TSTP Solution File: GEO269+3 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO269+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 : n009.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 23:22:53 EDT 2023
% Result : Theorem 46.56s 6.68s
% Output : Proof 47.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO269+3 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 19:47:50 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.56/0.60 ________ _____
% 0.56/0.60 ___ __ \_________(_)________________________________
% 0.56/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.56/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.56/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.56/0.60
% 0.56/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.56/0.60 (2023-06-19)
% 0.56/0.60
% 0.56/0.60 (c) Philipp Rümmer, 2009-2023
% 0.56/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.56/0.60 Amanda Stjerna.
% 0.56/0.60 Free software under BSD-3-Clause.
% 0.56/0.60
% 0.56/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.56/0.60
% 0.56/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.56/0.61 Running up to 7 provers in parallel.
% 0.56/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.56/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.56/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.56/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.56/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.56/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.56/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.60/1.16 Prover 1: Preprocessing ...
% 3.60/1.16 Prover 4: Preprocessing ...
% 3.60/1.18 Prover 5: Preprocessing ...
% 3.60/1.18 Prover 2: Preprocessing ...
% 3.60/1.18 Prover 6: Preprocessing ...
% 3.60/1.18 Prover 3: Preprocessing ...
% 3.60/1.18 Prover 0: Preprocessing ...
% 7.43/1.71 Prover 5: Proving ...
% 7.43/1.73 Prover 6: Constructing countermodel ...
% 7.43/1.74 Prover 2: Proving ...
% 8.13/1.77 Prover 1: Constructing countermodel ...
% 8.13/1.77 Prover 3: Constructing countermodel ...
% 8.76/1.88 Prover 6: gave up
% 8.76/1.88 Prover 3: gave up
% 8.76/1.89 Prover 1: gave up
% 8.76/1.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.76/1.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.22/1.91 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 9.67/2.00 Prover 7: Preprocessing ...
% 9.67/2.01 Prover 9: Preprocessing ...
% 9.67/2.01 Prover 8: Preprocessing ...
% 10.38/2.08 Prover 7: Warning: ignoring some quantifiers
% 10.64/2.11 Prover 7: Constructing countermodel ...
% 10.64/2.13 Prover 4: Constructing countermodel ...
% 11.12/2.17 Prover 0: Proving ...
% 11.12/2.20 Prover 8: Warning: ignoring some quantifiers
% 11.66/2.22 Prover 8: Constructing countermodel ...
% 11.66/2.26 Prover 7: gave up
% 11.66/2.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.12/2.32 Prover 10: Preprocessing ...
% 12.12/2.35 Prover 8: gave up
% 12.12/2.35 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.90/2.39 Prover 10: Warning: ignoring some quantifiers
% 12.90/2.40 Prover 11: Preprocessing ...
% 12.90/2.40 Prover 10: Constructing countermodel ...
% 13.39/2.51 Prover 10: gave up
% 13.39/2.52 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 13.99/2.54 Prover 9: Constructing countermodel ...
% 13.99/2.55 Prover 12: Preprocessing ...
% 15.82/2.81 Prover 12: Proving ...
% 16.46/2.83 Prover 11: Constructing countermodel ...
% 37.05/5.45 Prover 12: stopped
% 37.05/5.47 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 37.05/5.52 Prover 13: Preprocessing ...
% 38.06/5.62 Prover 13: Warning: ignoring some quantifiers
% 38.06/5.63 Prover 13: Constructing countermodel ...
% 39.33/5.76 Prover 13: gave up
% 39.33/5.76 Prover 14: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=414236379
% 39.33/5.78 Prover 14: Preprocessing ...
% 41.75/6.10 Prover 14: Proving ...
% 46.56/6.68 Prover 11: Found proof (size 88)
% 46.56/6.68 Prover 11: proved (4331ms)
% 46.56/6.68 Prover 2: stopped
% 46.56/6.68 Prover 9: stopped
% 46.56/6.68 Prover 5: stopped
% 46.56/6.68 Prover 0: stopped
% 46.56/6.68 Prover 14: stopped
% 46.56/6.68 Prover 4: stopped
% 46.56/6.68
% 46.56/6.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 46.56/6.68
% 46.56/6.69 % SZS output start Proof for theBenchmark
% 46.56/6.69 Assumptions after simplification:
% 46.56/6.69 ---------------------------------
% 46.56/6.69
% 46.56/6.69 (a1_defns)
% 46.56/6.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 46.56/6.72 (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ~
% 46.56/6.72 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) &
% 46.56/6.72 unequally_directed_opposite_lines(v0, v1) = v4)) & ! [v0: $i] : ! [v1:
% 46.56/6.72 $i] : ! [v2: int] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1)
% 46.56/6.72 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0)
% 46.56/6.72 & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4 & $i(v3)))
% 46.56/6.72 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (reverse_line(v1) = v2) | ~
% 46.56/6.72 (unequally_directed_lines(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) |
% 46.56/6.72 unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] :
% 46.56/6.72 ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 46.56/6.72 ? [v2: $i] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0 &
% 46.56/6.72 $i(v2)))
% 46.56/6.72
% 46.56/6.72 (a5_defns)
% 46.56/6.72 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 46.56/6.72 (equally_directed_opposite_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 46.56/6.72 unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] :
% 46.56/6.72 ! [v2: int] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) |
% 46.56/6.72 ~ $i(v1) | ~ $i(v0) | equally_directed_opposite_lines(v0, v1) = 0) & !
