TSTP Solution File: GEO226+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO226+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 : n006.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 7.32s 1.71s
% Output : Proof 10.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO226+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 22:30:06 EDT 2023
% 0.14/0.35 % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.36/1.05 Prover 1: Preprocessing ...
% 2.36/1.05 Prover 4: Preprocessing ...
% 2.36/1.09 Prover 5: Preprocessing ...
% 2.36/1.09 Prover 2: Preprocessing ...
% 2.36/1.09 Prover 3: Preprocessing ...
% 2.36/1.09 Prover 0: Preprocessing ...
% 2.36/1.09 Prover 6: Preprocessing ...
% 5.10/1.41 Prover 6: Proving ...
% 5.10/1.41 Prover 2: Proving ...
% 5.10/1.41 Prover 5: Proving ...
% 5.10/1.41 Prover 1: Constructing countermodel ...
% 5.10/1.42 Prover 3: Constructing countermodel ...
% 5.96/1.53 Prover 3: gave up
% 5.96/1.53 Prover 1: gave up
% 5.96/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.96/1.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.96/1.55 Prover 0: Proving ...
% 5.96/1.56 Prover 4: Constructing countermodel ...
% 5.96/1.57 Prover 7: Preprocessing ...
% 5.96/1.58 Prover 8: Preprocessing ...
% 6.49/1.61 Prover 7: Warning: ignoring some quantifiers
% 6.49/1.62 Prover 7: Constructing countermodel ...
% 7.32/1.70 Prover 8: Warning: ignoring some quantifiers
% 7.32/1.71 Prover 0: proved (1074ms)
% 7.32/1.71
% 7.32/1.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.32/1.71
% 7.32/1.71 Prover 5: stopped
% 7.32/1.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.32/1.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.32/1.71 Prover 2: stopped
% 7.32/1.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.32/1.72 Prover 6: stopped
% 7.32/1.72 Prover 8: Constructing countermodel ...
% 7.49/1.73 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.49/1.75 Prover 11: Preprocessing ...
% 7.49/1.76 Prover 10: Preprocessing ...
% 7.49/1.76 Prover 16: Preprocessing ...
% 7.49/1.76 Prover 13: Preprocessing ...
% 7.49/1.78 Prover 7: gave up
% 7.49/1.78 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 7.49/1.79 Prover 10: Warning: ignoring some quantifiers
% 7.49/1.79 Prover 16: Warning: ignoring some quantifiers
% 7.49/1.80 Prover 10: Constructing countermodel ...
% 7.49/1.82 Prover 16: Constructing countermodel ...
% 7.49/1.83 Prover 19: Preprocessing ...
% 7.49/1.83 Prover 8: gave up
% 7.49/1.84 Prover 13: Warning: ignoring some quantifiers
% 7.49/1.85 Prover 13: Constructing countermodel ...
% 7.49/1.87 Prover 10: gave up
% 8.53/1.91 Prover 19: Warning: ignoring some quantifiers
% 8.53/1.91 Prover 19: Constructing countermodel ...
% 8.53/1.93 Prover 11: Constructing countermodel ...
% 9.13/1.99 Prover 19: gave up
% 9.73/2.04 Prover 4: Found proof (size 90)
% 9.73/2.04 Prover 4: proved (1396ms)
% 9.73/2.04 Prover 11: stopped
% 9.73/2.04 Prover 16: stopped
% 9.73/2.04 Prover 13: stopped
% 9.73/2.04
% 9.73/2.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.73/2.04
% 9.73/2.05 % SZS output start Proof for theBenchmark
% 9.73/2.06 Assumptions after simplification:
% 9.73/2.06 ---------------------------------
% 9.73/2.06
% 9.73/2.06 (ci3)
% 9.97/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 9.97/2.08 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 9.97/2.08 (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4
% 9.97/2.08 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 9.97/2.08 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 9.97/2.08 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 &
% 9.97/2.09 apart_point_and_line(v2, v0) = v3 & $i(v2)))
% 9.97/2.09
% 9.97/2.09 (ci4)
% 9.97/2.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 9.97/2.09 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 9.97/2.09 (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4
% 9.97/2.09 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 9.97/2.09 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 9.97/2.09 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 &
% 9.97/2.09 apart_point_and_line(v2, v1) = v3 & $i(v2)))
% 9.97/2.09
% 9.97/2.09 (con)
% 9.97/2.09 ? [v0: $i] : ? [v1: $i] : (line(v1) = 0 & line(v0) = 0 &
% 9.97/2.09 convergent_lines(v0, v1) = 0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: int]
% 9.97/2.09 : (v3 = 0 | ~ (point(v2) = v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: int] :
% 9.97/2.09 (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ $i(v2) |
% 9.97/2.09 apart_point_and_line(v2, v0) = 0) & ! [v2: $i] : ! [v3: int] : (v3 = 0 |
% 9.97/2.09 ~ (apart_point_and_line(v2, v0) = v3) | ~ $i(v2) |
% 9.97/2.09 apart_point_and_line(v2, v1) = 0))
% 9.97/2.09
% 9.97/2.09 (cu1)
% 9.97/2.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 9.97/2.11 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 9.97/2.11 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 9.97/2.11 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 9.97/2.11 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0,
% 9.97/2.11 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 9.97/2.11 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 9.97/2.11 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) =
% 9.97/2.11 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3)
% 9.97/2.11 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 9.97/2.11 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 &
% 9.97/2.11 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6
% 9.97/2.11 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 9.97/2.11 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 9.97/2.11 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4)
% 9.97/2.11 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 9.97/2.11 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 9.97/2.11 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 9.97/2.11 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 =
% 9.97/2.11 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 9.97/2.11 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) =
% 9.97/2.11 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 9.97/2.11 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9:
% 9.97/2.11 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) =
% 9.97/2.11 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7
