TSTP Solution File: GEO225+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO225+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 : n008.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 6.23s 1.70s
% Output : Proof 10.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO225+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.33 % Computer : n008.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Aug 29 21:37:47 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.66/1.03 Prover 1: Preprocessing ...
% 2.66/1.03 Prover 4: Preprocessing ...
% 2.66/1.06 Prover 5: Preprocessing ...
% 2.66/1.06 Prover 0: Preprocessing ...
% 2.66/1.06 Prover 3: Preprocessing ...
% 2.66/1.06 Prover 6: Preprocessing ...
% 2.66/1.07 Prover 2: Preprocessing ...
% 4.79/1.33 Prover 2: Proving ...
% 4.79/1.35 Prover 3: Constructing countermodel ...
% 4.79/1.35 Prover 5: Proving ...
% 4.79/1.35 Prover 1: Constructing countermodel ...
% 4.79/1.40 Prover 6: Proving ...
% 5.53/1.43 Prover 3: gave up
% 5.53/1.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.53/1.44 Prover 1: gave up
% 5.53/1.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.53/1.48 Prover 8: Preprocessing ...
% 5.53/1.48 Prover 7: Preprocessing ...
% 5.53/1.52 Prover 4: Constructing countermodel ...
% 5.53/1.53 Prover 0: Proving ...
% 5.53/1.55 Prover 7: Warning: ignoring some quantifiers
% 5.53/1.58 Prover 7: Constructing countermodel ...
% 6.23/1.63 Prover 8: Warning: ignoring some quantifiers
% 6.23/1.64 Prover 8: Constructing countermodel ...
% 6.23/1.66 Prover 7: gave up
% 6.23/1.66 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 6.23/1.68 Prover 9: Preprocessing ...
% 6.23/1.70 Prover 0: proved (1083ms)
% 6.23/1.70
% 6.23/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.23/1.70
% 7.62/1.71 Prover 6: stopped
% 7.62/1.71 Prover 5: stopped
% 7.62/1.72 Prover 2: stopped
% 7.62/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.62/1.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.62/1.72 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.62/1.72 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.62/1.72 Prover 8: gave up
% 7.62/1.74 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 7.62/1.77 Prover 10: Preprocessing ...
% 7.62/1.77 Prover 16: Preprocessing ...
% 7.62/1.78 Prover 13: Preprocessing ...
% 7.62/1.78 Prover 19: Preprocessing ...
% 7.62/1.80 Prover 11: Preprocessing ...
% 7.62/1.80 Prover 10: Warning: ignoring some quantifiers
% 8.35/1.81 Prover 10: Constructing countermodel ...
% 8.35/1.83 Prover 16: Warning: ignoring some quantifiers
% 8.35/1.84 Prover 10: gave up
% 8.35/1.84 Prover 16: Constructing countermodel ...
% 8.35/1.84 Prover 13: Warning: ignoring some quantifiers
% 8.35/1.86 Prover 19: Warning: ignoring some quantifiers
% 8.35/1.86 Prover 13: Constructing countermodel ...
% 8.35/1.87 Prover 9: Constructing countermodel ...
% 8.35/1.87 Prover 19: Constructing countermodel ...
% 8.35/1.87 Prover 9: stopped
% 9.04/1.91 Prover 19: gave up
% 9.04/1.93 Prover 4: Found proof (size 69)
% 9.04/1.93 Prover 4: proved (1305ms)
% 9.04/1.93 Prover 13: stopped
% 9.04/1.93 Prover 16: stopped
% 9.04/1.96 Prover 11: Constructing countermodel ...