% 46.56/6.73 [v0: $i] : ! [v1: $i] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) |
% 46.56/6.73 ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 46.56/6.73 unequally_directed_opposite_lines(v0, v1) = v2)) & ! [v0: $i] : ! [v1:
% 46.56/6.73 $i] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ~ $i(v1) | ~
% 46.56/6.73 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & equally_directed_opposite_lines(v0,
% 46.56/6.73 v1) = v2))
% 46.56/6.73
% 46.56/6.73 (a7_defns)
% 46.96/6.73 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (convergent_lines(v0,
% 46.96/6.73 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~
% 46.96/6.73 (v4 = 0) & unequally_directed_opposite_lines(v0, v1) = v4) | ( ~ (v3 =
% 46.96/6.73 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1:
% 46.96/6.73 $i] : ! [v2: any] : ( ~ (unequally_directed_lines(v0, v1) = v2) | ~ $i(v1)
% 46.96/6.73 | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & v2 = 0 &
% 46.96/6.73 unequally_directed_opposite_lines(v0, v1) = 0) | ( ~ (v3 = 0) &
% 46.96/6.73 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 46.96/6.73 any] : ( ~ (unequally_directed_opposite_lines(v0, v1) = v2) | ~ $i(v1) | ~
% 46.96/6.73 $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & v2 = 0 &
% 46.96/6.73 unequally_directed_lines(v0, v1) = 0) | ( ~ (v3 = 0) &
% 46.96/6.73 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 46.96/6.73 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 46.96/6.73 (unequally_directed_lines(v0, v1) = 0 &
% 46.96/6.73 unequally_directed_opposite_lines(v0, v1) = 0)) & ! [v0: $i] : ! [v1:
% 46.96/6.73 $i] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 46.96/6.73 ? [v2: int] : ? [v3: int] : ((v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~
% 46.96/6.73 (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2))) & ! [v0:
% 46.96/6.73 $i] : ! [v1: $i] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ~
% 46.96/6.73 $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 &
% 46.96/6.73 convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) &
% 46.96/6.73 unequally_directed_lines(v0, v1) = v2)))
% 46.96/6.73
% 46.96/6.73 (ax11_basics)
% 46.96/6.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (left_convergent_lines(v0, v2) =
% 46.96/6.73 0) | ~ (reverse_line(v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] :
% 46.96/6.73 ! [v1: $i] : ( ~ (left_convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0))
% 46.96/6.73
% 46.96/6.73 (ax4_basics)
% 46.96/6.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 46.96/6.74 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) =
% 46.96/6.74 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 46.96/6.74 distinct_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 46.96/6.74 ! [v3: int] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~
% 46.96/6.74 (distinct_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 46.96/6.74 distinct_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 46.96/6.74 [v3: int] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~
% 46.96/6.74 (distinct_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 46.96/6.74 distinct_lines(v1, v2) = 0)
% 46.96/6.74
% 46.96/6.74 (ax6_basics)
% 46.96/6.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 46.96/6.74 0 | v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v4) | ~
% 46.96/6.74 (unequally_directed_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 46.96/6.74 | ? [v5: int] : ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)) & !
% 46.96/6.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 46.96/6.74 (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0,
% 46.96/6.74 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 46.96/6.74 unequally_directed_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 46.96/6.74 $i] : ! [v3: int] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) |
% 46.96/6.74 ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 46.96/6.74 | unequally_directed_lines(v1, v2) = 0)
% 46.96/6.74
% 46.96/6.74 (ax8_basics)
% 46.96/6.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 46.96/6.74 (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ~
% 46.96/6.74 $i(v1) | ~ $i(v0) | unequally_directed_lines(v0, v1) = 0) & ! [v0: $i] :
% 46.96/6.74 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) =
% 46.96/6.74 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (reverse_line(v1) = v3 &
% 46.96/6.74 unequally_directed_lines(v0, v3) = 0 & $i(v3)))
% 46.96/6.74
% 46.96/6.74 (ax8_cons_objs)
% 46.96/6.74 ! [v0: $i] : ! [v1: $i] : ( ~ (reverse_line(v0) = v1) | ~ $i(v0) | ? [v2:
% 46.96/6.74 int] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 46.96/6.74
% 46.96/6.74 (ax9_basics)
% 46.96/6.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 46.96/6.74 (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ~
% 46.96/6.74 $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ((v6 = 0 &
% 46.96/6.74 left_convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) &
% 46.96/6.74 unequally_directed_lines(v0, v2) = v5) | ( ~ (v4 = 0) &
% 46.96/6.74 unequally_directed_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] :
% 46.96/6.74 ! [v2: int] : (v2 = 0 | ~ (left_convergent_lines(v0, v1) = v2) | ~ $i(v1) |
% 46.96/6.74 ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : ((v6 =
% 46.96/6.74 0 & left_convergent_lines(v0, v4) = 0 & reverse_line(v1) = v4 & $i(v4))
% 46.96/6.74 | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4)
% 46.96/6.74 = v5 & $i(v4)) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 46.96/6.74 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (reverse_line(v1) = v2) | ~
% 46.96/6.74 (unequally_directed_lines(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 46.96/6.74 int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 & left_convergent_lines(v0,
% 46.96/6.74 v2) = 0) | (v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0)
% 46.96/6.74 & unequally_directed_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] :
% 46.96/6.74 ( ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 46.96/6.74 $i] : ? [v3: int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 &
% 46.96/6.74 left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2 & $i(v2)) |
% 46.96/6.74 (v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) &
% 46.96/6.74 reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3 &
% 46.96/6.74 $i(v2))))
% 46.96/6.74
% 46.96/6.74 (con)
% 46.96/6.74 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 46.96/6.74 equally_directed_opposite_lines(v0, v1) = v2 & reverse_line(v0) = v1 &
% 46.96/6.74 $i(v1) & $i(v0))
% 46.96/6.74
% 46.96/6.75 (function-axioms)
% 46.96/6.75 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 46.96/6.75 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_on_line(v5, v4,
% 46.96/6.75 v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0:
% 46.96/6.75 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 46.96/6.75 : ! [v4: $i] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~
% 46.96/6.75 (before_on_line(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 46.96/6.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 46.96/6.75 (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) &
% 46.96/6.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 46.96/6.75 (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) =
% 46.96/6.75 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 46.96/6.75 ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 46.96/6.75 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 46.96/6.75 [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~
% 46.96/6.75 (distinct_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 46.96/6.75 ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 46.96/6.75 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 46.96/6.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 46.96/6.75 (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & !
% 46.96/6.75 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 46.96/6.75 $i] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~
% 46.96/6.75 (incident_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 46.96/6.75 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 46.96/6.75 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & !
% 46.96/6.75 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 46.96/6.75 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 46.96/6.75 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 46.96/6.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 46.96/6.75 (equally_directed_opposite_lines(v3, v2) = v1) | ~
% 46.96/6.75 (equally_directed_opposite_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool]
% 46.96/6.75 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 46.96/6.75 (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) =
% 46.96/6.75 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 46.96/6.75 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~
% 46.96/6.75 (left_convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 46.96/6.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 46.96/6.75 (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) =
% 46.96/6.75 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 46.96/6.75 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~
% 46.96/6.75 (left_apart_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 46.96/6.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 46.96/6.75 (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0)) & !
% 46.96/6.75 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 46.96/6.75 $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~
% 46.96/6.75 (unequally_directed_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 46.96/6.75 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 46.96/6.75 (unequally_directed_opposite_lines(v3, v2) = v1) | ~
% 46.96/6.75 (unequally_directed_opposite_lines(v3, v2) = v0)) & ! [v0:
% 46.96/6.75 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 46.96/6.75 ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 46.96/6.75 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (line(v2) = v1) | ~
% 46.96/6.75 (line(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 46.96/6.75 (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 46.96/6.75
% 46.96/6.75 Further assumptions not needed in the proof:
% 46.96/6.75 --------------------------------------------
% 46.96/6.75 a2_defns, a3_defns, a4_defns, a6_defns, a8_defns, a9_defns, ax10_basics,
% 46.96/6.75 ax10_cons_objs, ax1_basics, ax1_cons_objs, ax1_subs, ax1_uniq_cons, ax2_basics,
% 46.96/6.75 ax2_cons_objs, ax2_subs, ax2_uniq_cons, ax3_basics, ax3_cons_objs, ax3_subs,
% 46.96/6.75 ax4_cons_objs, ax4_defns, ax5_basics, ax5_cons_objs, ax6_cons_objs, ax7_basics,
% 46.96/6.75 ax7_cons_objs, ax9_cons_objs
% 46.96/6.75
% 46.96/6.75 Those formulas are unsatisfiable:
% 46.96/6.75 ---------------------------------
% 46.96/6.75
% 46.96/6.75 Begin of proof
% 46.96/6.75 |
% 46.96/6.75 | ALPHA: (a1_defns) implies:
% 46.96/6.76 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (unequally_directed_opposite_lines(v0,
% 46.96/6.76 | v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 46.96/6.76 | (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0 &
% 46.96/6.76 | $i(v2)))
% 46.96/6.76 |
% 46.96/6.76 | ALPHA: (a5_defns) implies:
% 46.96/6.76 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 46.96/6.76 | (equally_directed_opposite_lines(v0, v1) = v2) | ~ $i(v1) | ~
% 46.96/6.76 | $i(v0) | unequally_directed_opposite_lines(v0, v1) = 0)
% 46.96/6.76 |
% 46.96/6.76 | ALPHA: (a7_defns) implies:
% 46.96/6.76 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (unequally_directed_opposite_lines(v0,
% 46.96/6.76 | v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] :
% 46.96/6.76 | ((v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) &
% 46.96/6.76 | unequally_directed_lines(v0, v1) = v2)))
% 46.96/6.76 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 46.96/6.76 | (unequally_directed_opposite_lines(v0, v1) = v2) | ~ $i(v1) | ~
