TSTP Solution File: GEO221+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO221+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 : n029.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 23:22:29 EDT 2023
% Result : Theorem 9.28s 1.98s
% Output : Proof 13.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO221+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n029.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 19:22:12 EDT 2023
% 0.18/0.33 % CPUTime :
% 0.59/0.59 ________ _____
% 0.59/0.59 ___ __ \_________(_)________________________________
% 0.59/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.59/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.59/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.59/0.59
% 0.59/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.59/0.59 (2023-06-19)
% 0.59/0.59
% 0.59/0.59 (c) Philipp Rümmer, 2009-2023
% 0.59/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.59/0.59 Amanda Stjerna.
% 0.59/0.59 Free software under BSD-3-Clause.
% 0.59/0.59
% 0.59/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.59/0.59
% 0.59/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.63/0.60 Running up to 7 provers in parallel.
% 0.63/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.63/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.63/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.63/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.63/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.63/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.63/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.63/1.05 Prover 4: Preprocessing ...
% 2.63/1.06 Prover 1: Preprocessing ...
% 3.16/1.09 Prover 5: Preprocessing ...
% 3.16/1.09 Prover 3: Preprocessing ...
% 3.16/1.09 Prover 6: Preprocessing ...
% 3.16/1.09 Prover 2: Preprocessing ...
% 3.16/1.09 Prover 0: Preprocessing ...
% 4.95/1.38 Prover 5: Proving ...
% 4.95/1.39 Prover 2: Proving ...
% 5.45/1.45 Prover 3: Constructing countermodel ...
% 5.45/1.45 Prover 1: Constructing countermodel ...
% 5.45/1.45 Prover 6: Constructing countermodel ...
% 6.44/1.57 Prover 6: gave up
% 6.44/1.57 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.44/1.57 Prover 3: gave up
% 6.44/1.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.44/1.63 Prover 8: Preprocessing ...
% 6.44/1.63 Prover 4: Constructing countermodel ...
% 7.12/1.63 Prover 1: gave up
% 7.12/1.63 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 7.12/1.63 Prover 7: Preprocessing ...
% 7.12/1.65 Prover 0: Proving ...
% 7.12/1.67 Prover 7: Warning: ignoring some quantifiers
% 7.12/1.67 Prover 9: Preprocessing ...
% 7.12/1.69 Prover 7: Constructing countermodel ...
% 7.69/1.75 Prover 8: Warning: ignoring some quantifiers
% 7.69/1.76 Prover 8: Constructing countermodel ...
% 8.58/1.84 Prover 8: gave up
% 8.58/1.85 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.58/1.88 Prover 7: gave up
% 8.58/1.89 Prover 10: Preprocessing ...
% 8.58/1.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.28/1.92 Prover 11: Preprocessing ...
% 9.28/1.93 Prover 9: Constructing countermodel ...
% 9.28/1.94 Prover 10: Warning: ignoring some quantifiers
% 9.28/1.95 Prover 10: Constructing countermodel ...
% 9.28/1.98 Prover 0: proved (1368ms)
% 9.28/1.98
% 9.28/1.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.28/1.98
% 9.82/2.00 Prover 9: stopped
% 9.82/2.00 Prover 2: stopped
% 9.82/2.01 Prover 5: stopped
% 9.82/2.01 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.82/2.01 Prover 10: gave up
% 9.82/2.01 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.82/2.01 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 9.82/2.02 Prover 16: Preprocessing ...
% 9.82/2.03 Prover 13: Preprocessing ...
% 9.82/2.05 Prover 16: Warning: ignoring some quantifiers
% 9.82/2.05 Prover 19: Preprocessing ...
% 9.82/2.05 Prover 16: Constructing countermodel ...
% 9.82/2.07 Prover 13: Warning: ignoring some quantifiers
% 10.39/2.08 Prover 13: Constructing countermodel ...
% 10.75/2.12 Prover 11: Constructing countermodel ...
% 10.75/2.12 Prover 19: Warning: ignoring some quantifiers
% 10.75/2.14 Prover 19: Constructing countermodel ...
