TSTP Solution File: GEO226+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO226+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 : 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 23:22:34 EDT 2023
% Result : Theorem 15.36s 2.92s
% Output : Proof 26.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GEO226+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Aug 29 21:02:06 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.18/0.59 ________ _____
% 0.18/0.59 ___ __ \_________(_)________________________________
% 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.59
% 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.59 (2023-06-19)
% 0.18/0.59
% 0.18/0.59 (c) Philipp Rümmer, 2009-2023
% 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.59 Amanda Stjerna.
% 0.18/0.59 Free software under BSD-3-Clause.
% 0.18/0.59
% 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.59
% 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.60 Running up to 7 provers in parallel.
% 0.18/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.82/1.26 Prover 4: Preprocessing ...
% 2.82/1.26 Prover 1: Preprocessing ...
% 3.50/1.32 Prover 0: Preprocessing ...
% 3.50/1.32 Prover 6: Preprocessing ...
% 3.50/1.32 Prover 5: Preprocessing ...
% 3.50/1.32 Prover 2: Preprocessing ...
% 3.50/1.32 Prover 3: Preprocessing ...
% 7.69/1.91 Prover 5: Proving ...
% 7.69/1.91 Prover 2: Proving ...
% 9.06/2.08 Prover 3: Constructing countermodel ...
% 9.06/2.09 Prover 6: Proving ...
% 9.48/2.11 Prover 1: Constructing countermodel ...
% 9.88/2.19 Prover 3: gave up
% 9.88/2.20 Prover 1: gave up
% 9.88/2.20 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.88/2.20 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.79/2.33 Prover 7: Preprocessing ...
% 11.14/2.34 Prover 8: Preprocessing ...
% 11.61/2.49 Prover 4: Constructing countermodel ...
% 11.61/2.51 Prover 7: Warning: ignoring some quantifiers
% 12.56/2.57 Prover 7: Constructing countermodel ...
% 12.56/2.58 Prover 0: Proving ...
% 13.55/2.69 Prover 8: Warning: ignoring some quantifiers
% 13.86/2.72 Prover 8: Constructing countermodel ...
% 14.90/2.87 Prover 8: gave up
% 15.36/2.90 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 15.36/2.92 Prover 0: proved (2312ms)
% 15.36/2.92
% 15.36/2.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.36/2.92
% 15.36/2.92 Prover 2: stopped
% 15.36/2.92 Prover 5: stopped
% 15.36/2.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.36/2.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.36/2.93 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.36/2.94 Prover 6: stopped
% 15.36/2.96 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 15.88/2.98 Prover 10: Preprocessing ...
% 15.88/2.98 Prover 9: Preprocessing ...
% 15.88/2.98 Prover 11: Preprocessing ...
% 16.18/3.02 Prover 13: Preprocessing ...
% 16.42/3.04 Prover 16: Preprocessing ...
% 16.42/3.07 Prover 10: Warning: ignoring some quantifiers
% 16.42/3.09 Prover 10: Constructing countermodel ...
% 17.15/3.17 Prover 13: Warning: ignoring some quantifiers
% 17.15/3.20 Prover 13: Constructing countermodel ...
% 17.15/3.24 Prover 16: Warning: ignoring some quantifiers
% 17.15/3.26 Prover 16: Constructing countermodel ...
% 17.89/3.31 Prover 7: gave up
% 17.89/3.33 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 18.68/3.39 Prover 9: Constructing countermodel ...
% 19.09/3.40 Prover 19: Preprocessing ...
% 19.09/3.41 Prover 9: stopped
% 19.09/3.43 Prover 10: gave up
% 19.09/3.45 Prover 11: Constructing countermodel ...
% 20.45/3.62 Prover 19: Warning: ignoring some quantifiers
% 20.45/3.63 Prover 13: gave up
% 20.45/3.64 Prover 19: Constructing countermodel ...
