%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO233+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 : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 23:22:37 EDT 2023 % Result : Theorem 48.00s 7.35s % Output : Proof 52.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO233+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.34 % Computer : n008.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Aug 29 19:21:47 EDT 2023 % 0.16/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.01/1.13 Prover 1: Preprocessing ... % 3.01/1.13 Prover 4: Preprocessing ... % 3.01/1.17 Prover 5: Preprocessing ... % 3.01/1.17 Prover 0: Preprocessing ... % 3.01/1.17 Prover 6: Preprocessing ... % 3.01/1.17 Prover 2: Preprocessing ... % 3.01/1.18 Prover 3: Preprocessing ... % 6.13/1.69 Prover 5: Proving ... % 7.35/1.80 Prover 2: Proving ... % 7.35/1.80 Prover 6: Constructing countermodel ... % 7.99/1.84 Prover 1: Constructing countermodel ... % 7.99/1.85 Prover 3: Constructing countermodel ... % 8.50/1.93 Prover 6: gave up % 8.50/1.95 Prover 3: gave up % 8.50/1.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.50/1.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.14/1.99 Prover 1: gave up % 9.14/1.99 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 9.41/2.02 Prover 8: Preprocessing ... % 9.41/2.02 Prover 7: Preprocessing ... % 9.55/2.04 Prover 9: Preprocessing ... % 10.22/2.16 Prover 7: Warning: ignoring some quantifiers % 10.72/2.21 Prover 7: Constructing countermodel ... % 10.72/2.21 Prover 4: Constructing countermodel ... % 10.72/2.24 Prover 8: Warning: ignoring some quantifiers % 10.72/2.26 Prover 8: Constructing countermodel ... % 10.72/2.32 Prover 0: Proving ... % 12.03/2.42 Prover 8: gave up % 12.49/2.45 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.76/2.50 Prover 10: Preprocessing ... % 12.76/2.50 Prover 9: Constructing countermodel ... % 13.47/2.58 Prover 10: Warning: ignoring some quantifiers % 13.47/2.58 Prover 7: gave up % 13.47/2.59 Prover 10: Constructing countermodel ... % 13.47/2.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.14/2.66 Prover 10: gave up % 14.14/2.68 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 14.14/2.69 Prover 11: Preprocessing ... % 14.14/2.72 Prover 12: Preprocessing ... % 15.71/2.95 Prover 12: Proving ... % 15.71/3.09 Prover 11: Constructing countermodel ... % 35.78/5.55 Prover 12: stopped % 35.78/5.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 35.78/5.57 Prover 13: Preprocessing ... % 36.46/5.67 Prover 13: Warning: ignoring some quantifiers % 37.04/5.72 Prover 13: Constructing countermodel ... % 41.04/6.22 Prover 13: gave up % 41.04/6.23 Prover 14: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=414236379 % 41.28/6.27 Prover 14: Preprocessing ... % 43.94/6.66 Prover 14: Proving ... % 48.00/7.35 Prover 14: proved (1128ms) % 48.00/7.35 % 48.00/7.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 49.08/7.35 % 49.08/7.35 Prover 9: stopped % 49.08/7.35 Prover 5: stopped % 49.08/7.35 Prover 0: stopped % 49.08/7.35 Prover 2: stopped % 49.08/7.35 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 49.08/7.35 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 49.08/7.38 Prover 16: Preprocessing ... % 49.08/7.38 Prover 19: Preprocessing ... % 49.08/7.42 Prover 16: Warning: ignoring some quantifiers % 49.08/7.43 Prover 16: Constructing countermodel ... % 50.49/7.46 Prover 19: Warning: ignoring some quantifiers % 50.49/7.47 Prover 19: Constructing countermodel ... % 51.30/7.63 Prover 16: gave up % 51.30/7.63 Prover 19: gave up % 52.36/7.78 Prover 11: Found proof (size 203) % 52.36/7.78 Prover 11: proved (5176ms) % 52.36/7.78 Prover 4: stopped % 52.36/7.78 % 52.36/7.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 52.36/7.78 % 52.36/7.79 % SZS output start Proof for theBenchmark % 52.36/7.79 Assumptions after simplification: % 52.36/7.79 --------------------------------- % 52.36/7.79 % 52.36/7.79 (a1_defns) % 52.66/7.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 52.66/7.82 (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ~ % 52.66/7.82 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & % 52.66/7.82 unequally_directed_opposite_lines(v0, v1) = v4)) & ! [v0: $i] : ! [v1: % 52.66/7.82 $i] : ! [v2: int] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) % 52.66/7.82 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) % 52.66/7.82 & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4 & $i(v3))) % 52.66/7.82 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (reverse_line(v1) = v2) | ~ % 52.66/7.82 (unequally_directed_lines(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | % 52.66/7.82 unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : % 52.66/7.82 ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 52.66/7.82 ? [v2: $i] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0 & % 52.66/7.82 $i(v2))) % 52.66/7.82 % 52.66/7.82 (a2_defns) % 52.66/7.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 52.66/7.83 (left_apart_point(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ~ $i(v1) | % 52.66/7.83 ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & right_apart_point(v0, v1) = v4)) & % 52.66/7.83 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (right_apart_point(v0, % 52.66/7.83 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 52.66/7.83 = 0) & left_apart_point(v0, v3) = v4 & reverse_line(v1) = v3 & $i(v3))) % 52.66/7.83 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (left_apart_point(v0, v2) = 0) % 52.66/7.83 | ~ (reverse_line(v1) = v2) | ~ $i(v1) | ~ $i(v0) | right_apart_point(v0, % 52.66/7.83 v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (right_apart_point(v0, v1) = 0) % 52.66/7.83 | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (left_apart_point(v0, v2) = 0 & % 52.66/7.83 reverse_line(v1) = v2 & $i(v2))) % 52.66/7.83 % 52.66/7.83 (a4_defns) % 52.66/7.83 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 52.66/7.83 (equally_directed_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 52.66/7.83 unequally_directed_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 52.66/7.83 int] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | ~ $i(v1) | ~ % 52.66/7.83 $i(v0) | equally_directed_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( % 52.66/7.83 ~ (equally_directed_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 52.66/7.83 int] : ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2)) & ! [v0: % 52.66/7.83 $i] : ! [v1: $i] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v1) | % 52.66/7.83 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & equally_directed_lines(v0, v1) = % 52.66/7.83 v2)) % 52.66/7.83 % 52.66/7.83 (a6_defns) % 52.66/7.83 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 52.66/7.83 (apart_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : % 52.66/7.83 ? [v4: int] : ( ~ (v4 = 0) & ~ (v3 = 0) & left_apart_point(v0, v1) = v3 & % 52.66/7.83 right_apart_point(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 52.66/7.83 int] : (v2 = 0 | ~ (left_apart_point(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 52.66/7.83 | ? [v3: int] : ? [v4: int] : ((v4 = 0 & right_apart_point(v0, v1) = 0) | % 52.66/7.83 ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3))) & ! [v0: $i] : ! % 52.66/7.83 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (right_apart_point(v0, v1) = v2) | ~ % 52.66/7.83 $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & % 52.66/7.83 left_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, % 52.66/7.83 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 52.66/7.83 (left_apart_point(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? % 52.66/7.83 [v4: int] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) & ~ % 52.66/7.83 (v2 = 0) & right_apart_point(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] % 52.66/7.83 : ! [v2: any] : ( ~ (right_apart_point(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 52.66/7.83 | ? [v3: int] : ? [v4: int] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) % 52.66/7.83 | ( ~ (v3 = 0) & ~ (v2 = 0) & left_apart_point(v0, v1) = v3))) & ! [v0: % 52.66/7.83 $i] : ! [v1: $i] : ( ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ % 52.66/7.83 $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & right_apart_point(v0, v1) % 52.66/7.83 = 0) | (v2 = 0 & left_apart_point(v0, v1) = 0))) % 52.66/7.83 % 52.66/7.83 (a7_defns) % 52.66/7.84 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (convergent_lines(v0, % 52.66/7.84 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ % 52.66/7.84 (v4 = 0) & unequally_directed_opposite_lines(v0, v1) = v4) | ( ~ (v3 = % 52.66/7.84 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: % 52.66/7.84 $i] : ! [v2: any] : ( ~ (unequally_directed_lines(v0, v1) = v2) | ~ $i(v1) % 52.66/7.84 | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & v2 = 0 & % 52.66/7.84 unequally_directed_opposite_lines(v0, v1) = 0) | ( ~ (v3 = 0) & % 52.66/7.84 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 52.66/7.84 any] : ( ~ (unequally_directed_opposite_lines(v0, v1) = v2) | ~ $i(v1) | ~ % 52.66/7.84 $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & v2 = 0 & % 52.66/7.84 unequally_directed_lines(v0, v1) = 0) | ( ~ (v3 = 0) & % 52.66/7.84 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 52.66/7.84 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 52.66/7.84 (unequally_directed_lines(v0, v1) = 0 & % 52.66/7.84 unequally_directed_opposite_lines(v0, v1) = 0)) & ! [v0: $i] : ! [v1: % 52.66/7.84 $i] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 52.66/7.84 ? [v2: int] : ? [v3: int] : ((v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ % 52.66/7.84 (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2))) & ! [v0: % 52.66/7.84 $i] : ! [v1: $i] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ~ % 52.66/7.84 $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 52.66/7.84 convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & % 52.66/7.84 unequally_directed_lines(v0, v1) = v2))) % 52.66/7.84 % 52.66/7.84 (ax11_basics) % 52.66/7.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (left_convergent_lines(v0, v2) = % 52.66/7.84 0) | ~ (reverse_line(v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : % 52.66/7.84 ! [v1: $i] : ( ~ (left_convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)) % 52.66/7.84 % 52.66/7.84 (ax1_uniq_cons) % 52.91/7.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 52.91/7.87 int] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | v5 = 0 | ~ % 52.91/7.87 (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v6) = v7) | ~ % 52.91/7.87 (left_apart_point(v1, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ % 52.91/7.87 (reverse_line(v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 52.91/7.87 [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int] : ? [v12: int] : % 52.91/7.87 ? [v13: int] : ? [v14: int] : ((v14 = 0 & left_apart_point(v0, v6) = 0) | % 52.91/7.87 (v13 = 0 & left_apart_point(v0, v4) = 0) | (v12 = 0 & left_apart_point(v1, % 52.91/7.87 v3) = 0) | (v11 = 0 & left_apart_point(v0, v3) = 0) | (v10 = 0 & % 52.91/7.87 left_apart_point(v1, v2) = 0) | (v9 = 0 & left_apart_point(v0, v2) = 0) % 52.91/7.87 | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8))) & ! [v0: $i] : ! [v1: % 52.91/7.87 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : ! [v6: $i] : % 52.91/7.87 ! [v7: int] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ % 52.91/7.87 (left_apart_point(v0, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ~ % 52.91/7.87 (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ~ $i(v3) | ~ $i(v2) % 52.91/7.87 | ~ $i(v1) | ~ $i(v0) | ? [v8: int] : ? [v9: int] : ? [v10: int] : ? % 52.91/7.87 [v11: int] : ? [v12: int] : ? [v13: int] : ? [v14: int] : ((v14 = 0 & % 52.91/7.87 left_apart_point(v1, v6) = 0) | (v13 = 0 & left_apart_point(v1, v4) = 0) % 52.91/7.87 | (v12 = 0 & left_apart_point(v1, v3) = 0) | (v11 = 0 & % 52.91/7.87 left_apart_point(v0, v3) = 0) | (v10 = 0 & left_apart_point(v1, v2) = 0) % 52.91/7.87 | (v9 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & % 52.91/7.87 distinct_lines(v2, v3) = v8))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 52.91/7.87 : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : ! [v6: $i] : ! [v7: int] : (v7 % 52.91/7.87 = 0 | v5 = 0 | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v0, % 