% 9.04/1.97 Prover 11: stopped
% 9.04/1.97
% 9.04/1.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.04/1.97
% 9.49/1.99 % SZS output start Proof for theBenchmark
% 9.49/1.99 Assumptions after simplification:
% 9.49/1.99 ---------------------------------
% 9.49/1.99
% 9.49/1.99 (ci1)
% 9.49/2.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 9.49/2.02 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 9.49/2.02 (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4
% 9.49/2.02 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 9.49/2.02 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 9.49/2.02 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 &
% 9.49/2.02 apart_point_and_line(v0, v2) = v3 & $i(v2)))
% 9.49/2.02
% 9.49/2.02 (ci2)
% 9.49/2.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 9.49/2.03 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 9.49/2.03 (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4
% 9.49/2.03 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 9.49/2.03 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 9.49/2.03 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 &
% 9.49/2.03 apart_point_and_line(v1, v2) = v3 & $i(v2)))
% 9.49/2.03
% 9.49/2.03 (con)
% 9.49/2.03 ? [v0: $i] : ? [v1: $i] : (point(v1) = 0 & point(v0) = 0 &
% 9.49/2.03 distinct_points(v0, v1) = 0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: int] :
% 9.49/2.03 (v3 = 0 | ~ (line(v2) = v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: int] : (v3
% 9.49/2.03 = 0 | ~ (apart_point_and_line(v1, v2) = v3) | ~ $i(v2) |
% 9.49/2.03 apart_point_and_line(v0, v2) = 0) & ! [v2: $i] : ! [v3: int] : (v3 = 0 |
% 9.49/2.03 ~ (apart_point_and_line(v0, v2) = v3) | ~ $i(v2) |
% 9.49/2.03 apart_point_and_line(v1, v2) = 0))
% 9.49/2.03
% 9.49/2.03 (con1)
% 9.49/2.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 9.49/2.04 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6:
% 9.49/2.04 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 &
% 9.49/2.04 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) |
% 9.49/2.04 v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) =
% 9.49/2.04 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] :
% 9.49/2.04 ? [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 &
% 9.49/2.04 line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 =
% 9.49/2.04 0)))
% 9.49/2.04
% 9.49/2.04 (cu1)
% 9.49/2.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 9.49/2.05 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 9.49/2.05 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 9.49/2.05 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 9.49/2.05 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0,
% 9.49/2.05 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 9.49/2.05 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 9.49/2.05 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) =
% 9.49/2.05 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3)
% 9.49/2.05 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 9.49/2.05 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 &
% 9.49/2.05 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6
% 9.49/2.05 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 9.49/2.05 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 9.49/2.05 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4)
% 9.49/2.05 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 9.49/2.05 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 9.49/2.05 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 9.49/2.05 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 =
% 9.49/2.05 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 9.49/2.05 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) =
% 9.49/2.05 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 9.49/2.05 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9:
% 9.49/2.05 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) =
% 9.49/2.05 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7
% 9.49/2.05 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 9.49/2.05 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 9.49/2.05 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4)
% 9.49/2.05 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 9.49/2.05 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 9.49/2.05 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 &
% 9.49/2.05 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0:
% 9.49/2.05 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 9.49/2.05 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~
% 9.49/2.05 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 9.49/2.05 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 9.49/2.05 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1,
% 9.49/2.05 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 9.49/2.05 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 9.49/2.05 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3)
% 9.49/2.05 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 9.49/2.05 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 9.49/2.05 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 9.49/2.05 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 9.49/2.05
% 9.49/2.05 (function-axioms)
% 9.49/2.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.49/2.06 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 9.49/2.06 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 9.49/2.06 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 9.49/2.06 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 9.49/2.06 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 9.49/2.06 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 9.49/2.06 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 9.49/2.06 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.49/2.06 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.49/2.06 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 9.49/2.06 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.49/2.06 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 9.49/2.06 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.49/2.06 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.49/2.06 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 9.49/2.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.49/2.06 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 9.49/2.06 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.49/2.06 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0:
% 9.49/2.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.49/2.06 ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 9.49/2.06
% 9.49/2.06 Further assumptions not needed in the proof:
% 9.49/2.06 --------------------------------------------
% 9.49/2.06 apart1, apart2, apart3, apart4, apart5, ax6, ceq1, ceq2, ceq3, ci3, ci4, int1,
% 9.49/2.06 orth1, par1
% 9.49/2.06
% 9.49/2.06 Those formulas are unsatisfiable:
% 9.49/2.06 ---------------------------------
% 9.49/2.06
% 9.49/2.06 Begin of proof
% 9.49/2.06 |
% 9.49/2.06 | ALPHA: (ci1) implies:
% 9.49/2.06 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~
% 9.49/2.06 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 9.49/2.06 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 &
% 9.49/2.06 | $i(v2)))
% 9.49/2.06 |
% 9.49/2.06 | ALPHA: (ci2) implies:
% 9.49/2.06 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~
% 9.49/2.06 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 9.49/2.06 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 &
% 9.49/2.06 | $i(v2)))
% 9.49/2.06 |
% 9.49/2.06 | ALPHA: (cu1) implies:
% 9.49/2.06 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 9.49/2.06 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5)
% 9.49/2.06 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 9.49/2.06 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ?