% 10.75/2.15 Prover 13: gave up
% 10.75/2.18 Prover 19: gave up
% 11.53/2.30 Prover 16: gave up
% 12.45/2.45 Prover 4: Found proof (size 101)
% 12.45/2.45 Prover 4: proved (1843ms)
% 12.45/2.45 Prover 11: stopped
% 12.45/2.45
% 12.45/2.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.45/2.45
% 12.45/2.47 % SZS output start Proof for theBenchmark
% 12.45/2.48 Assumptions after simplification:
% 12.45/2.48 ---------------------------------
% 12.45/2.48
% 12.45/2.48 (con)
% 13.04/2.50 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5:
% 13.04/2.50 $i] : ( ~ (v4 = 0) & orthogonal_through_point(v2, v1) = v5 &
% 13.04/2.50 orthogonal_through_point(v2, v0) = v3 & apart_point_and_line(v1, v3) = v4 &
% 13.04/2.50 distinct_lines(v3, v5) = 0 & $i(v5) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.04/2.50
% 13.04/2.50 (cu1)
% 13.17/2.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 13.17/2.52 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 13.17/2.52 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 13.17/2.52 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 13.17/2.52 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0,
% 13.17/2.52 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 13.17/2.52 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 13.17/2.52 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) =
% 13.17/2.52 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3)
% 13.17/2.52 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 13.17/2.52 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 &
% 13.17/2.52 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6
% 13.17/2.52 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 13.17/2.52 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 13.17/2.52 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4)
% 13.17/2.52 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 13.17/2.52 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 13.17/2.52 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 13.17/2.52 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 =
% 13.17/2.52 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 13.17/2.52 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) =
% 13.17/2.52 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 13.17/2.52 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9:
% 13.17/2.52 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) =
% 13.17/2.52 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7
% 13.17/2.52 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 13.17/2.52 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 13.17/2.52 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4)
% 13.17/2.52 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 13.17/2.52 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 13.17/2.52 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 &
% 13.17/2.52 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0:
% 13.17/2.52 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 13.17/2.52 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~
% 13.17/2.52 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 13.17/2.52 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 13.17/2.52 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1,
% 13.17/2.53 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 13.17/2.53 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 13.17/2.53 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3)
% 13.17/2.53 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 13.17/2.53 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 13.17/2.53 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 13.17/2.53 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 13.17/2.53
% 13.17/2.53 (ooc1)
% 13.17/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (orthogonal_through_point(v1,
% 13.17/2.53 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 13.17/2.53 unorthogonal_lines(v2, v1) = v3))
% 13.17/2.53
% 13.17/2.53 (ooc2)
% 13.17/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (orthogonal_through_point(v1,
% 13.17/2.53 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 13.17/2.53 apart_point_and_line(v0, v2) = v3))
% 13.17/2.53
% 13.17/2.53 (ouo1)
% 13.17/2.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 13.17/2.54 int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~
% 13.17/2.54 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ~
% 13.17/2.54 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 13.17/2.54 (unorthogonal_lines(v1, v3) = v7 & apart_point_and_line(v0, v1) = v6 & (v7 =
% 13.17/2.54 0 | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 13.17/2.54 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3)
% 13.17/2.54 = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) |
% 13.17/2.54 ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 13.17/2.54 (unorthogonal_lines(v1, v3) = v8 & apart_point_and_line(v0, v2) = v7 &
% 13.17/2.54 distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0:
% 13.17/2.54 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 13.17/2.54 : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~
% 13.17/2.54 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 13.17/2.54 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 13.17/2.54 (unorthogonal_lines(v2, v3) = v8 & apart_point_and_line(v0, v1) = v7 &
% 13.17/2.54 distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0:
% 13.17/2.54 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 13.17/2.54 : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~
% 13.17/2.54 (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ~
% 13.17/2.54 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 13.17/2.54 (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 =
% 13.17/2.54 0 | v6 = 0)))
% 13.17/2.54
% 13.17/2.54 (function-axioms)
