%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO202+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n027.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 23:22:14 EDT 2023 % Result : Theorem 13.97s 2.59s % Output : Proof 33.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO202+1 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n027.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 20:24:38 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.57/0.62 Running up to 7 provers in parallel. % 0.57/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.57/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.57/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.57/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.57/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.57/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.57/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.56/1.05 Prover 4: Preprocessing ... % 2.56/1.05 Prover 1: Preprocessing ... % 3.01/1.08 Prover 5: Preprocessing ... % 3.01/1.08 Prover 3: Preprocessing ... % 3.01/1.08 Prover 0: Preprocessing ... % 3.01/1.08 Prover 2: Preprocessing ... % 3.01/1.08 Prover 6: Preprocessing ... % 4.55/1.32 Prover 5: Proving ... % 4.55/1.32 Prover 2: Proving ... % 4.55/1.32 Prover 6: Constructing countermodel ... % 4.55/1.33 Prover 1: Constructing countermodel ... % 4.55/1.36 Prover 3: Constructing countermodel ... % 5.58/1.44 Prover 3: gave up % 5.58/1.44 Prover 1: gave up % 5.58/1.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.58/1.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.58/1.47 Prover 6: gave up % 5.58/1.47 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.58/1.48 Prover 7: Preprocessing ... % 5.58/1.50 Prover 4: Constructing countermodel ... % 5.58/1.50 Prover 8: Preprocessing ... % 5.58/1.50 Prover 9: Preprocessing ... % 5.58/1.51 Prover 0: Proving ... % 6.29/1.55 Prover 7: Warning: ignoring some quantifiers % 6.29/1.56 Prover 7: Constructing countermodel ... % 6.29/1.59 Prover 8: Warning: ignoring some quantifiers % 6.80/1.61 Prover 8: Constructing countermodel ... % 6.80/1.66 Prover 8: gave up % 7.33/1.67 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.65/1.71 Prover 9: Constructing countermodel ... % 7.65/1.71 Prover 10: Preprocessing ... % 7.65/1.72 Prover 7: gave up % 7.65/1.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.65/1.74 Prover 11: Preprocessing ... % 7.65/1.74 Prover 10: Warning: ignoring some quantifiers % 7.65/1.75 Prover 10: Constructing countermodel ... % 8.04/1.78 Prover 10: gave up % 8.04/1.81 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 8.04/1.82 Prover 12: Preprocessing ... % 8.90/1.94 Prover 11: Constructing countermodel ... % 9.38/1.96 Prover 12: Proving ... % 13.97/2.59 Prover 9: proved (1120ms) % 13.97/2.59 % 13.97/2.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.97/2.59 % 13.97/2.59 Prover 12: stopped % 13.97/2.60 Prover 0: stopped % 13.97/2.60 Prover 2: stopped % 13.97/2.60 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.97/2.60 Prover 5: stopped % 13.97/2.60 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 14.50/2.62 Prover 13: Preprocessing ... % 14.50/2.62 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 14.50/2.63 Prover 16: Preprocessing ... % 14.50/2.63 Prover 19: Preprocessing ... % 14.50/2.65 Prover 13: Warning: ignoring some quantifiers % 14.50/2.66 Prover 16: Warning: ignoring some quantifiers % 14.50/2.66 Prover 13: Constructing countermodel ... % 14.50/2.66 Prover 16: Constructing countermodel ... % 14.92/2.69 Prover 19: Warning: ignoring some quantifiers % 14.92/2.70 Prover 19: Constructing countermodel ... % 14.92/2.73 Prover 19: gave up % 15.81/2.80 Prover 13: gave up % 16.74/2.95 Prover 16: gave up % 31.97/5.81 Prover 11: Found proof (size 227) % 31.97/5.81 Prover 11: proved (4086ms) % 31.97/5.81 Prover 4: stopped % 31.97/5.81 % 31.97/5.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 31.97/5.81 % 31.97/5.84 % SZS output start Proof for theBenchmark % 31.97/5.85 Assumptions after simplification: % 31.97/5.85 --------------------------------- % 31.97/5.85 % 31.97/5.85 (apart3) % 32.44/5.89 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 32.44/5.89 % 32.44/5.89 (ceq3) % 32.44/5.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 32.44/5.90 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) % 32.44/5.90 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 32.44/5.90 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 32.44/5.90 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 32.44/5.90 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 32.52/5.91 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 32.52/5.91 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ % 32.52/5.91 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 32.52/5.91 convergent_lines(v0, v2) = 0) % 32.52/5.91 % 32.52/5.91 (ci1) % 32.52/5.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 32.52/5.91 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) & % 32.52/5.91 apart_point_and_line(v0, v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, % 32.52/5.91 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) % 32.52/5.91 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 32.52/5.91 line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 32.52/5.91 $i(v2))) % 32.52/5.91 % 32.52/5.91 (ci2) % 32.57/5.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 32.57/5.92 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) & % 32.57/5.92 apart_point_and_line(v1, v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, % 32.57/5.92 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) % 32.57/5.92 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 32.57/5.92 line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 32.57/5.92 $i(v2))) % 32.57/5.92 % 32.57/5.92 (ci3) % 32.57/5.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 32.57/5.92 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 32.57/5.92 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 32.57/5.92 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 32.57/5.92 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 32.57/5.92 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 32.57/5.92 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 32.57/5.92 % 32.57/5.92 (ci4) % 32.57/5.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 32.57/5.92 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 32.57/5.92 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 32.57/5.92 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 32.57/5.92 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 32.57/5.92 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 32.57/5.92 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 32.57/5.92 % 32.57/5.92 (con) % 32.57/5.92 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 32.57/5.92 $i] : (intersection_point(v3, v4) = v5 & line_connecting(v0, v2) = v4 & % 32.57/5.93 line_connecting(v0, v1) = v3 & convergent_lines(v3, v4) = 0 & % 32.57/5.93 distinct_points(v5, v0) = 0 & distinct_points(v0, v2) = 0 & % 32.57/5.93 distinct_points(v0, v1) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 32.57/5.93 $i(v0)) % 32.57/5.93 % 32.57/5.93 (cu1) % 32.57/5.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 32.57/5.94 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 32.57/5.94 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 32.57/5.94 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 32.57/5.94 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 32.57/5.94 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, % 32.57/5.94 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 32.57/5.94 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, % 32.57/5.94 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ % 32.57/5.94 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 32.57/5.94 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 32.57/5.94 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0, % 32.57/5.94 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 32.57/5.94 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 32.57/5.94 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 32.57/5.94 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 32.57/5.94 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 32.57/5.94 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 32.57/5.94 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 32.57/5.94 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 32.57/5.94 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 32.57/5.94 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 32.57/5.94 