TSTP Solution File: GEO263+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO263+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n029.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 23:22:51 EDT 2023
% Result : Theorem 253.99s 35.98s
% Output : Proof 254.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO263+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 22:01:12 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.61/0.63 ________ _____
% 0.61/0.63 ___ __ \_________(_)________________________________
% 0.61/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.61/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.61/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.61/0.63
% 0.61/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.61/0.63 (2023-06-19)
% 0.61/0.63
% 0.61/0.63 (c) Philipp Rümmer, 2009-2023
% 0.61/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.61/0.63 Amanda Stjerna.
% 0.61/0.63 Free software under BSD-3-Clause.
% 0.61/0.63
% 0.61/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.61/0.63
% 0.61/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.64 Running up to 7 provers in parallel.
% 0.68/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.68/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.68/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.68/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.68/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.68/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.68/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.98/1.14 Prover 4: Preprocessing ...
% 2.98/1.14 Prover 1: Preprocessing ...
% 3.57/1.18 Prover 2: Preprocessing ...
% 3.57/1.18 Prover 6: Preprocessing ...
% 3.57/1.18 Prover 5: Preprocessing ...
% 3.57/1.18 Prover 0: Preprocessing ...
% 3.57/1.18 Prover 3: Preprocessing ...
% 6.30/1.61 Prover 5: Proving ...
% 6.95/1.67 Prover 2: Proving ...
% 6.95/1.67 Prover 3: Constructing countermodel ...
% 6.95/1.68 Prover 6: Constructing countermodel ...
% 6.95/1.69 Prover 1: Constructing countermodel ...
% 8.45/1.89 Prover 3: gave up
% 8.45/1.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.06/1.93 Prover 6: gave up
% 9.06/1.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.06/1.95 Prover 1: gave up
% 9.06/1.96 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 9.06/1.96 Prover 7: Preprocessing ...
% 9.65/2.01 Prover 8: Preprocessing ...
% 9.65/2.02 Prover 4: Constructing countermodel ...
% 9.65/2.05 Prover 9: Preprocessing ...
% 9.65/2.06 Prover 7: Warning: ignoring some quantifiers
% 10.48/2.09 Prover 7: Constructing countermodel ...
% 10.72/2.21 Prover 8: Warning: ignoring some quantifiers
% 11.40/2.22 Prover 8: Constructing countermodel ...
% 11.40/2.30 Prover 0: Proving ...
% 12.09/2.38 Prover 7: gave up
% 12.09/2.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.89/2.41 Prover 8: gave up
% 12.89/2.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.89/2.45 Prover 10: Preprocessing ...
% 12.89/2.48 Prover 11: Preprocessing ...
% 13.65/2.55 Prover 10: Warning: ignoring some quantifiers
% 13.65/2.56 Prover 9: Constructing countermodel ...
% 13.65/2.57 Prover 10: Constructing countermodel ...
% 14.34/2.62 Prover 10: gave up
% 14.34/2.62 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 14.34/2.66 Prover 12: Preprocessing ...
% 15.09/2.78 Prover 12: Proving ...
% 15.99/2.89 Prover 11: Constructing countermodel ...
% 37.00/5.54 Prover 12: stopped
% 37.00/5.57 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 37.73/5.60 Prover 13: Preprocessing ...
% 37.92/5.69 Prover 13: Warning: ignoring some quantifiers
% 38.64/5.71 Prover 13: Constructing countermodel ...
% 38.64/5.76 Prover 13: gave up
% 38.64/5.77 Prover 14: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=414236379
% 39.30/5.83 Prover 14: Preprocessing ...
% 41.08/6.06 Prover 14: Proving ...
% 58.87/8.33 Prover 2: stopped
% 58.87/8.34 Prover 15: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=723048181
% 58.87/8.36 Prover 15: Preprocessing ...
% 60.03/8.45 Prover 15: Proving ...
% 103.05/13.98 Prover 5: stopped
% 103.05/13.99 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 103.39/14.02 Prover 16: Preprocessing ...
