%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO198+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 : n021.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 15.05s 2.74s % Output : Proof 22.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GEO198+1 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n021.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Wed Aug 30 00:11:30 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.63/0.63 Running up to 7 provers in parallel. % 0.63/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.63/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.63/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.63/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.63/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.63/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.63/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.60/1.05 Prover 4: Preprocessing ... % 2.60/1.05 Prover 1: Preprocessing ... % 3.03/1.09 Prover 0: Preprocessing ... % 3.03/1.09 Prover 5: Preprocessing ... % 3.03/1.09 Prover 3: Preprocessing ... % 3.03/1.09 Prover 6: Preprocessing ... % 3.03/1.09 Prover 2: Preprocessing ... % 4.55/1.36 Prover 2: Proving ... % 4.55/1.36 Prover 6: Constructing countermodel ... % 4.55/1.36 Prover 5: Proving ... % 4.55/1.37 Prover 1: Constructing countermodel ... % 4.55/1.39 Prover 3: Constructing countermodel ... % 5.24/1.49 Prover 0: Proving ... % 5.24/1.49 Prover 1: gave up % 5.24/1.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.92/1.49 Prover 4: Constructing countermodel ... % 5.92/1.50 Prover 3: gave up % 5.92/1.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.92/1.53 Prover 7: Preprocessing ... % 5.92/1.54 Prover 8: Preprocessing ... % 5.92/1.54 Prover 6: gave up % 5.92/1.55 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.92/1.58 Prover 7: Warning: ignoring some quantifiers % 5.92/1.58 Prover 9: Preprocessing ... % 6.66/1.59 Prover 7: Constructing countermodel ... % 6.82/1.63 Prover 8: Warning: ignoring some quantifiers % 6.82/1.64 Prover 8: Constructing countermodel ... % 7.52/1.71 Prover 8: gave up % 7.52/1.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.52/1.74 Prover 10: Preprocessing ... % 7.52/1.77 Prover 9: Constructing countermodel ... % 8.19/1.79 Prover 10: Warning: ignoring some quantifiers % 8.19/1.79 Prover 10: Constructing countermodel ... % 8.19/1.81 Prover 7: gave up % 8.19/1.81 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.19/1.84 Prover 11: Preprocessing ... % 8.19/1.88 Prover 10: gave up % 8.88/1.89 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 8.88/1.96 Prover 12: Preprocessing ... % 9.62/2.04 Prover 11: Constructing countermodel ... % 9.62/2.07 Prover 12: Proving ... % 15.05/2.74 Prover 9: proved (1193ms) % 15.05/2.74 % 15.05/2.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.05/2.74 % 15.05/2.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.05/2.75 Prover 2: stopped % 15.05/2.76 Prover 12: stopped % 15.05/2.76 Prover 5: stopped % 15.05/2.76 Prover 0: stopped % 15.05/2.76 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 15.05/2.76 Prover 13: Preprocessing ... % 15.05/2.76 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 15.05/2.77 Prover 19: Preprocessing ... % 15.05/2.78 Prover 16: Preprocessing ... % 15.05/2.78 Prover 13: Warning: ignoring some quantifiers % 15.05/2.79 Prover 13: Constructing countermodel ... % 15.05/2.80 Prover 16: Warning: ignoring some quantifiers % 15.05/2.80 Prover 16: Constructing countermodel ... % 15.05/2.82 Prover 19: Warning: ignoring some quantifiers % 15.81/2.83 Prover 19: Constructing countermodel ... % 15.81/2.87 Prover 19: gave up % 16.35/2.91 Prover 13: gave up % 17.15/3.10 Prover 16: gave up % 21.02/3.79 Prover 4: Found proof (size 180) % 21.02/3.79 Prover 4: proved (3142ms) % 21.02/3.79 Prover 11: stopped % 21.02/3.79 % 21.02/3.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 21.02/3.79 % 21.02/3.81 % SZS output start Proof for theBenchmark % 21.02/3.81 Assumptions after simplification: % 21.02/3.81 --------------------------------- % 21.02/3.81 % 21.02/3.81 (apart3) % 21.50/3.85 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 21.50/3.85 % 21.50/3.85 (ceq1) % 21.50/3.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 21.50/3.85 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ % 21.50/3.85 (distinct_points(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 21.50/3.85 int] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : % 21.50/3.85 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 21.50/3.85 (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) % 21.50/3.85 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) & ! [v0: % 21.50/3.85 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 21.50/3.85 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~ % 21.50/3.85 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0) % 21.50/3.85 % 21.50/3.85 (ceq3) % 21.50/3.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 21.50/3.86 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) % 21.50/3.86 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 21.50/3.86 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 21.50/3.86 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 21.50/3.86 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.50/3.86 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 21.50/3.86 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ % 21.50/3.86 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.50/3.86 convergent_lines(v0, v2) = 0) % 21.50/3.86 % 21.50/3.86 (ci3) % 21.50/3.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 21.50/3.86 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 21.50/3.86 (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 % 21.50/3.87 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 21.50/3.87 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 21.50/3.87 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 21.50/3.87 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 21.50/3.87 % 21.50/3.87 (ci4) % 21.50/3.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 21.50/3.87 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 21.50/3.87 (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 % 21.50/3.87 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 21.50/3.87 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 21.50/3.87 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 21.50/3.87 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 21.50/3.87 % 21.50/3.87 (con) % 21.50/3.87 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: % 21.50/3.87 $i] : ( ~ (v4 = 0) & intersection_point(v0, v2) = v5 & % 21.50/3.87 intersection_point(v0, v1) = v3 & apart_point_and_line(v5, v1) = 0 & % 21.50/3.87 apart_point_and_line(v3, v2) = v4 & convergent_lines(v2, v1) = 0 & % 21.50/3.87 convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0 & $i(v5) & % 21.50/3.87 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 21.50/3.87 % 21.50/3.87 (cu1) % 21.50/3.