TSTP Solution File: GEO204+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO204+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n010.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 23:22:16 EDT 2023
% Result : Theorem 10.68s 2.27s
% Output : Proof 14.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO204+2 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n010.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 21:28:03 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.62 ________ _____
% 0.19/0.62 ___ __ \_________(_)________________________________
% 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62
% 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62 (2023-06-19)
% 0.19/0.62
% 0.19/0.62 (c) Philipp Rümmer, 2009-2023
% 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62 Amanda Stjerna.
% 0.19/0.62 Free software under BSD-3-Clause.
% 0.19/0.62
% 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62
% 0.19/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.64 Running up to 7 provers in parallel.
% 0.19/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.79/1.14 Prover 1: Preprocessing ...
% 2.79/1.14 Prover 4: Preprocessing ...
% 3.24/1.19 Prover 2: Preprocessing ...
% 3.24/1.19 Prover 6: Preprocessing ...
% 3.24/1.19 Prover 3: Preprocessing ...
% 3.24/1.20 Prover 0: Preprocessing ...
% 3.24/1.20 Prover 5: Preprocessing ...
% 5.49/1.53 Prover 5: Proving ...
% 5.49/1.53 Prover 2: Proving ...
% 5.49/1.54 Prover 1: Constructing countermodel ...
% 5.49/1.55 Prover 6: Constructing countermodel ...
% 5.49/1.55 Prover 3: Constructing countermodel ...
% 6.73/1.70 Prover 4: Constructing countermodel ...
% 6.97/1.72 Prover 0: Proving ...
% 6.97/1.73 Prover 3: gave up
% 6.97/1.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.97/1.74 Prover 6: gave up
% 6.97/1.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.97/1.75 Prover 1: gave up
% 6.97/1.77 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 6.97/1.78 Prover 8: Preprocessing ...
% 6.97/1.78 Prover 7: Preprocessing ...
% 7.73/1.82 Prover 9: Preprocessing ...
% 7.73/1.84 Prover 7: Warning: ignoring some quantifiers
% 7.73/1.86 Prover 7: Constructing countermodel ...
% 7.73/1.94 Prover 8: Warning: ignoring some quantifiers
% 7.73/1.98 Prover 8: Constructing countermodel ...
% 8.72/2.01 Prover 7: gave up
% 8.72/2.01 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.74/2.09 Prover 10: Preprocessing ...
% 9.87/2.11 Prover 8: gave up
% 9.96/2.12 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.96/2.13 Prover 9: Constructing countermodel ...
% 9.96/2.15 Prover 11: Preprocessing ...
% 9.96/2.17 Prover 10: Warning: ignoring some quantifiers
% 9.96/2.20 Prover 10: Constructing countermodel ...
% 10.68/2.26 Prover 10: gave up
% 10.68/2.27 Prover 5: proved (1595ms)
% 10.68/2.27
% 10.68/2.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.68/2.27
% 10.68/2.27 Prover 9: stopped
% 10.68/2.27 Prover 2: stopped
% 10.68/2.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.68/2.27 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 10.68/2.27 Prover 0: stopped
% 10.68/2.27 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 10.68/2.27 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 11.33/2.32 Prover 13: Preprocessing ...
% 11.33/2.33 Prover 19: Preprocessing ...
% 11.33/2.33 Prover 12: Preprocessing ...
% 11.33/2.33 Prover 16: Preprocessing ...
% 11.33/2.38 Prover 16: Warning: ignoring some quantifiers
% 11.95/2.38 Prover 16: Constructing countermodel ...
% 11.95/2.40 Prover 13: Warning: ignoring some quantifiers
% 12.17/2.42 Prover 13: Constructing countermodel ...
% 12.17/2.43 Prover 12: stopped
% 12.17/2.44 Prover 11: Constructing countermodel ...
% 12.17/2.45 Prover 19: Warning: ignoring some quantifiers
% 12.17/2.46 Prover 19: Constructing countermodel ...
% 12.17/2.53 Prover 19: gave up
% 12.17/2.54 Prover 13: gave up
% 12.17/2.55 Prover 16: gave up
% 13.87/2.69 Prover 11: Found proof (size 76)
% 13.87/2.69 Prover 11: proved (570ms)
% 13.87/2.69 Prover 4: stopped
% 13.87/2.69
% 13.87/2.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.87/2.69
% 13.87/2.70 % SZS output start Proof for theBenchmark
% 13.87/2.71 Assumptions after simplification:
% 13.87/2.71 ---------------------------------
% 13.87/2.71
% 13.87/2.71 (apart1)
% 13.87/2.75 ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0))
% 13.87/2.75
% 13.87/2.75 (apart4)
% 13.87/2.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 13.87/2.75 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2)
% 13.87/2.75 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 13.87/2.75 distinct_points(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 13.87/2.75 ! [v3: int] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~
% 13.87/2.75 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 13.87/2.75 distinct_points(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 13.87/2.75 [v3: int] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~
% 13.87/2.75 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 13.87/2.75 distinct_points(v1, v2) = 0)
% 13.87/2.75
% 13.87/2.75 (con)
% 13.87/2.76 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ?