% 103.53/14.07 Prover 16: Warning: ignoring some quantifiers
% 103.53/14.07 Prover 16: Constructing countermodel ...
% 105.37/14.31 Prover 16: gave up
% 105.67/14.33 Prover 17: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=642448422
% 105.81/14.35 Prover 17: Preprocessing ...
% 105.81/14.40 Prover 17: Constructing countermodel ...
% 105.81/14.41 Prover 17: gave up
% 106.43/14.43 Prover 18: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-219651170
% 106.43/14.46 Prover 18: Preprocessing ...
% 106.94/14.50 Prover 18: Warning: ignoring some quantifiers
% 106.94/14.50 Prover 18: Constructing countermodel ...
% 106.94/14.56 Prover 18: gave up
% 107.65/14.58 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 107.81/14.62 Prover 19: Preprocessing ...
% 108.71/14.70 Prover 19: Warning: ignoring some quantifiers
% 108.71/14.72 Prover 19: Constructing countermodel ...
% 110.53/15.00 Prover 19: gave up
% 111.08/15.01 Prover 20: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=2065050644
% 111.65/15.08 Prover 20: Preprocessing ...
% 112.34/15.17 Prover 20: Proving ...
% 203.82/28.03 Prover 4: stopped
% 203.82/28.04 Prover 21: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=201956991
% 204.19/28.09 Prover 21: Preprocessing ...
% 205.09/28.22 Prover 21: Proving ...
% 206.60/28.47 Prover 9: stopped
% 229.41/31.85 Prover 14: stopped
% 253.74/35.91 Prover 11: Found proof (size 37)
% 253.74/35.91 Prover 11: proved (33488ms)
% 253.74/35.91 Prover 15: stopped
% 253.74/35.91 Prover 21: stopped
% 253.74/35.91 Prover 20: stopped
% 253.99/35.98 Prover 0: stopped
% 253.99/35.98
% 253.99/35.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 253.99/35.98
% 253.99/35.98 % SZS output start Proof for theBenchmark
% 253.99/35.99 Assumptions after simplification:
% 253.99/35.99 ---------------------------------
% 253.99/35.99
% 253.99/35.99 (bet_def)
% 254.16/36.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 254.16/36.02 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 254.16/36.02 $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8:
% 254.16/36.02 int] : ((( ~ (v8 = 0) & before_on_line(v0, v2, v1) = v8) | ( ~ (v7 = 0) &
% 254.16/36.02 before_on_line(v0, v3, v2) = v7)) & (( ~ (v6 = 0) & before_on_line(v0,
% 254.16/36.02 v2, v3) = v6) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5)))) &
% 254.16/36.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 254.16/36.02 (between_on_line(v0, v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 254.16/36.02 ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7
% 254.16/36.02 = 0 & v6 = 0 & before_on_line(v0, v3, v2) = 0 & before_on_line(v0, v2,
% 254.16/36.02 v1) = 0) | (v5 = 0 & v4 = 0 & before_on_line(v0, v2, v3) = 0 &
% 254.16/36.02 before_on_line(v0, v1, v2) = 0)))
% 254.16/36.02
% 254.16/36.02 (con)
% 254.16/36.03 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 254.16/36.03 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 254.16/36.03 ? [v11: $i] : ? [v12: int] : ( ~ (v12 = 0) & parallel_through_point(v2, v5)
% 254.16/36.03 = v10 & parallel_through_point(v2, v4) = v8 & parallel_through_point(v2, v3)
% 254.16/36.03 = v6 & intersection_point(v1, v10) = v11 & intersection_point(v1, v8) = v9 &
% 254.16/36.03 intersection_point(v1, v6) = v7 & between_on_line(v1, v7, v9, v11) = v12 &
% 254.16/36.03 between_on_line(v0, v3, v4, v5) = 0 & convergent_lines(v1, v2) = 0 &
% 254.16/36.03 convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0 & $i(v11) &
% 254.16/36.03 $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 254.16/36.03 $i(v2) & $i(v1) & $i(v0))
% 254.16/36.03
% 254.16/36.03 (con_def)
% 254.16/36.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 254.16/36.04 (unequally_directed_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ~
% 254.16/36.04 $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ((v5 = 0 & v3 = 0 &
% 254.16/36.04 unequally_directed_lines(v0, v1) = 0) | ( ~ (v4 = 0) &
% 254.16/36.04 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 254.16/36.04 int] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 254.16/36.04 | ? [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ (v5 = 0) &
% 254.16/36.04 unequally_directed_lines(v0, v4) = v5 & reverse_line(v1) = v4 & $i(v4))
% 254.16/36.04 | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0: $i] :
% 254.16/36.04 ! [v1: $i] : ! [v2: $i] : ( ~ (unequally_directed_lines(v0, v2) = 0) | ~
% 254.16/36.04 (reverse_line(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4:
% 254.16/36.04 int] : ((v4 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) &
% 254.16/36.04 unequally_directed_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] :
% 254.16/36.04 ! [v2: any] : ( ~ (unequally_directed_lines(v0, v1) = v2) | ~ $i(v1) | ~
% 254.16/36.04 $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ((v5 = 0 & v2 = 0 &
% 254.16/36.04 unequally_directed_lines(v0, v4) = 0 & reverse_line(v1) = v4 & $i(v4)) |