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 21.50/3.88 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 21.50/3.88 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 21.50/3.88 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 21.50/3.88 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, % 21.50/3.89 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 21.50/3.89 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 21.50/3.89 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 21.50/3.89 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 21.50/3.89 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 21.50/3.89 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 21.50/3.89 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 % 21.50/3.89 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 21.50/3.89 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 21.50/3.89 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 21.50/3.89 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 21.50/3.89 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 21.50/3.89 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 21.50/3.89 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = % 21.50/3.89 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 21.50/3.89 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = % 21.50/3.89 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 21.50/3.89 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 21.50/3.89 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = % 21.50/3.89 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 % 21.50/3.89 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : % 21.50/3.89 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 21.50/3.89 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 21.50/3.89 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 21.50/3.89 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 21.50/3.89 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & % 21.50/3.89 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 21.50/3.89 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 21.50/3.89 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ % 21.50/3.89 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 21.50/3.89 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 21.50/3.89 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, % 21.50/3.89 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 21.50/3.89 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 21.50/3.89 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 21.50/3.89 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 21.50/3.89 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 21.50/3.89 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 21.50/3.89 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 21.50/3.89 % 21.50/3.89 (function-axioms) % 21.50/3.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.50/3.89 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 21.50/3.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.50/3.89 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 21.50/3.89 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 21.50/3.89 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 21.50/3.89 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.50/3.89 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.50/3.89 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 21.50/3.89 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 21.50/3.89 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 21.50/3.89 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 21.50/3.89 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 21.50/3.89 (distinct_points(v3, v2) = v0)) % 21.50/3.89 % 21.50/3.89 Further assumptions not needed in the proof: % 21.50/3.89 -------------------------------------------- % 21.50/3.89 apart1, apart2, apart4, apart5, ax6, ceq2, ci1, ci2 % 21.50/3.89 % 21.50/3.89 Those formulas are unsatisfiable: % 21.50/3.89 --------------------------------- % 21.50/3.89 % 21.50/3.89 Begin of proof % 21.50/3.89 | % 21.50/3.89 | ALPHA: (ci3) implies: % 21.50/3.90 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 21.50/3.90 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 21.50/3.90 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 21.50/3.90 | & $i(v2))) % 21.50/3.90 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 21.50/3.90 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 21.50/3.90 | (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & % 21.50/3.90 | ( ~ (v4 = 0) | ~ (v3 = 0)))) % 21.50/3.90 | % 21.50/3.90 | ALPHA: (ci4) implies: % 21.50/3.90 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 21.50/3.90 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 21.50/3.90 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 21.50/3.90 | & $i(v2))) % 21.50/3.90 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 21.50/3.90 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 21.50/3.90 | (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & % 21.50/3.90 | ( ~ (v4 = 0) | ~ (v3 = 0)))) % 21.50/3.90 | % 21.50/3.90 | ALPHA: (cu1) implies: % 21.92/3.90 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 21.92/3.90 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 21.92/3.90 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 21.92/3.90 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 21.92/3.90 | [v9: any] : (apart_point_and_line(v1, v3) = v9 & % 21.92/3.90 | apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & % 21.92/3.90 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 21.92/3.90 | | v8 = 0))) % 21.92/3.90 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 21.92/3.90 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 21.92/3.90 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 21.92/3.90 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 21.92/3.90 | [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 21.92/3.90 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 21.92/3.90 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 21.92/3.90 | | v8 = 0))) % 21.92/3.90 | % 21.92/3.90 | ALPHA: (ceq1) implies: % 21.92/3.90 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 21.92/3.90 | (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, % 21.92/3.90 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.92/3.90 | distinct_points(v0, v2) = 0) % 21.92/3.90 | % 21.92/3.90 | ALPHA: (ceq3) implies: % 21.92/3.91 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 21.92/3.91 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | % 21.92/3.91 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 21.92/3.91 | % 21.92/3.91 | ALPHA: (function-axioms) implies: % 21.92/3.91 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 21.92/3.91 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 21.92/3.91 | (distinct_points(v3, v2) = v0)) % 21.92/3.91 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 21.92/3.91 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 21.92/3.91 | (distinct_lines(v3, v2) = v0)) % 21.92/3.91 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 21.92/3.91 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 21.92/3.91 | (convergent_lines(v3, v2) = v0)) % 21.92/3.91 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 21.92/3.91 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 21.92/3.91 | (apart_point_and_line(v3, v2) = v0)) % 21.92/3.91 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.92/3.91 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 21.92/3.91 | v0)) % 21.92/3.91 | % 21.92/3.91 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 21.92/3.91 | all_17_3, all_17_4, all_17_5 gives: % 21.92/3.91 | (14) ~ (all_17_1 = 0) & intersection_point(all_17_5, all_17_3) = all_17_0 % 21.92/3.91 | & intersection_point(all_17_5, all_17_4) = all_17_2 & % 21.92/3.91 | apart_point_and_line(all_17_0, all_17_4) = 0 & % 21.92/3.91 | apart_point_and_line(all_17_2, all_17_3) = all_17_1 & % 21.92/3.91 | convergent_lines(all_17_3, all_17_4) = 0 & convergent_lines(all_17_5, % 21.92/3.91 | all_17_3) = 0 & convergent_lines(all_17_5, all_17_4) = 0 & % 21.92/3.91 | $i(all_17_0) & $i(all_17_2) & $i(all_17_3) & $i(all_17_4) & % 21.92/3.91 | $i(all_17_5) % 21.92/3.91 | % 21.92/3.91 | ALPHA: (14) implies: % 21.92/3.91 | (15) ~ (all_17_1 = 0) % 21.92/3.91 | (16) $i(all_17_5) % 21.92/3.91 | (17) $i(all_17_4) % 21.92/3.91 | (18) $i(all_17_3) % 21.92/3.91 | (19) $i(all_17_2) % 21.92/3.91 | (20) convergent_lines(all_17_5, all_17_4) = 0 % 21.92/3.91 | (21) convergent_lines(all_17_5, all_17_3) = 0 % 21.92/3.91 | (22) convergent_lines(all_17_3, all_17_4) = 0 % 21.92/3.92 | (23) apart_point_and_line(all_17_2, all_17_3) = all_17_1 % 21.92/3.92 | (24) apart_point_and_line(all_17_0, all_17_4) = 0 % 21.92/3.92 | (25) intersection_point(all_17_5, all_17_4) = all_17_2 % 21.92/3.92 | (26) intersection_point(all_17_5, all_17_3) = all_17_0 % 21.92/3.92 | % 21.92/3.92 | GROUND_INST: instantiating (3) with all_17_5, all_17_4, simplifying with (16), % 21.92/3.92 | (17), (20) gives: % 21.92/3.92 | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 21.92/3.92 | intersection_point(all_17_5, all_17_4) = v0 & % 21.92/3.92 | apart_point_and_line(v0, all_17_4) = v1 & $i(v0)) % 21.92/3.92 | % 21.92/3.92 | GROUND_INST: instantiating (1) with all_17_5, all_17_4, simplifying with (16), % 21.92/3.92 | (17), (20) gives: % 21.92/3.92 | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 21.92/3.92 | intersection_point(all_17_5, all_17_4) = v0 & % 21.92/3.92 | apart_point_and_line(v0, all_17_5) = v1 & $i(v0)) % 21.92/3.92 | % 21.92/3.92 | GROUND_INST: instantiating (3) with all_17_5, all_17_3, simplifying with (16), % 21.92/3.92 | (18), (21) gives: % 21.92/3.92 | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 21.92/3.92 | intersection_point(all_17_5, all_17_3) = v0 & % 21.92/3.92 | apart_point_and_line(v0, all_17_3) = v1 & $i(v0)) % 21.92/3.92 | % 21.92/3.92 | GROUND_INST: instantiating (1) with all_17_5, all_17_3, simplifying with (16), % 21.92/3.92 | (18), (21) gives: % 21.92/3.92 | (30) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 21.92/3.92 | intersection_point(all_17_5, all_17_3) = v0 & % 21.92/3.92 | apart_point_and_line(v0, all_17_5) = v1 & $i(v0)) % 21.92/3.92 | % 21.92/3.92 | GROUND_INST: instantiating (3) with all_17_3, all_17_4, simplifying with (17), % 21.92/3.92 | (18), (22) gives: % 21.92/3.92 | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 21.92/3.92 | intersection_point(all_17_3, all_17_4) = v0 & % 21.92/3.92 | apart_point_and_line(v0, all_17_4) = v1 & $i(v0)) % 21.92/3.92 | % 21.92/3.92 | GROUND_INST: instantiating (1) with all_17_3, all_17_4, simplifying with (17), % 21.92/3.92 | (18), (22) gives: % 21.92/3.92 | (32) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 21.92/3.92 | intersection_point(all_17_3, all_17_4) = v0 & % 21.92/3.92 | apart_point_and_line(v0, all_17_3) = v1 & $i(v0)) % 21.92/3.92 | % 21.92/3.92 | GROUND_INST: instantiating (6) with all_17_2, all_17_2, all_17_3, all_17_3, % 21.92/3.92 | all_17_1, all_17_1, simplifying with (18), (19), (23) gives: % 21.92/3.92 | (33) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 21.92/3.92 | any] : (apart_point_and_line(all_17_2, all_17_3) = v3 & % 21.92/3.92 | apart_point_and_line(all_17_2, all_17_3) = v2 & % 21.92/3.92 | distinct_lines(all_17_3, all_17_3) = v1 & distinct_points(all_17_2, % 21.92/3.92 | all_17_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 21.92/3.92 | % 21.92/3.92 | GROUND_INST: instantiating (4) with all_17_5, all_17_4, all_17_2, simplifying % 21.92/3.92 | with (16), (17), (25) gives: % 21.92/3.92 | (34) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_2, % 21.92/3.92 | all_17_4) = v1 & convergent_lines(all_17_5, all_17_4) = v0 & ( ~ % 21.92/3.92 | (v1 = 0) | ~ (v0 = 0))) % 21.92/3.92 | % 21.92/3.92 | GROUND_INST: instantiating (2) with all_17_5, all_17_4, all_17_2, simplifying % 21.92/3.92 | with (16), (17), (25) gives: % 21.92/3.93 | (35) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_2, % 21.92/3.93 | all_17_5) = v1 & convergent_lines(all_17_5, all_17_4) = v0 & ( ~ % 21.92/3.93 | (v1 = 0) | ~ (v0 = 0))) % 21.92/3.93 | % 21.92/3.93 | GROUND_INST: instantiating (4) with all_17_5, all_17_3, all_17_0, simplifying % 21.92/3.93 | with (16), (18), (26) gives: % 21.92/3.93 | (36) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_0, % 21.92/3.93 | all_17_3) = v1 & convergent_lines(all_17_5, all_17_3) = v0 & ( ~ % 21.92/3.93 | (v1 = 0) | ~ (v0 = 0))) % 21.92/3.93 | % 21.92/3.93 | GROUND_INST: instantiating (2) with all_17_5, all_17_3, all_17_0, simplifying % 21.92/3.93 | with (16), (18), (26) gives: % 21.92/3.93 | (37) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_0, % 21.92/3.93 | all_17_5) = v1 & convergent_lines(all_17_5, all_17_3) = v0 & ( ~ % 21.92/3.93 | (v1 = 0) | ~ (v0 = 0))) % 21.92/3.93 | % 21.92/3.93 | DELTA: instantiating (37) with fresh symbols all_24_0, all_24_1 gives: % 21.92/3.93 | (38) apart_point_and_line(all_17_0, all_17_5) = all_24_0 & % 21.92/3.93 | convergent_lines(all_17_5, all_17_3) = all_24_1 & ( ~ (all_24_0 = 0) | % 21.92/3.93 | ~ (all_24_1 = 0)) % 21.92/3.93 | % 21.92/3.93 | ALPHA: (38) implies: % 21.92/3.93 | (39) convergent_lines(all_17_5, all_17_3) = all_24_1 % 21.92/3.93 | (40) apart_point_and_line(all_17_0, all_17_5) = all_24_0 % 21.92/3.93 | % 21.92/3.93 | DELTA: instantiating (34) with fresh symbols all_26_0, all_26_1 gives: % 21.92/3.93 | (41) apart_point_and_line(all_17_2, all_17_4) = all_26_0 & % 21.92/3.93 | convergent_lines(all_17_5, all_17_4) = all_26_1 & ( ~ (all_26_0 = 0) | % 21.92/3.93 | ~ (all_26_1 = 0)) % 21.92/3.93 | % 21.92/3.93 | ALPHA: (41) implies: % 21.92/3.93 | (42) apart_point_and_line(all_17_2, all_17_4) = all_26_0 % 21.92/3.93 | % 21.92/3.93 | DELTA: instantiating (32) with fresh symbols all_28_0, all_28_1 gives: % 21.92/3.93 | (43) ~ (all_28_0 = 0) & intersection_point(all_17_3, all_17_4) = all_28_1 % 21.92/3.93 | & apart_point_and_line(all_28_1, all_17_3) = all_28_0 & $i(all_28_1) % 21.92/3.93 | % 21.92/3.93 | ALPHA: (43) implies: % 21.92/3.93 | (44) ~ (all_28_0 = 0) % 21.92/3.93 | (45) apart_point_and_line(all_28_1, all_17_3) = all_28_0 % 21.92/3.93 | (46) intersection_point(all_17_3, all_17_4) = all_28_1 % 21.92/3.93 | % 21.92/3.93 | DELTA: instantiating (31) with fresh symbols all_30_0, all_30_1 gives: % 21.92/3.93 | (47) ~ (all_30_0 = 0) & intersection_point(all_17_3, all_17_4) = all_30_1 % 21.92/3.93 | & apart_point_and_line(all_30_1, all_17_4) = all_30_0 & $i(all_30_1) % 21.92/3.93 | % 21.92/3.93 | ALPHA: (47) implies: % 21.92/3.93 | (48) $i(all_30_1) % 21.92/3.93 | (49) intersection_point(all_17_3, all_17_4) = all_30_1 % 21.92/3.93 | % 21.92/3.93 | DELTA: instantiating (36) with fresh symbols all_32_0, all_32_1 gives: % 21.92/3.93 | (50) apart_point_and_line(all_17_0, all_17_3) = all_32_0 & % 21.92/3.93 | convergent_lines(all_17_5, all_17_3) = all_32_1 & ( ~ (all_32_0 = 0) | % 21.92/3.93 | ~ (all_32_1 = 0)) % 21.92/3.93 | % 21.92/3.93 | ALPHA: (50) implies: % 21.92/3.93 | (51) convergent_lines(all_17_5, all_17_3) = all_32_1 % 21.92/3.93 | (52) apart_point_and_line(all_17_0, all_17_3) = all_32_0 % 21.92/3.93 | (53) ~ (all_32_0 = 0) | ~ (all_32_1 = 0) % 21.92/3.93 | % 21.92/3.93 | DELTA: instantiating (35) with fresh symbols