%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO192+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 : n016.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 23:22:05 EDT 2023 % Result : Theorem 7.94s 1.78s % Output : Proof 11.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : GEO192+1 : TPTP v8.1.2. Released v3.3.0. % 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n016.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 22:07:46 EDT 2023 % 0.13/0.34 % CPUTime : % 0.50/0.61 ________ _____ % 0.50/0.61 ___ __ \_________(_)________________________________ % 0.50/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.50/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.50/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.50/0.61 % 0.50/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.50/0.61 (2023-06-19) % 0.50/0.61 % 0.50/0.61 (c) Philipp Rümmer, 2009-2023 % 0.50/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.50/0.61 Amanda Stjerna. % 0.50/0.61 Free software under BSD-3-Clause. % 0.50/0.61 % 0.50/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.50/0.61 % 0.50/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.50/0.63 Running up to 7 provers in parallel. % 0.72/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.72/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.72/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.72/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.72/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.72/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.72/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.26/1.02 Prover 4: Preprocessing ... % 2.26/1.02 Prover 1: Preprocessing ... % 2.71/1.06 Prover 3: Preprocessing ... % 2.71/1.06 Prover 6: Preprocessing ... % 2.71/1.06 Prover 5: Preprocessing ... % 2.71/1.06 Prover 2: Preprocessing ... % 2.71/1.06 Prover 0: Preprocessing ... % 4.39/1.27 Prover 2: Proving ... % 4.39/1.27 Prover 5: Proving ... % 4.39/1.30 Prover 3: Constructing countermodel ... % 4.39/1.30 Prover 1: Constructing countermodel ... % 4.39/1.30 Prover 6: Constructing countermodel ... % 5.05/1.41 Prover 3: gave up % 5.05/1.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.05/1.42 Prover 6: gave up % 5.05/1.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.47/1.42 Prover 4: Constructing countermodel ... % 5.47/1.43 Prover 1: gave up % 5.47/1.43 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.47/1.46 Prover 7: Preprocessing ... % 5.47/1.46 Prover 0: Proving ... % 5.76/1.47 Prover 9: Preprocessing ... % 5.76/1.47 Prover 8: Preprocessing ... % 5.76/1.51 Prover 7: Warning: ignoring some quantifiers % 5.76/1.52 Prover 7: Constructing countermodel ... % 6.30/1.55 Prover 8: Warning: ignoring some quantifiers % 6.30/1.56 Prover 8: Constructing countermodel ... % 6.59/1.61 Prover 8: gave up % 6.59/1.63 Prover 9: Constructing countermodel ... % 6.59/1.63 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.13/1.67 Prover 7: gave up % 7.31/1.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.31/1.70 Prover 10: Preprocessing ... % 7.31/1.71 Prover 11: Preprocessing ... % 7.76/1.74 Prover 10: Warning: ignoring some quantifiers % 7.76/1.75 Prover 10: Constructing countermodel ... % 7.94/1.78 Prover 0: proved (1152ms) % 7.94/1.78 % 7.94/1.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.94/1.78 % 7.94/1.79 Prover 9: stopped % 7.94/1.79 Prover 5: stopped % 7.94/1.79 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 7.94/1.79 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.94/1.81 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.94/1.81 Prover 10: gave up % 7.94/1.82 Prover 2: stopped % 8.38/1.83 Prover 13: Preprocessing ... % 8.38/1.83 Prover 19: Preprocessing ... % 8.38/1.84 Prover 16: Preprocessing ... % 8.65/1.86 Prover 16: Warning: ignoring some quantifiers % 8.65/1.87 Prover 16: Constructing countermodel ... % 8.65/1.88 Prover 11: Constructing countermodel ... % 8.65/1.88 Prover 13: Warning: ignoring some quantifiers % 8.65/1.89 Prover 19: Warning: ignoring some quantifiers % 8.65/1.89 Prover 13: Constructing countermodel ... % 8.65/1.89 Prover 19: Constructing countermodel ... % 9.22/1.94 Prover 19: gave up % 9.48/1.98 Prover 16: gave up % 9.48/2.00 Prover 13: gave up % 10.04/2.12 Prover 11: Found proof (size 89) % 10.04/2.12 Prover 11: proved (439ms) % 10.04/2.12 Prover 4: stopped % 10.04/2.12 % 10.04/2.