52.91/7.87 v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ~ % 52.91/7.87 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: int] : ? [v9: int] : % 52.91/7.87 ? [v10: int] : ? [v11: int] : ? [v12: int] : ? [v13: int] : ? [v14: int] % 52.91/7.87 : ? [v15: int] : ((v15 = 0 & left_apart_point(v0, v6) = 0) | (v14 = 0 & % 52.91/7.87 left_apart_point(v1, v4) = 0) | (v13 = 0 & left_apart_point(v1, v3) = 0) % 52.91/7.87 | (v12 = 0 & left_apart_point(v0, v3) = 0) | (v11 = 0 & % 52.91/7.87 left_apart_point(v1, v2) = 0) | (v10 = 0 & left_apart_point(v0, v2) = 0) % 52.91/7.87 | ( ~ (v9 = 0) & distinct_lines(v2, v3) = v9) | ( ~ (v8 = 0) & % 52.91/7.87 distinct_points(v0, v1) = v8))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 52.91/7.87 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : ! [v6: $i] : ! [v7: int] % 52.91/7.87 : (v7 = 0 | v5 = 0 | ~ (left_apart_point(v1, v4) = v5) | ~ % 52.91/7.87 (left_apart_point(v0, v6) = v7) | ~ (reverse_line(v3) = v6) | ~ % 52.91/7.87 (reverse_line(v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 52.91/7.87 [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int] : ? [v12: int] : % 52.91/7.87 ? [v13: int] : ? [v14: int] : ? [v15: int] : ((v15 = 0 & % 52.91/7.87 left_apart_point(v1, v6) = 0) | (v14 = 0 & left_apart_point(v0, v4) = 0) % 52.91/7.87 | (v13 = 0 & left_apart_point(v1, v3) = 0) | (v12 = 0 & % 52.91/7.87 left_apart_point(v0, v3) = 0) | (v11 = 0 & left_apart_point(v1, v2) = 0) % 52.91/7.87 | (v10 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v9 = 0) & % 52.91/7.87 distinct_lines(v2, v3) = v9) | ( ~ (v8 = 0) & distinct_points(v0, v1) = % 52.91/7.87 v8))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 52.91/7.87 $i] : ! [v5: int] : ! [v6: int] : (v6 = 0 | v5 = 0 | ~ % 52.91/7.87 (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v4) = v6) | ~ % 52.91/7.87 (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v4) | ~ $i(v3) | % 52.91/7.87 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: int] : ? [v8: int] : ? [v9: % 52.91/7.87 int] : ? [v10: int] : ? [v11: int] : ? [v12: $i] : ? [v13: int] : ? % 52.91/7.87 [v14: int] : ((v14 = 0 & left_apart_point(v1, v12) = 0 & reverse_line(v2) = % 52.91/7.87 v12 & $i(v12)) | (v13 = 0 & left_apart_point(v0, v12) = 0 & % 52.91/7.87 reverse_line(v2) = v12 & $i(v12)) | (v11 = 0 & left_apart_point(v1, v3) % 52.91/7.87 = 0) | (v10 = 0 & left_apart_point(v0, v3) = 0) | (v9 = 0 & % 52.91/7.87 left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) % 52.91/7.87 | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0: $i] : ! [v1: % 52.91/7.87 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : ! [v6: int] % 52.91/7.87 : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ % 52.91/7.87 (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ~ % 52.91/7.87 (reverse_line(v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 52.91/7.87 [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int] : ? % 52.91/7.87 [v12: $i] : ? [v13: int] : ? [v14: int] : ((v14 = 0 & left_apart_point(v1, % 52.91/7.87 v12) = 0 & reverse_line(v3) = v12 & $i(v12)) | (v13 = 0 & % 52.91/7.87 left_apart_point(v0, v12) = 0 & reverse_line(v3) = v12 & $i(v12)) | (v11 % 52.91/7.87 = 0 & left_apart_point(v1, v3) = 0) | (v10 = 0 & left_apart_point(v0, % 52.91/7.87 v3) = 0) | (v9 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & % 52.91/7.87 left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = % 52.91/7.87 v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 52.91/7.87 int] : ! [v5: $i] : ! [v6: int] : (v6 = 0 | v4 = 0 | ~ % 52.91/7.87 (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ % 52.91/7.87 (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v3) = v5) | ~ $i(v3) | % 52.91/7.87 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: int] : ? [v8: int] : ? [v9: % 52.91/7.87 int] : ? [v10: int] : ? [v11: $i] : ? [v12: int] : ? [v13: int] : ? % 52.91/7.87 [v14: int] : ((v14 = 0 & left_apart_point(v0, v5) = 0) | (v13 = 0 & % 52.91/7.87 left_apart_point(v1, v11) = 0 & reverse_line(v2) = v11 & $i(v11)) | (v12 % 52.91/7.87 = 0 & left_apart_point(v0, v11) = 0 & reverse_line(v2) = v11 & $i(v11)) % 52.91/7.87 | (v10 = 0 & left_apart_point(v1, v3) = 0) | (v9 = 0 & % 52.91/7.87 left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) % 52.91/7.87 | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0: $i] : ! [v1: % 52.91/7.87 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: $i] : ! [v6: int] % 52.91/7.87 : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ % 52.91/7.88 (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ % 52.91/7.88 (reverse_line(v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 52.91/7.88 [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int] : ? % 52.91/7.88 [v12: $i] : ? [v13: int] : ? [v14: int] : ((v14 = 0 & left_apart_point(v1, % 52.91/7.88 v12) = 0 & reverse_line(v3) = v12 & $i(v12)) | (v13 = 0 & % 52.91/7.88 left_apart_point(v0, v12) = 0 & reverse_line(v3) = v12 & $i(v12)) | (v11 % 52.91/7.88 = 0 & left_apart_point(v0, v5) = 0) | (v10 = 0 & left_apart_point(v1, % 52.91/7.88 v3) = 0) | (v9 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & % 52.91/7.88 left_apart_point(v1, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = % 52.91/7.88 v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 52.91/7.88 int] : ! [v5: $i] : ! [v6: int] : (v6 = 0 | v4 = 0 | ~ % 52.91/7.88 (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v3) = v4) | ~ % 52.91/7.88 (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v3) = v5) | ~ $i(v3) | % 52.91/7.88 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: int] : ? [v8: int] : ? [v9: % 52.91/7.88 int] : ? [v10: int] : ? [v11: $i] : ? [v12: int] : ? [v13: int] : ? % 52.91/7.88 [v14: int] : ((v14 = 0 & left_apart_point(v1, v5) = 0) | (v13 = 0 & % 52.91/7.88 left_apart_point(v1, v11) = 0 & reverse_line(v2) = v11 & $i(v11)) | (v12 % 52.91/7.88 = 0 & left_apart_point(v0, v11) = 0 & reverse_line(v2) = v11 & $i(v11)) % 52.91/7.88 | (v10 = 0 & left_apart_point(v0, v3) = 0) | (v9 = 0 & % 52.91/7.88 left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) % 52.91/7.88 | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0: $i] : ! [v1: % 52.91/7.88 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: $i] : ! [v6: int] % 52.91/7.88 : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ % 52.91/7.88 (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ % 52.91/7.88 (reverse_line(v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 52.91/7.88 [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int] : ? % 52.91/7.88 [v12: $i] : ? [v13: int] : ? [v14: int] : ((v14 = 0 & left_apart_point(v1, % 52.91/7.88 v12) = 0 & reverse_line(v3) = v12 & $i(v12)) | (v13 = 0 & % 52.91/7.88 left_apart_point(v0, v12) = 0 & reverse_line(v3) = v12 & $i(v12)) | (v11 % 52.91/7.88 = 0 & left_apart_point(v1, v5) = 0) | (v10 = 0 & left_apart_point(v1, % 52.91/7.88 v3) = 0) | (v9 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & % 52.91/7.88 left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = % 52.91/7.88 v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 52.91/7.88 int] : ! [v5: $i] : ! [v6: int] : (v6 = 0 | v4 = 0 | ~ % 52.91/7.88 (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ % 52.91/7.88 (left_apart_point(v1, v3) = v4) | ~ (reverse_line(v2) = v5) | ~ $i(v3) | % 52.91/7.88 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: int] : ? [v8: int] : ? [v9: % 52.91/7.88 int] : ? [v10: int] : ? [v11: int] : ? [v12: $i] : ? [v13: int] : ? % 52.91/7.88 [v14: int] : ((v14 = 0 & left_apart_point(v1, v12) = 0 & reverse_line(v3) = % 52.91/7.88 v12 & $i(v12)) | (v13 = 0 & left_apart_point(v0, v12) = 0 & % 52.91/7.88 reverse_line(v3) = v12 & $i(v12)) | (v11 = 0 & left_apart_point(v0, v5) % 52.91/7.88 = 0) | (v10 = 0 & left_apart_point(v0, v3) = 0) | (v9 = 0 & % 52.91/7.88 left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) % 52.91/7.88 | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) & ! [v0: $i] : ! [v1: % 52.91/7.88 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: $i] : ! [v6: int] % 52.91/7.88 : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ % 52.91/7.88 (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v1, v2) = v4) | ~ % 52.91/7.88 (reverse_line(v3) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 52.91/7.88 [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: $i] : ? % 52.91/7.88 [v12: int] : ? [v13: int] : ? [v14: int] : ((v14 = 0 & % 52.91/7.88 left_apart_point(v0, v5) = 0) | (v13 = 0 & left_apart_point(v1, v11) = 0 % 52.91/7.88 & reverse_line(v2) = v11 & $i(v11)) | (v12 = 0 & left_apart_point(v0, % 52.91/7.88 v11) = 0 & reverse_line(v2) = v11 & $i(v11)) | (v10 = 0 & % 52.91/7.88 left_apart_point(v1, v3) = 0) | (v9 = 0 & left_apart_point(v0, v3) = 0) % 52.91/7.88 | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & % 52.91/7.88 distinct_lines(v2, v3) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 52.91/7.88 : ! [v3: $i] : ! [v4: int] : ! [v5: $i] : ! [v6: int] : (v6 = 0 | v4 = 0 | % 52.91/7.88 ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v5) = v6) | ~ % 52.91/7.88 (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v5) | ~ $i(v3) | % 52.91/7.88 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: int] : ? [v8: int] : ? [v9: % 52.91/7.88 int] : ? [v10: int] : ? [v11: int] : ? [v12: $i] : ? [v13: int] : ? % 52.91/7.88 [v14: int] : ((v14 = 0 & left_apart_point(v1, v12) = 0 & reverse_line(v3) = % 52.91/7.88 v12 & $i(v12)) | (v13 = 0 & left_apart_point(v0, v12) = 0 & % 52.91/7.88 reverse_line(v3) = v12 & $i(v12)) | (v11 = 0 & left_apart_point(v1, v5) % 52.91/7.88 = 0) | (v10 = 0 & left_apart_point(v1, v3) = 0) | (v9 = 0 & % 52.91/7.88 left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) % 52.91/7.88 | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) & ! [v0: $i] : ! [v1: % 52.91/7.88 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: $i] : ! [v6: int] % 52.91/7.88 : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ % 52.91/7.88 (left_apart_point(v0, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ % 52.91/7.88 (reverse_line(v3) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 52.91/7.88 [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: $i] : ? % 52.91/7.88 [v12: int] : ? [v13: int] : ? [v14: int] : ((v14 = 0 & % 52.91/7.88 left_apart_point(v1, v5) = 0) | (v13 = 0 & left_apart_point(v1, v11) = 0 % 52.91/7.88 & reverse_line(v2) = v11 & $i(v11)) | (v12 = 0 & left_apart_point(v0, % 52.91/7.88 v11) = 0 & reverse_line(v2) = v11 & $i(v11)) | (v10 = 0 & % 52.91/7.88 left_apart_point(v1, v3) = 0) | (v9 = 0 & left_apart_point(v0, v3) = 0) % 52.91/7.88 | (v8 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v7 = 0) & % 52.91/7.88 distinct_lines(v2, v3) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 52.91/7.88 : ! [v3: $i] : ! [v4: int] : ! [v5: $i] : ! [v6: int] : (v6 = 0 | v4 = 0 | % 52.91/7.88 ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ % 52.91/7.88 (reverse_line(v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 52.91/7.88 [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int] : ? % 52.91/7.88 [v12: int] : ? [v13: $i] : ? [v14: int] : ? [v15: int] : ((v15 = 0 & % 52.91/7.88 left_apart_point(v1, v13) = 0 & reverse_line(v3) = v13 & $i(v13)) | (v14 % 52.91/7.88 = 0 & left_apart_point(v0, v13) = 0 & reverse_line(v3) = v13 & $i(v13)) % 52.91/7.88 | (v12 = 0 & left_apart_point(v0, v5) = 0) | (v11 = 0 & % 52.91/7.88 left_apart_point(v1, v3) = 0) | (v10 = 0 & left_apart_point(v1, v2) = 0) % 52.91/7.88 | (v9 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & % 52.91/7.88 distinct_lines(v2, v3) = v8) | ( ~ (v7 = 0) & distinct_points(v0, v1) = % 52.91/7.88 v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 52.91/7.88 int] : ! [v5: $i] : ! [v6: int] : (v6 = 0 | v4 = 0 | ~ % 52.91/7.88 (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ % 52.91/7.88 (reverse_line(v3) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 52.91/7.88 [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int] : ? % 52.91/7.88 [v12: $i] : ? [v13: int] : ? [v14: int] : ? [v15: int] : ((v15 = 0 & % 52.91/7.88 left_apart_point(v0, v5) = 0) | (v14 = 0 & left_apart_point(v1, v12) = 0 % 52.91/7.88 & reverse_line(v2) = v12 & $i(v12)) | (v13 = 0 & left_apart_point(v0, % 52.91/7.88 v12) = 0 & reverse_line(v2) = v12 & $i(v12)) | (v11 = 0 & % 52.91/7.88 