TSTP Solution File: GEO225+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO225+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : 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 23:22:33 EDT 2023
% Result : Theorem 10.69s 2.19s
% Output : Proof 13.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO225+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 22:25:03 EDT 2023
% 0.12/0.33 % 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.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 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 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 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 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 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
% 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
% 2.88/1.15 Prover 1: Preprocessing ...
% 2.88/1.15 Prover 4: Preprocessing ...
% 3.48/1.19 Prover 0: Preprocessing ...
% 3.48/1.19 Prover 3: Preprocessing ...
% 3.48/1.19 Prover 6: Preprocessing ...
% 3.48/1.19 Prover 2: Preprocessing ...
% 3.48/1.19 Prover 5: Preprocessing ...
% 6.04/1.59 Prover 5: Proving ...
% 6.04/1.60 Prover 2: Proving ...
% 6.77/1.65 Prover 3: Constructing countermodel ...
% 6.77/1.67 Prover 1: Constructing countermodel ...
% 6.77/1.68 Prover 6: Proving ...
% 7.22/1.74 Prover 3: gave up
% 7.22/1.74 Prover 1: gave up
% 7.22/1.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.22/1.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.97/1.83 Prover 7: Preprocessing ...
% 8.23/1.85 Prover 8: Preprocessing ...
% 8.23/1.91 Prover 7: Warning: ignoring some quantifiers
% 8.23/1.93 Prover 7: Constructing countermodel ...
% 8.96/1.98 Prover 0: Proving ...
% 9.42/2.00 Prover 4: Constructing countermodel ...
% 9.42/2.03 Prover 8: Warning: ignoring some quantifiers
% 9.90/2.08 Prover 8: Constructing countermodel ...
% 10.69/2.19 Prover 0: proved (1571ms)
% 10.69/2.19
% 10.69/2.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.69/2.19
% 10.69/2.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.69/2.19 Prover 2: stopped
% 10.69/2.19 Prover 5: stopped
% 10.69/2.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.69/2.19 Prover 6: stopped
% 10.97/2.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.97/2.21 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 10.97/2.21 Prover 8: gave up
% 10.97/2.22 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 10.97/2.22 Prover 10: Preprocessing ...
% 10.97/2.23 Prover 11: Preprocessing ...
% 11.22/2.25 Prover 13: Preprocessing ...
% 11.22/2.25 Prover 19: Preprocessing ...
% 11.22/2.26 Prover 10: Warning: ignoring some quantifiers
% 11.22/2.26 Prover 16: Preprocessing ...
% 11.22/2.28 Prover 10: Constructing countermodel ...
% 12.00/2.35 Prover 13: Warning: ignoring some quantifiers
% 12.00/2.35 Prover 16: Warning: ignoring some quantifiers
% 12.00/2.36 Prover 13: Constructing countermodel ...
% 12.00/2.37 Prover 16: Constructing countermodel ...
% 12.43/2.40 Prover 7: gave up
% 12.43/2.42 Prover 10: gave up
% 12.43/2.42 Prover 19: Warning: ignoring some quantifiers
% 12.43/2.43 Prover 19: Constructing countermodel ...
% 12.43/2.43 Prover 4: Found proof (size 46)
% 12.43/2.43 Prover 4: proved (1807ms)
% 12.43/2.43 Prover 16: stopped
% 12.43/2.43 Prover 13: stopped
% 12.43/2.43 Prover 19: stopped
% 13.18/2.55 Prover 11: Constructing countermodel ...