% 21.71/3.84 Prover 19: gave up
% 25.22/4.26 Prover 11: Found proof (size 58)
% 25.22/4.26 Prover 11: proved (1339ms)
% 25.22/4.26 Prover 4: stopped
% 25.22/4.27 Prover 16: stopped
% 25.22/4.27
% 25.22/4.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.22/4.27
% 25.22/4.28 % SZS output start Proof for theBenchmark
% 25.22/4.28 Assumptions after simplification:
% 25.22/4.28 ---------------------------------
% 25.22/4.28
% 25.22/4.28 (a4)
% 25.43/4.33 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 25.43/4.33 (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 25.43/4.33 apart_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int]
% 25.43/4.33 : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 25.43/4.33 incident_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 25.43/4.33 (incident_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int]
% 25.43/4.33 : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0: $i] : ! [v1:
% 25.43/4.33 $i] : ( ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 25.43/4.33 [v2: int] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 25.43/4.33
% 25.43/4.33 (ci3)
% 25.43/4.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 25.43/4.33 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0)
% 25.43/4.33 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) &
% 25.43/4.33 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 25.43/4.33 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 25.43/4.33 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 &
% 25.43/4.34 apart_point_and_line(v2, v0) = v3 & $i(v2)))
% 25.43/4.34
% 25.43/4.34 (ci4)
% 25.43/4.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 25.43/4.34 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0)
% 25.43/4.34 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) &
% 25.43/4.34 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 25.43/4.34 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 25.43/4.34 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 &
% 25.43/4.34 apart_point_and_line(v2, v1) = v3 & $i(v2)))
% 25.43/4.34
% 25.43/4.34 (con)
% 25.59/4.35 ? [v0: $i] : ? [v1: $i] : (line(v1) = 0 & line(v0) = 0 &
% 25.59/4.35 convergent_lines(v0, v1) = 0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: int]
% 25.59/4.35 : (v3 = 0 | ~ (point(v2) = v3) | ~ $i(v2)) & ! [v2: $i] : ( ~
% 25.59/4.35 (incident_point_and_line(v2, v1) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3
% 25.59/4.35 = 0) & incident_point_and_line(v2, v0) = v3)) & ! [v2: $i] : ( ~
% 25.59/4.35 (incident_point_and_line(v2, v0) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3
% 25.59/4.35 = 0) & incident_point_and_line(v2, v1) = v3)))
% 25.59/4.35
% 25.59/4.35 (cu1)
% 25.59/4.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 25.59/4.37 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 25.59/4.37 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 25.59/4.37 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 25.59/4.37 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 &
% 25.59/4.37 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2,
% 25.59/4.37 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 25.59/4.37 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1,
% 25.59/4.37 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~
% 25.59/4.37 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 25.59/4.37 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 25.59/4.37 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0,
% 25.59/4.37 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 25.59/4.37 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 25.59/4.37 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 25.59/4.37 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 25.59/4.37 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 =
% 25.59/4.37 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 &
% 25.59/4.37 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2,
% 25.59/4.37 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 25.59/4.37 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 25.59/4.37 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~
% 25.59/4.37 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 25.59/4.37 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 =
% 25.59/4.37 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 &
% 25.59/4.37 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2,
% 25.59/4.37 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 25.59/4.37 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 25.59/4.37 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~
% 25.59/4.37 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~
% 25.59/4.37 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 25.59/4.37 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 &
% 25.59/4.37 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0,
% 25.59/4.37 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 25.59/4.37 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0,
% 25.59/4.37 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~
% 25.59/4.37 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 25.59/4.37 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 25.59/4.37 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1,
% 25.59/4.37 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i]
% 25.59/4.37 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) |
% 25.59/4.37 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 25.59/4.37 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 =
% 25.59/4.37 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 &
% 25.59/4.37 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0,
% 25.59/4.37 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 25.59/4.37
% 25.59/4.37 (int1)
% 25.59/4.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 25.59/4.39 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ? [v5: int] :
% 25.59/4.39 ? [v6: int] : ((v6 = 0 & point(v2) = 0) | ( ~ (v5 = 0) &
% 25.59/4.39 convergent_lines(v0, v1) = v5) | ( ~ (v4 = 0) & line(v1) = v4) | ( ~ (v3
% 25.59/4.39 = 0) & line(v0) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 25.59/4.39 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ?