% 46.96/6.76 | $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & v2 = 0 &
% 46.96/6.76 | unequally_directed_lines(v0, v1) = 0) | ( ~ (v3 = 0) &
% 46.96/6.76 | convergent_lines(v0, v1) = v3)))
% 46.96/6.76 |
% 46.96/6.76 | ALPHA: (ax4_basics) implies:
% 46.96/6.76 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] :
% 46.96/6.76 | (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~
% 46.96/6.76 | (distinct_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 46.96/6.76 | ? [v5: int] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5))
% 46.96/6.76 |
% 46.96/6.76 | ALPHA: (ax6_basics) implies:
% 46.96/6.76 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] :
% 46.96/6.76 | (v4 = 0 | v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v4) | ~
% 46.96/6.76 | (unequally_directed_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 46.96/6.76 | $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & unequally_directed_lines(v0,
% 46.96/6.76 | v1) = v5))
% 46.96/6.76 |
% 46.96/6.76 | ALPHA: (ax8_basics) implies:
% 46.96/6.76 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 46.96/6.76 | (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3)
% 46.96/6.76 | | ~ $i(v1) | ~ $i(v0) | unequally_directed_lines(v0, v1) = 0)
% 46.96/6.76 |
% 46.96/6.76 | ALPHA: (ax9_basics) implies:
% 46.96/6.76 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (reverse_line(v1) = v2) |
% 46.96/6.76 | ~ (unequally_directed_lines(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) |
% 46.96/6.76 | ? [v3: int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 &
% 46.96/6.76 | left_convergent_lines(v0, v2) = 0) | (v4 = 0 &
% 46.96/6.76 | left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) &
% 46.96/6.76 | unequally_directed_lines(v0, v1) = v3)))
% 46.96/6.76 |
% 46.96/6.76 | ALPHA: (ax11_basics) implies:
% 46.96/6.76 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (left_convergent_lines(v0, v1) = 0) |
% 46.96/6.76 | ~ $i(v1) | ~ $i(v0))
% 46.96/6.76 |
% 46.96/6.76 | ALPHA: (function-axioms) implies:
% 46.96/6.76 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 46.96/6.76 | : ! [v3: $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1)
% 46.96/6.76 | | ~ (unequally_directed_lines(v3, v2) = v0))
% 46.96/6.77 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 46.96/6.77 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 46.96/6.77 | (convergent_lines(v3, v2) = v0))
% 46.96/6.77 |
% 46.96/6.77 | DELTA: instantiating (con) with fresh symbols all_39_0, all_39_1, all_39_2
% 46.96/6.77 | gives:
% 47.14/6.77 | (12) ~ (all_39_0 = 0) & equally_directed_opposite_lines(all_39_2,
% 47.14/6.77 | all_39_1) = all_39_0 & reverse_line(all_39_2) = all_39_1 &
% 47.14/6.77 | $i(all_39_1) & $i(all_39_2)
% 47.14/6.77 |
% 47.14/6.77 | ALPHA: (12) implies:
% 47.14/6.77 | (13) ~ (all_39_0 = 0)
% 47.14/6.77 | (14) $i(all_39_2)
% 47.14/6.77 | (15) $i(all_39_1)
% 47.14/6.77 | (16) reverse_line(all_39_2) = all_39_1
% 47.14/6.77 | (17) equally_directed_opposite_lines(all_39_2, all_39_1) = all_39_0
% 47.14/6.77 |
% 47.14/6.77 | GROUND_INST: instantiating (ax8_cons_objs) with all_39_2, all_39_1,
% 47.14/6.77 | simplifying with (14), (16) gives:
% 47.14/6.77 | (18) ? [v0: int] : ( ~ (v0 = 0) & distinct_lines(all_39_2, all_39_1) = v0)
% 47.14/6.77 |
% 47.14/6.77 | GROUND_INST: instantiating (2) with all_39_2, all_39_1, all_39_0, simplifying
% 47.14/6.77 | with (14), (15), (17) gives:
% 47.14/6.77 | (19) all_39_0 = 0 | unequally_directed_opposite_lines(all_39_2, all_39_1) =
% 47.14/6.77 | 0
% 47.14/6.77 |
% 47.14/6.77 | DELTA: instantiating (18) with fresh symbol all_46_0 gives:
% 47.14/6.77 | (20) ~ (all_46_0 = 0) & distinct_lines(all_39_2, all_39_1) = all_46_0
% 47.14/6.77 |
% 47.14/6.77 | ALPHA: (20) implies:
% 47.14/6.77 | (21) ~ (all_46_0 = 0)
% 47.14/6.77 | (22) distinct_lines(all_39_2, all_39_1) = all_46_0
% 47.14/6.77 |
% 47.14/6.77 | BETA: splitting (19) gives:
% 47.14/6.77 |
% 47.14/6.77 | Case 1:
% 47.14/6.77 | |
