TSTP Solution File: GEO186+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO186+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n019.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 23:22:00 EDT 2023
% Result : Theorem 11.61s 2.31s
% Output : Proof 21.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO186+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 19:14:27 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.70/1.06 Prover 4: Preprocessing ...
% 2.70/1.06 Prover 1: Preprocessing ...
% 2.83/1.10 Prover 3: Preprocessing ...
% 2.83/1.10 Prover 2: Preprocessing ...
% 2.83/1.10 Prover 0: Preprocessing ...
% 2.83/1.10 Prover 5: Preprocessing ...
% 2.83/1.10 Prover 6: Preprocessing ...
% 3.88/1.31 Prover 5: Proving ...
% 3.88/1.32 Prover 2: Proving ...
% 4.55/1.37 Prover 3: Constructing countermodel ...
% 4.55/1.37 Prover 6: Constructing countermodel ...
% 4.55/1.39 Prover 1: Constructing countermodel ...
% 5.40/1.47 Prover 3: gave up
% 5.40/1.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.40/1.48 Prover 4: Constructing countermodel ...
% 5.40/1.48 Prover 1: gave up
% 5.40/1.48 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.40/1.48 Prover 6: gave up
% 5.40/1.49 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 5.40/1.49 Prover 0: Proving ...
% 6.02/1.52 Prover 8: Preprocessing ...
% 6.02/1.52 Prover 9: Preprocessing ...
% 6.02/1.54 Prover 7: Preprocessing ...
% 6.50/1.58 Prover 7: Warning: ignoring some quantifiers
% 6.50/1.59 Prover 7: Constructing countermodel ...
% 6.50/1.63 Prover 8: Warning: ignoring some quantifiers
% 6.50/1.64 Prover 8: Constructing countermodel ...
% 7.27/1.68 Prover 9: Constructing countermodel ...
% 7.27/1.69 Prover 8: gave up
% 7.27/1.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.61/1.75 Prover 10: Preprocessing ...
% 7.61/1.75 Prover 7: gave up
% 7.61/1.76 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.61/1.77 Prover 10: Warning: ignoring some quantifiers
% 7.61/1.78 Prover 11: Preprocessing ...
% 7.61/1.79 Prover 10: Constructing countermodel ...
% 8.24/1.85 Prover 10: gave up
% 8.24/1.86 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 8.74/1.92 Prover 12: Preprocessing ...
% 8.74/1.97 Prover 11: Constructing countermodel ...
% 8.74/2.02 Prover 12: Proving ...
% 11.61/2.31 Prover 0: proved (1663ms)
% 11.61/2.31
% 11.61/2.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.61/2.31
% 11.61/2.31 Prover 5: stopped
% 11.61/2.31 Prover 9: stopped
% 11.61/2.31 Prover 12: stopped
% 11.61/2.31 Prover 2: stopped
% 11.61/2.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.61/2.31 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 11.61/2.32 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 11.61/2.33 Prover 13: Preprocessing ...
% 11.61/2.33 Prover 19: Preprocessing ...
% 11.61/2.34 Prover 16: Preprocessing ...
% 12.30/2.36 Prover 16: Warning: ignoring some quantifiers
% 12.30/2.36 Prover 16: Constructing countermodel ...
% 12.30/2.37 Prover 13: Warning: ignoring some quantifiers
% 12.30/2.37 Prover 13: Constructing countermodel ...
% 12.58/2.39 Prover 19: Warning: ignoring some quantifiers
% 12.58/2.39 Prover 19: Constructing countermodel ...
