TSTP Solution File: GEO175+3 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO175+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.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 23:21:52 EDT 2023
% Result : Theorem 16.73s 3.01s
% Output : Proof 29.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO175+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 22:56:57 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.01/1.18 Prover 1: Preprocessing ...
% 3.01/1.19 Prover 4: Preprocessing ...
% 3.55/1.22 Prover 5: Preprocessing ...
% 3.55/1.22 Prover 0: Preprocessing ...
% 3.55/1.22 Prover 6: Preprocessing ...
% 3.55/1.22 Prover 2: Preprocessing ...
% 3.55/1.22 Prover 3: Preprocessing ...
% 5.87/1.59 Prover 5: Proving ...
% 5.87/1.59 Prover 2: Proving ...
% 7.00/1.71 Prover 6: Constructing countermodel ...
% 7.00/1.73 Prover 1: Constructing countermodel ...
% 7.00/1.74 Prover 3: Constructing countermodel ...
% 8.04/1.84 Prover 6: gave up
% 8.04/1.84 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.04/1.84 Prover 3: gave up
% 8.04/1.85 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.04/1.91 Prover 1: gave up
% 8.04/1.91 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 8.04/1.92 Prover 8: Preprocessing ...
% 8.04/1.93 Prover 7: Preprocessing ...
% 8.04/1.97 Prover 9: Preprocessing ...
% 9.01/2.02 Prover 4: Constructing countermodel ...
% 9.01/2.02 Prover 7: Warning: ignoring some quantifiers
% 9.01/2.05 Prover 7: Constructing countermodel ...
% 9.61/2.10 Prover 8: Warning: ignoring some quantifiers
% 9.61/2.11 Prover 0: Proving ...
% 9.61/2.11 Prover 8: Constructing countermodel ...
% 11.27/2.28 Prover 9: Constructing countermodel ...
% 11.93/2.39 Prover 8: gave up
% 11.93/2.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.60/2.45 Prover 10: Preprocessing ...
% 12.99/2.51 Prover 10: Warning: ignoring some quantifiers
% 12.99/2.53 Prover 10: Constructing countermodel ...
% 13.47/2.58 Prover 7: gave up
% 13.47/2.58 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.95/2.64 Prover 11: Preprocessing ...
% 14.40/2.70 Prover 10: gave up
% 14.40/2.71 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 14.82/2.76 Prover 12: Preprocessing ...
% 15.90/2.88 Prover 11: Constructing countermodel ...
% 15.90/2.92 Prover 12: Proving ...
% 16.73/3.01 Prover 0: proved (2372ms)
% 16.73/3.01
% 16.73/3.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.73/3.01
% 16.73/3.01 Prover 9: stopped
% 16.73/3.01 Prover 5: stopped
% 16.73/3.01 Prover 12: stopped
% 17.02/3.02 Prover 2: stopped
% 17.02/3.02 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 17.02/3.02 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 17.02/3.02 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 17.13/3.05 Prover 16: Preprocessing ...
% 17.13/3.06 Prover 19: Preprocessing ...
% 17.13/3.06 Prover 13: Preprocessing ...
% 17.13/3.10 Prover 16: Warning: ignoring some quantifiers
% 17.69/3.11 Prover 16: Constructing countermodel ...
% 17.69/3.11 Prover 13: Warning: ignoring some quantifiers
% 17.69/3.12 Prover 13: Constructing countermodel ...
% 17.69/3.16 Prover 19: Warning: ignoring some quantifiers
% 17.69/3.17 Prover 19: Constructing countermodel ...
