%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO171+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 : n010.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 23:21:48 EDT 2023 % Result : Theorem 8.54s 1.94s % Output : Proof 10.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEO171+1 : TPTP v8.1.2. Released v3.3.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n010.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 20:49:48 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/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.71/1.10 Prover 4: Preprocessing ... % 2.71/1.10 Prover 1: Preprocessing ... % 3.07/1.15 Prover 3: Preprocessing ... % 3.07/1.15 Prover 5: Preprocessing ... % 3.07/1.15 Prover 6: Preprocessing ... % 3.07/1.15 Prover 0: Preprocessing ... % 3.28/1.16 Prover 2: Preprocessing ... % 4.42/1.36 Prover 5: Proving ... % 4.42/1.37 Prover 2: Proving ... % 4.92/1.39 Prover 3: Constructing countermodel ... % 4.92/1.39 Prover 6: Constructing countermodel ... % 4.92/1.41 Prover 1: Constructing countermodel ... % 5.51/1.48 Prover 3: gave up % 5.51/1.48 Prover 1: gave up % 5.51/1.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.51/1.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.51/1.49 Prover 6: gave up % 5.51/1.49 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.74/1.53 Prover 4: Constructing countermodel ... % 5.92/1.53 Prover 8: Preprocessing ... % 5.92/1.54 Prover 9: Preprocessing ... % 5.92/1.54 Prover 7: Preprocessing ... % 5.92/1.57 Prover 0: Proving ... % 6.62/1.62 Prover 7: Warning: ignoring some quantifiers % 6.62/1.63 Prover 7: Constructing countermodel ... % 6.62/1.67 Prover 8: Warning: ignoring some quantifiers % 6.62/1.68 Prover 8: Constructing countermodel ... % 7.13/1.72 Prover 7: gave up % 7.13/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.13/1.72 Prover 8: gave up % 7.13/1.73 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.13/1.75 Prover 9: Constructing countermodel ... % 7.13/1.76 Prover 10: Preprocessing ... % 7.73/1.77 Prover 11: Preprocessing ... % 7.79/1.79 Prover 10: Warning: ignoring some quantifiers % 7.79/1.79 Prover 10: Constructing countermodel ... % 7.79/1.82 Prover 10: gave up % 7.79/1.82 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 7.79/1.85 Prover 12: Preprocessing ... % 8.54/1.94 Prover 9: proved (454ms) % 8.54/1.94 % 8.54/1.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.54/1.94 % 8.54/1.94 Prover 12: Proving ... % 8.54/1.96 Prover 5: stopped % 8.54/1.96 Prover 0: stopped % 8.54/1.97 Prover 2: stopped % 8.54/1.97 Prover 12: stopped % 8.54/1.97 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.54/1.97 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.54/1.97 Prover 11: Constructing countermodel ... % 8.54/1.97 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 9.23/1.97 Prover 13: Preprocessing ... % 9.23/1.97 Prover 16: Preprocessing ... % 9.23/1.98 Prover 19: Preprocessing ... % 9.39/2.00 Prover 16: Warning: ignoring some quantifiers % 9.39/2.00 Prover 13: Warning: ignoring some quantifiers % 9.39/2.00 Prover 16: Constructing countermodel ... % 9.39/2.01 Prover 13: Constructing countermodel ... % 9.39/2.01 Prover 4: Found proof (size 66) % 9.39/2.01 Prover 4: proved (1367ms) % 9.39/2.01 Prover 16: stopped % 9.39/2.01 Prover 13: stopped % 9.39/2.01 Prover 11: stopped % 9.61/2.04 Prover 19: Warning: ignoring some quantifiers % 9.61/2.04 Prover 19: Constructing countermodel ... % 9.61/2.05 Prover 19: stopped % 9.61/2.05 % 9.61/2.