% 13.87/2.76 [v5: $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v3 = 0) & distinct_points(v1, v2)
% 13.87/2.76 = v3 & distinct_points(v0, v1) = 0 & $i(v2) & $i(v1) & $i(v0) & ((v7 = 0 &
% 13.87/2.76 line_connecting(v0, v2) = v6 & line_connecting(v0, v1) = v5 &
% 13.87/2.76 distinct_lines(v5, v6) = 0 & $i(v6) & $i(v5)) | ( ~ (v4 = 0) &
% 13.87/2.76 distinct_points(v0, v2) = v4)))
% 13.87/2.76
% 13.87/2.76 (con1)
% 13.87/2.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 13.87/2.76 (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ~
% 13.87/2.76 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int]
% 13.87/2.76 : ((v6 = 0 & v5 = 0 & distinct_points(v2, v1) = 0 & distinct_points(v2, v0)
% 13.87/2.76 = 0) | ( ~ (v4 = 0) & distinct_points(v0, v1) = v4)))
% 13.87/2.76
% 13.87/2.76 (cu1)
% 14.40/2.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 14.40/2.79 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 14.40/2.79 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 14.40/2.79 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 14.40/2.79 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 &
% 14.40/2.79 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2,
% 14.40/2.79 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 14.40/2.79 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1,
% 14.40/2.79 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~
% 14.40/2.79 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 14.40/2.79 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 14.40/2.79 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0,
% 14.40/2.79 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 14.40/2.79 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 14.40/2.79 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 14.40/2.79 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 14.40/2.79 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 =
% 14.40/2.79 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 &
% 14.40/2.79 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2,
% 14.40/2.79 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 14.40/2.79 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 14.40/2.79 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~
% 14.40/2.79 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 14.40/2.79 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 =
% 14.40/2.79 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 &
% 14.40/2.79 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2,
% 14.40/2.79 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 14.40/2.79 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 14.40/2.79 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~
% 14.40/2.79 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~
% 14.40/2.79 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 14.40/2.79 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 &
% 14.40/2.79 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0,
% 14.40/2.79 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 14.40/2.79 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0,
% 14.40/2.79 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~
% 14.40/2.79 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 14.40/2.79 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 14.40/2.79 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1,
% 14.40/2.79 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i]
% 14.40/2.79 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) |
% 14.40/2.79 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 14.40/2.79 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 =
% 14.40/2.79 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 &
% 14.40/2.79 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0,
% 14.40/2.79 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 14.40/2.79
% 14.40/2.79 (function-axioms)
% 14.40/2.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.40/2.79 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) &