% 9.49/2.06 | [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 9.49/2.06 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 9.49/2.06 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0
% 9.49/2.06 | | v8 = 0)))
% 9.49/2.06 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 9.49/2.06 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5)
% 9.49/2.06 | | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0,
% 9.49/2.06 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 9.49/2.07 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v0,
% 9.49/2.07 | v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2,
% 9.49/2.07 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 9.49/2.07 |
% 9.49/2.07 | ALPHA: (con1) implies:
% 9.49/2.07 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~
% 9.49/2.07 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ?
% 9.49/2.07 | [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 &
% 9.49/2.07 | line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0)
% 9.49/2.07 | | v5 = 0)))
% 9.49/2.07 |
% 9.49/2.07 | ALPHA: (function-axioms) implies:
% 9.49/2.07 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.49/2.07 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 9.49/2.07 | (apart_point_and_line(v3, v2) = v0))
% 9.49/2.07 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.49/2.07 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 9.49/2.07 |
% 9.49/2.07 | DELTA: instantiating (con) with fresh symbols all_21_0, all_21_1 gives:
% 9.49/2.07 | (8) point(all_21_0) = 0 & point(all_21_1) = 0 & distinct_points(all_21_1,
% 9.49/2.07 | all_21_0) = 0 & $i(all_21_0) & $i(all_21_1) & ! [v0: $i] : ! [v1:
% 9.49/2.07 | int] : (v1 = 0 | ~ (line(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : !
% 9.49/2.07 | [v1: int] : (v1 = 0 | ~ (apart_point_and_line(all_21_0, v0) = v1) | ~
% 9.49/2.07 | $i(v0) | apart_point_and_line(all_21_1, v0) = 0) & ! [v0: $i] : !
% 9.49/2.07 | [v1: int] : (v1 = 0 | ~ (apart_point_and_line(all_21_1, v0) = v1) | ~
% 9.49/2.07 | $i(v0) | apart_point_and_line(all_21_0, v0) = 0)
% 9.49/2.07 |
% 9.49/2.07 | ALPHA: (8) implies:
% 9.49/2.07 | (9) $i(all_21_1)
% 9.49/2.07 | (10) $i(all_21_0)
% 9.49/2.07 | (11) distinct_points(all_21_1, all_21_0) = 0
% 9.49/2.07 | (12) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 9.49/2.07 | (apart_point_and_line(all_21_0, v0) = v1) | ~ $i(v0) |
% 9.49/2.07 | apart_point_and_line(all_21_1, v0) = 0)
% 9.49/2.07 |
% 9.49/2.07 | GROUND_INST: instantiating (5) with all_21_1, all_21_0, simplifying with (9),
% 9.49/2.07 | (10), (11) gives:
% 9.49/2.07 | (13) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 9.49/2.07 | (point(all_21_0) = v1 & point(all_21_1) = v0 & line(v2) = v3 &