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.61/2.05 % 9.61/2.06 % SZS output start Proof for theBenchmark % 9.61/2.06 Assumptions after simplification: % 9.61/2.06 --------------------------------- % 9.61/2.06 % 9.61/2.06 (apart2) % 9.61/2.09 ! [v0: $i] : ( ~ (distinct_lines(v0, v0) = 0) | ~ $i(v0)) % 9.61/2.09 % 9.61/2.09 (apart3) % 9.61/2.09 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 9.61/2.09 % 9.61/2.09 (apart5) % 9.61/2.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 9.61/2.09 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = % 9.61/2.09 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 9.61/2.09 distinct_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 9.61/2.09 ! [v3: int] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ % 9.61/2.09 (distinct_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 9.61/2.09 distinct_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 9.61/2.09 [v3: int] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ % 9.61/2.09 (distinct_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 9.61/2.09 distinct_lines(v1, v2) = 0) % 9.61/2.09 % 9.61/2.09 (ceq3) % 9.61/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 9.61/2.10 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) % 9.61/2.10 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 9.61/2.10 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 9.61/2.10 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 9.61/2.10 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 9.61/2.10 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 9.61/2.10 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ % 9.61/2.10 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 9.61/2.10 convergent_lines(v0, v2) = 0) % 9.61/2.10 % 9.61/2.10 (ci3) % 9.61/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 9.61/2.10 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 9.61/2.10 (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 % 9.61/2.10 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 9.61/2.10 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 9.61/2.10 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 9.61/2.10 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 9.61/2.10 % 9.61/2.10 (ci4) % 9.61/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 9.61/2.10 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 9.61/2.10 (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 % 9.61/2.10 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 9.61/2.10 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 9.61/2.10 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 9.61/2.10 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 9.61/2.10 % 9.61/2.10 (con) % 10.01/2.10 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & convergent_lines(v0, % 10.01/2.10 v1) = 0 & distinct_lines(v0, v1) = v2 & $i(v1) & $i(v0)) % 10.01/2.10 % 10.01/2.10 (cu1) % 10.01/2.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 10.01/2.12 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 10.01/2.12 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 10.01/2.12 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 10.01/2.12 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, % 10.01/2.12 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 10.01/2.12 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 10.01/2.12 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 10.01/2.12 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 10.01/2.12 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 10.01/2.12 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 10.01/2.12 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 % 10.01/2.12 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 10.01/2.12 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 10.01/2.12 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 