% 9.97/2.11 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 9.97/2.11 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 9.97/2.11 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4)
% 9.97/2.11 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 9.97/2.11 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 9.97/2.11 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 &
% 9.97/2.11 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0:
% 9.97/2.11 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 9.97/2.11 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~
% 9.97/2.11 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 9.97/2.11 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 9.97/2.11 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1,
% 9.97/2.11 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 9.97/2.11 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 9.97/2.11 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3)
% 9.97/2.11 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 9.97/2.11 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 9.97/2.11 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 9.97/2.11 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 9.97/2.11
% 9.97/2.11 (int1)
% 9.97/2.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 9.97/2.12 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 9.97/2.12 ? [v6: any] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 &
% 9.97/2.12 convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) |
% 9.97/2.12 v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) =
% 9.97/2.12 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] :
% 9.97/2.12 ? [v5: any] : (point(v4) = v5 & line(v1) = v3 & line(v0) = v2 &
% 9.97/2.12 intersection_point(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5
% 9.97/2.12 = 0)))
% 9.97/2.12
% 9.97/2.12 (function-axioms)
% 9.97/2.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.97/2.12 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 9.97/2.12 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 9.97/2.12 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 9.97/2.12 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 9.97/2.12 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 9.97/2.12 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 9.97/2.12 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 9.97/2.12 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.97/2.12 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.97/2.12 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 9.97/2.12 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.97/2.12 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 9.97/2.12 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.97/2.12 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.97/2.12 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 9.97/2.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.97/2.12 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 9.97/2.12 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.97/2.12 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0:
% 9.97/2.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.97/2.12 ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 9.97/2.12
% 9.97/2.12 Further assumptions not needed in the proof:
% 9.97/2.12 --------------------------------------------
% 9.97/2.12 apart1, apart2, apart3, apart4, apart5, ax6, ceq1, ceq2, ceq3, ci1, ci2, con1,
% 9.97/2.12 orth1, par1
% 9.97/2.12
% 9.97/2.12 Those formulas are unsatisfiable:
% 9.97/2.12 ---------------------------------
% 9.97/2.12
% 9.97/2.12 Begin of proof
% 9.97/2.12 |
% 9.97/2.12 | ALPHA: (ci3) implies:
% 9.97/2.13 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~
% 9.97/2.13 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 9.97/2.13 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3
% 9.97/2.13 | & $i(v2)))
% 9.97/2.13 |
% 9.97/2.13 | ALPHA: (ci4) implies:
% 9.97/2.13 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~
% 9.97/2.13 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 9.97/2.13 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3
% 9.97/2.13 | & $i(v2)))
% 9.97/2.13 |
% 9.97/2.13 | ALPHA: (cu1) implies:
% 9.97/2.13 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 9.97/2.13 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5)
% 9.97/2.13 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 9.97/2.13 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ?
% 9.97/2.13 | [v9: any] : (apart_point_and_line(v1, v3) = v9 &
% 9.97/2.13 | apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 &
% 9.97/2.13 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0
% 9.97/2.13 | | v8 = 0)))
% 9.97/2.13 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 9.97/2.13 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5)
% 9.97/2.13 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 9.97/2.13 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ?
% 9.97/2.13 | [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 9.97/2.13 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 9.97/2.13 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0
% 9.97/2.13 | | v8 = 0)))
% 9.97/2.13 |
% 9.97/2.13 | ALPHA: (int1) implies:
% 9.97/2.13 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~
% 9.97/2.13 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ?
% 9.97/2.13 | [v5: any] : (point(v4) = v5 & line(v1) = v3 & line(v0) = v2 &
% 9.97/2.13 | intersection_point(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 =
% 9.97/2.13 | 0) | v5 = 0)))
% 9.97/2.13 |
% 9.97/2.13 | ALPHA: (function-axioms) implies:
% 9.97/2.14 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.97/2.14 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 9.97/2.14 | (apart_point_and_line(v3, v2) = v0))
% 9.97/2.14 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.97/2.14 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) =
% 9.97/2.14 | v0))
% 9.97/2.14 |
% 9.97/2.14 | DELTA: instantiating (con) with fresh symbols all_21_0, all_21_1 gives:
% 9.97/2.14 | (8) line(all_21_0) = 0 & line(all_21_1) = 0 & convergent_lines(all_21_1,
% 9.97/2.14 | all_21_0) = 0 & $i(all_21_0) & $i(all_21_1) & ! [v0: $i] : ! [v1:
% 9.97/2.14 | int] : (v1 = 0 | ~ (point(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : !
% 9.97/2.14 | [v1: int] : (v1 = 0 | ~ (apart_point_and_line(v0, all_21_0) = v1) | ~
% 9.97/2.14 | $i(v0) | apart_point_and_line(v0, all_21_1) = 0) & ! [v0: $i] : !
