%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO198+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 : 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 23:22:11 EDT 2023 % Result : Theorem 22.96s 3.84s % Output : Proof 53.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO198+3 : TPTP v8.1.2. Released v4.0.0. % 0.06/0.13 % 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 21:16:53 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 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.58/0.63 Running up to 7 provers in parallel. % 0.58/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.58/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.58/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.58/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.58/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.58/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.58/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.60/1.19 Prover 4: Preprocessing ... % 3.60/1.19 Prover 1: Preprocessing ... % 3.60/1.22 Prover 5: Preprocessing ... % 3.60/1.22 Prover 6: Preprocessing ... % 3.60/1.22 Prover 3: Preprocessing ... % 3.60/1.22 Prover 0: Preprocessing ... % 3.60/1.22 Prover 2: Preprocessing ... % 6.44/1.64 Prover 5: Proving ... % 6.44/1.64 Prover 2: Proving ... % 7.11/1.71 Prover 6: Constructing countermodel ... % 7.40/1.72 Prover 1: Constructing countermodel ... % 7.40/1.73 Prover 3: Constructing countermodel ... % 7.84/1.87 Prover 3: gave up % 8.55/1.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.55/1.91 Prover 6: gave up % 8.55/1.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.10/1.97 Prover 7: Preprocessing ... % 9.10/1.98 Prover 8: Preprocessing ... % 9.68/2.06 Prover 0: Proving ... % 9.68/2.08 Prover 7: Warning: ignoring some quantifiers % 9.68/2.08 Prover 4: Constructing countermodel ... % 9.68/2.08 Prover 1: gave up % 9.68/2.10 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 9.68/2.11 Prover 7: Constructing countermodel ... % 10.33/2.15 Prover 9: Preprocessing ... % 10.33/2.17 Prover 8: Warning: ignoring some quantifiers % 10.74/2.19 Prover 8: Constructing countermodel ... % 12.25/2.44 Prover 8: gave up % 12.25/2.44 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.25/2.46 Prover 9: Constructing countermodel ... % 13.04/2.51 Prover 10: Preprocessing ... % 13.52/2.57 Prover 10: Warning: ignoring some quantifiers % 13.52/2.58 Prover 10: Constructing countermodel ... % 14.95/2.77 Prover 7: gave up % 14.95/2.79 Prover 10: gave up % 14.95/2.79 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.95/2.79 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 15.30/2.81 Prover 12: Preprocessing ... % 15.30/2.83 Prover 11: Preprocessing ... % 16.21/2.95 Prover 12: Proving ... % 17.64/3.13 Prover 11: Constructing countermodel ... % 22.96/3.84 Prover 9: proved (1737ms) % 22.96/3.84 % 22.96/3.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 22.96/3.84 % 22.96/3.84 Prover 0: stopped % 22.96/3.86 Prover 12: stopped % 22.96/3.86 Prover 5: stopped % 22.96/3.86 Prover 2: stopped % 22.96/3.86 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 22.96/3.86 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 22.96/3.86 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 22.96/3.87 Prover 13: Preprocessing ... % 22.96/3.88 Prover 19: Preprocessing ... % 22.96/3.89 Prover 16: Preprocessing ... % 23.89/3.92 Prover 13: Warning: ignoring some quantifiers % 23.89/3.92 Prover 13: Constructing countermodel ... % 24.22/3.95 Prover 16: Warning: ignoring some quantifiers % 24.22/3.96 Prover 16: Constructing countermodel ... % 24.22/4.03 Prover 19: Warning: ignoring some quantifiers % 24.22/4.03 Prover 19: Constructing countermodel ... % 25.27/4.11 Prover 13: gave up % 25.74/4.16 Prover 19: gave up % 28.26/4.62 Prover 16: gave up % 52.96/9.49 Prover 11: Found proof (size 141) % 52.96/9.49 Prover 11: proved (6700ms) % 52.96/9.49 Prover 4: stopped % 52.96/9.49 % 52.96/9.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 52.96/9.49 % 52.96/9.51 % SZS output start Proof for theBenchmark % 52.96/9.52 Assumptions after simplification: % 52.96/9.52 --------------------------------- % 52.96/9.52 % 52.96/9.52 (a4) % 52.96/9.58 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 52.96/9.58 (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 52.96/9.58 apart_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] % 52.96/9.58 : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 52.96/9.58 incident_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 52.96/9.58 (incident_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] % 52.96/9.58 : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0: $i] : ! [v1: % 52.96/9.58 $i] : ( ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 52.96/9.58 [v2: int] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) % 52.96/9.58 % 52.96/9.58 (apart3) % 52.96/9.58 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 52.96/9.58 % 52.96/9.58 (ceq1) % 52.96/9.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 52.96/9.58 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ % 52.96/9.58 (distinct_points(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 52.96/9.58 int] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : % 52.96/9.58 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 52.96/9.58 (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) % 52.96/9.58 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) & ! [v0: % 52.96/9.58 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 52.96/9.58 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~ % 52.96/9.58 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0) % 52.96/9.58 % 52.96/9.58 (ceq3) % 52.96/9.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 52.96/9.59 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) % 52.96/9.59 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 52.96/9.59 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 52.96/9.59 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 52.96/9.59 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 52.96/9.59 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 52.96/9.59 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ % 52.96/9.59 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 52.96/9.59 convergent_lines(v0, v2) = 0) % 52.96/9.59 % 52.96/9.59 (ci3) % 52.96/9.