10.01/2.12 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 10.01/2.12 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 10.01/2.12 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 10.01/2.12 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = % 10.01/2.12 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 10.01/2.12 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = % 10.01/2.12 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 10.01/2.12 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 10.01/2.12 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = % 10.01/2.12 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 % 10.01/2.12 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : % 10.01/2.12 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 10.01/2.12 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 10.01/2.12 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 10.01/2.12 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 10.01/2.12 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & % 10.01/2.12 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 10.01/2.12 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 10.01/2.12 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ % 10.01/2.12 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 10.01/2.12 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 10.01/2.12 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, % 10.01/2.12 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 10.01/2.12 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 10.01/2.12 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 10.01/2.12 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 10.01/2.12 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 10.01/2.12 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 10.01/2.12 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 10.01/2.12 % 10.01/2.12 (function-axioms) % 10.01/2.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.01/2.12 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 10.01/2.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.01/2.12 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 10.01/2.12 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 10.01/2.12 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 10.01/2.12 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.01/2.12 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.01/2.12 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 10.01/2.12 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 10.01/2.12 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 10.01/2.12 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 10.01/2.12 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 10.01/2.12 (distinct_points(v3, v2) = v0)) % 10.01/2.12 % 10.01/2.12 Further assumptions not needed in the proof: % 10.01/2.12 -------------------------------------------- % 10.01/2.12 apart1, apart4, ax6, ceq1, ceq2, ci1, ci2 % 10.01/2.12 % 10.01/2.12 Those formulas are unsatisfiable: % 10.01/2.12 --------------------------------- % 10.01/2.12 % 10.01/2.12 Begin of proof % 10.01/2.12 | % 10.01/2.12 | ALPHA: (apart5) implies: % 10.01/2.13 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 10.01/2.13 | (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ % 10.01/2.13 | (distinct_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 10.01/2.13 | ? [v5: int] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) % 10.01/2.13 | % 10.01/2.13 | ALPHA: (ci3) implies: % 10.01/2.13 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 10.01/2.13 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 10.01/2.13 