% 9.97/2.14 | [v1: int] : (v1 = 0 | ~ (apart_point_and_line(v0, all_21_1) = v1) | ~
% 9.97/2.14 | $i(v0) | apart_point_and_line(v0, all_21_0) = 0)
% 9.97/2.14 |
% 9.97/2.14 | ALPHA: (8) implies:
% 9.97/2.14 | (9) $i(all_21_1)
% 9.97/2.14 | (10) $i(all_21_0)
% 9.97/2.14 | (11) convergent_lines(all_21_1, all_21_0) = 0
% 10.30/2.14 | (12) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apart_point_and_line(v0,
% 10.30/2.14 | all_21_0) = v1) | ~ $i(v0) | apart_point_and_line(v0, all_21_1)
% 10.30/2.14 | = 0)
% 10.30/2.14 |
% 10.30/2.14 | GROUND_INST: instantiating (5) with all_21_1, all_21_0, simplifying with (9),
% 10.30/2.14 | (10), (11) gives:
% 10.30/2.14 | (13) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : (point(v2)
% 10.30/2.14 | = v3 & line(all_21_0) = v1 & line(all_21_1) = v0 &
% 10.30/2.14 | intersection_point(all_21_1, all_21_0) = v2 & $i(v2) & ( ~ (v1 = 0)
% 10.30/2.14 | | ~ (v0 = 0) | v3 = 0))
% 10.30/2.14 |
% 10.30/2.14 | GROUND_INST: instantiating (2) with all_21_1, all_21_0, simplifying with (9),
% 10.30/2.14 | (10), (11) gives:
% 10.30/2.14 | (14) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 10.30/2.14 | intersection_point(all_21_1, all_21_0) = v0 &
% 10.30/2.14 | apart_point_and_line(v0, all_21_0) = v1 & $i(v0))
% 10.30/2.14 |
% 10.30/2.14 | GROUND_INST: instantiating (1) with all_21_1, all_21_0, simplifying with (9),
% 10.30/2.14 | (10), (11) gives:
% 10.30/2.15 | (15) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 10.30/2.15 | intersection_point(all_21_1, all_21_0) = v0 &
% 10.30/2.15 | apart_point_and_line(v0, all_21_1) = v1 & $i(v0))
% 10.30/2.15 |
% 10.30/2.15 | DELTA: instantiating (15) with fresh symbols all_29_0, all_29_1 gives:
% 10.30/2.15 | (16) ~ (all_29_0 = 0) & intersection_point(all_21_1, all_21_0) = all_29_1
% 10.30/2.15 | & apart_point_and_line(all_29_1, all_21_1) = all_29_0 & $i(all_29_1)
% 10.30/2.15 |
% 10.30/2.15 | ALPHA: (16) implies:
% 10.30/2.15 | (17) ~ (all_29_0 = 0)
% 10.30/2.15 | (18) apart_point_and_line(all_29_1, all_21_1) = all_29_0
% 10.30/2.15 | (19) intersection_point(all_21_1, all_21_0) = all_29_1
% 10.30/2.15 |
% 10.30/2.15 | DELTA: instantiating (14) with fresh symbols all_31_0, all_31_1 gives:
% 10.30/2.15 | (20) ~ (all_31_0 = 0) & intersection_point(all_21_1, all_21_0) = all_31_1
% 10.30/2.15 | & apart_point_and_line(all_31_1, all_21_0) = all_31_0 & $i(all_31_1)
% 10.30/2.15 |
% 10.30/2.15 | ALPHA: (20) implies:
% 10.30/2.15 | (21) ~ (all_31_0 = 0)
% 10.30/2.15 | (22) $i(all_31_1)
% 10.30/2.15 | (23) apart_point_and_line(all_31_1, all_21_0) = all_31_0
% 10.30/2.15 | (24) intersection_point(all_21_1, all_21_0) = all_31_1
% 10.30/2.15 |
% 10.30/2.15 | DELTA: instantiating (13) with fresh symbols all_33_0, all_33_1, all_33_2,
% 10.30/2.15 | all_33_3 gives:
% 10.30/2.15 | (25) point(all_33_1) = all_33_0 & line(all_21_0) = all_33_2 &
% 10.30/2.15 | line(all_21_1) = all_33_3 & intersection_point(all_21_1, all_21_0) =
% 10.30/2.15 | all_33_1 & $i(all_33_1) & ( ~ (all_33_2 = 0) | ~ (all_33_3 = 0) |
% 10.30/2.15 | all_33_0 = 0)
% 10.30/2.15 |
% 10.30/2.15 | ALPHA: (25) implies:
% 10.30/2.15 | (26) intersection_point(all_21_1, all_21_0) = all_33_1
% 10.30/2.15 |
% 10.30/2.15 | GROUND_INST: instantiating (7) with all_31_1, all_33_1, all_21_0, all_21_1,
% 10.30/2.15 | simplifying with (24), (26) gives:
% 10.30/2.15 | (27) all_33_1 = all_31_1
% 10.30/2.15 |
% 10.30/2.15 | GROUND_INST: instantiating (7) with all_29_1, all_33_1, all_21_0, all_21_1,
% 10.30/2.15 | simplifying with (19), (26) gives:
% 10.30/2.15 | (28) all_33_1 = all_29_1
% 10.30/2.15 |
% 10.30/2.15 | COMBINE_EQS: (27), (28) imply:
% 10.30/2.15 | (29) all_31_1 = all_29_1
% 10.30/2.15 |
% 10.30/2.15 | REDUCE: (23), (29) imply:
% 10.30/2.15 | (30) apart_point_and_line(all_29_1, all_21_0) = all_31_0
% 10.30/2.15 |
% 10.30/2.15 | REDUCE: (22), (29) imply:
% 10.30/2.15 | (31) $i(all_29_1)
% 10.30/2.15 |
% 10.30/2.15 | GROUND_INST: instantiating (4) with all_29_1, all_29_1, all_21_1, all_21_1,
% 10.30/2.15 | all_29_0, all_29_0, simplifying with (9), (18), (31) gives:
% 10.30/2.15 | (32) all_29_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 10.30/2.15 | any] : (apart_point_and_line(all_29_1, all_21_1) = v3 &
% 10.30/2.15 | apart_point_and_line(all_29_1, all_21_1) = v2 &
% 10.30/2.15 | distinct_lines(all_21_1, all_21_1) = v1 & distinct_points(all_29_1,
% 10.30/2.15 | all_29_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 10.30/2.15 |
% 10.30/2.15 | GROUND_INST: instantiating (4) with all_29_1, all_29_1, all_21_1, all_21_0,
