v0: $i]
% 14.53/2.80 : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (reverse_line(v1) = v2) | ~
% 14.53/2.80 (left_apart_point(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ?
% 14.53/2.80 [v5: int] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v4 = 0) & ~
% 14.53/2.80 (v3 = 0) & left_apart_point(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i]
% 14.53/2.80 : ! [v2: int] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ~ $i(v1)
% 14.53/2.80 | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & ~
% 14.53/2.80 (v3 = 0) & reverse_line(v1) = v4 & left_apart_point(v0, v4) = v5 &
% 14.53/2.80 left_apart_point(v0, v1) = v3 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : !
% 14.53/2.80 [v2: int] : (v2 = 0 | ~ (left_apart_point(v0, v1) = v2) | ~ $i(v1) | ~
% 14.53/2.80 $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ((v5 = 0 &
% 14.53/2.80 reverse_line(v1) = v4 & left_apart_point(v0, v4) = 0 & $i(v4)) | ( ~ (v3
% 14.53/2.80 = 0) & apart_point_and_line(v0, v1) = v3))) & ! [v0: $i] : ! [v1:
% 14.53/2.80 $i] : ! [v2: any] : ( ~ (left_apart_point(v0, v1) = v2) | ~ $i(v1) | ~
% 14.53/2.80 $i(v0) | ? [v3: $i] : ? [v4: int] : ? [v5: int] : ((v5 = 0 &
% 14.53/2.80 apart_point_and_line(v0, v1) = 0) | ( ~ (v4 = 0) & ~ (v2 = 0) &
% 14.53/2.80 reverse_line(v1) = v3 & left_apart_point(v0, v3) = v4 & $i(v3)))) & !
% 14.53/2.80 [v0: $i] : ! [v1: $i] : ( ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v1) |
% 14.53/2.80 ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 &
% 14.53/2.80 reverse_line(v1) = v3 & left_apart_point(v0, v3) = 0 & $i(v3)) | (v2 = 0
% 14.53/2.80 & left_apart_point(v0, v1) = 0)))
% 14.53/2.80
% 14.53/2.80 (con)
% 14.53/2.80 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5:
% 14.53/2.80 int] : ( ~ (v5 = 0) & ~ (v4 = 0) & divides_points(v3, v1, v2) = v5 &
% 14.53/2.80 divides_points(v3, v0, v2) = v4 & divides_points(v3, v0, v1) = 0 &
% 14.53/2.80 apart_point_and_line(v2, v3) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 14.53/2.80
% 14.53/2.80 (div_def)
% 14.53/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 14.53/2.80 (divides_points(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 14.53/2.80 [v4: int] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((( ~
% 14.53/2.80 (v8 = 0) & left_apart_point(v1, v2) = v8) | ( ~ (v7 = 0) &
% 14.53/2.80 reverse_line(v2) = v5 & left_apart_point(v0, v5) = v7 & $i(v5))) & ((
% 14.53/2.80 ~ (v6 = 0) & reverse_line(v2) = v5 & left_apart_point(v1, v5) = v6 &
% 14.53/2.80 $i(v5)) | ( ~ (v4 = 0) & left_apart_point(v0, v2) = v4)))) & ! [v0:
% 14.53/2.80 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (divides_points(v2, v0, v1) = 0) | ~
% 14.53/2.80 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] :
% 14.53/2.80 ? [v6: int] : ? [v7: int] : (reverse_line(v2) = v4 & $i(v4) & ((v7 = 0 &
% 14.53/2.80 v6 = 0 & left_apart_point(v1, v2) = 0 & left_apart_point(v0, v4) = 0)
% 14.53/2.80 | (v5 = 0 & v3 = 0 & left_apart_point(v1, v4) = 0 & left_apart_point(v0,
% 14.53/2.81 v2) = 0))))
% 14.53/2.81
% 14.53/2.81 (function-axioms)
% 14.53/2.81 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.53/2.81 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_on_line(v5, v4,
% 14.53/2.81 v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0:
% 14.53/2.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.53/2.81 : ! [v4: $i] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~
% 14.53/2.81 (before_on_line(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.53/2.81 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 14.53/2.81 (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) &
% 14.53/2.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.53/2.81 (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) =
% 14.53/2.81 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 14.53/2.81 ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 14.53/2.81 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.53/2.81 [v3: $i] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~
% 14.53/2.81 (left_convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.53/2.81 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.53/2.81 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 14.53/2.81 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.53/2.81 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 14.53/2.81 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 14.53/2.81 $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3,
% 14.53/2.81 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 14.53/2.81 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 14.53/2.81 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.53/2.81 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.53/2.81 (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3,
% 14.53/2.81 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 14.53/2.81 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) |
% 14.53/2.81 ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 14.53/2.81 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.53/2.81 (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0)) & !