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 10.01/2.13 | & $i(v2))) % 10.01/2.13 | % 10.01/2.13 | ALPHA: (ci4) implies: % 10.01/2.13 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 10.01/2.13 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 10.01/2.13 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 10.01/2.13 | & $i(v2))) % 10.01/2.13 | % 10.01/2.13 | ALPHA: (cu1) implies: % 10.01/2.13 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 10.01/2.13 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 10.01/2.13 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 10.01/2.13 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 10.01/2.13 | [v9: any] : (apart_point_and_line(v1, v3) = v9 & % 10.01/2.13 | apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & % 10.01/2.13 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 10.01/2.13 | | v8 = 0))) % 10.01/2.13 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 10.01/2.13 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 10.01/2.13 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 10.01/2.13 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 10.01/2.13 | [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 10.01/2.13 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 10.01/2.13 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 10.01/2.13 | | v8 = 0))) % 10.01/2.13 | % 10.01/2.13 | ALPHA: (ceq3) implies: % 10.01/2.13 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 10.01/2.13 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | % 10.01/2.13 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 10.01/2.13 | % 10.01/2.13 | ALPHA: (function-axioms) implies: % 10.01/2.13 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.01/2.13 | ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 10.01/2.13 | (distinct_lines(v3, v2) = v0)) % 10.01/2.13 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.01/2.13 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 10.01/2.13 | v0)) % 10.01/2.13 | % 10.01/2.14 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2 % 10.01/2.14 | gives: % 10.01/2.14 | (9) ~ (all_17_0 = 0) & convergent_lines(all_17_2, all_17_1) = 0 & % 10.01/2.14 | distinct_lines(all_17_2, all_17_1) = all_17_0 & $i(all_17_1) & % 10.01/2.14 | $i(all_17_2) % 10.01/2.14 | % 10.01/2.14 | ALPHA: (9) implies: % 10.01/2.14 | (10) ~ (all_17_0 = 0) % 10.01/2.14 | (11) $i(all_17_2) % 10.01/2.14 | (12) $i(all_17_1) % 10.01/2.14 | (13) distinct_lines(all_17_2, all_17_1) = all_17_0 % 10.01/2.14 | (14) convergent_lines(all_17_2, all_17_1) = 0 % 10.01/2.14 | % 10.01/2.14 | GROUND_INST: instantiating (3) with all_17_2, all_17_1, simplifying with (11), % 10.01/2.14 | (12), (14) gives: % 10.01/2.14 | (15) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 10.01/2.14 | intersection_point(all_17_2, all_17_1) = v0 & % 10.01/2.14 | apart_point_and_line(v0, all_17_1) = v1 & $i(v0)) % 10.01/2.14 | % 10.01/2.14 | GROUND_INST: instantiating (2) with all_17_2, all_17_1, simplifying with (11), % 10.01/2.14 | (12), (14) gives: % 10.01/2.14 | (16) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 10.01/2.14 | intersection_point(all_17_2, all_17_1) = v0 & % 10.01/2.14 | apart_point_and_line(v0, all_17_2) = v1 & $i(v0)) % 10.01/2.14 | % 10.01/2.14 | DELTA: instantiating (16) with fresh symbols all_24_0, all_24_1 gives: % 10.01/2.14 | (17) ~ (all_24_0 = 0) & intersection_point(all_17_2, all_17_1) = all_24_1 % 10.01/2.14 | & apart_point_and_line(all_24_1, all_17_2) = all_24_0 & $i(all_24_1) % 10.01/2.14 | % 10.01/2.14 | ALPHA: (17) implies: % 10.01/2.14 | (18) ~ (all_24_0 = 0) % 10.01/2.14 | (19) apart_point_and_line(all_24_1, all_17_2) = all_24_0 % 10.01/2.14 | (20) intersection_point(all_17_2, all_17_1) = all_24_1 % 10.01/2.14 | % 10.01/2.14 | DELTA: instantiating (15) with fresh symbols all_26_0, all_26_1 gives: % 10.01/2.14 | (21) ~ (all_26_0 = 0) & intersection_point(all_17_2, all_17_1) = all_26_1 % 10.01/2.14 | & apart_point_and_line(all_26_1, all_17_1) = all_26_0 & $i(all_26_1) % 10.01/2.14 | % 10.01/2.14 | ALPHA: (21) implies: % 10.01/2.14 | (22) ~ (all_26_0 = 0) % 10.01/2.14 | (23) $i(all_26_1) % 10.01/2.14 | (24) apart_point_and_line(all_26_1, all_17_1) = all_26_0 % 10.01/2.14 | (25) intersection_point(all_17_2, all_17_1) = all_26_1 % 10.01/2.14 | % 10.01/2.14 | GROUND_INST: instantiating (8) with all_24_1, all_26_1, all_17_1, all_17_2, % 10.01/2.14 | simplifying with (20), (25) gives: % 10.01/2.14 | (26) all_26_1 = all_24_1 % 10.01/2.14 | % 10.01/2.14 | REDUCE: (24), (26) imply: % 10.01/2.14 | (27) apart_point_and_line(all_24_1, all_17_1) = all_26_0 % 10.01/2.14 | % 10.01/2.14 | REDUCE: (23), (26) imply: % 10.01/2.14 | (28) $i(all_24_1) % 10.01/2.14 | % 10.01/2.14 | GROUND_INST: instantiating (5) with all_24_1, all_24_1, all_17_1, all_17_1, % 10.01/2.14 | all_26_0, all_26_0, simplifying with (12), (27), (28) gives: % 10.01/2.15 | (29) all_26_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 10.01/2.15 | any] : (apart_point_and_line(all_24_1, all_17_1) = v3 & % 10.01/2.15 | apart_point_and_line(all_24_1, all_17_1) = v2 & % 10.01/2.15 | distinct_lines(all_17_1, all_17_1) = v1 & distinct_points(all_24_1, % 10.01/2.15 | all_24_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 10.01/2.15 | % 10.01/2.15 | GROUND_INST: instantiating (5) with all_24_1, all_24_1, all_17_1, all_17_2, % 10.01/2.15 | all_26_0, all_24_0, simplifying with (11), (12), (19), (27), (28) % 10.01/2.15 | gives: % 10.01/2.15 | (30) all_26_0 = 0 | all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 10.01/2.15 | any] : ? [v3: any] : (apart_point_and_line(all_24_1, all_17_1) = v3 % 10.01/2.15 | & apart_point_and_line(all_24_1, all_17_2) = v2 & % 10.01/2.15 | distinct_lines(all_17_1, all_17_2) = v1 & distinct_points(all_24_1, % 10.01/2.15 | all_24_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 10.01/2.15 | % 10.01/2.15 | GROUND_INST: instantiating (4) with all_24_1, all_24_1, all_17_1, all_17_2, % 10.01/2.15 | all_24_0, all_26_0, simplifying with (11), (12), (19), (27), (28) % 10.01/2.15 | gives: % 10.01/2.15 | (31) all_26_0 = 0 | all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 10.01/2.15 | any] : ? [v3: any] : (apart_point_and_line(all_24_1, all_17_1) = v2 % 10.01/2.15 | & apart_point_and_line(all_24_1, all_17_2) = v3 & % 10.01/2.15 | distinct_lines(all_17_1, all_17_2) = v1 & distinct_points(all_24_1, % 10.01/2.15 | all_24_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 10.01/2.15 | % 10.01/2.15 | BETA: splitting (29) gives: % 10.01/2.15 | % 10.01/2.15 | Case 1: % 10.01/2.15 | | % 10.01/2.15 | | (32) all_26_0 = 0 % 10.01/2.15 | | % 10.01/2.15 | | REDUCE: (22), (32) imply: % 10.01/2.15 | | (33) $false % 10.01/2.15 | | % 10.01/2.15 | | CLOSE: (33) is inconsistent. % 10.01/2.15 | | % 10.01/2.15 | Case 2: % 10.01/2.15 | | % 10.01/2.15 | | (34) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 10.01/2.15 | | (apart_point_and_line(all_24_1, all_17_1) = v3 & % 10.01/2.15 | | apart_point_and_line(all_24_1, all_17_1) = v2 & % 10.01/2.15 | | distinct_lines(all_17_1, all_17_1) = v1 & % 10.01/2.15 | | distinct_points(all_24_1, all_24_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 10.01/2.15 | | 0) | v3 = 0 | v2 = 0)) % 10.01/2.15 | | % 10.01/2.15 | | DELTA: instantiating (34) with fresh symbols all_45_0, all_45_1, all_45_2, % 10.01/2.15 | | all_45_3 gives: % 10.01/2.15 | | (35) apart_point_and_line(all_24_1, all_17_1) = all_45_0 & % 10.01/2.15 | | apart_point_and_line(all_24_1, all_17_1) = all_45_1 & % 10.01/2.15 | | distinct_lines(all_17_1, all_17_1) = all_45_2 & % 10.01/2.15 | | distinct_points(all_24_1, all_24_1) = all_45_3 & ( ~ (all_45_2 = 0) % 10.01/2.15 | | | ~ (all_45_3 = 0) | all_45_0 = 0 | all_45_1 = 0) % 10.01/2.15 | | % 10.01/2.15 | | ALPHA: (35) implies: % 10.01/2.15 | | (36) distinct_lines(all_17_1, all_17_1) = all_45_2 % 10.01/2.15 | | (37) ~ (all_45_2 = 0) | ~ (all_45_3 = 0) | all_45_0 = 0 | all_45_1 = 0 % 10.01/2.15 | | % 10.01/2.15 | | BETA: splitting (30) gives: % 10.01/2.15 | | % 10.01/2.15 | | Case 1: % 10.01/2.15 | | | % 10.01/2.15 | | | (38) all_26_0 = 0 % 10.01/2.15 | | | % 10.01/2.15 | | | REDUCE: (22), (38) imply: % 10.01/2.15 | | | (39) $false % 10.01/2.15 | | | % 10.01/2.15 | | | CLOSE: (39) is inconsistent. % 10.01/2.15 | | | % 10.01/2.15 | | Case 2: % 10.01/2.15 | | | % 10.01/2.16 | | | (40) all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 10.01/2.16 | | | [v3: any] : (apart_point_and_line(all_24_1, all_17_1) = v3 & % 10.01/2.16 | | | apart_point_and_line(all_24_1, all_17_2) = v2 & % 10.01/2.16 | | | distinct_lines(all_17_1, all_17_2) = v1 & % 10.01/2.16 | | | distinct_points(all_24_1, all_24_1) = v0 & ( ~ (v1 = 0) | ~ (v0 % 10.01/2.16 | | | = 0) | v3 = 0 | v2 = 0)) % 10.01/2.16 | | | % 10.01/2.16 | | | BETA: splitting (31) gives: % 10.01/2.16 | | | % 10.01/2.16 | | | Case 1: % 10.01/2.16 | | | | % 10.01/2.16 | | | | (41) all_26_0 = 0 % 10.01/2.16 | | | | % 10.01/2.16 | | | | REDUCE: (22), (41) imply: % 10.01/2.16 | | | | (42) $false % 10.01/2.16 | | | | % 10.01/2.16 | | | | CLOSE: (42) is inconsistent. % 10.01/2.16 | | | | % 10.01/2.16 | | | Case 2: % 10.01/2.16 | | | | % 10.01/2.16 | | | | (43) all_24_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 10.01/2.16 | | | | [v3: any] : (apart_point_and_line(all_24_1, all_17_1) = v2 & % 10.01/2.16 | | | | apart_point_and_line(all_24_1, all_17_2) = v3 & % 10.01/2.16 | | | | distinct_lines(all_17_1, all_17_2) = v1 & % 10.01/2.16 | | | | distinct_points(all_24_1, all_24_1) = v0 & ( ~ (v1 = 0) | ~ % 10.01/2.16 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 10.01/2.16 | | | | % 10.01/2.16 | | | | BETA: splitting (40) gives: % 10.01/2.16 | | | | % 10.01/2.16 | | | | Case 1: % 10.01/2.16 | | | | | % 10.01/2.16 | | | | | (44) all_24_0 = 0 % 10.01/2.16 | | | | | % 10.01/2.16 | | | | | REDUCE: (18), (44) imply: % 10.01/2.16 | | | | | (45) $false % 10.01/2.16 | | | | | % 10.01/2.16 | | | | | CLOSE: (45) is inconsistent. % 10.01/2.16 | | | | | % 10.01/2.16 | | | | Case 2: % 10.01/2.16 | | | | | % 10.01/2.16 | | | | | (46) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 10.01/2.16 | | | | | (apart_point_and_line(all_24_1, all_17_1) = v3 & % 10.01/2.16 | | | | | apart_point_and_line(all_24_1, all_17_2) = v2 & % 10.01/2.16 | | | | | distinct_lines(all_17_1, all_17_2) = v1 & % 10.01/2.16 | | | | | distinct_points(all_24_1, all_24_1) = v0 & ( ~ (v1 = 0) | ~ % 10.01/2.16 | | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 10.01/2.16 | | | | | % 10.01/2.16 | | | | | DELTA: instantiating (46) with fresh symbols all_58_0, all_58_1, % 10.01/2.16 | | | | | all_58_2, all_58_3 gives: % 10.01/2.16 | | | | | (47) apart_point_and_line(all_24_1, all_17_1) = all_58_0 & % 10.01/2.16 | | | | | apart_point_and_line(all_24_1, all_17_2) = all_58_1 & % 10.01/2.16 | | | | | distinct_lines(all_17_1, all_17_2) = all_58_2 & % 10.01/2.16 | | | | | distinct_points(all_24_1, all_24_1) = all_58_3 & ( ~ (all_58_2 % 10.01/2.16 | | | | | = 0) | ~ (all_58_3 = 0) | all_58_0 = 0 | all_58_1 = 0) % 10.01/2.16 | | | | | % 10.01/2.16 | | | | | ALPHA: (47) implies: % 10.01/2.16 | | | | | (48) distinct_lines(all_17_1, all_17_2) = all_58_2 % 10.01/2.16 | | | | | % 10.01/2.16 | | | | | BETA: splitting (43) gives: % 10.01/2.16 | | | | | % 10.01/2.16 | | | | | Case 1: % 10.01/2.16 | | | | | | % 10.01/2.16 | | | | | | (49) all_24_0 = 0 % 10.01/2.16 | | | | | | % 10.01/2.16 | | | | | | REDUCE: (18), (49) imply: % 10.01/2.16 | | | | | | (50) $false % 10.01/2.16 | | | | | | % 10.01/2.16 | | | | | | CLOSE: (50) is inconsistent. % 10.01/2.16 | | | | | | % 10.01/2.16 | | | | | Case 2: % 10.01/2.16 | | | | | | % 10.01/2.16 | | | | | | (51) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 10.01/2.16 | | | | | | (apart_point_and_line(all_24_1, all_17_1) = v2 & % 10.01/2.16 | | | | | | apart_point_and_line(all_24_1, all_17_2) = v3 & % 10.01/2.16 | | | | | | distinct_lines(all_17_1, all_17_2) = v1 & % 10.01/2.16 | | | | | | distinct_points(all_24_1, all_24_1) = v0 & ( ~ (v1 = 0) | % 10.01/2.16 | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 10.01/2.16 | | | | | | % 10.01/2.16 | | | | | | DELTA: instantiating (51) with fresh symbols all_63_0, all_63_1, % 10.01/2.16 | | | | | | all_63_2, all_63_3 gives: % 10.01/2.16 | | | | | | (52) apart_point_and_line(all_24_1, all_17_1) = all_63_1 & % 10.01/2.16 | | | | | | apart_point_and_line(all_24_1, all_17_2) = all_63_0 & % 10.01/2.16 | | | | | | distinct_lines(all_17_1, all_17_2) = all_63_2 & % 10.01/2.16 | | | | | | distinct_points(all_24_1, all_24_1) = all_63_3 & ( ~ % 10.01/2.16 | | | | | | (all_63_2 = 0) | ~ (all_63_3 = 0) | all_63_0 = 0 | % 10.01/2.16 | | | | | | all_63_1 = 0) % 10.01/2.16 | | | | | | % 10.01/2.16 | | | | | | ALPHA: (52) implies: % 10.01/2.16 | | | | | | (53) distinct_lines(all_17_1, all_17_2) = all_63_2 % 10.01/2.16 | | | | | | % 10.01/2.16 | | | | | | GROUND_INST: instantiating (7) with all_58_2, all_63_2, all_17_2, % 10.01/2.16 | | | | | | all_17_1, simplifying with (48), (53) gives: % 10.01/2.16 | | | | | | (54) all_63_2 = all_58_2 % 10.01/2.16 | | | | | | % 10.01/2.16 | | | | | | GROUND_INST: instantiating (6) with all_17_2, all_17_1, all_17_2, % 10.01/2.16 | | | | | | all_58_2, simplifying with (11), (12), (14), (48) % 10.01/2.16 | | | | | | gives: % 10.01/2.16 | | | | | | (55) all_58_2 = 0 | convergent_lines(all_17_2, all_17_2) = 0 % 10.01/2.16 | | | | | | % 10.01/2.16 | | | | | | GROUND_INST: instantiating (1) with all_17_1, all_17_2, all_17_1, % 10.01/2.16 | | | | | | all_45_2, all_17_0, simplifying with (11), (12), (13), % 10.01/2.16 | | | | | | (36) gives: % 10.01/2.17 | | | | | | (56) all_45_2 = 0 | all_17_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 10.01/2.17 | | | | | | distinct_lines(all_17_1, all_17_2) = v0) % 10.01/2.17 | | | | | | % 10.01/2.17 | | | | | | BETA: splitting (37) gives: % 10.01/2.17 | | | | | | % 10.01/2.17 | | | | | | Case 1: % 10.01/2.17 | | | | | | | % 10.01/2.17 | | | | | | | (57) ~ (all_45_2 = 0) % 10.01/2.17 | | | | | | | % 10.01/2.17 | | | | | | | BETA: splitting (56) gives: % 10.01/2.17 | | | | | | | % 10.01/2.17 | | | | | | | Case 1: % 10.01/2.17 | | | | | | | | % 10.01/2.17 | | | | | | | | (58) all_45_2 = 0 % 10.01/2.17 | | | | | | | | % 10.01/2.17 | | | | | | | | REDUCE: (57), (58) imply: % 10.01/2.17 | | | | | | | | (59) $false % 10.01/2.17 | | | | | | | | % 10.01/2.17 | | | | | | | | CLOSE: (59) is inconsistent. % 10.01/2.17 | | | | | | | | % 10.01/2.17 | | | | | | | Case 2: % 10.01/2.17 | | | | | | | | % 10.01/2.17 | | | | | | | | (60) all_17_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 10.01/2.17 | | | | | | | | distinct_lines(all_17_1, all_17_2) = v0) % 10.01/2.17 | | | | | | | | % 10.01/2.17 | | | | | | | | BETA: splitting (60) gives: % 10.01/2.17 | | | | | | | | % 10.01/2.17 | | | | | | | | Case 1: % 10.01/2.17 | | | | | | | | | % 