% 13.17/2.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.17/2.54 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 13.17/2.54 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 13.17/2.54 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 13.17/2.54 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 13.17/2.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 13.17/2.54 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 13.17/2.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 13.17/2.54 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 13.17/2.54 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 13.17/2.54 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.17/2.54 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.17/2.54 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 13.17/2.54 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.17/2.54 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 13.17/2.54 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.17/2.54 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.17/2.54 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 13.17/2.54 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.17/2.54 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 13.17/2.54 v0))
% 13.17/2.54
% 13.17/2.54 Further assumptions not needed in the proof:
% 13.17/2.54 --------------------------------------------
% 13.17/2.54 apart1, apart2, apart3, apart4, apart5, ax6, ceq1, ceq2, ceq3, ci1, ci2, ci3,
% 13.17/2.54 ci4, cp1, cp2, cup1, oac1, occu1
% 13.17/2.54
% 13.17/2.54 Those formulas are unsatisfiable:
% 13.17/2.54 ---------------------------------
% 13.17/2.54
% 13.17/2.54 Begin of proof
% 13.17/2.54 |
% 13.17/2.54 | ALPHA: (cu1) implies:
% 13.17/2.55 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 13.17/2.55 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5)
% 13.17/2.55 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 13.17/2.55 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ?
% 13.17/2.55 | [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 13.17/2.55 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 13.17/2.55 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0
% 13.17/2.55 | | v8 = 0)))
% 13.17/2.55 |
% 13.17/2.55 | ALPHA: (ouo1) implies:
% 13.17/2.55 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 13.17/2.55 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) |
% 13.17/2.55 | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) =
% 13.17/2.55 | 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] :
% 13.17/2.55 | ? [v7: any] : (unorthogonal_lines(v2, v3) = v7 &
% 13.17/2.55 | apart_point_and_line(v0, v2) = v6 & (v7 = 0 | v6 = 0)))
% 13.17/2.55 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 13.17/2.55 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) |
% 13.17/2.55 | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 13.17/2.55 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 13.17/2.55 | (unorthogonal_lines(v2, v3) = v8 & apart_point_and_line(v0, v1) = v7
% 13.17/2.55 | & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 13.17/2.55 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 13.17/2.55 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) |
% 13.17/2.55 | ~ (apart_point_and_line(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 13.17/2.55 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 13.17/2.55 | (unorthogonal_lines(v1, v3) = v8 & apart_point_and_line(v0, v2) = v7
% 13.17/2.55 | & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 13.17/2.55 |
% 13.17/2.55 | ALPHA: (function-axioms) implies:
% 13.17/2.55 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.17/2.55 | ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~
% 13.17/2.55 | (distinct_lines(v3, v2) = v0))
% 13.17/2.55 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.17/2.55 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 13.17/2.55 | (apart_point_and_line(v3, v2) = v0))
% 13.17/2.55 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.17/2.55 | ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~
% 13.17/2.55 | (unorthogonal_lines(v3, v2) = v0))
% 13.17/2.55 |
% 13.17/2.55 | DELTA: instantiating (con) with fresh symbols all_25_0, all_25_1, all_25_2,
% 13.17/2.55 | all_25_3, all_25_4, all_25_5 gives:
% 13.17/2.55 | (8) ~ (all_25_1 = 0) & orthogonal_through_point(all_25_3, all_25_4) =
% 13.17/2.55 | all_25_0 & orthogonal_through_point(all_25_3, all_25_5) = all_25_2 &
% 13.17/2.55 | apart_point_and_line(all_25_4, all_25_2) = all_25_1 &
% 13.17/2.55 | distinct_lines(all_25_2, all_25_0) = 0 & $i(all_25_0) & $i(all_25_2) &
% 13.17/2.55 | $i(all_25_3) & $i(all_25_4) & $i(all_25_5)
% 13.17/2.55 |
% 13.17/2.55 | ALPHA: (8) implies:
% 13.17/2.55 | (9) ~ (all_25_1 = 0)
% 13.17/2.55 | (10) $i(all_25_5)
% 13.17/2.55 | (11) $i(all_25_4)
% 13.17/2.56 | (12) $i(all_25_3)
% 13.17/2.56 | (13) $i(all_25_2)
% 13.17/2.56 | (14) $i(all_25_0)
% 13.17/2.56 | (15) distinct_lines(all_25_2, all_25_0) = 0
% 13.17/2.56 | (16) apart_point_and_line(all_25_4, all_25_2) = all_25_1
% 13.17/2.56 | (17) orthogonal_through_point(all_25_3, all_25_5) = all_25_2
% 13.17/2.56 | (18) orthogonal_through_point(all_25_3, all_25_4) = all_25_0
% 13.17/2.56 |
% 13.17/2.56 | GROUND_INST: instantiating (ooc1) with all_25_5, all_25_3, all_25_2,
% 13.17/2.56 | simplifying with (10), (12), (17) gives:
% 13.17/2.56 | (19) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_25_2, all_25_3) =
% 13.17/2.56 | v0)
% 13.17/2.56 |
% 13.17/2.56 | GROUND_INST: instantiating (ooc2) with all_25_5, all_25_3, all_25_2,
% 13.17/2.56 | simplifying with (10), (12), (17) gives:
% 13.17/2.56 | (20) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_25_5, all_25_2)
% 13.17/2.56 | = v0)
% 13.17/2.56 |
% 13.17/2.56 | GROUND_INST: instantiating (ooc1) with all_25_4, all_25_3, all_25_0,
% 13.17/2.56 | simplifying with (11), (12), (18) gives:
% 13.17/2.56 | (21) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_25_0, all_25_3) =
% 13.17/2.56 | v0)