% 14.53/2.81 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 14.53/2.81 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: MultipleValueBool] :
% 14.53/2.81 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (line(v2) = v1) | ~
% 14.53/2.81 (line(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 14.53/2.81 (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 14.53/2.81
% 14.53/2.81 Further assumptions not needed in the proof:
% 14.53/2.81 --------------------------------------------
% 14.53/2.81 bet_def, bf_def, con_def, oag1, oag10, oag11, oag2, oag3, oag4, oag5, oag6,
% 14.53/2.81 oag7, oag8, oag9, oagco1, oagco10, oagco2, oagco3, oagco4, oagco5, oagco6,
% 14.53/2.81 oagco7, oagco8, oagco9, oagsub1, oagsub2, oagsub3, oaguc1, oaguc2
% 14.53/2.81
% 14.53/2.81 Those formulas are unsatisfiable:
% 14.53/2.81 ---------------------------------
% 14.53/2.81
% 14.53/2.81 Begin of proof
% 14.53/2.81 |
% 14.53/2.81 | ALPHA: (apt_def) implies:
% 14.53/2.81 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (apart_point_and_line(v0, v1) = 0) | ~
% 14.53/2.81 | $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] : ((v4
% 14.53/2.81 | = 0 & reverse_line(v1) = v3 & left_apart_point(v0, v3) = 0 &
% 14.53/2.81 | $i(v3)) | (v2 = 0 & left_apart_point(v0, v1) = 0)))
% 14.53/2.81 |
% 14.53/2.81 | ALPHA: (div_def) implies:
% 14.53/2.82 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (divides_points(v2, v0,
% 14.53/2.82 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ?
% 14.53/2.82 | [v4: $i] : ? [v5: int] : ? [v6: int] : ? [v7: int] :
% 14.53/2.82 | (reverse_line(v2) = v4 & $i(v4) & ((v7 = 0 & v6 = 0 &
% 14.53/2.82 | left_apart_point(v1, v2) = 0 & left_apart_point(v0, v4) = 0) |
% 14.53/2.82 | (v5 = 0 & v3 = 0 & left_apart_point(v1, v4) = 0 &
% 14.53/2.82 | left_apart_point(v0, v2) = 0))))
% 14.53/2.82 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 14.53/2.82 | (divides_points(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 14.53/2.82 | | ? [v4: int] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8:
% 14.53/2.82 | int] : ((( ~ (v8 = 0) & left_apart_point(v1, v2) = v8) | ( ~ (v7 =
% 14.53/2.82 | 0) & reverse_line(v2) = v5 & left_apart_point(v0, v5) = v7 &
% 14.53/2.82 | $i(v5))) & (( ~ (v6 = 0) & reverse_line(v2) = v5 &
% 14.53/2.82 | left_apart_point(v1, v5) = v6 & $i(v5)) | ( ~ (v4 = 0) &
% 14.53/2.82 | left_apart_point(v0, v2) = v4))))
% 14.53/2.82 |
% 14.53/2.82 | ALPHA: (function-axioms) implies:
% 14.53/2.82 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 14.53/2.82 | (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 14.53/2.82 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.53/2.82 | ! [v3: $i] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~
% 14.53/2.82 | (left_apart_point(v3, v2) = v0))
% 14.53/2.82 |
% 14.53/2.82 | DELTA: instantiating (con) with fresh symbols all_34_0, all_34_1, all_34_2,
% 14.53/2.82 | all_34_3, all_34_4, all_34_5 gives:
% 14.53/2.82 | (6) ~ (all_34_0 = 0) & ~ (all_34_1 = 0) & divides_points(all_34_2,
% 14.53/2.82 | all_34_4, all_34_3) = all_34_0 & divides_points(all_34_2, all_34_5,
% 14.53/2.82 | all_34_3) = all_34_1 & divides_points(all_34_2, all_34_5, all_34_4) =
% 14.53/2.82 | 0 & apart_point_and_line(all_34_3, all_34_2) = 0 & $i(all_34_2) &
% 14.53/2.82 | $i(all_34_3) & $i(all_34_4) & $i(all_34_5)
% 14.53/2.82 |
% 14.53/2.82 | ALPHA: (6) implies:
% 14.53/2.82 | (7) ~ (all_34_1 = 0)
% 14.53/2.82 | (8) ~ (all_34_0 = 0)
% 14.53/2.82 | (9) $i(all_34_5)
% 15.15/2.82 | (10) $i(all_34_4)
% 15.15/2.82 | (11) $i(all_34_3)
% 15.15/2.82 | (12) $i(all_34_2)
% 15.15/2.82 | (13) apart_point_and_line(all_34_3, all_34_2) = 0
% 15.15/2.82 | (14) divides_points(all_34_2, all_34_5, all_34_4) = 0
% 15.15/2.82 | (15) divides_points(all_34_2, all_34_5, all_34_3) = all_34_1
% 15.15/2.82 | (16) divides_points(all_34_2, all_34_4, all_34_3) = all_34_0