% 14.40/2.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.40/2.79 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 14.40/2.79 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 14.40/2.79 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 14.40/2.79 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.40/2.79 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.40/2.79 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & !
% 14.40/2.79 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 14.40/2.79 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3,
% 14.40/2.79 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 14.40/2.79 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 14.40/2.79 (distinct_points(v3, v2) = v0))
% 14.40/2.79
% 14.40/2.79 Further assumptions not needed in the proof:
% 14.40/2.79 --------------------------------------------
% 14.40/2.80 apart2, apart3, apart5, apart6, ceq1, ceq2, ceq3, con2
% 14.40/2.80
% 14.40/2.80 Those formulas are unsatisfiable:
% 14.40/2.80 ---------------------------------
% 14.40/2.80
% 14.40/2.80 Begin of proof
% 14.40/2.80 |
% 14.40/2.80 | ALPHA: (apart4) implies:
% 14.40/2.80 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 14.40/2.80 | (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) |
% 14.40/2.80 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0)
% 14.40/2.80 |
% 14.40/2.80 | ALPHA: (cu1) implies:
% 14.40/2.80 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 14.40/2.80 | (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~
% 14.40/2.80 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5:
% 14.40/2.80 | int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 &
% 14.40/2.80 | apart_point_and_line(v1, v3) = 0) | (v6 = 0 &
% 14.40/2.80 | apart_point_and_line(v1, v2) = 0) | (v5 = 0 &
% 14.40/2.80 | apart_point_and_line(v0, v3) = 0) | (v4 = 0 &
% 14.40/2.80 | apart_point_and_line(v0, v2) = 0)))
% 14.40/2.80 |
% 14.40/2.80 | ALPHA: (function-axioms) implies:
% 14.40/2.80 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.40/2.80 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 14.40/2.80 | (distinct_points(v3, v2) = v0))
% 14.40/2.80 |
% 14.40/2.80 | DELTA: instantiating (con) with fresh symbols all_15_0, all_15_1, all_15_2,
% 14.40/2.80 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7 gives:
% 14.40/2.81 | (4) ~ (all_15_4 = 0) & distinct_points(all_15_6, all_15_5) = all_15_4 &
% 14.40/2.81 | distinct_points(all_15_7, all_15_6) = 0 & $i(all_15_5) & $i(all_15_6) &
% 14.40/2.81 | $i(all_15_7) & ((all_15_0 = 0 & line_connecting(all_15_7, all_15_5) =
% 14.40/2.81 | all_15_1 & line_connecting(all_15_7, all_15_6) = all_15_2 &
% 14.40/2.81 | distinct_lines(all_15_2, all_15_1) = 0 & $i(all_15_1) &
% 14.40/2.81 | $i(all_15_2)) | ( ~ (all_15_3 = 0) & distinct_points(all_15_7,
% 14.40/2.81 | all_15_5) = all_15_3))
% 14.40/2.81 |
% 14.40/2.81 | ALPHA: (4) implies:
% 14.40/2.81 | (5) ~ (all_15_4 = 0)
% 14.40/2.81 | (6) $i(all_15_7)
% 14.40/2.81 | (7) $i(all_15_6)
% 14.40/2.81 | (8) $i(all_15_5)
% 14.40/2.81 | (9) distinct_points(all_15_7, all_15_6) = 0
% 14.40/2.81 | (10) distinct_points(all_15_6, all_15_5) = all_15_4
% 14.40/2.81 | (11) (all_15_0 = 0 & line_connecting(all_15_7, all_15_5) = all_15_1 &
% 14.40/2.81 | line_connecting(all_15_7, all_15_6) = all_15_2 &
% 14.40/2.81 | distinct_lines(all_15_2, all_15_1) = 0 & $i(all_15_1) &
% 14.40/2.81 | $i(all_15_2)) | ( ~ (all_15_3 = 0) & distinct_points(all_15_7,
% 14.40/2.81 | all_15_5) = all_15_3)
% 14.40/2.81 |
% 14.40/2.81 | GROUND_INST: instantiating (1) with all_15_7, all_15_6, all_15_5, all_15_4,
% 14.40/2.81 | simplifying with (6), (7), (8), (9), (10) gives:
% 14.40/2.81 | (12) all_15_4 = 0 | distinct_points(all_15_7, all_15_5) = 0
% 14.40/2.81 |
% 14.40/2.81 | BETA: splitting (11) gives:
% 14.40/2.81 |
% 14.40/2.81 | Case 1:
% 14.40/2.81 | |
% 14.40/2.81 | | (13) all_15_0 = 0 & line_connecting(all_15_7, all_15_5) = all_15_1 &
% 14.40/2.81 | | line_connecting(all_15_7, all_15_6) = all_15_2 &