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 52.96/9.59 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 52.96/9.59 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 52.96/9.59 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 52.96/9.59 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 52.96/9.59 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 52.96/9.59 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 52.96/9.59 % 52.96/9.59 (ci4) % 52.96/9.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 52.96/9.59 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 52.96/9.59 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 52.96/9.59 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 52.96/9.59 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 52.96/9.59 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 52.96/9.59 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 52.96/9.59 % 52.96/9.59 (con) % 52.96/9.60 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 52.96/9.60 int] : ( ~ (v5 = 0) & incident_point_and_line(v4, v1) = v5 & % 52.96/9.60 incident_point_and_line(v3, v2) = 0 & intersection_point(v0, v2) = v4 & % 52.96/9.60 intersection_point(v0, v1) = v3 & convergent_lines(v2, v1) = 0 & % 52.96/9.60 convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0 & $i(v4) & % 52.96/9.60 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 52.96/9.60 % 52.96/9.60 (cu1) % 52.96/9.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 52.96/9.61 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 52.96/9.61 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 52.96/9.61 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 52.96/9.61 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 52.96/9.61 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, % 52.96/9.61 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 52.96/9.61 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, % 52.96/9.61 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ % 52.96/9.61 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 52.96/9.61 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 52.96/9.61 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0, % 52.96/9.61 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 52.96/9.61 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 52.96/9.61 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 52.96/9.61 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 52.96/9.61 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 52.96/9.61 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 52.96/9.61 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 52.96/9.61 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 52.96/9.61 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 52.96/9.61 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 52.96/9.61 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 52.96/9.61 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 52.96/9.61 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 52.96/9.61 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 52.96/9.61 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 52.96/9.61 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 52.96/9.61 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 52.96/9.61 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~ % 52.96/9.61 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 52.96/9.61 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 52.96/9.61 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, % 52.96/9.61 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 52.96/9.61 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, % 52.96/9.61 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 52.96/9.61 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 52.96/9.61 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 52.96/9.61 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1, % 52.96/9.61 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i] % 52.96/9.61 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | % 52.96/9.61 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 52.96/9.61 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = % 52.96/9.61 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 52.96/9.61 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0, % 52.96/9.61 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 52.96/9.61 % 52.96/9.61 (cup1) % 52.96/9.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 52.96/9.62 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 52.96/9.62 (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 52.96/9.62 [v5: int] : ? [v6: int] : ((v6 = 0 & convergent_lines(v1, v2) = 0) | ( ~ % 52.96/9.62 (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0: $i] : ! [v1: $i] : % 52.96/9.62 ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~ % 52.96/9.62 (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | % 52.96/9.62 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ((v6 = 0 & % 52.96/9.62 apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, % 52.96/9.62 v2) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : % 52.96/9.62 ! [v4: int] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ % 52.96/9.62 (convergent_lines(v1, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 52.96/9.62 [v5: int] : ? [v6: int] : ((v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( % 52.96/9.62 ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0: $i] : ! [v1: $i] % 52.96/9.62 : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = % 52.96/9.62 v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 52.96/9.62 | ? [v4: int] : ? [v5: int] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | % 52.96/9.62 (v4 = 0 & apart_point_and_line(v0, v1) = 0))) & ! [v0: $i] : ! [v1: $i] % 52.96/9.62 : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = % 52.96/9.62 