% 18.65/3.31 Prover 13: gave up
% 18.65/3.33 Prover 19: gave up
% 27.31/4.67 Prover 16: gave up
% 28.80/4.91 Prover 11: Found proof (size 67)
% 28.80/4.91 Prover 11: proved (2328ms)
% 28.80/4.91 Prover 4: stopped
% 28.80/4.91
% 28.80/4.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.80/4.91
% 28.80/4.92 % SZS output start Proof for theBenchmark
% 28.80/4.92 Assumptions after simplification:
% 28.80/4.92 ---------------------------------
% 28.80/4.92
% 28.96/4.92 (apart3)
% 28.97/4.96 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0))
% 28.97/4.96
% 28.97/4.96 (ceq3)
% 28.97/4.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 28.97/4.97 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2)
% 28.97/4.97 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 28.97/4.97 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 28.97/4.97 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~
% 28.97/4.97 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 28.97/4.97 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 28.97/4.97 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~
% 28.97/4.97 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 28.97/4.97 convergent_lines(v0, v2) = 0)
% 28.97/4.97
% 28.97/4.97 (ci3)
% 28.97/4.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 28.97/4.97 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0)
% 28.97/4.97 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) &
% 28.97/4.97 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 28.97/4.97 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 28.97/4.97 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 &
% 28.97/4.97 apart_point_and_line(v2, v0) = v3 & $i(v2)))
% 28.97/4.97
% 28.97/4.97 (ci4)
% 28.97/4.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 28.97/4.97 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0)
% 28.97/4.97 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) &
% 28.97/4.97 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 28.97/4.97 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 28.97/4.97 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 &
% 28.97/4.97 apart_point_and_line(v2, v1) = v3 & $i(v2)))
% 28.97/4.97
% 28.97/4.97 (con)
% 28.97/4.98 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 28.97/4.98 int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & intersection_point(v2,
% 28.97/4.98 v3) = v4 & apart_point_and_line(v0, v3) = v6 & apart_point_and_line(v0,
% 28.97/4.98 v2) = v5 & convergent_lines(v2, v3) = 0 & distinct_points(v0, v4) = 0 &
% 28.97/4.98 distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 28.97/4.98
% 28.97/4.98 (cu1)
% 29.32/5.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 29.32/5.00 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 29.32/5.00 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 29.32/5.00 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 29.32/5.00 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 &
% 29.32/5.00 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2,
% 29.32/5.00 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 29.32/5.00 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1,
% 29.32/5.00 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~
% 29.32/5.01 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 29.32/5.01 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 29.32/5.01 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0,
% 29.32/5.01 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 29.32/5.01 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 29.32/5.01 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 29.32/5.01 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 29.32/5.01 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 =
% 29.32/5.01 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 &
% 29.32/5.01 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2,
% 29.32/5.01 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 29.32/5.01 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 29.32/5.01 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~