% 14.40/2.81 | | distinct_lines(all_15_2, all_15_1) = 0 & $i(all_15_1) & $i(all_15_2)
% 14.40/2.81 | |
% 14.40/2.81 | | ALPHA: (13) implies:
% 14.56/2.82 | | (14) $i(all_15_2)
% 14.56/2.82 | | (15) $i(all_15_1)
% 14.56/2.82 | | (16) distinct_lines(all_15_2, all_15_1) = 0
% 14.56/2.82 | | (17) line_connecting(all_15_7, all_15_6) = all_15_2
% 14.56/2.82 | | (18) line_connecting(all_15_7, all_15_5) = all_15_1
% 14.56/2.82 | |
% 14.56/2.82 | | BETA: splitting (12) gives:
% 14.56/2.82 | |
% 14.56/2.82 | | Case 1:
% 14.56/2.82 | | |
% 14.56/2.82 | | | (19) distinct_points(all_15_7, all_15_5) = 0
% 14.56/2.82 | | |
% 14.56/2.82 | | | GROUND_INST: instantiating (2) with all_15_7, all_15_5, all_15_2,
% 14.56/2.82 | | | all_15_1, simplifying with (6), (8), (14), (15), (16), (19)
% 14.56/2.82 | | | gives:
% 14.56/2.82 | | | (20) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 =
% 14.56/2.82 | | | 0 & apart_point_and_line(all_15_5, all_15_1) = 0) | (v2 = 0 &
% 14.56/2.82 | | | apart_point_and_line(all_15_5, all_15_2) = 0) | (v1 = 0 &
% 14.56/2.82 | | | apart_point_and_line(all_15_7, all_15_1) = 0) | (v0 = 0 &
% 14.56/2.82 | | | apart_point_and_line(all_15_7, all_15_2) = 0))
% 14.56/2.82 | | |
% 14.56/2.82 | | | DELTA: instantiating (20) with fresh symbols all_39_0, all_39_1, all_39_2,
% 14.56/2.82 | | | all_39_3 gives:
% 14.56/2.82 | | | (21) (all_39_0 = 0 & apart_point_and_line(all_15_5, all_15_1) = 0) |
% 14.56/2.82 | | | (all_39_1 = 0 & apart_point_and_line(all_15_5, all_15_2) = 0) |
% 14.56/2.82 | | | (all_39_2 = 0 & apart_point_and_line(all_15_7, all_15_1) = 0) |
% 14.56/2.82 | | | (all_39_3 = 0 & apart_point_and_line(all_15_7, all_15_2) = 0)
% 14.56/2.82 | | |
% 14.56/2.82 | | | BETA: splitting (21) gives:
% 14.56/2.82 | | |
% 14.56/2.82 | | | Case 1:
% 14.56/2.82 | | | |
% 14.56/2.82 | | | | (22) (all_39_0 = 0 & apart_point_and_line(all_15_5, all_15_1) = 0) |
% 14.56/2.82 | | | | (all_39_1 = 0 & apart_point_and_line(all_15_5, all_15_2) = 0)
% 14.56/2.82 | | | |
% 14.56/2.82 | | | | BETA: splitting (22) gives:
% 14.56/2.82 | | | |
% 14.56/2.82 | | | | Case 1:
% 14.56/2.82 | | | | |
% 14.56/2.82 | | | | | (23) all_39_0 = 0 & apart_point_and_line(all_15_5, all_15_1) = 0
% 14.56/2.82 | | | | |
% 14.56/2.82 | | | | | ALPHA: (23) implies:
% 14.56/2.82 | | | | | (24) apart_point_and_line(all_15_5, all_15_1) = 0
% 14.56/2.82 | | | | |
% 14.56/2.83 | | | | | GROUND_INST: instantiating (con1) with all_15_7, all_15_5, all_15_5,
% 14.56/2.83 | | | | | all_15_1, simplifying with (6), (8), (18), (24) gives:
% 14.56/2.83 | | | | | (25) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & v1 = 0
% 14.56/2.83 | | | | | & distinct_points(all_15_5, all_15_5) = 0 &
% 14.56/2.83 | | | | | distinct_points(all_15_5, all_15_7) = 0) | ( ~ (v0 = 0) &
% 14.56/2.83 | | | | | distinct_points(all_15_7, all_15_5) = v0))
% 14.56/2.83 | | | | |
% 14.56/2.83 | | | | | DELTA: instantiating (25) with fresh symbols all_48_0, all_48_1,
% 14.56/2.83 | | | | | all_48_2 gives:
% 14.62/2.83 | | | | | (26) (all_48_0 = 0 & all_48_1 = 0 & distinct_points(all_15_5,
% 14.62/2.83 | | | | | all_15_5) = 0 & distinct_points(all_15_5, all_15_7) = 0) |
% 14.62/2.83 | | | | | ( ~ (all_48_2 = 0) & distinct_points(all_15_7, all_15_5) =
% 14.62/2.83 | | | | | all_48_2)
% 14.62/2.83 | | | | |
% 14.62/2.83 | | | | | BETA: splitting (26) gives:
% 14.62/2.83 | | | | |
% 14.62/2.83 | | | | | Case 1:
% 14.62/2.83 | | | | | |
% 14.62/2.83 | | | | | | (27) all_48_0 = 0 & all_48_1 = 0 & distinct_points(all_15_5,
% 14.62/2.83 | | | | | | all_15_5) = 0 & distinct_points(all_15_5, all_15_7) = 0
% 14.62/2.83 | | | | | |
% 14.62/2.83 | | | | | | ALPHA: (27) implies:
% 14.62/2.83 | | | | | | (28) distinct_points(all_15_5, all_15_5) = 0
% 14.62/2.83 | | | | | |
% 14.62/2.83 | | | | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying with
% 14.62/2.83 | | | | | | (8), (28) gives:
% 14.62/2.83 | | | | | | (29) $false
% 14.62/2.83 | | | | | |
% 14.62/2.83 | | | | | | CLOSE: (29) is inconsistent.