% 12.58/2.42 Prover 19: gave up
% 13.01/2.45 Prover 13: gave up
% 13.01/2.52 Prover 16: gave up
% 20.42/3.89 Prover 11: Found proof (size 67)
% 20.42/3.89 Prover 11: proved (2134ms)
% 20.42/3.89 Prover 4: stopped
% 20.42/3.89
% 20.42/3.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.42/3.89
% 20.42/3.90 % SZS output start Proof for theBenchmark
% 20.42/3.91 Assumptions after simplification:
% 20.42/3.91 ---------------------------------
% 20.42/3.91
% 20.42/3.91 (apart3)
% 20.42/3.95 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0))
% 20.42/3.95
% 20.42/3.95 (ceq3)
% 20.42/3.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 20.42/3.96 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2)
% 20.42/3.96 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 20.42/3.96 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 20.42/3.96 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~
% 20.42/3.96 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 20.42/3.96 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 20.42/3.96 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~
% 20.42/3.96 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 20.42/3.96 convergent_lines(v0, v2) = 0)
% 20.42/3.96
% 20.42/3.96 (ci3)
% 20.42/3.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 20.42/3.97 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0)
% 20.42/3.97 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) &
% 20.42/3.97 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 20.42/3.97 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 20.42/3.97 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 &
% 20.42/3.97 apart_point_and_line(v2, v0) = v3 & $i(v2)))
% 20.42/3.97
% 20.42/3.97 (ci4)
% 20.42/3.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 20.42/3.97 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0)
% 20.42/3.97 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) &
% 20.42/3.97 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 20.42/3.97 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 20.42/3.97 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 &
% 20.42/3.97 apart_point_and_line(v2, v1) = v3 & $i(v2)))
% 20.42/3.97
% 20.42/3.97 (con)
% 20.42/3.98 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5:
% 20.42/3.98 int] : ? [v6: $i] : ( ~ (v5 = 0) & ~ (v4 = 0) & intersection_point(v2, v3)
% 20.42/3.98 = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4
% 20.42/3.98 & convergent_lines(v2, v3) = 0 & distinct_points(v0, v6) = 0 &
% 20.42/3.98 distinct_points(v0, v1) = 0 & $i(v6) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 20.42/3.98
% 20.42/3.98 (cu1)
% 21.42/4.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 21.42/4.00 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 21.42/4.00 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 21.42/4.00 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 21.42/4.00 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 &
% 21.42/4.00 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2,
% 21.42/4.00 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 21.42/4.00 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1,
% 21.42/4.00 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~
% 21.42/4.00 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 21.42/4.00 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 21.42/4.00 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0,
% 21.42/4.00 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 21.42/4.00 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 21.42/4.00 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 21.42/4.00 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 21.42/4.00 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 =
% 21.42/4.00 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 &
% 21.42/4.00 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2,
% 21.42/4.00 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 21.42/4.00 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 21.42/4.00 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~
% 21.42/4.00 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 21.42/4.00 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 =
% 21.42/4.00 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 &
% 21.42/4.00 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2,
% 21.42/4.00 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 21.42/4.00 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 21.42/4.00 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~
% 21.42/4.00 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~
% 21.42/4.00 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 21.42/4.00 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 &
% 21.42/4.00 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0,
% 21.42/4.00 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 21.42/4.00 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0,
% 21.42/4.00 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~
% 21.42/4.00 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 21.42/4.00 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 21.42/4.00 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1,
% 21.42/4.00 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i]
% 21.42/4.00 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) |
% 21.42/4.00 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 21.42/4.00 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 =
% 21.42/4.00 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 &
% 21.42/4.00 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0,
% 21.42/4.00 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 21.42/4.00
% 21.42/4.00 (function-axioms)
% 21.42/4.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 21.42/4.01 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) &
% 21.42/4.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 21.42/4.01 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 21.42/4.01 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 21.42/4.01 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 21.42/4.01 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 21.42/4.01 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 21.42/4.01 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & !
% 21.42/4.01 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 21.42/4.01 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3,
% 21.42/4.01 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 21.42/4.01 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 21.42/4.01 (distinct_points(v3, v2) = v0))
% 21.42/4.01
% 21.42/4.01 Further assumptions not needed in the proof:
% 21.42/4.01 --------------------------------------------
% 21.42/4.01 apart1, apart2, apart4, apart5, ax6, ceq1, ceq2, ci1, ci2
% 21.42/4.01
% 21.42/4.01 Those formulas are unsatisfiable:
% 21.42/4.01 ---------------------------------
% 21.42/4.01
% 21.42/4.01 Begin of proof
% 21.42/4.01 |
% 21.53/4.01 | ALPHA: (ci3) implies:
% 21.53/4.01 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0,
% 21.53/4.01 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] :
% 21.53/4.01 | (( ~ (v4 = 0) & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) &
% 21.53/4.01 | convergent_lines(v0, v1) = v3)))
% 21.53/4.01 |
% 21.53/4.01 | ALPHA: (ci4) implies:
% 21.53/4.01 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0,
% 21.53/4.01 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] :
% 21.53/4.01 | (( ~ (v4 = 0) & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) &
% 21.53/4.01 | convergent_lines(v0, v1) = v3)))
% 21.53/4.01 |
% 21.53/4.01 | ALPHA: (cu1) implies:
% 21.53/4.02 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 21.53/4.02 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5)
% 21.53/4.02 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0,
% 21.53/4.02 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 21.53/4.02 | [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 21.53/4.02 | apart_point_and_line(v1, v3) = 0) | (v7 = 0 &
% 21.53/4.02 | apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) &
% 21.53/4.02 | distinct_lines(v2, v3) = v6)))
% 21.53/4.02 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 21.53/4.02 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5)
% 21.53/4.02 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 21.53/4.02 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ?
% 21.53/4.02 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 &
% 21.53/4.02 | apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) &
% 21.53/4.02 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0,
% 21.53/4.02 | v1) = v6)))
% 21.53/4.02 |
% 21.58/4.02 | ALPHA: (ceq3) implies:
% 21.58/4.02 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 21.58/4.02 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) |
% 21.58/4.02 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0)
% 21.58/4.02 |
% 21.58/4.02 | ALPHA: (function-axioms) implies:
% 21.58/4.02 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 21.58/4.02 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 21.58/4.02 | (convergent_lines(v3, v2) = v0))
% 21.58/4.02 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 21.58/4.02 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 21.58/4.02 | (apart_point_and_line(v3, v2) = v0))
% 21.58/4.02 |
% 21.58/4.02 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2,
% 21.58/4.02 | all_17_3, all_17_4, all_17_5, all_17_6 gives:
% 21.58/4.02 | (8) ~ (all_17_1 = 0) & ~ (all_17_2 = 0) & intersection_point(all_17_4,
% 21.58/4.02 | all_17_3) = all_17_0 & apart_point_and_line(all_17_6, all_17_3) =
% 21.58/4.02 | all_17_1 & apart_point_and_line(all_17_6, all_17_4) = all_17_2 &
% 21.58/4.02 | convergent_lines(all_17_4, all_17_3) = 0 & distinct_points(all_17_6,
% 21.58/4.02 | all_17_0) = 0 & distinct_points(all_17_6, all_17_5) = 0 &
% 21.58/4.02 | $i(all_17_0) & $i(all_17_3) & $i(all_17_4) & $i(all_17_5) &
% 21.58/4.02 | $i(all_17_6)
% 21.58/4.02 |
% 21.58/4.02 | ALPHA: (8) implies:
% 21.58/4.03 | (9) ~ (all_17_2 = 0)
% 21.58/4.03 | (10) ~ (all_17_1 = 0)
% 21.58/4.03 | (11) $i(all_17_6)
% 21.58/4.03 | (12) $i(all_17_4)
% 21.58/4.03 | (13) $i(all_17_3)
% 21.58/4.03 | (14) $i(all_17_0)
% 21.58/4.03 | (15) distinct_points(all_17_6, all_17_0) = 0
% 21.58/4.03 | (16) convergent_lines(all_17_4, all_17_3) = 0
% 21.58/4.03 | (17) apart_point_and_line(all_17_6, all_17_4) = all_17_2
% 21.58/4.03 | (18) apart_point_and_line(all_17_6, all_17_3) = all_17_1
% 21.58/4.03 | (19) intersection_point(all_17_4, all_17_3) = all_17_0
% 21.58/4.03 |
% 21.58/4.03 | GROUND_INST: instantiating (3) with all_17_6, all_17_0, all_17_3, all_17_4,
% 21.58/4.03 | all_17_1, all_17_2, simplifying with (11), (12), (13), (14),
% 21.58/4.03 | (15), (17), (18) gives:
% 21.58/4.03 | (20) all_17_1 = 0 | all_17_2 = 0 | ? [v0: int] : ? [v1: int] : ? [v2:
% 21.58/4.03 | int] : ((v2 = 0 & apart_point_and_line(all_17_0, all_17_4) = 0) |
% 21.58/4.03 | (v1 = 0 & apart_point_and_line(all_17_0, all_17_3) = 0) | ( ~ (v0 =
% 21.58/4.03 | 0) & distinct_lines(all_17_3, all_17_4) = v0))
% 21.58/4.03 |
% 21.58/4.03 | GROUND_INST: instantiating (4) with all_17_6, all_17_6, all_17_3, all_17_4,
% 21.58/4.03 | all_17_1, all_17_2, simplifying with (11), (12), (13), (17), (18)
% 21.58/4.03 | gives:
% 21.58/4.03 | (21) all_17_1 = 0 | all_17_2 = 0 | ? [v0: int] : ? [v1: int] : ? [v2:
% 21.58/4.03 | int] : ? [v3: int] : ((v3 = 0 & apart_point_and_line(all_17_6,
% 21.58/4.03 | all_17_3) = 0) | (v2 = 0 & apart_point_and_line(all_17_6,
% 21.58/4.03 | all_17_4) = 0) | ( ~ (v1 = 0) & distinct_lines(all_17_3,
% 21.58/4.03 | all_17_4) = v1) | ( ~ (v0 = 0) & distinct_points(all_17_6,
% 21.58/4.03 | all_17_6) = v0))
% 21.58/4.03 |
% 21.58/4.03 | GROUND_INST: instantiating (2) with all_17_4, all_17_3, all_17_0, simplifying
% 21.58/4.03 | with (12), (13), (19) gives:
% 21.58/4.03 | (22) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) &
% 21.58/4.03 | apart_point_and_line(all_17_0, all_17_3) = v1) | ( ~ (v0 = 0) &
% 21.58/4.03 | convergent_lines(all_17_4, all_17_3) = v0))
% 21.58/4.03 |
% 21.58/4.03 | GROUND_INST: instantiating (1) with all_17_4, all_17_3, all_17_0, simplifying
% 21.58/4.03 | with (12), (13), (19) gives:
% 21.58/4.03 | (23) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) &
% 21.58/4.03 | apart_point_and_line(all_17_0, all_17_4) = v1) | ( ~ (v0 = 0) &
% 21.58/4.03 | convergent_lines(all_17_4, all_17_3) = v0))
% 21.58/4.03 |
% 21.58/4.03 | DELTA: instantiating (23) with fresh symbols all_24_0, all_24_1 gives:
% 21.58/4.03 | (24) ( ~ (all_24_0 = 0) & apart_point_and_line(all_17_0, all_17_4) =
