%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO221+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : 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 23:22:30 EDT 2023 % Result : Theorem 11.58s 2.29s % Output : Proof 15.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO221+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n016.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Wed Aug 30 00:38:17 EDT 2023 % 0.12/0.35 % CPUTime : % 0.61/0.67 ________ _____ % 0.61/0.67 ___ __ \_________(_)________________________________ % 0.61/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.61/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.61/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.61/0.67 % 0.61/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.61/0.67 (2023-06-19) % 0.61/0.67 % 0.61/0.67 (c) Philipp Rümmer, 2009-2023 % 0.61/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.61/0.67 Amanda Stjerna. % 0.61/0.67 Free software under BSD-3-Clause. % 0.61/0.67 % 0.61/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.61/0.67 % 0.61/0.67 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.72/0.68 Running up to 7 provers in parallel. % 0.72/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.72/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.72/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.72/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.72/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.72/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.72/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.17/1.17 Prover 1: Preprocessing ... % 3.17/1.17 Prover 4: Preprocessing ... % 3.17/1.22 Prover 0: Preprocessing ... % 3.17/1.22 Prover 5: Preprocessing ... % 3.17/1.22 Prover 3: Preprocessing ... % 3.17/1.22 Prover 6: Preprocessing ... % 3.17/1.22 Prover 2: Preprocessing ... % 6.24/1.61 Prover 5: Proving ... % 6.24/1.64 Prover 2: Proving ... % 6.99/1.70 Prover 1: Constructing countermodel ... % 6.99/1.70 Prover 6: Constructing countermodel ... % 6.99/1.70 Prover 3: Constructing countermodel ... % 8.07/1.83 Prover 6: gave up % 8.07/1.83 Prover 3: gave up % 8.07/1.84 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.07/1.85 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.37/1.88 Prover 7: Preprocessing ... % 8.37/1.92 Prover 1: gave up % 8.37/1.92 Prover 8: Preprocessing ... % 8.37/1.92 Prover 4: Constructing countermodel ... % 8.37/1.92 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 8.98/1.94 Prover 7: Warning: ignoring some quantifiers % 8.98/1.96 Prover 7: Constructing countermodel ... % 8.98/1.97 Prover 0: Proving ... % 9.23/1.97 Prover 9: Preprocessing ... % 9.83/2.07 Prover 8: Warning: ignoring some quantifiers % 9.83/2.11 Prover 8: Constructing countermodel ... % 10.75/2.24 Prover 8: gave up % 10.75/2.24 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.36/2.26 Prover 9: Constructing countermodel ... % 11.36/2.27 Prover 10: Preprocessing ... % 11.58/2.29 Prover 0: proved (1595ms) % 11.58/2.29 % 11.58/2.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.58/2.29 % 11.58/2.29 Prover 2: stopped % 11.58/2.29 Prover 5: stopped % 11.58/2.31 Prover 9: stopped % 11.58/2.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.58/2.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.58/2.31 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.58/2.31 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 11.58/2.31 Prover 10: Warning: ignoring some quantifiers % 11.58/2.32 Prover 11: Preprocessing ... % 11.94/2.33 Prover 13: Preprocessing ... % 11.94/2.34 Prover 10: Constructing countermodel ... % 12.04/2.35 Prover 16: Preprocessing ... % 12.04/2.38 Prover 19: Preprocessing ... % 12.04/2.40 Prover 13: Warning: ignoring some quantifiers % 12.47/2.42 Prover 13: Constructing countermodel ... % 12.47/2.43 Prover 16: Warning: ignoring some quantifiers % 12.47/2.45 Prover 16: Constructing countermodel ... % 12.88/2.49 Prover 10: gave up % 12.88/2.52 Prover 19: Warning: ignoring some quantifiers % 12.88/2.54 Prover 19: Constructing countermodel ... % 13.55/2.57 Prover 13: gave up % 13.81/2.61 Prover 11: Constructing countermodel ... % 14.28/2.67 Prover 7: gave up % 14.87/2.74 Prover 4: Found proof (size 99) % 14.87/2.74 Prover 4: proved (2042ms) % 14.87/2.74 Prover 11: stopped % 14.87/2.74 Prover 16: stopped % 14.87/2.74 Prover 19: stopped % 14.87/2.74 % 14.87/2.