% 14.62/2.83 | | | | | |
% 14.62/2.83 | | | | | Case 2:
% 14.62/2.83 | | | | | |
% 14.62/2.83 | | | | | | (30) ~ (all_48_2 = 0) & distinct_points(all_15_7, all_15_5) =
% 14.62/2.83 | | | | | | all_48_2
% 14.62/2.83 | | | | | |
% 14.62/2.83 | | | | | | ALPHA: (30) implies:
% 14.62/2.83 | | | | | | (31) ~ (all_48_2 = 0)
% 14.62/2.83 | | | | | | (32) distinct_points(all_15_7, all_15_5) = all_48_2
% 14.62/2.83 | | | | | |
% 14.62/2.83 | | | | | | GROUND_INST: instantiating (3) with 0, all_48_2, all_15_5, all_15_7,
% 14.62/2.83 | | | | | | simplifying with (19), (32) gives:
% 14.62/2.83 | | | | | | (33) all_48_2 = 0
% 14.62/2.83 | | | | | |
% 14.62/2.83 | | | | | | REDUCE: (31), (33) imply:
% 14.62/2.84 | | | | | | (34) $false
% 14.62/2.84 | | | | | |
% 14.62/2.84 | | | | | | CLOSE: (34) is inconsistent.
% 14.62/2.84 | | | | | |
% 14.62/2.84 | | | | | End of split
% 14.62/2.84 | | | | |
% 14.62/2.84 | | | | Case 2:
% 14.62/2.84 | | | | |
% 14.62/2.84 | | | | | (35) all_39_1 = 0 & apart_point_and_line(all_15_5, all_15_2) = 0
% 14.62/2.84 | | | | |
% 14.62/2.84 | | | | | ALPHA: (35) implies:
% 14.62/2.84 | | | | | (36) apart_point_and_line(all_15_5, all_15_2) = 0
% 14.62/2.84 | | | | |
% 14.62/2.84 | | | | | GROUND_INST: instantiating (con1) with all_15_7, all_15_6, all_15_5,
% 14.62/2.84 | | | | | all_15_2, simplifying with (6), (7), (8), (17), (36)
% 14.62/2.84 | | | | | gives:
% 14.62/2.84 | | | | | (37) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & v1 = 0
% 14.62/2.84 | | | | | & distinct_points(all_15_5, all_15_6) = 0 &
% 14.62/2.84 | | | | | distinct_points(all_15_5, all_15_7) = 0) | ( ~ (v0 = 0) &
% 14.62/2.84 | | | | | distinct_points(all_15_7, all_15_6) = v0))
% 14.62/2.84 | | | | |
% 14.62/2.84 | | | | | DELTA: instantiating (37) with fresh symbols all_48_0, all_48_1,
% 14.62/2.84 | | | | | all_48_2 gives:
% 14.62/2.84 | | | | | (38) (all_48_0 = 0 & all_48_1 = 0 & distinct_points(all_15_5,
% 14.62/2.84 | | | | | all_15_6) = 0 & distinct_points(all_15_5, all_15_7) = 0) |
% 14.62/2.84 | | | | | ( ~ (all_48_2 = 0) & distinct_points(all_15_7, all_15_6) =
% 14.62/2.84 | | | | | all_48_2)
% 14.62/2.84 | | | | |
% 14.62/2.84 | | | | | BETA: splitting (38) gives:
% 14.62/2.84 | | | | |
% 14.62/2.84 | | | | | Case 1:
% 14.62/2.84 | | | | | |
% 14.62/2.84 | | | | | | (39) all_48_0 = 0 & all_48_1 = 0 & distinct_points(all_15_5,
% 14.62/2.84 | | | | | | all_15_6) = 0 & distinct_points(all_15_5, all_15_7) = 0
% 14.62/2.84 | | | | | |
% 14.62/2.84 | | | | | | ALPHA: (39) implies:
% 14.62/2.84 | | | | | | (40) distinct_points(all_15_5, all_15_6) = 0
% 14.62/2.84 | | | | | |
% 14.62/2.84 | | | | | | GROUND_INST: instantiating (1) with all_15_5, all_15_6, all_15_5,
% 14.62/2.84 | | | | | | all_15_4, simplifying with (7), (8), (10), (40) gives:
% 14.62/2.84 | | | | | | (41) all_15_4 = 0 | distinct_points(all_15_5, all_15_5) = 0
% 14.62/2.84 | | | | | |
% 14.62/2.84 | | | | | | BETA: splitting (41) gives:
% 14.62/2.84 | | | | | |
% 14.62/2.84 | | | | | | Case 1:
% 14.62/2.84 | | | | | | |
% 14.62/2.84 | | | | | | | (42) distinct_points(all_15_5, all_15_5) = 0
% 14.62/2.84 | | | | | | |
% 14.62/2.84 | | | | | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying
% 14.62/2.84 | | | | | | | with (8), (42) gives:
% 14.62/2.84 | | | | | | | (43) $false
% 14.62/2.84 | | | | | | |
% 14.62/2.84 | | | | | | | CLOSE: (43) is inconsistent.