left_apart_point(v1, v3) = 0) | (v10 = 0 & left_apart_point(v0, v3) = 0) % 52.91/7.88 | (v9 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v8 = 0) & % 52.91/7.88 distinct_lines(v2, v3) = v8) | ( ~ (v7 = 0) & distinct_points(v0, v1) = % 52.91/7.88 v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 52.91/7.88 int] : ! [v5: $i] : ! [v6: int] : (v6 = 0 | v4 = 0 | ~ % 52.91/7.88 (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ % 52.91/7.88 (reverse_line(v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 52.91/7.88 [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int] : ? % 52.91/7.88 [v12: int] : ? [v13: $i] : ? [v14: int] : ? [v15: int] : ((v15 = 0 & % 52.91/7.88 left_apart_point(v1, v13) = 0 & reverse_line(v3) = v13 & $i(v13)) | (v14 % 52.91/7.88 = 0 & left_apart_point(v0, v13) = 0 & reverse_line(v3) = v13 & $i(v13)) % 52.91/7.88 | (v12 = 0 & left_apart_point(v1, v5) = 0) | (v11 = 0 & % 52.91/7.88 left_apart_point(v0, v3) = 0) | (v10 = 0 & left_apart_point(v1, v2) = 0) % 52.91/7.88 | (v9 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & % 52.91/7.88 distinct_lines(v2, v3) = v8) | ( ~ (v7 = 0) & distinct_points(v0, v1) = % 52.91/7.88 v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 52.91/7.88 int] : ! [v5: $i] : ! [v6: int] : (v6 = 0 | v4 = 0 | ~ % 52.91/7.88 (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ % 52.91/7.88 (reverse_line(v3) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 52.91/7.88 [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int] : ? % 52.91/7.88 [v12: $i] : ? [v13: int] : ? [v14: int] : ? [v15: int] : ((v15 = 0 & % 52.91/7.88 left_apart_point(v1, v5) = 0) | (v14 = 0 & left_apart_point(v1, v12) = 0 % 52.91/7.88 & reverse_line(v2) = v12 & $i(v12)) | (v13 = 0 & left_apart_point(v0, % 52.91/7.88 v12) = 0 & reverse_line(v2) = v12 & $i(v12)) | (v11 = 0 & % 52.91/7.88 left_apart_point(v1, v3) = 0) | (v10 = 0 & left_apart_point(v0, v3) = 0) % 52.91/7.88 | (v9 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & % 52.91/7.88 distinct_lines(v2, v3) = v8) | ( ~ (v7 = 0) & distinct_points(v0, v1) = % 52.91/7.88 v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 52.91/7.88 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | % 52.91/7.88 ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v3) = v4) | ~ % 52.91/7.88 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 52.91/7.88 ? [v8: int] : ? [v9: $i] : ? [v10: int] : ? [v11: int] : ? [v12: $i] : % 52.91/7.88 ? [v13: int] : ? [v14: int] : ((v14 = 0 & left_apart_point(v1, v12) = 0 & % 52.91/7.88 reverse_line(v3) = v12 & $i(v12)) | (v13 = 0 & left_apart_point(v0, v12) % 52.91/7.88 = 0 & reverse_line(v3) = v12 & $i(v12)) | (v11 = 0 & % 52.91/7.88 left_apart_point(v1, v9) = 0 & reverse_line(v2) = v9 & $i(v9)) | (v10 = % 52.91/7.88 0 & left_apart_point(v0, v9) = 0 & reverse_line(v2) = v9 & $i(v9)) | (v8 % 52.91/7.88 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v2) % 52.91/7.88 = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: $i] : ! % 52.91/7.88 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | % 52.91/7.88 v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v2) = % 52.91/7.88 v5) | ~ (left_apart_point(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 52.91/7.88 $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: % 52.91/7.88 $i] : ? [v10: int] : ? [v11: int] : ? [v12: $i] : ? [v13: int] : ? % 52.91/7.88 [v14: int] : ((v14 = 0 & left_apart_point(v1, v12) = 0 & reverse_line(v3) = % 52.91/7.88 v12 & $i(v12)) | (v13 = 0 & left_apart_point(v0, v12) = 0 & % 52.91/7.88 reverse_line(v3) = v12 & $i(v12)) | (v11 = 0 & left_apart_point(v1, v9) % 52.91/7.88 = 0 & reverse_line(v2) = v9 & $i(v9)) | (v10 = 0 & left_apart_point(v0, % 52.91/7.88 v9) = 0 & reverse_line(v2) = v9 & $i(v9)) | (v8 = 0 & % 52.91/7.88 left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) % 52.91/7.88 | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: $i] : ! [v1: % 52.91/7.88 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 % 52.91/7.88 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v3) = v5) % 52.91/7.88 | ~ (left_apart_point(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 52.91/7.88 ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: $i] : ? % 52.91/7.88 [v10: int] : ? [v11: int] : ? [v12: $i] : ? [v13: int] : ? [v14: int] : % 52.91/7.88 ((v14 = 0 & left_apart_point(v1, v12) = 0 & reverse_line(v3) = v12 & % 52.91/7.88 $i(v12)) | (v13 = 0 & left_apart_point(v0, v12) = 0 & reverse_line(v3) = % 52.91/7.88 v12 & $i(v12)) | (v11 = 0 & left_apart_point(v1, v9) = 0 & % 52.91/7.88 reverse_line(v2) = v9 & $i(v9)) | (v10 = 0 & left_apart_point(v0, v9) = % 52.91/7.88 0 & reverse_line(v2) = v9 & $i(v9)) | (v8 = 0 & left_apart_point(v0, v3) % 52.91/7.88 = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & % 52.91/7.88 distinct_lines(v2, v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 52.91/7.88 : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 52.91/7.88 (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v3) = v5) | ~ % 52.91/7.88 (left_apart_point(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 52.91/7.88 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: $i] : ? [v10: % 52.91/7.88 int] : ? [v11: int] : ? [v12: $i] : ? [v13: int] : ? [v14: int] : % 52.91/7.88 ((v14 = 0 & left_apart_point(v1, v12) = 0 & reverse_line(v3) = v12 & % 52.91/7.88 $i(v12)) | (v13 = 0 & left_apart_point(v0, v12) = 0 & reverse_line(v3) = % 52.91/7.88 v12 & $i(v12)) | (v11 = 0 & left_apart_point(v1, v9) = 0 & % 52.91/7.88 reverse_line(v2) = v9 & $i(v9)) | (v10 = 0 & left_apart_point(v0, v9) = % 52.91/7.88 0 & reverse_line(v2) = v9 & $i(v9)) | (v8 = 0 & left_apart_point(v1, v3) % 52.91/7.88 = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v6 = 0) & % 52.91/7.88 distinct_lines(v2, v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 52.91/7.88 : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 52.91/7.88 (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v2) = v4) | ~ % 52.91/7.88 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 52.91/7.88 ? [v8: int] : ? [v9: int] : ? [v10: $i] : ? [v11: int] : ? [v12: int] : % 52.91/7.88 ? [v13: $i] : ? [v14: int] : ? [v15: int] : ((v15 = 0 & % 52.91/7.88 left_apart_point(v1, v13) = 0 & reverse_line(v3) = v13 & $i(v13)) | (v14 % 52.91/7.88 = 0 & left_apart_point(v0, v13) = 0 & reverse_line(v3) = v13 & $i(v13)) % 52.91/7.88 | (v12 = 0 & left_apart_point(v1, v10) = 0 & reverse_line(v2) = v10 & % 52.91/7.88 $i(v10)) | (v11 = 0 & left_apart_point(v0, v10) = 0 & reverse_line(v2) = % 52.91/7.88 v10 & $i(v10)) | (v9 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & % 52.91/7.88 left_apart_point(v1, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = % 52.91/7.88 v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: $i] : ! % 52.91/7.88 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | % 52.91/7.88 v4 = 0 | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v3) = % 52.91/7.88 v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? % 52.91/7.88 [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: $i] : ? [v11: int] : ? % 52.91/7.88 [v12: int] : ? [v13: $i] : ? [v14: int] : ? [v15: int] : ((v15 = 0 & % 52.91/7.88 left_apart_point(v1, v13) = 0 & reverse_line(v3) = v13 & $i(v13)) | (v14 % 52.91/7.88 = 0 & left_apart_point(v0, v13) = 0 & reverse_line(v3) = v13 & $i(v13)) % 52.91/7.88 | (v12 = 0 & left_apart_point(v1, v10) = 0 & reverse_line(v2) = v10 & % 52.91/7.88 $i(v10)) | (v11 = 0 & left_apart_point(v0, v10) = 0 & reverse_line(v2) = % 52.91/7.88 v10 & $i(v10)) | (v9 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & % 52.91/7.88 left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = % 52.91/7.88 v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: $i] : ! % 52.91/7.88 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | ~ % 52.91/7.88 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 52.91/7.88 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: % 52.91/7.88 $i] : ? [v9: int] : ? [v10: int] : ? [v11: $i] : ? [v12: int] : ? % 52.91/7.88 [v13: int] : ((v13 = 0 & left_apart_point(v1, v11) = 0 & reverse_line(v3) = % 52.91/7.88 v11 & $i(v11)) | (v12 = 0 & left_apart_point(v0, v11) = 0 & % 52.91/7.88 reverse_line(v3) = v11 & $i(v11)) | (v10 = 0 & left_apart_point(v1, v8) % 52.91/7.88 = 0 & reverse_line(v2) = v8 & $i(v8)) | (v9 = 0 & left_apart_point(v0, % 52.91/7.88 v8) = 0 & reverse_line(v2) = v8 & $i(v8)) | (v7 = 0 & % 52.91/7.88 left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) % 52.91/7.88 | (v5 = 0 & left_apart_point(v1, v2) = 0) | (v4 = 0 & left_apart_point(v0, % 52.91/7.88 v2) = 0))) % 52.91/7.88 % 52.91/7.88 (ax6_basics) % 52.91/7.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 52.91/7.88 0 | v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v4) | ~ % 52.91/7.88 (unequally_directed_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 52.91/7.88 | ? [v5: int] : ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)) & ! % 52.91/7.88 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 52.91/7.88 (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, % 52.91/7.88 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 52.91/7.88 unequally_directed_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 52.91/7.88 $i] : ! [v3: int] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) | % 52.91/7.88 ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 52.91/7.88 | unequally_directed_lines(v1, v2) = 0) % 52.91/7.88 % 52.91/7.88 (ax6_cons_objs) % 52.91/7.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 52.91/7.88 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : % 52.91/7.88 ? [v6: int] : ? [v7: int] : (( ~ (v7 = 0) & ~ (v6 = 0) & % 52.91/7.88 apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6) | % 52.91/7.88 ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = % 52.91/7.88 v5 & $i(v4)) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & % 52.91/7.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (reverse_line(v1) = v2) | ~ % 52.91/7.88 (unequally_directed_lines(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 52.91/7.88 int] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : (( ~ (v6 = 0) & ~ (v5 % 52.91/7.88 = 0) & intersection_point(v0, v1) = v4 & apart_point_and_line(v4, v1) % 52.91/7.88 = v6 & apart_point_and_line(v4, v0) = v5 & $i(v4)) | ( ~ (v3 = 0) & % 52.91/7.88 unequally_directed_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( % 52.91/7.88 ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 52.91/7.88 $i] : ? [v3: int] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : (( ~ (v6 % 52.91/7.88 = 0) & ~ (v5 = 0) & intersection_point(v0, v1) = v4 & % 52.91/7.88 apart_point_and_line(v4, v1) = v6 & apart_point_and_line(v4, v0) = v5 & % 52.91/7.88 $i(v4)) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & % 52.91/7.88 unequally_directed_lines(v0, v2) = v3 & $i(v2)))) % 52.91/7.88 % 52.91/7.88 (ax8_basics) % 52.91/7.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 52.91/7.89 (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ~ % 52.91/7.89 $i(v1) | ~ $i(v0) | unequally_directed_lines(v0, v1) = 0) & ! [v0: $i] : % 52.91/7.89 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = % 52.91/7.89 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (reverse_line(v1) = v3 & % 52.91/7.89 unequally_directed_lines(v0, v3) = 0 & $i(v3))) % 52.91/7.89 % 52.91/7.89 (ax9_basics) % 52.91/7.