% 9.49/2.07 | line_connecting(all_21_1, all_21_0) = v2 & $i(v2) & ( ~ (v1 = 0) |
% 9.49/2.07 | ~ (v0 = 0) | v3 = 0))
% 9.49/2.07 |
% 9.49/2.07 | GROUND_INST: instantiating (2) with all_21_1, all_21_0, simplifying with (9),
% 9.49/2.07 | (10), (11) gives:
% 9.49/2.08 | (14) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_21_1,
% 9.49/2.08 | all_21_0) = v0 & apart_point_and_line(all_21_0, v0) = v1 & $i(v0))
% 9.49/2.08 |
% 9.49/2.08 | GROUND_INST: instantiating (1) with all_21_1, all_21_0, simplifying with (9),
% 9.49/2.08 | (10), (11) gives:
% 9.49/2.08 | (15) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_21_1,
% 9.49/2.08 | all_21_0) = v0 & apart_point_and_line(all_21_1, v0) = v1 & $i(v0))
% 9.49/2.08 |
% 9.49/2.08 | DELTA: instantiating (15) with fresh symbols all_29_0, all_29_1 gives:
% 9.49/2.08 | (16) ~ (all_29_0 = 0) & line_connecting(all_21_1, all_21_0) = all_29_1 &
% 9.49/2.08 | apart_point_and_line(all_21_1, all_29_1) = all_29_0 & $i(all_29_1)
% 9.49/2.08 |
% 9.49/2.08 | ALPHA: (16) implies:
% 9.49/2.08 | (17) ~ (all_29_0 = 0)
% 9.49/2.08 | (18) apart_point_and_line(all_21_1, all_29_1) = all_29_0
% 9.49/2.08 | (19) line_connecting(all_21_1, all_21_0) = all_29_1
% 9.49/2.08 |
% 9.49/2.08 | DELTA: instantiating (14) with fresh symbols all_31_0, all_31_1 gives:
% 9.49/2.08 | (20) ~ (all_31_0 = 0) & line_connecting(all_21_1, all_21_0) = all_31_1 &
% 9.49/2.08 | apart_point_and_line(all_21_0, all_31_1) = all_31_0 & $i(all_31_1)
% 9.49/2.08 |
% 9.49/2.08 | ALPHA: (20) implies:
% 9.49/2.08 | (21) ~ (all_31_0 = 0)
% 9.49/2.08 | (22) $i(all_31_1)
% 9.49/2.08 | (23) apart_point_and_line(all_21_0, all_31_1) = all_31_0
% 9.49/2.08 | (24) line_connecting(all_21_1, all_21_0) = all_31_1
% 9.49/2.08 |
% 9.49/2.08 | DELTA: instantiating (13) with fresh symbols all_33_0, all_33_1, all_33_2,
% 9.49/2.08 | all_33_3 gives:
% 9.49/2.08 | (25) point(all_21_0) = all_33_2 & point(all_21_1) = all_33_3 &
% 9.49/2.08 | line(all_33_1) = all_33_0 & line_connecting(all_21_1, all_21_0) =
% 9.49/2.08 | all_33_1 & $i(all_33_1) & ( ~ (all_33_2 = 0) | ~ (all_33_3 = 0) |
% 9.49/2.08 | all_33_0 = 0)
% 9.49/2.08 |
% 9.49/2.08 | ALPHA: (25) implies:
% 9.49/2.08 | (26) line_connecting(all_21_1, all_21_0) = all_33_1
% 9.49/2.08 |
% 9.49/2.08 | GROUND_INST: instantiating (7) with all_31_1, all_33_1, all_21_0, all_21_1,
% 9.49/2.08 | simplifying with (24), (26) gives:
% 9.49/2.08 | (27) all_33_1 = all_31_1
% 9.49/2.08 |
% 9.49/2.08 | GROUND_INST: instantiating (7) with all_29_1, all_33_1, all_21_0, all_21_1,
% 9.49/2.08 | simplifying with (19), (26) gives:
% 9.49/2.08 | (28) all_33_1 = all_29_1
