TSTP Solution File: GEO172+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO172+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 : n022.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 23:21:49 EDT 2023
% Result : Theorem 9.83s 2.08s
% Output : Proof 16.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GEO172+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 20:49:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.68/0.66 ________ _____
% 0.68/0.66 ___ __ \_________(_)________________________________
% 0.68/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.68/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.68/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.68/0.66
% 0.68/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.68/0.66 (2023-06-19)
% 0.68/0.66
% 0.68/0.66 (c) Philipp Rümmer, 2009-2023
% 0.68/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.68/0.66 Amanda Stjerna.
% 0.68/0.66 Free software under BSD-3-Clause.
% 0.68/0.66
% 0.68/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.68/0.66
% 0.68/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.68 Running up to 7 provers in parallel.
% 0.68/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.68/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.68/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.68/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.68/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.68/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.68/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.29/1.15 Prover 1: Preprocessing ...
% 2.29/1.15 Prover 4: Preprocessing ...
% 2.93/1.19 Prover 2: Preprocessing ...
% 2.93/1.19 Prover 3: Preprocessing ...
% 2.93/1.19 Prover 6: Preprocessing ...
% 2.93/1.19 Prover 0: Preprocessing ...
% 2.93/1.19 Prover 5: Preprocessing ...
% 4.46/1.41 Prover 5: Proving ...
% 4.46/1.42 Prover 2: Proving ...
% 4.46/1.45 Prover 6: Constructing countermodel ...
% 4.46/1.45 Prover 1: Constructing countermodel ...
% 4.46/1.46 Prover 3: Constructing countermodel ...
% 5.66/1.53 Prover 1: gave up
% 5.66/1.53 Prover 3: gave up
% 5.69/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.69/1.53 Prover 6: gave up
% 5.69/1.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.69/1.54 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 5.69/1.55 Prover 4: Constructing countermodel ...
% 5.69/1.55 Prover 0: Proving ...
% 5.69/1.56 Prover 8: Preprocessing ...
% 5.69/1.56 Prover 7: Preprocessing ...
% 5.69/1.57 Prover 9: Preprocessing ...
% 6.26/1.62 Prover 7: Warning: ignoring some quantifiers
% 6.26/1.63 Prover 7: Constructing countermodel ...
% 6.26/1.66 Prover 8: Warning: ignoring some quantifiers
% 6.26/1.68 Prover 8: Constructing countermodel ...
% 6.79/1.72 Prover 7: gave up
% 6.79/1.72 Prover 8: gave up
% 6.79/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.79/1.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.79/1.73 Prover 9: Constructing countermodel ...
% 6.79/1.74 Prover 10: Preprocessing ...
% 6.79/1.74 Prover 11: Preprocessing ...
% 6.79/1.77 Prover 10: Warning: ignoring some quantifiers
% 7.53/1.78 Prover 10: Constructing countermodel ...
% 7.69/1.80 Prover 10: gave up
% 7.69/1.81 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 7.87/1.84 Prover 12: Preprocessing ...
% 7.87/1.89 Prover 11: Constructing countermodel ...
% 8.50/1.94 Prover 12: Proving ...
% 9.83/2.08 Prover 5: proved (1378ms)
% 9.83/2.08
% 9.83/2.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.83/2.08
% 9.83/2.08 Prover 9: stopped
% 9.83/2.08 Prover 0: stopped
% 9.83/2.08 Prover 2: stopped
% 9.83/2.09 Prover 12: stopped
% 9.83/2.09 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.83/2.09 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.83/2.09 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 9.96/2.10 Prover 16: Preprocessing ...
% 9.96/2.10 Prover 13: Preprocessing ...
% 9.96/2.10 Prover 19: Preprocessing ...
% 10.13/2.12 Prover 16: Warning: ignoring some quantifiers
% 10.13/2.12 Prover 16: Constructing countermodel ...
% 10.13/2.13 Prover 13: Warning: ignoring some quantifiers
% 10.22/2.13 Prover 13: Constructing countermodel ...