% 254.16/36.04 ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1:
% 254.16/36.04 $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 254.16/36.04 $i] : (unequally_directed_lines(v0, v2) = 0 & unequally_directed_lines(v0,
% 254.16/36.04 v1) = 0 & reverse_line(v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] :
% 254.16/36.04 ( ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 254.16/36.04 $i] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & convergent_lines(v0, v1) =
% 254.16/36.04 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v2) = v3 &
% 254.16/36.04 reverse_line(v1) = v2 & $i(v2))))
% 254.16/36.04
% 254.16/36.04 (oag11)
% 254.16/36.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (left_convergent_lines(v0, v2) =
% 254.16/36.04 0) | ~ (reverse_line(v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] :
% 254.16/36.04 ! [v1: $i] : ( ~ (left_convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0))
% 254.16/36.04
% 254.16/36.04 (oag9)
% 254.16/36.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 254.16/36.04 (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ~
% 254.16/36.04 $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ((v6 = 0 &
% 254.16/36.04 left_convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) &
% 254.16/36.04 unequally_directed_lines(v0, v2) = v5) | ( ~ (v4 = 0) &
% 254.16/36.04 unequally_directed_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] :
% 254.16/36.04 ! [v2: int] : (v2 = 0 | ~ (left_convergent_lines(v0, v1) = v2) | ~ $i(v1) |
% 254.16/36.04 ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : ((v6 =
% 254.16/36.04 0 & left_convergent_lines(v0, v4) = 0 & reverse_line(v1) = v4 & $i(v4))
% 254.16/36.04 | ( ~ (v5 = 0) & unequally_directed_lines(v0, v4) = v5 & reverse_line(v1)
% 254.16/36.04 = v4 & $i(v4)) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 254.16/36.04 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unequally_directed_lines(v0,
% 254.16/36.04 v2) = 0) | ~ (reverse_line(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 254.16/36.04 int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 & left_convergent_lines(v0,
% 254.16/36.04 v2) = 0) | (v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0)
% 254.16/36.04 & unequally_directed_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] :
% 254.16/36.04 ( ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 254.16/36.04 $i] : ? [v3: int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 &
% 254.16/36.04 left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2 & $i(v2)) |
% 254.16/36.04 (v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) &
% 254.16/36.04 unequally_directed_lines(v0, v2) = v3 & reverse_line(v1) = v2 &
% 254.16/36.04 $i(v2))))
% 254.16/36.04
% 254.16/36.04 (function-axioms)
% 254.16/36.05 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 254.16/36.05 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_on_line(v5, v4,
% 254.16/36.05 v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0:
% 254.16/36.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 254.16/36.05 : ! [v4: $i] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~
% 254.16/36.05 (before_on_line(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 254.16/36.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 254.16/36.05 (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) &
% 254.16/36.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 254.16/36.05 (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) =
% 254.16/36.05 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 254.16/36.05 ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 254.16/36.05 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 254.16/36.05 [v3: $i] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~
% 254.16/36.05 (left_convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 254.16/36.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 254.16/36.05 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 254.16/36.05 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 254.16/36.05 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 254.16/36.05 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 254.16/36.05 $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3,
% 254.16/36.05 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 254.16/36.05 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 254.16/36.05 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 254.16/36.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 254.16/36.05 (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3,
% 254.16/36.05 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 254.16/36.05 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) |
% 254.16/36.05 ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 254.16/36.05 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 254.16/36.05 (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0)) & !