% 21.58/4.03 | all_24_0) | ( ~ (all_24_1 = 0) & convergent_lines(all_17_4,
% 21.58/4.03 | all_17_3) = all_24_1)
% 21.58/4.03 |
% 21.58/4.03 | DELTA: instantiating (22) with fresh symbols all_25_0, all_25_1 gives:
% 21.58/4.03 | (25) ( ~ (all_25_0 = 0) & apart_point_and_line(all_17_0, all_17_3) =
% 21.58/4.03 | all_25_0) | ( ~ (all_25_1 = 0) & convergent_lines(all_17_4,
% 21.58/4.03 | all_17_3) = all_25_1)
% 21.58/4.03 |
% 21.58/4.03 | BETA: splitting (24) gives:
% 21.58/4.04 |
% 21.58/4.04 | Case 1:
% 21.58/4.04 | |
% 21.58/4.04 | | (26) ~ (all_24_0 = 0) & apart_point_and_line(all_17_0, all_17_4) =
% 21.58/4.04 | | all_24_0
% 21.58/4.04 | |
% 21.58/4.04 | | ALPHA: (26) implies:
% 21.58/4.04 | | (27) ~ (all_24_0 = 0)
% 21.58/4.04 | | (28) apart_point_and_line(all_17_0, all_17_4) = all_24_0
% 21.58/4.04 | |
% 21.58/4.04 | | BETA: splitting (21) gives:
% 21.58/4.04 | |
% 21.58/4.04 | | Case 1:
% 21.58/4.04 | | |
% 21.58/4.04 | | | (29) all_17_1 = 0
% 21.58/4.04 | | |
% 21.58/4.04 | | | REDUCE: (10), (29) imply:
% 21.58/4.04 | | | (30) $false
% 21.58/4.04 | | |
% 21.58/4.04 | | | CLOSE: (30) is inconsistent.
% 21.58/4.04 | | |
% 21.58/4.04 | | Case 2:
% 21.58/4.04 | | |
% 21.58/4.04 | | | (31) all_17_2 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 21.58/4.04 | | | [v3: int] : ((v3 = 0 & apart_point_and_line(all_17_6, all_17_3) =
% 21.58/4.04 | | | 0) | (v2 = 0 & apart_point_and_line(all_17_6, all_17_4) = 0) |
% 21.58/4.04 | | | ( ~ (v1 = 0) & distinct_lines(all_17_3, all_17_4) = v1) | ( ~
% 21.58/4.04 | | | (v0 = 0) & distinct_points(all_17_6, all_17_6) = v0))
% 21.58/4.04 | | |
% 21.58/4.04 | | | BETA: splitting (20) gives:
% 21.58/4.04 | | |
% 21.58/4.04 | | | Case 1:
% 21.58/4.04 | | | |
% 21.58/4.04 | | | | (32) all_17_1 = 0
% 21.58/4.04 | | | |
% 21.58/4.04 | | | | REDUCE: (10), (32) imply:
% 21.58/4.04 | | | | (33) $false
% 21.58/4.04 | | | |
% 21.58/4.04 | | | | CLOSE: (33) is inconsistent.
% 21.58/4.04 | | | |
% 21.58/4.04 | | | Case 2:
% 21.58/4.04 | | | |
% 21.58/4.04 | | | | (34) all_17_2 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2
% 21.58/4.04 | | | | = 0 & apart_point_and_line(all_17_0, all_17_4) = 0) | (v1 =
% 21.58/4.04 | | | | 0 & apart_point_and_line(all_17_0, all_17_3) = 0) | ( ~ (v0
% 21.58/4.04 | | | | = 0) & distinct_lines(all_17_3, all_17_4) = v0))
% 21.58/4.04 | | | |
% 21.58/4.04 | | | | BETA: splitting (25) gives:
% 21.58/4.04 | | | |
% 21.58/4.04 | | | | Case 1:
% 21.58/4.04 | | | | |
% 21.58/4.04 | | | | | (35) ~ (all_25_0 = 0) & apart_point_and_line(all_17_0, all_17_3) =
% 21.58/4.04 | | | | | all_25_0
% 21.58/4.04 | | | | |
% 21.58/4.04 | | | | | ALPHA: (35) implies:
% 21.58/4.04 | | | | | (36) ~ (all_25_0 = 0)
% 21.58/4.04 | | | | | (37) apart_point_and_line(all_17_0, all_17_3) = all_25_0
% 21.58/4.04 | | | | |
% 21.58/4.04 | | | | | BETA: splitting (34) gives:
% 21.58/4.04 | | | | |
% 21.58/4.04 | | | | | Case 1:
% 21.58/4.04 | | | | | |
% 21.58/4.04 | | | | | | (38) all_17_2 = 0
% 21.58/4.04 | | | | | |
% 21.58/4.04 | | | | | | REDUCE: (9), (38) imply:
% 21.58/4.04 | | | | | | (39) $false
% 21.58/4.04 | | | | | |
% 21.58/4.04 | | | | | | CLOSE: (39) is inconsistent.