10.01/2.17 | | | | | | | | | (61) all_17_0 = 0 % 10.01/2.17 | | | | | | | | | % 10.01/2.17 | | | | | | | | | REDUCE: (10), (61) imply: % 10.01/2.17 | | | | | | | | | (62) $false % 10.01/2.17 | | | | | | | | | % 10.01/2.17 | | | | | | | | | CLOSE: (62) is inconsistent. % 10.01/2.17 | | | | | | | | | % 10.01/2.17 | | | | | | | | Case 2: % 10.01/2.17 | | | | | | | | | % 10.01/2.17 | | | | | | | | | (63) ? [v0: int] : ( ~ (v0 = 0) & distinct_lines(all_17_1, % 10.01/2.17 | | | | | | | | | all_17_2) = v0) % 10.01/2.17 | | | | | | | | | % 10.01/2.17 | | | | | | | | | DELTA: instantiating (63) with fresh symbol all_84_0 gives: % 10.01/2.17 | | | | | | | | | (64) ~ (all_84_0 = 0) & distinct_lines(all_17_1, all_17_2) % 10.01/2.17 | | | | | | | | | = all_84_0 % 10.01/2.17 | | | | | | | | | % 10.01/2.17 | | | | | | | | | ALPHA: (64) implies: % 10.01/2.17 | | | | | | | | | (65) ~ (all_84_0 = 0) % 10.01/2.17 | | | | | | | | | (66) distinct_lines(all_17_1, all_17_2) = all_84_0 % 10.01/2.17 | | | | | | | | | % 10.01/2.17 | | | | | | | | | GROUND_INST: instantiating (7) with all_58_2, all_84_0, % 10.01/2.17 | | | | | | | | | all_17_2, all_17_1, simplifying with (48), (66) % 10.01/2.17 | | | | | | | | | gives: % 10.01/2.17 | | | | | | | | | (67) all_84_0 = all_58_2 % 10.01/2.17 | | | | | | | | | % 10.01/2.17 | | | | | | | | | REDUCE: (65), (67) imply: % 10.01/2.17 | | | | | | | | | (68) ~ (all_58_2 = 0) % 10.01/2.17 | | | | | | | | | % 10.01/2.17 | | | | | | | | | BETA: splitting (55) gives: % 10.01/2.17 | | | | | | | | | % 10.01/2.17 | | | | | | | | | Case 1: % 10.01/2.17 | | | | | | | | | | % 10.01/2.17 | | | | | | | | | | (69) convergent_lines(all_17_2, all_17_2) = 0 % 10.01/2.17 | | | | | | | | | | % 10.01/2.17 | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_17_2, simplifying % 10.01/2.17 | | | | | | | | | | with (11), (69) gives: % 10.01/2.17 | | | | | | | | | | (70) $false % 10.01/2.17 | | | | | | | | | | % 10.01/2.17 | | | | | | | | | | CLOSE: (70) is inconsistent. % 10.01/2.17 | | | | | | | | | | % 10.01/2.17 | | | | | | | | | Case 2: % 10.01/2.17 | | | | | | | | | | % 10.01/2.17 | | | | | | | | | | (71) all_58_2 = 0 % 10.01/2.17 | | | | | | | | | | % 10.01/2.17 | | | | | | | | | | REDUCE: (68), (71) imply: % 10.01/2.17 | | | | | | | | | | (72) $false % 10.01/2.17 | | | | | | | | | | % 10.01/2.17 | | | | | | | | | | CLOSE: (72) is inconsistent. % 10.01/2.17 | | | | | | | | | | % 10.01/2.17 | | | | | | | | | End of split % 10.01/2.17 | | | | | | | | | % 10.01/2.17 | | | | | | | | End of split % 10.01/2.17 | | | | | | | | % 10.01/2.17 | | | | | | | End of split % 10.01/2.17 | | | | | | | % 10.01/2.17 | | | | | | Case 2: % 10.01/2.17 | | | | | | | % 10.01/2.17 | | | | | | | (73) all_45_2 = 0 % 10.01/2.17 | | | | | | | % 10.01/2.17 | | | | | | | REDUCE: (36), (73) imply: % 10.01/2.17 | | | | | | | (74) distinct_lines(all_17_1, all_17_1) = 0 % 10.01/2.17 | | | | | | | % 10.01/2.17 | | | | | | | GROUND_INST: instantiating (apart2) with all_17_1, simplifying % 10.01/2.17 | | | | | | | with (12), (74) gives: % 10.01/2.17 | | | | | | | (75) $false % 10.01/2.17 | | | | | | | % 10.01/2.17 | | | | | | | CLOSE: (75) is inconsistent. % 10.01/2.17 | | | | | | | % 10.01/2.17 | | | | | | End of split % 10.01/2.17 | | | | | | % 10.01/2.17 | | | | | End of split % 10.01/2.17 | | | | | % 10.01/2.17 | | | | End of split % 10.01/2.17 | | | | % 10.01/2.17 | | | End of split % 10.01/2.17 | | | % 10.01/2.17 | | End of split % 10.01/2.17 | | % 10.01/2.17 | End of split % 10.01/2.17 | % 10.01/2.17 End of proof % 10.01/2.17 % SZS output end Proof for theBenchmark % 10.01/2.17 % 10.01/2.17 1551ms %------------------------------------------------------------------------------