% 15.15/2.82 |
% 15.15/2.82 | GROUND_INST: instantiating (1) with all_34_3, all_34_2, simplifying with (11),
% 15.15/2.82 | (12), (13) gives:
% 15.15/2.82 | (17) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v2 = 0 &
% 15.15/2.82 | reverse_line(all_34_2) = v1 & left_apart_point(all_34_3, v1) = 0 &
% 15.15/2.82 | $i(v1)) | (v0 = 0 & left_apart_point(all_34_3, all_34_2) = 0))
% 15.15/2.82 |
% 15.15/2.83 | GROUND_INST: instantiating (2) with all_34_5, all_34_4, all_34_2, simplifying
% 15.15/2.83 | with (9), (10), (12), (14) gives:
% 15.15/2.83 | (18) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : ? [v4:
% 15.15/2.83 | int] : (reverse_line(all_34_2) = v1 & $i(v1) & ((v4 = 0 & v3 = 0 &
% 15.15/2.83 | left_apart_point(all_34_4, all_34_2) = 0 &
% 15.15/2.83 | left_apart_point(all_34_5, v1) = 0) | (v2 = 0 & v0 = 0 &
% 15.15/2.83 | left_apart_point(all_34_4, v1) = 0 & left_apart_point(all_34_5,
% 15.15/2.83 | all_34_2) = 0)))
% 15.15/2.83 |
% 15.15/2.83 | GROUND_INST: instantiating (3) with all_34_5, all_34_3, all_34_2, all_34_1,
% 15.15/2.83 | simplifying with (9), (11), (12), (15) gives:
% 15.15/2.83 | (19) all_34_1 = 0 | ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3:
% 15.15/2.83 | int] : ? [v4: int] : ((( ~ (v4 = 0) & left_apart_point(all_34_3,
% 15.15/2.83 | all_34_2) = v4) | ( ~ (v3 = 0) & reverse_line(all_34_2) = v1 &
% 15.15/2.83 | left_apart_point(all_34_5, v1) = v3 & $i(v1))) & (( ~ (v2 = 0) &
% 15.15/2.83 | reverse_line(all_34_2) = v1 & left_apart_point(all_34_3, v1) =
% 15.15/2.83 | v2 & $i(v1)) | ( ~ (v0 = 0) & left_apart_point(all_34_5,
% 15.15/2.83 | all_34_2) = v0)))
% 15.15/2.83 |
% 15.15/2.83 | GROUND_INST: instantiating (3) with all_34_4, all_34_3, all_34_2, all_34_0,
% 15.15/2.83 | simplifying with (10), (11), (12), (16) gives:
% 15.15/2.83 | (20) all_34_0 = 0 | ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3:
% 15.15/2.83 | int] : ? [v4: int] : ((( ~ (v4 = 0) & left_apart_point(all_34_3,
% 15.15/2.83 | all_34_2) = v4) | ( ~ (v3 = 0) & reverse_line(all_34_2) = v1 &
% 15.15/2.83 | left_apart_point(all_34_4, v1) = v3 & $i(v1))) & (( ~ (v2 = 0) &
% 15.15/2.83 | reverse_line(all_34_2) = v1 & left_apart_point(all_34_3, v1) =
% 15.15/2.83 | v2 & $i(v1)) | ( ~ (v0 = 0) & left_apart_point(all_34_4,
% 15.15/2.83 | all_34_2) = v0)))
% 15.15/2.83 |
% 15.15/2.83 | DELTA: instantiating (17) with fresh symbols all_41_0, all_41_1, all_41_2
% 15.15/2.83 | gives:
% 15.15/2.83 | (21) (all_41_0 = 0 & reverse_line(all_34_2) = all_41_1 &
% 15.15/2.83 | left_apart_point(all_34_3, all_41_1) = 0 & $i(all_41_1)) | (all_41_2
% 15.15/2.83 | = 0 & left_apart_point(all_34_3, all_34_2) = 0)
% 15.15/2.83 |
% 15.15/2.83 | DELTA: instantiating (18) with fresh symbols all_42_0, all_42_1, all_42_2,
% 15.15/2.83 | all_42_3, all_42_4 gives:
% 15.37/2.83 | (22) reverse_line(all_34_2) = all_42_3 & $i(all_42_3) & ((all_42_0 = 0 &
% 15.37/2.83 | all_42_1 = 0 & left_apart_point(all_34_4, all_34_2) = 0 &
% 15.37/2.83 | left_apart_point(all_34_5, all_42_3) = 0) | (all_42_2 = 0 &
% 15.37/2.83 | all_42_4 = 0 & left_apart_point(all_34_4, all_42_3) = 0 &
% 15.37/2.83 | left_apart_point(all_34_5, all_34_2) = 0))
% 15.37/2.83 |
% 15.37/2.83 | ALPHA: (22) implies:
% 15.37/2.83 | (23) reverse_line(all_34_2) = all_42_3
% 15.37/2.83 | (24) (all_42_0 = 0 & all_42_1 = 0 & left_apart_point(all_34_4, all_34_2) =
% 15.37/2.83 | 0 & left_apart_point(all_34_5, all_42_3) = 0) | (all_42_2 = 0 &
% 15.37/2.83 | all_42_4 = 0 & left_apart_point(all_34_4, all_42_3) = 0 &
% 15.37/2.83 | left_apart_point(all_34_5, all_34_2) = 0)
% 15.37/2.83 |
% 15.37/2.83 | BETA: splitting (20) gives:
% 15.37/2.83 |
% 15.37/2.83 | Case 1:
% 15.37/2.83 | |
% 15.37/2.83 | | (25) all_34_0 = 0
% 15.37/2.83 | |
% 15.37/2.83 | | REDUCE: (8), (25) imply:
% 15.37/2.83 | | (26) $false
% 15.37/2.83 | |
% 15.37/2.83 | | CLOSE: (26) is inconsistent.