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 52.91/7.89 (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ~ % 52.91/7.89 $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ((v6 = 0 & % 52.91/7.89 left_convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & % 52.91/7.89 unequally_directed_lines(v0, v2) = v5) | ( ~ (v4 = 0) & % 52.91/7.89 unequally_directed_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : % 52.91/7.89 ! [v2: int] : (v2 = 0 | ~ (left_convergent_lines(v0, v1) = v2) | ~ $i(v1) | % 52.91/7.89 ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : ((v6 = % 52.91/7.89 0 & left_convergent_lines(v0, v4) = 0 & reverse_line(v1) = v4 & $i(v4)) % 52.91/7.89 | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) % 52.91/7.89 = v5 & $i(v4)) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) % 52.91/7.89 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (reverse_line(v1) = v2) | ~ % 52.91/7.89 (unequally_directed_lines(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 52.91/7.89 int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 & left_convergent_lines(v0, % 52.91/7.89 v2) = 0) | (v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) % 52.91/7.89 & unequally_directed_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : % 52.91/7.89 ( ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 52.91/7.89 $i] : ? [v3: int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 & % 52.91/7.89 left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2 & $i(v2)) | % 52.91/7.89 (v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & % 52.91/7.89 reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3 & % 52.91/7.89 $i(v2)))) % 52.91/7.89 % 52.91/7.89 (con) % 52.91/7.89 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 52.91/7.89 equally_directed_lines(v2, v0) = v3 & reverse_line(v1) = v2 & % 52.91/7.89 reverse_line(v0) = v1 & $i(v2) & $i(v1) & $i(v0)) % 52.91/7.89 % 52.91/7.89 (function-axioms) % 52.91/7.89 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 52.91/7.89 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_on_line(v5, v4, % 52.91/7.89 v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0: % 52.91/7.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 52.91/7.89 : ! [v4: $i] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ % 52.91/7.89 (before_on_line(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 52.91/7.89 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 52.91/7.89 (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) & % 52.91/7.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.91/7.89 (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = % 52.91/7.89 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 52.91/7.89 ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 52.91/7.89 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 52.91/7.89 [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 52.91/7.89 (distinct_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 52.91/7.89 ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 52.91/7.89 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 52.91/7.89 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.91/7.89 (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! % 52.91/7.89 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 52.91/7.89 $i] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ % 52.91/7.89 (incident_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 52.91/7.89 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.91/7.89 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 52.91/7.89 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 52.91/7.89 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 52.91/7.89 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 52.91/7.89 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.91/7.89 (equally_directed_opposite_lines(v3, v2) = v1) | ~ % 52.91/7.89 (equally_directed_opposite_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 52.91/7.89 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.91/7.89 (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) = % 52.91/7.89 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 52.91/7.89 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ % 52.91/7.89 (left_convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 52.91/7.89 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.91/7.89 (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) = % 52.91/7.89 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 52.91/7.89 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ % 52.91/7.89 (left_apart_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 52.91/7.89 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.91/7.89 (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0)) & ! % 52.91/7.89 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 52.91/7.89 $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ % 52.91/7.89 (unequally_directed_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 52.91/7.89 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.91/7.89 (unequally_directed_opposite_lines(v3, v2) = v1) | ~ % 52.91/7.89 (unequally_directed_opposite_lines(v3, v2) = v0)) & ! [v0: % 52.91/7.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 52.91/7.89 ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 52.91/7.89 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (line(v2) = v1) | ~ % 52.91/7.89 (line(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 52.91/7.89 (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 52.91/7.89 % 52.91/7.89 Further assumptions not needed in the proof: % 52.91/7.89 -------------------------------------------- % 52.91/7.89 a3_defns, a5_defns, a8_defns, a9_defns, ax10_basics, ax10_cons_objs, ax1_basics, % 52.91/7.89 ax1_cons_objs, ax1_subs, ax2_basics, ax2_cons_objs, ax2_subs, ax2_uniq_cons, % 52.91/7.89 ax3_basics, ax3_cons_objs, ax3_subs, ax4_basics, ax4_cons_objs, ax4_defns, % 52.91/7.89 ax5_basics, ax5_cons_objs, ax7_basics, ax7_cons_objs, ax8_cons_objs, % 52.91/7.89 ax9_cons_objs % 52.91/7.89 % 52.91/7.89 Those formulas are unsatisfiable: % 52.91/7.89 --------------------------------- % 52.91/7.89 % 52.91/7.89 Begin of proof % 52.91/7.89 | % 52.91/7.90 | ALPHA: (a1_defns) implies: % 52.91/7.90 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (unequally_directed_opposite_lines(v0, % 52.91/7.90 | v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : % 52.91/7.90 | (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0 & % 52.91/7.90 | $i(v2))) % 52.91/7.90 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 52.91/7.90 | (unequally_directed_opposite_lines(v0, v1) = v2) | ~ $i(v1) | ~ % 52.91/7.90 | $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & reverse_line(v1) % 52.91/7.90 | = v3 & unequally_directed_lines(v0, v3) = v4 & $i(v3))) % 52.91/7.90 | % 52.91/7.90 | ALPHA: (a2_defns) implies: % 52.91/7.90 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 52.91/7.90 | (right_apart_point(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 52.91/7.90 | $i] : ? [v4: int] : ( ~ (v4 = 0) & left_apart_point(v0, v3) = v4 & % 52.91/7.90 | reverse_line(v1) = v3 & $i(v3))) % 52.91/7.90 | % 52.91/7.90 | ALPHA: (a4_defns) implies: % 52.91/7.90 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 52.91/7.90 | (equally_directed_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 52.91/7.90 | unequally_directed_lines(v0, v1) = 0) % 52.91/7.90 | % 52.91/7.90 | ALPHA: (a6_defns) implies: % 52.91/7.90 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 52.91/7.90 | (apart_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 52.91/7.90 | int] : ? [v4: int] : ( ~ (v4 = 0) & ~ (v3 = 0) & % 52.91/7.90 | left_apart_point(v0, v1) = v3 & right_apart_point(v0, v1) = v4)) % 52.91/7.90 | % 52.91/7.90 | ALPHA: (a7_defns) implies: % 52.91/7.90 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (unequally_directed_lines(v0, v1) = 0) % 52.91/7.90 | | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 52.91/7.90 | convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & % 52.91/7.90 | unequally_directed_opposite_lines(v0, v1) = v2))) % 52.91/7.90 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 52.91/7.90 | (unequally_directed_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 52.91/7.90 | [v3: int] : ? [v4: int] : ((v4 = 0 & v2 = 0 & % 52.91/7.90 | unequally_directed_opposite_lines(v0, v1) = 0) | ( ~ (v3 = 0) & % 52.91/7.90 | convergent_lines(v0, v1) = v3))) % 52.91/7.90 | % 52.91/7.90 | ALPHA: (ax6_basics) implies: % 52.91/7.90 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 52.91/7.90 | (v4 = 0 | v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v4) | ~ % 52.91/7.90 | (unequally_directed_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 52.91/7.90 | $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & unequally_directed_lines(v0, % 52.91/7.90 | v1) = v5)) % 52.91/7.90 | % 52.91/7.90 | ALPHA: (ax8_basics) implies: % 52.91/7.90 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 52.91/7.90 | (unequally_directed_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 52.91/7.90 | [v3: $i] : (reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) % 52.91/7.90 | = 0 & $i(v3))) % 52.91/7.90 | % 52.91/7.90 | ALPHA: (ax9_basics) implies: % 52.91/7.90 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (unequally_directed_lines(v0, v1) = 0) % 52.91/7.90 | | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ? [v4: int] % 52.91/7.90 | : ? [v5: int] : ((v5 = 0 & left_convergent_lines(v0, v2) = 0 & % 52.91/7.90 | reverse_line(v1) = v2 & $i(v2)) | (v4 = 0 & % 52.91/7.90 | left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & % 52.91/7.90 | reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3 & % 52.91/7.90 | $i(v2)))) % 52.91/7.90 | % 52.91/7.90 | ALPHA: (ax11_basics) implies: % 52.91/7.90 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (left_convergent_lines(v0, v1) = 0) | % 52.91/7.90 | ~ $i(v1) | ~ $i(v0)) % 52.91/7.90 | % 52.91/7.90 | ALPHA: (ax6_cons_objs) implies: % 52.91/7.90 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (unequally_directed_lines(v0, v1) = 0) % 52.91/7.90 | | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ? [v4: $i] : % 52.91/7.90 | ? [v5: int] : ? [v6: int] : (( ~ (v6 = 0) & ~ (v5 = 0) & % 52.91/7.90 | intersection_point(v0, v1) = v4 & apart_point_and_line(v4, v1) = % 52.91/7.90 | v6 & apart_point_and_line(v4, v0) = v5 & $i(v4)) | ( ~ (v3 = 0) % 52.91/7.90 | & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3 % 52.91/7.90 | & $i(v2)))) % 52.91/7.90 | % 52.91/7.90 | ALPHA: (ax1_uniq_cons) implies: % 52.91/7.91 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 52.91/7.91 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v5) | % 52.91/7.91 | ~ (left_apart_point(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 52.91/7.91 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 52.91/7.91 | [v9: int] : ? [v10: $i] : ? [v11: int] : ? [v12: int] : ? [v13: % 52.91/7.91 | $i] : ? [v14: int] : ? [v15: int] : ((v15 = 0 & % 52.91/7.91 | left_apart_point(v1, v13) = 0 & reverse_line(v3) = v13 & % 52.91/7.91 | $i(v13)) | (v14 = 0 & left_apart_point(v0, v13) = 0 & % 52.91/7.91 | reverse_line(v3) = v13 & $i(v13)) | (v12 = 0 & % 52.91/7.91 | left_apart_point(v1, v10) = 0 & reverse_line(v2) = v10 & % 52.91/7.91 | $i(v10)) | (v11 = 0 & left_apart_point(v0, v10) = 0 & % 52.91/7.91 | reverse_line(v2) = v10 & $i(v10)) | (v9 = 0 & % 52.91/7.91 | left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v1, % 52.91/7.91 | v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ % 52.91/7.91 | (v6 = 0) & distinct_points(v0, v1) = v6))) % 52.91/7.91 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 52.91/7.91 | ! [v5: $i] : ! [v6: int] : (v6 = 0 | v4 = 0 | ~ % 52.91/7.91 | (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) % 52.91/7.91 | | ~ (reverse_line(v3) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 52.91/7.91 | ~ $i(v0) | ? [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: % 52.91/7.91 | int] : ? [v11: int] : ? [v12: $i] : ? [v13: int] : ? [v14: % 52.91/7.91 | int] : ? [v15: int] : ((v15 = 0 & left_apart_point(v0, v5) = 0) | % 52.91/7.91 | (v14 = 0 & left_apart_point(v1, v12) = 0 & reverse_line(v2) = v12 % 52.91/7.91 | & $i(v12)) | (v13 = 0 & left_apart_point(v0, v12) = 0 & % 52.91/7.91 | reverse_line(v2) = v12 & $i(v12)) | (v11 = 0 & % 52.91/7.91 | left_apart_point(v1, v3) = 0) | (v10 = 0 & left_apart_point(v0, % 52.91/7.91 | v3) = 0) | (v9 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v8 = % 52.91/7.91 | 0) & distinct_lines(v2, v3) = v8) | ( ~ (v7 = 0) & % 52.91/7.91 | distinct_points(v0, v1) = v7))) % 52.91/7.91 | % 52.91/7.91 | ALPHA: (function-axioms) implies: % 52.91/7.91 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 52.91/7.91 | (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 52.91/7.91 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 52.91/7.91 | : ! [v3: $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) % 52.91/7.91 | | ~ (unequally_directed_lines(v3, v2) = v0)) % 52.91/7.91 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 52.91/7.91 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 52.91/7.91 | (convergent_lines(v3, v2) = v0)) % 52.91/7.91 | % 52.91/7.91 | DELTA: instantiating (con) with fresh symbols all_39_0, all_39_1, all_39_2, % 