% 25.59/4.39 [v3: int] : ? [v4: $i] : ? [v5: int] : ((v5 = 0 & point(v4) = 0 &
% 25.59/4.39 intersection_point(v0, v1) = v4 & $i(v4)) | ( ~ (v3 = 0) & line(v1) =
% 25.59/4.39 v3) | ( ~ (v2 = 0) & line(v0) = v2)))
% 25.59/4.39
% 25.59/4.39 (function-axioms)
% 25.59/4.39 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 25.59/4.39 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~
% 25.59/4.39 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 25.59/4.39 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 25.59/4.39 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2)
% 25.59/4.39 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 25.59/4.39 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~
% 25.59/4.40 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 25.59/4.40 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 25.59/4.40 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0:
% 25.59/4.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 25.59/4.40 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 25.59/4.40 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 25.59/4.40 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 25.59/4.40 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 25.59/4.40 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 25.59/4.40 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 25.59/4.40 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 25.59/4.40 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 25.59/4.40 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 25.59/4.40 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 25.59/4.40 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 25.59/4.40 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 25.59/4.40 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 25.59/4.40 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 25.59/4.40 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 25.59/4.40 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 25.59/4.40 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 25.59/4.40 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 25.59/4.40 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 25.59/4.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 25.59/4.40 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 25.59/4.40 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 25.59/4.40 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0:
% 25.59/4.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 25.59/4.40 ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 25.59/4.40
% 25.59/4.40 Further assumptions not needed in the proof:
% 25.59/4.40 --------------------------------------------
% 25.59/4.40 a3, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ax6, ceq1, ceq2, ceq3,
% 25.59/4.40 ci1, ci2, coipo1, con1, cotno1, couo1, cp1, cp2, cup1, oac1, occu1, ooc1, ooc2,
% 25.59/4.40 orth1, ouo1, p1, par1
% 25.59/4.40
% 25.59/4.40 Those formulas are unsatisfiable:
% 25.59/4.40 ---------------------------------
% 25.59/4.40
% 25.59/4.40 Begin of proof
% 25.59/4.40 |
% 25.59/4.40 | ALPHA: (ci3) implies:
% 25.59/4.40 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~
% 25.59/4.40 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 25.59/4.40 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3
% 25.59/4.40 | & $i(v2)))
% 25.59/4.40 |
% 25.59/4.40 | ALPHA: (ci4) implies:
% 25.59/4.40 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~
% 25.59/4.40 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 25.59/4.40 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3
% 25.59/4.40 | & $i(v2)))
% 25.59/4.40 |
% 25.59/4.40 | ALPHA: (cu1) implies:
% 25.59/4.41 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 25.59/4.41 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5)
% 25.59/4.41 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 25.59/4.41 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ?
% 25.59/4.41 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 &
% 25.59/4.41 | apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) &