% 13.17/2.56 |
% 13.17/2.56 | GROUND_INST: instantiating (ooc2) with all_25_4, all_25_3, all_25_0,
% 13.17/2.56 | simplifying with (11), (12), (18) gives:
% 13.17/2.56 | (22) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_25_4, all_25_0)
% 13.17/2.56 | = v0)
% 13.17/2.56 |
% 13.17/2.56 | DELTA: instantiating (22) with fresh symbol all_32_0 gives:
% 13.17/2.56 | (23) ~ (all_32_0 = 0) & apart_point_and_line(all_25_4, all_25_0) =
% 13.17/2.56 | all_32_0
% 13.17/2.56 |
% 13.17/2.56 | ALPHA: (23) implies:
% 13.17/2.56 | (24) ~ (all_32_0 = 0)
% 13.17/2.56 | (25) apart_point_and_line(all_25_4, all_25_0) = all_32_0
% 13.17/2.56 |
% 13.17/2.56 | DELTA: instantiating (21) with fresh symbol all_34_0 gives:
% 13.17/2.56 | (26) ~ (all_34_0 = 0) & unorthogonal_lines(all_25_0, all_25_3) = all_34_0
% 13.17/2.56 |
% 13.17/2.56 | ALPHA: (26) implies:
% 13.17/2.56 | (27) ~ (all_34_0 = 0)
% 13.17/2.56 | (28) unorthogonal_lines(all_25_0, all_25_3) = all_34_0
% 13.17/2.56 |
% 13.17/2.56 | DELTA: instantiating (20) with fresh symbol all_36_0 gives:
% 13.17/2.56 | (29) ~ (all_36_0 = 0) & apart_point_and_line(all_25_5, all_25_2) =
% 13.17/2.56 | all_36_0
% 13.17/2.56 |
% 13.17/2.56 | ALPHA: (29) implies:
% 13.17/2.56 | (30) ~ (all_36_0 = 0)
% 13.17/2.56 | (31) apart_point_and_line(all_25_5, all_25_2) = all_36_0
% 13.17/2.56 |
% 13.17/2.56 | DELTA: instantiating (19) with fresh symbol all_38_0 gives:
% 13.17/2.56 | (32) ~ (all_38_0 = 0) & unorthogonal_lines(all_25_2, all_25_3) = all_38_0
% 13.17/2.56 |
% 13.17/2.56 | ALPHA: (32) implies:
% 13.17/2.56 | (33) ~ (all_38_0 = 0)
% 13.17/2.56 | (34) unorthogonal_lines(all_25_2, all_25_3) = all_38_0
% 13.17/2.56 |
% 13.17/2.56 | GROUND_INST: instantiating (1) with all_25_4, all_25_5, all_25_2, all_25_2,
% 13.17/2.56 | all_25_1, all_36_0, simplifying with (10), (11), (13), (16), (31)
% 13.17/2.56 | gives:
% 13.17/2.56 | (35) all_36_0 = 0 | all_25_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 13.17/2.56 | any] : ? [v3: any] : (apart_point_and_line(all_25_4, all_25_2) = v2
% 13.17/2.56 | & apart_point_and_line(all_25_5, all_25_2) = v3 &
% 13.17/2.56 | distinct_lines(all_25_2, all_25_2) = v1 & distinct_points(all_25_4,
% 13.17/2.56 | all_25_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 13.17/2.56 |
% 13.17/2.56 | GROUND_INST: instantiating (1) with all_25_5, all_25_4, all_25_2, all_25_2,
% 13.17/2.56 | all_36_0, all_25_1, simplifying with (10), (11), (13), (16), (31)
% 13.17/2.57 | gives:
% 13.17/2.57 | (36) all_36_0 = 0 | all_25_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 13.17/2.57 | any] : ? [v3: any] : (apart_point_and_line(all_25_4, all_25_2) = v3
% 13.17/2.57 | & apart_point_and_line(all_25_5, all_25_2) = v2 &
% 13.17/2.57 | distinct_lines(all_25_2, all_25_2) = v1 & distinct_points(all_25_5,
% 13.17/2.57 | all_25_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 13.17/2.57 |
% 13.17/2.57 | GROUND_INST: instantiating (1) with all_25_5, all_25_5, all_25_2, all_25_2,
% 13.17/2.57 | all_36_0, all_36_0, simplifying with (10), (13), (31) gives:
% 13.17/2.57 | (37) all_36_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 13.17/2.57 | any] : (apart_point_and_line(all_25_5, all_25_2) = v3 &
% 13.17/2.57 | apart_point_and_line(all_25_5, all_25_2) = v2 &
% 13.17/2.57 | distinct_lines(all_25_2, all_25_2) = v1 & distinct_points(all_25_5,
% 13.17/2.57 | all_25_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 13.17/2.57 |
% 13.17/2.57 | GROUND_INST: instantiating (4) with all_25_4, all_25_0, all_25_2, all_25_3,
% 13.17/2.57 | all_32_0, all_38_0, simplifying with (11), (12), (13), (14),
% 13.17/2.57 | (25), (34) gives:
% 13.17/2.57 | (38) all_38_0 = 0 | all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 13.17/2.57 | any] : (unorthogonal_lines(all_25_0, all_25_3) = v2 &
% 13.17/2.57 | apart_point_and_line(all_25_4, all_25_2) = v1 &
% 13.17/2.57 | distinct_lines(all_25_0, all_25_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1
% 13.17/2.57 | = 0))
% 13.17/2.57 |
% 13.17/2.57 | GROUND_INST: instantiating (3) with all_25_4, all_25_2, all_25_0, all_25_3,
% 13.17/2.57 | all_32_0, all_38_0, simplifying with (11), (12), (13), (14),
% 13.17/2.57 | (25), (34) gives:
% 13.17/2.57 | (39) all_38_0 = 0 | all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 13.17/2.57 | any] : (unorthogonal_lines(all_25_0, all_25_3) = v2 &
% 13.17/2.57 | apart_point_and_line(all_25_4, all_25_2) = v1 &
% 13.17/2.57 | distinct_lines(all_25_2, all_25_0) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1
% 13.17/2.57 | = 0))
% 13.17/2.57 |
% 13.17/2.57 | GROUND_INST: instantiating (2) with all_25_5, all_25_2, all_25_0, all_25_3,
% 13.17/2.57 | all_36_0, all_38_0, simplifying with (10), (12), (13), (14),
% 13.17/2.57 | (15), (31), (34) gives:
% 13.17/2.57 | (40) all_38_0 = 0 | all_36_0 = 0 | ? [v0: any] : ? [v1: any] :
% 13.17/2.57 | (unorthogonal_lines(all_25_0, all_25_3) = v1 &
% 13.17/2.57 | apart_point_and_line(all_25_5, all_25_0) = v0 & (v1 = 0 | v0 = 0))
% 13.17/2.57 |
% 13.17/2.57 | BETA: splitting (39) gives:
% 13.17/2.57 |
% 13.17/2.57 | Case 1:
% 13.17/2.57 | |
% 13.17/2.57 | | (41) all_38_0 = 0
% 13.17/2.57 | |
% 13.17/2.57 | | REDUCE: (33), (41) imply:
% 13.17/2.57 | | (42) $false
% 13.17/2.57 | |
% 13.17/2.57 | | CLOSE: (42) is inconsistent.
% 13.17/2.57 | |
% 13.17/2.57 | Case 2:
% 13.17/2.57 | |
% 13.17/2.58 | | (43) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 13.17/2.58 | | (unorthogonal_lines(all_25_0, all_25_3) = v2 &
% 13.17/2.58 | | apart_point_and_line(all_25_4, all_25_2) = v1 &
% 13.17/2.58 | | distinct_lines(all_25_2, all_25_0) = v0 & ( ~ (v0 = 0) | v2 = 0 |
% 13.17/2.58 | | v1 = 0))
% 13.17/2.58 | |
% 13.17/2.58 | | BETA: splitting (43) gives:
% 13.17/2.58 | |
% 13.17/2.58 | | Case 1:
% 13.17/2.58 | | |
% 13.17/2.58 | | | (44) all_32_0 = 0
% 13.17/2.58 | | |
% 13.17/2.58 | | | REDUCE: (24), (44) imply:
% 13.17/2.58 | | | (45) $false
% 13.17/2.58 | | |
% 13.17/2.58 | | | CLOSE: (45) is inconsistent.