% 254.16/36.05 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 254.16/36.05 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: MultipleValueBool] :
% 254.16/36.05 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (line(v2) = v1) | ~
% 254.16/36.05 (line(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 254.16/36.05 (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 254.16/36.05
% 254.16/36.05 Further assumptions not needed in the proof:
% 254.16/36.05 --------------------------------------------
% 254.16/36.05 apt_def, bf_def, div_def, oag1, oag10, oag2, oag3, oag4, oag5, oag6, oag7, oag8,
% 254.16/36.05 oagco1, oagco10, oagco2, oagco3, oagco4, oagco5, oagco6, oagco7, oagco8, oagco9,
% 254.16/36.05 oagsub1, oagsub2, oagsub3, oaguc1, oaguc2
% 254.16/36.05
% 254.16/36.05 Those formulas are unsatisfiable:
% 254.16/36.05 ---------------------------------
% 254.16/36.05
% 254.16/36.05 Begin of proof
% 254.16/36.05 |
% 254.16/36.05 | ALPHA: (con_def) implies:
% 254.16/36.05 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~
% 254.16/36.05 | $i(v1) | ~ $i(v0) | ? [v2: $i] : (unequally_directed_lines(v0, v2)
% 254.16/36.05 | = 0 & unequally_directed_lines(v0, v1) = 0 & reverse_line(v1) = v2
% 254.16/36.05 | & $i(v2)))
% 254.16/36.05 |
% 254.16/36.05 | ALPHA: (bet_def) implies:
% 254.16/36.06 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 254.16/36.06 | (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~
% 254.16/36.06 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ?
% 254.16/36.06 | [v7: int] : ? [v8: int] : ((( ~ (v8 = 0) & before_on_line(v0, v2,
% 254.16/36.06 | v1) = v8) | ( ~ (v7 = 0) & before_on_line(v0, v3, v2) = v7))
% 254.16/36.06 | & (( ~ (v6 = 0) & before_on_line(v0, v2, v3) = v6) | ( ~ (v5 = 0) &
% 254.16/36.06 | before_on_line(v0, v1, v2) = v5))))
% 254.16/36.06 |
% 254.16/36.06 | ALPHA: (oag9) implies:
% 254.16/36.06 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 254.16/36.06 | (unequally_directed_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) |
% 254.16/36.06 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ? [v5: int] :
% 254.16/36.06 | ((v5 = 0 & left_convergent_lines(v0, v2) = 0) | (v4 = 0 &
% 254.16/36.06 | left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) &
% 254.16/36.06 | unequally_directed_lines(v0, v1) = v3)))
% 254.16/36.06 |
% 254.16/36.06 | ALPHA: (oag11) implies:
% 254.16/36.06 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (left_convergent_lines(v0, v1) = 0) |
% 254.16/36.06 | ~ $i(v1) | ~ $i(v0))
% 254.16/36.06 |
% 254.16/36.06 | ALPHA: (function-axioms) implies:
% 254.16/36.06 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 254.16/36.06 | (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 254.16/36.06 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 254.16/36.06 | ! [v3: $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) |
% 254.16/36.06 | ~ (unequally_directed_lines(v3, v2) = v0))
% 254.16/36.06 |
% 254.16/36.06 | DELTA: instantiating (con) with fresh symbols all_34_0, all_34_1, all_34_2,
% 254.16/36.06 | all_34_3, all_34_4, all_34_5, all_34_6, all_34_7, all_34_8, all_34_9,