% 10.30/2.15 | all_29_0, all_31_0, simplifying with (9), (10), (18), (30), (31)
% 10.30/2.15 | gives:
% 10.30/2.16 | (33) all_31_0 = 0 | all_29_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 10.30/2.16 | any] : ? [v3: any] : (apart_point_and_line(all_29_1, all_21_0) = v2
% 10.30/2.16 | & apart_point_and_line(all_29_1, all_21_1) = v3 &
% 10.30/2.16 | distinct_lines(all_21_1, all_21_0) = v1 & distinct_points(all_29_1,
% 10.30/2.16 | all_29_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 10.30/2.16 |
% 10.30/2.16 | GROUND_INST: instantiating (4) with all_29_1, all_29_1, all_21_0, all_21_1,
% 10.30/2.16 | all_31_0, all_29_0, simplifying with (9), (10), (18), (30), (31)
% 10.30/2.16 | gives:
% 10.30/2.16 | (34) all_31_0 = 0 | all_29_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 10.30/2.16 | any] : ? [v3: any] : (apart_point_and_line(all_29_1, all_21_0) = v3
% 10.30/2.16 | & apart_point_and_line(all_29_1, all_21_1) = v2 &
% 10.30/2.16 | distinct_lines(all_21_0, all_21_1) = v1 & distinct_points(all_29_1,
% 10.30/2.16 | all_29_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 10.30/2.16 |
% 10.30/2.16 | GROUND_INST: instantiating (3) with all_29_1, all_29_1, all_21_0, all_21_1,
% 10.30/2.16 | all_29_0, all_31_0, simplifying with (9), (10), (18), (30), (31)
% 10.30/2.16 | gives:
% 10.30/2.16 | (35) all_31_0 = 0 | all_29_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 10.30/2.16 | any] : ? [v3: any] : (apart_point_and_line(all_29_1, all_21_0) = v2
% 10.30/2.16 | & apart_point_and_line(all_29_1, all_21_1) = v3 &
% 10.30/2.16 | distinct_lines(all_21_0, all_21_1) = v1 & distinct_points(all_29_1,
% 10.30/2.16 | all_29_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 10.30/2.16 |
% 10.30/2.16 | GROUND_INST: instantiating (3) with all_29_1, all_29_1, all_21_1, all_21_0,
% 10.30/2.16 | all_31_0, all_29_0, simplifying with (9), (10), (18), (30), (31)
% 10.30/2.16 | gives:
% 10.30/2.16 | (36) all_31_0 = 0 | all_29_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 10.30/2.16 | any] : ? [v3: any] : (apart_point_and_line(all_29_1, all_21_0) = v3
% 10.30/2.16 | & apart_point_and_line(all_29_1, all_21_1) = v2 &
% 10.30/2.16 | distinct_lines(all_21_1, all_21_0) = v1 & distinct_points(all_29_1,
% 10.30/2.16 | all_29_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 10.30/2.16 |
% 10.30/2.16 | GROUND_INST: instantiating (12) with all_29_1, all_31_0, simplifying with
% 10.30/2.16 | (30), (31) gives:
% 10.30/2.16 | (37) all_31_0 = 0 | apart_point_and_line(all_29_1, all_21_1) = 0
% 10.30/2.16 |
% 10.30/2.16 | BETA: splitting (37) gives:
% 10.30/2.16 |
% 10.30/2.16 | Case 1:
% 10.30/2.16 | |
% 10.30/2.16 | | (38) apart_point_and_line(all_29_1, all_21_1) = 0
% 10.30/2.16 | |
% 10.30/2.16 | | BETA: splitting (32) gives:
% 10.30/2.16 | |
% 10.30/2.16 | | Case 1:
% 10.30/2.16 | | |
% 10.30/2.16 | | | (39) all_29_0 = 0
% 10.30/2.16 | | |
% 10.30/2.16 | | | REDUCE: (17), (39) imply:
% 10.42/2.16 | | | (40) $false
% 10.42/2.16 | | |
% 10.42/2.16 | | | CLOSE: (40) is inconsistent.
% 10.42/2.16 | | |
% 10.42/2.16 | | Case 2:
% 10.42/2.16 | | |
% 10.42/2.17 | | | (41) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 10.42/2.17 | | | (apart_point_and_line(all_29_1, all_21_1) = v3 &
% 10.42/2.17 | | | apart_point_and_line(all_29_1, all_21_1) = v2 &
% 10.42/2.17 | | | distinct_lines(all_21_1, all_21_1) = v1 &
% 10.42/2.17 | | | distinct_points(all_29_1, all_29_1) = v0 & ( ~ (v1 = 0) | ~ (v0
% 10.42/2.17 | | | = 0) | v3 = 0 | v2 = 0))
% 10.42/2.17 | | |
% 10.42/2.17 | | | DELTA: instantiating (41) with fresh symbols all_67_0, all_67_1, all_67_2,
% 10.42/2.17 | | | all_67_3 gives:
% 10.42/2.17 | | | (42) apart_point_and_line(all_29_1, all_21_1) = all_67_0 &
% 10.42/2.17 | | | apart_point_and_line(all_29_1, all_21_1) = all_67_1 &
% 10.42/2.17 | | | distinct_lines(all_21_1, all_21_1) = all_67_2 &
% 10.42/2.17 | | | distinct_points(all_29_1, all_29_1) = all_67_3 & ( ~ (all_67_2 =
% 10.42/2.17 | | | 0) | ~ (all_67_3 = 0) | all_67_0 = 0 | all_67_1 = 0)
% 10.42/2.17 | | |
% 10.42/2.17 | | | ALPHA: (42) implies:
% 10.42/2.17 | | | (43) apart_point_and_line(all_29_1, all_21_1) = all_67_1
% 10.42/2.17 | | | (44) apart_point_and_line(all_29_1, all_21_1) = all_67_0
% 10.42/2.17 | | |
% 10.42/2.17 | | | BETA: splitting (36) gives:
% 10.42/2.17 | | |
% 10.42/2.17 | | | Case 1:
% 10.42/2.17 | | | |
% 10.42/2.17 | | | | (45) all_31_0 = 0
% 10.42/2.17 | | | |
% 10.42/2.17 | | | | REDUCE: (21), (45) imply:
% 10.42/2.17 | | | | (46) $false
% 10.42/2.17 | | | |
% 10.42/2.17 | | | | CLOSE: (46) is inconsistent.