% 14.62/2.84 | | | | | | |
% 14.62/2.84 | | | | | | Case 2:
% 14.62/2.84 | | | | | | |
% 14.62/2.84 | | | | | | | (44) all_15_4 = 0
% 14.62/2.84 | | | | | | |
% 14.62/2.84 | | | | | | | REDUCE: (5), (44) imply:
% 14.62/2.85 | | | | | | | (45) $false
% 14.62/2.85 | | | | | | |
% 14.62/2.85 | | | | | | | CLOSE: (45) is inconsistent.
% 14.62/2.85 | | | | | | |
% 14.62/2.85 | | | | | | End of split
% 14.62/2.85 | | | | | |
% 14.62/2.85 | | | | | Case 2:
% 14.62/2.85 | | | | | |
% 14.62/2.85 | | | | | | (46) ~ (all_48_2 = 0) & distinct_points(all_15_7, all_15_6) =
% 14.62/2.85 | | | | | | all_48_2
% 14.62/2.85 | | | | | |
% 14.62/2.85 | | | | | | ALPHA: (46) implies:
% 14.62/2.85 | | | | | | (47) ~ (all_48_2 = 0)
% 14.62/2.85 | | | | | | (48) distinct_points(all_15_7, all_15_6) = all_48_2
% 14.62/2.85 | | | | | |
% 14.62/2.85 | | | | | | GROUND_INST: instantiating (3) with 0, all_48_2, all_15_6, all_15_7,
% 14.62/2.85 | | | | | | simplifying with (9), (48) gives:
% 14.62/2.85 | | | | | | (49) all_48_2 = 0
% 14.62/2.85 | | | | | |
% 14.62/2.85 | | | | | | REDUCE: (47), (49) imply:
% 14.62/2.85 | | | | | | (50) $false
% 14.62/2.85 | | | | | |
% 14.62/2.85 | | | | | | CLOSE: (50) is inconsistent.
% 14.62/2.85 | | | | | |
% 14.62/2.85 | | | | | End of split
% 14.62/2.85 | | | | |
% 14.62/2.85 | | | | End of split
% 14.62/2.85 | | | |
% 14.62/2.85 | | | Case 2:
% 14.62/2.85 | | | |
% 14.62/2.85 | | | | (51) (all_39_2 = 0 & apart_point_and_line(all_15_7, all_15_1) = 0) |
% 14.62/2.85 | | | | (all_39_3 = 0 & apart_point_and_line(all_15_7, all_15_2) = 0)
% 14.62/2.85 | | | |
% 14.62/2.85 | | | | BETA: splitting (51) gives:
% 14.62/2.85 | | | |
% 14.62/2.85 | | | | Case 1:
% 14.62/2.85 | | | | |
% 14.62/2.85 | | | | | (52) all_39_2 = 0 & apart_point_and_line(all_15_7, all_15_1) = 0
% 14.62/2.85 | | | | |
% 14.62/2.85 | | | | | ALPHA: (52) implies:
% 14.62/2.85 | | | | | (53) apart_point_and_line(all_15_7, all_15_1) = 0
% 14.62/2.85 | | | | |
% 14.62/2.85 | | | | | GROUND_INST: instantiating (con1) with all_15_7, all_15_5, all_15_7,
% 14.62/2.85 | | | | | all_15_1, simplifying with (6), (8), (18), (53) gives:
% 14.62/2.85 | | | | | (54) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & v1 = 0
% 14.62/2.85 | | | | | & distinct_points(all_15_7, all_15_5) = 0 &
% 14.62/2.85 | | | | | distinct_points(all_15_7, all_15_7) = 0) | ( ~ (v0 = 0) &
% 14.62/2.85 | | | | | distinct_points(all_15_7, all_15_5) = v0))
% 14.62/2.85 | | | | |
% 14.62/2.85 | | | | | DELTA: instantiating (54) with fresh symbols all_48_0, all_48_1,
% 14.62/2.85 | | | | | all_48_2 gives:
% 14.62/2.85 | | | | | (55) (all_48_0 = 0 & all_48_1 = 0 & distinct_points(all_15_7,
% 14.62/2.85 | | | | | all_15_5) = 0 & distinct_points(all_15_7, all_15_7) = 0) |
% 14.62/2.85 | | | | | ( ~ (all_48_2 = 0) & distinct_points(all_15_7, all_15_5) =
% 14.62/2.85 | | | | | all_48_2)
% 14.62/2.85 | | | | |
% 14.62/2.85 | | | | | BETA: splitting (55) gives:
% 14.62/2.85 | | | | |
% 14.62/2.85 | | | | | Case 1:
% 14.62/2.85 | | | | | |
% 14.62/2.85 | | | | | | (56) all_48_0 = 0 & all_48_1 = 0 & distinct_points(all_15_7,
% 14.62/2.85 | | | | | | all_15_5) = 0 & distinct_points(all_15_7, all_15_7) = 0
% 14.62/2.85 | | | | | |
% 14.62/2.85 | | | | | | ALPHA: (56) implies:
% 14.62/2.86 | | | | | | (57) distinct_points(all_15_7, all_15_7) = 0
% 14.62/2.86 | | | | | |
% 14.62/2.86 | | | | | | GROUND_INST: instantiating (apart1) with all_15_7, simplifying with
% 14.62/2.86 | | | | | | (6), (57) gives:
% 14.62/2.86 | | | | | | (58) $false
% 14.62/2.86 | | | | | |
% 14.62/2.86 | | | | | | CLOSE: (58) is inconsistent.