% 15.37/2.83 | |
% 15.37/2.83 | Case 2:
% 15.37/2.83 | |
% 15.37/2.84 | | (27) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : ? [v4:
% 15.37/2.84 | | int] : ((( ~ (v4 = 0) & left_apart_point(all_34_3, all_34_2) = v4)
% 15.37/2.84 | | | ( ~ (v3 = 0) & reverse_line(all_34_2) = v1 &
% 15.37/2.84 | | left_apart_point(all_34_4, v1) = v3 & $i(v1))) & (( ~ (v2 = 0)
% 15.37/2.84 | | & reverse_line(all_34_2) = v1 & left_apart_point(all_34_3, v1)
% 15.37/2.84 | | = v2 & $i(v1)) | ( ~ (v0 = 0) & left_apart_point(all_34_4,
% 15.37/2.84 | | all_34_2) = v0)))
% 15.37/2.84 | |
% 15.37/2.84 | | DELTA: instantiating (27) with fresh symbols all_48_0, all_48_1, all_48_2,
% 15.37/2.84 | | all_48_3, all_48_4 gives:
% 15.37/2.84 | | (28) (( ~ (all_48_0 = 0) & left_apart_point(all_34_3, all_34_2) =
% 15.37/2.84 | | all_48_0) | ( ~ (all_48_1 = 0) & reverse_line(all_34_2) =
% 15.37/2.84 | | all_48_3 & left_apart_point(all_34_4, all_48_3) = all_48_1 &
% 15.37/2.84 | | $i(all_48_3))) & (( ~ (all_48_2 = 0) & reverse_line(all_34_2) =
% 15.37/2.84 | | all_48_3 & left_apart_point(all_34_3, all_48_3) = all_48_2 &
% 15.37/2.84 | | $i(all_48_3)) | ( ~ (all_48_4 = 0) & left_apart_point(all_34_4,
% 15.37/2.84 | | all_34_2) = all_48_4))
% 15.37/2.84 | |
% 15.37/2.84 | | ALPHA: (28) implies:
% 15.37/2.84 | | (29) ( ~ (all_48_2 = 0) & reverse_line(all_34_2) = all_48_3 &
% 15.37/2.84 | | left_apart_point(all_34_3, all_48_3) = all_48_2 & $i(all_48_3)) |
% 15.37/2.84 | | ( ~ (all_48_4 = 0) & left_apart_point(all_34_4, all_34_2) =
% 15.37/2.84 | | all_48_4)
% 15.37/2.84 | | (30) ( ~ (all_48_0 = 0) & left_apart_point(all_34_3, all_34_2) =
% 15.37/2.84 | | all_48_0) | ( ~ (all_48_1 = 0) & reverse_line(all_34_2) = all_48_3
% 15.37/2.84 | | & left_apart_point(all_34_4, all_48_3) = all_48_1 & $i(all_48_3))
% 15.37/2.84 | |
% 15.37/2.84 | | BETA: splitting (19) gives:
% 15.37/2.84 | |
% 15.37/2.84 | | Case 1:
% 15.37/2.84 | | |
% 15.37/2.84 | | | (31) all_34_1 = 0
% 15.37/2.84 | | |
% 15.37/2.84 | | | REDUCE: (7), (31) imply:
% 15.37/2.84 | | | (32) $false
% 15.37/2.84 | | |
% 15.37/2.84 | | | CLOSE: (32) is inconsistent.
% 15.37/2.84 | | |
% 15.37/2.84 | | Case 2:
% 15.37/2.84 | | |
% 15.37/2.84 | | | (33) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : ? [v4:
% 15.37/2.84 | | | int] : ((( ~ (v4 = 0) & left_apart_point(all_34_3, all_34_2) =
% 15.37/2.84 | | | v4) | ( ~ (v3 = 0) & reverse_line(all_34_2) = v1 &
% 15.37/2.84 | | | left_apart_point(all_34_5, v1) = v3 & $i(v1))) & (( ~ (v2 =
% 15.37/2.84 | | | 0) & reverse_line(all_34_2) = v1 &
% 15.37/2.84 | | | left_apart_point(all_34_3, v1) = v2 & $i(v1)) | ( ~ (v0 = 0)
% 15.37/2.84 | | | & left_apart_point(all_34_5, all_34_2) = v0)))
% 15.37/2.84 | | |
% 15.37/2.84 | | | DELTA: instantiating (33) with fresh symbols all_52_0, all_52_1, all_52_2,
% 15.37/2.84 | | | all_52_3, all_52_4 gives:
% 15.37/2.84 | | | (34) (( ~ (all_52_0 = 0) & left_apart_point(all_34_3, all_34_2) =
% 15.37/2.84 | | | all_52_0) | ( ~ (all_52_1 = 0) & reverse_line(all_34_2) =