% 47.14/6.77 | | (23) unequally_directed_opposite_lines(all_39_2, all_39_1) = 0
% 47.14/6.77 | |
% 47.14/6.77 | | GROUND_INST: instantiating (3) with all_39_2, all_39_1, simplifying with
% 47.14/6.77 | | (14), (15), (23) gives:
% 47.14/6.77 | | (24) ? [v0: int] : ? [v1: int] : ((v1 = 0 & convergent_lines(all_39_2,
% 47.14/6.77 | | all_39_1) = 0) | ( ~ (v0 = 0) &
% 47.14/6.77 | | unequally_directed_lines(all_39_2, all_39_1) = v0))
% 47.14/6.77 | |
% 47.14/6.77 | | GROUND_INST: instantiating (1) with all_39_2, all_39_1, simplifying with
% 47.14/6.77 | | (14), (15), (23) gives:
% 47.14/6.77 | | (25) ? [v0: $i] : (reverse_line(all_39_1) = v0 &
% 47.14/6.77 | | unequally_directed_lines(all_39_2, v0) = 0 & $i(v0))
% 47.14/6.77 | |
% 47.14/6.77 | | GROUND_INST: instantiating (4) with all_39_2, all_39_1, 0, simplifying with
% 47.14/6.77 | | (14), (15), (23) gives:
% 47.14/6.77 | | (26) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 47.14/6.77 | | unequally_directed_lines(all_39_2, all_39_1) = 0) | ( ~ (v0 = 0)
% 47.14/6.77 | | & convergent_lines(all_39_2, all_39_1) = v0))
% 47.14/6.77 | |
% 47.14/6.77 | | GROUND_INST: instantiating (5) with all_39_2, all_39_2, all_39_1, all_46_0,
% 47.14/6.77 | | all_46_0, simplifying with (14), (15), (22) gives:
% 47.14/6.77 | | (27) all_46_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 47.14/6.77 | | distinct_lines(all_39_2, all_39_2) = v0)
% 47.14/6.77 | |
% 47.14/6.77 | | DELTA: instantiating (25) with fresh symbol all_58_0 gives:
% 47.14/6.78 | | (28) reverse_line(all_39_1) = all_58_0 &
% 47.14/6.78 | | unequally_directed_lines(all_39_2, all_58_0) = 0 & $i(all_58_0)
% 47.14/6.78 | |
% 47.14/6.78 | | ALPHA: (28) implies:
% 47.14/6.78 | | (29) $i(all_58_0)
% 47.14/6.78 | | (30) unequally_directed_lines(all_39_2, all_58_0) = 0
% 47.14/6.78 | | (31) reverse_line(all_39_1) = all_58_0
% 47.14/6.78 | |
% 47.14/6.78 | | DELTA: instantiating (26) with fresh symbols all_60_0, all_60_1 gives:
% 47.14/6.78 | | (32) (all_60_0 = 0 & unequally_directed_lines(all_39_2, all_39_1) = 0) |
% 47.14/6.78 | | ( ~ (all_60_1 = 0) & convergent_lines(all_39_2, all_39_1) =
% 47.14/6.78 | | all_60_1)
% 47.14/6.78 | |
% 47.14/6.78 | | DELTA: instantiating (24) with fresh symbols all_61_0, all_61_1 gives:
% 47.14/6.78 | | (33) (all_61_0 = 0 & convergent_lines(all_39_2, all_39_1) = 0) | ( ~
% 47.14/6.78 | | (all_61_1 = 0) & unequally_directed_lines(all_39_2, all_39_1) =
% 47.14/6.78 | | all_61_1)
% 47.14/6.78 | |
% 47.14/6.78 | | BETA: splitting (27) gives:
% 47.14/6.78 | |
% 47.14/6.78 | | Case 1:
% 47.14/6.78 | | |
% 47.14/6.78 | | | (34) all_46_0 = 0
% 47.14/6.78 | | |
% 47.14/6.78 | | | REDUCE: (21), (34) imply:
% 47.14/6.78 | | | (35) $false
% 47.14/6.78 | | |
% 47.14/6.78 | | | CLOSE: (35) is inconsistent.
% 47.14/6.78 | | |
% 47.14/6.78 | | Case 2:
% 47.14/6.78 | | |
% 47.14/6.78 | | |
% 47.14/6.78 | | | GROUND_INST: instantiating (8) with all_39_2, all_39_1, all_58_0,
% 47.14/6.78 | | | simplifying with (14), (15), (30), (31) gives:
% 47.14/6.78 | | | (36) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 47.14/6.78 | | | left_convergent_lines(all_39_2, all_58_0) = 0) | (v1 = 0 &
% 47.14/6.78 | | | left_convergent_lines(all_39_2, all_39_1) = 0) | ( ~ (v0 = 0)
% 47.14/6.78 | | | & unequally_directed_lines(all_39_2, all_39_1) = v0))
% 47.14/6.78 | | |
% 47.14/6.78 | | | GROUND_INST: instantiating (ax8_cons_objs) with all_39_1, all_58_0,
% 47.14/6.78 | | | simplifying with (15), (31) gives:
% 47.14/6.78 | | | (37) ? [v0: int] : ( ~ (v0 = 0) & distinct_lines(all_39_1, all_58_0) =
% 47.14/6.78 | | | v0)
% 47.14/6.78 | | |
% 47.14/6.78 | | | DELTA: instantiating (37) with fresh symbol all_73_0 gives:
% 47.14/6.78 | | | (38) ~ (all_73_0 = 0) & distinct_lines(all_39_1, all_58_0) = all_73_0
% 47.14/6.78 | | |
% 47.14/6.78 | | | ALPHA: (38) implies:
% 47.14/6.78 | | | (39) ~ (all_73_0 = 0)
% 47.14/6.78 | | | (40) distinct_lines(all_39_1, all_58_0) = all_73_0
% 47.14/6.78 | | |
% 47.14/6.78 | | | DELTA: instantiating (36) with fresh symbols all_80_0, all_80_1, all_80_2
% 47.14/6.78 | | | gives:
% 47.14/6.78 | | | (41) (all_80_0 = 0 & left_convergent_lines(all_39_2, all_58_0) = 0) |
% 47.14/6.78 | | | (all_80_1 = 0 & left_convergent_lines(all_39_2, all_39_1) = 0) | (
% 47.14/6.78 | | | ~ (all_80_2 = 0) & unequally_directed_lines(all_39_2, all_39_1)
% 47.14/6.78 | | | = all_80_2)
% 47.14/6.78 | | |
% 47.14/6.78 | | | GROUND_INST: instantiating (5) with all_39_1, all_39_1, all_58_0,
% 47.14/6.78 | | | all_73_0, all_73_0, simplifying with (15), (29), (40) gives:
% 47.14/6.78 | | | (42) all_73_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 47.14/6.78 | | | distinct_lines(all_39_1, all_39_1) = v0)
% 47.14/6.78 | | |
% 47.14/6.78 | | | BETA: splitting (42) gives:
% 47.14/6.78 | | |
% 47.14/6.78 | | | Case 1:
% 47.14/6.78 | | | |
% 47.14/6.78 | | | | (43) all_73_0 = 0
% 47.14/6.78 | | | |
% 47.14/6.78 | | | | REDUCE: (39), (43) imply:
% 47.14/6.78 | | | | (44) $false
% 47.14/6.78 | | | |
% 47.14/6.78 | | | | CLOSE: (44) is inconsistent.
% 47.14/6.78 | | | |
% 47.14/6.78 | | | Case 2:
% 47.14/6.78 | | | |
% 47.14/6.78 | | | | (45) ? [v0: int] : ( ~ (v0 = 0) & distinct_lines(all_39_1, all_39_1)
% 47.14/6.78 | | | | = v0)
% 47.14/6.78 | | | |
% 47.14/6.78 | | | | DELTA: instantiating (45) with fresh symbol all_103_0 gives:
% 47.14/6.78 | | | | (46) ~ (all_103_0 = 0) & distinct_lines(all_39_1, all_39_1) =
% 47.14/6.78 | | | | all_103_0
% 47.14/6.78 | | | |
% 47.14/6.78 | | | | ALPHA: (46) implies:
% 47.14/6.78 | | | | (47) ~ (all_103_0 = 0)
% 47.14/6.78 | | | | (48) distinct_lines(all_39_1, all_39_1) = all_103_0
% 47.14/6.78 | | | |
% 47.14/6.78 | | | | GROUND_INST: instantiating (5) with all_39_1, all_39_2, all_39_1,
% 47.14/6.78 | | | | all_103_0, all_46_0, simplifying with (14), (15), (22),
% 47.14/6.78 | | | | (48) gives:
% 47.14/6.78 | | | | (49) all_103_0 = 0 | all_46_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 47.14/6.78 | | | | distinct_lines(all_39_1, all_39_2) = v0)
% 47.14/6.78 | | | |
% 47.14/6.78 | | | | BETA: splitting (32) gives:
% 47.14/6.78 | | | |
% 47.14/6.78 | | | | Case 1:
% 47.14/6.78 | | | | |
% 47.14/6.78 | | | | | (50) all_60_0 = 0 & unequally_directed_lines(all_39_2, all_39_1) =
% 47.14/6.78 | | | | | 0
% 47.14/6.79 | | | | |
% 47.14/6.79 | | | | | ALPHA: (50) implies:
% 47.14/6.79 | | | | | (51) unequally_directed_lines(all_39_2, all_39_1) = 0
% 47.14/6.79 | | | | |
% 47.14/6.79 | | | | | BETA: splitting (41) gives:
% 47.14/6.79 | | | | |
% 47.14/6.79 | | | | | Case 1:
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | | (52) all_80_0 = 0 & left_convergent_lines(all_39_2, all_58_0) = 0
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | | ALPHA: (52) implies:
% 47.14/6.79 | | | | | | (53) left_convergent_lines(all_39_2, all_58_0) = 0
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | | GROUND_INST: instantiating (9) with all_39_2, all_58_0, simplifying
% 47.14/6.79 | | | | | | with (14), (29), (53) gives:
% 47.14/6.79 | | | | | | (54) $false
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | | CLOSE: (54) is inconsistent.
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | Case 2:
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | | (55) (all_80_1 = 0 & left_convergent_lines(all_39_2, all_39_1) =
% 47.14/6.79 | | | | | | 0) | ( ~ (all_80_2 = 0) &
% 47.14/6.79 | | | | | | unequally_directed_lines(all_39_2, all_39_1) = all_80_2)
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | | BETA: splitting (55) gives:
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | | Case 1:
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | | (56) all_80_1 = 0 & left_convergent_lines(all_39_2, all_39_1) =
% 47.14/6.79 | | | | | | | 0
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | | ALPHA: (56) implies:
% 47.14/6.79 | | | | | | | (57) left_convergent_lines(all_39_2, all_39_1) = 0
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | | GROUND_INST: instantiating (9) with all_39_2, all_39_1,
% 47.14/6.79 | | | | | | | simplifying with (14), (15), (57) gives:
% 47.14/6.79 | | | | | | | (58) $false
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | | CLOSE: (58) is inconsistent.