% 9.49/2.08 |
% 9.49/2.08 | COMBINE_EQS: (27), (28) imply:
% 9.49/2.08 | (29) all_31_1 = all_29_1
% 9.49/2.08 |
% 9.49/2.08 | REDUCE: (23), (29) imply:
% 9.49/2.08 | (30) apart_point_and_line(all_21_0, all_29_1) = all_31_0
% 9.49/2.08 |
% 9.49/2.08 | REDUCE: (22), (29) imply:
% 9.49/2.08 | (31) $i(all_29_1)
% 9.49/2.08 |
% 9.49/2.08 | GROUND_INST: instantiating (3) with all_21_1, all_21_1, all_29_1, all_29_1,
% 9.49/2.08 | all_29_0, all_29_0, simplifying with (9), (18), (31) gives:
% 9.49/2.08 | (32) all_29_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 9.49/2.08 | any] : (apart_point_and_line(all_21_1, all_29_1) = v3 &
% 9.49/2.08 | apart_point_and_line(all_21_1, all_29_1) = v2 &
% 9.49/2.08 | distinct_lines(all_29_1, all_29_1) = v1 & distinct_points(all_21_1,
% 9.49/2.08 | all_21_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 9.49/2.08 |
% 9.49/2.08 | GROUND_INST: instantiating (4) with all_21_1, all_21_0, all_29_1, all_29_1,
% 9.49/2.08 | all_31_0, all_31_0, simplifying with (9), (10), (11), (30), (31)
% 9.49/2.08 | gives:
% 9.49/2.09 | (33) all_31_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 9.49/2.09 | (apart_point_and_line(all_21_1, all_29_1) = v2 &
% 9.49/2.09 | apart_point_and_line(all_21_1, all_29_1) = v1 &
% 9.49/2.09 | distinct_lines(all_29_1, all_29_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1
% 9.49/2.09 | = 0))
% 9.49/2.09 |
% 9.49/2.09 | GROUND_INST: instantiating (3) with all_21_0, all_21_1, all_29_1, all_29_1,
% 9.49/2.09 | all_31_0, all_29_0, simplifying with (9), (10), (18), (30), (31)
% 9.49/2.09 | gives:
% 9.49/2.09 | (34) all_31_0 = 0 | all_29_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 9.49/2.09 | any] : ? [v3: any] : (apart_point_and_line(all_21_0, all_29_1) = v2
% 9.49/2.09 | & apart_point_and_line(all_21_1, all_29_1) = v3 &
% 9.49/2.09 | distinct_lines(all_29_1, all_29_1) = v1 & distinct_points(all_21_0,
% 9.49/2.09 | all_21_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 9.49/2.09 |
% 9.49/2.09 | GROUND_INST: instantiating (12) with all_29_1, all_31_0, simplifying with
% 9.49/2.09 | (30), (31) gives:
% 9.49/2.09 | (35) all_31_0 = 0 | apart_point_and_line(all_21_1, all_29_1) = 0
% 9.49/2.09 |
% 9.49/2.09 | BETA: splitting (35) gives:
% 9.49/2.09 |
% 9.98/2.09 | Case 1:
% 9.98/2.09 | |
% 9.98/2.09 | | (36) apart_point_and_line(all_21_1, all_29_1) = 0
% 9.98/2.09 | |
% 9.98/2.09 | | BETA: splitting (33) gives:
% 9.98/2.09 | |
% 9.98/2.09 | | Case 1:
% 9.98/2.09 | | |
% 9.98/2.09 | | | (37) all_31_0 = 0
% 9.98/2.09 | | |
% 9.98/2.09 | | | REDUCE: (21), (37) imply:
% 9.98/2.09 | | | (38) $false
% 9.98/2.09 | | |
% 9.98/2.09 | | | CLOSE: (38) is inconsistent.