% 15.37/2.84 | | | all_52_3 & left_apart_point(all_34_5, all_52_3) = all_52_1 &
% 15.37/2.84 | | | $i(all_52_3))) & (( ~ (all_52_2 = 0) & reverse_line(all_34_2)
% 15.37/2.84 | | | = all_52_3 & left_apart_point(all_34_3, all_52_3) = all_52_2 &
% 15.37/2.84 | | | $i(all_52_3)) | ( ~ (all_52_4 = 0) &
% 15.37/2.84 | | | left_apart_point(all_34_5, all_34_2) = all_52_4))
% 15.37/2.84 | | |
% 15.37/2.84 | | | ALPHA: (34) implies:
% 15.37/2.84 | | | (35) ( ~ (all_52_2 = 0) & reverse_line(all_34_2) = all_52_3 &
% 15.37/2.84 | | | left_apart_point(all_34_3, all_52_3) = all_52_2 & $i(all_52_3))
% 15.37/2.84 | | | | ( ~ (all_52_4 = 0) & left_apart_point(all_34_5, all_34_2) =
% 15.37/2.84 | | | all_52_4)
% 15.37/2.84 | | | (36) ( ~ (all_52_0 = 0) & left_apart_point(all_34_3, all_34_2) =
% 15.37/2.84 | | | all_52_0) | ( ~ (all_52_1 = 0) & reverse_line(all_34_2) =
% 15.37/2.84 | | | all_52_3 & left_apart_point(all_34_5, all_52_3) = all_52_1 &
% 15.37/2.84 | | | $i(all_52_3))
% 15.37/2.84 | | |
% 15.37/2.84 | | | BETA: splitting (21) gives:
% 15.37/2.84 | | |
% 15.37/2.84 | | | Case 1:
% 15.37/2.84 | | | |
% 15.37/2.84 | | | | (37) all_41_0 = 0 & reverse_line(all_34_2) = all_41_1 &
% 15.37/2.84 | | | | left_apart_point(all_34_3, all_41_1) = 0 & $i(all_41_1)
% 15.37/2.84 | | | |
% 15.37/2.84 | | | | ALPHA: (37) implies:
% 15.37/2.84 | | | | (38) left_apart_point(all_34_3, all_41_1) = 0
% 15.37/2.84 | | | | (39) reverse_line(all_34_2) = all_41_1
% 15.37/2.85 | | | |
% 15.37/2.85 | | | | GROUND_INST: instantiating (4) with all_42_3, all_41_1, all_34_2,
% 15.37/2.85 | | | | simplifying with (23), (39) gives:
% 15.37/2.85 | | | | (40) all_42_3 = all_41_1
% 15.37/2.85 | | | |
% 15.37/2.85 | | | | BETA: splitting (29) gives:
% 15.37/2.85 | | | |
% 15.37/2.85 | | | | Case 1:
% 15.37/2.85 | | | | |
% 15.37/2.85 | | | | | (41) ~ (all_48_2 = 0) & reverse_line(all_34_2) = all_48_3 &
% 15.37/2.85 | | | | | left_apart_point(all_34_3, all_48_3) = all_48_2 & $i(all_48_3)
% 15.37/2.85 | | | | |
% 15.37/2.85 | | | | | ALPHA: (41) implies:
% 15.37/2.85 | | | | | (42) ~ (all_48_2 = 0)
% 15.37/2.85 | | | | | (43) left_apart_point(all_34_3, all_48_3) = all_48_2
% 15.37/2.85 | | | | | (44) reverse_line(all_34_2) = all_48_3
% 15.37/2.85 | | | | |
% 15.37/2.85 | | | | | GROUND_INST: instantiating (4) with all_41_1, all_48_3, all_34_2,
% 15.37/2.85 | | | | | simplifying with (39), (44) gives:
% 15.37/2.85 | | | | | (45) all_48_3 = all_41_1
% 15.37/2.85 | | | | |
% 15.37/2.85 | | | | | REDUCE: (43), (45) imply:
% 15.37/2.85 | | | | | (46) left_apart_point(all_34_3, all_41_1) = all_48_2
% 15.37/2.85 | | | | |
% 15.37/2.85 | | | | | GROUND_INST: instantiating (5) with 0, all_48_2, all_41_1, all_34_3,
% 15.37/2.85 | | | | | simplifying with (38), (46) gives:
% 15.37/2.85 | | | | | (47) all_48_2 = 0
% 15.37/2.85 | | | | |
% 15.37/2.85 | | | | | REDUCE: (42), (47) imply:
% 15.37/2.85 | | | | | (48) $false
% 15.37/2.85 | | | | |
% 15.37/2.85 | | | | | CLOSE: (48) is inconsistent.