% 25.59/4.41 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0,
% 25.59/4.41 | v1) = v6)))
% 25.59/4.41 |
% 25.59/4.41 | ALPHA: (int1) implies:
% 25.59/4.41 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~
% 25.59/4.41 | $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ? [v4: $i] : ?
% 25.59/4.41 | [v5: int] : ((v5 = 0 & point(v4) = 0 & intersection_point(v0, v1) =
% 25.59/4.41 | v4 & $i(v4)) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v2 = 0) &
% 25.59/4.41 | line(v0) = v2)))
% 25.59/4.41 |
% 25.59/4.41 | ALPHA: (a4) implies:
% 25.59/4.41 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 25.59/4.41 | (apart_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 25.59/4.41 | incident_point_and_line(v0, v1) = 0)
% 25.59/4.41 |
% 25.59/4.41 | ALPHA: (function-axioms) implies:
% 25.59/4.41 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 25.59/4.41 | (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 25.59/4.41 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 25.59/4.41 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) =
% 25.59/4.41 | v0))
% 25.59/4.41 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 25.59/4.41 | ! [v3: $i] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~
% 25.59/4.41 | (incident_point_and_line(v3, v2) = v0))
% 25.59/4.41 |
% 25.59/4.41 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1 gives:
% 25.59/4.42 | (9) line(all_38_0) = 0 & line(all_38_1) = 0 & convergent_lines(all_38_1,
% 25.59/4.42 | all_38_0) = 0 & $i(all_38_0) & $i(all_38_1) & ! [v0: $i] : ! [v1:
% 25.59/4.42 | int] : (v1 = 0 | ~ (point(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( ~
% 25.59/4.42 | (incident_point_and_line(v0, all_38_0) = 0) | ~ $i(v0) | ? [v1:
% 25.59/4.42 | int] : ( ~ (v1 = 0) & incident_point_and_line(v0, all_38_1) = v1))
% 25.59/4.42 | & ! [v0: $i] : ( ~ (incident_point_and_line(v0, all_38_1) = 0) | ~
% 25.59/4.42 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & incident_point_and_line(v0,
% 25.59/4.42 | all_38_0) = v1))
% 25.59/4.42 |
% 25.59/4.42 | ALPHA: (9) implies:
% 25.59/4.42 | (10) $i(all_38_1)
% 25.59/4.42 | (11) $i(all_38_0)
% 25.59/4.42 | (12) convergent_lines(all_38_1, all_38_0) = 0
% 25.59/4.42 | (13) line(all_38_1) = 0
% 25.59/4.42 | (14) line(all_38_0) = 0
% 25.59/4.42 | (15) ! [v0: $i] : ( ~ (incident_point_and_line(v0, all_38_0) = 0) | ~
% 25.59/4.42 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & incident_point_and_line(v0,
% 25.59/4.42 | all_38_1) = v1))
% 25.59/4.42 |
% 25.59/4.42 | GROUND_INST: instantiating (4) with all_38_1, all_38_0, simplifying with (10),
% 25.59/4.42 | (11), (12) gives:
% 25.59/4.42 | (16) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? [v3: int] : ((v3 = 0 &
% 25.59/4.42 | point(v2) = 0 & intersection_point(all_38_1, all_38_0) = v2 &
% 25.59/4.42 | $i(v2)) | ( ~ (v1 = 0) & line(all_38_0) = v1) | ( ~ (v0 = 0) &
% 25.59/4.42 | line(all_38_1) = v0))
% 25.59/4.42 |
% 25.59/4.42 | GROUND_INST: instantiating (2) with all_38_1, all_38_0, simplifying with (10),
% 25.59/4.42 | (11), (12) gives:
% 25.59/4.43 | (17) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 25.59/4.43 | intersection_point(all_38_1, all_38_0) = v0 &
% 25.59/4.43 | apart_point_and_line(v0, all_38_0) = v1 & $i(v0))
% 25.59/4.43 |
% 25.59/4.43 | GROUND_INST: instantiating (1) with all_38_1, all_38_0, simplifying with (10),
% 25.59/4.43 | (11), (12) gives:
% 25.59/4.43 | (18) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 25.59/4.43 | intersection_point(all_38_1, all_38_0) = v0 &
% 25.59/4.43 | apart_point_and_line(v0, all_38_1) = v1 & $i(v0))
% 25.59/4.43 |
% 25.59/4.43 | DELTA: instantiating (18) with fresh symbols all_48_0, all_48_1 gives:
% 25.59/4.43 | (19) ~ (all_48_0 = 0) & intersection_point(all_38_1, all_38_0) = all_48_1
% 25.59/4.43 | & apart_point_and_line(all_48_1, all_38_1) = all_48_0 & $i(all_48_1)
% 25.59/4.43 |
% 25.59/4.43 | ALPHA: (19) implies:
% 25.59/4.43 | (20) ~ (all_48_0 = 0)
% 25.59/4.43 | (21) apart_point_and_line(all_48_1, all_38_1) = all_48_0
% 25.59/4.43 | (22) intersection_point(all_38_1, all_38_0) = all_48_1