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.87/2.74 % 14.87/2.75 % SZS output start Proof for theBenchmark % 14.87/2.75 Assumptions after simplification: % 14.87/2.75 --------------------------------- % 14.87/2.75 % 14.87/2.75 (a4) % 15.18/2.78 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 15.18/2.78 (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 15.18/2.78 apart_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] % 15.18/2.78 : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 15.18/2.78 incident_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 15.18/2.78 (incident_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] % 15.18/2.78 : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0: $i] : ! [v1: % 15.18/2.78 $i] : ( ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 15.18/2.78 [v2: int] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) % 15.18/2.78 % 15.18/2.78 (ax2) % 15.18/2.78 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_lines(v0, v1) = % 15.18/2.78 v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v0, v1) = 0) & ! [v0: $i] : % 15.18/2.78 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ~ % 15.18/2.78 $i(v1) | ~ $i(v0) | equal_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : % 15.18/2.78 ( ~ (equal_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 % 15.18/2.78 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 15.18/2.78 (distinct_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ % 15.18/2.78 (v2 = 0) & equal_lines(v0, v1) = v2)) % 15.18/2.78 % 15.18/2.78 (con) % 15.18/2.79 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 15.18/2.79 int] : ( ~ (v5 = 0) & incident_point_and_line(v1, v3) = 0 & equal_lines(v3, % 15.18/2.79 v4) = v5 & orthogonal_through_point(v2, v1) = v4 & % 15.18/2.79 orthogonal_through_point(v2, v0) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 15.18/2.79 $i(v0)) % 15.18/2.79 % 15.18/2.79 (cu1) % 15.18/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 15.18/2.80 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 15.18/2.80 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 15.18/2.80 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 15.18/2.80 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, % 15.18/2.80 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 15.18/2.80 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 15.18/2.80 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 15.18/2.80 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 15.18/2.80 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 15.18/2.80 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 15.18/2.80 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 % 15.18/2.80 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.18/2.80 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 15.18/2.80 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 15.18/2.80 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 15.18/2.80 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 15.18/2.80 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 15.18/2.80 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = % 15.18/2.80 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 15.18/2.80 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = % 15.18/2.80 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 15.18/2.80 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 15.18/2.80 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = % 15.18/2.80 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 % 15.18/2.80 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : % 15.18/2.80 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 15.18/2.80 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 15.18/2.80 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 15.18/2.80 