all_34_0, all_34_1 gives: % 21.92/3.93 | (54) apart_point_and_line(all_17_2, all_17_5) = all_34_0 & % 21.92/3.93 | convergent_lines(all_17_5, all_17_4) = all_34_1 & ( ~ (all_34_0 = 0) | % 21.92/3.93 | ~ (all_34_1 = 0)) % 21.92/3.93 | % 21.92/3.93 | ALPHA: (54) implies: % 21.92/3.93 | (55) apart_point_and_line(all_17_2, all_17_5) = all_34_0 % 21.92/3.93 | % 21.92/3.93 | DELTA: instantiating (30) with fresh symbols all_36_0, all_36_1 gives: % 21.92/3.93 | (56) ~ (all_36_0 = 0) & intersection_point(all_17_5, all_17_3) = all_36_1 % 21.92/3.93 | & apart_point_and_line(all_36_1, all_17_5) = all_36_0 & $i(all_36_1) % 21.92/3.93 | % 21.92/3.93 | ALPHA: (56) implies: % 21.92/3.93 | (57) ~ (all_36_0 = 0) % 21.92/3.93 | (58) $i(all_36_1) % 21.92/3.93 | (59) apart_point_and_line(all_36_1, all_17_5) = all_36_0 % 21.92/3.93 | (60) intersection_point(all_17_5, all_17_3) = all_36_1 % 21.92/3.93 | % 21.92/3.93 | DELTA: instantiating (29) with fresh symbols all_38_0, all_38_1 gives: % 21.92/3.94 | (61) ~ (all_38_0 = 0) & intersection_point(all_17_5, all_17_3) = all_38_1 % 21.92/3.94 | & apart_point_and_line(all_38_1, all_17_3) = all_38_0 & $i(all_38_1) % 21.92/3.94 | % 21.92/3.94 | ALPHA: (61) implies: % 21.92/3.94 | (62) ~ (all_38_0 = 0) % 21.92/3.94 | (63) apart_point_and_line(all_38_1, all_17_3) = all_38_0 % 21.92/3.94 | (64) intersection_point(all_17_5, all_17_3) = all_38_1 % 21.92/3.94 | % 21.92/3.94 | DELTA: instantiating (28) with fresh symbols all_40_0, all_40_1 gives: % 21.92/3.94 | (65) ~ (all_40_0 = 0) & intersection_point(all_17_5, all_17_4) = all_40_1 % 21.92/3.94 | & apart_point_and_line(all_40_1, all_17_5) = all_40_0 & $i(all_40_1) % 21.92/3.94 | % 21.92/3.94 | ALPHA: (65) implies: % 21.92/3.94 | (66) ~ (all_40_0 = 0) % 21.92/3.94 | (67) $i(all_40_1) % 21.92/3.94 | (68) apart_point_and_line(all_40_1, all_17_5) = all_40_0 % 21.92/3.94 | (69) intersection_point(all_17_5, all_17_4) = all_40_1 % 21.92/3.94 | % 21.92/3.94 | DELTA: instantiating (27) with fresh symbols all_42_0, all_42_1 gives: % 21.92/3.94 | (70) ~ (all_42_0 = 0) & intersection_point(all_17_5, all_17_4) = all_42_1 % 21.92/3.94 | & apart_point_and_line(all_42_1, all_17_4) = all_42_0 & $i(all_42_1) % 21.92/3.94 | % 21.92/3.94 | ALPHA: (70) implies: % 21.92/3.94 | (71) ~ (all_42_0 = 0) % 21.92/3.94 | (72) apart_point_and_line(all_42_1, all_17_4) = all_42_0 % 21.92/3.94 | (73) intersection_point(all_17_5, all_17_4) = all_42_1 % 21.92/3.94 | % 21.92/3.94 | BETA: splitting (33) gives: % 21.92/3.94 | % 21.92/3.94 | Case 1: % 21.92/3.94 | | % 21.92/3.94 | | (74) all_17_1 = 0 % 21.92/3.94 | | % 21.92/3.94 | | REDUCE: (15), (74) imply: % 21.92/3.94 | | (75) $false % 21.92/3.94 | | % 21.92/3.94 | | CLOSE: (75) is inconsistent. % 21.92/3.94 | | % 21.92/3.94 | Case 2: % 21.92/3.94 | | % 21.92/3.94 | | (76) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 21.92/3.94 | | (apart_point_and_line(all_17_2, all_17_3) = v3 & % 21.92/3.94 | | apart_point_and_line(all_17_2, all_17_3) = v2 & % 21.92/3.94 | | distinct_lines(all_17_3, all_17_3) = v1 & % 21.92/3.94 | | distinct_points(all_17_2, all_17_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 21.92/3.94 | | 0) | v3 = 0 | v2 = 0)) % 21.92/3.94 | | % 21.92/3.94 | | DELTA: instantiating (76) with fresh symbols all_48_0, all_48_1, all_48_2, % 21.92/3.94 | | all_48_3 gives: % 21.92/3.94 | | (77) apart_point_and_line(all_17_2, all_17_3) = all_48_0 & % 21.92/3.94 | | apart_point_and_line(all_17_2, all_17_3) = all_48_1 & % 21.92/3.94 | | distinct_lines(all_17_3, all_17_3) = all_48_2 & % 21.92/3.94 | | distinct_points(all_17_2, all_17_2) = all_48_3 & ( ~ (all_48_2 = 0) % 21.92/3.94 | | | ~ (all_48_3 = 0) | all_48_0 = 0 | all_48_1 = 0) % 21.92/3.94 | | % 21.92/3.94 | | ALPHA: (77) implies: % 21.92/3.94 | | (78) apart_point_and_line(all_17_2, all_17_3) = all_48_1 % 21.92/3.94 | | (79) apart_point_and_line(all_17_2, all_17_3) = all_48_0 % 21.92/3.94 | | % 21.92/3.94 | | GROUND_INST: instantiating (11) with 0, all_32_1, all_17_3, all_17_5, % 21.92/3.94 | | simplifying with (21), (51) gives: % 21.92/3.94 | | (80) all_32_1 = 0 % 21.92/3.94 | | % 21.92/3.94 | | GROUND_INST: instantiating (11) with all_24_1, all_32_1, all_17_3, all_17_5, % 21.92/3.94 | | simplifying with (39), (51) gives: % 21.92/3.94 | | (81) all_32_1 = all_24_1 % 21.92/3.94 | | % 21.92/3.94 | | GROUND_INST: instantiating (12) with all_17_1, all_48_0, all_17_3, all_17_2, % 21.92/3.94 | | simplifying with (23), (79) gives: % 21.92/3.94 | | (82) all_48_0 = all_17_1 % 21.92/3.94 | | % 21.92/3.94 | | GROUND_INST: instantiating (12) with all_48_1, all_48_0, all_17_3, all_17_2, % 21.92/3.94 | | simplifying with (78), (79) gives: % 21.92/3.94 | | (83) all_48_0 = all_48_1 % 21.92/3.94 | | % 21.92/3.94 | | GROUND_INST: instantiating (13) with all_17_2, all_42_1, all_17_4, all_17_5, % 21.92/3.94 | | simplifying with (25), (73) gives: % 21.92/3.94 | | (84) all_42_1 = all_17_2 % 21.92/3.94 | | % 21.92/3.94 | | GROUND_INST: instantiating (13) with all_40_1, all_42_1, all_17_4, all_17_5, % 21.92/3.94 | | simplifying with (69), (73) gives: % 21.92/3.94 | | (85) all_42_1 = all_40_1 % 21.92/3.94 | | % 21.92/3.94 | | GROUND_INST: instantiating (13) with all_17_0, all_38_1, all_17_3, all_17_5, % 21.92/3.94 | | simplifying with (26), (64) gives: % 21.92/3.94 | | (86) all_38_1 = all_17_0 % 21.92/3.94 | | % 21.92/3.94 | | GROUND_INST: instantiating (13) with all_36_1, all_38_1, all_17_3, all_17_5, % 21.92/3.94 | | simplifying with (60), (64) gives: % 21.92/3.94 | | (87) all_38_1 = all_36_1 % 21.92/3.94 | | % 21.92/3.94 | | GROUND_INST: instantiating (13) with all_28_1, all_30_1, all_17_4, all_17_3, % 21.92/3.94 | | simplifying with (46), (49) gives: % 21.92/3.94 | | (88) all_30_1 = all_28_1 % 21.92/3.94 | | % 21.92/3.95 | | COMBINE_EQS: (82), (83) imply: % 21.92/3.95 | | (89) all_48_1 = all_17_1 % 21.92/3.95 | | % 21.92/3.95 | | SIMP: (89) implies: % 21.92/3.95 | | (90) all_48_1 = all_17_1 % 21.92/3.95 | | % 21.92/3.95 | | COMBINE_EQS: (84), (85) imply: % 21.92/3.95 | | (91) all_40_1 = all_17_2 % 21.92/3.95 | | % 21.92/3.95 | | SIMP: (91) implies: % 21.92/3.95 | | (92) all_40_1 = all_17_2 % 21.92/3.95 | | % 21.92/3.95 | | COMBINE_EQS: (86), (87) imply: % 21.92/3.95 | | (93) all_36_1 = all_17_0 % 21.92/3.95 | | % 21.92/3.95 | | COMBINE_EQS: (80), (81) imply: % 21.92/3.95 | | (94) all_24_1 = 0 % 21.92/3.95 | | % 21.92/3.95 | | SIMP: (94) implies: % 21.92/3.95 | | (95) all_24_1 = 0 % 21.92/3.95 | | % 21.92/3.95 | | REDUCE: (72), (84) imply: % 21.92/3.95 | | (96) apart_point_and_line(all_17_2, all_17_4) = all_42_0 % 21.92/3.95 | | % 22.15/3.95 | | REDUCE: (68), (92) imply: % 22.15/3.95 | | (97) apart_point_and_line(all_17_2, all_17_5) = all_40_0 % 22.15/3.95 | | % 22.15/3.95 | | REDUCE: (63), (86) imply: % 22.15/3.95 | | (98) apart_point_and_line(all_17_0, all_17_3) = all_38_0 % 22.15/3.95 | | % 22.15/3.95 | | REDUCE: (59), (93) imply: % 22.15/3.95 | | (99) apart_point_and_line(all_17_0, all_17_5) = all_36_0 % 22.15/3.95 | | % 22.15/3.95 | | REDUCE: (58), (93) imply: % 22.15/3.95 | | (100) $i(all_17_0) % 22.15/3.95 | | % 22.15/3.95 | | REDUCE: (48), (88) imply: % 22.15/3.95 | | (101) $i(all_28_1) % 22.15/3.95 | | % 22.15/3.95 | | BETA: splitting (53) gives: % 22.15/3.95 | | % 22.15/3.95 | | Case 1: % 22.15/3.95 | | | % 22.15/3.95 | | | % 22.15/3.95 | | | GROUND_INST: instantiating (12) with all_34_0, all_40_0, all_17_5, % 22.15/3.95 | | | all_17_2, simplifying with (55), (97) gives: % 22.15/3.95 | | | (102) all_40_0 = all_34_0 % 22.15/3.95 | | | % 