% 13.18/2.56 Prover 11: stopped
% 13.18/2.56
% 13.18/2.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.18/2.56
% 13.18/2.57 % SZS output start Proof for theBenchmark
% 13.18/2.58 Assumptions after simplification:
% 13.18/2.58 ---------------------------------
% 13.18/2.58
% 13.18/2.58 (a4)
% 13.18/2.60 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 13.18/2.60 (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 13.18/2.60 apart_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int]
% 13.18/2.60 : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 13.18/2.60 incident_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 13.18/2.60 (incident_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int]
% 13.18/2.60 : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0: $i] : ! [v1:
% 13.18/2.60 $i] : ( ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 13.18/2.60 [v2: int] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 13.18/2.60
% 13.18/2.60 (ci1)
% 13.18/2.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 13.18/2.61 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 13.18/2.61 (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4
% 13.18/2.61 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 13.18/2.61 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 13.18/2.61 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 &
% 13.18/2.61 apart_point_and_line(v0, v2) = v3 & $i(v2)))
% 13.18/2.61
% 13.18/2.61 (ci2)
% 13.18/2.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 13.18/2.61 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 13.18/2.61 (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4
% 13.18/2.61 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 13.18/2.61 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 13.18/2.61 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 &
% 13.18/2.61 apart_point_and_line(v1, v2) = v3 & $i(v2)))
% 13.18/2.61
% 13.18/2.61 (con)
% 13.18/2.61 ? [v0: $i] : ? [v1: $i] : (point(v1) = 0 & point(v0) = 0 &
% 13.18/2.61 distinct_points(v0, v1) = 0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: int] :
% 13.18/2.61 (v3 = 0 | ~ (line(v2) = v3) | ~ $i(v2)) & ! [v2: $i] : ( ~
% 13.18/2.61 (incident_point_and_line(v1, v2) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3
% 13.18/2.61 = 0) & incident_point_and_line(v0, v2) = v3)) & ! [v2: $i] : ( ~
% 13.18/2.61 (incident_point_and_line(v0, v2) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3
% 13.18/2.61 = 0) & incident_point_and_line(v1, v2) = v3)))
% 13.18/2.61
% 13.18/2.61 (con1)
% 13.18/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 13.18/2.62 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6:
% 13.18/2.62 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 &
% 13.18/2.62 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) |
% 13.18/2.62 v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) =
% 13.18/2.62 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] :
% 13.18/2.62 ? [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 &
% 13.18/2.62 line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 =
% 13.18/2.62 0)))
% 13.18/2.62
% 13.18/2.62 (cu1)
% 13.18/2.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 13.18/2.63 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 13.18/2.63 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 13.18/2.63 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 13.18/2.63 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0,
% 13.18/2.63 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 13.18/2.63 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 13.18/2.63 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) =
% 13.18/2.63 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3)
% 13.18/2.63 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 13.18/2.63 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 &
% 13.18/2.63 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6
% 13.18/2.63 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 13.18/2.63 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 13.18/2.63 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4)