% 14.62/2.86 | | | | | |
% 14.62/2.86 | | | | | Case 2:
% 14.62/2.86 | | | | | |
% 14.62/2.86 | | | | | | (59) ~ (all_48_2 = 0) & distinct_points(all_15_7, all_15_5) =
% 14.62/2.86 | | | | | | all_48_2
% 14.62/2.86 | | | | | |
% 14.62/2.86 | | | | | | ALPHA: (59) implies:
% 14.62/2.86 | | | | | | (60) ~ (all_48_2 = 0)
% 14.62/2.86 | | | | | | (61) distinct_points(all_15_7, all_15_5) = all_48_2
% 14.62/2.86 | | | | | |
% 14.62/2.86 | | | | | | GROUND_INST: instantiating (3) with 0, all_48_2, all_15_5, all_15_7,
% 14.62/2.86 | | | | | | simplifying with (19), (61) gives:
% 14.62/2.86 | | | | | | (62) all_48_2 = 0
% 14.62/2.86 | | | | | |
% 14.62/2.86 | | | | | | REDUCE: (60), (62) imply:
% 14.62/2.86 | | | | | | (63) $false
% 14.62/2.86 | | | | | |
% 14.62/2.86 | | | | | | CLOSE: (63) is inconsistent.
% 14.62/2.86 | | | | | |
% 14.62/2.86 | | | | | End of split
% 14.62/2.86 | | | | |
% 14.62/2.86 | | | | Case 2:
% 14.62/2.86 | | | | |
% 14.62/2.86 | | | | | (64) all_39_3 = 0 & apart_point_and_line(all_15_7, all_15_2) = 0
% 14.62/2.86 | | | | |
% 14.62/2.86 | | | | | ALPHA: (64) implies:
% 14.62/2.86 | | | | | (65) apart_point_and_line(all_15_7, all_15_2) = 0
% 14.62/2.86 | | | | |
% 14.62/2.86 | | | | | GROUND_INST: instantiating (con1) with all_15_7, all_15_6, all_15_7,
% 14.62/2.86 | | | | | all_15_2, simplifying with (6), (7), (17), (65) gives:
% 14.62/2.86 | | | | | (66) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & v1 = 0
% 14.62/2.86 | | | | | & distinct_points(all_15_7, all_15_6) = 0 &
% 14.62/2.86 | | | | | distinct_points(all_15_7, all_15_7) = 0) | ( ~ (v0 = 0) &
% 14.62/2.86 | | | | | distinct_points(all_15_7, all_15_6) = v0))
% 14.62/2.86 | | | | |
% 14.62/2.86 | | | | | DELTA: instantiating (66) with fresh symbols all_48_0, all_48_1,
% 14.62/2.86 | | | | | all_48_2 gives:
% 14.62/2.86 | | | | | (67) (all_48_0 = 0 & all_48_1 = 0 & distinct_points(all_15_7,
% 14.62/2.86 | | | | | all_15_6) = 0 & distinct_points(all_15_7, all_15_7) = 0) |
% 14.62/2.86 | | | | | ( ~ (all_48_2 = 0) & distinct_points(all_15_7, all_15_6) =
% 14.62/2.86 | | | | | all_48_2)
% 14.62/2.86 | | | | |
% 14.62/2.86 | | | | | BETA: splitting (67) gives:
% 14.62/2.86 | | | | |
% 14.62/2.86 | | | | | Case 1:
% 14.62/2.86 | | | | | |
% 14.62/2.86 | | | | | | (68) all_48_0 = 0 & all_48_1 = 0 & distinct_points(all_15_7,
% 14.62/2.86 | | | | | | all_15_6) = 0 & distinct_points(all_15_7, all_15_7) = 0
% 14.62/2.86 | | | | | |
% 14.62/2.87 | | | | | | ALPHA: (68) implies:
% 14.62/2.87 | | | | | | (69) distinct_points(all_15_7, all_15_7) = 0
% 14.62/2.87 | | | | | |
% 14.62/2.87 | | | | | | GROUND_INST: instantiating (apart1) with all_15_7, simplifying with
% 14.62/2.87 | | | | | | (6), (69) gives:
% 14.62/2.87 | | | | | | (70) $false
% 14.62/2.87 | | | | | |
% 14.62/2.87 | | | | | | CLOSE: (70) is inconsistent.