v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 52.96/9.62 | ? [v4: int] : ? [v5: int] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | % 52.96/9.62 (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 52.96/9.62 % 52.96/9.62 (function-axioms) % 52.96/9.62 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 52.96/9.62 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 52.96/9.62 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 52.96/9.62 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.96/9.62 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 52.96/9.62 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 52.96/9.62 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 52.96/9.62 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 52.96/9.62 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.96/9.62 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 52.96/9.62 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 52.96/9.62 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 52.96/9.62 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.96/9.62 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 52.96/9.62 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 52.96/9.62 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 52.96/9.62 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 52.96/9.63 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 52.96/9.63 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 52.96/9.63 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 52.96/9.63 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 52.96/9.63 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 52.96/9.63 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 52.96/9.63 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.96/9.63 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 52.96/9.63 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 52.96/9.63 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 52.96/9.63 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 52.96/9.63 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 52.96/9.63 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 52.96/9.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 52.96/9.63 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 52.96/9.63 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 52.96/9.63 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 52.96/9.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 52.96/9.63 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 52.96/9.63 % 52.96/9.63 Further assumptions not needed in the proof: % 52.96/9.63 -------------------------------------------- % 52.96/9.63 a3, a5, apart1, apart2, apart4, apart5, ax1, ax2, ax6, ceq2, ci1, ci2, coipo1, % 52.96/9.63 con1, cotno1, couo1, cp1, cp2, int1, oac1, occu1, ooc1, ooc2, orth1, ouo1, p1, % 52.96/9.63 par1 % 52.96/9.63 % 52.96/9.63 Those formulas are unsatisfiable: % 52.96/9.63 --------------------------------- % 52.96/9.63 % 52.96/9.63 Begin of proof % 52.96/9.63 | % 52.96/9.63 | ALPHA: (ci3) implies: % 52.96/9.63 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 52.96/9.63 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 52.96/9.63 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 52.96/9.63 | & $i(v2))) % 52.96/9.63 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 52.96/9.63 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 52.96/9.63 | (( ~ (v4 = 0) & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 52.96/9.63 | convergent_lines(v0, v1) = v3))) % 52.96/9.63 | % 52.96/9.63 | ALPHA: (ci4) implies: % 52.96/9.63 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 52.96/9.63 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 52.96/9.63 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 52.96/9.63 | & $i(v2))) % 52.96/9.63 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 52.96/9.63 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 52.96/9.63 | (( ~ (v4 = 0) & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 52.96/9.63 | convergent_lines(v0, v1) = v3))) % 52.96/9.63 | % 52.96/9.63 | ALPHA: (cu1) implies: % 53.51/9.63 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 53.51/9.63 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 53.51/9.63 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 53.51/9.63 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 53.51/9.63 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 53.51/9.63 | apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & % 53.51/9.63 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 53.51/9.63 | v1) = v6))) % 53.51/9.63 | % 53.51/9.63 | ALPHA: (ceq1) implies: % 53.51/9.63 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 53.51/9.63 | (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, % 53.51/9.63 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 53.51/9.64 | distinct_points(v0, v2) = 0) % 53.51/9.64 | % 53.51/9.64 | ALPHA: (ceq3) implies: % 53.51/9.64 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 53.51/9.64 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | % 53.51/9.64 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 53.51/9.64 | % 53.51/9.64 | ALPHA: (cup1) implies: % 53.51/9.64 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 53.51/9.64 | (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 53.51/9.64 | (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 53.51/9.64 | $i(v0) | ? [v5: int] : ? [v6: int] : ((v6 = 0 & % 53.51/9.64 | convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, % 53.51/9.64 | v2) = v5))) % 53.51/9.64 | % 53.51/9.64 | ALPHA: (a4) implies: % 53.51/9.64 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (incident_point_and_line(v0, v1) = 0) | % 53.51/9.64 | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 53.51/9.64 | apart_point_and_line(v0, v1) = v2)) % 53.51/9.64 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 53.51/9.64 | (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 53.51/9.64 | apart_point_and_line(v0, v1) = 0) % 53.51/9.64 | % 53.51/9.64 | ALPHA: (function-axioms) implies: % 53.51/9.64 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 