% 13.18/2.63 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 13.18/2.63 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 13.18/2.63 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 13.18/2.63 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 =
% 13.18/2.63 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 13.18/2.63 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) =
% 13.18/2.63 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 13.18/2.63 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9:
% 13.18/2.63 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) =
% 13.18/2.63 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7
% 13.18/2.63 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 13.18/2.63 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 13.18/2.63 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4)
% 13.18/2.63 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 13.18/2.63 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 13.18/2.63 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 &
% 13.18/2.63 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0:
% 13.18/2.63 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 13.18/2.63 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~
% 13.18/2.63 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 13.18/2.63 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 13.66/2.63 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1,
% 13.66/2.63 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 13.66/2.63 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 13.66/2.63 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3)
% 13.66/2.63 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 13.66/2.63 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 13.66/2.63 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 13.66/2.63 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 13.66/2.63
% 13.66/2.63 (function-axioms)
% 13.66/2.64 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.66/2.64 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~
% 13.66/2.64 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.66/2.64 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.66/2.64 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2)
% 13.66/2.64 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.66/2.64 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~
% 13.66/2.64 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.66/2.64 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.66/2.64 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0:
% 13.66/2.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.66/2.64 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 13.66/2.64 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.66/2.64 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 13.66/2.64 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 13.66/2.64 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 13.66/2.64 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 13.66/2.64 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 13.66/2.64 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 13.66/2.64 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 13.66/2.64 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 13.66/2.64 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 13.66/2.64 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.66/2.64 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.66/2.64 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 13.66/2.64 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.66/2.64 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 13.66/2.64 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.66/2.64 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.66/2.64 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 13.66/2.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.66/2.64 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 13.66/2.64 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.66/2.64 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0:
% 13.66/2.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 13.66/2.64 ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 13.66/2.64
% 13.66/2.64 Further assumptions not needed in the proof:
% 13.66/2.64 --------------------------------------------