% 254.16/36.06 | all_34_10, all_34_11, all_34_12 gives:
% 254.16/36.06 | (7) ~ (all_34_0 = 0) & parallel_through_point(all_34_10, all_34_7) =
% 254.16/36.06 | all_34_2 & parallel_through_point(all_34_10, all_34_8) = all_34_4 &
% 254.16/36.06 | parallel_through_point(all_34_10, all_34_9) = all_34_6 &
% 254.16/36.06 | intersection_point(all_34_11, all_34_2) = all_34_1 &
% 254.16/36.06 | intersection_point(all_34_11, all_34_4) = all_34_3 &
% 254.16/36.06 | intersection_point(all_34_11, all_34_6) = all_34_5 &
% 254.16/36.06 | between_on_line(all_34_11, all_34_5, all_34_3, all_34_1) = all_34_0 &
% 254.16/36.06 | between_on_line(all_34_12, all_34_9, all_34_8, all_34_7) = 0 &
% 254.16/36.06 | convergent_lines(all_34_11, all_34_10) = 0 &
% 254.16/36.06 | convergent_lines(all_34_12, all_34_10) = 0 &
% 254.16/36.06 | convergent_lines(all_34_12, all_34_11) = 0 & $i(all_34_1) &
% 254.16/36.06 | $i(all_34_2) & $i(all_34_3) & $i(all_34_4) & $i(all_34_5) &
% 254.16/36.06 | $i(all_34_6) & $i(all_34_7) & $i(all_34_8) & $i(all_34_9) &
% 254.16/36.06 | $i(all_34_10) & $i(all_34_11) & $i(all_34_12)
% 254.16/36.06 |
% 254.16/36.06 | ALPHA: (7) implies:
% 254.16/36.06 | (8) ~ (all_34_0 = 0)
% 254.16/36.06 | (9) $i(all_34_12)
% 254.16/36.06 | (10) $i(all_34_11)
% 254.16/36.06 | (11) $i(all_34_10)
% 254.16/36.06 | (12) $i(all_34_5)
% 254.16/36.06 | (13) $i(all_34_3)
% 254.16/36.06 | (14) $i(all_34_1)
% 254.16/36.06 | (15) convergent_lines(all_34_12, all_34_10) = 0
% 254.16/36.06 | (16) convergent_lines(all_34_11, all_34_10) = 0
% 254.16/36.06 | (17) between_on_line(all_34_11, all_34_5, all_34_3, all_34_1) = all_34_0
% 254.16/36.06 |
% 254.16/36.07 | GROUND_INST: instantiating (1) with all_34_12, all_34_10, simplifying with
% 254.16/36.07 | (9), (11), (15) gives:
% 254.16/36.07 | (18) ? [v0: $i] : (unequally_directed_lines(all_34_12, v0) = 0 &
% 254.16/36.07 | unequally_directed_lines(all_34_12, all_34_10) = 0 &
% 254.16/36.07 | reverse_line(all_34_10) = v0 & $i(v0))
% 254.16/36.07 |
% 254.16/36.07 | GROUND_INST: instantiating (1) with all_34_11, all_34_10, simplifying with
% 254.16/36.07 | (10), (11), (16) gives:
% 254.16/36.07 | (19) ? [v0: $i] : (unequally_directed_lines(all_34_11, v0) = 0 &
% 254.16/36.07 | unequally_directed_lines(all_34_11, all_34_10) = 0 &
% 254.16/36.07 | reverse_line(all_34_10) = v0 & $i(v0))
% 254.16/36.07 |
% 254.16/36.07 | GROUND_INST: instantiating (2) with all_34_11, all_34_5, all_34_3, all_34_1,
% 254.16/36.07 | all_34_0, simplifying with (10), (12), (13), (14), (17) gives:
% 254.16/36.07 | (20) all_34_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3:
% 254.16/36.07 | int] : ((( ~ (v3 = 0) & before_on_line(all_34_11, all_34_3,
% 254.16/36.07 | all_34_5) = v3) | ( ~ (v2 = 0) & before_on_line(all_34_11,
% 254.16/36.07 | all_34_1, all_34_3) = v2)) & (( ~ (v1 = 0) &
% 254.16/36.07 | before_on_line(all_34_11, all_34_3, all_34_1) = v1) | ( ~ (v0 =
% 254.16/36.07 | 0) & before_on_line(all_34_11, all_34_5, all_34_3) = v0)))
% 254.16/36.07 |
% 254.16/36.07 | DELTA: instantiating (19) with fresh symbol all_53_0 gives:
% 254.16/36.07 | (21) unequally_directed_lines(all_34_11, all_53_0) = 0 &
% 254.16/36.07 | unequally_directed_lines(all_34_11, all_34_10) = 0 &
% 254.16/36.07 | reverse_line(all_34_10) = all_53_0 & $i(all_53_0)
% 254.16/36.07 |
% 254.16/36.07 | ALPHA: (21) implies:
% 254.16/36.07 | (22) reverse_line(all_34_10) = all_53_0
% 254.16/36.07 | (23) unequally_directed_lines(all_34_11, all_34_10) = 0
% 254.16/36.07 | (24) unequally_directed_lines(all_34_11, all_53_0) = 0
% 254.16/36.07 |
% 254.16/36.07 | DELTA: instantiating (18) with fresh symbol all_55_0 gives:
% 254.16/36.07 | (25) unequally_directed_lines(all_34_12, all_55_0) = 0 &
% 254.16/36.07 | unequally_directed_lines(all_34_12, all_34_10) = 0 &
% 254.16/36.07 | reverse_line(all_34_10) = all_55_0 & $i(all_55_0)
% 254.16/36.07 |
% 254.16/36.07 | ALPHA: (25) implies:
% 254.16/36.07 | (26) $i(all_55_0)
% 254.16/36.07 | (27) reverse_line(all_34_10) = all_55_0
% 254.16/36.07 |
% 254.16/36.07 | BETA: splitting (20) gives:
% 254.16/36.07 |
% 254.16/36.07 | Case 1:
% 254.16/36.07 | |
% 254.16/36.07 | | (28) all_34_0 = 0
% 254.16/36.07 | |
% 254.16/36.07 | | REDUCE: (8), (28) imply:
% 254.16/36.07 | | (29) $false
% 254.47/36.07 | |
% 254.47/36.07 | | CLOSE: (29) is inconsistent.
% 254.47/36.07 | |
% 254.47/36.07 | Case 2:
% 254.47/36.07 | |
% 254.47/36.07 | |
% 254.47/36.07 | | GROUND_INST: instantiating (5) with all_53_0, all_55_0, all_34_10,
% 254.47/36.07 | | simplifying with (22), (27) gives:
% 254.47/36.07 | | (30) all_55_0 = all_53_0
% 254.47/36.07 | |
% 254.47/36.07 | | REDUCE: (26), (30) imply:
% 254.47/36.07 | | (31) $i(all_53_0)
% 254.47/36.07 | |
% 254.47/36.07 | | GROUND_INST: instantiating (3) with all_34_11, all_34_10, all_53_0,
% 254.47/36.07 | | simplifying with (10), (11), (22), (24) gives:
% 254.47/36.08 | | (32) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 254.47/36.08 | | left_convergent_lines(all_34_11, all_53_0) = 0) | (v1 = 0 &
% 254.47/36.08 | | left_convergent_lines(all_34_11, all_34_10) = 0) | ( ~ (v0 = 0)
% 254.47/36.08 | | & unequally_directed_lines(all_34_11, all_34_10) = v0))
% 254.47/36.08 | |
% 254.47/36.08 | | DELTA: instantiating (32) with fresh symbols all_94_0, all_94_1, all_94_2
% 254.47/36.08 | | gives:
% 254.47/36.08 | | (33) (all_94_0 = 0 & left_convergent_lines(all_34_11, all_53_0) = 0) |
% 254.47/36.08 | | (all_94_1 = 0 & left_convergent_lines(all_34_11, all_34_10) = 0) | (
% 254.47/36.08 | | ~ (all_94_2 = 0) & unequally_directed_lines(all_34_11, all_34_10)
% 254.47/36.08 | | = all_94_2)
% 254.47/36.08 | |
% 254.47/36.08 | | BETA: splitting (33) gives:
% 254.47/36.08 | |
% 254.47/36.08 | | Case 1:
% 254.47/36.08 | | |
% 254.47/36.08 | | | (34) all_94_0 = 0 & left_convergent_lines(all_34_11, all_53_0) = 0
% 254.47/36.08 | | |
% 254.47/36.08 | | | ALPHA: (34) implies:
% 254.47/36.08 | | | (35) left_convergent_lines(all_34_11, all_53_0) = 0
% 254.47/36.08 | | |
% 254.47/36.08 | | | GROUND_INST: instantiating (4) with all_34_11, all_53_0, simplifying with
% 254.47/36.08 | | | (10), (31), (35) gives:
% 254.47/36.08 | | | (36) $false
% 254.47/36.08 | | |
% 254.47/36.08 | | | CLOSE: (36) is inconsistent.