% 10.42/2.17 | | | |
% 10.42/2.17 | | | Case 2:
% 10.42/2.17 | | | |
% 10.42/2.17 | | | | (47) all_29_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 10.42/2.17 | | | | [v3: any] : (apart_point_and_line(all_29_1, all_21_0) = v3 &
% 10.42/2.17 | | | | apart_point_and_line(all_29_1, all_21_1) = v2 &
% 10.42/2.17 | | | | distinct_lines(all_21_1, all_21_0) = v1 &
% 10.42/2.17 | | | | distinct_points(all_29_1, all_29_1) = v0 & ( ~ (v1 = 0) | ~
% 10.42/2.17 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 10.42/2.17 | | | |
% 10.42/2.17 | | | | BETA: splitting (35) gives:
% 10.42/2.17 | | | |
% 10.42/2.17 | | | | Case 1:
% 10.42/2.17 | | | | |
% 10.42/2.17 | | | | | (48) all_31_0 = 0
% 10.42/2.17 | | | | |
% 10.42/2.17 | | | | | REDUCE: (21), (48) imply:
% 10.42/2.17 | | | | | (49) $false
% 10.42/2.17 | | | | |
% 10.42/2.17 | | | | | CLOSE: (49) is inconsistent.
% 10.42/2.17 | | | | |
% 10.42/2.17 | | | | Case 2:
% 10.42/2.17 | | | | |
% 10.42/2.17 | | | | | (50) all_29_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 10.42/2.17 | | | | | [v3: any] : (apart_point_and_line(all_29_1, all_21_0) = v2 &
% 10.42/2.17 | | | | | apart_point_and_line(all_29_1, all_21_1) = v3 &
% 10.42/2.17 | | | | | distinct_lines(all_21_0, all_21_1) = v1 &
% 10.42/2.17 | | | | | distinct_points(all_29_1, all_29_1) = v0 & ( ~ (v1 = 0) | ~
% 10.42/2.17 | | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 10.42/2.17 | | | | |
% 10.42/2.17 | | | | | BETA: splitting (33) gives:
% 10.42/2.17 | | | | |
% 10.42/2.17 | | | | | Case 1:
% 10.42/2.17 | | | | | |
% 10.42/2.17 | | | | | | (51) all_31_0 = 0
% 10.42/2.17 | | | | | |
% 10.42/2.17 | | | | | | REDUCE: (21), (51) imply:
% 10.42/2.17 | | | | | | (52) $false
% 10.42/2.17 | | | | | |
% 10.42/2.17 | | | | | | CLOSE: (52) is inconsistent.
% 10.42/2.17 | | | | | |
% 10.42/2.17 | | | | | Case 2:
% 10.42/2.17 | | | | | |
% 10.42/2.17 | | | | | | (53) all_29_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 10.42/2.17 | | | | | | ? [v3: any] : (apart_point_and_line(all_29_1, all_21_0) = v2
% 10.42/2.17 | | | | | | & apart_point_and_line(all_29_1, all_21_1) = v3 &
% 10.42/2.17 | | | | | | distinct_lines(all_21_1, all_21_0) = v1 &
% 10.42/2.17 | | | | | | distinct_points(all_29_1, all_29_1) = v0 & ( ~ (v1 = 0) |
% 10.42/2.17 | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 10.42/2.17 | | | | | |
% 10.42/2.17 | | | | | | BETA: splitting (34) gives:
% 10.42/2.17 | | | | | |
% 10.42/2.17 | | | | | | Case 1:
% 10.42/2.17 | | | | | | |
% 10.42/2.17 | | | | | | | (54) all_31_0 = 0
% 10.42/2.17 | | | | | | |
% 10.42/2.17 | | | | | | | REDUCE: (21), (54) imply:
% 10.42/2.17 | | | | | | | (55) $false
% 10.42/2.17 | | | | | | |
% 10.42/2.17 | | | | | | | CLOSE: (55) is inconsistent.
% 10.42/2.17 | | | | | | |
% 10.42/2.17 | | | | | | Case 2:
% 10.42/2.17 | | | | | | |
% 10.42/2.17 | | | | | | | (56) all_29_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any]
% 10.42/2.17 | | | | | | | : ? [v3: any] : (apart_point_and_line(all_29_1, all_21_0)
% 10.42/2.17 | | | | | | | = v3 & apart_point_and_line(all_29_1, all_21_1) = v2 &
% 10.42/2.18 | | | | | | | distinct_lines(all_21_0, all_21_1) = v1 &
% 10.42/2.18 | | | | | | | distinct_points(all_29_1, all_29_1) = v0 & ( ~ (v1 = 0)
% 10.42/2.18 | | | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 10.42/2.18 | | | | | | |
% 10.42/2.18 | | | | | | | BETA: splitting (47) gives:
% 10.42/2.18 | | | | | | |
% 10.42/2.18 | | | | | | | Case 1:
% 10.42/2.18 | | | | | | | |
% 10.42/2.18 | | | | | | | | (57) all_29_0 = 0
% 10.42/2.18 | | | | | | | |
% 10.42/2.18 | | | | | | | | REDUCE: (17), (57) imply:
% 10.42/2.18 | | | | | | | | (58) $false
% 10.42/2.18 | | | | | | | |
% 10.42/2.18 | | | | | | | | CLOSE: (58) is inconsistent.