% 13.66/2.64 a3, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ax6, ceq1, ceq2, ceq3,
% 13.66/2.64 ci3, ci4, coipo1, cotno1, couo1, cp1, cp2, cup1, int1, oac1, occu1, ooc1, ooc2,
% 13.66/2.64 orth1, ouo1, p1, par1
% 13.66/2.64
% 13.66/2.64 Those formulas are unsatisfiable:
% 13.66/2.64 ---------------------------------
% 13.66/2.64
% 13.66/2.64 Begin of proof
% 13.66/2.64 |
% 13.66/2.64 | ALPHA: (ci1) implies:
% 13.66/2.64 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~
% 13.66/2.64 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 13.66/2.64 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 &
% 13.66/2.64 | $i(v2)))
% 13.66/2.64 |
% 13.66/2.64 | ALPHA: (ci2) implies:
% 13.66/2.64 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~
% 13.66/2.64 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 13.66/2.64 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 &
% 13.66/2.64 | $i(v2)))
% 13.66/2.64 |
% 13.66/2.64 | ALPHA: (cu1) implies:
% 13.66/2.65 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 13.66/2.65 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5)
% 13.66/2.65 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 13.66/2.65 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ?
% 13.66/2.65 | [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 13.66/2.65 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 13.66/2.65 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0
% 13.66/2.65 | | v8 = 0)))
% 13.66/2.65 |
% 13.66/2.65 | ALPHA: (con1) implies:
% 13.66/2.65 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~
% 13.66/2.65 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ?
% 13.66/2.65 | [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 &
% 13.66/2.65 | line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0)
% 13.66/2.65 | | v5 = 0)))
% 13.66/2.65 |
% 13.66/2.65 | ALPHA: (a4) implies:
% 13.66/2.65 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 13.66/2.65 | (apart_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 13.66/2.65 | incident_point_and_line(v0, v1) = 0)
% 13.66/2.65 |
% 13.66/2.65 | ALPHA: (function-axioms) implies:
% 13.66/2.65 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.66/2.65 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 13.66/2.65 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.66/2.65 | ! [v3: $i] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~
% 13.66/2.65 | (incident_point_and_line(v3, v2) = v0))
% 13.66/2.65 |
% 13.66/2.65 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1 gives:
% 13.66/2.65 | (8) point(all_38_0) = 0 & point(all_38_1) = 0 & distinct_points(all_38_1,
% 13.66/2.65 | all_38_0) = 0 & $i(all_38_0) & $i(all_38_1) & ! [v0: $i] : ! [v1:
% 13.66/2.65 | int] : (v1 = 0 | ~ (line(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( ~
% 13.66/2.65 | (incident_point_and_line(all_38_0, v0) = 0) | ~ $i(v0) | ? [v1:
% 13.66/2.65 | int] : ( ~ (v1 = 0) & incident_point_and_line(all_38_1, v0) = v1))
% 13.66/2.65 | & ! [v0: $i] : ( ~ (incident_point_and_line(all_38_1, v0) = 0) | ~
% 13.66/2.65 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 13.66/2.65 | incident_point_and_line(all_38_0, v0) = v1))
% 13.66/2.65 |
% 13.66/2.65 | ALPHA: (8) implies:
% 13.66/2.65 | (9) $i(all_38_1)
% 13.66/2.65 | (10) $i(all_38_0)
% 13.66/2.65 | (11) distinct_points(all_38_1, all_38_0) = 0
% 13.66/2.65 | (12) ! [v0: $i] : ( ~ (incident_point_and_line(all_38_0, v0) = 0) | ~
% 13.66/2.65 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 13.66/2.65 | incident_point_and_line(all_38_1, v0) = v1))
% 13.66/2.65 |
% 13.66/2.66 | GROUND_INST: instantiating (4) with all_38_1, all_38_0, simplifying with (9),
% 13.66/2.66 | (10), (11) gives:
% 13.66/2.66 | (13) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 13.66/2.66 | (point(all_38_0) = v1 & point(all_38_1) = v0 & line(v2) = v3 &
% 13.66/2.66 | line_connecting(all_38_1, all_38_0) = v2 & $i(v2) & ( ~ (v1 = 0) |
% 13.66/2.66 | ~ (v0 = 0) | v3 = 0))
% 13.66/2.66 |
% 13.66/2.66 | GROUND_INST: instantiating (2) with all_38_1, all_38_0, simplifying with (9),
% 13.66/2.66 | (10), (11) gives:
% 13.66/2.66 | (14) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_1,
% 13.66/2.66 | all_38_0) = v0 & apart_point_and_line(all_38_0, v0) = v1 & $i(v0))
% 13.66/2.66 |