% 13.17/2.58 | | |
% 13.17/2.58 | | Case 2:
% 13.17/2.58 | | |
% 13.17/2.58 | | | (46) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 13.17/2.58 | | | (unorthogonal_lines(all_25_0, all_25_3) = v2 &
% 13.17/2.58 | | | apart_point_and_line(all_25_4, all_25_2) = v1 &
% 13.17/2.58 | | | distinct_lines(all_25_2, all_25_0) = v0 & ( ~ (v0 = 0) | v2 = 0
% 13.17/2.58 | | | | v1 = 0))
% 13.17/2.58 | | |
% 13.17/2.58 | | | DELTA: instantiating (46) with fresh symbols all_111_0, all_111_1,
% 13.17/2.58 | | | all_111_2 gives:
% 13.17/2.58 | | | (47) unorthogonal_lines(all_25_0, all_25_3) = all_111_0 &
% 13.17/2.58 | | | apart_point_and_line(all_25_4, all_25_2) = all_111_1 &
% 13.17/2.58 | | | distinct_lines(all_25_2, all_25_0) = all_111_2 & ( ~ (all_111_2 =
% 13.17/2.58 | | | 0) | all_111_0 = 0 | all_111_1 = 0)
% 13.17/2.58 | | |
% 13.17/2.58 | | | ALPHA: (47) implies:
% 13.17/2.58 | | | (48) distinct_lines(all_25_2, all_25_0) = all_111_2
% 13.17/2.58 | | | (49) apart_point_and_line(all_25_4, all_25_2) = all_111_1
% 13.17/2.58 | | | (50) unorthogonal_lines(all_25_0, all_25_3) = all_111_0
% 13.17/2.58 | | | (51) ~ (all_111_2 = 0) | all_111_0 = 0 | all_111_1 = 0
% 13.17/2.58 | | |
% 13.17/2.58 | | | BETA: splitting (36) gives:
% 13.17/2.58 | | |
% 13.17/2.58 | | | Case 1:
% 13.17/2.58 | | | |
% 13.17/2.58 | | | | (52) all_36_0 = 0
% 13.17/2.58 | | | |
% 13.17/2.58 | | | | REDUCE: (30), (52) imply:
% 13.17/2.58 | | | | (53) $false
% 13.17/2.58 | | | |
% 13.17/2.58 | | | | CLOSE: (53) is inconsistent.
% 13.17/2.58 | | | |
% 13.17/2.58 | | | Case 2:
% 13.17/2.58 | | | |
% 13.17/2.58 | | | | (54) all_25_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 13.17/2.58 | | | | [v3: any] : (apart_point_and_line(all_25_4, all_25_2) = v3 &
% 13.17/2.58 | | | | apart_point_and_line(all_25_5, all_25_2) = v2 &
% 13.17/2.58 | | | | distinct_lines(all_25_2, all_25_2) = v1 &
% 13.17/2.58 | | | | distinct_points(all_25_5, all_25_4) = v0 & ( ~ (v1 = 0) | ~
% 13.17/2.58 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 13.17/2.58 | | | |
% 13.17/2.58 | | | | BETA: splitting (38) gives:
% 13.17/2.58 | | | |
% 13.17/2.58 | | | | Case 1:
% 13.17/2.58 | | | | |
% 13.17/2.58 | | | | | (55) all_38_0 = 0
% 13.17/2.58 | | | | |
% 13.17/2.58 | | | | | REDUCE: (33), (55) imply:
% 13.17/2.58 | | | | | (56) $false
% 13.17/2.58 | | | | |
% 13.17/2.58 | | | | | CLOSE: (56) is inconsistent.
% 13.17/2.58 | | | | |
% 13.17/2.58 | | | | Case 2:
% 13.17/2.58 | | | | |
% 13.17/2.58 | | | | | (57) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 13.17/2.58 | | | | | (unorthogonal_lines(all_25_0, all_25_3) = v2 &
% 13.17/2.58 | | | | | apart_point_and_line(all_25_4, all_25_2) = v1 &
% 13.17/2.58 | | | | | distinct_lines(all_25_0, all_25_2) = v0 & ( ~ (v0 = 0) | v2
% 13.17/2.58 | | | | | = 0 | v1 = 0))
% 13.17/2.58 | | | | |
% 13.17/2.58 | | | | | BETA: splitting (40) gives:
% 13.17/2.58 | | | | |
% 13.17/2.58 | | | | | Case 1:
% 13.17/2.58 | | | | | |
% 13.17/2.58 | | | | | | (58) all_38_0 = 0
% 13.17/2.58 | | | | | |
% 13.17/2.58 | | | | | | REDUCE: (33), (58) imply:
% 13.17/2.58 | | | | | | (59) $false
% 13.17/2.58 | | | | | |
% 13.17/2.58 | | | | | | CLOSE: (59) is inconsistent.
% 13.17/2.58 | | | | | |
% 13.17/2.58 | | | | | Case 2:
% 13.17/2.58 | | | | | |
% 13.17/2.58 | | | | | | (60) all_36_0 = 0 | ? [v0: any] : ? [v1: any] :
% 13.17/2.58 | | | | | | (unorthogonal_lines(all_25_0, all_25_3) = v1 &
% 13.17/2.58 | | | | | | apart_point_and_line(all_25_5, all_25_0) = v0 & (v1 = 0 |
% 13.17/2.58 | | | | | | v0 = 0))
% 13.17/2.58 | | | | | |
% 13.17/2.58 | | | | | | BETA: splitting (35) gives:
% 13.17/2.58 | | | | | |
% 13.17/2.58 | | | | | | Case 1:
% 13.17/2.58 | | | | | | |
% 13.17/2.58 | | | | | | | (61) all_36_0 = 0
% 13.17/2.58 | | | | | | |
% 13.17/2.58 | | | | | | | REDUCE: (30), (61) imply:
% 13.17/2.58 | | | | | | | (62) $false
% 13.17/2.58 | | | | | | |
% 13.17/2.58 | | | | | | | CLOSE: (62) is inconsistent.