% 10.42/2.18 | | | | | | | |
% 10.42/2.18 | | | | | | | Case 2:
% 10.42/2.18 | | | | | | | |
% 10.42/2.18 | | | | | | | | (59) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 10.42/2.18 | | | | | | | | any] : (apart_point_and_line(all_29_1, all_21_0) = v3
% 10.42/2.18 | | | | | | | | & apart_point_and_line(all_29_1, all_21_1) = v2 &
% 10.42/2.18 | | | | | | | | distinct_lines(all_21_1, all_21_0) = v1 &
% 10.42/2.18 | | | | | | | | distinct_points(all_29_1, all_29_1) = v0 & ( ~ (v1 =
% 10.42/2.18 | | | | | | | | 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 10.42/2.18 | | | | | | | |
% 10.42/2.18 | | | | | | | | DELTA: instantiating (59) with fresh symbols all_85_0, all_85_1,
% 10.42/2.18 | | | | | | | | all_85_2, all_85_3 gives:
% 10.42/2.18 | | | | | | | | (60) apart_point_and_line(all_29_1, all_21_0) = all_85_0 &
% 10.42/2.18 | | | | | | | | apart_point_and_line(all_29_1, all_21_1) = all_85_1 &
% 10.42/2.18 | | | | | | | | distinct_lines(all_21_1, all_21_0) = all_85_2 &
% 10.42/2.18 | | | | | | | | distinct_points(all_29_1, all_29_1) = all_85_3 & ( ~
% 10.42/2.18 | | | | | | | | (all_85_2 = 0) | ~ (all_85_3 = 0) | all_85_0 = 0 |
% 10.42/2.18 | | | | | | | | all_85_1 = 0)
% 10.42/2.18 | | | | | | | |
% 10.42/2.18 | | | | | | | | ALPHA: (60) implies:
% 10.42/2.18 | | | | | | | | (61) apart_point_and_line(all_29_1, all_21_1) = all_85_1
% 10.42/2.18 | | | | | | | |
% 10.42/2.18 | | | | | | | | BETA: splitting (50) gives:
% 10.42/2.18 | | | | | | | |
% 10.42/2.18 | | | | | | | | Case 1:
% 10.42/2.18 | | | | | | | | |
% 10.42/2.18 | | | | | | | | | (62) all_29_0 = 0
% 10.42/2.18 | | | | | | | | |
% 10.42/2.18 | | | | | | | | | REDUCE: (17), (62) imply:
% 10.42/2.18 | | | | | | | | | (63) $false
% 10.42/2.18 | | | | | | | | |
% 10.42/2.18 | | | | | | | | | CLOSE: (63) is inconsistent.
% 10.42/2.18 | | | | | | | | |
% 10.42/2.18 | | | | | | | | Case 2:
% 10.42/2.18 | | | | | | | | |
% 10.42/2.18 | | | | | | | | | (64) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 10.42/2.18 | | | | | | | | | any] : (apart_point_and_line(all_29_1, all_21_0) =
% 10.42/2.18 | | | | | | | | | v2 & apart_point_and_line(all_29_1, all_21_1) = v3 &
% 10.42/2.18 | | | | | | | | | distinct_lines(all_21_0, all_21_1) = v1 &
% 10.42/2.18 | | | | | | | | | distinct_points(all_29_1, all_29_1) = v0 & ( ~ (v1 =
% 10.42/2.18 | | | | | | | | | 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 10.42/2.18 | | | | | | | | |
% 10.42/2.18 | | | | | | | | | DELTA: instantiating (64) with fresh symbols all_90_0,
% 10.42/2.18 | | | | | | | | | all_90_1, all_90_2, all_90_3 gives:
% 10.42/2.18 | | | | | | | | | (65) apart_point_and_line(all_29_1, all_21_0) = all_90_1 &
% 10.42/2.18 | | | | | | | | | apart_point_and_line(all_29_1, all_21_1) = all_90_0 &
% 10.42/2.18 | | | | | | | | | distinct_lines(all_21_0, all_21_1) = all_90_2 &
% 10.42/2.18 | | | | | | | | | distinct_points(all_29_1, all_29_1) = all_90_3 & ( ~
% 10.42/2.18 | | | | | | | | | (all_90_2 = 0) | ~ (all_90_3 = 0) | all_90_0 = 0 |
% 10.42/2.18 | | | | | | | | | all_90_1 = 0)
% 10.42/2.18 | | | | | | | | |
% 10.42/2.18 | | | | | | | | | ALPHA: (65) implies:
% 10.42/2.18 | | | | | | | | | (66) apart_point_and_line(all_29_1, all_21_1) = all_90_0
% 10.42/2.18 | | | | | | | | |
% 10.42/2.18 | | | | | | | | | BETA: splitting (53) gives:
% 10.42/2.18 | | | | | | | | |
% 10.42/2.18 | | | | | | | | | Case 1:
% 10.42/2.18 | | | | | | | | | |
% 10.42/2.18 | | | | | | | | | | (67) all_29_0 = 0
% 10.42/2.18 | | | | | | | | | |
% 10.42/2.18 | | | | | | | | | | REDUCE: (17), (67) imply:
% 10.42/2.18 | | | | | | | | | | (68) $false
% 10.42/2.18 | | | | | | | | | |
% 10.42/2.18 | | | | | | | | | | CLOSE: (68) is inconsistent.