% 10.22/2.15 Prover 19: Warning: ignoring some quantifiers
% 10.22/2.15 Prover 19: Constructing countermodel ...
% 10.22/2.19 Prover 19: gave up
% 10.86/2.23 Prover 16: gave up
% 10.86/2.24 Prover 13: gave up
% 15.25/3.03 Prover 11: Found proof (size 58)
% 15.25/3.03 Prover 11: proved (1312ms)
% 15.25/3.03 Prover 4: stopped
% 15.25/3.03
% 15.25/3.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.25/3.03
% 15.25/3.04 % SZS output start Proof for theBenchmark
% 15.25/3.04 Assumptions after simplification:
% 15.25/3.04 ---------------------------------
% 15.25/3.05
% 15.25/3.05 (apart3)
% 15.77/3.09 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0))
% 15.77/3.09
% 15.77/3.09 (ceq3)
% 15.91/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 15.91/3.10 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2)
% 15.91/3.10 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 15.91/3.10 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 15.91/3.10 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~
% 15.91/3.10 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 15.91/3.10 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 15.91/3.10 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~
% 15.91/3.10 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 15.91/3.10 convergent_lines(v0, v2) = 0)
% 15.91/3.10
% 15.91/3.10 (ci3)
% 15.91/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 15.91/3.10 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0)
% 15.91/3.10 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) &
% 15.91/3.10 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 15.91/3.10 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 15.91/3.10 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 &
% 15.91/3.10 apart_point_and_line(v2, v0) = v3 & $i(v2)))
% 15.91/3.10
% 15.91/3.10 (ci4)
% 15.91/3.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) =
% 15.91/3.11 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0)
% 15.91/3.11 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) &
% 15.91/3.11 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 15.91/3.11 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 15.91/3.11 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 &
% 15.91/3.11 apart_point_and_line(v2, v1) = v3 & $i(v2)))
% 15.91/3.11
% 15.91/3.11 (con)
% 15.91/3.11 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ?
% 15.91/3.11 [v5: $i] : ( ~ (v4 = 0) & ~ (v3 = 0) & intersection_point(v0, v1) = v5 &
% 15.91/3.11 apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3 &
% 15.91/3.11 convergent_lines(v0, v1) = 0 & distinct_points(v2, v5) = 0 & $i(v5) & $i(v2)
% 15.91/3.11 & $i(v1) & $i(v0))
% 15.91/3.11
% 15.91/3.11 (cu1)
% 16.07/3.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 16.07/3.13 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 16.07/3.13 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 16.07/3.13 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 16.07/3.13 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 &
% 16.07/3.13 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2,
% 16.07/3.13 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 16.07/3.13 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1,
% 16.07/3.13 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~
% 16.07/3.13 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 16.07/3.13 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 16.07/3.13 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0,
% 16.07/3.13 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 16.07/3.13 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 16.07/3.13 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 16.07/3.13 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 16.07/3.13 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 =
% 16.07/3.13 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 &
% 16.07/3.13 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2,
% 16.07/3.13 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 16.07/3.13 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 16.07/3.13 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~
% 16.07/3.13 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 16.07/3.13 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 =
% 16.07/3.13 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 &
% 16.07/3.13 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2,
% 16.07/3.13 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0:
% 16.07/3.13 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 16.07/3.13 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~
% 16.07/3.13 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~
% 16.07/3.13 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 16.07/3.13 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 &
% 16.07/3.13 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0,
% 16.07/3.13 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 16.07/3.13 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0,
% 16.07/3.13 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~
% 16.07/3.13 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 16.07/3.13 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 16.07/3.13 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1,
% 16.07/3.13 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i]
% 16.07/3.13 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) |
% 16.07/3.13 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 16.07/3.13 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 =
% 16.07/3.13 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 &
% 16.07/3.13 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0,
% 16.07/3.13 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 16.07/3.13
% 16.07/3.13 (function-axioms)
% 16.07/3.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.07/3.14 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) &
% 16.07/3.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.07/3.14 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 16.07/3.14 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 16.07/3.14 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 16.07/3.14 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.07/3.14 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.07/3.14 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & !
% 16.07/3.14 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 16.07/3.14 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3,
% 16.07/3.14 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 16.07/3.14 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 16.07/3.14 (distinct_points(v3, v2) = v0))
% 16.07/3.14
% 16.07/3.14 Further assumptions not needed in the proof:
% 16.07/3.14 --------------------------------------------
% 16.07/3.14 apart1, apart2, apart4, apart5, ax6, ceq1, ceq2, ci1, ci2
% 16.07/3.14
% 16.07/3.14 Those formulas are unsatisfiable:
% 16.07/3.14 ---------------------------------
% 16.07/3.14
% 16.07/3.14 Begin of proof
% 16.07/3.14 |
% 16.07/3.14 | ALPHA: (ci3) implies:
% 16.07/3.14 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0,
% 16.07/3.14 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] :
% 16.07/3.14 | (( ~ (v4 = 0) & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) &
% 16.07/3.14 | convergent_lines(v0, v1) = v3)))
% 16.07/3.14 |
% 16.07/3.14 | ALPHA: (ci4) implies:
% 16.07/3.14 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0,
% 16.07/3.14 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] :
% 16.07/3.14 | (( ~ (v4 = 0) & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) &
% 16.07/3.14 | convergent_lines(v0, v1) = v3)))
% 16.07/3.14 |
% 16.07/3.14 | ALPHA: (cu1) implies:
% 16.07/3.14 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 16.07/3.14 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5)
% 16.07/3.14 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0,
% 16.07/3.14 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 16.07/3.14 | [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 &
% 16.07/3.14 | apart_point_and_line(v1, v3) = 0) | (v7 = 0 &
% 16.07/3.15 | apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) &
% 16.07/3.15 | distinct_lines(v2, v3) = v6)))
% 16.07/3.15 |
% 16.07/3.15 | ALPHA: (ceq3) implies:
% 16.07/3.15 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 16.07/3.15 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) |
% 16.07/3.15 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0)
% 16.07/3.15 |
% 16.07/3.15 | ALPHA: (function-axioms) implies:
% 16.07/3.15 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 16.07/3.15 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 16.07/3.15 | (convergent_lines(v3, v2) = v0))
% 16.07/3.15 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 16.07/3.15 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 16.07/3.15 | (apart_point_and_line(v3, v2) = v0))
% 16.07/3.15 |
% 16.07/3.15 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2,
% 16.07/3.15 | all_17_3, all_17_4, all_17_5 gives:
% 16.07/3.15 | (7) ~ (all_17_1 = 0) & ~ (all_17_2 = 0) & intersection_point(all_17_5,
% 16.07/3.15 | all_17_4) = all_17_0 & apart_point_and_line(all_17_3, all_17_4) =
% 16.07/3.15 | all_17_1 & apart_point_and_line(all_17_3, all_17_5) = all_17_2 &
% 16.07/3.15 | convergent_lines(all_17_5, all_17_4) = 0 & distinct_points(all_17_3,
% 16.07/3.15 | all_17_0) = 0 & $i(all_17_0) & $i(all_17_3) & $i(all_17_4) &
% 16.07/3.15 | $i(all_17_5)
% 16.07/3.15 |
% 16.07/3.15 | ALPHA: (7) implies:
% 16.07/3.15 | (8) ~ (all_17_2 = 0)
% 16.07/3.15 | (9) ~ (all_17_1 = 0)
% 16.07/3.15 | (10) $i(all_17_5)
% 16.07/3.15 | (11) $i(all_17_4)
% 16.07/3.15 | (12) $i(all_17_3)