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 32.57/5.94 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 32.57/5.94 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 32.57/5.94 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 32.57/5.94 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 32.57/5.94 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 32.57/5.94 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 32.57/5.94 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~ % 32.57/5.94 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 32.57/5.94 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 32.57/5.94 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, % 32.57/5.94 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 32.57/5.94 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, % 32.57/5.94 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 32.57/5.94 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 32.57/5.94 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 32.57/5.94 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1, % 32.57/5.94 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i] % 32.57/5.94 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | % 32.57/5.94 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 32.57/5.94 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = % 32.57/5.94 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 32.57/5.94 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0, % 32.57/5.94 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 32.57/5.94 % 32.57/5.94 (function-axioms) % 32.57/5.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 32.57/5.94 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 32.57/5.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 32.57/5.94 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 32.57/5.94 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 32.57/5.94 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 32.57/5.94 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 32.57/5.94 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 32.57/5.94 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 32.57/5.94 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 32.57/5.94 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 32.57/5.94 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 32.57/5.95 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 32.57/5.95 (distinct_points(v3, v2) = v0)) % 32.57/5.95 % 32.57/5.95 Further assumptions not needed in the proof: % 32.57/5.95 -------------------------------------------- % 32.57/5.95 apart1, apart2, apart4, apart5, ax6, ceq1, ceq2 % 32.57/5.95 % 32.57/5.95 Those formulas are unsatisfiable: % 32.57/5.95 --------------------------------- % 32.57/5.95 % 32.57/5.95 Begin of proof % 32.57/5.95 | % 32.57/5.95 | ALPHA: (ci1) implies: % 32.57/5.95 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 32.57/5.95 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 32.57/5.95 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 32.57/5.95 | $i(v2))) % 32.57/5.95 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 32.57/5.95 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ % 32.57/5.95 | (v4 = 0) & apart_point_and_line(v0, v2) = v4) | ( ~ (v3 = 0) & % 32.57/5.95 | distinct_points(v0, v1) = v3))) % 32.57/5.95 | % 32.57/5.95 | ALPHA: (ci2) implies: % 32.57/5.95 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 32.57/5.95 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 32.57/5.95 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 32.57/5.95 | $i(v2))) % 32.57/5.95 | % 32.57/5.95 | ALPHA: (ci3) implies: % 32.57/5.95 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 32.57/5.95 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 32.57/5.95 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 32.57/5.95 | & $i(v2))) % 32.57/5.95 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 32.57/5.95 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 32.57/5.95 | (( ~ (v4 = 0) & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 32.57/5.95 | convergent_lines(v0, v1) = v3))) % 32.57/5.95 | % 32.57/5.95 | ALPHA: (ci4) implies: % 32.57/5.95 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 32.57/5.95 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 32.57/5.95 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 32.57/5.95 | & $i(v2))) % 32.57/5.95 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 32.57/5.95 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 32.57/5.95 | (( ~ (v4 = 0) & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 32.57/5.95 | convergent_lines(v0, v1) = v3))) % 32.57/5.95 | % 32.57/5.95 | ALPHA: (cu1) implies: % 32.57/5.96 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 32.57/5.96 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) % 32.57/5.96 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, % 32.57/5.96 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 32.57/5.96 | [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 32.57/5.96 | apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 32.57/5.96 | apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & % 32.57/5.96 | distinct_lines(v2, v3) = v6))) % 32.57/5.96 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 32.57/5.96 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 32.57/5.96 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 32.57/5.96 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 32.57/5.96 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 32.57/5.96 | apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & % 32.57/5.96 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 32.57/5.96 | v1) = v6))) % 32.57/5.96 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 32.57/5.96 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 32.57/5.96 | v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ % 32.57/5.96 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? % 32.57/5.96 | [v8: int] : ? [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = % 32.57/5.96 | 0) | (v8 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) % 32.57/5.96 | & distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & % 32.57/5.96 | distinct_points(v0, v1) = v6))) % 32.57/5.96 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 32.57/5.96 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 32.57/5.96 | v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ % 32.57/5.96 | (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 32.57/5.96 | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 32.57/5.96 | apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 32.57/5.96 | apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & % 32.57/5.96 | distinct_lines(v2, v3) = v6))) % 32.57/5.96 | % 32.57/5.96 | ALPHA: (ceq3) implies: % 32.57/5.96 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 32.57/5.96 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | % 32.57/5.96 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 32.57/5.96 | % 32.57/5.96 | ALPHA: (function-axioms) implies: % 32.57/5.96 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 32.57/5.96 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 32.57/5.96 | (distinct_points(v3, v2) = v0)) % 32.57/5.96 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 32.57/5.96 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 32.57/5.96 | (distinct_lines(v3, v2) = v0)) % 32.57/5.96 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 32.57/5.96 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 32.57/5.96 | (convergent_lines(v3, v2) = v0)) % 32.57/5.96 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 32.57/5.96 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 32.57/5.96 | (apart_point_and_line(v3, v2) = v0)) % 32.57/5.97 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 32.57/5.97 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 32.57/5.97 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 32.57/5.97 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 32.57/5.97 | v0)) % 32.57/5.97 | % 32.57/5.97 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 32.57/5.97 | all_17_3, all_17_4, all_17_5 gives: % 32.57/5.97 | (19) intersection_point(all_17_2, all_17_1) = all_17_0 & % 32.57/5.97 | line_connecting(all_17_5, all_17_3) = all_17_1 & % 32.57/5.97 | line_connecting(all_17_5, all_17_4) = all_17_2 & % 32.57/5.97 | convergent_lines(all_17_2, all_17_1) = 0 & distinct_points(all_17_0, % 32.57/5.97 | all_17_5) = 0 & distinct_points(all_17_5, all_17_3) = 0 & % 32.57/5.97 | distinct_points(all_17_5, all_17_4) = 0 & $i(all_17_0) & $i(all_17_1) % 32.57/5.97 | & $i(all_17_2) & $i(all_17_3) & $i(all_17_4) & $i(all_17_5) % 