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.04/2.12 % 10.38/2.14 % SZS output start Proof for theBenchmark % 10.38/2.15 Assumptions after simplification: % 10.38/2.15 --------------------------------- % 10.38/2.15 % 10.38/2.15 (apart2) % 10.60/2.17 ! [v0: $i] : ( ~ (distinct_lines(v0, v0) = 0) | ~ $i(v0)) % 10.60/2.17 % 10.60/2.17 (apart5) % 10.60/2.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 10.60/2.17 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = % 10.60/2.17 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 10.60/2.18 distinct_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 10.60/2.18 ! [v3: int] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ % 10.60/2.18 (distinct_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 10.60/2.18 distinct_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 10.60/2.18 [v3: int] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ % 10.60/2.18 (distinct_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 10.60/2.18 distinct_lines(v1, v2) = 0) % 10.60/2.18 % 10.60/2.18 (ceq2) % 10.60/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 10.60/2.18 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 10.60/2.18 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 10.60/2.18 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 10.60/2.18 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 10.60/2.18 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 10.60/2.18 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 10.60/2.18 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 10.60/2.18 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 10.60/2.18 apart_point_and_line(v0, v2) = 0) % 10.60/2.18 % 10.60/2.18 (ci3) % 10.60/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 10.60/2.18 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 10.60/2.18 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 10.60/2.18 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 10.60/2.18 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 10.60/2.19 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 10.60/2.19 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 10.60/2.19 % 10.60/2.19 (ci4) % 10.60/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 10.60/2.19 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 10.60/2.19 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 10.60/2.19 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 10.60/2.19 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 10.60/2.19 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 10.60/2.19 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 10.60/2.19 % 10.60/2.19 (con) % 10.60/2.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: % 10.60/2.19 int] : (intersection_point(v0, v1) = v3 & apart_point_and_line(v3, v2) = 0 & % 10.60/2.19 convergent_lines(v0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (( ~ (v5 % 10.60/2.19 = 0) & distinct_lines(v1, v2) = v5) | ( ~ (v4 = 0) & % 10.60/2.19 distinct_lines(v0, v2) = v4))) % 10.60/2.19 % 10.60/2.19 (cu1) % 10.60/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 10.60/2.21 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 10.60/2.21 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 10.60/2.21 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 10.60/2.21 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 10.60/2.21 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, % 10.60/2.21 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 10.60/2.21 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, % 10.60/2.21 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ % 10.60/2.21 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 