% 15.37/2.85 | | | | |
% 15.37/2.85 | | | | Case 2:
% 15.37/2.85 | | | | |
% 15.37/2.85 | | | | | (49) ~ (all_48_4 = 0) & left_apart_point(all_34_4, all_34_2) =
% 15.37/2.85 | | | | | all_48_4
% 15.37/2.85 | | | | |
% 15.37/2.85 | | | | | ALPHA: (49) implies:
% 15.37/2.85 | | | | | (50) ~ (all_48_4 = 0)
% 15.37/2.85 | | | | | (51) left_apart_point(all_34_4, all_34_2) = all_48_4
% 15.37/2.85 | | | | |
% 15.37/2.85 | | | | | BETA: splitting (24) gives:
% 15.37/2.85 | | | | |
% 15.37/2.85 | | | | | Case 1:
% 15.37/2.85 | | | | | |
% 15.37/2.85 | | | | | | (52) all_42_0 = 0 & all_42_1 = 0 & left_apart_point(all_34_4,
% 15.37/2.85 | | | | | | all_34_2) = 0 & left_apart_point(all_34_5, all_42_3) = 0
% 15.37/2.85 | | | | | |
% 15.37/2.85 | | | | | | ALPHA: (52) implies:
% 15.37/2.85 | | | | | | (53) left_apart_point(all_34_4, all_34_2) = 0
% 15.37/2.85 | | | | | |
% 15.37/2.85 | | | | | | GROUND_INST: instantiating (5) with 0, all_48_4, all_34_2, all_34_4,
% 15.37/2.85 | | | | | | simplifying with (51), (53) gives:
% 15.37/2.85 | | | | | | (54) all_48_4 = 0
% 15.37/2.85 | | | | | |
% 15.37/2.85 | | | | | | REDUCE: (50), (54) imply:
% 15.37/2.85 | | | | | | (55) $false
% 15.37/2.85 | | | | | |
% 15.37/2.85 | | | | | | CLOSE: (55) is inconsistent.
% 15.37/2.85 | | | | | |
% 15.37/2.85 | | | | | Case 2:
% 15.37/2.85 | | | | | |
% 15.37/2.85 | | | | | | (56) all_42_2 = 0 & all_42_4 = 0 & left_apart_point(all_34_4,
% 15.37/2.85 | | | | | | all_42_3) = 0 & left_apart_point(all_34_5, all_34_2) = 0
% 15.37/2.85 | | | | | |
% 15.37/2.85 | | | | | | ALPHA: (56) implies:
% 15.37/2.85 | | | | | | (57) left_apart_point(all_34_5, all_34_2) = 0
% 15.37/2.85 | | | | | |
% 15.37/2.85 | | | | | | BETA: splitting (35) gives:
% 15.37/2.85 | | | | | |
% 15.37/2.85 | | | | | | Case 1:
% 15.37/2.85 | | | | | | |
% 15.37/2.85 | | | | | | | (58) ~ (all_52_2 = 0) & reverse_line(all_34_2) = all_52_3 &
% 15.37/2.85 | | | | | | | left_apart_point(all_34_3, all_52_3) = all_52_2 &
% 15.37/2.85 | | | | | | | $i(all_52_3)
% 15.37/2.85 | | | | | | |
% 15.37/2.85 | | | | | | | ALPHA: (58) implies:
% 15.37/2.85 | | | | | | | (59) ~ (all_52_2 = 0)
% 15.37/2.85 | | | | | | | (60) left_apart_point(all_34_3, all_52_3) = all_52_2
% 15.37/2.85 | | | | | | | (61) reverse_line(all_34_2) = all_52_3
% 15.37/2.85 | | | | | | |
% 15.37/2.85 | | | | | | | GROUND_INST: instantiating (4) with all_41_1, all_52_3, all_34_2,
% 15.37/2.85 | | | | | | | simplifying with (39), (61) gives:
% 15.37/2.85 | | | | | | | (62) all_52_3 = all_41_1
% 15.37/2.85 | | | | | | |
% 15.37/2.85 | | | | | | | REDUCE: (60), (62) imply:
% 15.37/2.85 | | | | | | | (63) left_apart_point(all_34_3, all_41_1) = all_52_2
% 15.37/2.85 | | | | | | |
% 15.37/2.85 | | | | | | | GROUND_INST: instantiating (5) with 0, all_52_2, all_41_1,
% 15.37/2.85 | | | | | | | all_34_3, simplifying with (38), (63) gives:
% 15.37/2.85 | | | | | | | (64) all_52_2 = 0
% 15.37/2.85 | | | | | | |
% 15.37/2.85 | | | | | | | REDUCE: (59), (64) imply:
% 15.37/2.85 | | | | | | | (65) $false
% 15.37/2.85 | | | | | | |
% 15.37/2.85 | | | | | | | CLOSE: (65) is inconsistent.
% 15.37/2.85 | | | | | | |
% 15.37/2.85 | | | | | | Case 2:
% 15.37/2.85 | | | | | | |
% 15.37/2.85 | | | | | | | (66) ~ (all_52_4 = 0) & left_apart_point(all_34_5, all_34_2) =
% 15.37/2.85 | | | | | | | all_52_4
% 15.37/2.85 | | | | | | |
% 15.37/2.85 | | | | | | | ALPHA: (66) implies:
% 15.37/2.85 | | | | | | | (67) ~ (all_52_4 = 0)
% 15.37/2.85 | | | | | | | (68) left_apart_point(all_34_5, all_34_2) = all_52_4
% 15.37/2.85 | | | | | | |
% 15.37/2.85 | | | | | | | GROUND_INST: instantiating (5) with 0, all_52_4, all_34_2,
% 15.37/2.85 | | | | | | | all_34_5, simplifying with (57), (68) gives:
% 15.37/2.85 | | | | | | | (69) all_52_4 = 0
% 15.37/2.85 | | | | | | |
% 15.37/2.85 | | | | | | | REDUCE: (67), (69) imply:
% 15.37/2.85 | | | | | | | (70) $false
% 15.37/2.85 | | | | | | |
% 15.37/2.85 | | | | | | | CLOSE: (70) is inconsistent.