% 29.32/5.01 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 29.32/5.01 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 =
% 29.32/5.01 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 &
% 29.32/5.01 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2,
% 29.32/5.01 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 29.32/5.01 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 29.32/5.01 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~
% 29.32/5.01 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~
% 29.32/5.01 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 29.32/5.01 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 &
% 29.32/5.01 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0,
% 29.32/5.01 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 29.32/5.01 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0,
% 29.32/5.01 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~
% 29.32/5.01 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 29.32/5.01 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 29.32/5.01 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1,
% 29.32/5.01 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i]
% 29.32/5.01 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) |
% 29.32/5.01 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 29.32/5.01 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 =
% 29.32/5.01 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 &
% 29.32/5.01 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0,
% 29.32/5.01 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 29.32/5.01
% 29.32/5.01 (function-axioms)
% 29.32/5.02 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 29.32/5.02 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~
% 29.32/5.02 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 29.32/5.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.32/5.02 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2)
% 29.32/5.02 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 29.32/5.02 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~
% 29.32/5.02 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 29.32/5.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.32/5.02 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0:
% 29.32/5.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 29.32/5.02 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 29.32/5.02 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.32/5.02 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 29.32/5.02 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 29.32/5.02 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 29.32/5.02 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 29.32/5.02 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 29.32/5.02 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 29.32/5.02 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 29.32/5.02 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 29.32/5.02 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 29.32/5.02 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 29.32/5.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.32/5.02 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 29.32/5.02 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 29.32/5.02 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 29.32/5.02 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 29.32/5.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.32/5.02 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 29.32/5.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 29.32/5.02 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 29.32/5.02 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 29.32/5.02 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0:
% 29.32/5.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 29.32/5.02 ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 29.32/5.02
% 29.32/5.02 Further assumptions not needed in the proof:
% 29.32/5.02 --------------------------------------------
% 29.32/5.02 a3, a4, a5, apart1, apart2, apart4, apart5, ax1, ax2, ax6, ceq1, ceq2, ci1, ci2,