% 13.17/2.58 | | | | | | |
% 13.17/2.58 | | | | | | Case 2:
% 13.17/2.58 | | | | | | |
% 13.17/2.58 | | | | | | | (63) all_25_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any]
% 13.17/2.58 | | | | | | | : ? [v3: any] : (apart_point_and_line(all_25_4, all_25_2)
% 13.17/2.58 | | | | | | | = v2 & apart_point_and_line(all_25_5, all_25_2) = v3 &
% 13.17/2.58 | | | | | | | distinct_lines(all_25_2, all_25_2) = v1 &
% 13.17/2.59 | | | | | | | distinct_points(all_25_4, all_25_5) = v0 & ( ~ (v1 = 0)
% 13.17/2.59 | | | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 13.17/2.59 | | | | | | |
% 13.17/2.59 | | | | | | | BETA: splitting (54) gives:
% 13.17/2.59 | | | | | | |
% 13.17/2.59 | | | | | | | Case 1:
% 13.17/2.59 | | | | | | | |
% 13.17/2.59 | | | | | | | | (64) all_25_1 = 0
% 13.17/2.59 | | | | | | | |
% 13.17/2.59 | | | | | | | | REDUCE: (9), (64) imply:
% 13.17/2.59 | | | | | | | | (65) $false
% 13.17/2.59 | | | | | | | |
% 13.17/2.59 | | | | | | | | CLOSE: (65) is inconsistent.
% 13.17/2.59 | | | | | | | |
% 13.17/2.59 | | | | | | | Case 2:
% 13.17/2.59 | | | | | | | |
% 13.17/2.59 | | | | | | | | (66) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 13.17/2.59 | | | | | | | | any] : (apart_point_and_line(all_25_4, all_25_2) = v3
% 13.17/2.59 | | | | | | | | & apart_point_and_line(all_25_5, all_25_2) = v2 &
% 13.17/2.59 | | | | | | | | distinct_lines(all_25_2, all_25_2) = v1 &
% 13.17/2.59 | | | | | | | | distinct_points(all_25_5, all_25_4) = v0 & ( ~ (v1 =
% 13.17/2.59 | | | | | | | | 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 13.17/2.59 | | | | | | | |
% 13.17/2.59 | | | | | | | | DELTA: instantiating (66) with fresh symbols all_174_0,
% 13.17/2.59 | | | | | | | | all_174_1, all_174_2, all_174_3 gives:
% 13.17/2.59 | | | | | | | | (67) apart_point_and_line(all_25_4, all_25_2) = all_174_0 &
% 13.17/2.59 | | | | | | | | apart_point_and_line(all_25_5, all_25_2) = all_174_1 &
% 13.17/2.59 | | | | | | | | distinct_lines(all_25_2, all_25_2) = all_174_2 &
% 13.17/2.59 | | | | | | | | distinct_points(all_25_5, all_25_4) = all_174_3 & ( ~
% 13.17/2.59 | | | | | | | | (all_174_2 = 0) | ~ (all_174_3 = 0) | all_174_0 = 0 |
% 13.17/2.59 | | | | | | | | all_174_1 = 0)
% 13.17/2.59 | | | | | | | |
% 13.17/2.59 | | | | | | | | ALPHA: (67) implies:
% 13.17/2.59 | | | | | | | | (68) apart_point_and_line(all_25_4, all_25_2) = all_174_0
% 13.17/2.59 | | | | | | | |
% 13.17/2.59 | | | | | | | | BETA: splitting (57) gives:
% 13.17/2.59 | | | | | | | |
% 13.17/2.59 | | | | | | | | Case 1:
% 13.17/2.59 | | | | | | | | |
% 13.17/2.59 | | | | | | | | | (69) all_32_0 = 0
% 13.17/2.59 | | | | | | | | |
% 13.17/2.59 | | | | | | | | | REDUCE: (24), (69) imply:
% 13.17/2.59 | | | | | | | | | (70) $false
% 13.17/2.59 | | | | | | | | |
% 13.17/2.59 | | | | | | | | | CLOSE: (70) is inconsistent.
% 13.17/2.59 | | | | | | | | |
% 13.17/2.59 | | | | | | | | Case 2:
% 13.17/2.59 | | | | | | | | |
% 13.17/2.59 | | | | | | | | | (71) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 13.17/2.59 | | | | | | | | | (unorthogonal_lines(all_25_0, all_25_3) = v2 &
% 13.17/2.59 | | | | | | | | | apart_point_and_line(all_25_4, all_25_2) = v1 &
% 13.17/2.59 | | | | | | | | | distinct_lines(all_25_0, all_25_2) = v0 & ( ~ (v0 =
% 13.17/2.59 | | | | | | | | | 0) | v2 = 0 | v1 = 0))
% 13.17/2.59 | | | | | | | | |
% 13.17/2.59 | | | | | | | | | DELTA: instantiating (71) with fresh symbols all_179_0,
% 13.17/2.59 | | | | | | | | | all_179_1, all_179_2 gives:
% 13.17/2.59 | | | | | | | | | (72) unorthogonal_lines(all_25_0, all_25_3) = all_179_0 &
% 13.17/2.59 | | | | | | | | | apart_point_and_line(all_25_4, all_25_2) = all_179_1 &
% 13.17/2.59 | | | | | | | | | distinct_lines(all_25_0, all_25_2) = all_179_2 & ( ~
% 13.17/2.59 | | | | | | | | | (all_179_2 = 0) | all_179_0 = 0 | all_179_1 = 0)
% 13.17/2.59 | | | | | | | | |
% 13.17/2.59 | | | | | | | | | ALPHA: (72) implies:
% 13.17/2.59 | | | | | | | | | (73) apart_point_and_line(all_25_4, all_25_2) = all_179_1
% 13.17/2.59 | | | | | | | | | (74) unorthogonal_lines(all_25_0, all_25_3) = all_179_0
% 13.17/2.59 | | | | | | | | |
% 13.17/2.59 | | | | | | | | | BETA: splitting (60) gives:
% 13.17/2.59 | | | | | | | | |
% 13.17/2.59 | | | | | | | | | Case 1:
% 13.17/2.59 | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | (75) all_36_0 = 0
% 13.17/2.59 | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | REDUCE: (30), (75) imply:
% 13.17/2.59 | | | | | | | | | | (76) $false
% 13.17/2.59 | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | CLOSE: (76) is inconsistent.