% 21.58/4.04 | | | | | |
% 21.58/4.04 | | | | | Case 2:
% 21.58/4.04 | | | | | |
% 21.58/4.04 | | | | | | (40) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 21.58/4.04 | | | | | | apart_point_and_line(all_17_0, all_17_4) = 0) | (v1 = 0
% 21.58/4.04 | | | | | | & apart_point_and_line(all_17_0, all_17_3) = 0) | ( ~
% 21.58/4.04 | | | | | | (v0 = 0) & distinct_lines(all_17_3, all_17_4) = v0))
% 21.58/4.04 | | | | | |
% 21.58/4.04 | | | | | | DELTA: instantiating (40) with fresh symbols all_113_0, all_113_1,
% 21.58/4.04 | | | | | | all_113_2 gives:
% 21.58/4.04 | | | | | | (41) (all_113_0 = 0 & apart_point_and_line(all_17_0, all_17_4) =
% 21.58/4.04 | | | | | | 0) | (all_113_1 = 0 & apart_point_and_line(all_17_0,
% 21.58/4.04 | | | | | | all_17_3) = 0) | ( ~ (all_113_2 = 0) &
% 21.58/4.04 | | | | | | distinct_lines(all_17_3, all_17_4) = all_113_2)
% 21.58/4.04 | | | | | |
% 21.58/4.04 | | | | | | BETA: splitting (41) gives:
% 21.58/4.04 | | | | | |
% 21.58/4.04 | | | | | | Case 1:
% 21.58/4.04 | | | | | | |
% 21.58/4.04 | | | | | | | (42) all_113_0 = 0 & apart_point_and_line(all_17_0, all_17_4) =
% 21.58/4.04 | | | | | | | 0
% 21.58/4.04 | | | | | | |
% 21.58/4.04 | | | | | | | ALPHA: (42) implies:
% 21.58/4.04 | | | | | | | (43) apart_point_and_line(all_17_0, all_17_4) = 0
% 21.58/4.04 | | | | | | |
% 21.58/4.04 | | | | | | | GROUND_INST: instantiating (7) with 0, all_24_0, all_17_4,
% 21.58/4.04 | | | | | | | all_17_0, simplifying with (28), (43) gives:
% 21.58/4.04 | | | | | | | (44) all_24_0 = 0
% 21.58/4.04 | | | | | | |
% 21.58/4.04 | | | | | | | REDUCE: (27), (44) imply:
% 21.58/4.04 | | | | | | | (45) $false
% 21.58/4.04 | | | | | | |
% 21.58/4.04 | | | | | | | CLOSE: (45) is inconsistent.