% 9.98/2.09 | | |
% 9.98/2.09 | | Case 2:
% 9.98/2.09 | | |
% 9.98/2.09 | | | (39) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 9.98/2.09 | | | (apart_point_and_line(all_21_1, all_29_1) = v2 &
% 9.98/2.09 | | | apart_point_and_line(all_21_1, all_29_1) = v1 &
% 9.98/2.09 | | | distinct_lines(all_29_1, all_29_1) = v0 & ( ~ (v0 = 0) | v2 = 0
% 9.98/2.09 | | | | v1 = 0))
% 9.98/2.09 | | |
% 9.98/2.09 | | | DELTA: instantiating (39) with fresh symbols all_67_0, all_67_1, all_67_2
% 9.98/2.09 | | | gives:
% 9.98/2.09 | | | (40) apart_point_and_line(all_21_1, all_29_1) = all_67_0 &
% 9.98/2.09 | | | apart_point_and_line(all_21_1, all_29_1) = all_67_1 &
% 9.98/2.09 | | | distinct_lines(all_29_1, all_29_1) = all_67_2 & ( ~ (all_67_2 = 0)
% 9.98/2.09 | | | | all_67_0 = 0 | all_67_1 = 0)
% 9.98/2.09 | | |
% 9.98/2.09 | | | ALPHA: (40) implies:
% 9.98/2.09 | | | (41) apart_point_and_line(all_21_1, all_29_1) = all_67_1
% 9.98/2.09 | | | (42) apart_point_and_line(all_21_1, all_29_1) = all_67_0
% 9.98/2.09 | | |
% 9.98/2.09 | | | BETA: splitting (32) gives:
% 9.98/2.09 | | |
% 9.98/2.09 | | | Case 1:
% 9.98/2.09 | | | |
% 9.98/2.09 | | | | (43) all_29_0 = 0
% 9.98/2.09 | | | |
% 9.98/2.09 | | | | REDUCE: (17), (43) imply:
% 9.98/2.09 | | | | (44) $false
% 9.98/2.09 | | | |
% 9.98/2.09 | | | | CLOSE: (44) is inconsistent.
% 9.98/2.09 | | | |
% 9.98/2.09 | | | Case 2:
% 9.98/2.09 | | | |
% 9.98/2.09 | | | | (45) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 9.98/2.09 | | | | (apart_point_and_line(all_21_1, all_29_1) = v3 &
% 9.98/2.10 | | | | apart_point_and_line(all_21_1, all_29_1) = v2 &
% 9.98/2.10 | | | | distinct_lines(all_29_1, all_29_1) = v1 &
% 9.98/2.10 | | | | distinct_points(all_21_1, all_21_1) = v0 & ( ~ (v1 = 0) | ~
% 9.98/2.10 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 9.98/2.10 | | | |
% 9.98/2.10 | | | | DELTA: instantiating (45) with fresh symbols all_77_0, all_77_1,
% 9.98/2.10 | | | | all_77_2, all_77_3 gives:
% 9.98/2.10 | | | | (46) apart_point_and_line(all_21_1, all_29_1) = all_77_0 &
% 9.98/2.10 | | | | apart_point_and_line(all_21_1, all_29_1) = all_77_1 &
% 9.98/2.10 | | | | distinct_lines(all_29_1, all_29_1) = all_77_2 &
% 9.98/2.10 | | | | distinct_points(all_21_1, all_21_1) = all_77_3 & ( ~ (all_77_2 =
% 9.98/2.10 | | | | 0) | ~ (all_77_3 = 0) | all_77_0 = 0 | all_77_1 = 0)
% 9.98/2.10 | | | |
% 9.98/2.10 | | | | ALPHA: (46) implies:
% 9.98/2.10 | | | | (47) apart_point_and_line(all_21_1, all_29_1) = all_77_1
% 9.98/2.10 | | | | (48) apart_point_and_line(all_21_1, all_29_1) = all_77_0
% 9.98/2.10 | | | |
% 9.98/2.10 | | | | BETA: splitting (34) gives:
% 9.98/2.10 | | | |
% 9.98/2.10 | | | | Case 1:
% 9.98/2.10 | | | | |
% 9.98/2.10 | | | | | (49) all_31_0 = 0
% 9.98/2.10 | | | | |
% 9.98/2.10 | | | | | REDUCE: (21), (49) imply:
% 9.98/2.10 | | | | | (50) $false
% 9.98/2.10 | | | | |
% 9.98/2.10 | | | | | CLOSE: (50) is inconsistent.