% 13.17/2.59 | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | Case 2:
% 13.17/2.59 | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | (77) ? [v0: any] : ? [v1: any] :
% 13.17/2.59 | | | | | | | | | | (unorthogonal_lines(all_25_0, all_25_3) = v1 &
% 13.17/2.59 | | | | | | | | | | apart_point_and_line(all_25_5, all_25_0) = v0 &
% 13.17/2.59 | | | | | | | | | | (v1 = 0 | v0 = 0))
% 13.17/2.59 | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | DELTA: instantiating (77) with fresh symbols all_184_0,
% 13.17/2.59 | | | | | | | | | | all_184_1 gives:
% 13.17/2.59 | | | | | | | | | | (78) unorthogonal_lines(all_25_0, all_25_3) = all_184_0 &
% 13.17/2.59 | | | | | | | | | | apart_point_and_line(all_25_5, all_25_0) = all_184_1
% 13.17/2.59 | | | | | | | | | | & (all_184_0 = 0 | all_184_1 = 0)
% 13.17/2.59 | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | ALPHA: (78) implies:
% 13.17/2.59 | | | | | | | | | | (79) unorthogonal_lines(all_25_0, all_25_3) = all_184_0
% 13.17/2.59 | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | BETA: splitting (63) gives:
% 13.17/2.59 | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | Case 1:
% 13.17/2.59 | | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | | (80) all_25_1 = 0
% 13.17/2.59 | | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | | REDUCE: (9), (80) imply:
% 13.17/2.59 | | | | | | | | | | | (81) $false
% 13.17/2.59 | | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | | CLOSE: (81) is inconsistent.
% 13.17/2.59 | | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | Case 2:
% 13.17/2.59 | | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | | (82) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 13.17/2.59 | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_25_4,
% 13.17/2.59 | | | | | | | | | | | all_25_2) = v2 &
% 13.17/2.59 | | | | | | | | | | | apart_point_and_line(all_25_5, all_25_2) = v3 &
% 13.17/2.59 | | | | | | | | | | | distinct_lines(all_25_2, all_25_2) = v1 &
% 13.17/2.59 | | | | | | | | | | | distinct_points(all_25_4, all_25_5) = v0 & ( ~
% 13.17/2.59 | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 13.17/2.59 | | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | | DELTA: instantiating (82) with fresh symbols all_189_0,
% 13.17/2.59 | | | | | | | | | | | all_189_1, all_189_2, all_189_3 gives:
% 13.17/2.59 | | | | | | | | | | | (83) apart_point_and_line(all_25_4, all_25_2) =
% 13.17/2.59 | | | | | | | | | | | all_189_1 & apart_point_and_line(all_25_5,
% 13.17/2.59 | | | | | | | | | | | all_25_2) = all_189_0 & distinct_lines(all_25_2,
% 13.17/2.59 | | | | | | | | | | | all_25_2) = all_189_2 &
% 13.17/2.59 | | | | | | | | | | | distinct_points(all_25_4, all_25_5) = all_189_3 &
% 13.17/2.59 | | | | | | | | | | | ( ~ (all_189_2 = 0) | ~ (all_189_3 = 0) |
% 13.17/2.59 | | | | | | | | | | | all_189_0 = 0 | all_189_1 = 0)
% 13.17/2.59 | | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | | ALPHA: (83) implies:
% 13.17/2.59 | | | | | | | | | | | (84) apart_point_and_line(all_25_4, all_25_2) =
% 13.17/2.59 | | | | | | | | | | | all_189_1
% 13.17/2.59 | | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | | BETA: splitting (37) gives:
% 13.17/2.59 | | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | | Case 1:
% 13.17/2.59 | | | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | | | (85) all_36_0 = 0
% 13.17/2.59 | | | | | | | | | | | |
% 13.17/2.59 | | | | | | | | | | | | REDUCE: (30), (85) imply:
% 13.17/2.59 | | | | | | | | | | | | (86) $false
% 13.17/2.59 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | CLOSE: (86) is inconsistent.