% 21.58/4.04 | | | | | | |
% 21.58/4.04 | | | | | | Case 2:
% 21.58/4.04 | | | | | | |
% 21.58/4.05 | | | | | | | (46) (all_113_1 = 0 & apart_point_and_line(all_17_0, all_17_3)
% 21.58/4.05 | | | | | | | = 0) | ( ~ (all_113_2 = 0) & distinct_lines(all_17_3,
% 21.58/4.05 | | | | | | | all_17_4) = all_113_2)
% 21.58/4.05 | | | | | | |
% 21.58/4.05 | | | | | | | BETA: splitting (46) gives:
% 21.58/4.05 | | | | | | |
% 21.58/4.05 | | | | | | | Case 1:
% 21.58/4.05 | | | | | | | |
% 21.58/4.05 | | | | | | | | (47) all_113_1 = 0 & apart_point_and_line(all_17_0, all_17_3)
% 21.58/4.05 | | | | | | | | = 0
% 21.58/4.05 | | | | | | | |
% 21.58/4.05 | | | | | | | | ALPHA: (47) implies:
% 21.58/4.05 | | | | | | | | (48) apart_point_and_line(all_17_0, all_17_3) = 0
% 21.58/4.05 | | | | | | | |
% 21.58/4.05 | | | | | | | | GROUND_INST: instantiating (7) with 0, all_25_0, all_17_3,
% 21.58/4.05 | | | | | | | | all_17_0, simplifying with (37), (48) gives:
% 21.58/4.05 | | | | | | | | (49) all_25_0 = 0
% 21.58/4.05 | | | | | | | |
% 21.58/4.05 | | | | | | | | REDUCE: (36), (49) imply:
% 21.58/4.05 | | | | | | | | (50) $false
% 21.58/4.05 | | | | | | | |
% 21.58/4.05 | | | | | | | | CLOSE: (50) is inconsistent.
% 21.58/4.05 | | | | | | | |
% 21.58/4.05 | | | | | | | Case 2:
% 21.58/4.05 | | | | | | | |
% 21.58/4.05 | | | | | | | | (51) ~ (all_113_2 = 0) & distinct_lines(all_17_3, all_17_4)
% 21.58/4.05 | | | | | | | | = all_113_2
% 21.58/4.05 | | | | | | | |
% 21.58/4.05 | | | | | | | | ALPHA: (51) implies:
% 21.58/4.05 | | | | | | | | (52) ~ (all_113_2 = 0)
% 21.58/4.05 | | | | | | | | (53) distinct_lines(all_17_3, all_17_4) = all_113_2
% 21.58/4.05 | | | | | | | |
% 21.58/4.05 | | | | | | | | BETA: splitting (31) gives:
% 21.58/4.05 | | | | | | | |
% 21.58/4.05 | | | | | | | | Case 1:
% 21.58/4.05 | | | | | | | | |
% 21.58/4.05 | | | | | | | | | (54) all_17_2 = 0
% 21.58/4.05 | | | | | | | | |
% 21.58/4.05 | | | | | | | | | REDUCE: (9), (54) imply:
% 21.58/4.05 | | | | | | | | | (55) $false
% 21.58/4.05 | | | | | | | | |
% 21.58/4.05 | | | | | | | | | CLOSE: (55) is inconsistent.
% 21.58/4.05 | | | | | | | | |
% 21.58/4.05 | | | | | | | | Case 2:
% 21.58/4.05 | | | | | | | | |
% 21.58/4.05 | | | | | | | | |
% 21.58/4.05 | | | | | | | | | GROUND_INST: instantiating (5) with all_17_4, all_17_3,
% 21.58/4.05 | | | | | | | | | all_17_4, all_113_2, simplifying with (12), (13),
% 21.58/4.05 | | | | | | | | | (16), (53) gives:
% 21.58/4.05 | | | | | | | | | (56) all_113_2 = 0 | convergent_lines(all_17_4, all_17_4) =
% 21.58/4.05 | | | | | | | | | 0
% 21.58/4.05 | | | | | | | | |
% 21.58/4.05 | | | | | | | | | BETA: splitting (56) gives:
% 21.58/4.05 | | | | | | | | |
% 21.58/4.05 | | | | | | | | | Case 1:
% 21.58/4.05 | | | | | | | | | |
% 21.58/4.05 | | | | | | | | | | (57) convergent_lines(all_17_4, all_17_4) = 0
% 21.58/4.05 | | | | | | | | | |
% 21.58/4.05 | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_17_4, simplifying
% 21.58/4.05 | | | | | | | | | | with (12), (57) gives:
% 21.58/4.05 | | | | | | | | | | (58) $false
% 21.58/4.05 | | | | | | | | | |
% 21.58/4.05 | | | | | | | | | | CLOSE: (58) is inconsistent.