% 29.32/5.02 coipo1, con1, cotno1, couo1, cp1, cp2, cup1, int1, oac1, occu1, ooc1, ooc2,
% 29.32/5.02 orth1, ouo1, p1, par1
% 29.32/5.02
% 29.32/5.02 Those formulas are unsatisfiable:
% 29.32/5.02 ---------------------------------
% 29.32/5.02
% 29.32/5.02 Begin of proof
% 29.32/5.02 |
% 29.32/5.02 | ALPHA: (ci3) implies:
% 29.32/5.03 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0,
% 29.32/5.03 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] :
% 29.32/5.03 | (( ~ (v4 = 0) & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) &
% 29.32/5.03 | convergent_lines(v0, v1) = v3)))
% 29.32/5.03 |
% 29.32/5.03 | ALPHA: (ci4) implies:
% 29.32/5.03 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0,
% 29.32/5.03 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] :
% 29.32/5.03 | (( ~ (v4 = 0) & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) &
% 29.32/5.03 | convergent_lines(v0, v1) = v3)))
% 29.32/5.03 |
% 29.32/5.03 | ALPHA: (cu1) implies:
% 29.32/5.03 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 29.32/5.03 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5)
% 29.32/5.03 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0,
% 29.32/5.03 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 29.32/5.03 | [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 29.32/5.03 | apart_point_and_line(v1, v3) = 0) | (v7 = 0 &
% 29.32/5.03 | apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) &
% 29.32/5.03 | distinct_lines(v2, v3) = v6)))
% 29.32/5.03 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 29.32/5.03 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5)
% 29.32/5.03 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 29.32/5.03 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ?
% 29.32/5.03 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 &
% 29.32/5.03 | apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) &
% 29.32/5.03 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0,
% 29.32/5.03 | v1) = v6)))
% 29.32/5.03 |
% 29.32/5.03 | ALPHA: (ceq3) implies:
% 29.32/5.04 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 29.32/5.04 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) |
% 29.32/5.04 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0)
% 29.32/5.04 |
% 29.32/5.04 | ALPHA: (function-axioms) implies:
% 29.32/5.04 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 29.32/5.04 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 29.32/5.04 | (convergent_lines(v3, v2) = v0))
% 29.32/5.04 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 29.32/5.04 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 29.32/5.04 | (apart_point_and_line(v3, v2) = v0))
% 29.32/5.04 |
% 29.32/5.04 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2,
% 29.32/5.04 | all_38_3, all_38_4, all_38_5, all_38_6 gives:
% 29.32/5.04 | (8) ~ (all_38_0 = 0) & ~ (all_38_1 = 0) & intersection_point(all_38_4,
% 29.32/5.04 | all_38_3) = all_38_2 & apart_point_and_line(all_38_6, all_38_3) =
% 29.32/5.04 | all_38_0 & apart_point_and_line(all_38_6, all_38_4) = all_38_1 &
% 29.32/5.04 | convergent_lines(all_38_4, all_38_3) = 0 & distinct_points(all_38_6,
% 29.32/5.04 | all_38_2) = 0 & distinct_points(all_38_6, all_38_5) = 0 &
% 29.32/5.04 | $i(all_38_2) & $i(all_38_3) & $i(all_38_4) & $i(all_38_5) &
% 29.32/5.04 | $i(all_38_6)
% 29.32/5.04 |
% 29.32/5.04 | ALPHA: (8) implies:
% 29.32/5.04 | (9) ~ (all_38_1 = 0)
% 29.32/5.04 | (10) ~ (all_38_0 = 0)
% 29.32/5.04 | (11) $i(all_38_6)
% 29.32/5.04 | (12) $i(all_38_4)
% 29.32/5.04 | (13) $i(all_38_3)
% 29.32/5.04 | (14) $i(all_38_2)
% 29.32/5.04 | (15) distinct_points(all_38_6, all_38_2) = 0
% 29.32/5.04 | (16) convergent_lines(all_38_4, all_38_3) = 0
% 29.32/5.04 | (17) apart_point_and_line(all_38_6, all_38_4) = all_38_1
% 29.32/5.04 | (18) apart_point_and_line(all_38_6, all_38_3) = all_38_0
% 29.32/5.04 | (19) intersection_point(all_38_4, all_38_3) = all_38_2
% 29.32/5.04 |
% 29.32/5.05 | GROUND_INST: instantiating (3) with all_38_6, all_38_2, all_38_3, all_38_4,
% 29.32/5.05 | all_38_0, all_38_1, simplifying with (11), (12), (13), (14),
% 29.32/5.05 | (15), (17), (18) gives:
% 29.32/5.05 | (20) all_38_0 = 0 | all_38_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2:
% 29.32/5.05 | int] : ((v2 = 0 & apart_point_and_line(all_38_2, all_38_4) = 0) |
% 29.32/5.05 | (v1 = 0 & apart_point_and_line(all_38_2, all_38_3) = 0) | ( ~ (v0 =
% 29.32/5.05 | 0) & distinct_lines(all_38_3, all_38_4) = v0))
% 29.32/5.05 |
% 29.32/5.05 | GROUND_INST: instantiating (4) with all_38_6, all_38_6, all_38_3, all_38_4,
% 29.32/5.05 | all_38_1, all_38_0, simplifying with (11), (12), (13), (17), (18)
% 29.32/5.05 | gives:
% 29.32/5.05 | (21) all_38_0 = 0 | all_38_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2:
% 29.32/5.05 | int] : ? [v3: int] : ((v3 = 0 & apart_point_and_line(all_38_6,
% 29.32/5.05 | all_38_4) = 0) | (v2 = 0 & apart_point_and_line(all_38_6,
% 29.32/5.05 | all_38_3) = 0) | ( ~ (v1 = 0) & distinct_lines(all_38_3,
% 29.32/5.05 | all_38_4) = v1) | ( ~ (v0 = 0) & distinct_points(all_38_6,
% 29.32/5.05 | all_38_6) = v0))
% 29.32/5.05 |
% 29.32/5.05 | GROUND_INST: instantiating (2) with all_38_4, all_38_3, all_38_2, simplifying
% 29.32/5.05 | with (12), (13), (19) gives:
% 29.32/5.05 | (22) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) &
% 29.32/5.05 | apart_point_and_line(all_38_2, all_38_3) = v1) | ( ~ (v0 = 0) &
% 29.32/5.05 | convergent_lines(all_38_4, all_38_3) = v0))
% 29.32/5.05 |
% 29.32/5.05 | GROUND_INST: instantiating (1) with all_38_4, all_38_3, all_38_2, simplifying
% 29.32/5.05 | with (12), (13), (19) gives:
% 29.32/5.05 | (23) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) &
% 29.32/5.05 | apart_point_and_line(all_38_2, all_38_4) = v1) | ( ~ (v0 = 0) &
% 29.32/5.05 | convergent_lines(all_38_4, all_38_3) = v0))
% 29.32/5.05 |
% 29.32/5.05 | DELTA: instantiating (23) with fresh symbols all_51_0, all_51_1 gives:
% 29.32/5.05 | (24) ( ~ (all_51_0 = 0) & apart_point_and_line(all_38_2, all_38_4) =
% 29.32/5.05 | all_51_0) | ( ~ (all_51_1 = 0) & convergent_lines(all_38_4,
% 29.32/5.05 | all_38_3) = all_51_1)
% 29.32/5.05 |
% 29.32/5.05 | DELTA: instantiating (22) with fresh symbols all_62_0, all_62_1 gives:
% 29.32/5.06 | (25) ( ~ (all_62_0 = 0) & apart_point_and_line(all_38_2, all_38_3) =
% 29.32/5.06 | all_62_0) | ( ~ (all_62_1 = 0) & convergent_lines(all_38_4,
% 29.32/5.06 | all_38_3) = all_62_1)
% 29.32/5.06 |
% 29.32/5.06 | BETA: splitting (24) gives:
% 29.32/5.06 |
% 29.32/5.06 | Case 1:
% 29.32/5.06 | |
% 29.32/5.06 | | (26) ~ (all_51_0 = 0) & apart_point_and_line(all_38_2, all_38_4) =
% 29.32/5.06 | | all_51_0
% 29.32/5.06 | |
% 29.32/5.06 | | ALPHA: (26) implies:
% 29.32/5.06 | | (27) ~ (all_51_0 = 0)
% 29.32/5.06 | | (28) apart_point_and_line(all_38_2, all_38_4) = all_51_0
% 29.32/5.06 | |
% 29.32/5.06 | | BETA: splitting (20) gives:
% 29.32/5.06 | |
% 29.32/5.06 | | Case 1:
% 29.32/5.06 | | |
% 29.32/5.06 | | | (29) all_38_0 = 0
% 29.32/5.06 | | |
% 29.32/5.06 | | | REDUCE: (10), (29) imply:
% 29.32/5.06 | | | (30) $false
% 29.32/5.06 | | |
% 29.32/5.06 | | | CLOSE: (30) is inconsistent.
% 29.32/5.06 | | |
% 29.32/5.06 | | Case 2:
% 29.32/5.06 | | |
% 29.32/5.06 | | | (31) all_38_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 =
% 29.32/5.06 | | | 0 & apart_point_and_line(all_38_2, all_38_4) = 0) | (v1 = 0 &
% 29.32/5.06 | | | apart_point_and_line(all_38_2, all_38_3) = 0) | ( ~ (v0 = 0) &
% 29.32/5.06 | | | distinct_lines(all_38_3, all_38_4) = v0))
% 29.32/5.06 | | |
% 29.32/5.06 | | | BETA: splitting (25) gives:
% 29.32/5.06 | | |
% 29.32/5.06 | | | Case 1:
% 29.32/5.06 | | | |
% 29.32/5.06 | | | | (32) ~ (all_62_0 = 0) & apart_point_and_line(all_38_2, all_38_3) =
% 29.32/5.06 | | | | all_62_0
% 29.32/5.06 | | | |
% 29.32/5.06 | | | | ALPHA: (32) implies:
% 29.32/5.06 | | | | (33) ~ (all_62_0 = 0)
% 29.32/5.06 | | | | (34) apart_point_and_line(all_38_2, all_38_3) = all_62_0
% 29.32/5.06 | | | |
% 29.32/5.06 | | | | BETA: splitting (21) gives:
% 29.32/5.06 | | | |
% 29.32/5.06 | | | | Case 1:
% 29.32/5.06 | | | | |
% 29.32/5.06 | | | | | (35) all_38_0 = 0
% 29.32/5.06 | | | | |
% 29.32/5.06 | | | | | REDUCE: (10), (35) imply:
% 29.32/5.06 | | | | | (36) $false
% 29.32/5.06 | | | | |
% 29.32/5.06 | | | | | CLOSE: (36) is inconsistent.