10.60/2.21 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 10.60/2.21 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0, % 10.60/2.21 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 10.60/2.21 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 10.60/2.22 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 10.60/2.22 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 10.60/2.22 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 10.60/2.22 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 10.60/2.22 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 10.60/2.22 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 10.60/2.22 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 10.60/2.22 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 10.60/2.22 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 10.60/2.22 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 10.60/2.22 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 10.60/2.22 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 10.60/2.22 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 10.60/2.22 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 10.60/2.22 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 10.60/2.22 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~ % 10.60/2.22 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 10.60/2.22 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 10.60/2.22 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, % 10.60/2.22 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 10.60/2.22 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, % 10.60/2.22 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 10.60/2.22 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 10.60/2.22 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 10.60/2.22 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1, % 10.60/2.22 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i] % 10.60/2.22 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | % 10.60/2.22 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 10.60/2.22 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = % 10.60/2.22 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 10.60/2.22 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0, % 10.60/2.22 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 10.60/2.22 % 10.60/2.22 (function-axioms) % 10.60/2.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.60/2.22 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 10.60/2.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.60/2.22 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 10.60/2.22 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 10.60/2.22 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 10.60/2.22 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.60/2.22 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.60/2.22 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 10.60/2.22 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 10.60/2.22 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 10.60/2.22 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 10.60/2.22 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 10.60/2.22 (distinct_points(v3, v2) = v0)) % 10.60/2.22 % 10.60/2.22 Further assumptions not needed in the proof: % 10.60/2.22 -------------------------------------------- % 10.60/2.22 apart1, apart3, apart4, ax6, ceq1, ceq3, ci1, ci2 % 10.60/2.22 % 10.60/2.22 Those formulas are unsatisfiable: % 10.60/2.22 --------------------------------- % 10.60/2.22 % 10.60/2.22 Begin of proof % 10.60/2.23 | % 10.60/2.23 | ALPHA: (apart5) implies: % 10.60/2.23 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 10.60/2.23 | (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | ~ % 10.60/2.23 | $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v0, v2) = 0) % 10.60/2.23 | % 10.60/2.23 | ALPHA: (ci3) implies: % 10.60/2.23 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 10.60/2.23 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 