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 15.18/2.80 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & % 15.18/2.80 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 15.18/2.80 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 15.18/2.80 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ % 15.18/2.80 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 15.18/2.80 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 15.18/2.80 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, % 15.18/2.80 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 15.18/2.80 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 15.18/2.80 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 15.18/2.80 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 15.18/2.80 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 15.18/2.80 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 15.18/2.80 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 15.18/2.80 % 15.18/2.80 (ooc1) % 15.18/2.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (orthogonal_through_point(v1, % 15.18/2.80 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 15.18/2.81 unorthogonal_lines(v2, v1) = v3)) % 15.18/2.81 % 15.18/2.81 (ooc2) % 15.18/2.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (orthogonal_through_point(v1, % 15.18/2.81 v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 15.18/2.81 apart_point_and_line(v0, v2) = v3)) % 15.18/2.81 % 15.18/2.81 (ouo1) % 15.18/2.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 15.18/2.81 int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ % 15.18/2.81 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ~ % 15.18/2.81 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 15.18/2.81 (unorthogonal_lines(v1, v3) = v7 & apart_point_and_line(v0, v1) = v6 & (v7 = % 15.18/2.81 0 | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 15.18/2.81 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) % 15.18/2.81 = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 15.18/2.81 ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 15.18/2.81 (unorthogonal_lines(v1, v3) = v8 & apart_point_and_line(v0, v2) = v7 & % 15.18/2.81 distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 15.18/2.81 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 15.18/2.81 : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ % 15.18/2.81 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 15.18/2.81 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 15.18/2.81 (unorthogonal_lines(v2, v3) = v8 & apart_point_and_line(v0, v1) = v7 & % 15.18/2.81 distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 15.18/2.81 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 15.18/2.81 : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ % 15.18/2.81 (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ~ % 15.18/2.81 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 15.18/2.81 (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = % 15.18/2.81 0 | v6 = 0))) % 15.18/2.81 % 15.18/2.81 (function-axioms) % 15.18/2.82 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.18/2.82 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 15.18/2.82 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.18/2.82 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.18/2.82 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 15.18/2.82 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.18/2.82 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 15.18/2.82 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.18/2.82 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.18/2.82 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 15.18/2.