22.15/3.95 | | | GROUND_INST: instantiating (12) with all_26_0, all_42_0, all_17_4, % 22.15/3.95 | | | all_17_2, simplifying with (42), (96) gives: % 22.15/3.95 | | | (103) all_42_0 = all_26_0 % 22.15/3.95 | | | % 22.15/3.95 | | | GROUND_INST: instantiating (12) with all_24_0, all_36_0, all_17_5, % 22.15/3.95 | | | all_17_0, simplifying with (40), (99) gives: % 22.15/3.95 | | | (104) all_36_0 = all_24_0 % 22.15/3.95 | | | % 22.15/3.95 | | | GROUND_INST: instantiating (12) with all_32_0, all_38_0, all_17_3, % 22.15/3.95 | | | all_17_0, simplifying with (52), (98) gives: % 22.15/3.95 | | | (105) all_38_0 = all_32_0 % 22.15/3.95 | | | % 22.15/3.95 | | | REDUCE: (71), (103) imply: % 22.15/3.95 | | | (106) ~ (all_26_0 = 0) % 22.15/3.95 | | | % 22.15/3.95 | | | REDUCE: (66), (102) imply: % 22.15/3.95 | | | (107) ~ (all_34_0 = 0) % 22.15/3.95 | | | % 22.15/3.95 | | | REDUCE: (62), (105) imply: % 22.15/3.95 | | | (108) ~ (all_32_0 = 0) % 22.15/3.95 | | | % 22.15/3.95 | | | REDUCE: (57), (104) imply: % 22.15/3.95 | | | (109) ~ (all_24_0 = 0) % 22.15/3.95 | | | % 22.15/3.95 | | | GROUND_INST: instantiating (7) with all_17_0, all_17_4, all_17_2, % 22.15/3.95 | | | all_26_0, simplifying with (17), (19), (24), (42), (100) % 22.15/3.95 | | | gives: % 22.15/3.95 | | | (110) all_26_0 = 0 | distinct_points(all_17_0, all_17_2) = 0 % 22.15/3.95 | | | % 22.15/3.95 | | | GROUND_INST: instantiating (5) with all_17_2, all_17_2, all_17_4, % 22.15/3.95 | | | all_17_3, all_17_1, all_26_0, simplifying with (17), (18), % 22.15/3.95 | | | (19), (23), (42) gives: % 22.15/3.95 | | | (111) all_26_0 = 0 | all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? % 22.15/3.95 | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_2, % 22.15/3.95 | | | all_17_3) = v3 & apart_point_and_line(all_17_2, all_17_4) = % 22.15/3.95 | | | v2 & distinct_lines(all_17_4, all_17_3) = v1 & % 22.15/3.95 | | | distinct_points(all_17_2, all_17_2) = v0 & ( ~ (v1 = 0) | ~ % 22.15/3.95 | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 22.15/3.95 | | | % 22.15/3.95 | | | GROUND_INST: instantiating (6) with all_17_0, all_17_2, all_17_5, % 22.15/3.95 | | | all_17_5, all_24_0, all_34_0, simplifying with (16), (19), % 22.15/3.95 | | | (40), (55), (100) gives: % 22.15/3.95 | | | (112) all_34_0 = 0 | all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 22.15/3.95 | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_0, % 22.15/3.95 | | | all_17_5) = v2 & apart_point_and_line(all_17_2, all_17_5) = % 22.15/3.95 | | | v3 & distinct_lines(all_17_5, all_17_5) = v1 & % 22.15/3.95 | | | distinct_points(all_17_0, all_17_2) = v0 & ( ~ (v1 = 0) | ~ % 22.15/3.95 | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 22.15/3.95 | | | % 22.15/3.95 | | | GROUND_INST: instantiating (6) with all_17_0, all_17_2, all_17_3, % 22.15/3.95 | | | all_17_5, all_32_0, all_34_0, simplifying with (16), (18), % 22.15/3.95 | | | (19), (52), (55), (100) gives: % 22.15/3.95 | | | (113) all_34_0 = 0 | all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 22.15/3.95 | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_17_0, % 22.15/3.95 | | | all_17_5) = v2 & apart_point_and_line(all_17_2, all_17_3) = % 22.15/3.95 | | | v3 & distinct_lines(all_17_3, all_17_5) = v1 & % 22.15/3.95 | | | distinct_points(all_17_0, all_17_2) = v0 & ( ~ (v1 = 0) | ~ % 22.15/3.95 | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 22.15/3.95 | | | % 22.15/3.96 | | | GROUND_INST: instantiating (5) with all_17_0, all_28_1, all_17_3, % 22.15/3.96 | | | all_17_5, all_24_0, all_28_0, simplifying with (16), (18), % 22.15/3.96 | | | (40), (45), (100), (101) gives: % 22.15/3.96 | | | (114) all_28_0 = 0 | all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 22.15/3.96 | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_28_1, % 22.15/3.96 | | | all_17_5) = v3 & apart_point_and_line(all_17_0, all_17_3) = % 22.15/3.96 | | | v2 & distinct_lines(all_17_3, all_17_5) = v1 & % 22.15/3.96 | | | distinct_points(all_17_0, all_28_1) = v0 & ( ~ (v1 = 0) | ~ % 22.15/3.96 | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 22.15/3.96 | | | % 22.15/3.96 | | | GROUND_INST: instantiating (6) with all_17_2, all_28_1, all_17_4, % 22.15/3.96 | | | all_17_3, all_26_0, all_28_0, simplifying with (17), (18), % 22.15/3.96 | | | (19), (42), (45), (101) gives: % 22.15/3.96 | | | (115) all_28_0 = 0 | all_26_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 22.15/3.96 | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_28_1, % 22.15/3.96 | | | all_17_4) = v3 & apart_point_and_line(all_17_2, all_17_3) = % 22.15/3.96 | | | v2 & distinct_lines(all_17_4, all_17_3) = v1 & % 22.15/3.96 | | | distinct_points(all_17_2, all_28_1) = v0 & ( ~ (v1 = 0) | ~ % 22.15/3.96 | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 22.15/3.96 | | | % 22.15/3.96 | | | BETA: splitting (110) gives: % 22.15/3.96 | | | % 22.15/3.96 | | | Case 1: % 22.15/3.96 | | | | % 22.15/3.96 | | | | (116) distinct_points(all_17_0, all_17_2) = 0 % 22.15/3.96 | | | | % 22.15/3.96 | | | | BETA: splitting (111) gives: % 22.15/3.96 | | | | % 22.15/3.96 | | | | Case 1: % 22.15/3.96 | | | | | % 22.15/3.96 | | | | | (117) all_26_0 = 0 % 22.15/3.96 | | | | | % 22.15/3.96 | | | | | REDUCE: (106), (117) imply: % 22.15/3.96 | | | | | (118) $false % 22.15/3.96 | | | | | % 22.15/3.96 | | | | | CLOSE: (118) is inconsistent. % 22.15/3.96 | | | | | % 22.15/3.96 | | | | Case 2: % 22.15/3.96 | | | | | % 22.15/3.96 | | | | | (119) all_17_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.15/3.96 | | | | | ? [v3: any] : (apart_point_and_line(all_17_2, all_17_3) = v3 % 22.15/3.96 | | | | | & apart_point_and_line(all_17_2, all_17_4) = v2 & % 22.15/3.96 | | | | | distinct_lines(all_17_4, all_17_3) = v1 & % 22.15/3.96 | | | | | distinct_points(all_17_2, all_17_2) = v0 & ( ~ (v1 = 0) | % 22.15/3.96 | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 22.15/3.96 | | | | | % 22.15/3.96 | | | | | BETA: splitting (115) gives: % 22.15/3.96 | | | | | % 22.15/3.96 | | | | | Case 1: % 22.15/3.96 | | | | | | % 22.15/3.96 | | | | | | (120) all_28_0 = 0 % 22.15/3.96 | | | | | | % 22.15/3.96 | | | | | | REDUCE: (44), (120) imply: % 22.15/3.96 | | | | | | (121) $false % 22.15/3.96 | | | | | | % 22.15/3.96 | | | | | | CLOSE: (121) is inconsistent. % 22.15/3.96 | | | | | | % 22.15/3.96 | | | | | Case 2: % 22.15/3.96 | | | | | | % 22.15/3.96 | | | | | | (122) all_26_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.15/3.96 | | | | | | ? [v3: any] : (apart_point_and_line(all_28_1, all_17_4) = % 22.15/3.96 | | | | | | v3 & apart_point_and_line(all_17_2, all_17_3) = v2 & % 22.15/3.96 | | | | | | distinct_lines(all_17_4, all_17_3) = v1 & % 22.15/3.96 | | | | | | distinct_points(all_17_2, all_28_1) = v0 & ( ~ (v1 = 0) | % 22.15/3.96 | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 22.15/3.96 | | | | | | % 22.15/3.96 | | | | | | BETA: splitting (114) gives: % 22.15/3.96 | | | | | | % 22.15/3.96 | | | | | | Case 1: % 22.15/3.96 | | | | | | | % 22.15/3.96 | | | | | | | (123) all_28_0 = 0 % 22.15/3.96 | | | | | | | % 22.15/3.96 | | | | | | | REDUCE: (44), (123) imply: % 22.15/3.96 | | | | | | | (124) $false % 22.15/3.96 | | | | | | | % 22.15/3.96 | | | | | | | CLOSE: (124) is inconsistent. % 22.15/3.96 | | | | | | | % 22.15/3.96 | | | | | | Case 2: % 22.15/3.96 | | | | | | | % 22.15/3.96 | | | | | | | (125) all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] % 22.15/3.96 | | | | | | | : ? [v3: any] : (apart_point_and_line(all_28_1, % 22.15/3.96 | | | | | | | all_17_5) = v3 & apart_point_and_line(all_17_0, % 22.15/3.96 | | | | | | | all_17_3) = v2 & distinct_lines(all_17_3, all_17_5) = % 22.15/3.96 | | | | | | | v1 & distinct_points(all_17_0, all_28_1) = v0 & ( ~ (v1 % 22.15/3.96 | | | | | | | = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 22.15/3.96 | | | | | | | % 22.15/3.96 | | | | | | | BETA: splitting (112) gives: % 22.15/3.96 | | | | | | | % 22.15/3.96 | | | | | | | Case 1: % 22.15/3.96 | | | | | | | | % 22.15/3.96 | | | | | | | | (126) all_34_0 = 0 % 22.15/3.96 | | | | | | | | % 22.15/3.96 | | | | | | | | REDUCE: (107), (126) imply: % 22.15/3.96 | | | | | | | | (127) $false % 22.15/3.96 | | | | | | | | % 22.15/3.96 | | | | | | | | CLOSE: (127) is inconsistent. % 22.15/3.96 | | | | | | | | % 22.15/3.96 | | | | | | | Case 2: % 22.15/3.96 | | | | | | | | % 22.15/3.96 | | | | | | | | (128) all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 22.15/3.96 | | | | | | | | any] : ? [v3: any] : (apart_point_and_line(all_17_0, % 22.15/3.96 | | | | | | | | all_17_5) = v2 & apart_point_and_line(all_17_2, % 22.15/3.96 | | | | | | | | all_17_5) = v3 & distinct_lines(all_17_5, all_17_5) % 22.15/3.96 | | | | | | | | = v1 & distinct_points(all_17_0, all_17_2) = v0 & ( ~ % 22.15/3.96 | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 22.15/3.96 | | | | | | | | % 22.15/3.96 | | | | | | | | BETA: splitting (125) gives: % 22.15/3.96 | | | | | | | | % 22.15/3.96 | | | | | | | | Case 1: % 22.15/3.96 | | | | | | | | | % 22.15/3.96 | | | | | | | | | (129) all_24_0 = 0 % 22.15/3.96 | | | | | | | | | % 22.15/3.96 | | | | | | | | | REDUCE: (109), (129) imply: % 22.15/3.96 | | | | | | | | | (130) $false % 22.15/3.96 | | | | | | | | | % 22.15/3.96 | | | | | | | | | CLOSE: (130) is inconsistent. % 22.15/3.96 | | | | | | | | | % 22.15/3.96 | | | | | | | | Case 2: % 22.15/3.96 | | | | | | | | | % 22.15/3.96 | | | | | | | | | (131) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 22.15/3.96 | | | | | | | | | any] : (apart_point_and_line(all_28_1, all_17_5) = % 22.15/3.96 | | | | | | | | | v3 & apart_point_and_line(all_17_0, all_17_3) = v2 % 22.15/3.96 | | | | | | | | | & distinct_lines(all_17_3, all_17_5) = v1 & % 22.15/3.96 | | | | | | | | | distinct_points(all_17_0, all_28_1) = v0 & ( ~ (v1 % 22.15/3.96 | | | | | | | | | = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 22.15/3.96 | | | | | | | | | % 22.15/3.96 | | | | | | | | | DELTA: instantiating (131) with fresh symbols all_223_0, % 22.15/3.96 | | | | | | | | | all_223_1, all_223_2, all_223_3 gives: % 22.15/3.96 | | | | | | | | | (132) apart_point_and_line(all_28_1, all_17_5) = all_223_0 % 22.15/3.96 | | | | | | | | | & apart_point_and_line(all_17_0, all_17_3) = % 22.15/3.96 | | | | | | | | | all_223_1 & distinct_lines(all_17_3, all_17_5) = % 22.15/3.96 | | | | | | | | | all_223_2 & distinct_points(all_17_0, all_28_1) = % 22.15/3.96 | | | | | | | | | all_223_3 & ( ~ (all_223_2 = 0) | ~ (all_223_3 = 0) % 22.15/3.96 | | | | | | | | | | all_223_0 = 0 | all_223_1 = 0) % 22.15/3.96 | | | | | | | | | % 22.15/3.96 | | | | | | | | | ALPHA: (132) implies: % 22.15/3.96 | | | | | | | | | (133) distinct_lines(all_17_3, all_17_5) = all_223_2 % 22.15/3.96 | | | | | | | | | % 22.15/3.96 | | | | | | | | | BETA: splitting (113) gives: % 22.15/3.96 | | | | | | | | | % 22.15/3.96 | | | | | | | | | Case 1: % 22.15/3.96 | | | | | | | | | | % 22.15/3.96 | | | | | | | | | | (134) all_34_0 = 0 % 22.15/3.96 | | | | | | | | | | % 22.15/3.96 | | | | | | | | | | REDUCE: (107), (134) imply: % 22.15/3.96 | | | | | | | | | | (135) $false % 22.15/3.96 | | | | | | | | | | % 22.15/3.96 | | | | | | | | | | CLOSE: (135) is inconsistent. % 22.15/3.96 | | | | | | | | | | % 22.15/3.96 | | | | | | | | | Case 2: % 22.15/3.96 | | | | | | | | | | % 22.15/3.96 | | | | | | | | | | (136) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 22.15/3.96 | | | | | | | | | | [v2: any] : ? [v3: any] : % 22.15/3.96 | | | | | | | | | | (apart_point_and_line(all_17_0, all_17_5) = v2 & % 22.15/3.96 | | | | | | | | | | apart_point_and_line(all_17_2, all_17_3) = v3 & % 22.15/3.96 | | | | | | | | | | distinct_lines(all_17_3, all_17_5) = v1 & % 22.15/3.96 | | | | | | | | | | distinct_points(all_17_0, all_17_2) = v0 & ( ~ % 22.15/3.96 | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 22.15/3.96 | | | | | | | | | | % 22.15/3.96 | | | | | | | | | | BETA: splitting (136) gives: % 22.15/3.96 | | | | | | | | | | % 22.15/3.96 | | | | | | | | | | Case 1: % 22.15/3.96 | | | | | | | | | | | % 22.15/3.96 | | | | | | | | | | | (137) all_32_0 = 0 % 22.15/3.96 | | | | | | | | | | | % 22.15/3.96 | | | | | | | | | | | REDUCE: (108), (137) imply: % 22.15/3.96 | | | | | | | | | | | (138) $false % 22.15/3.96 | | | | | | | | | | | % 22.15/3.96 | | | | | | | | | | | CLOSE: (138) is inconsistent. % 22.15/3.96 | | | | | | | | | | | % 22.15/3.96 | | | | | | | | | | Case 2: % 22.15/3.96 | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | (139) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 22.15/3.97 | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_0, % 22.15/3.97 | | | | | | | | | | | all_17_5) = v2 & % 22.15/3.97 | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_3) = v3 & % 22.15/3.97 | | | | | | | | | | | distinct_lines(all_17_3, all_17_5) = v1 & % 22.15/3.97 | | | | | | | | | | | distinct_points(all_17_0, all_17_2) = v0 & ( ~ % 22.15/3.97 | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 22.15/3.97 | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | DELTA: instantiating (139) with fresh symbols all_355_0, % 22.15/3.97 | | | | | | | | | | | all_355_1, all_355_2, all_355_3 gives: % 22.15/3.97 | | | | | | | | | | | (140) apart_point_and_line(all_17_0, all_17_5) = % 22.15/3.97 | | | | | | | | | | | all_355_1 & apart_point_and_line(all_17_2, % 22.15/3.97 | | | | | | | | | | | all_17_3) = all_355_0 & distinct_lines(all_17_3, % 22.15/3.97 | | | | | | | | | | | all_17_5) = all_355_2 & % 22.15/3.97 | | | | | | | | | | | distinct_points(all_17_0, all_17_2) = all_355_3 & % 22.15/3.97 | | | | | | | | | | | ( ~ (all_355_2 = 0) | ~ (all_355_3 = 0) | % 22.15/3.97 | | | | | | | | | | | all_355_0 = 0 | all_355_1 = 0) % 22.15/3.97 | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | ALPHA: (140) implies: % 22.15/3.97 | | | | | | | | | | | (141) distinct_points(all_17_0, all_17_2) = all_355_3 % 22.15/3.97 | | | | | | | | | | | (142) distinct_lines(all_17_3, all_17_5) = all_355_2 % 22.15/3.97 | | | | | | | | | | | (143) apart_point_and_line(all_17_2, all_17_3) = % 22.15/3.97 | | | | | | | | | | | all_355_0 % 22.15/3.97 | | | | | | | | | | | (144) apart_point_and_line(all_17_0, all_17_5) = % 22.15/3.97 | | | | | | | | | | | all_355_1 % 22.15/3.97 | | | | | | | | | | | (145) ~ (all_355_2 = 0) | ~ (all_355_3 = 0) | % 22.15/3.97 | | | | | | | | | | | all_355_0 = 0 | all_355_1 = 0 % 22.15/3.97 | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | BETA: splitting (122) gives: % 22.15/3.97 | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | Case 1: % 22.15/3.97 | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | (146) all_26_0 = 0 % 22.15/3.97 | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | REDUCE: (106), (146) imply: % 22.15/3.97 | | | | | | | | | | | | (147) $false % 22.15/3.97 | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | CLOSE: (147) is inconsistent. % 22.15/3.97 | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | Case 2: % 22.15/3.97 | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | (148) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 22.15/3.97 | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_28_1, % 22.15/3.97 | | | | | | | | | | | | all_17_4) = v3 & % 22.15/3.97 | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_3) = v2 & % 22.15/3.97 | | | | | | | | | | | | distinct_lines(all_17_4, all_17_3) = v1 & % 22.15/3.97 | | | | | | | | | | | | distinct_points(all_17_2, all_28_1) = v0 & ( ~ % 22.15/3.97 | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 22.15/3.97 | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | DELTA: instantiating (148) with fresh symbols all_373_0, % 22.15/3.97 | | | | | | | | | | | | all_373_1, all_373_2, all_373_3 gives: % 22.15/3.97 | | | | | | | | | | | | (149) apart_point_and_line(all_28_1, all_17_4) = % 22.15/3.97 | | | | | | | | | | | | all_373_0 & apart_point_and_line(all_17_2, % 22.15/3.97 | | | | | | | | | | | | all_17_3) = all_373_1 & distinct_lines(all_17_4, % 22.15/3.97 | | | | | | | | | | | | all_17_3) = all_373_2 & % 22.15/3.97 | | | | | | | | | | | | distinct_points(all_17_2, all_28_1) = all_373_3 & % 22.15/3.97 | | | | | | | | | | | | ( ~ (all_373_2 = 0) | ~ (all_373_3 = 0) | % 22.15/3.97 | | | | | | | | | | | | all_373_0 = 0 | all_373_1 = 0) % 22.15/3.97 | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | ALPHA: (149) implies: % 22.15/3.97 | | | | | | | | | | | | (150) apart_point_and_line(all_17_2, all_17_3) = % 22.15/3.97 | | | | | | | | | | | | all_373_1 % 22.15/3.97 | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | BETA: splitting (128) gives: % 22.15/3.97 | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | Case 1: % 22.15/3.97 | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | (151) all_24_0 = 0 % 22.15/3.97 | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | REDUCE: (109), (151) imply: % 22.15/3.97 | | | | | | | | | | | | | (152) $false % 22.15/3.97 | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | CLOSE: (152) is inconsistent. % 22.15/3.97 | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | Case 2: % 22.15/3.97 | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | (153) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 22.15/3.97 | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_0, % 22.15/3.97 | | | | | | | | | | | | | all_17_5) = v2 & % 22.15/3.97 | | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_5) = v3 & % 22.15/3.97 | | | | | | | | | | | | | distinct_lines(all_17_5, all_17_5) = v1 & % 22.15/3.97 | | | | | | | | | | | | | distinct_points(all_17_0, all_17_2) = v0 & ( ~ % 22.15/3.97 | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 22.15/3.97 | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | DELTA: instantiating (153) with fresh symbols all_379_0, % 22.15/3.97 | | | | | | | | | | | | | all_379_1, all_379_2, all_379_3 gives: % 22.15/3.97 | | | | | | | | | | | | | (154) apart_point_and_line(all_17_0, all_17_5) = % 22.15/3.97 | | | | | | | | | | | | | all_379_1 & apart_point_and_line(all_17_2, % 22.15/3.97 | | | | | | | | | | | | | all_17_5) = all_379_0 & distinct_lines(all_17_5, % 22.15/3.97 | | | | | | | | | | | | | all_17_5) = all_379_2 & % 22.15/3.97 | | | | | | | | | | | | | distinct_points(all_17_0, all_17_2) = all_379_3 & % 22.15/3.97 | | | | | | | | | | | | | ( ~ (all_379_2 = 0) | ~ (all_379_3 = 0) | % 22.15/3.97 | | | | | | | | | | | | | all_379_0 = 0 | all_379_1 = 0) % 22.15/3.97 | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | ALPHA: (154) implies: % 22.15/3.97 | | | | | | | | | | | | | (155) distinct_points(all_17_0, all_17_2) = all_379_3 % 22.15/3.97 | | | | | | | | | | | | | (156) apart_point_and_line(all_17_0, all_17_5) = % 22.15/3.97 | | | | | | | | | | | | | all_379_1 % 22.15/3.97 | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | BETA: splitting (119) gives: % 22.15/3.97 | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | Case 1: % 22.15/3.97 | | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | | (157) all_17_1 = 0 % 22.15/3.97 | | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | | REDUCE: (15), (157) imply: % 22.15/3.97 | | | | | | | | | | | | | | (158) $false % 22.15/3.97 | | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | | CLOSE: (158) is inconsistent. % 22.15/3.97 | | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | Case 2: % 22.15/3.97 | | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | | (159) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 22.15/3.97 | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_17_2, % 22.15/3.97 | | | | | | | | | | | | | | all_17_3) = v3 & % 22.15/3.97 | | | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_4) = v2 & % 22.15/3.97 | | | | | | | | | | | | | | distinct_lines(all_17_4, all_17_3) = v1 & % 22.15/3.97 | | | | | | | | | | | | | | distinct_points(all_17_2, all_17_2) = v0 & ( ~ % 22.15/3.97 | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 22.15/3.97 | | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | | DELTA: instantiating (159) with fresh symbols all_393_0, % 22.15/3.97 | | | | | | | | | | | | | | all_393_1, all_393_2, all_393_3 gives: % 22.15/3.97 | | | | | | | | | | | | | | (160) apart_point_and_line(all_17_2, all_17_3) = % 22.15/3.97 | | | | | | | | | | | | | | all_393_0 & apart_point_and_line(all_17_2, % 22.15/3.97 | | | | | | | | | | | | | | all_17_4) = all_393_1 & distinct_lines(all_17_4, % 22.15/3.97 | | | | | | | | | | | | | | all_17_3) = all_393_2 & % 22.15/3.97 | | | | | | | | | | | | | | distinct_points(all_17_2, all_17_2) = all_393_3 & % 22.15/3.97 | | | | | | | | | | | | | | ( ~ (all_393_2 = 0) | ~ (all_393_3 = 0) | % 22.15/3.97 | | | | | | | | | | | | | | all_393_0 = 0 | all_393_1 = 0) % 22.15/3.97 | | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | | ALPHA: (160) implies: % 22.15/3.97 | | | | | | | | | | | | | | (161) apart_point_and_line(all_17_2, all_17_3) = % 22.15/3.97 | | | | | | | | | | | | | | all_393_0 % 22.15/3.97 | | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_379_3, all_17_2, % 22.15/3.97 | | | | | | | | | | | | | | all_17_0, simplifying with (116), (155) gives: % 22.15/3.97 | | | | | | | | | | | | | | (162) all_379_3 = 0 % 22.15/3.97 | | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_355_3, all_379_3, % 22.15/3.97 | | | | | | | | | | | | | | all_17_2, all_17_0, simplifying with (141), (155) % 22.15/3.97 | | | | | | | | | | | | | | gives: % 22.15/3.97 | | | | | | | | | | | | | | (163) all_379_3 = all_355_3 % 22.15/3.97 | | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_223_2, all_355_2, % 22.15/3.97 | | | | | | | | | | | | | | all_17_5, all_17_3, simplifying with (133), (142) % 22.15/3.97 | | | | | | | | | | | | | | gives: % 22.15/3.97 | | | | | | | | | | | | | | (164) all_355_2 = all_223_2 % 22.15/3.97 | | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_17_1, all_393_0, % 22.15/3.97 | | | | | | | | | | | | | | all_17_3, all_17_2, simplifying with (23), (161) % 22.15/3.97 | | | | | | | | | | | | | | gives: % 22.15/3.97 | | | | | | | | | | | | | | (165) all_393_0 = all_17_1 % 22.15/3.97 | | | | | | | | | | | | | | % 22.15/3.97 | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_373_1, all_393_0, % 22.15/3.97 | | | | | | | | | | | | | | all_17_3, all_17_2, simplifying with (150), (161) % 22.15/3.97 | | | | | | | | | | | | | | gives: % 22.15/3.97 | | | | | | | | | | | | | | (166) all_393_0 = all_373_1 % 22.15/3.97 | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_355_0, all_393_0, % 22.15/3.98 | | | | | | | | | | | | | | all_17_3, all_17_2, simplifying with (143), (161) % 22.15/3.98 | | | | | | | | | | | | | | gives: % 22.15/3.98 | | | | | | | | | | | | | | (167) all_393_0 = all_355_0 % 22.15/3.98 | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_24_0, all_379_1, % 22.15/3.98 | | | | | | | | | | | | | | all_17_5, all_17_0, simplifying with (40), (156) % 22.15/3.98 | | | | | | | | | | | | | | gives: % 22.15/3.98 | | | | | | | | | | | | | | (168) all_379_1 = all_24_0 % 22.15/3.98 | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_355_1, all_379_1, % 22.15/3.98 | | | | | | | | | | | | | | all_17_5, all_17_0, simplifying with (144), (156) % 22.15/3.98 | | | | | | | | | | | | | | gives: % 22.15/3.98 | | | | | | | | | | | | | | (169) all_379_1 = all_355_1 % 22.15/3.98 | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | COMBINE_EQS: (165), (166) imply: % 22.15/3.98 | | | | | | | | | | | | | | (170) all_373_1 = all_17_1 % 22.15/3.98 | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | COMBINE_EQS: (166), (167) imply: % 22.15/3.98 | | | | | | | | | | | | | | (171) all_373_1 = all_355_0 % 22.15/3.98 | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | COMBINE_EQS: (168), (169) imply: % 22.15/3.98 | | | | | | | | | | | | | | (172) all_355_1 = all_24_0 % 22.15/3.98 | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | COMBINE_EQS: (162), (163) imply: % 22.15/3.98 | | | | | | | | | | | | | | (173) all_355_3 = 0 % 22.15/3.98 | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | COMBINE_EQS: (170), (171) imply: % 22.15/3.98 | | | | | | | | | | | | | | (174) all_355_0 = all_17_1 % 22.15/3.98 | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | BETA: splitting (145) gives: % 22.15/3.98 | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | Case 1: % 22.15/3.98 | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | (175) ~ (all_355_2 = 0) % 22.15/3.98 | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | REDUCE: (164), (175) imply: % 22.15/3.98 | | | | | | | | | | | | | | | (176) ~ (all_223_2 = 0) % 22.15/3.98 | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_17_5, all_17_3, % 22.15/3.98 | | | | | | | | | | | | | | | all_17_5, all_223_2, simplifying with (16), (18), % 22.15/3.98 | | | | | | | | | | | | | | | (21), (133) gives: % 22.15/3.98 | | | | | | | | | | | | | | | (177) all_223_2 = 0 | convergent_lines(all_17_5, % 22.15/3.98 | | | | | | | | | | | | | | | all_17_5) = 0 % 22.15/3.98 | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 22.15/3.98 | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | Case 1: % 22.15/3.98 | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | (178) convergent_lines(all_17_5, all_17_5) = 0 % 22.15/3.98 | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_17_5, simplifying % 22.15/3.98 | | | | | | | | | | | | | | | | with (16), (178) gives: % 22.15/3.98 | | | | | | | | | | | | | | | | (179) $false % 22.15/3.98 | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | CLOSE: (179) is inconsistent. % 22.15/3.98 | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | Case 2: % 22.15/3.98 | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | (180) all_223_2 = 0 % 22.15/3.98 | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | REDUCE: (176), (180) imply: % 22.15/3.98 | | | | | | | | | | | | | | | | (181) $false % 22.15/3.98 | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | CLOSE: (181) is inconsistent. % 22.15/3.98 | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | End of split % 22.15/3.98 | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | Case 2: % 22.15/3.98 | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | (182) ~ (all_355_3 = 0) | all_355_0 = 0 | all_355_1 = 0 % 22.15/3.98 | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 22.15/3.98 | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | Case 1: % 22.15/3.98 | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | (183) ~ (all_355_3 = 0) % 22.15/3.98 | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | REDUCE: (173), (183) imply: % 22.15/3.98 | | | | | | | | | | | | | | | | (184) $false % 22.15/3.98 | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | CLOSE: (184) is inconsistent. % 22.15/3.98 | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | Case 2: % 22.15/3.98 | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | (185) all_355_0 = 0 | all_355_1 = 0 % 22.15/3.98 | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | BETA: splitting (185) gives: % 22.15/3.98 | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | Case 1: % 22.15/3.98 | | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | | (186) all_355_0 = 0 % 22.15/3.98 | | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (186) imply: % 22.15/3.98 | | | | | | | | | | | | | | | | | (187) all_17_1 = 0 % 22.15/3.98 | | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | | REDUCE: (15), (187) imply: % 22.15/3.98 | | | | | | | | | | | | | | | | | (188) $false % 22.15/3.98 | | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent. % 22.15/3.98 | | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | Case 2: % 22.15/3.98 | | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | | (189) all_355_1 = 0 % 22.15/3.98 | | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (189) imply: % 22.15/3.98 | | | | | | | | | | | | | | | | | (190) all_24_0 = 0 % 22.15/3.98 | | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | | REDUCE: (109), (190) imply: % 22.15/3.98 | | | | | | | | | | | | | | | | | (191) $false % 22.15/3.98 | | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | | CLOSE: (191) is inconsistent. % 22.15/3.98 | | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | | End of split % 22.15/3.98 | | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | | End of split % 22.15/3.98 | | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | | End of split % 22.15/3.98 | | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | | End of split % 22.15/3.98 | | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | | End of split % 22.15/3.98 | | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | | End of split % 22.15/3.98 | | | | | | | | | | | % 22.15/3.98 | | | | | | | | | | End of split % 22.15/3.98 | | | | | | | | | | % 22.15/3.98 | | | | | | | | | End of split % 22.15/3.98 | | | | | | | | | % 22.15/3.98 | | | | | | | | End of split % 22.15/3.98 | | | | | | | | % 22.15/3.98 | | | | | | | End of split % 22.15/3.98 | | | | | | | % 22.15/3.98 | | | | | | End of split % 22.15/3.98 | | | | | | % 22.15/3.98 | | | | | End of split % 22.15/3.98 | | | | | % 22.15/3.98 | | | | End of split % 22.15/3.98 | | | | % 22.15/3.98 | | | Case 2: % 22.15/3.98 | | | | % 22.15/3.98 | | | | (192) all_26_0 = 0 % 22.15/3.98 | | | | % 22.15/3.98 | | | | REDUCE: (106), (192) imply: % 22.15/3.98 | | | | (193) $false % 22.15/3.98 | | | | % 22.15/3.98 | | | | CLOSE: (193) is inconsistent. % 22.15/3.98 | | | | % 22.15/3.98 | | | End of split % 22.15/3.98 | | | % 22.15/3.98 | | Case 2: % 22.15/3.98 | | | % 22.15/3.98 | | | (194) ~ (all_32_1 = 0) % 22.15/3.98 | | | % 22.15/3.98 | | | REDUCE: (80), (194) imply: % 22.15/3.98 | | | (195) $false % 22.15/3.98 | | | % 22.15/3.98 | | | CLOSE: (195) is inconsistent. % 22.15/3.98 | | | % 22.15/3.98 | | End of split % 22.15/3.98 | | % 22.15/3.98 | End of split % 22.15/3.98 | % 22.15/3.98 End of proof % 22.15/3.98 % SZS output end Proof for theBenchmark % 22.15/3.98 % 22.15/3.98 3360ms %------------------------------------------------------------------------------