% 16.07/3.15 | (13) $i(all_17_0)
% 16.07/3.15 | (14) distinct_points(all_17_3, all_17_0) = 0
% 16.07/3.15 | (15) convergent_lines(all_17_5, all_17_4) = 0
% 16.07/3.15 | (16) apart_point_and_line(all_17_3, all_17_5) = all_17_2
% 16.07/3.15 | (17) apart_point_and_line(all_17_3, all_17_4) = all_17_1
% 16.07/3.15 | (18) intersection_point(all_17_5, all_17_4) = all_17_0
% 16.07/3.15 |
% 16.07/3.16 | GROUND_INST: instantiating (3) with all_17_3, all_17_0, all_17_4, all_17_5,
% 16.07/3.16 | all_17_1, all_17_2, simplifying with (10), (11), (12), (13),
% 16.07/3.16 | (14), (16), (17) gives:
% 16.07/3.16 | (19) all_17_1 = 0 | all_17_2 = 0 | ? [v0: int] : ? [v1: int] : ? [v2:
% 16.07/3.16 | int] : ((v2 = 0 & apart_point_and_line(all_17_0, all_17_5) = 0) |
% 16.07/3.16 | (v1 = 0 & apart_point_and_line(all_17_0, all_17_4) = 0) | ( ~ (v0 =
% 16.07/3.16 | 0) & distinct_lines(all_17_4, all_17_5) = v0))
% 16.07/3.16 |
% 16.07/3.16 | GROUND_INST: instantiating (2) with all_17_5, all_17_4, all_17_0, simplifying
% 16.07/3.16 | with (10), (11), (18) gives:
% 16.07/3.16 | (20) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) &
% 16.07/3.16 | apart_point_and_line(all_17_0, all_17_4) = v1) | ( ~ (v0 = 0) &
% 16.07/3.16 | convergent_lines(all_17_5, all_17_4) = v0))
% 16.07/3.16 |
% 16.07/3.16 | GROUND_INST: instantiating (1) with all_17_5, all_17_4, all_17_0, simplifying
% 16.07/3.16 | with (10), (11), (18) gives:
% 16.07/3.16 | (21) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) &
% 16.07/3.16 | apart_point_and_line(all_17_0, all_17_5) = v1) | ( ~ (v0 = 0) &
% 16.07/3.16 | convergent_lines(all_17_5, all_17_4) = v0))
% 16.07/3.16 |
% 16.07/3.16 | DELTA: instantiating (21) with fresh symbols all_24_0, all_24_1 gives:
% 16.07/3.16 | (22) ( ~ (all_24_0 = 0) & apart_point_and_line(all_17_0, all_17_5) =
% 16.07/3.16 | all_24_0) | ( ~ (all_24_1 = 0) & convergent_lines(all_17_5,
% 16.07/3.16 | all_17_4) = all_24_1)
% 16.07/3.16 |
% 16.07/3.16 | DELTA: instantiating (20) with fresh symbols all_33_0, all_33_1 gives:
% 16.07/3.16 | (23) ( ~ (all_33_0 = 0) & apart_point_and_line(all_17_0, all_17_4) =
% 16.07/3.16 | all_33_0) | ( ~ (all_33_1 = 0) & convergent_lines(all_17_5,
% 16.07/3.16 | all_17_4) = all_33_1)
% 16.07/3.16 |
% 16.07/3.16 | BETA: splitting (23) gives:
% 16.07/3.16 |
% 16.07/3.16 | Case 1:
% 16.07/3.16 | |
% 16.07/3.16 | | (24) ~ (all_33_0 = 0) & apart_point_and_line(all_17_0, all_17_4) =
% 16.07/3.16 | | all_33_0
% 16.07/3.16 | |
% 16.07/3.16 | | ALPHA: (24) implies:
% 16.07/3.16 | | (25) ~ (all_33_0 = 0)
% 16.07/3.16 | | (26) apart_point_and_line(all_17_0, all_17_4) = all_33_0
% 16.07/3.16 | |
% 16.07/3.16 | | BETA: splitting (22) gives:
% 16.07/3.16 | |
% 16.07/3.16 | | Case 1:
% 16.07/3.16 | | |
% 16.07/3.16 | | | (27) ~ (all_24_0 = 0) & apart_point_and_line(all_17_0, all_17_5) =
% 16.07/3.16 | | | all_24_0
% 16.07/3.16 | | |
% 16.07/3.16 | | | ALPHA: (27) implies:
% 16.07/3.16 | | | (28) ~ (all_24_0 = 0)
% 16.07/3.16 | | | (29) apart_point_and_line(all_17_0, all_17_5) = all_24_0
% 16.07/3.16 | | |
% 16.07/3.16 | | | BETA: splitting (19) gives:
% 16.07/3.16 | | |
% 16.07/3.16 | | | Case 1:
% 16.07/3.16 | | | |
% 16.07/3.16 | | | | (30) all_17_1 = 0
% 16.07/3.16 | | | |
% 16.07/3.16 | | | | REDUCE: (9), (30) imply:
% 16.07/3.16 | | | | (31) $false
% 16.07/3.16 | | | |
% 16.07/3.16 | | | | CLOSE: (31) is inconsistent.