% 14.62/2.87 | | | | | |
% 14.62/2.87 | | | | | Case 2:
% 14.62/2.87 | | | | | |
% 14.62/2.87 | | | | | | (71) ~ (all_48_2 = 0) & distinct_points(all_15_7, all_15_6) =
% 14.62/2.87 | | | | | | all_48_2
% 14.62/2.87 | | | | | |
% 14.62/2.87 | | | | | | ALPHA: (71) implies:
% 14.62/2.87 | | | | | | (72) ~ (all_48_2 = 0)
% 14.62/2.87 | | | | | | (73) distinct_points(all_15_7, all_15_6) = all_48_2
% 14.62/2.87 | | | | | |
% 14.62/2.87 | | | | | | GROUND_INST: instantiating (3) with 0, all_48_2, all_15_6, all_15_7,
% 14.62/2.87 | | | | | | simplifying with (9), (73) gives:
% 14.62/2.87 | | | | | | (74) all_48_2 = 0
% 14.62/2.87 | | | | | |
% 14.62/2.87 | | | | | | REDUCE: (72), (74) imply:
% 14.62/2.87 | | | | | | (75) $false
% 14.62/2.87 | | | | | |
% 14.62/2.87 | | | | | | CLOSE: (75) is inconsistent.
% 14.62/2.87 | | | | | |
% 14.62/2.87 | | | | | End of split
% 14.62/2.87 | | | | |
% 14.62/2.87 | | | | End of split
% 14.62/2.87 | | | |
% 14.62/2.87 | | | End of split
% 14.62/2.87 | | |
% 14.62/2.87 | | Case 2:
% 14.62/2.87 | | |
% 14.62/2.87 | | | (76) all_15_4 = 0
% 14.62/2.87 | | |
% 14.62/2.87 | | | REDUCE: (5), (76) imply:
% 14.62/2.87 | | | (77) $false
% 14.62/2.87 | | |
% 14.62/2.87 | | | CLOSE: (77) is inconsistent.
% 14.62/2.87 | | |
% 14.62/2.87 | | End of split
% 14.62/2.87 | |
% 14.62/2.87 | Case 2:
% 14.62/2.87 | |
% 14.62/2.87 | | (78) ~ (all_15_3 = 0) & distinct_points(all_15_7, all_15_5) = all_15_3
% 14.62/2.87 | |
% 14.62/2.87 | | ALPHA: (78) implies:
% 14.62/2.87 | | (79) ~ (all_15_3 = 0)
% 14.62/2.87 | | (80) distinct_points(all_15_7, all_15_5) = all_15_3
% 14.62/2.87 | |
% 14.62/2.87 | | BETA: splitting (12) gives:
% 14.62/2.87 | |
% 14.62/2.87 | | Case 1:
% 14.62/2.87 | | |
% 14.62/2.87 | | | (81) distinct_points(all_15_7, all_15_5) = 0
% 14.62/2.87 | | |
% 14.62/2.87 | | | GROUND_INST: instantiating (3) with 0, all_15_3, all_15_5, all_15_7,
% 14.62/2.87 | | | simplifying with (80), (81) gives:
% 14.62/2.87 | | | (82) all_15_3 = 0
% 14.62/2.87 | | |
% 14.62/2.87 | | | REDUCE: (79), (82) imply:
% 14.62/2.87 | | | (83) $false
% 14.62/2.87 | | |
% 14.62/2.87 | | | CLOSE: (83) is inconsistent.
% 14.62/2.87 | | |
% 14.62/2.87 | | Case 2:
% 14.62/2.87 | | |
% 14.62/2.87 | | | (84) all_15_4 = 0
% 14.62/2.87 | | |
% 14.62/2.87 | | | REDUCE: (5), (84) imply:
% 14.62/2.87 | | | (85) $false
% 14.62/2.87 | | |
% 14.62/2.87 | | | CLOSE: (85) is inconsistent.
% 14.62/2.87 | | |
% 14.62/2.87 | | End of split
% 14.62/2.87 | |
% 14.62/2.87 | End of split
% 14.62/2.87 |
% 14.62/2.87 End of proof
% 14.62/2.87 % SZS output end Proof for theBenchmark
% 14.62/2.87
% 14.62/2.87 2248ms
%------------------------------------------------------------------------------