52.91/7.91 | all_39_3 gives: % 52.91/7.91 | (18) ~ (all_39_0 = 0) & equally_directed_lines(all_39_1, all_39_3) = % 52.91/7.91 | all_39_0 & reverse_line(all_39_2) = all_39_1 & reverse_line(all_39_3) % 52.91/7.91 | = all_39_2 & $i(all_39_1) & $i(all_39_2) & $i(all_39_3) % 52.91/7.91 | % 52.91/7.91 | ALPHA: (18) implies: % 52.91/7.91 | (19) ~ (all_39_0 = 0) % 52.91/7.91 | (20) $i(all_39_3) % 52.91/7.91 | (21) $i(all_39_2) % 52.91/7.91 | (22) $i(all_39_1) % 52.91/7.91 | (23) reverse_line(all_39_3) = all_39_2 % 52.91/7.91 | (24) reverse_line(all_39_2) = all_39_1 % 52.91/7.91 | (25) equally_directed_lines(all_39_1, all_39_3) = all_39_0 % 52.91/7.91 | % 52.91/7.91 | GROUND_INST: instantiating (4) with all_39_1, all_39_3, all_39_0, simplifying % 52.91/7.91 | with (20), (22), (25) gives: % 52.91/7.91 | (26) all_39_0 = 0 | unequally_directed_lines(all_39_1, all_39_3) = 0 % 52.91/7.91 | % 52.91/7.91 | BETA: splitting (26) gives: % 52.91/7.91 | % 52.91/7.91 | Case 1: % 52.91/7.91 | | % 52.91/7.91 | | (27) unequally_directed_lines(all_39_1, all_39_3) = 0 % 52.91/7.91 | | % 52.91/7.91 | | GROUND_INST: instantiating (12) with all_39_1, all_39_3, simplifying with % 52.91/7.91 | | (20), (22), (27) gives: % 52.91/7.91 | | (28) ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ? [v3: int] : ? [v4: % 52.91/7.91 | | int] : (( ~ (v4 = 0) & ~ (v3 = 0) & intersection_point(all_39_1, % 52.91/7.91 | | all_39_3) = v2 & apart_point_and_line(v2, all_39_1) = v3 & % 52.91/7.91 | | apart_point_and_line(v2, all_39_3) = v4 & $i(v2)) | ( ~ (v1 = 0) % 52.91/7.91 | | & reverse_line(all_39_3) = v0 & % 52.91/7.91 | | unequally_directed_lines(all_39_1, v0) = v1 & $i(v0))) % 52.91/7.91 | | % 52.91/7.91 | | GROUND_INST: instantiating (10) with all_39_1, all_39_3, simplifying with % 52.91/7.91 | | (20), (22), (27) gives: % 52.91/7.91 | | (29) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 % 52.91/7.91 | | & left_convergent_lines(all_39_1, v0) = 0 & % 52.91/7.91 | | reverse_line(all_39_3) = v0 & $i(v0)) | (v2 = 0 & % 52.91/7.91 | | left_convergent_lines(all_39_1, all_39_3) = 0) | ( ~ (v1 = 0) & % 52.91/7.91 | | reverse_line(all_39_3) = v0 & unequally_directed_lines(all_39_1, % 52.91/7.91 | | v0) = v1 & $i(v0))) % 52.91/7.91 | | % 52.91/7.91 | | GROUND_INST: instantiating (6) with all_39_1, all_39_3, simplifying with % 52.91/7.91 | | (20), (22), (27) gives: % 52.91/7.91 | | (30) ? [v0: int] : ? [v1: int] : ((v1 = 0 & convergent_lines(all_39_1, % 52.91/7.91 | | all_39_3) = 0) | ( ~ (v0 = 0) & % 52.91/7.91 | | unequally_directed_opposite_lines(all_39_1, all_39_3) = v0)) % 52.91/7.91 | | % 52.91/7.91 | | GROUND_INST: instantiating (7) with all_39_1, all_39_3, 0, simplifying with % 52.91/7.91 | | (20), (22), (27) gives: % 52.91/7.91 | | (31) ? [v0: int] : ? [v1: int] : ((v1 = 0 & % 52.91/7.91 | | unequally_directed_opposite_lines(all_39_1, all_39_3) = 0) | ( ~ % 52.91/7.91 | | (v0 = 0) & convergent_lines(all_39_1, all_39_3) = v0)) % 52.91/7.91 | | % 52.91/7.91 | | DELTA: instantiating (31) with fresh symbols all_61_0, all_61_1 gives: % 52.91/7.91 | | (32) (all_61_0 = 0 & unequally_directed_opposite_lines(all_39_1, % 52.91/7.91 | | all_39_3) = 0) | ( ~ (all_61_1 = 0) & convergent_lines(all_39_1, % 52.91/7.91 | | all_39_3) = all_61_1) % 52.91/7.91 | | % 52.91/7.91 | | DELTA: instantiating (30) with fresh symbols all_62_0, all_62_1 gives: % 52.91/7.92 | | (33) (all_62_0 = 0 & convergent_lines(all_39_1, all_39_3) = 0) | ( ~ % 52.91/7.92 | | (all_62_1 = 0) & unequally_directed_opposite_lines(all_39_1, % 52.91/7.92 | | all_39_3) = all_62_1) % 52.91/7.92 | | % 52.91/7.92 | | DELTA: instantiating (28) with fresh symbols all_63_0, all_63_1, all_63_2, % 52.91/7.92 | | all_63_3, all_63_4 gives: % 52.91/7.92 | | (34) ( ~ (all_63_0 = 0) & ~ (all_63_1 = 0) & % 52.91/7.92 | | intersection_point(all_39_1, all_39_3) = all_63_2 & % 52.91/7.92 | | apart_point_and_line(all_63_2, all_39_1) = all_63_1 & % 52.91/7.92 | | apart_point_and_line(all_63_2, all_39_3) = all_63_0 & % 52.91/7.92 | | $i(all_63_2)) | ( ~ (all_63_3 = 0) & reverse_line(all_39_3) = % 52.91/7.92 | | all_63_4 & unequally_directed_lines(all_39_1, all_63_4) = all_63_3 % 52.91/7.92 | | & $i(all_63_4)) % 52.91/7.92 | | % 52.91/7.92 | | DELTA: instantiating (29) with fresh symbols all_64_0, all_64_1, all_64_2, % 52.91/7.92 | | all_64_3 gives: % 52.91/7.92 | | (35) (all_64_0 = 0 & left_convergent_lines(all_39_1, all_64_3) = 0 & % 52.91/7.92 | | reverse_line(all_39_3) = all_64_3 & $i(all_64_3)) | (all_64_1 = 0 % 52.91/7.92 | | & left_convergent_lines(all_39_1, all_39_3) = 0) | ( ~ (all_64_2 = % 52.91/7.92 | | 0) & reverse_line(all_39_3) = all_64_3 & % 52.91/7.92 | | unequally_directed_lines(all_39_1, all_64_3) = all_64_2 & % 52.91/7.92 | | $i(all_64_3)) % 52.91/7.92 | | % 52.91/7.92 | | BETA: splitting (34) gives: % 52.91/7.92 | | % 52.91/7.92 | | Case 1: % 52.91/7.92 | | | % 52.91/7.92 | | | (36) ~ (all_63_0 = 0) & ~ (all_63_1 = 0) & % 52.91/7.92 | | | intersection_point(all_39_1, all_39_3) = all_63_2 & % 52.91/7.92 | | | apart_point_and_line(all_63_2, all_39_1) = all_63_1 & % 52.91/7.92 | | | apart_point_and_line(all_63_2, all_39_3) = all_63_0 & $i(all_63_2) % 52.91/7.92 | | | % 52.91/7.92 | | | ALPHA: (36) implies: % 52.91/7.92 | | | (37) ~ (all_63_1 = 0) % 52.91/7.92 | | | (38) ~ (all_63_0 = 0) % 52.91/7.92 | | | (39) $i(all_63_2) % 52.91/7.92 | | | (40) apart_point_and_line(all_63_2, all_39_3) = all_63_0 % 52.91/7.92 | | | (41) apart_point_and_line(all_63_2, all_39_1) = all_63_1 % 52.91/7.92 | | | % 52.91/7.92 | | | GROUND_INST: instantiating (5) with all_63_2, all_39_3, all_63_0, % 52.91/7.92 | | | simplifying with (20), (39), (40) gives: % 52.91/7.92 | | | (42) all_63_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 % 52.91/7.92 | | | = 0) & left_apart_point(all_63_2, all_39_3) = v0 & % 52.91/7.92 | | | right_apart_point(all_63_2, all_39_3) = v1) % 52.91/7.92 | | | % 52.91/7.92 | | | GROUND_INST: instantiating (5) with all_63_2, all_39_1, all_63_1, % 52.91/7.92 | | | simplifying with (22), (39), (41) gives: % 52.91/7.92 | | | (43) all_63_1 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 % 52.91/7.92 | | | = 0) & left_apart_point(all_63_2, all_39_1) = v0 & % 52.91/7.92 | | | right_apart_point(all_63_2, all_39_1) = v1) % 52.91/7.92 | | | % 52.91/7.92 | | | BETA: splitting (32) gives: % 52.91/7.92 | | | % 52.91/7.92 | | | Case 1: % 52.91/7.92 | | | | % 52.91/7.92 | | | | (44) all_61_0 = 0 & unequally_directed_opposite_lines(all_39_1, % 52.91/7.92 | | | | all_39_3) = 0 % 52.91/7.92 | | | | % 52.91/7.92 | | | | ALPHA: (44) implies: % 52.91/7.92 | | | | (45) unequally_directed_opposite_lines(all_39_1, all_39_3) = 0 % 52.91/7.92 | | | | % 52.91/7.92 | | | | BETA: splitting (43) gives: % 52.91/7.92 | | | | % 52.91/7.92 | | | | Case 1: % 52.91/7.92 | | | | | % 52.91/7.92 | | | | | (46) all_63_1 = 0 % 52.91/7.92 | | | | | % 52.91/7.92 | | | | | REDUCE: (37), (46) imply: % 52.91/7.92 | | | | | (47) $false % 52.91/7.92 | | | | | % 52.91/7.92 | | | | | CLOSE: (47) is inconsistent. % 52.91/7.92 | | | | | % 52.91/7.92 | | | | Case 2: % 52.91/7.92 | | | | | % 52.91/7.92 | | | | | (48) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 52.91/7.92 | | | | | left_apart_point(all_63_2, all_39_1) = v0 & % 52.91/7.92 | | | | | right_apart_point(all_63_2, all_39_1) = v1) % 52.91/7.92 | | | | | % 52.91/7.92 | | | | | DELTA: instantiating (48) with fresh symbols all_122_0, all_122_1 % 52.91/7.92 | | | | | gives: % 52.91/7.92 | | | | | (49) ~ (all_122_0 = 0) & ~ (all_122_1 = 0) & % 52.91/7.92 | | | | | left_apart_point(all_63_2, all_39_1) = all_122_1 & % 52.91/7.92 | | | | | right_apart_point(all_63_2, all_39_1) = all_122_0 % 52.91/7.92 | | | | | % 52.91/7.92 | | | | | ALPHA: (49) implies: % 52.91/7.92 | | | | | (50) ~ (all_122_1 = 0) % 52.91/7.92 | | | | | (51) left_apart_point(all_63_2, all_39_1) = all_122_1 % 52.91/7.92 | | | | | % 52.91/7.92 | | | | | BETA: splitting (42) gives: % 52.91/7.92 | | | | | % 52.91/7.92 | | | | | Case 1: % 52.91/7.92 | | | | | | % 52.91/7.92 | | | | | | (52) all_63_0 = 0 % 52.91/7.92 | | | | | | % 52.91/7.92 | | | | | | REDUCE: (38), (52) imply: % 52.91/7.92 | | | | | | (53) $false % 52.91/7.92 | | | | | | % 52.91/7.92 | | | | | | CLOSE: (53) is inconsistent. % 52.91/7.92 | | | | | | % 52.91/7.92 | | | | | Case 2: % 52.91/7.92 | | | | | | % 52.91/7.92 | | | | | | (54) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 52.91/7.92 | | | | | | left_apart_point(all_63_2, all_39_3) = v0 & % 52.91/7.92 | | | | | | right_apart_point(all_63_2, all_39_3) = v1) % 52.91/7.92 | | | | | | % 52.91/7.92 | | | | | | DELTA: instantiating (54) with fresh symbols all_127_0, all_127_1 % 52.91/7.92 | | | | | | gives: % 52.91/7.92 | | | | | | (55) ~ (all_127_0 = 0) & ~ (all_127_1 = 0) & % 52.91/7.92 | | | | | | left_apart_point(all_63_2, all_39_3) = all_127_1 & % 52.91/7.92 | | | | | | right_apart_point(all_63_2, all_39_3) = all_127_0 % 52.91/7.92 | | | | | | % 52.91/7.92 | | | | | | ALPHA: (55) implies: % 52.91/7.92 | | | | | | (56) ~ (all_127_1 = 0) % 52.91/7.92 | | | | | | (57) ~ (all_127_0 = 0) % 52.91/7.92 | | | | | | (58) right_apart_point(all_63_2, all_39_3) = all_127_0 % 52.91/7.92 | | | | | | (59) left_apart_point(all_63_2, all_39_3) = all_127_1 % 52.91/7.92 | | | | | | % 52.91/7.92 | | | | | | GROUND_INST: instantiating (1) with all_39_1, all_39_3, simplifying % 52.91/7.92 | | | | | | with (20), (22), (45) gives: % 52.91/7.92 | | | | | | (60) ? [v0: $i] : (reverse_line(all_39_3) = v0 & % 52.91/7.92 | | | | | | unequally_directed_lines(all_39_1, v0) = 0 & $i(v0)) % 52.91/7.92 | | | | | | % 52.91/7.92 | | | | | | GROUND_INST: instantiating (3) with all_63_2, all_39_3, all_127_0, % 52.91/7.92 | | | | | | simplifying with (20), (39), (58) gives: % 52.91/7.92 | | | | | | (61) all_127_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 52.91/7.92 | | | | | | left_apart_point(all_63_2, v0) = v1 & % 52.91/7.92 | | | | | | reverse_line(all_39_3) = v0 & $i(v0)) % 52.91/7.92 | | | | | | % 52.91/7.93 | | | | | | GROUND_INST: instantiating (14) with all_63_2, all_63_2, all_39_3, % 52.91/7.93 | | | | | | all_39_2, all_127_1, all_39_1, all_122_1, simplifying % 52.91/7.93 | | | | | | with (20), (21), (24), (39), (51), (59) gives: % 52.91/7.93 | | | | | | (62) all_127_1 = 0 | all_122_1 = 0 | ? [v0: int] : ? [v1: int] % 52.91/7.93 | | | | | | : ? [v2: int] : ? [v3: int] : ? [v4: int] : ? [v5: $i] : % 52.91/7.93 | | | | | | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 52.91/7.93 | | | | | | left_apart_point(all_63_2, all_39_1) = 0) | (v7 = 0 & % 52.91/7.93 | | | | | | left_apart_point(all_63_2, v5) = 0 & % 52.91/7.93 | | | | | | reverse_line(all_39_3) = v5 & $i(v5)) | (v6 = 0 & % 52.91/7.93 | | | | | | left_apart_point(all_63_2, v5) = 0 & % 52.91/7.93 | | | | | | reverse_line(all_39_3) = v5 & $i(v5)) | (v4 = 0 & % 52.91/7.93 | | | | | | left_apart_point(all_63_2, all_39_2) = 0) | (v3 = 0 & % 52.91/7.93 | | | | | | left_apart_point(all_63_2, all_39_2) = 0) | (v2 = 0 & % 52.91/7.93 | | | | | | left_apart_point(all_63_2, all_39_3) = 0) | ( ~ (v1 = 0) % 52.91/7.93 | | | | | | & distinct_lines(all_39_3, all_39_2) = v1) | ( ~ (v0 = % 52.91/7.93 | | | | | | 0) & distinct_points(all_63_2, all_63_2) = v0)) % 52.91/7.93 | | | | | | % 52.91/7.93 | | | | | | DELTA: instantiating (60) with fresh symbol all_136_0 gives: % 52.91/7.93 | | | | | | (63) reverse_line(all_39_3) = all_136_0 & % 52.91/7.93 | | | | | | unequally_directed_lines(all_39_1, all_136_0) = 0 & % 52.91/7.93 | | | | | | $i(all_136_0) % 52.91/7.93 | | | | | | % 52.91/7.93 | | | | | | ALPHA: (63) implies: % 52.91/7.93 | | | | | | (64) unequally_directed_lines(all_39_1, all_136_0) = 0 % 52.91/7.93 | | | | | | (65) reverse_line(all_39_3) = all_136_0 % 52.91/7.93 | | | | | | % 52.91/7.93 | | | | | | BETA: splitting (61) gives: % 52.91/7.93 | | | | | | % 52.91/7.93 | | | | | | Case 1: % 52.91/7.93 | | | | | | | % 52.91/7.93 | | | | | | | (66) all_127_0 = 0 % 52.91/7.93 | | | | | | | % 52.91/7.93 | | | | | | | REDUCE: (57), (66) imply: % 52.91/7.93 | | | | | | | (67) $false % 52.91/7.93 | | | | | | | % 52.91/7.93 | | | | | | | CLOSE: (67) is inconsistent. % 52.91/7.93 | | | | | | | % 52.91/7.93 | | | | | | Case 2: % 52.91/7.93 | | | | | | | % 52.91/7.93 | | | | | | | (68) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 52.91/7.93 | | | | | | | left_apart_point(all_63_2, v0) = v1 & % 52.91/7.93 | | | | | | | reverse_line(all_39_3) = v0 & $i(v0)) % 