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | Case 2:
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | GROUND_INST: instantiating (5) with 0, all_111_2, all_25_0,
% 13.17/2.60 | | | | | | | | | | | | all_25_2, simplifying with (15), (48) gives:
% 13.17/2.60 | | | | | | | | | | | | (87) all_111_2 = 0
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_25_1, all_174_0,
% 13.17/2.60 | | | | | | | | | | | | all_25_2, all_25_4, simplifying with (16), (68)
% 13.17/2.60 | | | | | | | | | | | | gives:
% 13.17/2.60 | | | | | | | | | | | | (88) all_174_0 = all_25_1
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_179_1, all_189_1,
% 13.17/2.60 | | | | | | | | | | | | all_25_2, all_25_4, simplifying with (73), (84)
% 13.17/2.60 | | | | | | | | | | | | gives:
% 13.17/2.60 | | | | | | | | | | | | (89) all_189_1 = all_179_1
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_174_0, all_189_1,
% 13.17/2.60 | | | | | | | | | | | | all_25_2, all_25_4, simplifying with (68), (84)
% 13.17/2.60 | | | | | | | | | | | | gives:
% 13.17/2.60 | | | | | | | | | | | | (90) all_189_1 = all_174_0
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_111_1, all_189_1,
% 13.17/2.60 | | | | | | | | | | | | all_25_2, all_25_4, simplifying with (49), (84)
% 13.17/2.60 | | | | | | | | | | | | gives:
% 13.17/2.60 | | | | | | | | | | | | (91) all_189_1 = all_111_1
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_34_0, all_179_0,
% 13.17/2.60 | | | | | | | | | | | | all_25_3, all_25_0, simplifying with (28), (74)
% 13.17/2.60 | | | | | | | | | | | | gives:
% 13.17/2.60 | | | | | | | | | | | | (92) all_179_0 = all_34_0
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_179_0, all_184_0,
% 13.17/2.60 | | | | | | | | | | | | all_25_3, all_25_0, simplifying with (74), (79)
% 13.17/2.60 | | | | | | | | | | | | gives:
% 13.17/2.60 | | | | | | | | | | | | (93) all_184_0 = all_179_0
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_111_0, all_184_0,
% 13.17/2.60 | | | | | | | | | | | | all_25_3, all_25_0, simplifying with (50), (79)
% 13.17/2.60 | | | | | | | | | | | | gives:
% 13.17/2.60 | | | | | | | | | | | | (94) all_184_0 = all_111_0
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | COMBINE_EQS: (89), (91) imply:
% 13.17/2.60 | | | | | | | | | | | | (95) all_179_1 = all_111_1
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | COMBINE_EQS: (89), (90) imply:
% 13.17/2.60 | | | | | | | | | | | | (96) all_179_1 = all_174_0
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | COMBINE_EQS: (93), (94) imply:
% 13.17/2.60 | | | | | | | | | | | | (97) all_179_0 = all_111_0
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | SIMP: (97) implies:
% 13.17/2.60 | | | | | | | | | | | | (98) all_179_0 = all_111_0
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | COMBINE_EQS: (92), (98) imply:
% 13.17/2.60 | | | | | | | | | | | | (99) all_111_0 = all_34_0
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | SIMP: (99) implies:
% 13.17/2.60 | | | | | | | | | | | | (100) all_111_0 = all_34_0
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | COMBINE_EQS: (95), (96) imply:
% 13.17/2.60 | | | | | | | | | | | | (101) all_174_0 = all_111_1
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | SIMP: (101) implies:
% 13.17/2.60 | | | | | | | | | | | | (102) all_174_0 = all_111_1
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | COMBINE_EQS: (88), (102) imply:
% 13.17/2.60 | | | | | | | | | | | | (103) all_111_1 = all_25_1
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | SIMP: (103) implies:
% 13.17/2.60 | | | | | | | | | | | | (104) all_111_1 = all_25_1
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | BETA: splitting (51) gives:
% 13.17/2.60 | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | Case 1:
% 13.17/2.60 | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | (105) ~ (all_111_2 = 0)
% 13.17/2.60 | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | REDUCE: (87), (105) imply:
% 13.17/2.60 | | | | | | | | | | | | | (106) $false
% 13.17/2.60 | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | CLOSE: (106) is inconsistent.
% 13.17/2.60 | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | Case 2:
% 13.17/2.60 | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | (107) all_111_0 = 0 | all_111_1 = 0
% 13.17/2.60 | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | BETA: splitting (107) gives:
% 13.17/2.60 | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | Case 1:
% 13.17/2.60 | | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | | (108) all_111_0 = 0
% 13.17/2.60 | | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | | COMBINE_EQS: (100), (108) imply:
% 13.17/2.60 | | | | | | | | | | | | | | (109) all_34_0 = 0
% 13.17/2.60 | | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | | SIMP: (109) implies:
% 13.17/2.60 | | | | | | | | | | | | | | (110) all_34_0 = 0
% 13.17/2.60 | | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | | REDUCE: (27), (110) imply:
% 13.17/2.60 | | | | | | | | | | | | | | (111) $false
% 13.17/2.60 | | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | | CLOSE: (111) is inconsistent.
% 13.17/2.60 | | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | Case 2:
% 13.17/2.60 | | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | | (112) all_111_1 = 0
% 13.17/2.60 | | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | | COMBINE_EQS: (104), (112) imply:
% 13.17/2.60 | | | | | | | | | | | | | | (113) all_25_1 = 0
% 13.17/2.60 | | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | | SIMP: (113) implies:
% 13.17/2.60 | | | | | | | | | | | | | | (114) all_25_1 = 0
% 13.17/2.60 | | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | | REDUCE: (9), (114) imply:
% 13.17/2.60 | | | | | | | | | | | | | | (115) $false
% 13.17/2.60 | | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | | CLOSE: (115) is inconsistent.
% 13.17/2.60 | | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | | End of split
% 13.17/2.60 | | | | | | | | | | | | |
% 13.17/2.60 | | | | | | | | | | | | End of split
% 13.17/2.60 | | | | | | | | | | | |
% 13.59/2.60 | | | | | | | | | | | End of split
% 13.59/2.60 | | | | | | | | | | |
% 13.59/2.60 | | | | | | | | | | End of split
% 13.59/2.60 | | | | | | | | | |
% 13.59/2.60 | | | | | | | | | End of split
% 13.59/2.60 | | | | | | | | |
% 13.59/2.60 | | | | | | | | End of split
% 13.59/2.60 | | | | | | | |
% 13.59/2.60 | | | | | | | End of split
% 13.59/2.60 | | | | | | |
% 13.59/2.60 | | | | | | End of split
% 13.59/2.60 | | | | | |
% 13.59/2.60 | | | | | End of split
% 13.59/2.60 | | | | |
% 13.59/2.60 | | | | End of split
% 13.59/2.60 | | | |
% 13.59/2.60 | | | End of split
% 13.59/2.60 | | |
% 13.59/2.60 | | End of split
% 13.59/2.60 | |
% 13.59/2.60 | End of split
% 13.59/2.60 |
% 13.59/2.60 End of proof
% 13.59/2.60 % SZS output end Proof for theBenchmark
% 13.59/2.60
% 13.59/2.60 2016ms
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