53.51/9.64 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 53.51/9.64 | (distinct_points(v3, v2) = v0)) % 53.51/9.64 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 53.51/9.64 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 53.51/9.64 | (convergent_lines(v3, v2) = v0)) % 53.51/9.64 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 53.51/9.64 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 53.51/9.64 | (apart_point_and_line(v3, v2) = v0)) % 53.51/9.64 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 53.51/9.64 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 53.51/9.64 | v0)) % 53.51/9.64 | % 53.51/9.64 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 53.51/9.64 | all_38_3, all_38_4, all_38_5 gives: % 53.51/9.64 | (15) ~ (all_38_0 = 0) & incident_point_and_line(all_38_1, all_38_4) = % 53.51/9.64 | all_38_0 & incident_point_and_line(all_38_2, all_38_3) = 0 & % 53.51/9.64 | intersection_point(all_38_5, all_38_3) = all_38_1 & % 53.51/9.64 | intersection_point(all_38_5, all_38_4) = all_38_2 & % 53.51/9.64 | convergent_lines(all_38_3, all_38_4) = 0 & convergent_lines(all_38_5, % 53.67/9.64 | all_38_3) = 0 & convergent_lines(all_38_5, all_38_4) = 0 & % 53.67/9.64 | $i(all_38_1) & $i(all_38_2) & $i(all_38_3) & $i(all_38_4) & % 53.67/9.64 | $i(all_38_5) % 53.67/9.64 | % 53.67/9.64 | ALPHA: (15) implies: % 53.67/9.64 | (16) ~ (all_38_0 = 0) % 53.67/9.64 | (17) $i(all_38_5) % 53.67/9.64 | (18) $i(all_38_4) % 53.67/9.64 | (19) $i(all_38_3) % 53.67/9.65 | (20) $i(all_38_2) % 53.67/9.65 | (21) $i(all_38_1) % 53.67/9.65 | (22) convergent_lines(all_38_5, all_38_4) = 0 % 53.67/9.65 | (23) convergent_lines(all_38_5, all_38_3) = 0 % 53.67/9.65 | (24) intersection_point(all_38_5, all_38_4) = all_38_2 % 53.67/9.65 | (25) intersection_point(all_38_5, all_38_3) = all_38_1 % 53.67/9.65 | (26) incident_point_and_line(all_38_2, all_38_3) = 0 % 53.67/9.65 | (27) incident_point_and_line(all_38_1, all_38_4) = all_38_0 % 53.67/9.65 | % 53.67/9.65 | GROUND_INST: instantiating (3) with all_38_5, all_38_4, simplifying with (17), % 53.67/9.65 | (18), (22) gives: % 53.67/9.65 | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 53.67/9.65 | intersection_point(all_38_5, all_38_4) = v0 & % 53.67/9.65 | apart_point_and_line(v0, all_38_4) = v1 & $i(v0)) % 53.67/9.65 | % 53.67/9.65 | GROUND_INST: instantiating (1) with all_38_5, all_38_4, simplifying with (17), % 53.67/9.65 | (18), (22) gives: % 53.67/9.65 | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 53.67/9.65 | intersection_point(all_38_5, all_38_4) = v0 & % 53.67/9.65 | apart_point_and_line(v0, all_38_5) = v1 & $i(v0)) % 53.67/9.65 | % 53.67/9.65 | GROUND_INST: instantiating (3) with all_38_5, all_38_3, simplifying with (17), % 53.67/9.65 | (19), (23) gives: % 53.67/9.65 | (30) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 53.67/9.65 | intersection_point(all_38_5, all_38_3) = v0 & % 53.67/9.65 | apart_point_and_line(v0, all_38_3) = v1 & $i(v0)) % 53.67/9.65 | % 53.67/9.65 | GROUND_INST: instantiating (1) with all_38_5, all_38_3, simplifying with (17), % 53.67/9.65 | (19), (23) gives: % 53.67/9.65 | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 53.67/9.65 | intersection_point(all_38_5, all_38_3) = v0 & % 53.67/9.65 | apart_point_and_line(v0, all_38_5) = v1 & $i(v0)) % 53.67/9.65 | % 53.67/9.65 | GROUND_INST: instantiating (4) with all_38_5, all_38_4, all_38_2, simplifying % 53.67/9.65 | with (17), (18), (24) gives: % 53.67/9.65 | (32) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 53.67/9.65 | apart_point_and_line(all_38_2, all_38_4) = v1) | ( ~ (v0 = 0) & % 53.67/9.65 | convergent_lines(all_38_5, all_38_4) = v0)) % 53.67/9.65 | % 53.67/9.65 | GROUND_INST: instantiating (2) with all_38_5, all_38_4, all_38_2, simplifying % 53.67/9.65 | with (17), (18), (24) gives: % 53.67/9.65 | (33) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 53.67/9.65 | apart_point_and_line(all_38_2, all_38_5) = v1) | ( ~ (v0 = 0) & % 53.67/9.65 | convergent_lines(all_38_5, all_38_4) = v0)) % 53.67/9.65 | % 53.67/9.65 | GROUND_INST: instantiating (4) with all_38_5, all_38_3, all_38_1, simplifying % 53.67/9.65 | with (17), (19), (25) gives: % 53.67/9.65 | (34) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 53.67/9.65 | apart_point_and_line(all_38_1, all_38_3) = v1) | ( ~ (v0 = 0) & % 53.67/9.65 | convergent_lines(all_38_5, all_38_3) = v0)) % 53.67/9.65 | % 53.67/9.65 | GROUND_INST: instantiating (2) with all_38_5, all_38_3, all_38_1, simplifying % 53.67/9.65 | with (17), (19), (25) gives: % 53.67/9.65 | (35) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 53.67/9.65 | apart_point_and_line(all_38_1, all_38_5) = v1) | ( ~ (v0 = 0) & % 53.67/9.65 | convergent_lines(all_38_5, all_38_3) = v0)) % 53.67/9.65 | % 53.67/9.65 | GROUND_INST: instantiating (9) with all_38_2, all_38_3, simplifying with (19), % 53.67/9.65 | (20), (26) gives: % 53.67/9.65 | (36) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_2, all_38_3) % 53.67/9.65 | = v0) % 53.67/9.65 | % 53.67/9.65 | GROUND_INST: instantiating (10) with all_38_1, all_38_4, all_38_0, simplifying % 53.67/9.65 | with (18), (21), (27) gives: % 53.67/9.66 | (37) all_38_0 = 0 | apart_point_and_line(all_38_1, all_38_4) = 0 % 53.67/9.66 | % 53.67/9.66 | DELTA: instantiating (36) with fresh symbol all_45_0 gives: % 53.67/9.66 | (38) ~ (all_45_0 = 0) & apart_point_and_line(all_38_2, all_38_3) = % 53.67/9.66 | all_45_0 % 53.67/9.66 | % 53.67/9.66 | ALPHA: (38) implies: % 53.67/9.66 | (39) ~ (all_45_0 = 0) % 53.67/9.66 | (40) apart_point_and_line(all_38_2, all_38_3) = all_45_0 % 53.67/9.66 | % 53.67/9.66 | DELTA: instantiating (30) with fresh symbols all_55_0, all_55_1 gives: % 53.67/9.66 | (41) ~ (all_55_0 = 0) & intersection_point(all_38_5, all_38_3) = all_55_1 % 53.67/9.66 | & apart_point_and_line(all_55_1, all_38_3) = all_55_0 & $i(all_55_1) % 53.67/9.66 | % 53.67/9.66 | ALPHA: (41) implies: % 53.67/9.66 | (42) $i(all_55_1) % 53.67/9.66 | (43) apart_point_and_line(all_55_1, all_38_3) = all_55_0 % 53.67/9.66 | (44) intersection_point(all_38_5, all_38_3) = all_55_1 % 53.67/9.66 | % 53.67/9.66 | DELTA: instantiating (35) with fresh symbols