% 13.66/2.66 | GROUND_INST: instantiating (1) with all_38_1, all_38_0, simplifying with (9),
% 13.66/2.66 | (10), (11) gives:
% 13.66/2.66 | (15) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_1,
% 13.66/2.66 | all_38_0) = v0 & apart_point_and_line(all_38_1, v0) = v1 & $i(v0))
% 13.66/2.66 |
% 13.66/2.66 | DELTA: instantiating (14) with fresh symbols all_48_0, all_48_1 gives:
% 13.66/2.66 | (16) ~ (all_48_0 = 0) & line_connecting(all_38_1, all_38_0) = all_48_1 &
% 13.66/2.66 | apart_point_and_line(all_38_0, all_48_1) = all_48_0 & $i(all_48_1)
% 13.66/2.66 |
% 13.66/2.66 | ALPHA: (16) implies:
% 13.66/2.66 | (17) ~ (all_48_0 = 0)
% 13.66/2.66 | (18) apart_point_and_line(all_38_0, all_48_1) = all_48_0
% 13.66/2.66 | (19) line_connecting(all_38_1, all_38_0) = all_48_1
% 13.66/2.66 |
% 13.66/2.66 | DELTA: instantiating (15) with fresh symbols all_50_0, all_50_1 gives:
% 13.66/2.66 | (20) ~ (all_50_0 = 0) & line_connecting(all_38_1, all_38_0) = all_50_1 &
% 13.66/2.66 | apart_point_and_line(all_38_1, all_50_1) = all_50_0 & $i(all_50_1)
% 13.66/2.66 |
% 13.66/2.66 | ALPHA: (20) implies:
% 13.66/2.66 | (21) ~ (all_50_0 = 0)
% 13.66/2.66 | (22) $i(all_50_1)
% 13.66/2.66 | (23) apart_point_and_line(all_38_1, all_50_1) = all_50_0
% 13.66/2.66 | (24) line_connecting(all_38_1, all_38_0) = all_50_1
% 13.66/2.66 |
% 13.66/2.66 | DELTA: instantiating (13) with fresh symbols all_52_0, all_52_1, all_52_2,
% 13.66/2.66 | all_52_3 gives:
% 13.66/2.66 | (25) point(all_38_0) = all_52_2 & point(all_38_1) = all_52_3 &
% 13.66/2.66 | line(all_52_1) = all_52_0 & line_connecting(all_38_1, all_38_0) =
% 13.66/2.66 | all_52_1 & $i(all_52_1) & ( ~ (all_52_2 = 0) | ~ (all_52_3 = 0) |
% 13.66/2.66 | all_52_0 = 0)
% 13.66/2.66 |
% 13.66/2.66 | ALPHA: (25) implies:
% 13.66/2.66 | (26) line_connecting(all_38_1, all_38_0) = all_52_1
% 13.66/2.66 |
% 13.66/2.66 | GROUND_INST: instantiating (6) with all_50_1, all_52_1, all_38_0, all_38_1,
% 13.66/2.66 | simplifying with (24), (26) gives:
% 13.66/2.66 | (27) all_52_1 = all_50_1
% 13.66/2.66 |
% 13.66/2.66 | GROUND_INST: instantiating (6) with all_48_1, all_52_1, all_38_0, all_38_1,
% 13.66/2.66 | simplifying with (19), (26) gives:
% 13.66/2.66 | (28) all_52_1 = all_48_1
% 13.66/2.66 |
% 13.66/2.66 | COMBINE_EQS: (27), (28) imply:
% 13.66/2.66 | (29) all_50_1 = all_48_1
% 13.66/2.66 |
% 13.66/2.66 | REDUCE: (23), (29) imply:
% 13.66/2.66 | (30) apart_point_and_line(all_38_1, all_48_1) = all_50_0
% 13.66/2.66 |
% 13.66/2.66 | REDUCE: (22), (29) imply:
% 13.66/2.66 | (31) $i(all_48_1)
% 13.66/2.66 |
% 13.66/2.66 | GROUND_INST: instantiating (5) with all_38_1, all_48_1, all_50_0, simplifying
% 13.66/2.66 | with (9), (30), (31) gives:
% 13.66/2.67 | (32) all_50_0 = 0 | incident_point_and_line(all_38_1, all_48_1) = 0
% 13.66/2.67 |
% 13.66/2.67 | GROUND_INST: instantiating (3) with all_38_0, all_38_1, all_48_1, all_48_1,
% 13.66/2.67 | all_48_0, all_50_0, simplifying with (9), (10), (18), (30), (31)
% 13.66/2.67 | gives:
% 13.66/2.67 | (33) all_50_0 = 0 | all_48_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 13.66/2.67 | any] : ? [v3: any] : (apart_point_and_line(all_38_0, all_48_1) = v2
% 13.66/2.67 | & apart_point_and_line(all_38_1, all_48_1) = v3 &
% 13.66/2.67 | distinct_lines(all_48_1, all_48_1) = v1 & distinct_points(all_38_0,
% 13.66/2.67 | all_38_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 13.66/2.67 |
% 13.66/2.67 | GROUND_INST: instantiating (5) with all_38_0, all_48_1, all_48_0, simplifying
% 13.66/2.67 | with (10), (18), (31) gives:
% 13.66/2.67 | (34) all_48_0 = 0 | incident_point_and_line(all_38_0, all_48_1) = 0
% 13.66/2.67 |
% 13.66/2.67 | BETA: splitting (34) gives:
% 13.66/2.67 |
% 13.66/2.67 | Case 1:
% 13.66/2.67 | |
% 13.66/2.67 | | (35) incident_point_and_line(all_38_0, all_48_1) = 0
% 13.66/2.67 | |
% 13.66/2.67 | | BETA: splitting (32) gives:
% 13.66/2.67 | |
% 13.66/2.67 | | Case 1:
% 13.66/2.67 | | |
% 13.66/2.67 | | | (36) incident_point_and_line(all_38_1, all_48_1) = 0
% 13.66/2.67 | | |
% 13.66/2.67 | | | BETA: splitting (33) gives:
% 13.66/2.67 | | |
% 13.66/2.67 | | | Case 1:
% 13.66/2.67 | | | |
% 13.66/2.67 | | | | (37) all_50_0 = 0
% 13.66/2.67 | | | |
% 13.66/2.67 | | | | REDUCE: (21), (37) imply:
% 13.66/2.67 | | | | (38) $false
% 13.66/2.67 | | | |
% 13.66/2.67 | | | | CLOSE: (38) is inconsistent.