% 29.32/5.06 | | | | |
% 29.32/5.06 | | | | Case 2:
% 29.32/5.06 | | | | |
% 29.32/5.06 | | | | | (37) all_38_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 29.32/5.06 | | | | | [v3: int] : ((v3 = 0 & apart_point_and_line(all_38_6,
% 29.32/5.06 | | | | | all_38_4) = 0) | (v2 = 0 &
% 29.32/5.06 | | | | | apart_point_and_line(all_38_6, all_38_3) = 0) | ( ~ (v1 =
% 29.32/5.06 | | | | | 0) & distinct_lines(all_38_3, all_38_4) = v1) | ( ~ (v0
% 29.32/5.06 | | | | | = 0) & distinct_points(all_38_6, all_38_6) = v0))
% 29.32/5.06 | | | | |
% 29.32/5.06 | | | | | BETA: splitting (31) gives:
% 29.32/5.06 | | | | |
% 29.32/5.06 | | | | | Case 1:
% 29.32/5.06 | | | | | |
% 29.32/5.07 | | | | | | (38) all_38_1 = 0
% 29.32/5.07 | | | | | |
% 29.32/5.07 | | | | | | REDUCE: (9), (38) imply:
% 29.32/5.07 | | | | | | (39) $false
% 29.32/5.07 | | | | | |
% 29.32/5.07 | | | | | | CLOSE: (39) is inconsistent.
% 29.32/5.07 | | | | | |
% 29.32/5.07 | | | | | Case 2:
% 29.32/5.07 | | | | | |
% 29.32/5.07 | | | | | | (40) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 29.32/5.07 | | | | | | apart_point_and_line(all_38_2, all_38_4) = 0) | (v1 = 0
% 29.32/5.07 | | | | | | & apart_point_and_line(all_38_2, all_38_3) = 0) | ( ~
% 29.32/5.07 | | | | | | (v0 = 0) & distinct_lines(all_38_3, all_38_4) = v0))
% 29.32/5.07 | | | | | |
% 29.32/5.07 | | | | | | DELTA: instantiating (40) with fresh symbols all_162_0, all_162_1,
% 29.32/5.07 | | | | | | all_162_2 gives:
% 29.32/5.07 | | | | | | (41) (all_162_0 = 0 & apart_point_and_line(all_38_2, all_38_4) =
% 29.32/5.07 | | | | | | 0) | (all_162_1 = 0 & apart_point_and_line(all_38_2,
% 29.32/5.07 | | | | | | all_38_3) = 0) | ( ~ (all_162_2 = 0) &
% 29.32/5.07 | | | | | | distinct_lines(all_38_3, all_38_4) = all_162_2)
% 29.32/5.07 | | | | | |
% 29.32/5.07 | | | | | | BETA: splitting (41) gives:
% 29.32/5.07 | | | | | |
% 29.32/5.07 | | | | | | Case 1:
% 29.32/5.07 | | | | | | |
% 29.32/5.07 | | | | | | | (42) all_162_0 = 0 & apart_point_and_line(all_38_2, all_38_4) =
% 29.32/5.07 | | | | | | | 0
% 29.32/5.07 | | | | | | |
% 29.32/5.07 | | | | | | | ALPHA: (42) implies:
% 29.32/5.07 | | | | | | | (43) apart_point_and_line(all_38_2, all_38_4) = 0
% 29.32/5.07 | | | | | | |
% 29.68/5.07 | | | | | | | GROUND_INST: instantiating (7) with 0, all_51_0, all_38_4,
% 29.68/5.07 | | | | | | | all_38_2, simplifying with (28), (43) gives:
% 29.68/5.07 | | | | | | | (44) all_51_0 = 0
% 29.68/5.07 | | | | | | |
% 29.68/5.07 | | | | | | | REDUCE: (27), (44) imply:
% 29.68/5.07 | | | | | | | (45) $false
% 29.68/5.07 | | | | | | |
% 29.68/5.07 | | | | | | | CLOSE: (45) is inconsistent.