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | Case 2:
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | | (59) ~ (all_80_2 = 0) & unequally_directed_lines(all_39_2,
% 47.14/6.79 | | | | | | | all_39_1) = all_80_2
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | | ALPHA: (59) implies:
% 47.14/6.79 | | | | | | | (60) ~ (all_80_2 = 0)
% 47.14/6.79 | | | | | | | (61) unequally_directed_lines(all_39_2, all_39_1) = all_80_2
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | | GROUND_INST: instantiating (10) with 0, all_80_2, all_39_1,
% 47.14/6.79 | | | | | | | all_39_2, simplifying with (51), (61) gives:
% 47.14/6.79 | | | | | | | (62) all_80_2 = 0
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | | REDUCE: (60), (62) imply:
% 47.14/6.79 | | | | | | | (63) $false
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | | CLOSE: (63) is inconsistent.
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | End of split
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | End of split
% 47.14/6.79 | | | | |
% 47.14/6.79 | | | | Case 2:
% 47.14/6.79 | | | | |
% 47.14/6.79 | | | | | (64) ~ (all_60_1 = 0) & convergent_lines(all_39_2, all_39_1) =
% 47.14/6.79 | | | | | all_60_1
% 47.14/6.79 | | | | |
% 47.14/6.79 | | | | | ALPHA: (64) implies:
% 47.14/6.79 | | | | | (65) ~ (all_60_1 = 0)
% 47.14/6.79 | | | | | (66) convergent_lines(all_39_2, all_39_1) = all_60_1
% 47.14/6.79 | | | | |
% 47.14/6.79 | | | | | BETA: splitting (33) gives:
% 47.14/6.79 | | | | |
% 47.14/6.79 | | | | | Case 1:
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | | (67) all_61_0 = 0 & convergent_lines(all_39_2, all_39_1) = 0
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | | ALPHA: (67) implies:
% 47.14/6.79 | | | | | | (68) convergent_lines(all_39_2, all_39_1) = 0
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | | GROUND_INST: instantiating (11) with 0, all_60_1, all_39_1,
% 47.14/6.79 | | | | | | all_39_2, simplifying with (66), (68) gives:
% 47.14/6.79 | | | | | | (69) all_60_1 = 0
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | | REDUCE: (65), (69) imply:
% 47.14/6.79 | | | | | | (70) $false
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | | CLOSE: (70) is inconsistent.
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | Case 2:
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | | (71) ~ (all_61_1 = 0) & unequally_directed_lines(all_39_2,
% 47.14/6.79 | | | | | | all_39_1) = all_61_1
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | | ALPHA: (71) implies:
% 47.14/6.79 | | | | | | (72) ~ (all_61_1 = 0)
% 47.14/6.79 | | | | | | (73) unequally_directed_lines(all_39_2, all_39_1) = all_61_1
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | | BETA: splitting (49) gives:
% 47.14/6.79 | | | | | |
% 47.14/6.79 | | | | | | Case 1:
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | | (74) all_103_0 = 0
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | | REDUCE: (47), (74) imply:
% 47.14/6.79 | | | | | | | (75) $false
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | | CLOSE: (75) is inconsistent.
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | Case 2:
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | | (76) all_46_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 47.14/6.79 | | | | | | | distinct_lines(all_39_1, all_39_2) = v0)
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | | BETA: splitting (76) gives:
% 47.14/6.79 | | | | | | |
% 47.14/6.79 | | | | | | | Case 1:
% 47.14/6.79 | | | | | | | |
% 47.14/6.79 | | | | | | | | (77) all_46_0 = 0
% 47.14/6.79 | | | | | | | |
% 47.14/6.79 | | | | | | | | REDUCE: (21), (77) imply:
% 47.14/6.79 | | | | | | | | (78) $false
% 47.14/6.79 | | | | | | | |
% 47.14/6.79 | | | | | | | | CLOSE: (78) is inconsistent.