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.18/2.82 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 15.18/2.82 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.18/2.82 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 15.18/2.82 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 15.18/2.82 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 15.18/2.82 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 15.18/2.82 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 15.18/2.82 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 15.18/2.82 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 15.18/2.82 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 15.18/2.82 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 15.18/2.82 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.18/2.82 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.18/2.82 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 15.18/2.82 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.18/2.82 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 15.18/2.82 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.18/2.82 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.18/2.82 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 15.18/2.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.18/2.82 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 15.18/2.82 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.18/2.82 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 15.18/2.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 15.18/2.82 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 15.18/2.82 % 15.18/2.82 Further assumptions not needed in the proof: % 15.18/2.82 -------------------------------------------- % 15.18/2.82 a3, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax6, ceq1, ceq2, ceq3, ci1, % 15.18/2.82 ci2, ci3, ci4, coipo1, con1, cotno1, couo1, cp1, cp2, cup1, int1, oac1, occu1, % 15.18/2.82 orth1, p1, par1 % 15.18/2.82 % 15.18/2.82 Those formulas are unsatisfiable: % 15.18/2.82 --------------------------------- % 15.18/2.82 % 15.18/2.82 Begin of proof % 15.18/2.82 | % 15.18/2.82 | ALPHA: (cu1) implies: % 15.18/2.82 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 15.18/2.82 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 15.18/2.82 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 15.18/2.82 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 15.18/2.82 | [v9: any] : (apart_point_and_line(v1, v3) = v9 & % 15.18/2.82 | apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & % 15.18/2.82 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 15.18/2.82 | | v8 = 0))) % 15.18/2.82 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 15.18/2.82 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 15.18/2.82 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 15.18/2.82 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 15.18/2.82 | [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 15.18/2.82 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 15.18/2.82 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 15.18/2.82 | | v8 = 0))) % 15.18/2.82 | % 15.18/2.82 | ALPHA: (ouo1) implies: % 15.18/2.82 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 15.18/2.82 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | % 15.18/2.82 | ~ (apart_point_and_line(v0, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 15.18/2.82 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 15.18/2.82 | (unorthogonal_lines(v1, v3) = v8 & apart_point_and_line(v0, v2) = v7 % 15.18/2.82 | & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 15.18/2.83 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 15.18/2.83 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | % 15.18/2.83 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = % 15.18/2.83 | 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : % 15.18/2.83 | ? [v7: any] : (unorthogonal_lines(v1, v3) = v7 & % 15.18/2.83 | apart_point_and_line(v0, v1) = v6 & (v7 = 0 | v6 = 0))) % 15.18/2.83 | % 15.18/2.83 | ALPHA: (ax2) implies: % 15.18/2.83 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 15.18/2.83 | (equal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 15.18/2.83 | distinct_lines(v0, v1) = 0) % 15.18/2.83 | % 15.18/2.83 | ALPHA: (a4) implies: % 15.18/2.83 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (incident_point_and_line(v0, v1) = 0) | % 15.18/2.83 | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 15.18/2.83 | apart_point_and_line(v0, v1) = v2)) % 15.18/2.83 | % 15.18/2.83 | ALPHA: (function-axioms) implies: % 15.18/2.83 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.18/2.83 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 15.18/2.83 | (apart_point_and_line(v3, v2) = v0)) % 15.18/2.83 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.18/2.83 | ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 15.18/2.83 | (unorthogonal_lines(v3, v2) = v0)) % 15.18/2.83 | % 15.18/2.83 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 15.18/2.83 | all_38_3, all_38_4, all_38_5 gives: % 15.18/2.83 | (9) ~ (all_38_0 = 0) & incident_point_and_line(all_38_4, all_38_2) = 0 & % 15.18/2.83 | equal_lines(all_38_2, all_38_1) = all_38_0 & % 15.18/2.83 | orthogonal_through_point(all_38_3, all_38_4) = all_38_1 & % 15.18/2.83 | orthogonal_through_point(all_38_3, all_38_5) = all_38_2 & $i(all_38_1) % 15.18/2.83 | & $i(all_38_2) & $i(all_38_3) & $i(all_38_4) & $i(all_38_5) % 15.18/2.83 | % 15.18/2.83 | ALPHA: (9) implies: % 15.18/2.83 | (10) ~ (all_38_0 = 0) % 15.18/2.83 | (11) $i(all_38_5) % 15.18/2.83 | (12) $i(all_38_4) % 15.18/2.83 | (13) $i(all_38_3) % 15.18/2.83 | (14) $i(all_38_2) % 15.18/2.83 | (15) $i(all_38_1) % 15.18/2.83 | (16) orthogonal_through_point(all_38_3, all_38_5) = all_38_2 % 15.18/2.83 | (17) orthogonal_through_point(all_38_3, all_38_4) = all_38_1 % 15.18/2.83 | (18) equal_lines(all_38_2, all_38_1) = all_38_0 % 15.18/2.83 | (19) incident_point_and_line(all_38_4, all_38_2) = 0 % 15.18/2.83 | % 15.18/2.83 | GROUND_INST: instantiating (ooc1) with all_38_5, all_38_3, all_38_2, % 15.18/2.83 | simplifying with (11), (13), (16) gives: % 15.18/2.83 | (20) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_38_2, all_38_3) = % 15.18/2.83 | v0) % 15.18/2.83 | % 15.18/2.83 | GROUND_INST: instantiating (ooc2) with all_38_5, all_38_3, all_38_2, % 15.18/2.83 | simplifying with (11), (13), (16) gives: % 15.18/2.83 | (21) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_5, all_38_2) % 15.18/2.83 | = v0) % 15.18/2.83 | % 15.18/2.83 | GROUND_INST: instantiating (ooc1) with all_38_4, all_38_3, all_38_1, % 15.18/2.83 | simplifying with (12), (13), (17) gives: % 15.18/2.83 | (22) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_38_1, all_38_3) = % 15.18/2.83 | v0) % 15.18/2.83 | % 15.18/2.83 | GROUND_INST: instantiating (ooc2) with all_38_4, all_38_3, all_38_1, % 15.18/2.83 | simplifying with (12), (13), (17) gives: % 15.18/2.83 | (23) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_4, all_38_1) % 15.18/2.83 | = v0) % 15.18/2.83 | % 15.18/2.83 | GROUND_INST: instantiating (5) with all_38_2, all_38_1, all_38_0, simplifying % 15.18/2.83 | with (14), (15), (18) gives: % 15.18/2.83 | (24) all_38_0 = 0 | distinct_lines(all_38_2, all_38_1) = 0 % 15.18/2.83 | % 15.18/2.84 | GROUND_INST: instantiating (6) with all_38_4, all_38_2, simplifying with (12), % 15.18/2.84 | (14), (19) gives: % 15.18/2.84 | (25) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_4, all_38_2) % 15.18/2.84 | = v0) % 15.18/2.84 | % 15.18/2.84 | DELTA: instantiating (25) with fresh symbol all_45_0 gives: % 15.18/2.84 | (26) ~ (all_45_0 = 0) & apart_point_and_line(all_38_4, all_38_2) = % 15.18/2.84 | all_45_0 % 15.18/2.84 | % 15.18/2.84 | ALPHA: (26) implies: % 15.18/2.84 | (27) ~ (all_45_0 = 0) % 15.18/2.84 | (28) apart_point_and_line(all_38_4, all_38_2) = all_45_0 % 15.18/2.84 | % 15.18/2.84 | DELTA: instantiating (22) with fresh symbol all_47_0 gives: % 15.18/2.84 | (29) ~ (all_47_0 = 0) & unorthogonal_lines(all_38_1, all_38_3) = all_47_0 % 15.18/2.84 | % 15.18/2.84 | ALPHA: (29) implies: % 15.18/2.84 | (30) ~ (all_47_0 = 0) % 15.18/2.84 | (31) unorthogonal_lines(all_38_1, all_38_3) = all_47_0 % 15.18/2.84 | % 15.18/2.84 | DELTA: instantiating (21) with fresh symbol all_49_0 gives: % 15.18/2.84 | (32) ~ (all_49_0 = 0) & apart_point_and_line(all_38_5, all_38_2) = % 15.18/2.84 | all_49_0 % 15.18/2.84 | % 15.18/2.84 | ALPHA: (32) implies: % 15.18/2.84 | (33) ~ (all_49_0 = 0) % 15.18/2.84 | (34) apart_point_and_line(all_38_5, all_38_2) = all_49_0 % 15.18/2.84 | % 15.18/2.84 | DELTA: instantiating (20) with fresh symbol all_51_0 gives: % 15.18/2.84 | (35) ~ (all_51_0 = 