% 25.59/4.43 |
% 25.59/4.43 | DELTA: instantiating (17) with fresh symbols all_50_0, all_50_1 gives:
% 25.59/4.43 | (23) ~ (all_50_0 = 0) & intersection_point(all_38_1, all_38_0) = all_50_1
% 25.59/4.43 | & apart_point_and_line(all_50_1, all_38_0) = all_50_0 & $i(all_50_1)
% 25.59/4.43 |
% 25.59/4.43 | ALPHA: (23) implies:
% 25.59/4.43 | (24) ~ (all_50_0 = 0)
% 25.59/4.43 | (25) $i(all_50_1)
% 25.59/4.43 | (26) apart_point_and_line(all_50_1, all_38_0) = all_50_0
% 26.03/4.43 | (27) intersection_point(all_38_1, all_38_0) = all_50_1
% 26.03/4.43 |
% 26.03/4.43 | DELTA: instantiating (16) with fresh symbols all_52_0, all_52_1, all_52_2,
% 26.03/4.43 | all_52_3 gives:
% 26.03/4.43 | (28) (all_52_0 = 0 & point(all_52_1) = 0 & intersection_point(all_38_1,
% 26.03/4.43 | all_38_0) = all_52_1 & $i(all_52_1)) | ( ~ (all_52_2 = 0) &
% 26.03/4.43 | line(all_38_0) = all_52_2) | ( ~ (all_52_3 = 0) & line(all_38_1) =
% 26.03/4.43 | all_52_3)
% 26.03/4.43 |
% 26.03/4.43 | BETA: splitting (28) gives:
% 26.03/4.43 |
% 26.03/4.43 | Case 1:
% 26.03/4.43 | |
% 26.03/4.43 | | (29) all_52_0 = 0 & point(all_52_1) = 0 & intersection_point(all_38_1,
% 26.03/4.43 | | all_38_0) = all_52_1 & $i(all_52_1)
% 26.03/4.43 | |
% 26.03/4.43 | | ALPHA: (29) implies:
% 26.03/4.43 | | (30) intersection_point(all_38_1, all_38_0) = all_52_1
% 26.03/4.44 | |
% 26.03/4.44 | | GROUND_INST: instantiating (7) with all_50_1, all_52_1, all_38_0, all_38_1,
% 26.03/4.44 | | simplifying with (27), (30) gives:
% 26.03/4.44 | | (31) all_52_1 = all_50_1
% 26.03/4.44 | |
% 26.03/4.44 | | GROUND_INST: instantiating (7) with all_48_1, all_52_1, all_38_0, all_38_1,
% 26.03/4.44 | | simplifying with (22), (30) gives:
% 26.03/4.44 | | (32) all_52_1 = all_48_1
% 26.03/4.44 | |
% 26.03/4.44 | | COMBINE_EQS: (31), (32) imply:
% 26.03/4.44 | | (33) all_50_1 = all_48_1
% 26.03/4.44 | |
% 26.03/4.44 | | SIMP: (33) implies:
% 26.03/4.44 | | (34) all_50_1 = all_48_1
% 26.03/4.44 | |
% 26.03/4.44 | | REDUCE: (26), (34) imply:
% 26.03/4.44 | | (35) apart_point_and_line(all_48_1, all_38_0) = all_50_0
% 26.03/4.44 | |
% 26.03/4.44 | | REDUCE: (25), (34) imply:
% 26.03/4.44 | | (36) $i(all_48_1)
% 26.03/4.44 | |
% 26.03/4.44 | | GROUND_INST: instantiating (5) with all_48_1, all_38_1, all_48_0,
% 26.03/4.44 | | simplifying with (10), (21), (36) gives:
% 26.03/4.44 | | (37) all_48_0 = 0 | incident_point_and_line(all_48_1, all_38_1) = 0
% 26.03/4.44 | |
% 26.03/4.44 | | GROUND_INST: instantiating (3) with all_48_1, all_48_1, all_38_0, all_38_1,
% 26.03/4.44 | | all_48_0, all_50_0, simplifying with (10), (11), (21), (35),
% 26.03/4.44 | | (36) gives:
% 26.03/4.44 | | (38) all_50_0 = 0 | all_48_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2:
% 26.03/4.44 | | int] : ? [v3: int] : ((v3 = 0 & apart_point_and_line(all_48_1,
% 26.03/4.44 | | all_38_1) = 0) | (v2 = 0 & apart_point_and_line(all_48_1,
% 26.03/4.44 | | all_38_0) = 0) | ( ~ (v1 = 0) & distinct_lines(all_38_0,
% 26.03/4.44 | | all_38_1) = v1) | ( ~ (v0 = 0) & distinct_points(all_48_1,
% 26.03/4.44 | | all_48_1) = v0))
% 26.03/4.44 | |
% 26.03/4.44 | | GROUND_INST: instantiating (5) with all_48_1, all_38_0, all_50_0,
% 26.03/4.44 | | simplifying with (11), (35), (36) gives:
% 26.03/4.44 | | (39) all_50_0 = 0 | incident_point_and_line(all_48_1, all_38_0) = 0
% 26.03/4.44 | |
% 26.03/4.44 | | BETA: splitting (37) gives:
% 26.03/4.44 | |
% 26.03/4.44 | | Case 1:
% 26.03/4.44 | | |
% 26.03/4.44 | | | (40) incident_point_and_line(all_48_1, all_38_1) = 0
% 26.03/4.44 | | |
% 26.03/4.44 | | | BETA: splitting (39) gives:
% 26.03/4.44 | | |
% 26.03/4.44 | | | Case 1:
% 26.03/4.44 | | | |
% 26.03/4.45 | | | | (41) incident_point_and_line(all_48_1, all_38_0) = 0
% 26.03/4.45 | | | |
% 26.03/4.45 | | | | BETA: splitting (38) gives:
% 26.03/4.45 | | | |
% 26.03/4.45 | | | | Case 1:
% 26.03/4.45 | | | | |
% 26.03/4.45 | | | | | (42) all_50_0 = 0
% 26.03/4.45 | | | | |
% 26.03/4.45 | | | | | REDUCE: (24), (42) imply:
% 26.03/4.45 | | | | | (43) $false
% 26.03/4.45 | | | | |
% 26.03/4.45 | | | | | CLOSE: (43) is inconsistent.