% 10.42/2.18 | | | | | | | | | |
% 10.42/2.18 | | | | | | | | | Case 2:
% 10.42/2.18 | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | (69) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 10.42/2.19 | | | | | | | | | | any] : (apart_point_and_line(all_29_1, all_21_0) =
% 10.42/2.19 | | | | | | | | | | v2 & apart_point_and_line(all_29_1, all_21_1) = v3
% 10.42/2.19 | | | | | | | | | | & distinct_lines(all_21_1, all_21_0) = v1 &
% 10.42/2.19 | | | | | | | | | | distinct_points(all_29_1, all_29_1) = v0 & ( ~ (v1
% 10.42/2.19 | | | | | | | | | | = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 10.42/2.19 | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | DELTA: instantiating (69) with fresh symbols all_95_0,
% 10.42/2.19 | | | | | | | | | | all_95_1, all_95_2, all_95_3 gives:
% 10.42/2.19 | | | | | | | | | | (70) apart_point_and_line(all_29_1, all_21_0) = all_95_1
% 10.42/2.19 | | | | | | | | | | & apart_point_and_line(all_29_1, all_21_1) =
% 10.42/2.19 | | | | | | | | | | all_95_0 & distinct_lines(all_21_1, all_21_0) =
% 10.42/2.19 | | | | | | | | | | all_95_2 & distinct_points(all_29_1, all_29_1) =
% 10.42/2.19 | | | | | | | | | | all_95_3 & ( ~ (all_95_2 = 0) | ~ (all_95_3 = 0) |
% 10.42/2.19 | | | | | | | | | | all_95_0 = 0 | all_95_1 = 0)
% 10.42/2.19 | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | ALPHA: (70) implies:
% 10.42/2.19 | | | | | | | | | | (71) apart_point_and_line(all_29_1, all_21_1) = all_95_0
% 10.42/2.19 | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | BETA: splitting (56) gives:
% 10.42/2.19 | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | Case 1:
% 10.42/2.19 | | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | | (72) all_29_0 = 0
% 10.42/2.19 | | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | | REDUCE: (17), (72) imply:
% 10.42/2.19 | | | | | | | | | | | (73) $false
% 10.42/2.19 | | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | | CLOSE: (73) is inconsistent.
% 10.42/2.19 | | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | Case 2:
% 10.42/2.19 | | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | | (74) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 10.42/2.19 | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_29_1,
% 10.42/2.19 | | | | | | | | | | | all_21_0) = v3 &
% 10.42/2.19 | | | | | | | | | | | apart_point_and_line(all_29_1, all_21_1) = v2 &
% 10.42/2.19 | | | | | | | | | | | distinct_lines(all_21_0, all_21_1) = v1 &
% 10.42/2.19 | | | | | | | | | | | distinct_points(all_29_1, all_29_1) = v0 & ( ~
% 10.42/2.19 | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 10.42/2.19 | | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | | DELTA: instantiating (74) with fresh symbols all_100_0,
% 10.42/2.19 | | | | | | | | | | | all_100_1, all_100_2, all_100_3 gives:
% 10.42/2.19 | | | | | | | | | | | (75) apart_point_and_line(all_29_1, all_21_0) =
% 10.42/2.19 | | | | | | | | | | | all_100_0 & apart_point_and_line(all_29_1,
% 10.42/2.19 | | | | | | | | | | | all_21_1) = all_100_1 & distinct_lines(all_21_0,
% 10.42/2.19 | | | | | | | | | | | all_21_1) = all_100_2 &
% 10.42/2.19 | | | | | | | | | | | distinct_points(all_29_1, all_29_1) = all_100_3 &
% 10.42/2.19 | | | | | | | | | | | ( ~ (all_100_2 = 0) | ~ (all_100_3 = 0) |
% 10.42/2.19 | | | | | | | | | | | all_100_0 = 0 | all_100_1 = 0)
% 10.42/2.19 | | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | | ALPHA: (75) implies:
% 10.42/2.19 | | | | | | | | | | | (76) apart_point_and_line(all_29_1, all_21_1) =
% 10.42/2.19 | | | | | | | | | | | all_100_1
% 10.42/2.19 | | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | | GROUND_INST: instantiating (6) with all_29_0, all_85_1,
% 10.42/2.19 | | | | | | | | | | | all_21_1, all_29_1, simplifying with (18), (61)
% 10.42/2.19 | | | | | | | | | | | gives:
% 10.42/2.19 | | | | | | | | | | | (77) all_85_1 = all_29_0
% 10.42/2.19 | | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_85_1, all_21_1,
% 10.42/2.19 | | | | | | | | | | | all_29_1, simplifying with (38), (61) gives:
% 10.42/2.19 | | | | | | | | | | | (78) all_85_1 = 0
% 10.42/2.19 | | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | | GROUND_INST: instantiating (6) with all_85_1, all_90_0,
% 10.42/2.19 | | | | | | | | | | | all_21_1, all_29_1, simplifying with (61), (66)
% 10.42/2.19 | | | | | | | | | | | gives:
% 10.42/2.19 | | | | | | | | | | | (79) all_90_0 = all_85_1