0) & unorthogonal_lines(all_38_2, all_38_3) = all_51_0 % 15.18/2.84 | % 15.18/2.84 | ALPHA: (35) implies: % 15.18/2.84 | (36) ~ (all_51_0 = 0) % 15.18/2.84 | (37) unorthogonal_lines(all_38_2, all_38_3) = all_51_0 % 15.18/2.84 | % 15.18/2.84 | DELTA: instantiating (23) with fresh symbol all_53_0 gives: % 15.18/2.84 | (38) ~ (all_53_0 = 0) & apart_point_and_line(all_38_4, all_38_1) = % 15.18/2.84 | all_53_0 % 15.18/2.84 | % 15.18/2.84 | ALPHA: (38) implies: % 15.18/2.84 | (39) ~ (all_53_0 = 0) % 15.18/2.84 | (40) apart_point_and_line(all_38_4, all_38_1) = all_53_0 % 15.18/2.84 | % 15.18/2.84 | BETA: splitting (24) gives: % 15.18/2.84 | % 15.18/2.84 | Case 1: % 15.18/2.84 | | % 15.18/2.84 | | (41) distinct_lines(all_38_2, all_38_1) = 0 % 15.18/2.84 | | % 15.18/2.84 | | GROUND_INST: instantiating (2) with all_38_4, all_38_4, all_38_2, all_38_2, % 15.18/2.84 | | all_45_0, all_45_0, simplifying with (12), (14), (28) gives: % 15.18/2.84 | | (42) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 15.18/2.84 | | any] : (apart_point_and_line(all_38_4, all_38_2) = v3 & % 15.18/2.84 | | apart_point_and_line(all_38_4, all_38_2) = v2 & % 15.18/2.84 | | distinct_lines(all_38_2, all_38_2) = v1 & % 15.18/2.84 | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 15.18/2.84 | | 0) | v3 = 0 | v2 = 0)) % 15.18/2.84 | | % 15.18/2.84 | | GROUND_INST: instantiating (2) with all_38_4, all_38_5, all_38_1, all_38_2, % 15.18/2.84 | | all_53_0, all_49_0, simplifying with (11), (12), (14), (15), % 15.18/2.84 | | (34), (40) gives: % 15.18/2.84 | | (43) all_53_0 = 0 | all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 15.18/2.84 | | any] : ? [v3: any] : (apart_point_and_line(all_38_4, all_38_2) = % 15.18/2.84 | | v2 & apart_point_and_line(all_38_5, all_38_1) = v3 & % 15.18/2.84 | | distinct_lines(all_38_1, all_38_2) = v1 & % 15.18/2.84 | | distinct_points(all_38_4, all_38_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 15.18/2.84 | | 0) | v3 = 0 | v2 = 0)) % 15.18/2.84 | | % 15.18/2.84 | | GROUND_INST: instantiating (1) with all_38_5, all_38_4, all_38_1, all_38_2, % 15.18/2.84 | | all_49_0, all_53_0, simplifying with (11), (12), (14), (15), % 15.18/2.84 | | (34), (40) gives: % 15.18/2.84 | | (44) all_53_0 = 0 | all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 15.18/2.84 | | any] : ? [v3: any] : (apart_point_and_line(all_38_4, all_38_2) = % 15.18/2.84 | | v3 & apart_point_and_line(all_38_5, all_38_1) = v2 & % 15.18/2.84 | | distinct_lines(all_38_1, all_38_2) = v1 & % 15.18/2.84 | | distinct_points(all_38_5, all_38_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 15.18/2.84 | | 0) | v3 = 0 | v2 = 0)) % 15.18/2.84 | | % 15.18/2.84 | | GROUND_INST: instantiating (3) with all_38_4, all_38_1, all_38_2, all_38_3, % 15.18/2.84 | | all_53_0, all_51_0, simplifying with (12), (13), (14), (15), % 15.18/2.85 | | (37), (40) gives: % 15.18/2.85 | | (45) all_53_0 = 0 | all_51_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 15.18/2.85 | | any] : (unorthogonal_lines(all_38_1, all_38_3) = v2 & % 15.18/2.85 | | apart_point_and_line(all_38_4, all_38_2) = v1 & % 15.18/2.85 | | distinct_lines(all_38_1, all_38_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | % 15.18/2.85 | | v1 = 0)) % 15.18/2.85 | | % 15.18/2.85 | | GROUND_INST: instantiating (4) with all_38_4, all_38_2, all_38_1, all_38_3, % 15.18/2.85 | | all_53_0, all_47_0, simplifying with (12), (13), (14), (15), % 15.18/2.85 | | (31), (40), (41) gives: % 15.18/2.85 | | (46) all_53_0 = 0 | all_47_0 = 0 | ? [v0: any] : ? [v1: any] : % 15.18/2.85 | | (unorthogonal_lines(all_38_2, all_38_3) = v1 & % 15.18/2.85 | | apart_point_and_line(all_38_4, all_38_2) = v0 & (v1 = 0 | v0 = 0)) % 15.18/2.85 | | % 15.18/2.85 | | BETA: splitting (42) gives: % 15.18/2.85 | | % 15.18/2.85 | | Case 1: % 15.18/2.85 | | | % 15.18/2.85 | | | (47) all_45_0 = 0 % 15.18/2.85 | | | % 15.18/2.85 | | | REDUCE: (27), (47) imply: % 15.18/2.85 | | | (48) $false % 15.18/2.85 | | | % 15.18/2.85 | | | CLOSE: (48) is inconsistent. % 15.18/2.85 | | | % 15.18/2.85 | | Case 2: % 15.18/2.85 | | | % 15.18/2.85 | | | (49) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 