10.60/2.23 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 10.60/2.23 | & $i(v2))) % 10.60/2.23 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 10.60/2.23 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 10.60/2.23 | (( ~ (v4 = 0) & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 10.60/2.23 | convergent_lines(v0, v1) = v3))) % 10.60/2.23 | % 10.60/2.23 | ALPHA: (ci4) implies: % 10.60/2.23 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 10.60/2.23 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 10.60/2.23 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 10.60/2.23 | & $i(v2))) % 10.60/2.23 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 10.60/2.23 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 10.60/2.23 | (( ~ (v4 = 0) & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 10.60/2.23 | convergent_lines(v0, v1) = v3))) % 10.60/2.23 | % 10.60/2.23 | ALPHA: (cu1) implies: % 10.60/2.23 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 10.60/2.23 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 10.60/2.23 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 10.60/2.23 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 10.60/2.23 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 10.60/2.23 | apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & % 10.60/2.23 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 10.60/2.23 | v1) = v6))) % 10.60/2.24 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 10.60/2.24 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 10.60/2.24 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 10.60/2.24 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 10.60/2.24 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 10.60/2.24 | apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & % 10.60/2.24 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 10.60/2.24 | v1) = v6))) % 10.60/2.24 | % 10.60/2.24 | ALPHA: (ceq2) implies: % 10.60/2.24 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 10.60/2.24 | (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, % 10.60/2.24 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v1, % 10.60/2.24 | v2) = 0) % 10.60/2.24 | % 10.60/2.24 | ALPHA: (function-axioms) implies: % 10.60/2.24 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.60/2.24 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 10.60/2.24 | (convergent_lines(v3, v2) = v0)) % 10.60/2.24 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 10.60/2.24 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 10.60/2.24 | (apart_point_and_line(v3, v2) = v0)) % 10.60/2.24 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.60/2.24 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 10.60/2.24 | v0)) % 10.60/2.24 | % 10.60/2.24 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 10.60/2.24 | all_17_3, all_17_4, all_17_5 gives: % 10.60/2.24 | (12) intersection_point(all_17_5, all_17_4) = all_17_2 & % 10.60/2.24 | apart_point_and_line(all_17_2, all_17_3) = 0 & % 10.60/2.24 | convergent_lines(all_17_5, all_17_4) = 0 & $i(all_17_2) & $i(all_17_3) % 10.60/2.24 | & $i(all_17_4) & $i(all_17_5) & (( ~ (all_17_0 = 0) & % 10.60/2.24 | distinct_lines(all_17_4, all_17_3) = all_17_0) | ( ~ (all_17_1 = % 10.60/2.24 | 0) & distinct_lines(all_17_5, all_17_3) = all_17_1)) % 10.60/2.24 | % 10.60/2.24 | ALPHA: (12) implies: % 10.60/2.24 | (13) $i(all_17_5) % 10.60/2.24 | (14) $i(all_17_4) % 10.60/2.24 | (15) $i(all_17_3) % 10.60/2.24 | (16) convergent_lines(all_17_5, all_17_4) = 0 % 10.60/2.24 | (17) apart_point_and_line(all_17_2, all_17_3) = 0 % 10.60/2.24 | (18) intersection_point(all_17_5, all_17_4) = all_17_2 % 10.60/2.24 | (19) ( ~ (all_17_0 = 0) & distinct_lines(all_17_4, all_17_3) = all_17_0) | % 10.60/2.24 | ( ~ (all_17_1 = 0) & distinct_lines(all_17_5, all_17_3) = all_17_1) % 10.60/2.24 | % 10.97/2.24 | GROUND_INST: instantiating (4) with all_17_5, all_17_4, simplifying with (13), % 10.97/2.24 | (14), (16) gives: % 10.97/2.24 | (20) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 10.97/2.24 | intersection_point(all_17_5, all_17_4) = v0 & % 10.97/2.24 | apart_point_and_line(v0, all_17_4) = v1 & $i(v0)) % 10.97/2.24 | % 10.97/2.24 | GROUND_INST: instantiating (2) with all_17_5, all_17_4, simplifying with (13), % 10.97/2.24 | (14), (16) gives: % 10.97/2.24 | (21) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 10.97/2.24 | intersection_point(all_17_5, all_17_4) = v0 & % 10.97/2.24 | apart_point_and_line(v0, all_17_5) = v1 & $i(v0)) % 10.97/2.24 | % 10.97/2.25 | GROUND_INST: instantiating (5) with all_17_5, all_17_4, all_17_2, simplifying % 10.97/2.25 | with (13), (14), (18) gives: % 10.97/2.25 | (22) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 10.97/2.25 | apart_point_and_line(all_17_2, all_17_4) = v1) | ( ~ (v0 = 0) & % 10.97/2.25 | convergent_lines(all_17_5, all_17_4) = v0)) % 10.97/2.25 | % 10.97/2.25 | GROUND_INST: instantiating (3) with all_17_5, all_17_4, all_17_2, simplifying % 10.97/2.25 | with (13), (14), (18) gives: % 10.97/2.25 | (23) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 10.97/2.25 | apart_point_and_line(all_17_2, all_17_5) = v1) | ( ~ (v0 = 0) & % 10.97/2.25 | convergent_lines(all_17_5, all_17_4) = v0)) % 10.97/2.25 | % 10.97/2.25 | DELTA: instantiating (23) with fresh symbols all_24_0, all_24_1 gives: % 10.97/2.25 | (24) ( ~ (all_24_0 = 0) & apart_point_and_line(all_17_2, all_17_5) = % 10.97/2.25 | all_24_0) | ( ~ (all_24_1 = 0) & convergent_lines(all_17_5, % 10.97/2.25 | all_17_4) = all_24_1) % 10.97/2.25 | % 10.97/2.25 | DELTA: instantiating (22) with fresh symbols all_25_0, all_25_1 gives: % 10.97/2.25 | (25) ( ~ (all_25_0 = 0) & apart_point_and_line(all_17_2, all_17_4) = % 10.97/2.25 | all_25_0) | ( ~ (all_25_1 = 0) & convergent_lines(all_17_5, % 10.97/2.25 | all_17_4) = all_25_1) % 10.97/2.25 | % 10.97/2.25 | DELTA: instantiating (21) with fresh symbols all_26_0, all_26_1 gives: % 10.97/2.25 | (26) ~ (all_26_0 = 0) & intersection_point(all_17_5, all_17_4) = all_26_1 % 10.97/2.25 | & apart_point_and_line(all_26_1, all_17_5) = all_26_0 & $i(all_26_1) % 10.97/2.25 | % 10.97/2.25 | ALPHA: (26) implies: % 10.97/2.25 | (27) ~ (all_26_0 = 0) % 10.97/2.25 | (28) $i(all_26_1) % 10.97/2.25 | (29) apart_point_and_line(all_26_1, all_17_5) = all_26_0 % 10.97/2.25 | (30) intersection_point(all_17_5, all_17_4) = all_26_1 % 10.97/2.25 | % 10.97/2.25 | DELTA: instantiating (20) with fresh symbols all_28_0, all_28_1 gives: % 10.97/2.25 | (31) ~ (all_28_0 = 0) & intersection_point(all_17_5, all_17_4) = all_28_1 % 10.97/2.25 | & apart_point_and_line(all_28_1, all_17_4) = all_28_0 & $i(all_28_1) % 10.97/2.25 | % 10.97/2.25 | ALPHA: (31) implies: % 10.97/2.25 | (32) ~ (all_28_0 = 0) % 10.97/2.25 | (33) apart_point_and_line(all_28_1, all_17_4) = all_28_0 % 10.97/2.25 | (34) intersection_point(all_17_5, all_17_4) = all_28_1 % 10.97/2.25 | % 10.97/2.25 | BETA: splitting (24) gives: % 10.97/2.25 | % 10.97/2.25 | Case 1: % 10.97/2.25 | | % 10.97/2.25 | | (35) ~ (all_24_0 = 0) & apart_point_and_line(all_17_2, all_17_5) = % 10.97/2.25 | | all_24_0 % 10.97/2.25 | | % 10.97/2.25 | | ALPHA: (35) implies: % 10.97/2.25 | | (36) apart_point_and_line(all_17_2, all_17_5) = all_24_0 % 10.97/2.25 | | % 10.97/2.25 | | BETA: splitting (25) gives: % 10.97/2.25 | | % 10.97/2.25 | | Case 1: % 10.97/2.25 | | | % 10.97/2.25 | | | (37) ~ (all_25_0 = 0) & apart_point_and_line(all_17_2, all_17_4) = % 10.97/2.25 | | | all_25_0 % 10.97/2.25 | | | % 10.97/2.25 | | | ALPHA: (37) implies: % 10.97/2.25 | | | (38) apart_point_and_line(all_17_2, all_17_4) = all_25_0 % 10.97/2.25 | | | % 10.97/2.25 | | | GROUND_INST: instantiating (11) with all_17_2, all_28_1, all_17_4, % 10.97/2.25 | | | all_17_5, simplifying with (18), (34) gives: % 10.97/2.25 | | | (39) all_28_1 = all_17_2 % 10.97/2.25 | | | % 10.97/2.25 | | | GROUND_INST: instantiating (11) with all_26_1, all_28_1, all_17_4, % 10.97/2.25 | | | all_17_5, simplifying with (30), (34) gives: % 10.97/2.25 | | | (40) all_28_1 = all_26_1 % 10.97/2.25 | | | % 10.97/2.25 | | | COMBINE_EQS: (39), (40) imply: % 10.97/2.25 | | | (41) all_26_1 = all_17_2 % 10.97/2.25 | | | % 10.97/2.25 | | | REDUCE: (33), (39) imply: % 10.97/2.25 | | | (42) apart_point_and_line(all_17_2, all_17_4) = all_28_0 % 10.97/2.25 | | | % 10.97/2.25 | | | REDUCE: (29), (41) imply: % 10.97/2.25 | | | (43) apart_point_and_line(all_17_2, all_17_5) = all_26_0 % 10.97/2.26 | | | % 10.97/2.26 | | | REDUCE: (28), (41) imply: % 10.97/2.26 | | | (44) $i(all_17_2) % 10.97/2.26 | | | % 10.97/2.26 | | | GROUND_INST: instantiating (10) with all_24_0, all_26_0, all_17_5, % 10.97/2.26 | | | all_17_2, simplifying with (36), (43) gives: % 10.97/2.26 | | | (45) all_26_0 = all_24_0 % 10.97/2.26 | | | % 10.97/2.26 | | | GROUND_INST: instantiating (10) with all_25_0, all_28_0, all_17_4, % 10.97/2.26 | | | all_17_2, simplifying with (38), (42) gives: % 10.97/2.26 | | | (46) all_28_0 = all_25_0 % 10.97/2.26 | | | % 10.97/2.26 | | | REDUCE: (32), (46) imply: % 10.97/2.26 | | | (47) ~ (all_25_0 = 0) % 10.97/2.26 | | | % 10.97/2.26 | | | REDUCE: (27), (45) imply: % 10.97/2.26 | | | (48) ~ (all_24_0 = 0) % 10.97/2.26 | | | % 10.97/2.26 | | | GROUND_INST: instantiating (8) with all_17_2, all_17_3, all_17_5, % 10.97/2.26 | | | all_24_0, simplifying with (13), (15), (17), (36), (44) % 10.97/2.26 | | | gives: % 10.97/2.26 | | | (49) all_24_0 = 0 | distinct_lines(all_17_3, all_17_5) = 0 % 10.97/2.26 | | | % 10.97/2.26 | | | GROUND_INST: instantiating (8) with all_17_2, all_17_3, all_17_4, % 10.97/2.26 | | | all_25_0, simplifying with (14), (15), (17), (38), (44) % 10.97/2.26 | | | gives: % 10.97/2.26 | | | (50) all_25_0 = 0 | distinct_lines(all_17_3, all_17_4) = 0 % 10.97/2.26 | | | % 10.97/2.26 | | | GROUND_INST: instantiating (7) with all_17_2, all_17_2, all_17_4, % 10.97/2.26 | | | all_17_5, all_25_0, all_24_0, simplifying with (13), (14), % 10.97/2.26 | | | (36), (38), (44) gives: % 10.97/2.26 | | | (51) all_25_0 = 0 | all_24_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 10.97/2.26 | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 10.97/2.26 | | | apart_point_and_line(all_17_2, all_17_4) = 0) | (v2 = 0 & % 10.97/2.26 | | | apart_point_and_line(all_17_2, all_17_5) = 0) | ( ~ (v1 = 0) & % 10.97/2.26 | | | distinct_lines(all_17_4, all_17_5) = v1) | ( ~ (v0 = 0) & % 10.97/2.26 | | | distinct_points(all_17_2, all_17_2) = v0)) % 10.97/2.26 | | | % 10.97/2.26 | | | GROUND_INST: instantiating (6) with all_17_2, all_17_2, all_17_4, % 10.97/2.26 | | | all_17_5, all_24_0, all_25_0, simplifying with (13), (14), % 10.97/2.26 | | | (36), (38), (44) gives: % 10.97/2.27 | | | (52) all_25_0 = 0 | all_24_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 10.97/2.27 | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 10.97/2.27 | | | apart_point_and_line(all_17_2, all_17_5) = 0) | (v2 = 0 & % 10.97/2.27 | | | apart_point_and_line(all_17_2, all_17_4) = 0) | ( ~ (v1 = 0) & % 10.97/2.27 | | | distinct_lines(all_17_4, all_17_5) = v1) | ( ~ (v0 = 0) & % 10.97/2.27 | | | distinct_points(all_17_2, all_17_2) = v0)) % 10.97/2.27 | | | % 10.97/2.27 | | | BETA: splitting (19) gives: % 10.97/2.27 | | | % 10.97/2.27 | | | Case 1: % 10.97/2.27 | | | | % 10.97/2.27 | | | | (53) ~ (all_17_0 = 0) & distinct_lines(all_17_4, all_17_3) = % 10.97/2.27 | | | | all_17_0 % 10.97/2.27 | | | | % 10.97/2.27 | | | | ALPHA: (53) implies: % 10.97/2.27 | | | | (54) ~ (all_17_0 = 0) % 10.97/2.27 | | | | (55) distinct_lines(all_17_4, all_17_3) = all_17_0 % 10.97/2.27 | | | | % 10.97/2.27 | | | | BETA: splitting (50) gives: % 10.97/2.27 | | | | % 10.97/2.27 | | | | Case 1: % 10.97/2.27 | | | | | % 10.97/2.27 | | | | | (56) distinct_lines(all_17_3, all_17_4) = 0 % 10.97/2.27 | | | | | % 10.97/2.27 | | | | | BETA: splitting (52) gives: % 10.97/2.27 | | | | | % 10.97/2.27 | | | | | Case 1: % 10.97/2.27 | | | | | | % 10.97/2.27 | | | | | | (57) all_25_0 = 0 % 10.97/2.27 | | | | | | % 10.97/2.27 | | | | | | REDUCE: (47), (57) imply: % 10.97/2.27 | | | | | | (58) $false % 10.97/2.27 | | | | | | % 10.97/2.27 | | | | | | CLOSE: (58) is inconsistent. % 10.97/2.27 | | | | | | % 10.97/2.27 | | | | | Case 2: % 10.97/2.27 | | | | | | % 10.97/2.27 | | | | | | (59) all_24_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : % 10.97/2.27 | | | | | | ? [v3: int] : ((v3 = 0 & apart_point_and_line(all_17_2, % 10.97/2.27 | | | | | | all_17_5) = 0) | (v2 = 0 & % 10.97/2.27 | | | | | | apart_point_and_line(all_17_2, all_17_4) = 0) | ( ~ (v1 % 10.97/2.27 | | | | | | = 0) & distinct_lines(all_17_4, all_17_5) = v1) | ( ~ % 10.97/2.27 | | | | | | (v0 = 0) & distinct_points(all_17_2, all_17_2) = v0)) % 10.97/2.27 | | | | | | % 10.97/2.27 | | | | | | BETA: splitting (59) gives: % 10.97/2.27 | | | | | | % 10.97/2.27 | | | | | | Case 1: % 10.97/2.27 | | | | | | | % 10.97/2.27 | | | | | | | (60) all_24_0 = 0 % 10.97/2.27 | | | | | | | % 10.97/2.27 | | | | | | | REDUCE: (48), (60) imply: % 10.97/2.27 | | | | | | | (61) $false % 10.97/2.27 | | | | | | | % 10.97/2.27 | | | | | | | CLOSE: (61) is inconsistent. % 10.97/2.27 | | | | | | | % 10.97/2.27 | | | | | | Case 2: % 10.97/2.27 | | | | | | | % 10.97/2.27 | | | | | | | % 10.97/2.27 | | | | | | | GROUND_INST: instantiating (1) with all_17_3, all_17_4, all_17_3, % 10.97/2.27 | | | | | | | all_17_0, simplifying with (14), (15), (55), (56) % 10.97/2.27 | | | | | | | gives: % 10.97/2.27 | | | | | | | (62) all_17_0 = 0 | distinct_lines(all_17_3, all_17_3) = 0 % 10.97/2.27 | | | | | | | % 10.97/2.27 | | | | | | | BETA: splitting (62) gives: % 10.97/2.27 | | | | | | | % 10.97/2.27 | | | | | | | Case 1: % 10.97/2.27 | | | | | | | | % 10.97/2.27 | | | | | | | | (63) distinct_lines(all_17_3, all_17_3) = 0 % 10.97/2.27 | | | | | | | | % 10.97/2.27 | | | | | | | | GROUND_INST: instantiating (apart2) with all_17_3, simplifying % 10.97/2.27 | | | | | | | | with (15), (63) gives: % 10.97/2.27 | | | | | | | | (64) $false % 10.97/2.27 | | | | | | | | % 10.97/2.27 | | | | | | | | CLOSE: (64) is inconsistent. % 10.97/2.27 | | | | | | | | % 10.97/2.27 | | | | | | | Case 2: % 10.97/2.27 | | | | | | | | % 10.97/2.27 | | | | | | | | (65) all_17_0 = 0 % 10.97/2.27 | | | | | | | | % 10.97/2.27 | | | | | | | | REDUCE: (54), (65) imply: % 10.97/2.27 | | | | | | | | (66) $false % 10.97/2.27 | | | | | | | | % 10.97/2.27 | | | | | | | | CLOSE: (66) is inconsistent. % 10.97/2.27 | | | | | | | | % 10.97/2.27 | | | | | | | End of split % 10.97/2.27 | | | | | | | % 10.97/2.27 | | | | | | End of split % 10.97/2.27 | | | | | | % 10.97/2.27 | | | | | End of split % 10.97/2.27 | | | | | % 10.97/2.27 | | | | Case 2: % 10.97/2.27 | | | | | % 10.97/2.27 | | | | | (67) all_25_0 = 0 % 10.97/2.27 | | | | | % 10.97/2.27 | | | | | REDUCE: (47), (67) imply: % 10.97/2.27 | | | | | (68) $false % 10.97/2.27 | | | | | % 10.97/2.27 | | | | | CLOSE: (68) is inconsistent. % 10.97/2.27 | | | | | % 10.97/2.27 | | | | End of split % 10.97/2.27 | | | | % 10.97/2.27 | | | Case 2: % 10.97/2.27 | | | | % 10.97/2.27 | | | | (69) ~ (all_17_1 = 0) & distinct_lines(all_17_5, all_17_3) = % 10.97/2.27 | | | | all_17_1 % 10.97/2.27 | | | | % 10.97/2.27 | | | | ALPHA: (69) implies: % 10.97/2.27 | | | | (70) ~ (all_17_1 = 0) % 10.97/2.27 | | | | (71) distinct_lines(all_17_5, all_17_3) = all_17_1 % 10.97/2.27 | | | | % 10.97/2.27 | | | | BETA: splitting (49) gives: % 10.97/2.27 | | | | % 10.97/2.28 | | | | Case 1: % 10.97/2.28 | | | | | % 10.97/2.28 | | | | | (72) distinct_lines(all_17_3, all_17_5) = 0 % 10.97/2.28 | | | | | % 10.97/2.28 | | | | | BETA: splitting (51) gives: % 10.97/2.28 | | | | | % 10.97/2.28 | | | | | Case 1: % 10.97/2.28 | | | | | | % 10.97/2.28 | | | | | | (73) all_25_0 = 0 % 10.97/2.28 | | | | | | % 10.97/2.28 | | | | | | REDUCE: (47), (73) imply: % 10.97/2.28 | | | | | | (74) $false % 10.97/2.28 | | | | | | % 10.97/2.28 | | | | | | CLOSE: (74) is inconsistent. % 10.97/2.28 | | | | | | % 10.97/2.28 | | | | | Case 2: % 10.97/2.28 | | | | | | % 10.97/2.28 | | | | | | (75) all_24_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : % 10.97/2.28 | | | | | | ? [v3: int] : ((v3 = 0 & apart_point_and_line(all_17_2, % 10.97/2.28 | | | | | | all_17_4) = 0) | (v2 = 0 & % 10.97/2.28 | | | | | | apart_point_and_line(all_17_2, all_17_5) = 0) | ( ~ (v1 % 10.97/2.28 | | | | | | = 