% 9.98/2.10 | | | | |
% 9.98/2.10 | | | | Case 2:
% 9.98/2.10 | | | | |
% 10.02/2.10 | | | | | (51) all_29_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 10.02/2.10 | | | | | [v3: any] : (apart_point_and_line(all_21_0, all_29_1) = v2 &
% 10.02/2.10 | | | | | apart_point_and_line(all_21_1, all_29_1) = v3 &
% 10.02/2.10 | | | | | distinct_lines(all_29_1, all_29_1) = v1 &
% 10.02/2.10 | | | | | distinct_points(all_21_0, all_21_1) = v0 & ( ~ (v1 = 0) | ~
% 10.02/2.10 | | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 10.02/2.10 | | | | |
% 10.02/2.10 | | | | | BETA: splitting (51) gives:
% 10.02/2.10 | | | | |
% 10.02/2.10 | | | | | Case 1:
% 10.02/2.10 | | | | | |
% 10.02/2.10 | | | | | | (52) all_29_0 = 0
% 10.02/2.10 | | | | | |
% 10.02/2.10 | | | | | | REDUCE: (17), (52) imply:
% 10.02/2.10 | | | | | | (53) $false
% 10.02/2.10 | | | | | |
% 10.02/2.10 | | | | | | CLOSE: (53) is inconsistent.
% 10.02/2.10 | | | | | |
% 10.02/2.10 | | | | | Case 2:
% 10.02/2.10 | | | | | |
% 10.02/2.10 | | | | | | (54) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 10.02/2.10 | | | | | | (apart_point_and_line(all_21_0, all_29_1) = v2 &
% 10.02/2.10 | | | | | | apart_point_and_line(all_21_1, all_29_1) = v3 &
% 10.02/2.10 | | | | | | distinct_lines(all_29_1, all_29_1) = v1 &
% 10.02/2.10 | | | | | | distinct_points(all_21_0, all_21_1) = v0 & ( ~ (v1 = 0) |
% 10.02/2.10 | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 10.02/2.10 | | | | | |
% 10.02/2.10 | | | | | | DELTA: instantiating (54) with fresh symbols all_89_0, all_89_1,
% 10.02/2.10 | | | | | | all_89_2, all_89_3 gives:
% 10.02/2.10 | | | | | | (55) apart_point_and_line(all_21_0, all_29_1) = all_89_1 &
% 10.02/2.10 | | | | | | apart_point_and_line(all_21_1, all_29_1) = all_89_0 &
% 10.02/2.10 | | | | | | distinct_lines(all_29_1, all_29_1) = all_89_2 &
% 10.02/2.10 | | | | | | distinct_points(all_21_0, all_21_1) = all_89_3 & ( ~
% 10.02/2.10 | | | | | | (all_89_2 = 0) | ~ (all_89_3 = 0) | all_89_0 = 0 |
% 10.02/2.10 | | | | | | all_89_1 = 0)
% 10.02/2.10 | | | | | |
% 10.02/2.10 | | | | | | ALPHA: (55) implies:
% 10.02/2.10 | | | | | | (56) apart_point_and_line(all_21_1, all_29_1) = all_89_0
% 10.02/2.10 | | | | | |
% 10.02/2.10 | | | | | | GROUND_INST: instantiating (6) with all_29_0, all_77_1, all_29_1,
% 10.02/2.10 | | | | | | all_21_1, simplifying with (18), (47) gives:
% 10.02/2.10 | | | | | | (57) all_77_1 = all_29_0
% 10.02/2.10 | | | | | |
% 10.02/2.10 | | | | | | GROUND_INST: instantiating (6) with 0, all_77_1, all_29_1, all_21_1,
% 10.02/2.10 | | | | | | simplifying with (36), (47) gives:
% 10.02/2.10 | | | | | | (58) all_77_1 = 0
% 10.02/2.10 | | | | | |
% 10.02/2.10 | | | | | | GROUND_INST: instantiating (6) with all_77_1, all_77_0, all_29_1,
% 10.02/2.10 | | | | | | all_21_1, simplifying with (47), (48) gives:
% 10.02/2.10 | | | | | | (59) all_77_0 = all_77_1
% 10.02/2.10 | | | | | |