% 254.47/36.08 | | |
% 254.47/36.08 | | Case 2:
% 254.47/36.08 | | |
% 254.47/36.08 | | | (37) (all_94_1 = 0 & left_convergent_lines(all_34_11, all_34_10) = 0) |
% 254.47/36.08 | | | ( ~ (all_94_2 = 0) & unequally_directed_lines(all_34_11,
% 254.47/36.08 | | | all_34_10) = all_94_2)
% 254.47/36.08 | | |
% 254.47/36.08 | | | BETA: splitting (37) gives:
% 254.47/36.08 | | |
% 254.47/36.08 | | | Case 1:
% 254.47/36.08 | | | |
% 254.47/36.08 | | | | (38) all_94_1 = 0 & left_convergent_lines(all_34_11, all_34_10) = 0
% 254.47/36.08 | | | |
% 254.47/36.08 | | | | ALPHA: (38) implies:
% 254.47/36.08 | | | | (39) left_convergent_lines(all_34_11, all_34_10) = 0
% 254.47/36.08 | | | |
% 254.47/36.08 | | | | GROUND_INST: instantiating (4) with all_34_11, all_34_10, simplifying
% 254.47/36.08 | | | | with (10), (11), (39) gives:
% 254.47/36.08 | | | | (40) $false
% 254.47/36.08 | | | |
% 254.47/36.08 | | | | CLOSE: (40) is inconsistent.
% 254.47/36.08 | | | |
% 254.47/36.08 | | | Case 2:
% 254.47/36.08 | | | |
% 254.47/36.08 | | | | (41) ~ (all_94_2 = 0) & unequally_directed_lines(all_34_11,
% 254.47/36.08 | | | | all_34_10) = all_94_2
% 254.47/36.08 | | | |
% 254.47/36.08 | | | | ALPHA: (41) implies:
% 254.47/36.08 | | | | (42) ~ (all_94_2 = 0)
% 254.47/36.08 | | | | (43) unequally_directed_lines(all_34_11, all_34_10) = all_94_2
% 254.47/36.08 | | | |
% 254.47/36.08 | | | | GROUND_INST: instantiating (6) with 0, all_94_2, all_34_10, all_34_11,
% 254.47/36.08 | | | | simplifying with (23), (43) gives:
% 254.47/36.08 | | | | (44) all_94_2 = 0
% 254.47/36.08 | | | |
% 254.47/36.08 | | | | REDUCE: (42), (44) imply:
% 254.47/36.08 | | | | (45) $false
% 254.47/36.08 | | | |
% 254.47/36.08 | | | | CLOSE: (45) is inconsistent.
% 254.47/36.08 | | | |
% 254.47/36.08 | | | End of split
% 254.47/36.08 | | |
% 254.47/36.08 | | End of split
% 254.47/36.08 | |
% 254.47/36.08 | End of split
% 254.47/36.08 |
% 254.47/36.08 End of proof
% 254.47/36.08 % SZS output end Proof for theBenchmark
% 254.47/36.08
% 254.47/36.08 35450ms
%------------------------------------------------------------------------------