% 26.03/4.45 | | | | |
% 26.03/4.45 | | | | Case 2:
% 26.03/4.45 | | | | |
% 26.03/4.45 | | | | | (44) all_48_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 26.03/4.45 | | | | | [v3: int] : ((v3 = 0 & apart_point_and_line(all_48_1,
% 26.03/4.45 | | | | | all_38_1) = 0) | (v2 = 0 &
% 26.03/4.45 | | | | | apart_point_and_line(all_48_1, all_38_0) = 0) | ( ~ (v1 =
% 26.03/4.45 | | | | | 0) & distinct_lines(all_38_0, all_38_1) = v1) | ( ~ (v0
% 26.03/4.45 | | | | | = 0) & distinct_points(all_48_1, all_48_1) = v0))
% 26.03/4.45 | | | | |
% 26.03/4.45 | | | | | BETA: splitting (44) gives:
% 26.03/4.45 | | | | |
% 26.03/4.45 | | | | | Case 1:
% 26.03/4.45 | | | | | |
% 26.03/4.45 | | | | | | (45) all_48_0 = 0
% 26.03/4.45 | | | | | |
% 26.03/4.45 | | | | | | REDUCE: (20), (45) imply:
% 26.03/4.45 | | | | | | (46) $false
% 26.03/4.45 | | | | | |
% 26.03/4.45 | | | | | | CLOSE: (46) is inconsistent.
% 26.03/4.45 | | | | | |
% 26.03/4.45 | | | | | Case 2:
% 26.03/4.45 | | | | | |
% 26.03/4.45 | | | | | |
% 26.03/4.45 | | | | | | GROUND_INST: instantiating (15) with all_48_1, simplifying with
% 26.03/4.45 | | | | | | (36), (41) gives:
% 26.03/4.45 | | | | | | (47) ? [v0: int] : ( ~ (v0 = 0) &
% 26.03/4.45 | | | | | | incident_point_and_line(all_48_1, all_38_1) = v0)
% 26.03/4.45 | | | | | |
% 26.03/4.45 | | | | | | DELTA: instantiating (47) with fresh symbol all_145_0 gives:
% 26.03/4.45 | | | | | | (48) ~ (all_145_0 = 0) & incident_point_and_line(all_48_1,
% 26.03/4.45 | | | | | | all_38_1) = all_145_0
% 26.03/4.45 | | | | | |
% 26.03/4.45 | | | | | | ALPHA: (48) implies:
% 26.03/4.45 | | | | | | (49) ~ (all_145_0 = 0)
% 26.03/4.45 | | | | | | (50) incident_point_and_line(all_48_1, all_38_1) = all_145_0
% 26.03/4.45 | | | | | |
% 26.03/4.45 | | | | | | GROUND_INST: instantiating (8) with 0, all_145_0, all_38_1,
% 26.03/4.45 | | | | | | all_48_1, simplifying with (40), (50) gives:
% 26.03/4.45 | | | | | | (51) all_145_0 = 0
% 26.03/4.46 | | | | | |
% 26.03/4.46 | | | | | | REDUCE: (49), (51) imply:
% 26.03/4.46 | | | | | | (52) $false
% 26.03/4.46 | | | | | |
% 26.03/4.46 | | | | | | CLOSE: (52) is inconsistent.