% 47.14/6.79 | | | | | | | |
% 47.14/6.79 | | | | | | | Case 2:
% 47.14/6.79 | | | | | | | |
% 47.14/6.79 | | | | | | | |
% 47.14/6.79 | | | | | | | | GROUND_INST: instantiating (7) with all_39_2, all_39_2,
% 47.14/6.79 | | | | | | | | all_39_1, all_61_1, simplifying with (14), (16),
% 47.14/6.79 | | | | | | | | (73) gives:
% 47.14/6.79 | | | | | | | | (79) all_61_1 = 0 | unequally_directed_lines(all_39_2,
% 47.14/6.79 | | | | | | | | all_39_2) = 0
% 47.14/6.79 | | | | | | | |
% 47.14/6.79 | | | | | | | | GROUND_INST: instantiating (6) with all_39_2, all_39_2,
% 47.14/6.79 | | | | | | | | all_39_1, all_61_1, all_61_1, simplifying with
% 47.14/6.79 | | | | | | | | (14), (15), (73) gives:
% 47.14/6.79 | | | | | | | | (80) all_61_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 47.14/6.79 | | | | | | | | unequally_directed_lines(all_39_2, all_39_2) = v0)
% 47.14/6.79 | | | | | | | |
% 47.14/6.79 | | | | | | | | BETA: splitting (79) gives:
% 47.14/6.79 | | | | | | | |
% 47.14/6.79 | | | | | | | | Case 1:
% 47.14/6.79 | | | | | | | | |
% 47.14/6.79 | | | | | | | | | (81) unequally_directed_lines(all_39_2, all_39_2) = 0
% 47.14/6.79 | | | | | | | | |
% 47.14/6.79 | | | | | | | | | BETA: splitting (80) gives:
% 47.14/6.79 | | | | | | | | |
% 47.14/6.79 | | | | | | | | | Case 1:
% 47.14/6.79 | | | | | | | | | |
% 47.14/6.79 | | | | | | | | | | (82) all_61_1 = 0
% 47.14/6.79 | | | | | | | | | |
% 47.14/6.79 | | | | | | | | | | REDUCE: (72), (82) imply:
% 47.14/6.79 | | | | | | | | | | (83) $false
% 47.14/6.79 | | | | | | | | | |
% 47.14/6.79 | | | | | | | | | | CLOSE: (83) is inconsistent.
% 47.14/6.79 | | | | | | | | | |
% 47.14/6.79 | | | | | | | | | Case 2:
% 47.14/6.79 | | | | | | | | | |
% 47.14/6.79 | | | | | | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) &
% 47.14/6.79 | | | | | | | | | | unequally_directed_lines(all_39_2, all_39_2) = v0)
% 47.14/6.79 | | | | | | | | | |
% 47.14/6.79 | | | | | | | | | | DELTA: instantiating (84) with fresh symbol all_149_0 gives:
% 47.14/6.79 | | | | | | | | | | (85) ~ (all_149_0 = 0) &
% 47.14/6.79 | | | | | | | | | | unequally_directed_lines(all_39_2, all_39_2) =
% 47.14/6.79 | | | | | | | | | | all_149_0
% 47.14/6.79 | | | | | | | | | |
% 47.14/6.79 | | | | | | | | | | ALPHA: (85) implies:
% 47.14/6.80 | | | | | | | | | | (86) ~ (all_149_0 = 0)
% 47.14/6.80 | | | | | | | | | | (87) unequally_directed_lines(all_39_2, all_39_2) =
% 47.14/6.80 | | | | | | | | | | all_149_0
% 47.14/6.80 | | | | | | | | | |
% 47.14/6.80 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_149_0, all_39_2,
% 47.14/6.80 | | | | | | | | | | all_39_2, simplifying with (81), (87) gives:
% 47.14/6.80 | | | | | | | | | | (88) all_149_0 = 0
% 47.14/6.80 | | | | | | | | | |
% 47.14/6.80 | | | | | | | | | | REDUCE: (86), (88) imply:
% 47.14/6.80 | | | | | | | | | | (89) $false
% 47.14/6.80 | | | | | | | | | |
% 47.14/6.80 | | | | | | | | | | CLOSE: (89) is inconsistent.
% 47.14/6.80 | | | | | | | | | |
% 47.14/6.80 | | | | | | | | | End of split
% 47.14/6.80 | | | | | | | | |
% 47.14/6.80 | | | | | | | | Case 2:
% 47.14/6.80 | | | | | | | | |
% 47.14/6.80 | | | | | | | | | (90) all_61_1 = 0
% 47.14/6.80 | | | | | | | | |
% 47.14/6.80 | | | | | | | | | REDUCE: (72), (90) imply:
% 47.14/6.80 | | | | | | | | | (91) $false
% 47.14/6.80 | | | | | | | | |
% 47.14/6.80 | | | | | | | | | CLOSE: (91) is inconsistent.
% 47.14/6.80 | | | | | | | | |
% 47.14/6.80 | | | | | | | | End of split
% 47.14/6.80 | | | | | | | |
% 47.14/6.80 | | | | | | | End of split
% 47.14/6.80 | | | | | | |
% 47.14/6.80 | | | | | | End of split
% 47.14/6.80 | | | | | |
% 47.14/6.80 | | | | | End of split
% 47.14/6.80 | | | | |
% 47.14/6.80 | | | | End of split
% 47.14/6.80 | | | |
% 47.14/6.80 | | | End of split
% 47.14/6.80 | | |
% 47.14/6.80 | | End of split
% 47.14/6.80 | |
% 47.14/6.80 | Case 2:
% 47.14/6.80 | |
% 47.14/6.80 | | (92) all_39_0 = 0
% 47.14/6.80 | |
% 47.14/6.80 | | REDUCE: (13), (92) imply:
% 47.14/6.80 | | (93) $false
% 47.14/6.80 | |
% 47.14/6.80 | | CLOSE: (93) is inconsistent.
% 47.14/6.80 | |
% 47.14/6.80 | End of split
% 47.14/6.80 |
% 47.14/6.80 End of proof
% 47.14/6.80 % SZS output end Proof for theBenchmark
% 47.14/6.80
% 47.14/6.80 6199ms
%------------------------------------------------------------------------------