% 15.37/2.85 | | | | | | |
% 15.37/2.85 | | | | | | End of split
% 15.37/2.85 | | | | | |
% 15.37/2.85 | | | | | End of split
% 15.37/2.85 | | | | |
% 15.37/2.85 | | | | End of split
% 15.37/2.85 | | | |
% 15.37/2.85 | | | Case 2:
% 15.37/2.85 | | | |
% 15.37/2.85 | | | | (71) all_41_2 = 0 & left_apart_point(all_34_3, all_34_2) = 0
% 15.37/2.85 | | | |
% 15.37/2.85 | | | | ALPHA: (71) implies:
% 15.37/2.85 | | | | (72) left_apart_point(all_34_3, all_34_2) = 0
% 15.37/2.85 | | | |
% 15.37/2.85 | | | | BETA: splitting (30) gives:
% 15.37/2.85 | | | |
% 15.37/2.85 | | | | Case 1:
% 15.37/2.85 | | | | |
% 15.37/2.86 | | | | | (73) ~ (all_48_0 = 0) & left_apart_point(all_34_3, all_34_2) =
% 15.37/2.86 | | | | | all_48_0
% 15.37/2.86 | | | | |
% 15.37/2.86 | | | | | ALPHA: (73) implies:
% 15.37/2.86 | | | | | (74) ~ (all_48_0 = 0)
% 15.37/2.86 | | | | | (75) left_apart_point(all_34_3, all_34_2) = all_48_0
% 15.37/2.86 | | | | |
% 15.37/2.86 | | | | | GROUND_INST: instantiating (5) with 0, all_48_0, all_34_2, all_34_3,
% 15.37/2.86 | | | | | simplifying with (72), (75) gives:
% 15.37/2.86 | | | | | (76) all_48_0 = 0
% 15.37/2.86 | | | | |
% 15.37/2.86 | | | | | REDUCE: (74), (76) imply:
% 15.37/2.86 | | | | | (77) $false
% 15.37/2.86 | | | | |
% 15.37/2.86 | | | | | CLOSE: (77) is inconsistent.
% 15.37/2.86 | | | | |
% 15.37/2.86 | | | | Case 2:
% 15.37/2.86 | | | | |
% 15.37/2.86 | | | | | (78) ~ (all_48_1 = 0) & reverse_line(all_34_2) = all_48_3 &
% 15.37/2.86 | | | | | left_apart_point(all_34_4, all_48_3) = all_48_1 & $i(all_48_3)
% 15.37/2.86 | | | | |
% 15.37/2.86 | | | | | ALPHA: (78) implies:
% 15.37/2.86 | | | | | (79) ~ (all_48_1 = 0)
% 15.37/2.86 | | | | | (80) left_apart_point(all_34_4, all_48_3) = all_48_1
% 15.37/2.86 | | | | | (81) reverse_line(all_34_2) = all_48_3
% 15.37/2.86 | | | | |
% 15.37/2.86 | | | | | BETA: splitting (36) gives:
% 15.37/2.86 | | | | |
% 15.37/2.86 | | | | | Case 1:
% 15.37/2.86 | | | | | |
% 15.37/2.86 | | | | | | (82) ~ (all_52_0 = 0) & left_apart_point(all_34_3, all_34_2) =
% 15.37/2.86 | | | | | | all_52_0
% 15.37/2.86 | | | | | |
% 15.37/2.86 | | | | | | ALPHA: (82) implies:
% 15.37/2.86 | | | | | | (83) ~ (all_52_0 = 0)
% 15.37/2.86 | | | | | | (84) left_apart_point(all_34_3, all_34_2) = all_52_0
% 15.37/2.86 | | | | | |
% 15.37/2.86 | | | | | | GROUND_INST: instantiating (5) with 0, all_52_0, all_34_2, all_34_3,
% 15.37/2.86 | | | | | | simplifying with (72), (84) gives:
% 15.37/2.86 | | | | | | (85) all_52_0 = 0
% 15.37/2.86 | | | | | |
% 15.37/2.86 | | | | | | REDUCE: (83), (85) imply:
% 15.37/2.86 | | | | | | (86) $false
% 15.37/2.86 | | | | | |
% 15.37/2.86 | | | | | | CLOSE: (86) is inconsistent.