32.57/5.97 | % 32.57/5.97 | ALPHA: (19) implies: % 32.57/5.97 | (20) $i(all_17_5) % 32.57/5.97 | (21) $i(all_17_4) % 32.57/5.97 | (22) $i(all_17_3) % 32.57/5.97 | (23) $i(all_17_2) % 32.57/5.97 | (24) $i(all_17_1) % 32.57/5.97 | (25) distinct_points(all_17_5, all_17_4) = 0 % 32.57/5.97 | (26) distinct_points(all_17_5, all_17_3) = 0 % 32.57/5.97 | (27) distinct_points(all_17_0, all_17_5) = 0 % 32.57/5.97 | (28) convergent_lines(all_17_2, all_17_1) = 0 % 32.57/5.97 | (29) line_connecting(all_17_5, all_17_4) = all_17_2 % 32.57/5.97 | (30) line_connecting(all_17_5, all_17_3) = all_17_1 % 32.57/5.97 | (31) intersection_point(all_17_2, all_17_1) = all_17_0 % 32.57/5.97 | % 32.57/5.97 | GROUND_INST: instantiating (3) with all_17_5, all_17_4, simplifying with (20), % 32.57/5.97 | (21), (25) gives: % 32.57/5.97 | (32) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5, % 32.57/5.97 | all_17_4) = v0 & apart_point_and_line(all_17_4, v0) = v1 & $i(v0)) % 32.57/5.97 | % 32.57/5.97 | GROUND_INST: instantiating (1) with all_17_5, all_17_4, simplifying with (20), % 32.57/5.97 | (21), (25) gives: % 32.57/5.97 | (33) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5, % 32.57/5.97 | all_17_4) = v0 & apart_point_and_line(all_17_5, v0) = v1 & $i(v0)) % 32.57/5.97 | % 32.57/5.97 | GROUND_INST: instantiating (3) with all_17_5, all_17_3, simplifying with (20), % 32.57/5.97 | (22), (26) gives: % 32.57/5.97 | (34) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5, % 32.57/5.97 | all_17_3) = v0 & apart_point_and_line(all_17_3, v0) = v1 & $i(v0)) % 32.57/5.97 | % 32.57/5.97 | GROUND_INST: instantiating (1) with all_17_5, all_17_3, simplifying with (20), % 32.57/5.97 | (22), (26) gives: % 32.57/5.97 | (35) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5, % 32.57/5.97 | all_17_3) = v0 & apart_point_and_line(all_17_5, v0) = v1 & $i(v0)) % 32.57/5.97 | % 32.57/5.97 | GROUND_INST: instantiating (6) with all_17_2, all_17_1, simplifying with (23), % 32.57/5.97 | (24), (28) gives: % 32.57/5.97 | (36) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 32.57/5.97 | intersection_point(all_17_2, all_17_1) = v0 & % 32.57/5.97 | apart_point_and_line(v0, all_17_1) = v1 & $i(v0)) % 32.57/5.97 | % 32.57/5.97 | GROUND_INST: instantiating (4) with all_17_2, all_17_1, simplifying with (23), % 32.57/5.97 | (24), (28) gives: % 32.57/5.98 | (37) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 32.57/5.98 | intersection_point(all_17_2, all_17_1) = v0 & % 32.57/5.98 | apart_point_and_line(v0, all_17_2) = v1 & $i(v0)) % 32.57/5.98 | % 32.57/5.98 | GROUND_INST: instantiating (2) with all_17_5, all_17_4, all_17_2, simplifying % 32.57/5.98 | with (20), (21), (29) gives: % 32.57/5.98 | (38) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 32.57/5.98 | apart_point_and_line(all_17_5, all_17_2) = v1) | ( ~ (v0 = 0) & % 32.57/5.98 | distinct_points(all_17_5, all_17_4) = v0)) % 32.57/5.98 | % 32.57/5.98 | GROUND_INST: instantiating (2) with all_17_5, all_17_3, all_17_1, simplifying % 32.57/5.98 | with (20), (22), (30) gives: % 32.57/5.98 | (39) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 32.57/5.98 | apart_point_and_line(all_17_5, all_17_1) = v1) | ( ~ (v0 = 0) & % 32.57/5.98 | distinct_points(all_17_5, all_17_3) = v0)) % 32.57/5.98 | % 32.57/5.98 | GROUND_INST: instantiating (7) with all_17_2, all_17_1, all_17_0, simplifying % 32.57/5.98 | with (23), (24), (31) gives: % 32.57/5.98 | (40) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 32.57/5.98 | apart_point_and_line(all_17_0, all_17_1) = v1) | ( ~ (v0 = 0) & % 32.57/5.98 | convergent_lines(all_17_2, all_17_1) = v0)) % 32.57/5.98 | % 32.57/5.98 | GROUND_INST: instantiating (5) with all_17_2, all_17_1, all_17_0, simplifying % 32.57/5.98 | with (23), (24), (31) gives: % 32.57/5.98 | (41) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 32.57/5.98 | apart_point_and_line(all_17_0, all_17_2) = v1) | ( ~ (v0 = 0) & % 32.57/5.98 | convergent_lines(all_17_2, all_17_1) = v0)) % 32.57/5.98 | % 32.57/5.98 | DELTA: instantiating (41) with fresh symbols all_24_0, all_24_1 gives: % 32.57/5.98 | (42) ( ~ (all_24_0 = 0) & apart_point_and_line(all_17_0, all_17_2) = % 32.57/5.98 | all_24_0) | ( ~ (all_24_1 = 0) & convergent_lines(all_17_2, % 32.57/5.98 | all_17_1) = all_24_1) % 32.57/5.98 | % 32.57/5.98 | DELTA: instantiating (39) with fresh symbols all_25_0, all_25_1 gives: % 32.57/5.98 | (43) ( ~ (all_25_0 = 0) & apart_point_and_line(all_17_5, all_17_1) = % 32.57/5.98 | all_25_0) | ( ~ (all_25_1 = 0) & distinct_points(all_17_5, all_17_3) % 32.57/5.98 | = all_25_1) % 32.57/5.98 | % 32.57/5.98 | DELTA: instantiating (38) with fresh symbols all_26_0, all_26_1 gives: % 32.57/5.98 | (44) ( ~ (all_26_0 = 0) & apart_point_and_line(all_17_5, all_17_2) = % 32.57/5.98 | all_26_0) | ( ~ (all_26_1 = 0) & distinct_points(all_17_5, all_17_4) % 32.57/5.98 | = all_26_1) % 32.57/5.98 | % 32.57/5.98 | DELTA: instantiating (40) with fresh symbols all_29_0, all_29_1 gives: % 32.57/5.98 | (45) ( ~ (all_29_0 = 0) & apart_point_and_line(all_17_0, all_17_1) = % 32.57/5.98 | all_29_0) | ( ~ (all_29_1 = 0) & convergent_lines(all_17_2, % 32.57/5.98 | all_17_1) = all_29_1) % 32.57/5.98 | % 32.57/5.98 | DELTA: instantiating (37) with fresh symbols all_30_0, all_30_1 gives: % 32.57/5.98 | (46) ~ (all_30_0 = 0) & intersection_point(all_17_2, all_17_1) = all_30_1 % 32.57/5.98 | & apart_point_and_line(all_30_1, all_17_2) = all_30_0 & $i(all_30_1) % 32.57/5.98 | % 32.57/5.98 | ALPHA: (46) implies: % 32.57/5.98 | (47) ~ (all_30_0 = 0) % 32.57/5.98 | (48) $i(all_30_1) % 32.57/5.98 | (49) apart_point_and_line(all_30_1, all_17_2) = all_30_0 % 32.57/5.98 | (50) intersection_point(all_17_2, all_17_1) = all_30_1 % 32.57/5.98 | % 32.57/5.98 | DELTA: instantiating (36) with fresh symbols all_32_0, all_32_1 gives: % 32.57/5.98 | (51) ~ (all_32_0 = 0) & intersection_point(all_17_2, all_17_1) = all_32_1 % 32.57/5.98 | & apart_point_and_line(all_32_1, all_17_1) = all_32_0 & $i(all_32_1) % 32.57/5.98 | % 32.57/5.98 | ALPHA: (51) implies: % 32.57/5.98 | (52) ~ (all_32_0 = 0) % 32.57/5.98 | (53) apart_point_and_line(all_32_1, all_17_1) = all_32_0 % 32.57/5.98 | (54) intersection_point(all_17_2, all_17_1) = all_32_1 % 32.57/5.98 | % 32.57/5.98 | DELTA: instantiating (35) with fresh symbols all_34_0, all_34_1 gives: % 32.57/5.98 | (55) ~ (all_34_0 = 0) & line_connecting(all_17_5, all_17_3) = all_34_1 & % 32.57/5.98 | apart_point_and_line(all_17_5, all_34_1) = all_34_0 & $i(all_34_1) % 32.57/5.98 | % 32.57/5.98 | ALPHA: (55) implies: % 32.57/5.98 | (56) ~ (all_34_0 = 0) % 32.57/5.98 | (57) $i(all_34_1) % 32.57/5.98 | (58) apart_point_and_line(all_17_5, all_34_1) = all_34_0 % 32.57/5.98 | (59) line_connecting(all_17_5, all_17_3) = all_34_1 % 32.57/5.98 | % 32.57/5.98 | DELTA: instantiating (33) with fresh symbols all_36_0, all_36_1 gives: % 32.57/5.98 | (60) ~ (all_36_0 = 0) & line_connecting(all_17_5, all_17_4) = all_36_1 & % 32.57/5.98 | apart_point_and_line(all_17_5, all_36_1) = all_36_0 & $i(all_36_1) % 32.57/5.98 | % 32.57/5.98 | ALPHA: (60) implies: % 32.57/5.98 | (61) ~ (all_36_0 = 0) % 32.57/5.98 | (62) $i(all_36_1) % 32.57/5.99 | (63) apart_point_and_line(all_17_5, all_36_1) = all_36_0 % 32.57/5.99 | (64) line_connecting(all_17_5, all_17_4) = all_36_1 % 32.57/5.99 | % 32.57/5.99 | DELTA: instantiating (32) with fresh symbols all_38_0, all_38_1 gives: % 32.57/5.99 | (65) ~ (all_38_0 = 0) & line_connecting(all_17_5, all_17_4) = all_38_1 & % 32.57/5.99 | apart_point_and_line(all_17_4, all_38_1) = all_38_0 & $i(all_38_1) % 32.57/5.99 | % 32.57/5.99 | ALPHA: (65) implies: % 32.57/5.99 | (66) line_connecting(all_17_5, all_17_4) = all_38_1 % 32.57/5.99 | % 32.57/5.99 | DELTA: instantiating (34) with fresh symbols all_40_0, all_40_1 gives: % 32.57/5.99 | (67) ~ (all_40_0 = 0) & line_connecting(all_17_5, all_17_3) = all_40_1 & % 32.57/5.99 | apart_point_and_line(all_17_3, all_40_1) = all_40_0 & $i(all_40_1) % 32.57/5.99 | % 32.57/5.99 | ALPHA: (67) implies: % 32.57/5.99 | (68) line_connecting(all_17_5, all_17_3) = all_40_1 % 32.57/5.99 | % 32.57/5.99 | BETA: splitting (42) gives: % 32.57/5.99 | % 32.57/5.99 | Case 1: % 32.57/5.99 | | % 32.57/5.99 | | (69) ~ (all_24_0 = 0) & apart_point_and_line(all_17_0, all_17_2) = % 32.57/5.99 | | all_24_0 % 32.57/5.99 | | % 32.57/5.99 | | ALPHA: (69) implies: % 32.57/5.99 | | (70) apart_point_and_line(all_17_0, all_17_2) = all_24_0 % 32.57/5.99 | | % 32.57/5.99 | | BETA: splitting (43) gives: % 32.57/5.99 | | % 32.57/5.99 | | Case 1: % 32.57/5.99 | | | % 32.57/5.99 | | | (71) ~ (all_25_0 = 0) & apart_point_and_line(all_17_5, all_17_1) = % 32.57/5.99 | | | all_25_0 % 32.57/5.99 | | | % 32.57/5.99 | | | ALPHA: (71) implies: % 32.57/5.99 | | | (72) apart_point_and_line(all_17_5, all_17_1) = all_25_0 % 32.57/5.99 | | | % 32.57/5.99 | | | BETA: splitting (44) gives: % 32.57/5.99 | | | % 32.57/5.99 | | | Case 1: % 32.57/5.99 | | | | % 32.57/5.99 | | | | (73) ~ (all_26_0 = 0) & apart_point_and_line(all_17_5, all_17_2) = % 32.57/5.99 | | | | all_26_0 % 32.57/5.99 | | | | % 32.57/5.99 | | | | ALPHA: (73) implies: % 32.57/5.99 | | | | (74) apart_point_and_line(all_17_5, all_17_2) = all_26_0 % 32.57/5.99 | | | | % 32.57/5.99 | | | | BETA: splitting (45) gives: % 32.57/5.99 | | | | % 32.57/5.99 | | | | Case 1: % 32.57/5.99 | | | | | % 32.57/5.99 | | | | | (75) ~ (all_29_0 = 0) & apart_point_and_line(all_17_0, all_17_1) = % 32.57/5.99 | | | | | all_29_0 % 32.57/5.99 | | | | | % 32.57/5.99 | | | | | ALPHA: (75) implies: % 32.57/5.99 | | | | | (76) apart_point_and_line(all_17_0, all_17_1) = all_29_0 % 32.57/5.99 | | | | | % 32.57/5.99 | | | | | GROUND_INST: instantiating (17) with all_17_2, all_38_1, all_17_4, % 32.57/5.99 | | | | | all_17_5, simplifying with (29), (66) gives: % 32.57/5.99 | | | | | (77) all_38_1 = all_17_2 % 32.57/5.99 | | | | | % 32.57/5.99 | | | | | GROUND_INST: instantiating (17) with all_36_1, all_38_1, all_17_4, % 32.57/5.99 | | | | | all_17_5, simplifying with (64), (66) gives: % 32.57/5.99 | | | | | (78) all_38_1 = all_36_1 % 32.57/5.99 | | | | | % 32.57/5.99 | | | | | GROUND_INST: instantiating (17) with all_17_1, all_40_1, all_17_3, % 32.57/5.99 | | | | | all_17_5, simplifying with (30), (68) gives: % 32.57/5.99 | | | | | (79) all_40_1 = all_17_1 % 32.57/5.99 | | | | | % 32.57/5.99 | | | | | GROUND_INST: instantiating (17) with all_34_1, all_40_1, all_17_3, % 32.57/5.99 | | | | | all_17_5, simplifying with (59), (68) gives: % 32.57/5.99 | | | | | (80) all_40_1 = all_34_1 % 32.57/5.99 | | | | | % 32.57/5.99 | | | | | GROUND_INST: instantiating (18) with all_17_0, all_32_1, all_17_1, % 32.57/5.99 | | | | | all_17_2, simplifying with (31), (54) gives: % 32.57/5.99 | | | | | (81) all_32_1 = all_17_0 % 32.57/5.99 | | | | | % 32.57/5.99 | | | | | GROUND_INST: instantiating (18) with all_30_1, all_32_1, all_17_1, % 32.57/5.99 | | | | | all_17_2, simplifying with (50), (54) gives: % 32.57/5.99 | | | | | (82) all_32_1 = all_30_1 % 32.57/5.99 | | | | | % 32.57/5.99 | | | | | COMBINE_EQS: (79), (80) imply: % 32.57/5.99 | | | | | (83) all_34_1 = all_17_1 % 32.57/5.99 | | | | | % 32.57/5.99 | | | | | SIMP: (83) implies: % 32.57/5.99 | | | | | (84) all_34_1 = all_17_1 % 32.57/5.99 | | | | | % 32.57/5.99 | | | | | COMBINE_EQS: (77), (78) imply: % 32.57/5.99 | | | | | (85) all_36_1 = all_17_2 % 32.57/5.99 | | | | | % 32.57/5.99 | | | | | SIMP: (85) implies: % 32.57/5.99 | | | | | (86) all_36_1 = all_17_2 % 32.57/5.99 | | | | | % 32.57/5.99 | | | | | COMBINE_EQS: (81), (82) imply: % 32.57/5.99 | | | | | (87) all_30_1 = all_17_0 % 32.57/5.99 | | | | | % 32.57/5.99 | | | | | REDUCE: (53), (81) imply: % 32.57/5.99 | | | | | (88) apart_point_and_line(all_17_0, all_17_1) = all_32_0 % 32.57/5.99 | | | | | % 32.57/5.99 | | | | | REDUCE: (49), (87) imply: % 32.57/5.99 | | | | | (89) apart_point_and_line(all_17_0, all_17_2) = all_30_0 % 32.57/5.99 | | | | | % 32.57/5.99 | | | | | REDUCE: (63), (86) imply: % 32.57/5.99 | | | | | (90) apart_point_and_line(all_17_5, all_17_2) = all_36_0 % 32.57/5.99 | | | | | % 32.57/5.99 | | | | | REDUCE: (58), (84) imply: % 32.57/5.99 | | | | | (91) apart_point_and_line(all_17_5, all_17_1) = all_34_0 % 32.57/6.00 | | | | | % 32.57/6.00 | | | | | REDUCE: (48), (87) imply: % 32.57/6.00 | | | | | (92) $i(all_17_0) % 32.57/6.00 | | | | | % 32.57/6.00 | | | | | GROUND_INST: instantiating (16) with all_26_0, all_36_0, all_17_2, % 32.57/6.00 | | | | | all_17_5, simplifying with (74), (90) gives: % 32.57/6.00 | | | | | (93) all_36_0 = all_26_0 % 32.57/6.00 | | | | | % 32.57/6.00 | | | | | GROUND_INST: instantiating (16) with all_25_0, all_34_0, all_17_1, % 32.57/6.00 | | | | | all_17_5, simplifying with (72), (91) gives: % 32.57/6.00 | | | | | (94) all_34_0 = all_25_0 % 32.57/6.00 | | | | | % 32.57/6.00 | | | | | GROUND_INST: instantiating (16) with all_24_0, all_30_0, all_17_2, % 32.57/6.00 | | | | | all_17_0, simplifying with (70), (89) gives: % 32.57/6.00 | | | | | (95) all_30_0 = all_24_0 % 32.57/6.00 | | | | | % 32.57/6.00 | | | | | GROUND_INST: instantiating (16) with all_29_0, all_32_0, all_17_1, % 32.57/6.00 | | | | | all_17_0, simplifying with (76), (88) gives: % 32.57/6.00 | | | | | (96) all_32_0 = all_29_0 % 32.57/6.00 | | | | | % 32.57/6.00 | | | | | REDUCE: (61), (93) imply: % 32.57/6.00 | | | | | (97) ~ (all_26_0 = 0) % 32.57/6.00 | | | | | % 32.57/6.00 | | | | | REDUCE: (56), (94) imply: % 32.57/6.00 | | | | | (98) ~ (all_25_0 = 0) % 32.57/6.00 | | | | | % 32.57/6.00 | | | | | REDUCE: (52), (96) imply: % 32.57/6.00 | | | | | (99) ~ (all_29_0 = 0) % 32.57/6.00 | | | | | % 32.57/6.00 | | | | | REDUCE: (47), (95) imply: % 32.57/6.00 | | | | | (100) ~ (all_24_0 = 0) % 32.57/6.00 | | | | | % 32.57/6.00 | | | | | GROUND_INST: instantiating (11) with all_17_0, all_17_5, all_17_1, % 32.57/6.00 | | | | | all_17_2, all_25_0, all_26_0, simplifying with (20), % 32.57/6.00 | | | | | (23), (24), (27), (72), (74), (92) gives: % 32.57/6.00 | | | | | (101) all_26_0 = 0 | all_25_0 = 0 | ? [v0: int] : ? [v1: int] : % 32.57/6.00 | | | | | ? [v2: int] : ((v2 = 0 & apart_point_and_line(all_17_0, % 32.57/6.00 | | | | | all_17_2) = 0) | (v1 = 0 & % 32.57/6.00 | | | | | apart_point_and_line(all_17_0, all_17_1) = 0) | ( ~ (v0 = % 32.57/6.00 | | | | | 0) & distinct_lines(all_17_1, all_17_2) = v0)) % 32.57/6.00 | | | | | % 32.57/6.00 | | | | | GROUND_INST: instantiating (9) with all_17_0, all_17_5, all_17_1, % 32.57/6.00 | | | | | all_17_2, all_24_0, all_25_0, simplifying with (20), % 32.57/6.00 | | | | | (23), (24), (70), (72), (92) gives: % 32.57/6.00 | | | | | (102) all_25_0 = 0 | all_24_0 = 0 | ? [v0: int] : ? [v1: int] : % 32.57/6.00 | | | | | ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 32.57/6.00 | | | | | apart_point_and_line(all_17_5, all_17_2) = 0) | (v2 = 0 & % 32.57/6.00 | | | | | apart_point_and_line(all_17_0, all_17_1) = 0) | ( ~ (v1 = % 32.57/6.00 | | | | | 0) & distinct_lines(all_17_1, all_17_2) = v1) | ( ~ (v0 % 32.57/6.00 | | | | | = 0) & distinct_points(all_17_0, all_17_5) = v0)) % 32.57/6.00 | | | | | % 32.57/6.00 | | | | | GROUND_INST: instantiating (8) with all_17_0, all_17_5, all_17_1, % 32.57/6.00 | | | | | all_17_2, all_29_0, all_24_0, simplifying with (20), % 32.57/6.00 | | | | | (23), (24), (27), (70), (76), (92) gives: % 32.57/6.00 | | | | | (103) all_29_0 = 0 | all_24_0 = 0 | ? [v0: int] : ? [v1: int] : % 32.57/6.00 | | | | | ? [v2: int] : ((v2 = 0 & apart_point_and_line(all_17_5, % 32.57/6.00 | | | | | all_17_2) = 0) | (v1 = 0 & % 32.57/6.00 | | | | | apart_point_and_line(all_17_5, all_17_1) = 0) | ( ~ (v0 = % 32.57/6.00 | | | | | 0) & distinct_lines(all_17_1, all_17_2) = v0)) % 32.57/6.00 | | | | | % 32.57/6.00 | | | | | GROUND_INST: instantiating (10) with all_17_0, all_17_0, all_17_2, % 32.57/6.00 | | | | | all_17_1, all_24_0, all_29_0, simplifying with (23), % 32.57/6.00 | | | | | (24), (70), (76), (92) gives: % 32.57/6.00 | | | | | (104) all_29_0 = 0 | all_24_0 = 0 | ? [v0: int] : ? [v1: int] : % 32.57/6.00 | | | | | ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 32.57/6.00 | | | | | apart_point_and_line(all_17_0, all_17_2) = 0) | (v2 = 0 & % 32.57/6.00 | | | | | apart_point_and_line(all_17_0, all_17_1) = 0) | ( ~ (v1 = % 32.57/6.00 | | | | | 0) & distinct_lines(all_17_2, all_17_1) = v1) | ( ~ (v0 % 32.57/6.00 | | | | | = 0) & distinct_points(all_17_0, all_17_0) = v0)) % 32.57/6.00 | | | | | % 32.57/6.00 | | | | | GROUND_INST: instantiating (10) with all_17_0, all_17_5, all_17_1, % 32.57/6.00 | | | | | all_17_2, all_29_0, all_26_0, simplifying with (20), % 32.57/6.00 | | | | | (23), (24), (74), (76), (92) gives: % 32.57/6.00 | | | | | (105) all_29_0 = 0 | all_26_0 = 0 | ? [v0: int] : ? [v1: int] : % 32.57/6.00 | | | | | ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 33.01/6.01 | | | | | apart_point_and_line(all_17_5, all_17_1) = 0) | (v2 = 0 & % 33.01/6.01 | | | | | apart_point_and_line(all_17_0, all_17_2) = 0) | ( ~ (v1 = % 33.01/6.01 | | | | | 0) & distinct_lines(all_17_1, all_17_2) = v1) | ( ~ (v0 % 33.01/6.01 | | | | | = 0) & distinct_points(all_17_0, all_17_5) = v0)) % 33.01/6.01 | | | | | % 33.01/6.01 | | | | | BETA: splitting (101) gives: % 33.01/6.01 | | | | | % 33.01/6.01 | | | | | Case 1: % 33.01/6.01 | | | | | | % 33.01/6.01 | | | | | | (106) all_26_0 = 0 % 33.01/6.01 | | | | | | % 33.01/6.01 | | | | | | REDUCE: (97), (106) imply: % 33.01/6.01 | | | | | | (107) $false % 33.01/6.01 | | | | | | % 33.01/6.01 | | | | | | CLOSE: (107) is inconsistent. % 33.01/6.01 | | | | | | % 33.01/6.01 | | | | | Case 2: % 33.01/6.01 | | | | | | % 33.01/6.01 | | | | | | (108) all_25_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : % 33.01/6.01 | | | | | | ((v2 = 0 & apart_point_and_line(all_17_0, all_17_2) = 0) | % 33.01/6.01 | | | | | | (v1 = 0 & apart_point_and_line(all_17_0, all_17_1) = 0) | % 33.01/6.01 | | | | | | ( ~ (v0 = 0) & distinct_lines(all_17_1, all_17_2) = v0)) % 33.01/6.01 | | | | | | % 33.01/6.01 | | | | | | BETA: splitting (103) gives: % 33.01/6.01 | | | | | | % 33.01/6.01 | | | | | | Case 1: % 33.01/6.01 | | | | | | | % 33.01/6.01 | | | | | | | (109) all_29_0 = 0 % 33.01/6.01 | | | | | | | % 33.01/6.01 | | | | | | | REDUCE: (99), (109) imply: % 33.01/6.01 | | | | | | | (110) $false % 33.01/6.01 | | | | | | | % 33.01/6.01 | | | | | | | CLOSE: (110) is inconsistent. % 33.01/6.01 | | | | | | | % 33.01/6.01 | | | | | | Case 2: % 33.01/6.01 | | | | | | | % 33.01/6.01 | | | | | | | (111) all_24_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] % 33.01/6.01 | | | | | | | : ((v2 = 0 & apart_point_and_line(all_17_5, all_17_2) = % 33.01/6.01 | | | | | | | 0) | (v1 = 0 & apart_point_and_line(all_17_5, % 33.01/6.01 | | | | | | | all_17_1) = 0) | ( ~ (v0 = 0) & % 33.01/6.01 | | | | | | | distinct_lines(all_17_1, all_17_2) = v0)) % 33.01/6.01 | | | | | | | % 33.01/6.01 | | | | | | | BETA: splitting (105) gives: % 33.01/6.01 | | | | | | | % 33.01/6.01 | | | | | | | Case 1: % 33.01/6.01 | | | | | | | | % 33.01/6.01 | | | | | | | | (112) all_29_0 = 0 % 33.01/6.01 | | | | | | | | % 33.01/6.01 | | | | | | | | REDUCE: (99), (112) imply: % 33.01/6.01 | | | | | | | | (113) $false % 33.01/6.01 | | | | | | | | % 33.01/6.01 | | | | | | | | CLOSE: (113) is inconsistent. % 33.01/6.01 | | | | | | | | % 33.01/6.01 | | | | | | | Case 2: % 33.01/6.01 | | | | | | | | % 33.01/6.01 | | | | | | | | (114) all_26_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 33.01/6.01 | | | | | | | | int] : ? [v3: int] : ((v3 = 0 & % 33.01/6.01 | | | | | | | | apart_point_and_line(all_17_5, all_17_1) = 0) | (v2 % 33.01/6.01 | | | | | | | | = 0 & apart_point_and_line(all_17_0, all_17_2) = 0) % 33.01/6.01 | | | | | | | | | ( ~ (v1 = 0) & distinct_lines(all_17_1, all_17_2) = % 33.01/6.01 | | | | | | | | v1) | ( ~ (v0 = 0) & distinct_points(all_17_0, % 33.01/6.01 | | | | | | | | all_17_5) = v0)) % 33.01/6.01 | | | | | | | | % 33.01/6.01 | | | | | | | | BETA: splitting (102) gives: % 33.01/6.01 | | | | | | | | % 33.01/6.01 | | | | | | | | Case 1: % 33.01/6.01 | | | | | | | | | % 33.01/6.01 | | | | | | | | | (115) all_25_0 = 0 % 33.01/6.01 | | | | | | | | | % 33.01/6.01 | | | | | | | | | REDUCE: (98), (115) imply: % 33.01/6.01 | | | | | | | | | (116) $false % 33.01/6.01 | | | | | | | | | % 33.01/6.01 | | | | | | | | | CLOSE: (116) is inconsistent. % 33.01/6.01 | | | | | | | | | % 33.01/6.01 | | | | | | | | Case 2: % 33.01/6.01 | | | | | | | | | % 33.01/6.01 | | | | | | | | | (117) all_24_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 33.01/6.01 | | | | | | | | | int] : ? [v3: int] : ((v3 = 0 & % 33.01/6.01 | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = 0) | % 33.01/6.01 | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_0, all_17_1) % 33.01/6.01 | | | | | | | | | = 0) | ( ~ (v1 = 0) & distinct_lines(all_17_1, % 33.01/6.01 | | | | | | | | | all_17_2) = v1) | ( ~ (v0 = 0) & % 33.01/6.01 | | | | | | | | | distinct_points(all_17_0, all_17_5) = v0)) % 33.01/6.01 | | | | | | | | | % 33.01/6.01 | | | | | | | | | BETA: splitting (104) gives: % 33.01/6.01 | | | | | | | | | % 33.01/6.01 | | | | | | | | | Case 1: % 33.01/6.01 | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | (118) all_29_0 = 0 % 33.01/6.01 | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | REDUCE: (99), (118) imply: % 33.01/6.01 | | | | | | | | | | (119) $false % 33.01/6.01 | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | CLOSE: (119) is inconsistent. % 33.01/6.01 | | | | | | | | | | % 33.01/6.01 | | | | | | | | | Case 2: % 33.01/6.01 | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | (120) all_24_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 33.01/6.01 | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 33.01/6.01 | | | | | | | | | | apart_point_and_line(all_17_0, all_17_2) = 0) | % 33.01/6.01 | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_0, % 33.01/6.01 | | | | | | | | | | all_17_1) = 0) | ( ~ (v1 = 0) & % 33.01/6.01 | | | | | | | | | | distinct_lines(all_17_2, all_17_1) = v1) | ( ~ % 33.01/6.01 | | | | | | | | | | (v0 = 0) & distinct_points(all_17_0, all_17_0) % 33.01/6.01 | | | | | | | | | | = v0)) % 33.01/6.01 | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | BETA: splitting (111) gives: % 33.01/6.01 | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | Case 1: % 33.01/6.01 | | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | | (121) all_24_0 = 0 % 33.01/6.01 | | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | | REDUCE: (100), (121) imply: % 33.01/6.01 | | | | | | | | | | | (122) $false % 33.01/6.01 | | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | | CLOSE: (122) is inconsistent. % 33.01/6.01 | | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | Case 2: % 33.01/6.01 | | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | | (123) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 33.01/6.01 | | | | | | | | | | | = 0 & apart_point_and_line(all_17_5, all_17_2) % 33.01/6.01 | | | | | | | | | | | = 0) | (v1 = 0 & % 33.01/6.01 | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_1) = 0) % 33.01/6.01 | | | | | | | | | | | | ( ~ (v0 = 0) & distinct_lines(all_17_1, % 33.01/6.01 | | | | | | | | | | | all_17_2) = v0)) % 33.01/6.01 | | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | | DELTA: instantiating (123) with fresh symbols all_696_0, % 33.01/6.01 | | | | | | | | | | | all_696_1, all_696_2 gives: % 33.01/6.01 | | | | | | | | | | | (124) (all_696_0 = 0 & apart_point_and_line(all_17_5, % 33.01/6.01 | | | | | | | | | | | all_17_2) = 0) | (all_696_1 = 0 & % 33.01/6.01 | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_1) = 0) | % 33.01/6.01 | | | | | | | | | | | ( ~ (all_696_2 = 0) & distinct_lines(all_17_1, % 33.01/6.01 | | | | | | | | | | | all_17_2) = all_696_2) % 33.01/6.01 | | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | | BETA: splitting (114) gives: % 33.01/6.01 | | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | | Case 1: % 33.01/6.01 | | | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | | | (125) all_26_0 = 0 % 33.01/6.01 | | | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | | | REDUCE: (97), (125) imply: % 33.01/6.01 | | | | | | | | | | | | (126) $false % 33.01/6.01 | | | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | | | CLOSE: (126) is inconsistent. % 33.01/6.01 | | | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | | Case 2: % 33.01/6.01 | | | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | | | (127) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 33.01/6.01 | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 33.01/6.01 | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_1) = 0) % 33.01/6.01 | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_0, % 33.01/6.01 | | | | | | | | | | | | all_17_2) = 0) | ( ~ (v1 = 0) & % 33.01/6.01 | | | | | | | | | | | | distinct_lines(all_17_1, all_17_2) = v1) | ( ~ % 33.01/6.01 | | | | | | | | | | | | (v0 = 0) & distinct_points(all_17_0, all_17_5) % 33.01/6.01 | | | | | | | | | | | | = v0)) % 33.01/6.01 | | | | | | | | | | | | % 33.01/6.01 | | | | | | | | | | | | DELTA: instantiating (127) with fresh symbols all_780_0, % 33.01/6.01 | | | | | | | | | | | | all_780_1, all_780_2, all_780_3 gives: % 33.01/6.01 | | | | | | | | | | | | (128) (all_780_0 = 0 & apart_point_and_line(all_17_5, % 33.01/6.01 | | | | | | | | | | | | all_17_1) = 0) | (all_780_1 = 0 & % 33.01/6.01 | | | | | | | | | | | | apart_point_and_line(all_17_0, all_17_2) = 0) | % 33.01/6.01 | | | | | | | | | | | | ( ~ (all_780_2 = 0) & distinct_lines(all_17_1, % 33.01/6.01 | | | | | | | | | | | | all_17_2) = all_780_2) | ( ~ (all_780_3 = 0) & % 33.01/6.01 | | | | | | | | | | | | distinct_points(all_17_0, all_17_5) = all_780_3) % 33.01/6.02 | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | BETA: splitting (108) gives: % 33.01/6.02 | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | Case 1: % 33.01/6.02 | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | (129) all_25_0 = 0 % 33.01/6.02 | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | REDUCE: (98), (129) imply: % 33.01/6.02 | | | | | | | | | | | | | (130) $false % 33.01/6.02 | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | CLOSE: (130) is inconsistent. % 33.01/6.02 | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | Case 2: % 33.01/6.02 | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | (131) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 33.01/6.02 | | | | | | | | | | | | | = 0 & apart_point_and_line(all_17_0, all_17_2) % 33.01/6.02 | | | | | | | | | | | | | = 0) | (v1 = 0 & % 33.01/6.02 | | | | | | | | | | | | | apart_point_and_line(all_17_0, all_17_1) = 0) % 33.01/6.02 | | | | | | | | | | | | | | ( ~ (v0 = 0) & distinct_lines(all_17_1, % 33.01/6.02 | | | | | | | | | | | | | all_17_2) = v0)) % 33.01/6.02 | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | DELTA: instantiating (131) with fresh symbols all_792_0, % 33.01/6.02 | | | | | | | | | | | | | all_792_1, all_792_2 gives: % 33.01/6.02 | | | | | | | | | | | | | (132) (all_792_0 = 0 & apart_point_and_line(all_17_0, % 33.01/6.02 | | | | | | | | | | | | | all_17_2) = 0) | (all_792_1 = 0 & % 33.01/6.02 | | | | | | | | | | | | | apart_point_and_line(all_17_0, all_17_1) = 0) | % 33.01/6.02 | | | | | | | | | | | | | ( ~ (all_792_2 = 0) & distinct_lines(all_17_1, % 33.01/6.02 | | | | | | | | | | | | | all_17_2) = all_792_2) % 33.01/6.02 | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | BETA: splitting (117) gives: % 33.01/6.02 | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | Case 1: % 33.01/6.02 | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | (133) all_24_0 = 0 % 33.01/6.02 | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | REDUCE: (100), (133) imply: % 33.01/6.02 | | | | | | | | | | | | | | (134) $false % 33.01/6.02 | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | CLOSE: (134) is inconsistent. % 33.01/6.02 | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | Case 2: % 33.01/6.02 | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | (135) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 33.01/6.02 | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 33.01/6.02 | | | | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = 0) % 33.01/6.02 | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_0, % 33.01/6.02 | | | | | | | | | | | | | | all_17_1) = 0) | ( ~ (v1 = 0) & % 33.01/6.02 | | | | | | | | | | | | | | distinct_lines(all_17_1, all_17_2) = v1) | ( ~ % 33.01/6.02 | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_17_0, all_17_5) % 33.01/6.02 | | | | | | | | | | | | | | = v0)) % 33.01/6.02 | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | DELTA: instantiating (135) with fresh symbols all_800_0, % 33.01/6.02 | | | | | | | | | | | | | | all_800_1, all_800_2, all_800_3 gives: % 33.01/6.02 | | | | | | | | | | | | | | (136) (all_800_0 = 0 & apart_point_and_line(all_17_5, % 33.01/6.02 | | | | | | | | | | | | | | all_17_2) = 0) | (all_800_1 = 0 & % 33.01/6.02 | | | | | | | | | | | | | | apart_point_and_line(all_17_0, all_17_1) = 0) | % 33.01/6.02 | | | | | | | | | | | | | | ( ~ (all_800_2 = 0) & distinct_lines(all_17_1, % 33.01/6.02 | | | | | | | | | | | | | | all_17_2) = all_800_2) | ( ~ (all_800_3 = 0) & % 33.01/6.02 | | | | | | | | | | | | | | distinct_points(all_17_0, all_17_5) = all_800_3) % 33.01/6.02 | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | BETA: splitting (132) gives: % 33.01/6.02 | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | Case 1: % 33.01/6.02 | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | (137) all_792_0 = 0 & apart_point_and_line(all_17_0, % 33.01/6.02 | | | | | | | | | | | | | | | all_17_2) = 0 % 33.01/6.02 | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | ALPHA: (137) implies: % 33.01/6.02 | | | | | | | | | | | | | | | (138) apart_point_and_line(all_17_0, all_17_2) = 0 % 33.01/6.02 | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | REF_CLOSE: (16), (70), (100), (138) are inconsistent by % 33.01/6.02 | | | | | | | | | | | | | | | sub-proof #4. % 33.01/6.02 | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | Case 2: % 33.01/6.02 | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | (139) (all_792_1 = 0 & apart_point_and_line(all_17_0, % 33.01/6.02 | | | | | | | | | | | | | | | all_17_1) = 0) | ( ~ (all_792_2 = 0) & % 33.01/6.02 | | | | | | | | | | | | | | | distinct_lines(all_17_1, all_17_2) = all_792_2) % 33.01/6.02 | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | BETA: splitting (139) gives: % 33.01/6.02 | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | Case 1: % 33.01/6.02 | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | (140) all_792_1 = 0 & apart_point_and_line(all_17_0, % 33.01/6.02 | | | | | | | | | | | | | | | | all_17_1) = 0 % 33.01/6.02 | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | ALPHA: (140) implies: % 33.01/6.02 | | | | | | | | | | | | | | | | (141) apart_point_and_line(all_17_0, all_17_1) = 0 % 33.01/6.02 | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | REF_CLOSE: (16), (76), (99), (141) are inconsistent by % 33.01/6.02 | | | | | | | | | | | | | | | | sub-proof #3. % 33.01/6.02 | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | Case 2: % 33.01/6.02 | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | (142) ~ (all_792_2 = 0) & distinct_lines(all_17_1, % 33.01/6.02 | | | | | | | | | | | | | | | | all_17_2) = all_792_2 % 33.01/6.02 | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | ALPHA: (142) implies: % 33.01/6.02 | | | | | | | | | | | | | | | | (143) distinct_lines(all_17_1, all_17_2) = all_792_2 % 33.01/6.02 | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | BETA: splitting (124) gives: % 33.01/6.02 | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | Case 1: % 33.01/6.02 | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | (144) all_696_0 = 0 & apart_point_and_line(all_17_5, % 33.01/6.02 | | | | | | | | | | | | | | | | | all_17_2) = 0 % 33.01/6.02 | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | ALPHA: (144) implies: % 33.01/6.02 | | | | | | | | | | | | | | | | | (145) apart_point_and_line(all_17_5, all_17_2) = 0 % 33.01/6.02 | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (74), (97), (145) are inconsistent by % 33.01/6.02 | | | | | | | | | | | | | | | | | sub-proof #2. % 33.01/6.02 | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | Case 2: % 33.01/6.02 | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | (146) (all_696_1 = 0 & apart_point_and_line(all_17_5, % 33.01/6.02 | | | | | | | | | | | | | | | | | all_17_1) = 0) | ( ~ (all_696_2 = 0) & % 33.01/6.02 | | | | | | | | | | | | | | | | | distinct_lines(all_17_1, all_17_2) = all_696_2) % 33.01/6.02 | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | BETA: splitting (146) gives: % 33.01/6.02 | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | Case 1: % 33.01/6.02 | | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | | (147) all_696_1 = 0 & apart_point_and_line(all_17_5, % 33.01/6.02 | | | | | | | | | | | | | | | | | | all_17_1) = 0 % 33.01/6.02 | | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | | ALPHA: (147) implies: % 33.01/6.02 | | | | | | | | | | | | | | | | | | (148) apart_point_and_line(all_17_5, all_17_1) = 0 % 33.01/6.02 | | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (72), (98), (148) are inconsistent by % 33.01/6.02 | | | | | | | | | | | | | | | | | | sub-proof #1. % 33.01/6.02 | | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | Case 2: % 33.01/6.02 | | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | | (149) ~ (all_696_2 = 0) & distinct_lines(all_17_1, % 33.01/6.02 | | | | | | | | | | | | | | | | | | all_17_2) = all_696_2 % 33.01/6.02 | | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | | ALPHA: (149) implies: % 33.01/6.02 | | | | | | | | | | | | | | | | | | (150) distinct_lines(all_17_1, all_17_2) = all_696_2 % 33.01/6.02 | | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives: % 33.01/6.02 | | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | | Case 1: % 33.01/6.02 | | | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | | | (151) (all_800_0 = 0 & apart_point_and_line(all_17_5, % 33.01/6.02 | | | | | | | | | | | | | | | | | | | all_17_2) = 0) | (all_800_1 = 0 & % 33.01/6.02 | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_0, all_17_1) = 0) % 33.01/6.02 | | | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives: % 33.01/6.02 | | | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | | | Case 1: % 33.01/6.02 | | | | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | | | | (152) all_800_0 = 0 & apart_point_and_line(all_17_5, % 33.01/6.02 | | | | | | | | | | | | | | | | | | | | all_17_2) = 0 % 33.01/6.02 | | | | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | | | | ALPHA: (152) implies: % 33.01/6.02 | | | | | | | | | | | | | | | | | | | | (153) apart_point_and_line(all_17_5, all_17_2) = 0 % 33.01/6.02 | | | | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (74), (97), (153) are inconsistent by % 33.01/6.02 | | | | | | | | | | | | | | | | | | | | sub-proof #2. % 33.01/6.02 | | | | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | | | Case 2: % 33.01/6.02 | | | | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | | | | (154) all_800_1 = 0 & apart_point_and_line(all_17_0, % 33.01/6.02 | | | | | | | | | | | | | | | | | | | | all_17_1) = 0 % 33.01/6.02 | | | | | | | | | | | | | | | | | | | | % 33.01/6.02 | | | | | | | | | | | | | | | | | | | | ALPHA: (154) implies: % 33.01/6.02 | | | | | | | | | | | | | | | | | | | | (155) apart_point_and_line(all_17_0, all_17_1) = 0 % 33.01/6.02 | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (76), (99), (155) are inconsistent by % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | sub-proof #3. % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | End of split % 33.01/6.03 | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | Case 2: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | (156) ( ~ (all_800_2 = 0) & distinct_lines(all_17_1, % 33.01/6.03 | | | | | | | | | | | | | | | | | | | all_17_2) = all_800_2) | ( ~ (all_800_3 = 0) & % 33.01/6.03 | | | | | | | | | | | | | | | | | | | distinct_points(all_17_0, all_17_5) = all_800_3) % 33.01/6.03 | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | Case 1: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | (157) ~ (all_800_2 = 0) & distinct_lines(all_17_1, % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | all_17_2) = all_800_2 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | ALPHA: (157) implies: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | (158) distinct_lines(all_17_1, all_17_2) = all_800_2 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | Case 1: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | (159) (all_780_0 = 0 & apart_point_and_line(all_17_5, % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | all_17_1) = 0) | (all_780_1 = 0 & % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_0, all_17_2) = 0) % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | Case 1: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | (160) all_780_0 = 0 & apart_point_and_line(all_17_5, % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | all_17_1) = 0 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (160) implies: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | (161) apart_point_and_line(all_17_5, all_17_1) = 0 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (72), (98), (161) are inconsistent by % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | Case 2: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | (162) all_780_1 = 0 & apart_point_and_line(all_17_0, % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | all_17_2) = 0 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (162) implies: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | (163) apart_point_and_line(all_17_0, all_17_2) = 0 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (70), (100), (163) are inconsistent by % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | sub-proof #4. % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | End of split % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | Case 2: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | (164) ( ~ (all_780_2 = 0) & distinct_lines(all_17_1, % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | all_17_2) = all_780_2) | ( ~ (all_780_3 = 0) & % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | distinct_points(all_17_0, all_17_5) = all_780_3) % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | Case 1: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | (165) ~ (all_780_2 = 0) & distinct_lines(all_17_1, % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | all_17_2) = all_780_2 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (165) implies: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | (166) ~ (all_780_2 = 0) % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | (167) distinct_lines(all_17_1, all_17_2) = all_780_2 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (120) gives: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | (168) all_24_0 = 0 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (100), (168) imply: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | (169) $false % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (169) is inconsistent. % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_780_2, all_792_2, % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | all_17_2, all_17_1, simplifying with (143), (167) % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | gives: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | (170) all_792_2 = all_780_2 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_792_2, all_800_2, % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | all_17_2, all_17_1, simplifying with (143), (158) % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | gives: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | (171) all_800_2 = all_792_2 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_696_2, all_800_2, % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | all_17_2, all_17_1, simplifying with (150), (158) % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | gives: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | (172) all_800_2 = all_696_2 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (171), (172) imply: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | (173) all_792_2 = all_696_2 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (173) implies: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | (174) all_792_2 = all_696_2 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (174) imply: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | (175) all_780_2 = all_696_2 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (175) implies: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | (176) all_780_2 = all_696_2 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (166), (176) imply: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | (177) ~ (all_696_2 = 0) % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_17_2, all_17_1, % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | all_17_2, all_696_2, simplifying with (23), (24), % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | (28), (150) gives: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | (178) all_696_2 = 0 | convergent_lines(all_17_2, % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | all_17_2) = 0 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | | (179) convergent_lines(all_17_2, all_17_2) = 0 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_17_2, simplifying % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | | with (23), (179) gives: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | | (180) $false % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (180) is inconsistent. % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | | (181) all_696_2 = 0 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (177), (181) imply: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | | (182) $false % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (182) is inconsistent. % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | End of split % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | End of split % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | Case 2: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | (183) ~ (all_780_3 = 0) & distinct_points(all_17_0, % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | all_17_5) = all_780_3 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | (184) ~ (all_780_3 = 0) % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | (185) distinct_points(all_17_0, all_17_5) = all_780_3 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_780_3, all_17_5, % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | all_17_0, simplifying with (27), (185) gives: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | (186) all_780_3 = 0 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (186) imply: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | (187) $false % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (187) is inconsistent. % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | End of split % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | End of split % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | Case 2: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | (188) ~ (all_800_3 = 0) & distinct_points(all_17_0, % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | all_17_5) = all_800_3 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | ALPHA: (188) implies: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | (189) ~ (all_800_3 = 0) % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | (190) distinct_points(all_17_0, all_17_5) = all_800_3 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_800_3, all_17_5, % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | all_17_0, simplifying with (27), (190) gives: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | (191) all_800_3 = 0 % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | REDUCE: (189), (191) imply: % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | (192) $false % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | CLOSE: (192) is inconsistent. % 33.01/6.03 | | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | | End of split % 33.01/6.03 | | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | | End of split % 33.01/6.03 | | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | | End of split % 33.01/6.03 | | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | | End of split % 33.01/6.03 | | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | | End of split % 33.01/6.03 | | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | | End of split % 33.01/6.03 | | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | | End of split % 33.01/6.03 | | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | | End of split % 33.01/6.03 | | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | | End of split % 33.01/6.03 | | | | | | | | | | | % 33.01/6.03 | | | | | | | | | | End of split % 33.01/6.03 | | | | | | | | | | % 33.01/6.03 | | | | | | | | | End of split % 33.01/6.03 | | | | | | | | | % 33.01/6.03 | | | | | | | | End of split % 33.01/6.03 | | | | | | | | % 33.01/6.03 | | | | | | | End of split % 33.01/6.03 | | | | | | | % 33.01/6.03 | | | | | | End of split % 33.01/6.03 | | | | | | % 33.01/6.03 | | | | | End of split % 33.01/6.03 | | | | | % 33.01/6.03 | | | | Case 2: % 33.01/6.03 | | | | | % 33.01/6.03 | | | | | (193) ~ (all_29_1 = 0) & convergent_lines(all_17_2, all_17_1) = % 33.01/6.04 | | | | | all_29_1 % 33.01/6.04 | | | | | % 33.01/6.04 | | | | | ALPHA: (193) implies: % 33.01/6.04 | | | | | (194) ~ (all_29_1 = 0) % 33.01/6.04 | | | | | (195) convergent_lines(all_17_2, all_17_1) = all_29_1 % 33.01/6.04 | | | | | % 33.01/6.04 | | | | | GROUND_INST: instantiating (15) with 0, all_29_1, all_17_1, all_17_2, % 33.01/6.04 | | | | | simplifying with (28), (195) gives: % 33.01/6.04 | | | | | (196) all_29_1 = 0 % 33.01/6.04 | | | | | % 33.01/6.04 | | | | | REDUCE: (194), (196) imply: % 33.01/6.04 | | | | | (197) $false % 33.01/6.04 | | | | | % 33.01/6.04 | | | | | CLOSE: (197) is inconsistent. % 33.01/6.04 | | | | | % 33.01/6.04 | | | | End of split % 33.01/6.04 | | | | % 33.01/6.04 | | | Case 2: % 33.01/6.04 | | | | % 33.01/6.04 | | | | (198) ~ (all_26_1 = 0) & distinct_points(all_17_5, all_17_4) = % 33.01/6.04 | | | | all_26_1 % 33.01/6.04 | | | | % 33.01/6.04 | | | | ALPHA: (198) implies: % 33.01/6.04 | | | | (199) ~ (all_26_1 = 0) % 33.01/6.04 | | | | (200) distinct_points(all_17_5, all_17_4) = all_26_1 % 33.01/6.04 | | | | % 33.01/6.04 | | | | GROUND_INST: instantiating (13) with 0, all_26_1, all_17_4, all_17_5, % 33.01/6.04 | | | | simplifying with (25), (200) gives: % 33.01/6.04 | | | | (201) all_26_1 = 0 % 33.01/6.04 | | | | % 33.01/6.04 | | | | REDUCE: (199), (201) imply: % 33.01/6.04 | | | | (202) $false % 33.01/6.04 | | | | % 33.01/6.04 | | | | CLOSE: (202) is inconsistent. % 33.01/6.04 | | | | % 33.01/6.04 | | | End of split % 33.01/6.04 | | | % 33.01/6.04 | | Case 2: % 33.01/6.04 | | | % 33.01/6.04 | | | (203) ~ (all_25_1 = 0) & distinct_points(all_17_5, all_17_3) = % 33.01/6.04 | | | all_25_1 % 33.01/6.04 | | | % 33.01/6.04 | | | ALPHA: (203) implies: % 33.01/6.04 | | | (204) ~ (all_25_1 = 0) % 33.01/6.04 | | | (205) distinct_points(all_17_5, all_17_3) = all_25_1 % 33.01/6.04 | | | % 33.01/6.04 | | | GROUND_INST: instantiating (13) with 0, all_25_1, all_17_3, all_17_5, % 33.01/6.04 | | | simplifying with (26), (205) gives: % 33.01/6.04 | | | (206) all_25_1 = 0 % 33.01/6.04 | | | % 33.01/6.04 | | | REDUCE: (204), (206) imply: % 33.01/6.04 | | | (207) $false % 33.01/6.04 | | | % 33.01/6.04 | | | CLOSE: (207) is inconsistent. % 33.01/6.04 | | | % 33.01/6.04 | | End of split % 33.01/6.04 | | % 33.01/6.04 | Case 2: % 33.01/6.04 | | % 33.01/6.04 | | (208) ~ (all_24_1 = 0) & convergent_lines(all_17_2, all_17_1) = all_24_1 % 33.01/6.04 | | % 33.01/6.04 | | ALPHA: (208) implies: % 33.01/6.04 | | (209) ~ (all_24_1 = 0) % 33.01/6.04 | | (210) convergent_lines(all_17_2, all_17_1) = all_24_1 % 33.01/6.04 | | % 33.01/6.04 | | GROUND_INST: instantiating (15) with 0, all_24_1, all_17_1, all_17_2, % 33.01/6.04 | | simplifying with (28), (210) gives: % 33.01/6.04 | | (211) all_24_1 = 0 % 33.01/6.04 | | % 33.01/6.04 | | REDUCE: (209), (211) imply: % 33.01/6.04 | | (212) $false % 33.01/6.04 | | % 33.01/6.04 | | CLOSE: (212) is inconsistent. % 33.01/6.04 | | % 33.01/6.04 | End of split % 33.01/6.04 | % 33.01/6.04 End of proof % 33.01/6.04 % 33.01/6.04 Sub-proof #1 shows that the following formulas are inconsistent: % 33.01/6.04 ---------------------------------------------------------------- % 33.01/6.04 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 33.01/6.04 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 33.01/6.04 (apart_point_and_line(v3, v2) = v0)) % 33.01/6.04 (2) apart_point_and_line(all_17_5, all_17_1) = all_25_0 % 33.01/6.04 (3) apart_point_and_line(all_17_5, all_17_1) = 0 % 33.01/6.04 (4) ~ (all_25_0 = 0) % 33.01/6.04 % 33.01/6.04 Begin of proof % 33.01/6.04 | % 33.01/6.04 | GROUND_INST: instantiating (1) with all_25_0, 0, all_17_1, all_17_5, % 33.01/6.04 | simplifying with (2), (3) gives: % 33.01/6.04 | (5) all_25_0 = 0 % 33.01/6.04 | % 33.01/6.04 | REDUCE: (4), (5) imply: % 33.01/6.04 | (6) $false % 33.01/6.04 | % 33.01/6.04 | CLOSE: (6) is inconsistent. % 33.01/6.04 | % 33.01/6.04 End of proof % 33.01/6.04 % 33.01/6.04 Sub-proof #2 shows that the following formulas are inconsistent: % 33.01/6.04 ---------------------------------------------------------------- % 33.01/6.04 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 33.01/6.04 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 33.01/6.04 (apart_point_and_line(v3, v2) = v0)) % 33.01/6.04 (2) apart_point_and_line(all_17_5, all_17_2) = all_26_0 % 33.01/6.04 (3) apart_point_and_line(all_17_5, all_17_2) = 0 % 33.01/6.04 (4) ~ (all_26_0 = 0) % 33.01/6.04 % 33.01/6.04 Begin of proof % 33.01/6.04 | % 33.01/6.04 | GROUND_INST: instantiating (1) with all_26_0, 0, all_17_2, all_17_5, % 33.01/6.04 | simplifying with (2), (3) gives: % 33.01/6.04 | (5) all_26_0 = 0 % 33.01/6.04 | % 33.01/6.04 | REDUCE: (4), (5) imply: % 33.01/6.04 | (6) $false % 33.01/6.04 | % 33.01/6.04 | CLOSE: (6) is inconsistent. % 33.01/6.04 | % 33.01/6.04 End of proof % 33.01/6.04 % 33.01/6.04 Sub-proof #3 shows that the following formulas are inconsistent: % 33.01/6.04 ---------------------------------------------------------------- % 33.01/6.04 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 33.01/6.04 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 33.01/6.04 (apart_point_and_line(v3, v2) = v0)) % 33.01/6.04 (2) apart_point_and_line(all_17_0, all_17_1) = all_29_0 % 33.01/6.04 (3) apart_point_and_line(all_17_0, all_17_1) = 0 % 33.01/6.04 (4) ~ (all_29_0 = 0) % 33.01/6.04 % 33.01/6.04 Begin of proof % 33.01/6.04 | % 33.01/6.04 | GROUND_INST: instantiating (1) with all_29_0, 0, all_17_1, all_17_0, % 33.01/6.04 | simplifying with (2), (3) gives: % 33.01/6.04 | (5) all_29_0 = 0 % 33.01/6.04 | % 33.01/6.04 | REDUCE: (4), (5) imply: % 33.01/6.04 | (6) $false % 33.01/6.04 | % 33.01/6.04 | CLOSE: (6) is inconsistent. % 33.01/6.04 | % 33.01/6.04 End of proof % 33.01/6.04 % 33.01/6.04 Sub-proof #4 shows that the following formulas are inconsistent: % 33.01/6.04 ---------------------------------------------------------------- % 33.01/6.04 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 33.01/6.04 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 33.01/6.04 (apart_point_and_line(v3, v2) = v0)) % 33.01/6.04 (2) apart_point_and_line(all_17_0, all_17_2) = all_24_0 % 33.01/6.04 (3) apart_point_and_line(all_17_0, all_17_2) = 0 % 33.01/6.04 (4) ~ (all_24_0 = 0) % 33.01/6.04 % 33.01/6.04 Begin of proof % 33.01/6.04 | % 33.01/6.04 | GROUND_INST: instantiating (1) with all_24_0, 0, all_17_2, all_17_0, % 33.01/6.04 | simplifying with (2), (3) gives: % 33.01/6.04 | (5) all_24_0 = 0 % 33.01/6.04 | % 33.01/6.04 | REDUCE: (4), (5) imply: % 33.01/6.04 | (6) $false % 33.01/6.04 | % 33.01/6.04 | CLOSE: (6) is inconsistent. % 33.01/6.04 | % 33.01/6.04 End of proof % 33.01/6.04 % SZS output end Proof for theBenchmark % 33.01/6.04 % 33.01/6.04 5433ms %------------------------------------------------------------------------------