all_57_0, all_57_1 gives: % 53.67/9.66 | (45) ( ~ (all_57_0 = 0) & apart_point_and_line(all_38_1, all_38_5) = % 53.67/9.66 | all_57_0) | ( ~ (all_57_1 = 0) & convergent_lines(all_38_5, % 53.67/9.66 | all_38_3) = all_57_1) % 53.67/9.66 | % 53.67/9.66 | DELTA: instantiating (33) with fresh symbols all_58_0, all_58_1 gives: % 53.67/9.66 | (46) ( ~ (all_58_0 = 0) & apart_point_and_line(all_38_2, all_38_5) = % 53.67/9.66 | all_58_0) | ( ~ (all_58_1 = 0) & convergent_lines(all_38_5, % 53.67/9.66 | all_38_4) = all_58_1) % 53.67/9.66 | % 53.67/9.66 | DELTA: instantiating (34) with fresh symbols all_59_0, all_59_1 gives: % 53.67/9.66 | (47) ( ~ (all_59_0 = 0) & apart_point_and_line(all_38_1, all_38_3) = % 53.67/9.66 | all_59_0) | ( ~ (all_59_1 = 0) & convergent_lines(all_38_5, % 53.67/9.66 | all_38_3) = all_59_1) % 53.67/9.66 | % 53.67/9.66 | DELTA: instantiating (31) with fresh symbols all_60_0, all_60_1 gives: % 53.67/9.66 | (48) ~ (all_60_0 = 0) & intersection_point(all_38_5, all_38_3) = all_60_1 % 53.67/9.66 | & apart_point_and_line(all_60_1, all_38_5) = all_60_0 & $i(all_60_1) % 53.67/9.66 | % 53.67/9.66 | ALPHA: (48) implies: % 53.67/9.66 | (49) ~ (all_60_0 = 0) % 53.67/9.66 | (50) apart_point_and_line(all_60_1, all_38_5) = all_60_0 % 53.67/9.66 | (51) intersection_point(all_38_5, all_38_3) = all_60_1 % 53.67/9.66 | % 53.67/9.66 | DELTA: instantiating (29) with fresh symbols all_62_0, all_62_1 gives: % 53.67/9.66 | (52) ~ (all_62_0 = 0) & intersection_point(all_38_5, all_38_4) = all_62_1 % 53.67/9.66 | & apart_point_and_line(all_62_1, all_38_5) = all_62_0 & $i(all_62_1) % 53.67/9.66 | % 53.67/9.66 | ALPHA: (52) implies: % 53.67/9.66 | (53) ~ (all_62_0 = 0) % 53.67/9.66 | (54) $i(all_62_1) % 53.67/9.66 | (55) apart_point_and_line(all_62_1, all_38_5) = all_62_0 % 53.67/9.66 | (56) intersection_point(all_38_5, all_38_4) = all_62_1 % 53.67/9.66 | % 53.67/9.66 | DELTA: instantiating (28) with fresh symbols all_66_0, all_66_1 gives: % 53.67/9.66 | (57) ~ (all_66_0 = 0) & intersection_point(all_38_5, all_38_4) = all_66_1 % 53.67/9.66 | & apart_point_and_line(all_66_1, all_38_4) = all_66_0 & $i(all_66_1) % 53.67/9.66 | % 53.67/9.66 | ALPHA: (57) implies: % 53.67/9.66 | (58) apart_point_and_line(all_66_1, all_38_4) = all_66_0 % 53.67/9.66 | (59) intersection_point(all_38_5, all_38_4) = all_66_1 % 53.67/9.66 | % 53.67/9.66 | DELTA: instantiating (32) with fresh symbols all_68_0, all_68_1 gives: % 53.67/9.66 | (60) ( ~ (all_68_0 = 0) & apart_point_and_line(all_38_2, all_38_4) = % 53.67/9.66 | all_68_0) | ( ~ (all_68_1 = 0) & convergent_lines(all_38_5, % 53.67/9.66 | all_38_4) = all_68_1) % 53.67/9.66 | % 53.67/9.66 | BETA: splitting (47) gives: % 53.67/9.66 | % 53.67/9.66 | Case 1: % 53.67/9.66 | | % 53.67/9.66 | | (61) ~ (all_59_0 = 0) & apart_point_and_line(all_38_1, all_38_3) = % 53.67/9.66 | | all_59_0 % 53.67/9.66 | | % 53.67/9.66 | | ALPHA: (61) implies: % 53.67/9.66 | | (62) ~ (all_59_0 = 0) % 53.67/9.66 | | (63) apart_point_and_line(all_38_1, all_38_3) = all_59_0 % 53.67/9.66 | | % 53.67/9.66 | | BETA: splitting (37) gives: % 53.67/9.66 | | % 53.67/9.66 | | Case 1: % 53.67/9.66 | | | % 53.67/9.66 | | | (64) apart_point_and_line(all_38_1, all_38_4) = 0 % 53.67/9.66 | | | % 53.67/9.66 | | | BETA: splitting (45) gives: % 53.67/9.66 | | | % 53.67/9.66 | | | Case 1: % 53.67/9.66 | | | | % 53.67/9.66 | | | | (65) ~ (all_57_0 = 0) & apart_point_and_line(all_38_1, all_38_5) = % 53.67/9.66 | | | | all_57_0 % 53.67/9.66 | | | | % 53.67/9.66 | | | | ALPHA: (65) implies: % 53.67/9.66 | | | | (66) apart_point_and_line(all_38_1, all_38_5) = all_57_0 % 53.67/9.66 | | | | % 53.67/9.66 | | | | BETA: splitting (60) gives: % 53.67/9.66 | | | | % 53.67/9.66 | | | | Case 1: % 53.67/9.66 | | | | | % 53.67/9.66 | | | | | (67) ~ (all_68_0 = 0) & apart_point_and_line(all_38_2, all_38_4) = % 53.67/9.66 | | | | | all_68_0 % 53.67/9.66 | | | | | % 53.67/9.66 | | | | | ALPHA: (67) implies: % 53.67/9.66 | | | | | (68) ~ (all_68_0 = 0) % 53.67/9.66 | | | | | (69) apart_point_and_line(all_38_2, all_38_4) = all_68_0 % 53.67/9.66 | | | | | % 53.67/9.66 | | | | | BETA: splitting (46) gives: % 53.67/9.66 | | | | | % 53.67/9.66 | | | | | Case 1: % 53.67/9.66 | | | | | | % 53.67/9.66 | | | | | | (70) ~ (all_58_0 = 0) & apart_point_and_line(all_38_2, all_38_5) % 53.67/9.67 | | | | | | = all_58_0 % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | ALPHA: (70) implies: % 53.67/9.67 | | | | | | (71) apart_point_and_line(all_38_2, all_38_5) = all_58_0 % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | GROUND_INST: instantiating (14) with all_38_2, all_66_1, all_38_4, % 53.67/9.67 | | | | | | all_38_5, simplifying with (24), (59) gives: % 53.67/9.67 | | | | | | (72) all_66_1 = all_38_2 % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | GROUND_INST: instantiating (14) with all_62_1, all_66_1, all_38_4, % 53.67/9.67 | | | | | | all_38_5, simplifying with (56), (59) gives: % 53.67/9.67 | | | | | | (73) all_66_1 = all_62_1 % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | GROUND_INST: instantiating (14) with all_38_1, all_60_1, all_38_3, % 53.67/9.67 | | | | | | all_38_5, simplifying with (25), (51) gives: % 53.67/9.67 | | | | | | (74) all_60_1 = all_38_1 % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | GROUND_INST: instantiating (14) with all_55_1, all_60_1, all_38_3, % 53.67/9.67 | | | | | | all_38_5, simplifying with (44), (51) gives: % 53.67/9.67 | | | | | | (75) all_60_1 = all_55_1 % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | COMBINE_EQS: (72), (73) imply: % 53.67/9.67 | | | | | | (76) all_62_1 = all_38_2 % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | COMBINE_EQS: (74), (75) imply: % 53.67/9.67 | | | | | | (77) all_55_1 = all_38_1 % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | SIMP: (77) implies: % 53.67/9.67 | | | | | | (78) all_55_1 = all_38_1 % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | REDUCE: (58), (72) imply: % 53.67/9.67 | | | | | | (79) apart_point_and_line(all_38_2, all_38_4) = all_66_0 % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | REDUCE: (55), (76) imply: % 53.67/9.67 | | | | | | (80) apart_point_and_line(all_38_2, all_38_5) = all_62_0 % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | REDUCE: (50), (74) imply: % 53.67/9.67 | | | | | | (81) apart_point_and_line(all_38_1, all_38_5) = all_60_0 % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | REDUCE: (43), (78) imply: % 53.67/9.67 | | | | | | (82) apart_point_and_line(all_38_1, all_38_3) = all_55_0 % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | GROUND_INST: instantiating (13) with all_58_0, all_62_0, all_38_5, % 53.67/9.67 | | | | | | all_38_2, simplifying with (71), (80) gives: % 53.67/9.67 | | | | | | (83) all_62_0 = all_58_0 % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | GROUND_INST: instantiating (13) with all_68_0, all_66_0, all_38_4, % 53.67/9.67 | | | | | | all_38_2, simplifying with (69), (79) gives: % 53.67/9.67 | | | | | | (84) all_68_0 = all_66_0 % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | GROUND_INST: instantiating (13) with all_57_0, all_60_0, all_38_5, % 53.67/9.67 | | | | | | all_38_1, simplifying with (66), (81) gives: % 53.67/9.67 | | | | | | (85) all_60_0 = all_57_0 % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | GROUND_INST: instantiating (13) with all_59_0, all_55_0, all_38_3, % 53.67/9.67 | | | | | | all_38_1, simplifying with (63), (82) gives: % 53.67/9.67 | | | | | | (86) all_59_0 = all_55_0 % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | REDUCE: (68), (84) imply: % 53.67/9.67 | | | | | | (87) ~ (all_66_0 = 0) % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | REDUCE: (53), (83) imply: % 53.67/9.67 | | | | | | (88) ~ (all_58_0 = 0) % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | REDUCE: (49), (85) imply: % 53.67/9.67 | | | | | | (89) ~ (all_57_0 = 0) % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | REDUCE: (62), (86) imply: % 53.67/9.67 | | | | | | (90) ~ (all_55_0 = 0) % 53.67/9.67 | | | | | | % 53.67/9.67 | | | | | | GROUND_INST: instantiating (8) with all_38_2, all_38_5, all_38_4, % 53.67/9.67 | | | | | | all_58_0, all_66_0, simplifying with (17), (18), (20), % 53.67/9.67 | | | | | | (71), (79) gives: % 53.81/9.67 | | | | | | (91) all_66_0 = 0 | all_58_0 = 0 | ? [v0: int] : ? [v1: int] : % 53.81/9.67 | | | | | | ((v1 = 0 & convergent_lines(all_38_5, all_38_4) = 0) | ( ~ % 53.81/9.67 | | | | | | (v0 = 0) & distinct_lines(all_38_5, all_38_4) = v0)) % 53.81/9.67 | | | | | | % 53.81/9.67 | | | | | | GROUND_INST: instantiating (6) with all_38_1, all_38_4, all_38_2, % 53.81/9.67 | | | | | | all_66_0, simplifying with (18), (20), (21), (64), (79) % 53.81/9.67 | | | | | | gives: % 53.81/9.67 | | | | | | (92) all_66_0 = 0 | distinct_points(all_38_1, all_38_2) = 0 % 53.81/9.67 | | | | | | % 53.81/9.67 | | | | | | GROUND_INST: instantiating (5) with all_38_1, all_38_2, all_38_3, % 53.81/9.67 | | | | | | all_38_5, all_55_0, all_58_0, simplifying with (17), % 53.81/9.67 | | | | | | (19), (20), (21), (71), (82) gives: % 53.81/9.67 | | | | | | (93) all_58_0 = 0 | all_55_0 = 0 | ? [v0: int] : ? [v1: int] : % 53.81/9.67 | | | | | | ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 53.81/9.67 | | | | | | apart_point_and_line(all_38_2, all_38_3) = 0) | (v2 = 0 % 53.81/9.67 | | | | | | & apart_point_and_line(all_38_1, all_38_5) = 0) | ( ~ % 53.81/9.67 | | | | | | (v1 = 0) & distinct_lines(all_38_3, all_38_5) = v1) | ( % 53.81/9.67 | | | | | | ~ (v0 = 0) & distinct_points(all_38_1, all_38_2) = v0)) % 53.81/9.67 | | | | | | % 53.81/9.67 | | | | | | BETA: splitting (93) gives: % 53.81/9.67 | | | | | | % 53.81/9.67 | | | | | | Case 1: % 53.81/9.67 | | | | | | | % 53.81/9.68 | | | | | | | (94) all_58_0 = 0 % 53.81/9.68 | | | | | | | % 53.81/9.68 | | | | | | | REDUCE: (88), (94) imply: % 53.81/9.68 | | | | | | | (95) $false % 53.81/9.68 | | | | | | | % 53.81/9.68 | | | | | | | CLOSE: (95) is inconsistent. % 53.81/9.68 | | | | | | | % 53.81/9.68 | | | | | | Case 2: % 53.81/9.68 | | | | | | | % 53.81/9.68 | | | | | | | (96) all_55_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] % 53.81/9.68 | | | | | | | : ? [v3: int] : ((v3 = 0 & apart_point_and_line(all_38_2, % 53.81/9.68 | | | | | | | all_38_3) = 0) | (v2 = 0 & % 53.81/9.68 | | | | | | | apart_point_and_line(all_38_1, all_38_5) = 0) | ( ~ % 53.81/9.68 | | | | | | | (v1 = 0) & distinct_lines(all_38_3, all_38_5) = v1) | % 53.81/9.68 | | | | | | | ( ~ (v0 = 0) & distinct_points(all_38_1, all_38_2) = % 53.81/9.68 | | | | | | | v0)) % 53.81/9.68 | | | | | | | % 53.81/9.68 | | | | | | | BETA: splitting (92) gives: % 53.81/9.68 | | | | | | | % 53.81/9.68 | | | | | | | Case 1: % 53.81/9.68 | | | | | | | | % 53.81/9.68 | | | | | | | | (97) distinct_points(all_38_1, all_38_2) = 0 % 53.81/9.68 | | | | | | | | % 53.81/9.68 | | | | | | | | BETA: splitting (96) gives: % 53.81/9.68 | | | | | | | | % 53.81/9.68 | | | | | | | | Case 1: % 53.81/9.68 | | | | | | | | | % 53.81/9.68 | | | | | | | | | (98) all_55_0 = 0 % 53.81/9.68 | | | | | | | | | % 53.81/9.68 | | | | | | | | | REDUCE: (90), (98) imply: % 53.81/9.68 | | | | | | | | | (99) $false % 53.81/9.68 | | | | | | | | | % 53.81/9.68 | | | | | | | | | CLOSE: (99) is inconsistent. % 53.81/9.68 | | | | | | | | | % 53.81/9.68 | | | | | | | | Case 2: % 53.81/9.68 | | | | | | | | | % 53.81/9.68 | | | | | | | | | (100) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 53.81/9.68 | | | | | | | | | int] : ((v3 = 0 & apart_point_and_line(all_38_2, % 53.81/9.68 | | | | | | | | | all_38_3) = 0) | (v2 = 0 & % 53.81/9.68 | | | | | | | | | apart_point_and_line(all_38_1, all_38_5) = 0) | ( % 53.81/9.68 | | | | | | | | | ~ (v1 = 0) & distinct_lines(all_38_3, all_38_5) = % 53.81/9.68 | | | | | | | | | v1) | ( ~ (v0 = 0) & distinct_points(all_38_1, % 53.81/9.68 | | | | | | | | | all_38_2) = v0)) % 53.81/9.68 | | | | | | | | | % 53.81/9.68 | | | | | | | | | DELTA: instantiating (100) with fresh symbols all_581_0, % 53.81/9.68 | | | | | | | | | all_581_1, all_581_2, all_581_3 gives: % 53.81/9.68 | | | | | | | | | (101) (all_581_0 = 0 & apart_point_and_line(all_38_2, % 53.81/9.68 | | | | | | | | | all_38_3) = 0) | (all_581_1 = 0 & % 53.81/9.68 | | | | | | | | | apart_point_and_line(all_38_1, all_38_5) = 0) | ( ~ % 53.81/9.68 | | | | | | | | | (all_581_2 = 0) & distinct_lines(all_38_3, % 53.81/9.68 | | | | | | | | | all_38_5) = all_581_2) | ( ~ (all_581_3 = 0) & % 53.81/9.68 | | | | | | | | | distinct_points(all_38_1, all_38_2) = all_581_3) % 53.81/9.68 | | | | | | | | | % 53.81/9.68 | | | | | | | | | BETA: splitting (101) gives: % 53.81/9.68 | | | | | | | | | % 53.81/9.68 | | | | | | | | | Case 1: % 53.81/9.68 | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | (102) (all_581_0 = 0 & apart_point_and_line(all_38_2, % 53.81/9.68 | | | | | | | | | | all_38_3) = 0) | (all_581_1 = 0 & % 53.81/9.68 | | | | | | | | | | apart_point_and_line(all_38_1, all_38_5) = 0) % 53.81/9.68 | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | BETA: splitting (102) gives: % 53.81/9.68 | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | Case 1: % 53.81/9.68 | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | (103) all_581_0 = 0 & apart_point_and_line(all_38_2, % 53.81/9.68 | | | | | | | | | | | all_38_3) = 0 % 53.81/9.68 | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | ALPHA: (103) implies: % 53.81/9.68 | | | | | | | | | | | (104) apart_point_and_line(all_38_2, all_38_3) = 0 % 53.81/9.68 | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | GROUND_INST: instantiating (13) with all_45_0, 0, all_38_3, % 53.81/9.68 | | | | | | | | | | | all_38_2, simplifying with (40), (104) gives: % 53.81/9.68 | | | | | | | | | | | (105) all_45_0 = 0 % 53.81/9.68 | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | REDUCE: (39), (105) imply: % 53.81/9.68 | | | | | | | | | | | (106) $false % 53.81/9.68 | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | CLOSE: (106) is inconsistent. % 53.81/9.68 | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | Case 2: % 53.81/9.68 | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | (107) all_581_1 = 0 & apart_point_and_line(all_38_1, % 53.81/9.68 | | | | | | | | | | | all_38_5) = 0 % 53.81/9.68 | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | ALPHA: (107) implies: % 53.81/9.68 | | | | | | | | | | | (108) apart_point_and_line(all_38_1, all_38_5) = 0 % 53.81/9.68 | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | GROUND_INST: instantiating (13) with all_57_0, 0, all_38_5, % 53.81/9.68 | | | | | | | | | | | all_38_1, simplifying with (66), (108) gives: % 53.81/9.68 | | | | | | | | | | | (109) all_57_0 = 0 % 53.81/9.68 | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | REDUCE: (89), (109) imply: % 53.81/9.68 | | | | | | | | | | | (110) $false % 53.81/9.68 | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | CLOSE: (110) is inconsistent. % 53.81/9.68 | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | End of split % 53.81/9.68 | | | | | | | | | | % 53.81/9.68 | | | | | | | | | Case 2: % 53.81/9.68 | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | (111) ( ~ (all_581_2 = 0) & distinct_lines(all_38_3, % 53.81/9.68 | | | | | | | | | | all_38_5) = all_581_2) | ( ~ (all_581_3 = 0) & % 53.81/9.68 | | | | | | | | | | distinct_points(all_38_1, all_38_2) = all_581_3) % 53.81/9.68 | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | BETA: splitting (111) gives: % 53.81/9.68 | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | Case 1: % 53.81/9.68 | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | (112) ~ (all_581_2 = 0) & distinct_lines(all_38_3, % 53.81/9.68 | | | | | | | | | | | all_38_5) = all_581_2 % 53.81/9.68 | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | ALPHA: (112) implies: % 53.81/9.68 | | | | | | | | | | | (113) ~ (all_581_2 = 0) % 53.81/9.68 | | | | | | | | | | | (114) distinct_lines(all_38_3, all_38_5) = all_581_2 % 53.81/9.68 | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | BETA: splitting (91) gives: % 53.81/9.68 | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | Case 1: % 53.81/9.68 | | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | | (115) all_66_0 = 0 % 53.81/9.68 | | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | | REDUCE: (87), (115) imply: % 53.81/9.68 | | | | | | | | | | | | (116) $false % 53.81/9.68 | | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | | CLOSE: (116) is inconsistent. % 53.81/9.68 | | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | Case 2: % 53.81/9.68 | | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | | (117) all_58_0 = 0 | ? [v0: int] : ? [v1: int] : ((v1 % 53.81/9.68 | | | | | | | | | | | | = 0 & convergent_lines(all_38_5, all_38_4) = % 53.81/9.68 | | | | | | | | | | | | 0) | ( ~ (v0 = 0) & distinct_lines(all_38_5, % 53.81/9.68 | | | | | | | | | | | | all_38_4) = v0)) % 53.81/9.68 | | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | | BETA: splitting (117) gives: % 53.81/9.68 | | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | | Case 1: % 53.81/9.68 | | | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | | | (118) all_58_0 = 0 % 53.81/9.68 | | | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | | | REDUCE: (88), (118) imply: % 53.81/9.68 | | | | | | | | | | | | | (119) $false % 53.81/9.68 | | | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | | | CLOSE: (119) is inconsistent. % 53.81/9.68 | | | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | | Case 2: % 53.81/9.68 | | | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_38_5, all_38_3, % 53.81/9.68 | | | | | | | | | | | | | all_38_5, all_581_2, simplifying with (17), (19), % 53.81/9.68 | | | | | | | | | | | | | (23), (114) gives: % 53.81/9.68 | | | | | | | | | | | | | (120) all_581_2 = 0 | convergent_lines(all_38_5, % 53.81/9.68 | | | | | | | | | | | | | all_38_5) = 0 % 53.81/9.68 | | | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | | | BETA: splitting (120) gives: % 53.81/9.68 | | | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | | | Case 1: % 53.81/9.68 | | | | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | | | | (121) convergent_lines(all_38_5, all_38_5) = 0 % 53.81/9.68 | | | | | | | | | | | | | | % 53.81/9.68 | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_38_5, simplifying % 53.81/9.68 | | | | | | | | | | | | | | with (17), (121) gives: % 53.81/9.69 | | | | | | | | | | | | | | (122) $false % 53.81/9.69 | | | | | | | | | | | | | | % 53.81/9.69 | | | | | | | | | | | | | | CLOSE: (122) is inconsistent. % 53.81/9.69 | | | | | | | | | | | | | | % 53.81/9.69 | | | | | | | | | | | | | Case 2: % 53.81/9.69 | | | | | | | | | | | | | | % 53.81/9.69 | | | | | | | | | | | | | | (123) all_581_2 = 0 % 53.81/9.69 | | | | | | | | | | | | | | % 53.81/9.69 | | | | | | | | | | | | | | REDUCE: (113), (123) imply: % 53.81/9.69 | | | | | | | | | | | | | | (124) $false % 53.81/9.69 | | | | | | | | | | | | | | % 53.81/9.69 | | | | | | | | | | | | | | CLOSE: (124) is inconsistent. % 53.81/9.69 | | | | | | | | | | | | | | % 53.81/9.69 | | | | | | | | | | | | | End of split % 53.81/9.69 | | | | | | | | | | | | | % 53.81/9.69 | | | | | | | | | | | | End of split % 53.81/9.69 | | | | | | | | | | | | % 53.81/9.69 | | | | | | | | | | | End of split % 53.81/9.69 | | | | | | | | | | | % 53.81/9.69 | | | | | | | | | | Case 2: % 53.81/9.69 | | | | | | | | | | | % 53.81/9.69 | | | | | | | | | | | (125) ~ (all_581_3 = 0) & distinct_points(all_38_1, % 53.81/9.69 | | | | | | | | | | | all_38_2) = all_581_3 % 53.81/9.69 | | | | | | | | | | | % 53.81/9.69 | | | | | | | | | | | ALPHA: (125) implies: % 53.81/9.69 | | | | | | | | | | | (126) ~ (all_581_3 = 0) % 53.81/9.69 | | | | | | | | | | | (127) distinct_points(all_38_1, all_38_2) = all_581_3 % 53.81/9.69 | | | | | | | | | | | % 53.81/9.69 | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_581_3, all_38_2, % 53.81/9.69 | | | | | | | | | | | all_38_1, simplifying with (97), (127) gives: % 53.81/9.69 | | | | | | | | | | | (128) all_581_3 = 0 % 53.81/9.69 | | | | | | | | | | | % 53.81/9.69 | | | | | | | | | | | REDUCE: (126), (128) imply: % 53.81/9.69 | | | | | | | | | | | (129) $false % 53.81/9.69 | | | | | | | | | | | % 53.81/9.69 | | | | | | | | | | | CLOSE: (129) is inconsistent. % 53.81/9.69 | | | | | | | | | | | % 53.81/9.69 | | | | | | | | | | End of split % 53.81/9.69 | | | | | | | | | | % 53.81/9.69 | | | | | | | | | End of split % 53.81/9.69 | | | | | | | | | % 53.81/9.69 | | | | | | | | End of split % 53.81/9.69 | | | | | | | | % 53.81/9.69 | | | | | | | Case 2: % 53.81/9.69 | | | | | | | | % 53.81/9.69 | | | | | | | | (130) all_66_0 = 0 % 53.81/9.69 | | | | | | | | % 53.81/9.69 | | | | | | | | REDUCE: (87), (130) imply: % 53.81/9.69 | | | | | | | | (131) $false % 53.81/9.69 | | | | | | | | % 53.81/9.69 | | | | | | | | CLOSE: (131) is inconsistent. % 53.81/9.69 | | | | | | | | % 53.81/9.69 | | | | | | | End of split % 53.81/9.69 | | | | | | | % 53.81/9.69 | | | | | | End of split % 53.81/9.69 | | | | | | % 53.81/9.69 | | | | | Case 2: % 53.81/9.69 | | | | | | % 53.81/9.69 | | | | | | (132) ~ (all_58_1 = 0) & convergent_lines(all_38_5, all_38_4) = % 53.81/9.69 | | | | | | all_58_1 % 53.81/9.69 | | | | | | % 53.81/9.69 | | | | | | ALPHA: (132) implies: % 53.81/9.69 | | | | | | (133) ~ (all_58_1 = 0) % 53.81/9.69 | | | | | | (134) convergent_lines(all_38_5, all_38_4) = all_58_1 % 53.81/9.69 | | | | | | % 53.81/9.69 | | | | | | GROUND_INST: instantiating (12) with 0, all_58_1, all_38_4, % 53.81/9.69 | | | | | | all_38_5, simplifying with (22), (134) gives: % 53.81/9.69 | | | | | | (135) all_58_1 = 0 % 53.81/9.69 | | | | | | % 53.81/9.69 | | | | | | REDUCE: (133), (135) imply: % 53.81/9.69 | | | | | | (136) $false % 53.81/9.69 | | | | | | % 53.81/9.69 | | | | | | CLOSE: (136) is inconsistent. % 53.81/9.69 | | | | | | % 53.81/9.69 | | | | | End of split % 53.81/9.69 | | | | | % 53.81/9.69 | | | | Case 2: % 53.81/9.69 | | | | | % 53.81/9.69 | | | | | (137) ~ (all_68_1 = 0) & convergent_lines(all_38_5, all_38_4) = % 53.81/9.69 | | | | | all_68_1 % 53.81/9.69 | | | | | % 53.81/9.69 | | | | | ALPHA: (137) implies: % 53.81/9.69 | | | | | (138) ~ (all_68_1 = 0) % 53.81/9.69 | | | | | (139) convergent_lines(all_38_5, all_38_4) = all_68_1 % 53.81/9.69 | | | | | % 53.81/9.69 | | | | | GROUND_INST: instantiating (12) with 0, all_68_1, all_38_4, all_38_5, % 53.81/9.69 | | | | | simplifying with (22), (139) gives: % 53.81/9.69 | | | | | (140) all_68_1 = 0 % 53.81/9.69 | | | | | % 53.81/9.69 | | | | | REDUCE: (138), (140) imply: % 53.81/9.69 | | | | | (141) $false % 53.81/9.69 | | | | | % 53.81/9.69 | | | | | CLOSE: (141) is inconsistent. % 53.81/9.69 | | | | | % 53.81/9.69 | | | | End of split % 53.81/9.69 | | | | % 53.81/9.69 | | | Case 2: % 53.81/9.69 | | | | % 53.81/9.69 | | | | (142) ~ (all_57_1 = 0) & convergent_lines(all_38_5, all_38_3) = % 53.81/9.69 | | | | all_57_1 % 53.81/9.69 | | | | % 53.81/9.69 | | | | ALPHA: (142) implies: % 53.81/9.69 | | | | (143) ~ (all_57_1 = 0) % 53.81/9.69 | | | | (144) convergent_lines(all_38_5, all_38_3) = all_57_1 % 53.81/9.69 | | | | % 53.81/9.69 | | | | GROUND_INST: instantiating (12) with 0, all_57_1, all_38_3, all_38_5, % 53.81/9.69 | | | | simplifying with (23), (144) gives: % 53.81/9.69 | | | | (145) all_57_1 = 0 % 53.81/9.69 | | | | % 53.81/9.69 | | | | REDUCE: (143), (145) imply: % 53.81/9.69 | | | | (146) $false % 53.81/9.69 | | | | % 53.81/9.69 | | | | CLOSE: (146) is inconsistent. % 53.81/9.69 | | | | % 53.81/9.69 | | | End of split % 53.81/9.69 | | | % 53.81/9.69 | | Case 2: % 53.81/9.69 | | | % 53.81/9.69 | | | (147) all_38_0 = 0 % 53.81/9.69 | | | % 53.81/9.69 | | | REDUCE: (16), (147) imply: % 53.81/9.69 | | | (148) $false % 53.81/9.69 | | | % 53.81/9.69 | | | CLOSE: (148) is inconsistent. % 53.81/9.69 | | | % 53.81/9.69 | | End of split % 53.81/9.69 | | % 53.81/9.69 | Case 2: % 53.81/9.69 | | % 53.81/9.69 | | (149) ~ (all_59_1 = 0) & convergent_lines(all_38_5, all_38_3) = all_59_1 % 53.81/9.69 | | % 53.81/9.69 | | ALPHA: (149) implies: % 53.81/9.69 | | (150) ~ (all_59_1 = 0) % 53.81/9.69 | | (151) convergent_lines(all_38_5, all_38_3) = all_59_1 % 53.81/9.69 | | % 53.81/9.69 | | GROUND_INST: instantiating (12) with 0, all_59_1, all_38_3, all_38_5, % 53.81/9.69 | | simplifying with (23), (151) gives: % 53.81/9.69 | | (152) all_59_1 = 0 % 53.81/9.69 | | % 53.81/9.69 | | REDUCE: (150), (152) imply: % 53.81/9.69 | | (153) $false % 53.81/9.69 | | % 53.81/9.69 | | CLOSE: (153) is inconsistent. % 53.81/9.69 | | % 53.81/9.69 | End of split % 53.81/9.69 | % 53.81/9.69 End of proof % 53.81/9.69 % SZS output end Proof for theBenchmark % 53.81/9.69 % 53.81/9.69 9076ms %------------------------------------------------------------------------------