% 21.58/4.05 | | | | | | | | | |
% 21.58/4.05 | | | | | | | | | Case 2:
% 21.58/4.05 | | | | | | | | | |
% 21.58/4.05 | | | | | | | | | | (59) all_113_2 = 0
% 21.58/4.05 | | | | | | | | | |
% 21.58/4.05 | | | | | | | | | | REDUCE: (52), (59) imply:
% 21.58/4.05 | | | | | | | | | | (60) $false
% 21.58/4.05 | | | | | | | | | |
% 21.58/4.05 | | | | | | | | | | CLOSE: (60) is inconsistent.
% 21.58/4.05 | | | | | | | | | |
% 21.58/4.05 | | | | | | | | | End of split
% 21.58/4.05 | | | | | | | | |
% 21.58/4.05 | | | | | | | | End of split
% 21.58/4.05 | | | | | | | |
% 21.58/4.05 | | | | | | | End of split
% 21.58/4.05 | | | | | | |
% 21.58/4.05 | | | | | | End of split
% 21.58/4.05 | | | | | |
% 21.58/4.05 | | | | | End of split
% 21.58/4.05 | | | | |
% 21.58/4.05 | | | | Case 2:
% 21.58/4.05 | | | | |
% 21.58/4.05 | | | | | (61) ~ (all_25_1 = 0) & convergent_lines(all_17_4, all_17_3) =
% 21.58/4.05 | | | | | all_25_1
% 21.58/4.05 | | | | |
% 21.58/4.05 | | | | | ALPHA: (61) implies:
% 21.58/4.05 | | | | | (62) ~ (all_25_1 = 0)
% 21.58/4.05 | | | | | (63) convergent_lines(all_17_4, all_17_3) = all_25_1
% 21.58/4.05 | | | | |
% 21.58/4.05 | | | | | GROUND_INST: instantiating (6) with 0, all_25_1, all_17_3, all_17_4,
% 21.58/4.05 | | | | | simplifying with (16), (63) gives:
% 21.58/4.05 | | | | | (64) all_25_1 = 0
% 21.58/4.05 | | | | |
% 21.58/4.05 | | | | | REDUCE: (62), (64) imply:
% 21.58/4.05 | | | | | (65) $false
% 21.58/4.05 | | | | |
% 21.58/4.05 | | | | | CLOSE: (65) is inconsistent.
% 21.58/4.05 | | | | |
% 21.58/4.05 | | | | End of split
% 21.58/4.05 | | | |
% 21.58/4.05 | | | End of split
% 21.58/4.05 | | |
% 21.58/4.05 | | End of split
% 21.58/4.05 | |
% 21.58/4.05 | Case 2:
% 21.58/4.05 | |
% 21.58/4.05 | | (66) ~ (all_24_1 = 0) & convergent_lines(all_17_4, all_17_3) = all_24_1
% 21.58/4.05 | |
% 21.58/4.05 | | ALPHA: (66) implies:
% 21.58/4.05 | | (67) ~ (all_24_1 = 0)
% 21.58/4.05 | | (68) convergent_lines(all_17_4, all_17_3) = all_24_1
% 21.58/4.05 | |
% 21.58/4.05 | | GROUND_INST: instantiating (6) with 0, all_24_1, all_17_3, all_17_4,
% 21.58/4.05 | | simplifying with (16), (68) gives:
% 21.58/4.05 | | (69) all_24_1 = 0
% 21.58/4.05 | |
% 21.58/4.05 | | REDUCE: (67), (69) imply:
% 21.58/4.05 | | (70) $false
% 21.58/4.05 | |
% 21.58/4.05 | | CLOSE: (70) is inconsistent.
% 21.58/4.05 | |
% 21.58/4.05 | End of split
% 21.58/4.05 |
% 21.58/4.05 End of proof
% 21.58/4.05 % SZS output end Proof for theBenchmark
% 21.58/4.05
% 21.58/4.05 3429ms
%------------------------------------------------------------------------------