% 10.42/2.19 | | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | | GROUND_INST: instantiating (6) with all_85_1, all_95_0,
% 10.42/2.19 | | | | | | | | | | | all_21_1, all_29_1, simplifying with (61), (71)
% 10.42/2.19 | | | | | | | | | | | gives:
% 10.42/2.19 | | | | | | | | | | | (80) all_95_0 = all_85_1
% 10.42/2.19 | | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | | GROUND_INST: instantiating (6) with all_67_0, all_95_0,
% 10.42/2.19 | | | | | | | | | | | all_21_1, all_29_1, simplifying with (44), (71)
% 10.42/2.19 | | | | | | | | | | | gives:
% 10.42/2.19 | | | | | | | | | | | (81) all_95_0 = all_67_0
% 10.42/2.19 | | | | | | | | | | |
% 10.42/2.19 | | | | | | | | | | | GROUND_INST: instantiating (6) with all_90_0, all_100_1,
% 10.42/2.19 | | | | | | | | | | | all_21_1, all_29_1, simplifying with (66), (76)
% 10.42/2.19 | | | | | | | | | | | gives:
% 10.42/2.19 | | | | | | | | | | | (82) all_100_1 = all_90_0
% 10.42/2.19 | | | | | | | | | | |
% 10.42/2.20 | | | | | | | | | | | GROUND_INST: instantiating (6) with all_67_1, all_100_1,
% 10.42/2.20 | | | | | | | | | | | all_21_1, all_29_1, simplifying with (43), (76)
% 10.42/2.20 | | | | | | | | | | | gives:
% 10.42/2.20 | | | | | | | | | | | (83) all_100_1 = all_67_1
% 10.42/2.20 | | | | | | | | | | |
% 10.42/2.20 | | | | | | | | | | | COMBINE_EQS: (82), (83) imply:
% 10.42/2.20 | | | | | | | | | | | (84) all_90_0 = all_67_1
% 10.42/2.20 | | | | | | | | | | |
% 10.42/2.20 | | | | | | | | | | | SIMP: (84) implies:
% 10.42/2.20 | | | | | | | | | | | (85) all_90_0 = all_67_1
% 10.42/2.20 | | | | | | | | | | |
% 10.42/2.20 | | | | | | | | | | | COMBINE_EQS: (80), (81) imply:
% 10.42/2.20 | | | | | | | | | | | (86) all_85_1 = all_67_0
% 10.42/2.20 | | | | | | | | | | |
% 10.42/2.20 | | | | | | | | | | | SIMP: (86) implies:
% 10.42/2.20 | | | | | | | | | | | (87) all_85_1 = all_67_0
% 10.42/2.20 | | | | | | | | | | |
% 10.42/2.20 | | | | | | | | | | | COMBINE_EQS: (79), (85) imply:
% 10.42/2.20 | | | | | | | | | | | (88) all_85_1 = all_67_1
% 10.42/2.20 | | | | | | | | | | |
% 10.42/2.20 | | | | | | | | | | | SIMP: (88) implies:
% 10.42/2.20 | | | | | | | | | | | (89) all_85_1 = all_67_1
% 10.42/2.20 | | | | | | | | | | |
% 10.42/2.20 | | | | | | | | | | | COMBINE_EQS: (78), (87) imply:
% 10.42/2.20 | | | | | | | | | | | (90) all_67_0 = 0
% 10.42/2.20 | | | | | | | | | | |
% 10.42/2.20 | | | | | | | | | | | COMBINE_EQS: (87), (89) imply:
% 10.42/2.20 | | | | | | | | | | | (91) all_67_0 = all_67_1
% 10.42/2.20 | | | | | | | | | | |
% 10.42/2.20 | | | | | | | | | | | COMBINE_EQS: (77), (87) imply:
% 10.42/2.20 | | | | | | | | | | | (92) all_67_0 = all_29_0
% 10.42/2.20 | | | | | | | | | | |
% 10.42/2.20 | | | | | | | | | | | COMBINE_EQS: (91), (92) imply:
% 10.42/2.20 | | | | | | | | | | | (93) all_67_1 = all_29_0
% 10.42/2.20 | | | | | | | | | | |
% 10.42/2.20 | | | | | | | | | | | COMBINE_EQS: (90), (91) imply:
% 10.42/2.20 | | | | | | | | | | | (94) all_67_1 = 0
% 10.42/2.20 | | | | | | | | | | |
% 10.42/2.20 | | | | | | | | | | | COMBINE_EQS: (93), (94) imply:
% 10.42/2.20 | | | | | | | | | | | (95) all_29_0 = 0
% 10.42/2.20 | | | | | | | | | | |
% 10.42/2.20 | | | | | | | | | | | REDUCE: (17), (95) imply:
% 10.42/2.20 | | | | | | | | | | | (96) $false
% 10.42/2.20 | | | | | | | | | | |
% 10.42/2.20 | | | | | | | | | | | CLOSE: (96) is inconsistent.
% 10.42/2.20 | | | | | | | | | | |
% 10.42/2.20 | | | | | | | | | | End of split
% 10.42/2.20 | | | | | | | | | |
% 10.42/2.20 | | | | | | | | | End of split
% 10.42/2.20 | | | | | | | | |
% 10.42/2.20 | | | | | | | | End of split
% 10.42/2.20 | | | | | | | |
% 10.42/2.20 | | | | | | | End of split
% 10.42/2.20 | | | | | | |
% 10.42/2.20 | | | | | | End of split
% 10.42/2.20 | | | | | |
% 10.42/2.20 | | | | | End of split
% 10.42/2.20 | | | | |
% 10.42/2.20 | | | | End of split
% 10.42/2.20 | | | |
% 10.42/2.20 | | | End of split
% 10.42/2.20 | | |
% 10.42/2.20 | | End of split
% 10.42/2.20 | |
% 10.42/2.20 | Case 2:
% 10.42/2.20 | |
% 10.42/2.20 | | (97) all_31_0 = 0
% 10.42/2.20 | |
% 10.42/2.20 | | REDUCE: (21), (97) imply:
% 10.42/2.20 | | (98) $false
% 10.42/2.20 | |
% 10.42/2.20 | | CLOSE: (98) is inconsistent.
% 10.42/2.20 | |
% 10.42/2.20 | End of split
% 10.42/2.20 |
% 10.42/2.20 End of proof
% 10.42/2.20 % SZS output end Proof for theBenchmark
% 10.42/2.20
% 10.42/2.20 1583ms
%------------------------------------------------------------------------------