% 26.03/4.46 | | | | | |
% 26.03/4.46 | | | | | End of split
% 26.03/4.46 | | | | |
% 26.03/4.46 | | | | End of split
% 26.03/4.46 | | | |
% 26.03/4.46 | | | Case 2:
% 26.03/4.46 | | | |
% 26.03/4.46 | | | | (53) all_50_0 = 0
% 26.03/4.46 | | | |
% 26.03/4.46 | | | | REDUCE: (24), (53) imply:
% 26.03/4.46 | | | | (54) $false
% 26.03/4.46 | | | |
% 26.03/4.46 | | | | CLOSE: (54) is inconsistent.
% 26.03/4.46 | | | |
% 26.03/4.46 | | | End of split
% 26.03/4.46 | | |
% 26.03/4.46 | | Case 2:
% 26.03/4.46 | | |
% 26.03/4.46 | | | (55) all_48_0 = 0
% 26.03/4.46 | | |
% 26.03/4.46 | | | REDUCE: (20), (55) imply:
% 26.03/4.46 | | | (56) $false
% 26.03/4.46 | | |
% 26.03/4.46 | | | CLOSE: (56) is inconsistent.
% 26.03/4.46 | | |
% 26.03/4.46 | | End of split
% 26.03/4.46 | |
% 26.03/4.46 | Case 2:
% 26.03/4.46 | |
% 26.03/4.46 | | (57) ( ~ (all_52_2 = 0) & line(all_38_0) = all_52_2) | ( ~ (all_52_3 = 0)
% 26.03/4.46 | | & line(all_38_1) = all_52_3)
% 26.03/4.46 | |
% 26.03/4.46 | | BETA: splitting (57) gives:
% 26.03/4.46 | |
% 26.03/4.46 | | Case 1:
% 26.03/4.46 | | |
% 26.03/4.46 | | | (58) ~ (all_52_2 = 0) & line(all_38_0) = all_52_2
% 26.03/4.46 | | |
% 26.03/4.46 | | | ALPHA: (58) implies:
% 26.03/4.46 | | | (59) ~ (all_52_2 = 0)
% 26.03/4.46 | | | (60) line(all_38_0) = all_52_2
% 26.03/4.46 | | |
% 26.03/4.46 | | | GROUND_INST: instantiating (6) with 0, all_52_2, all_38_0, simplifying
% 26.03/4.46 | | | with (14), (60) gives:
% 26.03/4.46 | | | (61) all_52_2 = 0
% 26.03/4.46 | | |
% 26.03/4.46 | | | REDUCE: (59), (61) imply:
% 26.03/4.46 | | | (62) $false
% 26.03/4.46 | | |
% 26.03/4.46 | | | CLOSE: (62) is inconsistent.
% 26.03/4.46 | | |
% 26.03/4.46 | | Case 2:
% 26.03/4.46 | | |
% 26.03/4.46 | | | (63) ~ (all_52_3 = 0) & line(all_38_1) = all_52_3
% 26.03/4.46 | | |
% 26.03/4.46 | | | ALPHA: (63) implies:
% 26.03/4.46 | | | (64) ~ (all_52_3 = 0)
% 26.03/4.46 | | | (65) line(all_38_1) = all_52_3
% 26.03/4.46 | | |
% 26.03/4.46 | | | GROUND_INST: instantiating (6) with 0, all_52_3, all_38_1, simplifying
% 26.03/4.46 | | | with (13), (65) gives:
% 26.03/4.46 | | | (66) all_52_3 = 0
% 26.03/4.47 | | |
% 26.03/4.47 | | | REDUCE: (64), (66) imply:
% 26.03/4.47 | | | (67) $false
% 26.03/4.47 | | |
% 26.03/4.47 | | | CLOSE: (67) is inconsistent.
% 26.03/4.47 | | |
% 26.03/4.47 | | End of split
% 26.03/4.47 | |
% 26.03/4.47 | End of split
% 26.03/4.47 |
% 26.03/4.47 End of proof
% 26.03/4.47 % SZS output end Proof for theBenchmark
% 26.03/4.47
% 26.03/4.47 3876ms
%------------------------------------------------------------------------------