52.91/7.93 | | | | | | | % 52.91/7.93 | | | | | | | DELTA: instantiating (68) with fresh symbols all_142_0, all_142_1 % 52.91/7.93 | | | | | | | gives: % 52.91/7.93 | | | | | | | (69) ~ (all_142_0 = 0) & left_apart_point(all_63_2, all_142_1) % 52.91/7.93 | | | | | | | = all_142_0 & reverse_line(all_39_3) = all_142_1 & % 52.91/7.93 | | | | | | | $i(all_142_1) % 52.91/7.93 | | | | | | | % 52.91/7.93 | | | | | | | ALPHA: (69) implies: % 52.91/7.93 | | | | | | | (70) reverse_line(all_39_3) = all_142_1 % 52.91/7.93 | | | | | | | % 52.91/7.93 | | | | | | | BETA: splitting (62) gives: % 52.91/7.93 | | | | | | | % 52.91/7.93 | | | | | | | Case 1: % 52.91/7.93 | | | | | | | | % 52.91/7.93 | | | | | | | | (71) all_127_1 = 0 % 52.91/7.93 | | | | | | | | % 52.91/7.93 | | | | | | | | REDUCE: (56), (71) imply: % 52.91/7.93 | | | | | | | | (72) $false % 52.91/7.93 | | | | | | | | % 52.91/7.93 | | | | | | | | CLOSE: (72) is inconsistent. % 52.91/7.93 | | | | | | | | % 52.91/7.93 | | | | | | | Case 2: % 52.91/7.93 | | | | | | | | % 52.91/7.93 | | | | | | | | (73) all_122_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 52.91/7.93 | | | | | | | | int] : ? [v3: int] : ? [v4: int] : ? [v5: $i] : ? % 52.91/7.93 | | | | | | | | [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 52.91/7.93 | | | | | | | | left_apart_point(all_63_2, all_39_1) = 0) | (v7 = 0 % 52.91/7.93 | | | | | | | | & left_apart_point(all_63_2, v5) = 0 & % 52.91/7.93 | | | | | | | | reverse_line(all_39_3) = v5 & $i(v5)) | (v6 = 0 & % 52.91/7.93 | | | | | | | | left_apart_point(all_63_2, v5) = 0 & % 52.91/7.93 | | | | | | | | reverse_line(all_39_3) = v5 & $i(v5)) | (v4 = 0 & % 52.91/7.93 | | | | | | | | left_apart_point(all_63_2, all_39_2) = 0) | (v3 = 0 % 52.91/7.93 | | | | | | | | & left_apart_point(all_63_2, all_39_2) = 0) | (v2 = % 52.91/7.93 | | | | | | | | 0 & left_apart_point(all_63_2, all_39_3) = 0) | ( ~ % 52.91/7.93 | | | | | | | | (v1 = 0) & distinct_lines(all_39_3, all_39_2) = v1) % 52.91/7.93 | | | | | | | | | ( ~ (v0 = 0) & distinct_points(all_63_2, all_63_2) = % 52.91/7.93 | | | | | | | | v0)) % 52.91/7.93 | | | | | | | | % 52.91/7.93 | | | | | | | | BETA: splitting (73) gives: % 52.91/7.93 | | | | | | | | % 52.91/7.93 | | | | | | | | Case 1: % 52.91/7.93 | | | | | | | | | % 52.91/7.93 | | | | | | | | | (74) all_122_1 = 0 % 52.91/7.93 | | | | | | | | | % 52.91/7.93 | | | | | | | | | REDUCE: (50), (74) imply: % 52.91/7.93 | | | | | | | | | (75) $false % 52.91/7.93 | | | | | | | | | % 52.91/7.93 | | | | | | | | | CLOSE: (75) is inconsistent. % 52.91/7.93 | | | | | | | | | % 52.91/7.93 | | | | | | | | Case 2: % 52.91/7.93 | | | | | | | | | % 52.91/7.93 | | | | | | | | | % 52.91/7.93 | | | | | | | | | GROUND_INST: instantiating (15) with all_39_2, all_142_1, % 52.91/7.93 | | | | | | | | | all_39_3, simplifying with (23), (70) gives: % 52.91/7.93 | | | | | | | | | (76) all_142_1 = all_39_2 % 52.91/7.93 | | | | | | | | | % 52.91/7.93 | | | | | | | | | GROUND_INST: instantiating (15) with all_136_0, all_142_1, % 52.91/7.93 | | | | | | | | | all_39_3, simplifying with (65), (70) gives: % 52.91/7.93 | | | | | | | | | (77) all_142_1 = all_136_0 % 52.91/7.93 | | | | | | | | | % 52.91/7.93 | | | | | | | | | COMBINE_EQS: (76), (77) imply: % 52.91/7.93 | | | | | | | | | (78) all_136_0 = all_39_2 % 52.91/7.93 | | | | | | | | | % 52.91/7.93 | | | | | | | | | REDUCE: (64), (78) imply: % 52.91/7.93 | | | | | | | | | (79) unequally_directed_lines(all_39_1, all_39_2) = 0 % 52.91/7.93 | | | | | | | | | % 52.91/7.93 | | | | | | | | | BETA: splitting (35) gives: % 52.91/7.93 | | | | | | | | | % 52.91/7.93 | | | | | | | | | Case 1: % 52.91/7.93 | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | (80) all_64_0 = 0 & left_convergent_lines(all_39_1, % 52.91/7.93 | | | | | | | | | | all_64_3) = 0 & reverse_line(all_39_3) = all_64_3 % 52.91/7.93 | | | | | | | | | | & $i(all_64_3) % 52.91/7.93 | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | ALPHA: (80) implies: % 52.91/7.93 | | | | | | | | | | (81) $i(all_64_3) % 52.91/7.93 | | | | | | | | | | (82) reverse_line(all_39_3) = all_64_3 % 52.91/7.93 | | | | | | | | | | (83) left_convergent_lines(all_39_1, all_64_3) = 0 % 52.91/7.93 | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | GROUND_INST: instantiating (15) with all_39_2, all_64_3, % 52.91/7.93 | | | | | | | | | | all_39_3, simplifying with (23), (82) gives: % 52.91/7.93 | | | | | | | | | | (84) all_64_3 = all_39_2 % 52.91/7.93 | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | REDUCE: (83), (84) imply: % 52.91/7.93 | | | | | | | | | | (85) left_convergent_lines(all_39_1, all_39_2) = 0 % 52.91/7.93 | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | GROUND_INST: instantiating (11) with all_39_1, all_39_2, % 52.91/7.93 | | | | | | | | | | simplifying with (21), (22), (85) gives: % 52.91/7.93 | | | | | | | | | | (86) $false % 52.91/7.93 | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | CLOSE: (86) is inconsistent. % 52.91/7.93 | | | | | | | | | | % 52.91/7.93 | | | | | | | | | Case 2: % 52.91/7.93 | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | (87) (all_64_1 = 0 & left_convergent_lines(all_39_1, % 52.91/7.93 | | | | | | | | | | all_39_3) = 0) | ( ~ (all_64_2 = 0) & % 52.91/7.93 | | | | | | | | | | reverse_line(all_39_3) = all_64_3 & % 52.91/7.93 | | | | | | | | | | unequally_directed_lines(all_39_1, all_64_3) = % 52.91/7.93 | | | | | | | | | | all_64_2 & $i(all_64_3)) % 52.91/7.93 | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | BETA: splitting (87) gives: % 52.91/7.93 | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | Case 1: % 52.91/7.93 | | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | | (88) all_64_1 = 0 & left_convergent_lines(all_39_1, % 52.91/7.93 | | | | | | | | | | | all_39_3) = 0 % 52.91/7.93 | | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | | ALPHA: (88) implies: % 52.91/7.93 | | | | | | | | | | | (89) left_convergent_lines(all_39_1, all_39_3) = 0 % 52.91/7.93 | | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | | GROUND_INST: instantiating (11) with all_39_1, all_39_3, % 52.91/7.93 | | | | | | | | | | | simplifying with (20), (22), (89) gives: % 52.91/7.93 | | | | | | | | | | | (90) $false % 52.91/7.93 | | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | | CLOSE: (90) is inconsistent. % 52.91/7.93 | | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | Case 2: % 52.91/7.93 | | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | | (91) ~ (all_64_2 = 0) & reverse_line(all_39_3) = % 52.91/7.93 | | | | | | | | | | | all_64_3 & unequally_directed_lines(all_39_1, % 52.91/7.93 | | | | | | | | | | | all_64_3) = all_64_2 & $i(all_64_3) % 52.91/7.93 | | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | | ALPHA: (91) implies: % 52.91/7.93 | | | | | | | | | | | (92) ~ (all_64_2 = 0) % 52.91/7.93 | | | | | | | | | | | (93) unequally_directed_lines(all_39_1, all_64_3) = % 52.91/7.93 | | | | | | | | | | | all_64_2 % 52.91/7.93 | | | | | | | | | | | (94) reverse_line(all_39_3) = all_64_3 % 52.91/7.93 | | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | | GROUND_INST: instantiating (15) with all_39_2, all_64_3, % 52.91/7.93 | | | | | | | | | | | all_39_3, simplifying with (23), (94) gives: % 52.91/7.93 | | | | | | | | | | | (95) all_64_3 = all_39_2 % 52.91/7.93 | | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | | REDUCE: (93), (95) imply: % 52.91/7.93 | | | | | | | | | | | (96) unequally_directed_lines(all_39_1, all_39_2) = % 52.91/7.93 | | | | | | | | | | | all_64_2 % 52.91/7.93 | | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | | GROUND_INST: instantiating (16) with all_64_2, 0, all_39_2, % 52.91/7.93 | | | | | | | | | | | all_39_1, simplifying with (79), (96) gives: % 52.91/7.93 | | | | | | | | | | | (97) all_64_2 = 0 % 52.91/7.93 | | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | | REDUCE: (92), (97) imply: % 52.91/7.93 | | | | | | | | | | | (98) $false % 52.91/7.93 | | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | | CLOSE: (98) is inconsistent. % 52.91/7.93 | | | | | | | | | | | % 52.91/7.93 | | | | | | | | | | End of split % 52.91/7.93 | | | | | | | | | | % 52.91/7.93 | | | | | | | | | End of split % 52.91/7.93 | | | | | | | | | % 52.91/7.93 | | | | | | | | End of split % 52.91/7.94 | | | | | | | | % 52.91/7.94 | | | | | | | End of split % 52.91/7.94 | | | | | | | % 52.91/7.94 | | | | | | End of split % 52.91/7.94 | | | | | | % 52.91/7.94 | | | | | End of split % 52.91/7.94 | | | | | % 52.91/7.94 | | | | End of split % 52.91/7.94 | | | | % 52.91/7.94 | | | Case 2: % 52.91/7.94 | | | | % 52.91/7.94 | | | | (99) ~ (all_61_1 = 0) & convergent_lines(all_39_1, all_39_3) = % 52.91/7.94 | | | | all_61_1 % 52.91/7.94 | | | | % 52.91/7.94 | | | | ALPHA: (99) implies: % 52.91/7.94 | | | | (100) ~ (all_61_1 = 0) % 52.91/7.94 | | | | (101) convergent_lines(all_39_1, all_39_3) = all_61_1 % 52.91/7.94 | | | | % 52.91/7.94 | | | | BETA: splitting (33) gives: % 52.91/7.94 | | | | % 52.91/7.94 | | | | Case 1: % 52.91/7.94 | | | | | % 52.91/7.94 | | | | | (102) all_62_0 = 0 & convergent_lines(all_39_1, all_39_3) = 0 % 52.91/7.94 | | | | | % 52.91/7.94 | | | | | ALPHA: (102) implies: % 52.91/7.94 | | | | | (103) convergent_lines(all_39_1, all_39_3) = 0 % 52.91/7.94 | | | | | % 52.91/7.94 | | | | | GROUND_INST: instantiating (17) with 0, all_61_1, all_39_3, all_39_1, % 52.91/7.94 | | | | | simplifying with (101), (103) gives: % 52.91/7.94 | | | | | (104) all_61_1 = 0 % 52.91/7.94 | | | | | % 52.91/7.94 | | | | | REDUCE: (100), (104) imply: % 52.91/7.94 | | | | | (105) $false % 52.91/7.94 | | | | | % 52.91/7.94 | | | | | CLOSE: (105) is inconsistent. % 52.91/7.94 | | | | | % 52.91/7.94 | | | | Case 2: % 52.91/7.94 | | | | | % 52.91/7.94 | | | | | (106) ~ (all_62_1 = 0) & % 52.91/7.94 | | | | | unequally_directed_opposite_lines(all_39_1, all_39_3) = % 52.91/7.94 | | | | | all_62_1 % 52.91/7.94 | | | | | % 52.91/7.94 | | | | | ALPHA: (106) implies: % 52.91/7.94 | | | | | (107) ~ (all_62_1 = 0) % 52.91/7.94 | | | | | (108) unequally_directed_opposite_lines(all_39_1, all_39_3) = % 52.91/7.94 | | | | | all_62_1 % 52.91/7.94 | | | | | % 52.91/7.94 | | | | | BETA: splitting (43) gives: % 52.91/7.94 | | | | | % 52.91/7.94 | | | | | Case 1: % 52.91/7.94 | | | | | | % 52.91/7.94 | | | | | | (109) all_63_1 = 0 % 52.91/7.94 | | | | | | % 52.91/7.94 | | | | | | REDUCE: (37), (109) imply: % 52.91/7.94 | | | | | | (110) $false % 52.91/7.94 | | | | | | % 52.91/7.94 | | | | | | CLOSE: (110) is inconsistent. % 52.91/7.94 | | | | | | % 52.91/7.94 | | | | | Case 2: % 52.91/7.94 | | | | | | % 52.91/7.94 | | | | | | (111) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 52.91/7.94 | | | | | | left_apart_point(all_63_2, all_39_1) = v0 & % 52.91/7.94 | | | | | | right_apart_point(all_63_2, all_39_1) = v1) % 52.91/7.94 | | | | | | % 52.91/7.94 | | | | | | DELTA: instantiating (111) with fresh symbols all_122_0, all_122_1 % 52.91/7.94 | | | | | | gives: % 52.91/7.94 | | | | | | (112) ~ (all_122_0 = 0) & ~ (all_122_1 = 0) & % 52.91/7.94 | | | | | | left_apart_point(all_63_2, all_39_1) = all_122_1 & % 52.91/7.94 | | | | | | right_apart_point(all_63_2, all_39_1) = all_122_0 % 52.91/7.94 | | | | | | % 52.91/7.94 | | | | | | ALPHA: (112) implies: % 52.91/7.94 | | | | | | (113) ~ (all_122_1 = 0) % 52.91/7.94 | | | | | | (114) left_apart_point(all_63_2, all_39_1) = all_122_1 % 52.91/7.94 | | | | | | % 52.91/7.94 | | | | | | BETA: splitting (42) gives: % 52.91/7.94 | | | | | | % 52.91/7.94 | | | | | | Case 1: % 52.91/7.94 | | | | | | | % 52.91/7.94 | | | | | | | (115) all_63_0 = 0 % 52.91/7.94 | | | | | | | % 52.91/7.94 | | | | | | | REDUCE: (38), (115) imply: % 52.91/7.94 | | | | | | | (116) $false % 52.91/7.94 | | | | | | | % 52.91/7.94 | | | | | | | CLOSE: (116) is inconsistent. % 52.91/7.94 | | | | | | | % 52.91/7.94 | | | | | | Case 2: % 52.91/7.94 | | | | | | | % 52.91/7.94 | | | | | | | (117) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) % 52.91/7.94 | | | | | | | & left_apart_point(all_63_2, all_39_3) = v0 & % 52.91/7.94 | | | | | | | right_apart_point(all_63_2, all_39_3) = v1) % 52.91/7.94 | | | | | | | % 52.91/7.94 | | | | | | | DELTA: instantiating (117) with fresh symbols all_127_0, all_127_1 % 52.91/7.94 | | | | | | | gives: % 52.91/7.94 | | | | | | | (118) ~ (all_127_0 = 0) & ~ (all_127_1 = 0) & % 52.91/7.94 | | | | | | | left_apart_point(all_63_2, all_39_3) = all_127_1 & % 