% 15.37/2.86 | | | | | |
% 15.37/2.86 | | | | | Case 2:
% 15.37/2.86 | | | | | |
% 15.37/2.86 | | | | | | (87) ~ (all_52_1 = 0) & reverse_line(all_34_2) = all_52_3 &
% 15.37/2.86 | | | | | | left_apart_point(all_34_5, all_52_3) = all_52_1 &
% 15.37/2.86 | | | | | | $i(all_52_3)
% 15.37/2.86 | | | | | |
% 15.37/2.86 | | | | | | ALPHA: (87) implies:
% 15.37/2.86 | | | | | | (88) ~ (all_52_1 = 0)
% 15.37/2.86 | | | | | | (89) left_apart_point(all_34_5, all_52_3) = all_52_1
% 15.37/2.86 | | | | | | (90) reverse_line(all_34_2) = all_52_3
% 15.37/2.86 | | | | | |
% 15.37/2.86 | | | | | | GROUND_INST: instantiating (4) with all_42_3, all_52_3, all_34_2,
% 15.37/2.86 | | | | | | simplifying with (23), (90) gives:
% 15.37/2.86 | | | | | | (91) all_52_3 = all_42_3
% 15.37/2.86 | | | | | |
% 15.37/2.86 | | | | | | GROUND_INST: instantiating (4) with all_48_3, all_52_3, all_34_2,
% 15.37/2.86 | | | | | | simplifying with (81), (90) gives:
% 15.37/2.86 | | | | | | (92) all_52_3 = all_48_3
% 15.37/2.86 | | | | | |
% 15.37/2.86 | | | | | | COMBINE_EQS: (91), (92) imply:
% 15.37/2.86 | | | | | | (93) all_48_3 = all_42_3
% 15.37/2.86 | | | | | |
% 15.37/2.86 | | | | | | REDUCE: (80), (93) imply:
% 15.37/2.86 | | | | | | (94) left_apart_point(all_34_4, all_42_3) = all_48_1
% 15.37/2.86 | | | | | |
% 15.37/2.86 | | | | | | REDUCE: (89), (91) imply:
% 15.37/2.86 | | | | | | (95) left_apart_point(all_34_5, all_42_3) = all_52_1
% 15.37/2.86 | | | | | |
% 15.37/2.86 | | | | | | BETA: splitting (24) gives:
% 15.37/2.86 | | | | | |
% 15.37/2.86 | | | | | | Case 1:
% 15.37/2.86 | | | | | | |
% 15.37/2.86 | | | | | | | (96) all_42_0 = 0 & all_42_1 = 0 & left_apart_point(all_34_4,
% 15.37/2.86 | | | | | | | all_34_2) = 0 & left_apart_point(all_34_5, all_42_3) = 0
% 15.37/2.86 | | | | | | |
% 15.37/2.86 | | | | | | | ALPHA: (96) implies:
% 15.37/2.86 | | | | | | | (97) left_apart_point(all_34_5, all_42_3) = 0
% 15.37/2.86 | | | | | | |
% 15.37/2.86 | | | | | | | GROUND_INST: instantiating (5) with 0, all_52_1, all_42_3,
% 15.37/2.86 | | | | | | | all_34_5, simplifying with (95), (97) gives:
% 15.37/2.86 | | | | | | | (98) all_52_1 = 0
% 15.37/2.86 | | | | | | |
% 15.37/2.86 | | | | | | | REDUCE: (88), (98) imply:
% 15.37/2.86 | | | | | | | (99) $false
% 15.37/2.86 | | | | | | |
% 15.37/2.86 | | | | | | | CLOSE: (99) is inconsistent.
% 15.37/2.86 | | | | | | |
% 15.37/2.86 | | | | | | Case 2:
% 15.37/2.86 | | | | | | |
% 15.37/2.86 | | | | | | | (100) all_42_2 = 0 & all_42_4 = 0 & left_apart_point(all_34_4,
% 15.37/2.86 | | | | | | | all_42_3) = 0 & left_apart_point(all_34_5, all_34_2) =
% 15.37/2.86 | | | | | | | 0
% 15.37/2.86 | | | | | | |
% 15.37/2.86 | | | | | | | ALPHA: (100) implies:
% 15.37/2.86 | | | | | | | (101) left_apart_point(all_34_4, all_42_3) = 0
% 15.37/2.86 | | | | | | |
% 15.37/2.86 | | | | | | | GROUND_INST: instantiating (5) with 0, all_48_1, all_42_3,
% 15.37/2.86 | | | | | | | all_34_4, simplifying with (94), (101) gives:
% 15.37/2.86 | | | | | | | (102) all_48_1 = 0
% 15.37/2.86 | | | | | | |
% 15.37/2.86 | | | | | | | REDUCE: (79), (102) imply:
% 15.37/2.86 | | | | | | | (103) $false
% 15.37/2.86 | | | | | | |
% 15.37/2.86 | | | | | | | CLOSE: (103) is inconsistent.
% 15.37/2.86 | | | | | | |
% 15.37/2.86 | | | | | | End of split
% 15.37/2.86 | | | | | |
% 15.37/2.86 | | | | | End of split
% 15.37/2.86 | | | | |
% 15.37/2.86 | | | | End of split
% 15.37/2.86 | | | |
% 15.37/2.86 | | | End of split
% 15.37/2.86 | | |
% 15.37/2.86 | | End of split
% 15.37/2.86 | |
% 15.37/2.86 | End of split
% 15.37/2.86 |
% 15.37/2.86 End of proof
% 15.37/2.86 % SZS output end Proof for theBenchmark
% 15.37/2.86
% 15.37/2.86 2271ms
%------------------------------------------------------------------------------