% 29.68/5.07 | | | | | | |
% 29.68/5.07 | | | | | | Case 2:
% 29.68/5.07 | | | | | | |
% 29.68/5.07 | | | | | | | (46) (all_162_1 = 0 & apart_point_and_line(all_38_2, all_38_3)
% 29.68/5.07 | | | | | | | = 0) | ( ~ (all_162_2 = 0) & distinct_lines(all_38_3,
% 29.68/5.07 | | | | | | | all_38_4) = all_162_2)
% 29.68/5.07 | | | | | | |
% 29.68/5.07 | | | | | | | BETA: splitting (46) gives:
% 29.68/5.07 | | | | | | |
% 29.68/5.07 | | | | | | | Case 1:
% 29.68/5.07 | | | | | | | |
% 29.68/5.07 | | | | | | | | (47) all_162_1 = 0 & apart_point_and_line(all_38_2, all_38_3)
% 29.68/5.07 | | | | | | | | = 0
% 29.68/5.07 | | | | | | | |
% 29.68/5.07 | | | | | | | | ALPHA: (47) implies:
% 29.68/5.07 | | | | | | | | (48) apart_point_and_line(all_38_2, all_38_3) = 0
% 29.68/5.07 | | | | | | | |
% 29.68/5.07 | | | | | | | | GROUND_INST: instantiating (7) with 0, all_62_0, all_38_3,
% 29.68/5.07 | | | | | | | | all_38_2, simplifying with (34), (48) gives:
% 29.68/5.07 | | | | | | | | (49) all_62_0 = 0
% 29.68/5.07 | | | | | | | |
% 29.68/5.07 | | | | | | | | REDUCE: (33), (49) imply:
% 29.68/5.07 | | | | | | | | (50) $false
% 29.68/5.07 | | | | | | | |
% 29.68/5.07 | | | | | | | | CLOSE: (50) is inconsistent.
% 29.68/5.07 | | | | | | | |
% 29.68/5.07 | | | | | | | Case 2:
% 29.68/5.07 | | | | | | | |
% 29.68/5.07 | | | | | | | | (51) ~ (all_162_2 = 0) & distinct_lines(all_38_3, all_38_4)
% 29.68/5.07 | | | | | | | | = all_162_2
% 29.68/5.07 | | | | | | | |
% 29.68/5.07 | | | | | | | | ALPHA: (51) implies:
% 29.68/5.07 | | | | | | | | (52) ~ (all_162_2 = 0)
% 29.68/5.07 | | | | | | | | (53) distinct_lines(all_38_3, all_38_4) = all_162_2
% 29.68/5.07 | | | | | | | |
% 29.68/5.07 | | | | | | | | BETA: splitting (37) gives:
% 29.68/5.07 | | | | | | | |
% 29.68/5.07 | | | | | | | | Case 1:
% 29.68/5.07 | | | | | | | | |
% 29.68/5.07 | | | | | | | | | (54) all_38_1 = 0
% 29.68/5.07 | | | | | | | | |
% 29.68/5.07 | | | | | | | | | REDUCE: (9), (54) imply:
% 29.68/5.07 | | | | | | | | | (55) $false
% 29.68/5.07 | | | | | | | | |
% 29.68/5.07 | | | | | | | | | CLOSE: (55) is inconsistent.
% 29.68/5.07 | | | | | | | | |
% 29.68/5.07 | | | | | | | | Case 2:
% 29.68/5.07 | | | | | | | | |
% 29.68/5.07 | | | | | | | | |
% 29.68/5.07 | | | | | | | | | GROUND_INST: instantiating (5) with all_38_4, all_38_3,
% 29.68/5.07 | | | | | | | | | all_38_4, all_162_2, simplifying with (12), (13),
% 29.68/5.07 | | | | | | | | | (16), (53) gives:
% 29.68/5.08 | | | | | | | | | (56) all_162_2 = 0 | convergent_lines(all_38_4, all_38_4) =
% 29.68/5.08 | | | | | | | | | 0
% 29.68/5.08 | | | | | | | | |
% 29.68/5.08 | | | | | | | | | BETA: splitting (56) gives:
% 29.68/5.08 | | | | | | | | |
% 29.68/5.08 | | | | | | | | | Case 1:
% 29.68/5.08 | | | | | | | | | |
% 29.68/5.08 | | | | | | | | | | (57) convergent_lines(all_38_4, all_38_4) = 0
% 29.68/5.08 | | | | | | | | | |
% 29.68/5.08 | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_38_4, simplifying
% 29.68/5.08 | | | | | | | | | | with (12), (57) gives:
% 29.68/5.08 | | | | | | | | | | (58) $false
% 29.68/5.08 | | | | | | | | | |
% 29.68/5.08 | | | | | | | | | | CLOSE: (58) is inconsistent.