52.91/7.94 | | | | | | | right_apart_point(all_63_2, all_39_3) = all_127_0 % 52.91/7.94 | | | | | | | % 52.91/7.94 | | | | | | | ALPHA: (118) implies: % 52.91/7.94 | | | | | | | (119) ~ (all_127_1 = 0) % 52.91/7.94 | | | | | | | (120) ~ (all_127_0 = 0) % 52.91/7.94 | | | | | | | (121) right_apart_point(all_63_2, all_39_3) = all_127_0 % 52.91/7.94 | | | | | | | (122) left_apart_point(all_63_2, all_39_3) = all_127_1 % 52.91/7.94 | | | | | | | % 52.91/7.94 | | | | | | | GROUND_INST: instantiating (2) with all_39_1, all_39_3, all_62_1, % 52.91/7.94 | | | | | | | simplifying with (20), (22), (108) gives: % 52.91/7.94 | | | | | | | (123) all_62_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) % 52.91/7.94 | | | | | | | & reverse_line(all_39_3) = v0 & % 52.91/7.94 | | | | | | | unequally_directed_lines(all_39_1, v0) = v1 & $i(v0)) % 52.91/7.94 | | | | | | | % 52.91/7.94 | | | | | | | GROUND_INST: instantiating (3) with all_63_2, all_39_3, all_127_0, % 52.91/7.94 | | | | | | | simplifying with (20), (39), (121) gives: % 52.91/7.94 | | | | | | | (124) all_127_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) % 52.91/7.94 | | | | | | | & left_apart_point(all_63_2, v0) = v1 & % 52.91/7.94 | | | | | | | reverse_line(all_39_3) = v0 & $i(v0)) % 52.91/7.94 | | | | | | | % 52.91/7.94 | | | | | | | GROUND_INST: instantiating (13) with all_63_2, all_63_2, all_39_1, % 52.91/7.94 | | | | | | | all_39_3, all_122_1, all_127_1, simplifying with % 52.91/7.94 | | | | | | | (20), (22), (39), (114), (122) gives: % 52.91/7.94 | | | | | | | (125) all_127_1 = 0 | all_122_1 = 0 | ? [v0: int] : ? [v1: % 52.91/7.94 | | | | | | | int] : ? [v2: int] : ? [v3: int] : ? [v4: $i] : ? % 52.91/7.94 | | | | | | | [v5: int] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : % 52.91/7.94 | | | | | | | ? [v9: int] : ((v9 = 0 & left_apart_point(all_63_2, v7) = % 52.91/7.94 | | | | | | | 0 & reverse_line(all_39_3) = v7 & $i(v7)) | (v8 = 0 & % 52.91/7.94 | | | | | | | left_apart_point(all_63_2, v7) = 0 & % 52.91/7.94 | | | | | | | reverse_line(all_39_3) = v7 & $i(v7)) | (v6 = 0 & % 52.91/7.94 | | | | | | | left_apart_point(all_63_2, v4) = 0 & % 52.91/7.94 | | | | | | | reverse_line(all_39_1) = v4 & $i(v4)) | (v5 = 0 & % 52.91/7.94 | | | | | | | left_apart_point(all_63_2, v4) = 0 & % 52.91/7.94 | | | | | | | reverse_line(all_39_1) = v4 & $i(v4)) | (v3 = 0 & % 52.91/7.94 | | | | | | | left_apart_point(all_63_2, all_39_3) = 0) | (v2 = 0 & % 52.91/7.94 | | | | | | | left_apart_point(all_63_2, all_39_1) = 0) | ( ~ (v1 = % 52.91/7.94 | | | | | | | 0) & distinct_lines(all_39_1, all_39_3) = v1) | ( ~ % 52.91/7.94 | | | | | | | (v0 = 0) & distinct_points(all_63_2, all_63_2) = v0)) % 52.91/7.94 | | | | | | | % 52.91/7.94 | | | | | | | BETA: splitting (35) gives: % 52.91/7.94 | | | | | | | % 52.91/7.94 | | | | | | | Case 1: % 52.91/7.94 | | | | | | | | % 52.91/7.94 | | | | | | | | (126) all_64_0 = 0 & left_convergent_lines(all_39_1, % 52.91/7.94 | | | | | | | | all_64_3) = 0 & reverse_line(all_39_3) = all_64_3 & % 52.91/7.94 | | | | | | | | $i(all_64_3) % 52.91/7.94 | | | | | | | | % 52.91/7.94 | | | | | | | | ALPHA: (126) implies: % 52.91/7.94 | | | | | | | | (127) $i(all_64_3) % 52.91/7.94 | | | | | | | | (128) reverse_line(all_39_3) = all_64_3 % 52.91/7.94 | | | | | | | | (129) left_convergent_lines(all_39_1, all_64_3) = 0 % 52.91/7.94 | | | | | | | | % 52.91/7.94 | | | | | | | | BETA: splitting (123) gives: % 52.91/7.94 | | | | | | | | % 52.91/7.94 | | | | | | | | Case 1: % 52.91/7.94 | | | | | | | | | % 52.91/7.94 | | | | | | | | | (130) all_62_1 = 0 % 52.91/7.94 | | | | | | | | | % 52.91/7.94 | | | | | | | | | REDUCE: (107), (130) imply: % 52.91/7.94 | | | | | | | | | (131) $false % 52.91/7.94 | | | | | | | | | % 52.91/7.94 | | | | | | | | | CLOSE: (131) is inconsistent. % 52.91/7.94 | | | | | | | | | % 52.91/7.94 | | | | | | | | Case 2: % 52.91/7.94 | | | | | | | | | % 52.91/7.94 | | | | | | | | | (132) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 52.91/7.94 | | | | | | | | | reverse_line(all_39_3) = v0 & % 52.91/7.94 | | | | | | | | | unequally_directed_lines(all_39_1, v0) = v1 & % 52.91/7.94 | | | | | | | | | $i(v0)) % 52.91/7.94 | | | | | | | | | % 52.91/7.94 | | | | | | | | | DELTA: instantiating (132) with fresh symbols all_143_0, % 52.91/7.94 | | | | | | | | | all_143_1 gives: % 52.91/7.94 | | | | | | | | | (133) ~ (all_143_0 = 0) & reverse_line(all_39_3) = % 52.91/7.94 | | | | | | | | | all_143_1 & unequally_directed_lines(all_39_1, % 52.91/7.94 | | | | | | | | | all_143_1) = all_143_0 & $i(all_143_1) % 52.91/7.94 | | | | | | | | | % 52.91/7.94 | | | | | | | | | ALPHA: (133) implies: % 52.91/7.94 | | | | | | | | | (134) reverse_line(all_39_3) = all_143_1 % 52.91/7.94 | | | | | | | | | % 52.91/7.94 | | | | | | | | | BETA: splitting (125) gives: % 52.91/7.94 | | | | | | | | | % 52.91/7.94 | | | | | | | | | Case 1: % 52.91/7.94 | | | | | | | | | | % 52.91/7.94 | | | | | | | | | | (135) all_127_1 = 0 % 52.91/7.94 | | | | | | | | | | % 52.91/7.94 | | | | | | | | | | REDUCE: (119), (135) imply: % 52.91/7.94 | | | | | | | | | | (136) $false % 52.91/7.94 | | | | | | | | | | % 52.91/7.94 | | | | | | | | | | CLOSE: (136) is inconsistent. % 52.91/7.94 | | | | | | | | | | % 52.91/7.94 | | | | | | | | | Case 2: % 52.91/7.94 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | (137) all_122_1 = 0 | ? [v0: int] : ? [v1: int] : ? % 52.91/7.95 | | | | | | | | | | [v2: int] : ? [v3: int] : ? [v4: $i] : ? [v5: % 52.91/7.95 | | | | | | | | | | int] : ? [v6: int] : ? [v7: $i] : ? [v8: int] % 52.91/7.95 | | | | | | | | | | : ? [v9: int] : ((v9 = 0 & % 52.91/7.95 | | | | | | | | | | left_apart_point(all_63_2, v7) = 0 & % 52.91/7.95 | | | | | | | | | | reverse_line(all_39_3) = v7 & $i(v7)) | (v8 = 0 % 52.91/7.95 | | | | | | | | | | & left_apart_point(all_63_2, v7) = 0 & % 52.91/7.95 | | | | | | | | | | reverse_line(all_39_3) = v7 & $i(v7)) | (v6 = 0 % 52.91/7.95 | | | | | | | | | | & left_apart_point(all_63_2, v4) = 0 & % 52.91/7.95 | | | | | | | | | | reverse_line(all_39_1) = v4 & $i(v4)) | (v5 = 0 % 52.91/7.95 | | | | | | | | | | & left_apart_point(all_63_2, v4) = 0 & % 52.91/7.95 | | | | | | | | | | reverse_line(all_39_1) = v4 & $i(v4)) | (v3 = 0 % 52.91/7.95 | | | | | | | | | | & left_apart_point(all_63_2, all_39_3) = 0) | % 52.91/7.95 | | | | | | | | | | (v2 = 0 & left_apart_point(all_63_2, all_39_1) = % 52.91/7.95 | | | | | | | | | | 0) | ( ~ (v1 = 0) & distinct_lines(all_39_1, % 52.91/7.95 | | | | | | | | | | all_39_3) = v1) | ( ~ (v0 = 0) & % 52.91/7.95 | | | | | | | | | | distinct_points(all_63_2, all_63_2) = v0)) % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | BETA: splitting (124) gives: % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | Case 1: % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | (138) all_127_0 = 0 % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | REDUCE: (120), (138) imply: % 52.91/7.95 | | | | | | | | | | | (139) $false % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | CLOSE: (139) is inconsistent. % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | Case 2: % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | (140) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 52.91/7.95 | | | | | | | | | | | left_apart_point(all_63_2, v0) = v1 & % 52.91/7.95 | | | | | | | | | | | reverse_line(all_39_3) = v0 & $i(v0)) % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | DELTA: instantiating (140) with fresh symbols all_189_0, % 52.91/7.95 | | | | | | | | | | | all_189_1 gives: % 52.91/7.95 | | | | | | | | | | | (141) ~ (all_189_0 = 0) & left_apart_point(all_63_2, % 52.91/7.95 | | | | | | | | | | | all_189_1) = all_189_0 & reverse_line(all_39_3) % 52.91/7.95 | | | | | | | | | | | = all_189_1 & $i(all_189_1) % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | ALPHA: (141) implies: % 52.91/7.95 | | | | | | | | | | | (142) reverse_line(all_39_3) = all_189_1 % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | BETA: splitting (137) gives: % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | Case 1: % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | (143) all_122_1 = 0 % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | REDUCE: (113), (143) imply: % 52.91/7.95 | | | | | | | | | | | | (144) $false % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | CLOSE: (144) is inconsistent. % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | Case 2: % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_39_2, all_143_1, % 52.91/7.95 | | | | | | | | | | | | all_39_3, simplifying with (23), (134) gives: % 52.91/7.95 | | | | | | | | | | | | (145) all_143_1 = all_39_2 % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_143_1, all_189_1, % 52.91/7.95 | | | | | | | | | | | | all_39_3, simplifying with (134), (142) gives: % 52.91/7.95 | | | | | | | | | | | | (146) all_189_1 = all_143_1 % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_64_3, all_189_1, % 52.91/7.95 | | | | | | | | | | | | all_39_3, simplifying with (128), (142) gives: % 52.91/7.95 | | | | | | | | | | | | (147) all_189_1 = all_64_3 % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | COMBINE_EQS: (146), (147) imply: % 52.91/7.95 | | | | | | | | | | | | (148) all_143_1 = all_64_3 % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | SIMP: (148) implies: % 52.91/7.95 | | | | | | | | | | | | (149) all_143_1 = all_64_3 % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | COMBINE_EQS: (145), (149) imply: % 52.91/7.95 | | | | | | | | | | | | (150) all_64_3 = all_39_2 % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | SIMP: (150) implies: % 52.91/7.95 | | | | | | | | | | | | (151) all_64_3 = all_39_2 % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | REDUCE: (129), (151) imply: % 52.91/7.95 | | | | | | | | | | | | (152) left_convergent_lines(all_39_1, all_39_2) = 0 % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_39_1, all_39_2, % 52.91/7.95 | | | | | | | | | | | | simplifying with (21), (22), (152) gives: % 52.91/7.95 | | | | | | | | | | | | (153) $false % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | CLOSE: (153) is inconsistent. % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | End of split % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | End of split % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | End of split % 52.91/7.95 | | | | | | | | | % 52.91/7.95 | | | | | | | | End of split % 52.91/7.95 | | | | | | | | % 52.91/7.95 | | | | | | | Case 2: % 52.91/7.95 | | | | | | | | % 52.91/7.95 | | | | | | | | (154) (all_64_1 = 0 & left_convergent_lines(all_39_1, % 52.91/7.95 | | | | | | | | all_39_3) = 0) | ( ~ (all_64_2 = 0) & % 52.91/7.95 | | | | | | | | reverse_line(all_39_3) = all_64_3 & % 52.91/7.95 | | | | | | | | unequally_directed_lines(all_39_1, all_64_3) = % 52.91/7.95 | | | | | | | | all_64_2 & $i(all_64_3)) % 52.91/7.95 | | | | | | | | % 52.91/7.95 | | | | | | | | BETA: splitting (154) gives: % 52.91/7.95 | | | | | | | | % 52.91/7.95 | | | | | | | | Case 1: % 52.91/7.95 | | | | | | | | | % 52.91/7.95 | | | | | | | | | (155) all_64_1 = 0 & left_convergent_lines(all_39_1, % 52.91/7.95 | | | | | | | | | all_39_3) = 0 % 52.91/7.95 | | | | | | | | | % 52.91/7.95 | | | | | | | | | ALPHA: (155) implies: % 52.91/7.95 | | | | | | | | | (156) left_convergent_lines(all_39_1, all_39_3) = 0 % 52.91/7.95 | | | | | | | | | % 52.91/7.95 | | | | | | | | | GROUND_INST: instantiating (11) with all_39_1, all_39_3, % 52.91/7.95 | | | | | | | | | simplifying with (20), (22), (156) gives: % 52.91/7.95 | | | | | | | | | (157) $false % 52.91/7.95 | | | | | | | | | % 52.91/7.95 | | | | | | | | | CLOSE: (157) is inconsistent. % 52.91/7.95 | | | | | | | | | % 52.91/7.95 | | | | | | | | Case 2: % 52.91/7.95 | | | | | | | | | % 52.91/7.95 | | | | | | | | | (158) ~ (all_64_2 = 0) & reverse_line(all_39_3) = all_64_3 % 52.91/7.95 | | | | | | | | | & unequally_directed_lines(all_39_1, all_64_3) = % 52.91/7.95 | | | | | | | | | all_64_2 & $i(all_64_3) % 52.91/7.95 | | | | | | | | | % 52.91/7.95 | | | | | | | | | ALPHA: (158) implies: % 52.91/7.95 | | | | | | | | | (159) ~ (all_64_2 = 0) % 52.91/7.95 | | | | | | | | | (160) $i(all_64_3) % 52.91/7.95 | | | | | | | | | (161) unequally_directed_lines(all_39_1, all_64_3) = % 52.91/7.95 | | | | | | | | | all_64_2 % 52.91/7.95 | | | | | | | | | (162) reverse_line(all_39_3) = all_64_3 % 52.91/7.95 | | | | | | | | | % 52.91/7.95 | | | | | | | | | BETA: splitting (124) gives: % 52.91/7.95 | | | | | | | | | % 52.91/7.95 | | | | | | | | | Case 1: % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | (163) all_127_0 = 0 % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | REDUCE: (120), (163) imply: % 52.91/7.95 | | | | | | | | | | (164) $false % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | CLOSE: (164) is inconsistent. % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | Case 2: % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | (165) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 52.91/7.95 | | | | | | | | | | left_apart_point(all_63_2, v0) = v1 & % 52.91/7.95 | | | | | | | | | | reverse_line(all_39_3) = v0 & $i(v0)) % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | DELTA: instantiating (165) with fresh symbols all_184_0, % 52.91/7.95 | | | | | | | | | | all_184_1 gives: % 52.91/7.95 | | | | | | | | | | (166) ~ (all_184_0 = 0) & left_apart_point(all_63_2, % 52.91/7.95 | | | | | | | | | | all_184_1) = all_184_0 & reverse_line(all_39_3) = % 52.91/7.95 | | | | | | | | | | all_184_1 & $i(all_184_1) % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | ALPHA: (166) implies: % 52.91/7.95 | | | | | | | | | | (167) reverse_line(all_39_3) = all_184_1 % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | GROUND_INST: instantiating (15) with all_39_2, all_184_1, % 52.91/7.95 | | | | | | | | | | all_39_3, simplifying with (23), (167) gives: % 52.91/7.95 | | | | | | | | | | (168) all_184_1 = all_39_2 % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | GROUND_INST: instantiating (15) with all_64_3, all_184_1, % 52.91/7.95 | | | | | | | | | | all_39_3, simplifying with (162), (167) gives: % 52.91/7.95 | | | | | | | | | | (169) all_184_1 = all_64_3 % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | COMBINE_EQS: (168), (169) imply: % 52.91/7.95 | | | | | | | | | | (170) all_64_3 = all_39_2 % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | REDUCE: (161), (170) imply: % 52.91/7.95 | | | | | | | | | | (171) unequally_directed_lines(all_39_1, all_39_2) = % 52.91/7.95 | | | | | | | | | | all_64_2 % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | GROUND_INST: instantiating (8) with all_39_1, all_39_1, % 52.91/7.95 | | | | | | | | | | all_39_2, all_64_2, all_64_2, simplifying with % 52.91/7.95 | | | | | | | | | | (21), (22), (171) gives: % 52.91/7.95 | | | | | | | | | | (172) all_64_2 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 52.91/7.95 | | | | | | | | | | unequally_directed_lines(all_39_1, all_39_1) = % 52.91/7.95 | | | | | | | | | | v0) % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | GROUND_INST: instantiating (9) with all_39_1, all_39_2, % 52.91/7.95 | | | | | | | | | | all_64_2, simplifying with (21), (22), (171) % 52.91/7.95 | | | | | | | | | | gives: % 52.91/7.95 | | | | | | | | | | (173) all_64_2 = 0 | ? [v0: $i] : % 52.91/7.95 | | | | | | | | | | (reverse_line(all_39_2) = v0 & % 52.91/7.95 | | | | | | | | | | unequally_directed_lines(all_39_1, v0) = 0 & % 52.91/7.95 | | | | | | | | | | $i(v0)) % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | BETA: splitting (173) gives: % 52.91/7.95 | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | Case 1: % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | (174) all_64_2 = 0 % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | REDUCE: (159), (174) imply: % 52.91/7.95 | | | | | | | | | | | (175) $false % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | CLOSE: (175) is inconsistent. % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | Case 2: % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | (176) ? [v0: $i] : (reverse_line(all_39_2) = v0 & % 52.91/7.95 | | | | | | | | | | | unequally_directed_lines(all_39_1, v0) = 0 & % 52.91/7.95 | | | | | | | | | | | $i(v0)) % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | DELTA: instantiating (176) with fresh symbol all_244_0 % 52.91/7.95 | | | | | | | | | | | gives: % 52.91/7.95 | | | | | | | | | | | (177) reverse_line(all_39_2) = all_244_0 & % 52.91/7.95 | | | | | | | | | | | unequally_directed_lines(all_39_1, all_244_0) = 0 % 52.91/7.95 | | | | | | | | | | | & $i(all_244_0) % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | ALPHA: (177) implies: % 52.91/7.95 | | | | | | | | | | | (178) unequally_directed_lines(all_39_1, all_244_0) = 0 % 52.91/7.95 | | | | | | | | | | | (179) reverse_line(all_39_2) = all_244_0 % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | BETA: splitting (172) gives: % 52.91/7.95 | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | Case 1: % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | (180) all_64_2 = 0 % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | REDUCE: (159), (180) imply: % 52.91/7.95 | | | | | | | | | | | | (181) $false % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | CLOSE: (181) is inconsistent. % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | Case 2: % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | (182) ? [v0: int] : ( ~ (v0 = 0) & % 52.91/7.95 | | | | | | | | | | | | unequally_directed_lines(all_39_1, all_39_1) = % 52.91/7.95 | | | | | | | | | | | | v0) % 52.91/7.95 | | | | | | | | | | | | % 52.91/7.95 | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_339_0 % 52.91/7.95 | | | | | | | | | | | | gives: % 52.91/7.96 | | | | | | | | | | | | (183) ~ (all_339_0 = 0) & % 52.91/7.96 | | | | | | | | | | | | unequally_directed_lines(all_39_1, all_39_1) = % 52.91/7.96 | | | | | | | | | | | | all_339_0 % 52.91/7.96 | | | | | | | | | | | | % 52.91/7.96 | | | | | | | | | | | | ALPHA: (183) implies: % 52.91/7.96 | | | | | | | | | | | | (184) ~ (all_339_0 = 0) % 52.91/7.96 | | | | | | | | | | | | (185) unequally_directed_lines(all_39_1, all_39_1) = % 52.91/7.96 | | | | | | | | | | | | all_339_0 % 52.91/7.96 | | | | | | | | | | | | % 52.91/7.96 | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_39_1, all_244_0, % 52.91/7.96 | | | | | | | | | | | | all_39_2, simplifying with (24), (179) gives: % 52.91/7.96 | | | | | | | | | | | | (186) all_244_0 = all_39_1 % 52.91/7.96 | | | | | | | | | | | | % 52.91/7.96 | | | | | | | | | | | | REDUCE: (178), (186) imply: % 52.91/7.96 | | | | | | | | | | | | (187) unequally_directed_lines(all_39_1, all_39_1) = 0 % 52.91/7.96 | | | | | | | | | | | | % 52.91/7.96 | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_339_0, 0, all_39_1, % 52.91/7.96 | | | | | | | | | | | | all_39_1, simplifying with (185), (187) gives: % 52.91/7.96 | | | | | | | | | | | | (188) all_339_0 = 0 % 52.91/7.96 | | | | | | | | | | | | % 52.91/7.96 | | | | | | | | | | | | REDUCE: (184), (188) imply: % 52.91/7.96 | | | | | | | | | | | | (189) $false % 52.91/7.96 | | | | | | | | | | | | % 52.91/7.96 | | | | | | | | | | | | CLOSE: (189) is inconsistent. % 52.91/7.96 | | | | | | | | | | | | % 52.91/7.96 | | | | | | | | | | | End of split % 52.91/7.96 | | | | | | | | | | | % 52.91/7.96 | | | | | | | | | | End of split % 52.91/7.96 | | | | | | | | | | % 52.91/7.96 | | | | | | | | | End of split % 52.91/7.96 | | | | | | | | | % 52.91/7.96 | | | | | | | | End of split % 52.91/7.96 | | | | | | | | % 52.91/7.96 | | | | | | | End of split % 52.91/7.96 | | | | | | | % 52.91/7.96 | | | | | | End of split % 52.91/7.96 | | | | | | % 52.91/7.96 | | | | | End of split % 52.91/7.96 | | | | | % 52.91/7.96 | | | | End of split % 52.91/7.96 | | | | % 52.91/7.96 | | | End of split % 52.91/7.96 | | | % 52.91/7.96 | | Case 2: % 52.91/7.96 | | | % 52.91/7.96 | | | (190) ~ (all_63_3 = 0) & reverse_line(all_39_3) = all_63_4 & % 52.91/7.96 | | | unequally_directed_lines(all_39_1, all_63_4) = all_63_3 & % 52.91/7.96 | | | $i(all_63_4) % 52.91/7.96 | | | % 52.91/7.96 | | | ALPHA: (190) implies: % 52.91/7.96 | | | (191) ~ (all_63_3 = 0) % 52.91/7.96 | | | (192) $i(all_63_4) % 52.91/7.96 | | | (193) unequally_directed_lines(all_39_1, all_63_4) = all_63_3 % 52.91/7.96 | | | (194) reverse_line(all_39_3) = all_63_4 % 52.91/7.96 | | | % 52.91/7.96 | | | GROUND_INST: instantiating (15) with all_39_2, all_63_4, all_39_3, % 52.91/7.96 | | | simplifying with (23), (194) gives: % 52.91/7.96 | | | (195) all_63_4 = all_39_2 % 52.91/7.96 | | | % 52.91/7.96 | | | REDUCE: (193), (195) imply: % 52.91/7.96 | | | (196) unequally_directed_lines(all_39_1, all_39_2) = all_63_3 % 52.91/7.96 | | | % 52.91/7.96 | | | GROUND_INST: instantiating (8) with all_39_1, all_39_1, all_39_2, % 52.91/7.96 | | | all_63_3, all_63_3, simplifying with (21), (22), (196) gives: % 52.91/7.96 | | | (197) all_63_3 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 52.91/7.96 | | | unequally_directed_lines(all_39_1, all_39_1) = v0) % 52.91/7.96 | | | % 52.91/7.96 | | | GROUND_INST: instantiating (9) with all_39_1, all_39_2, all_63_3, % 52.91/7.96 | | | simplifying with (21), (22), (196) gives: % 52.91/7.96 | | | (198) all_63_3 = 0 | ? [v0: $i] : (reverse_line(all_39_2) = v0 & % 52.91/7.96 | | | unequally_directed_lines(all_39_1, v0) = 0 & $i(v0)) % 52.91/7.96 | | | % 52.91/7.96 | | | BETA: splitting (198) gives: % 52.91/7.96 | | | % 52.91/7.96 | | | Case 1: % 52.91/7.96 | | | | % 52.91/7.96 | | | | (199) all_63_3 = 0 % 52.91/7.96 | | | | % 52.91/7.96 | | | | REDUCE: (191), (199) imply: % 52.91/7.96 | | | | (200) $false % 52.91/7.96 | | | | % 52.91/7.96 | | | | CLOSE: (200) is inconsistent. % 52.91/7.96 | | | | % 52.91/7.96 | | | Case 2: % 52.91/7.96 | | | | % 52.91/7.96 | | | | (201) ? [v0: $i] : (reverse_line(all_39_2) = v0 & % 52.91/7.96 | | | | unequally_directed_lines(all_39_1, v0) = 0 & $i(v0)) % 52.91/7.96 | | | | % 52.91/7.96 | | | | DELTA: instantiating (201) with fresh symbol all_135_0 gives: % 52.91/7.96 | | | | (202) reverse_line(all_39_2) = all_135_0 & % 52.91/7.96 | | | | unequally_directed_lines(all_39_1, all_135_0) = 0 & % 52.91/7.96 | | | | $i(all_135_0) % 52.91/7.96 | | | | % 52.91/7.96 | | | | ALPHA: (202) implies: % 52.91/7.96 | | | | (203) unequally_directed_lines(all_39_1, all_135_0) = 0 % 52.91/7.96 | | | | (204) reverse_line(all_39_2) = all_135_0 % 52.91/7.96 | | | | % 52.91/7.96 | | | | BETA: splitting (197) gives: % 52.91/7.96 | | | | % 52.91/7.96 | | | | Case 1: % 52.91/7.96 | | | | | % 52.91/7.96 | | | | | (205) all_63_3 = 0 % 52.91/7.96 | | | | | % 52.91/7.96 | | | | | REDUCE: (191), (205) imply: % 52.91/7.96 | | | | | (206) $false % 52.91/7.96 | | | | | % 52.91/7.96 | | | | | CLOSE: (206) is inconsistent. % 52.91/7.96 | | | | | % 52.91/7.96 | | | | Case 2: % 52.91/7.96 | | | | | % 52.91/7.96 | | | | | (207) ? [v0: int] : ( ~ (v0 = 0) & % 52.91/7.96 | | | | | unequally_directed_lines(all_39_1, all_39_1) = v0) % 52.91/7.96 | | | | | % 52.91/7.96 | | | | | DELTA: instantiating (207) with fresh symbol all_144_0 gives: % 52.91/7.96 | | | | | (208) ~ (all_144_0 = 0) & unequally_directed_lines(all_39_1, % 52.91/7.96 | | | | | all_39_1) = all_144_0 % 52.91/7.96 | | | | | % 52.91/7.96 | | | | | ALPHA: (208) implies: % 52.91/7.96 | | | | | (209) ~ (all_144_0 = 0) % 52.91/7.96 | | | | | (210) unequally_directed_lines(all_39_1, all_39_1) = all_144_0 % 52.91/7.96 | | | | | % 52.91/7.96 | | | | | GROUND_INST: instantiating (15) with all_39_1, all_135_0, all_39_2, % 52.91/7.96 | | | | | simplifying with (24), (204) gives: % 52.91/7.96 | | | | | (211) all_135_0 = all_39_1 % 52.91/7.96 | | | | | % 52.91/7.96 | | | | | REDUCE: (203), (211) imply: % 52.91/7.96 | | | | | (212) unequally_directed_lines(all_39_1, all_39_1) = 0 % 52.91/7.96 | | | | | % 52.91/7.96 | | | | | GROUND_INST: instantiating (16) with all_144_0, 0, all_39_1, all_39_1, % 52.91/7.96 | | | | | simplifying with (210), (212) gives: % 52.91/7.96 | | | | | (213) all_144_0 = 0 % 52.91/7.96 | | | | | % 52.91/7.96 | | | | | REDUCE: (209), (213) imply: % 52.91/7.96 | | | | | (214) $false % 52.91/7.96 | | | | | % 52.91/7.96 | | | | | CLOSE: (214) is inconsistent. % 52.91/7.96 | | | | | % 52.91/7.96 | | | | End of split % 52.91/7.96 | | | | % 52.91/7.96 | | | End of split % 52.91/7.96 | | | % 52.91/7.96 | | End of split % 52.91/7.96 | | % 52.91/7.96 | Case 2: % 52.91/7.96 | | % 52.91/7.96 | | (215) all_39_0 = 0 % 52.91/7.96 | | % 52.91/7.96 | | REDUCE: (19), (215) imply: % 52.91/7.96 | | (216) $false % 52.91/7.96 | | % 52.91/7.96 | | CLOSE: (216) is inconsistent. % 52.91/7.96 | | % 52.91/7.96 | End of split % 52.91/7.96 | % 52.91/7.96 End of proof % 52.91/7.96 % SZS output end Proof for theBenchmark % 52.91/7.96 % 52.91/7.96 7362ms %------------------------------------------------------------------------------