0) & distinct_lines(all_17_4, all_17_5) = v1) | ( ~ % 10.97/2.28 | | | | | | (v0 = 0) & distinct_points(all_17_2, all_17_2) = v0)) % 10.97/2.28 | | | | | | % 10.97/2.28 | | | | | | BETA: splitting (75) gives: % 10.97/2.28 | | | | | | % 10.97/2.28 | | | | | | Case 1: % 10.97/2.28 | | | | | | | % 10.97/2.28 | | | | | | | (76) all_24_0 = 0 % 10.97/2.28 | | | | | | | % 10.97/2.28 | | | | | | | REDUCE: (48), (76) imply: % 10.97/2.28 | | | | | | | (77) $false % 10.97/2.28 | | | | | | | % 10.97/2.28 | | | | | | | CLOSE: (77) is inconsistent. % 10.97/2.28 | | | | | | | % 10.97/2.28 | | | | | | Case 2: % 10.97/2.28 | | | | | | | % 10.97/2.28 | | | | | | | % 10.97/2.28 | | | | | | | GROUND_INST: instantiating (1) with all_17_3, all_17_5, all_17_3, % 10.97/2.28 | | | | | | | all_17_1, simplifying with (13), (15), (71), (72) % 10.97/2.28 | | | | | | | gives: % 10.97/2.28 | | | | | | | (78) all_17_1 = 0 | distinct_lines(all_17_3, all_17_3) = 0 % 10.97/2.28 | | | | | | | % 10.97/2.28 | | | | | | | BETA: splitting (78) gives: % 10.97/2.28 | | | | | | | % 10.97/2.28 | | | | | | | Case 1: % 10.97/2.28 | | | | | | | | % 10.97/2.28 | | | | | | | | (79) distinct_lines(all_17_3, all_17_3) = 0 % 10.97/2.28 | | | | | | | | % 10.97/2.28 | | | | | | | | GROUND_INST: instantiating (apart2) with all_17_3, simplifying % 10.97/2.28 | | | | | | | | with (15), (79) gives: % 10.97/2.28 | | | | | | | | (80) $false % 10.97/2.28 | | | | | | | | % 10.97/2.28 | | | | | | | | CLOSE: (80) is inconsistent. % 10.97/2.28 | | | | | | | | % 10.97/2.28 | | | | | | | Case 2: % 10.97/2.28 | | | | | | | | % 10.97/2.28 | | | | | | | | (81) all_17_1 = 0 % 10.97/2.28 | | | | | | | | % 10.97/2.28 | | | | | | | | REDUCE: (70), (81) imply: % 10.97/2.28 | | | | | | | | (82) $false % 10.97/2.28 | | | | | | | | % 10.97/2.28 | | | | | | | | CLOSE: (82) is inconsistent. % 10.97/2.28 | | | | | | | | % 10.97/2.28 | | | | | | | End of split % 10.97/2.28 | | | | | | | % 10.97/2.28 | | | | | | End of split % 10.97/2.28 | | | | | | % 10.97/2.28 | | | | | End of split % 10.97/2.28 | | | | | % 10.97/2.28 | | | | Case 2: % 10.97/2.28 | | | | | % 10.97/2.28 | | | | | (83) all_24_0 = 0 % 10.97/2.28 | | | | | % 10.97/2.28 | | | | | REDUCE: (48), (83) imply: % 10.97/2.28 | | | | | (84) $false % 10.97/2.28 | | | | | % 10.97/2.28 | | | | | CLOSE: (84) is inconsistent. % 10.97/2.28 | | | | | % 10.97/2.28 | | | | End of split % 10.97/2.28 | | | | % 10.97/2.28 | | | End of split % 10.97/2.28 | | | % 10.97/2.28 | | Case 2: % 10.97/2.28 | | | % 11.15/2.28 | | | (85) ~ (all_25_1 = 0) & convergent_lines(all_17_5, all_17_4) = % 11.15/2.28 | | | all_25_1 % 11.15/2.28 | | | % 11.15/2.28 | | | ALPHA: (85) implies: % 11.15/2.28 | | | (86) ~ (all_25_1 = 0) % 11.15/2.28 | | | (87) convergent_lines(all_17_5, all_17_4) = all_25_1 % 11.15/2.28 | | | % 11.15/2.28 | | | GROUND_INST: instantiating (9) with 0, all_25_1, all_17_4, all_17_5, % 11.15/2.28 | | | simplifying with (16), (87) gives: % 11.15/2.28 | | | (88) all_25_1 = 0 % 11.15/2.28 | | | % 11.15/2.28 | | | REDUCE: (86), (88) imply: % 11.15/2.28 | | | (89) $false % 11.15/2.28 | | | % 11.15/2.28 | | | CLOSE: (89) is inconsistent. % 11.15/2.28 | | | % 11.15/2.28 | | End of split % 11.15/2.28 | | % 11.15/2.28 | Case 2: % 11.15/2.28 | | % 11.15/2.28 | | (90) ~ (all_24_1 = 0) & convergent_lines(all_17_5, all_17_4) = all_24_1 % 11.15/2.28 | | % 11.15/2.28 | | ALPHA: (90) implies: % 11.15/2.28 | | (91) ~ (all_24_1 = 0) % 11.15/2.28 | | (92) convergent_lines(all_17_5, all_17_4) = all_24_1 % 11.15/2.28 | | % 11.15/2.28 | | GROUND_INST: instantiating (9) with 0, all_24_1, all_17_4, all_17_5, % 11.15/2.28 | | simplifying with (16), (92) gives: % 11.15/2.28 | | (93) all_24_1 = 0 % 11.15/2.28 | | % 11.15/2.28 | | REDUCE: (91), (93) imply: % 11.15/2.28 | | (94) $false % 11.15/2.28 | | % 11.15/2.28 | | CLOSE: (94) is inconsistent. % 11.15/2.28 | | % 11.15/2.28 | End of split % 11.15/2.28 | % 11.15/2.28 End of proof % 11.15/2.28 % SZS output end Proof for theBenchmark % 11.15/2.28 % 11.15/2.28 1670ms %------------------------------------------------------------------------------