% 13.66/2.67 | | | |
% 13.66/2.67 | | | Case 2:
% 13.66/2.67 | | | |
% 13.66/2.67 | | | | (39) all_48_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 13.66/2.67 | | | | [v3: any] : (apart_point_and_line(all_38_0, all_48_1) = v2 &
% 13.66/2.67 | | | | apart_point_and_line(all_38_1, all_48_1) = v3 &
% 13.66/2.67 | | | | distinct_lines(all_48_1, all_48_1) = v1 &
% 13.66/2.67 | | | | distinct_points(all_38_0, all_38_1) = v0 & ( ~ (v1 = 0) | ~
% 13.66/2.67 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 13.66/2.67 | | | |
% 13.66/2.67 | | | | BETA: splitting (39) gives:
% 13.66/2.67 | | | |
% 13.66/2.67 | | | | Case 1:
% 13.66/2.67 | | | | |
% 13.66/2.67 | | | | | (40) all_48_0 = 0
% 13.66/2.67 | | | | |
% 13.66/2.67 | | | | | REDUCE: (17), (40) imply:
% 13.66/2.67 | | | | | (41) $false
% 13.66/2.67 | | | | |
% 13.66/2.67 | | | | | CLOSE: (41) is inconsistent.
% 13.66/2.67 | | | | |
% 13.66/2.67 | | | | Case 2:
% 13.66/2.67 | | | | |
% 13.66/2.67 | | | | |
% 13.66/2.67 | | | | | GROUND_INST: instantiating (12) with all_48_1, simplifying with (31),
% 13.66/2.67 | | | | | (35) gives:
% 13.66/2.67 | | | | | (42) ? [v0: int] : ( ~ (v0 = 0) &
% 13.66/2.67 | | | | | incident_point_and_line(all_38_1, all_48_1) = v0)
% 13.66/2.67 | | | | |
% 13.66/2.67 | | | | | DELTA: instantiating (42) with fresh symbol all_133_0 gives:
% 13.66/2.67 | | | | | (43) ~ (all_133_0 = 0) & incident_point_and_line(all_38_1,
% 13.66/2.67 | | | | | all_48_1) = all_133_0
% 13.66/2.67 | | | | |
% 13.66/2.67 | | | | | ALPHA: (43) implies:
% 13.66/2.67 | | | | | (44) ~ (all_133_0 = 0)
% 13.66/2.67 | | | | | (45) incident_point_and_line(all_38_1, all_48_1) = all_133_0
% 13.66/2.67 | | | | |
% 13.66/2.67 | | | | | GROUND_INST: instantiating (7) with 0, all_133_0, all_48_1, all_38_1,
% 13.66/2.67 | | | | | simplifying with (36), (45) gives:
% 13.66/2.67 | | | | | (46) all_133_0 = 0
% 13.66/2.67 | | | | |
% 13.66/2.67 | | | | | REDUCE: (44), (46) imply:
% 13.66/2.67 | | | | | (47) $false
% 13.66/2.67 | | | | |
% 13.66/2.67 | | | | | CLOSE: (47) is inconsistent.
% 13.66/2.67 | | | | |
% 13.66/2.67 | | | | End of split
% 13.66/2.67 | | | |
% 13.66/2.67 | | | End of split
% 13.66/2.67 | | |
% 13.66/2.67 | | Case 2:
% 13.66/2.67 | | |
% 13.66/2.67 | | | (48) all_50_0 = 0
% 13.66/2.68 | | |
% 13.66/2.68 | | | REDUCE: (21), (48) imply:
% 13.66/2.68 | | | (49) $false
% 13.66/2.68 | | |
% 13.66/2.68 | | | CLOSE: (49) is inconsistent.
% 13.66/2.68 | | |
% 13.66/2.68 | | End of split
% 13.66/2.68 | |
% 13.66/2.68 | Case 2:
% 13.66/2.68 | |
% 13.66/2.68 | | (50) all_48_0 = 0
% 13.66/2.68 | |
% 13.66/2.68 | | REDUCE: (17), (50) imply:
% 13.66/2.68 | | (51) $false
% 13.66/2.68 | |
% 13.66/2.68 | | CLOSE: (51) is inconsistent.
% 13.66/2.68 | |
% 13.66/2.68 | End of split
% 13.66/2.68 |
% 13.66/2.68 End of proof
% 13.66/2.68 % SZS output end Proof for theBenchmark
% 13.66/2.68
% 13.66/2.68 2080ms
%------------------------------------------------------------------------------