% 29.68/5.08 | | | | | | | | | |
% 29.68/5.08 | | | | | | | | | Case 2:
% 29.68/5.08 | | | | | | | | | |
% 29.68/5.08 | | | | | | | | | | (59) all_162_2 = 0
% 29.68/5.08 | | | | | | | | | |
% 29.68/5.08 | | | | | | | | | | REDUCE: (52), (59) imply:
% 29.68/5.08 | | | | | | | | | | (60) $false
% 29.68/5.08 | | | | | | | | | |
% 29.68/5.08 | | | | | | | | | | CLOSE: (60) is inconsistent.
% 29.68/5.08 | | | | | | | | | |
% 29.68/5.08 | | | | | | | | | End of split
% 29.68/5.08 | | | | | | | | |
% 29.68/5.08 | | | | | | | | End of split
% 29.68/5.08 | | | | | | | |
% 29.68/5.08 | | | | | | | End of split
% 29.68/5.08 | | | | | | |
% 29.68/5.08 | | | | | | End of split
% 29.68/5.08 | | | | | |
% 29.68/5.08 | | | | | End of split
% 29.68/5.08 | | | | |
% 29.68/5.08 | | | | End of split
% 29.68/5.08 | | | |
% 29.68/5.08 | | | Case 2:
% 29.68/5.08 | | | |
% 29.68/5.08 | | | | (61) ~ (all_62_1 = 0) & convergent_lines(all_38_4, all_38_3) =
% 29.68/5.08 | | | | all_62_1
% 29.68/5.08 | | | |
% 29.68/5.08 | | | | ALPHA: (61) implies:
% 29.68/5.08 | | | | (62) ~ (all_62_1 = 0)
% 29.68/5.08 | | | | (63) convergent_lines(all_38_4, all_38_3) = all_62_1
% 29.68/5.08 | | | |
% 29.68/5.08 | | | | GROUND_INST: instantiating (6) with 0, all_62_1, all_38_3, all_38_4,
% 29.68/5.08 | | | | simplifying with (16), (63) gives:
% 29.68/5.08 | | | | (64) all_62_1 = 0
% 29.68/5.08 | | | |
% 29.68/5.08 | | | | REDUCE: (62), (64) imply:
% 29.68/5.08 | | | | (65) $false
% 29.68/5.08 | | | |
% 29.68/5.08 | | | | CLOSE: (65) is inconsistent.
% 29.68/5.08 | | | |
% 29.68/5.08 | | | End of split
% 29.68/5.08 | | |
% 29.68/5.08 | | End of split
% 29.68/5.08 | |
% 29.68/5.08 | Case 2:
% 29.68/5.08 | |
% 29.68/5.08 | | (66) ~ (all_51_1 = 0) & convergent_lines(all_38_4, all_38_3) = all_51_1
% 29.68/5.08 | |
% 29.68/5.08 | | ALPHA: (66) implies:
% 29.68/5.08 | | (67) ~ (all_51_1 = 0)
% 29.68/5.08 | | (68) convergent_lines(all_38_4, all_38_3) = all_51_1
% 29.68/5.08 | |
% 29.68/5.08 | | GROUND_INST: instantiating (6) with 0, all_51_1, all_38_3, all_38_4,
% 29.68/5.08 | | simplifying with (16), (68) gives:
% 29.68/5.08 | | (69) all_51_1 = 0
% 29.68/5.08 | |
% 29.68/5.08 | | REDUCE: (67), (69) imply:
% 29.68/5.08 | | (70) $false
% 29.68/5.08 | |
% 29.68/5.08 | | CLOSE: (70) is inconsistent.
% 29.68/5.08 | |
% 29.68/5.08 | End of split
% 29.68/5.08 |
% 29.68/5.08 End of proof
% 29.68/5.08 % SZS output end Proof for theBenchmark
% 29.68/5.08
% 29.68/5.08 4469ms
%------------------------------------------------------------------------------