% 10.02/2.10 | | | | | | GROUND_INST: instantiating (6) with all_67_0, all_77_0, all_29_1,
% 10.02/2.10 | | | | | | all_21_1, simplifying with (42), (48) gives:
% 10.02/2.10 | | | | | | (60) all_77_0 = all_67_0
% 10.02/2.10 | | | | | |
% 10.02/2.10 | | | | | | GROUND_INST: instantiating (6) with all_77_1, all_89_0, all_29_1,
% 10.02/2.10 | | | | | | all_21_1, simplifying with (47), (56) gives:
% 10.02/2.10 | | | | | | (61) all_89_0 = all_77_1
% 10.02/2.10 | | | | | |
% 10.02/2.10 | | | | | | GROUND_INST: instantiating (6) with all_67_1, all_89_0, all_29_1,
% 10.02/2.10 | | | | | | all_21_1, simplifying with (41), (56) gives:
% 10.02/2.10 | | | | | | (62) all_89_0 = all_67_1
% 10.02/2.10 | | | | | |
% 10.02/2.10 | | | | | | COMBINE_EQS: (61), (62) imply:
% 10.02/2.10 | | | | | | (63) all_77_1 = all_67_1
% 10.02/2.10 | | | | | |
% 10.02/2.11 | | | | | | SIMP: (63) implies:
% 10.02/2.11 | | | | | | (64) all_77_1 = all_67_1
% 10.02/2.11 | | | | | |
% 10.02/2.11 | | | | | | COMBINE_EQS: (59), (60) imply:
% 10.02/2.11 | | | | | | (65) all_77_1 = all_67_0
% 10.02/2.11 | | | | | |
% 10.02/2.11 | | | | | | SIMP: (65) implies:
% 10.02/2.11 | | | | | | (66) all_77_1 = all_67_0
% 10.06/2.11 | | | | | |
% 10.06/2.11 | | | | | | COMBINE_EQS: (57), (66) imply:
% 10.06/2.11 | | | | | | (67) all_67_0 = all_29_0
% 10.06/2.11 | | | | | |
% 10.06/2.11 | | | | | | COMBINE_EQS: (58), (66) imply:
% 10.06/2.11 | | | | | | (68) all_67_0 = 0
% 10.06/2.11 | | | | | |
% 10.06/2.11 | | | | | | COMBINE_EQS: (64), (66) imply:
% 10.06/2.11 | | | | | | (69) all_67_0 = all_67_1
% 10.06/2.11 | | | | | |
% 10.06/2.11 | | | | | | COMBINE_EQS: (68), (69) imply:
% 10.06/2.11 | | | | | | (70) all_67_1 = 0
% 10.06/2.11 | | | | | |
% 10.06/2.11 | | | | | | COMBINE_EQS: (67), (69) imply:
% 10.06/2.11 | | | | | | (71) all_67_1 = all_29_0
% 10.06/2.11 | | | | | |
% 10.06/2.11 | | | | | | COMBINE_EQS: (70), (71) imply:
% 10.06/2.11 | | | | | | (72) all_29_0 = 0
% 10.06/2.11 | | | | | |
% 10.06/2.11 | | | | | | SIMP: (72) implies:
% 10.06/2.11 | | | | | | (73) all_29_0 = 0
% 10.06/2.11 | | | | | |
% 10.06/2.11 | | | | | | REDUCE: (17), (73) imply:
% 10.06/2.11 | | | | | | (74) $false
% 10.06/2.11 | | | | | |
% 10.06/2.11 | | | | | | CLOSE: (74) is inconsistent.
% 10.06/2.11 | | | | | |
% 10.06/2.11 | | | | | End of split
% 10.06/2.11 | | | | |
% 10.06/2.11 | | | | End of split
% 10.06/2.11 | | | |
% 10.06/2.11 | | | End of split
% 10.06/2.11 | | |
% 10.06/2.11 | | End of split
% 10.06/2.11 | |
% 10.06/2.11 | Case 2:
% 10.06/2.11 | |
% 10.06/2.11 | | (75) all_31_0 = 0
% 10.06/2.11 | |
% 10.06/2.11 | | REDUCE: (21), (75) imply:
% 10.06/2.11 | | (76) $false
% 10.06/2.11 | |
% 10.06/2.11 | | CLOSE: (76) is inconsistent.
% 10.06/2.11 | |
% 10.06/2.11 | End of split
% 10.06/2.11 |
% 10.06/2.11 End of proof
% 10.06/2.11 % SZS output end Proof for theBenchmark
% 10.06/2.11
% 10.06/2.11 1511ms
%------------------------------------------------------------------------------