% 16.07/3.16 | | | |
% 16.07/3.17 | | | Case 2:
% 16.07/3.17 | | | |
% 16.07/3.17 | | | | (32) all_17_2 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2
% 16.07/3.17 | | | | = 0 & apart_point_and_line(all_17_0, all_17_5) = 0) | (v1 =
% 16.07/3.17 | | | | 0 & apart_point_and_line(all_17_0, all_17_4) = 0) | ( ~ (v0
% 16.07/3.17 | | | | = 0) & distinct_lines(all_17_4, all_17_5) = v0))
% 16.07/3.17 | | | |
% 16.07/3.17 | | | | BETA: splitting (32) gives:
% 16.07/3.17 | | | |
% 16.07/3.17 | | | | Case 1:
% 16.07/3.17 | | | | |
% 16.07/3.17 | | | | | (33) all_17_2 = 0
% 16.07/3.17 | | | | |
% 16.07/3.17 | | | | | REDUCE: (8), (33) imply:
% 16.07/3.17 | | | | | (34) $false
% 16.07/3.17 | | | | |
% 16.07/3.17 | | | | | CLOSE: (34) is inconsistent.
% 16.07/3.17 | | | | |
% 16.07/3.17 | | | | Case 2:
% 16.07/3.17 | | | | |
% 16.07/3.17 | | | | | (35) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 16.07/3.17 | | | | | apart_point_and_line(all_17_0, all_17_5) = 0) | (v1 = 0 &
% 16.07/3.17 | | | | | apart_point_and_line(all_17_0, all_17_4) = 0) | ( ~ (v0 =
% 16.07/3.17 | | | | | 0) & distinct_lines(all_17_4, all_17_5) = v0))
% 16.07/3.17 | | | | |
% 16.07/3.17 | | | | | DELTA: instantiating (35) with fresh symbols all_96_0, all_96_1,
% 16.07/3.17 | | | | | all_96_2 gives:
% 16.07/3.17 | | | | | (36) (all_96_0 = 0 & apart_point_and_line(all_17_0, all_17_5) = 0)
% 16.07/3.17 | | | | | | (all_96_1 = 0 & apart_point_and_line(all_17_0, all_17_4) =
% 16.07/3.17 | | | | | 0) | ( ~ (all_96_2 = 0) & distinct_lines(all_17_4, all_17_5)
% 16.07/3.17 | | | | | = all_96_2)
% 16.07/3.17 | | | | |
% 16.07/3.17 | | | | | BETA: splitting (36) gives:
% 16.07/3.17 | | | | |
% 16.07/3.17 | | | | | Case 1:
% 16.07/3.17 | | | | | |
% 16.07/3.17 | | | | | | (37) all_96_0 = 0 & apart_point_and_line(all_17_0, all_17_5) = 0
% 16.07/3.17 | | | | | |
% 16.07/3.17 | | | | | | ALPHA: (37) implies:
% 16.07/3.17 | | | | | | (38) apart_point_and_line(all_17_0, all_17_5) = 0
% 16.07/3.17 | | | | | |
% 16.07/3.17 | | | | | | GROUND_INST: instantiating (6) with 0, all_24_0, all_17_5, all_17_0,
% 16.07/3.17 | | | | | | simplifying with (29), (38) gives:
% 16.07/3.17 | | | | | | (39) all_24_0 = 0
% 16.07/3.17 | | | | | |
% 16.07/3.17 | | | | | | REDUCE: (28), (39) imply:
% 16.07/3.17 | | | | | | (40) $false
% 16.07/3.17 | | | | | |
% 16.07/3.17 | | | | | | CLOSE: (40) is inconsistent.
% 16.07/3.17 | | | | | |
% 16.07/3.17 | | | | | Case 2:
% 16.07/3.17 | | | | | |
% 16.07/3.17 | | | | | | (41) (all_96_1 = 0 & apart_point_and_line(all_17_0, all_17_4) =
% 16.07/3.17 | | | | | | 0) | ( ~ (all_96_2 = 0) & distinct_lines(all_17_4,
% 16.07/3.17 | | | | | | all_17_5) = all_96_2)
% 16.07/3.17 | | | | | |
% 16.07/3.17 | | | | | | BETA: splitting (41) gives:
% 16.07/3.17 | | | | | |
% 16.07/3.17 | | | | | | Case 1:
% 16.07/3.17 | | | | | | |
% 16.07/3.17 | | | | | | | (42) all_96_1 = 0 & apart_point_and_line(all_17_0, all_17_4) =
% 16.07/3.17 | | | | | | | 0
% 16.07/3.17 | | | | | | |
% 16.07/3.17 | | | | | | | ALPHA: (42) implies:
% 16.07/3.17 | | | | | | | (43) apart_point_and_line(all_17_0, all_17_4) = 0
% 16.07/3.17 | | | | | | |
% 16.07/3.17 | | | | | | | GROUND_INST: instantiating (6) with 0, all_33_0, all_17_4,
% 16.07/3.17 | | | | | | | all_17_0, simplifying with (26), (43) gives:
% 16.07/3.17 | | | | | | | (44) all_33_0 = 0
% 16.07/3.17 | | | | | | |
% 16.07/3.17 | | | | | | | REDUCE: (25), (44) imply:
% 16.07/3.17 | | | | | | | (45) $false
% 16.07/3.17 | | | | | | |
% 16.07/3.17 | | | | | | | CLOSE: (45) is inconsistent.
% 16.07/3.17 | | | | | | |
% 16.07/3.17 | | | | | | Case 2:
% 16.07/3.17 | | | | | | |
% 16.07/3.17 | | | | | | | (46) ~ (all_96_2 = 0) & distinct_lines(all_17_4, all_17_5) =
% 16.07/3.17 | | | | | | | all_96_2
% 16.07/3.17 | | | | | | |
% 16.07/3.17 | | | | | | | ALPHA: (46) implies:
% 16.07/3.17 | | | | | | | (47) ~ (all_96_2 = 0)
% 16.07/3.17 | | | | | | | (48) distinct_lines(all_17_4, all_17_5) = all_96_2
% 16.07/3.17 | | | | | | |
% 16.07/3.17 | | | | | | | GROUND_INST: instantiating (4) with all_17_5, all_17_4, all_17_5,
% 16.07/3.17 | | | | | | | all_96_2, simplifying with (10), (11), (15), (48)
% 16.07/3.17 | | | | | | | gives:
% 16.07/3.17 | | | | | | | (49) all_96_2 = 0 | convergent_lines(all_17_5, all_17_5) = 0
% 16.07/3.17 | | | | | | |
% 16.07/3.17 | | | | | | | BETA: splitting (49) gives:
% 16.07/3.17 | | | | | | |
% 16.07/3.17 | | | | | | | Case 1:
% 16.07/3.17 | | | | | | | |
% 16.07/3.17 | | | | | | | | (50) convergent_lines(all_17_5, all_17_5) = 0
% 16.07/3.17 | | | | | | | |
% 16.07/3.17 | | | | | | | | GROUND_INST: instantiating (apart3) with all_17_5, simplifying
% 16.07/3.17 | | | | | | | | with (10), (50) gives:
% 16.07/3.17 | | | | | | | | (51) $false
% 16.07/3.17 | | | | | | | |
% 16.07/3.17 | | | | | | | | CLOSE: (51) is inconsistent.
% 16.07/3.17 | | | | | | | |
% 16.07/3.17 | | | | | | | Case 2:
% 16.07/3.17 | | | | | | | |
% 16.07/3.17 | | | | | | | | (52) all_96_2 = 0
% 16.07/3.17 | | | | | | | |
% 16.07/3.17 | | | | | | | | REDUCE: (47), (52) imply:
% 16.07/3.17 | | | | | | | | (53) $false
% 16.07/3.17 | | | | | | | |
% 16.07/3.17 | | | | | | | | CLOSE: (53) is inconsistent.
% 16.07/3.17 | | | | | | | |
% 16.07/3.17 | | | | | | | End of split
% 16.07/3.17 | | | | | | |
% 16.07/3.17 | | | | | | End of split
% 16.07/3.17 | | | | | |
% 16.07/3.17 | | | | | End of split
% 16.07/3.17 | | | | |
% 16.07/3.17 | | | | End of split
% 16.07/3.17 | | | |
% 16.07/3.17 | | | End of split
% 16.07/3.17 | | |
% 16.07/3.17 | | Case 2:
% 16.07/3.17 | | |
% 16.07/3.17 | | | (54) ~ (all_24_1 = 0) & convergent_lines(all_17_5, all_17_4) =
% 16.07/3.17 | | | all_24_1
% 16.07/3.17 | | |
% 16.07/3.17 | | | ALPHA: (54) implies:
% 16.07/3.17 | | | (55) ~ (all_24_1 = 0)
% 16.07/3.17 | | | (56) convergent_lines(all_17_5, all_17_4) = all_24_1
% 16.07/3.17 | | |
% 16.07/3.17 | | | GROUND_INST: instantiating (5) with 0, all_24_1, all_17_4, all_17_5,
% 16.07/3.17 | | | simplifying with (15), (56) gives:
% 16.07/3.17 | | | (57) all_24_1 = 0
% 16.07/3.18 | | |
% 16.07/3.18 | | | REDUCE: (55), (57) imply:
% 16.07/3.18 | | | (58) $false
% 16.07/3.18 | | |
% 16.07/3.18 | | | CLOSE: (58) is inconsistent.
% 16.07/3.18 | | |
% 16.07/3.18 | | End of split
% 16.07/3.18 | |
% 16.07/3.18 | Case 2:
% 16.07/3.18 | |
% 16.07/3.18 | | (59) ~ (all_33_1 = 0) & convergent_lines(all_17_5, all_17_4) = all_33_1
% 16.07/3.18 | |
% 16.07/3.18 | | ALPHA: (59) implies:
% 16.07/3.18 | | (60) ~ (all_33_1 = 0)
% 16.07/3.18 | | (61) convergent_lines(all_17_5, all_17_4) = all_33_1
% 16.07/3.18 | |
% 16.07/3.18 | | GROUND_INST: instantiating (5) with 0, all_33_1, all_17_4, all_17_5,
% 16.07/3.18 | | simplifying with (15), (61) gives:
% 16.07/3.18 | | (62) all_33_1 = 0
% 16.07/3.18 | |
% 16.07/3.18 | | REDUCE: (60), (62) imply:
% 16.07/3.18 | | (63) $false
% 16.07/3.18 | |
% 16.07/3.18 | | CLOSE: (63) is inconsistent.
% 16.07/3.18 | |
% 16.07/3.18 | End of split
% 16.07/3.18 |
% 16.07/3.18 End of proof
% 16.07/3.18 % SZS output end Proof for theBenchmark
% 16.07/3.18
% 16.07/3.18 2514ms
%------------------------------------------------------------------------------