15.18/2.85 | | | (apart_point_and_line(all_38_4, all_38_2) = v3 & % 15.18/2.85 | | | apart_point_and_line(all_38_4, all_38_2) = v2 & % 15.18/2.85 | | | distinct_lines(all_38_2, all_38_2) = v1 & % 15.18/2.85 | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ (v1 = 0) | ~ (v0 % 15.18/2.85 | | | = 0) | v3 = 0 | v2 = 0)) % 15.18/2.85 | | | % 15.18/2.85 | | | DELTA: instantiating (49) with fresh symbols all_120_0, all_120_1, % 15.18/2.85 | | | all_120_2, all_120_3 gives: % 15.18/2.85 | | | (50) apart_point_and_line(all_38_4, all_38_2) = all_120_0 & % 15.18/2.85 | | | apart_point_and_line(all_38_4, all_38_2) = all_120_1 & % 15.18/2.85 | | | distinct_lines(all_38_2, all_38_2) = all_120_2 & % 15.18/2.85 | | | distinct_points(all_38_4, all_38_4) = all_120_3 & ( ~ (all_120_2 = % 15.18/2.85 | | | 0) | ~ (all_120_3 = 0) | all_120_0 = 0 | all_120_1 = 0) % 15.18/2.85 | | | % 15.18/2.85 | | | ALPHA: (50) implies: % 15.18/2.85 | | | (51) apart_point_and_line(all_38_4, all_38_2) = all_120_1 % 15.18/2.85 | | | (52) apart_point_and_line(all_38_4, all_38_2) = all_120_0 % 15.18/2.85 | | | % 15.18/2.85 | | | BETA: splitting (45) gives: % 15.18/2.85 | | | % 15.18/2.85 | | | Case 1: % 15.18/2.85 | | | | % 15.18/2.85 | | | | (53) all_53_0 = 0 % 15.18/2.85 | | | | % 15.18/2.85 | | | | REDUCE: (39), (53) imply: % 15.18/2.85 | | | | (54) $false % 15.18/2.85 | | | | % 15.18/2.85 | | | | CLOSE: (54) is inconsistent. % 15.18/2.85 | | | | % 15.18/2.85 | | | Case 2: % 15.18/2.85 | | | | % 15.18/2.85 | | | | (55) all_51_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 15.18/2.85 | | | | (unorthogonal_lines(all_38_1, all_38_3) = v2 & % 15.18/2.85 | | | | apart_point_and_line(all_38_4, all_38_2) = v1 & % 15.18/2.85 | | | | distinct_lines(all_38_1, all_38_2) = v0 & ( ~ (v0 = 0) | v2 = % 15.18/2.85 | | | | 0 | v1 = 0)) % 15.18/2.85 | | | | % 15.18/2.85 | | | | BETA: splitting (44) gives: % 15.18/2.85 | | | | % 15.18/2.85 | | | | Case 1: % 15.18/2.85 | | | | | % 15.18/2.85 | | | | | (56) all_53_0 = 0 % 15.18/2.85 | | | | | % 15.18/2.85 | | | | | REDUCE: (39), (56) imply: % 15.18/2.85 | | | | | (57) $false % 15.18/2.85 | | | | | % 15.18/2.85 | | | | | CLOSE: (57) is inconsistent. % 15.18/2.85 | | | | | % 15.18/2.85 | | | | Case 2: % 15.18/2.85 | | | | | % 15.18/2.85 | | | | | (58) all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 15.18/2.85 | | | | | [v3: any] : (apart_point_and_line(all_38_4, all_38_2) = v3 & % 15.18/2.85 | | | | | apart_point_and_line(all_38_5, all_38_1) = v2 & % 15.18/2.85 | | | | | distinct_lines(all_38_1, all_38_2) = v1 & % 15.18/2.85 | | | | | distinct_points(all_38_5, all_38_4) = v0 & ( ~ (v1 = 0) | ~ % 15.18/2.86 | | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 15.18/2.86 | | | | | % 15.18/2.86 | | | | | BETA: splitting (43) gives: % 15.18/2.86 | | | | | % 15.18/2.86 | | | | | Case 1: % 15.18/2.86 | | | | | | % 15.18/2.86 | | | | | | (59) all_53_0 = 0 % 15.18/2.86 | | | | | | % 15.18/2.86 | | | | | | REDUCE: (39), (59) imply: % 15.18/2.86 | | | | | | (60) $false % 15.18/2.86 | | | | | | % 15.18/2.86 | | | | | | CLOSE: (60) is inconsistent. % 15.18/2.86 | | | | | | % 15.18/2.86 | | | | | Case 2: % 15.18/2.86 | | | | | | % 15.18/2.86 | | | | | | (61) all_49_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 15.18/2.86 | | | | | | ? [v3: any] : (apart_point_and_line(all_38_4, all_38_2) = v2 % 15.18/2.86 | | | | | | & apart_point_and_line(all_38_5, all_38_1) = v3 & % 15.18/2.86 | | | | | | distinct_lines(all_38_1, all_38_2) = v1 & % 15.18/2.86 | | | | | | distinct_points(all_38_4, all_38_5) = v0 & ( ~ (v1 = 0) | % 15.18/2.86 | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 15.18/2.86 | | | | | | % 15.18/2.86 | | | | | | BETA: splitting (55) gives: % 15.18/2.86 | | | | | | % 15.18/2.86 | | | | | | Case 1: % 15.18/2.86 | | | | | | | % 15.18/2.86 | | | | | | | (62) all_51_0 = 0 % 15.18/2.86 | | | | | | | % 15.18/2.86 | | | | | | | REDUCE: (36), (62) imply: % 15.18/2.86 | | | | | | | (63) $false % 15.18/2.86 | | | | | | | % 15.18/2.86 | | | | | | | CLOSE: (63) is inconsistent. % 15.18/2.86 | | | | | | | % 15.18/2.86 | | | | | | Case 2: % 15.18/2.86 | | | | | | | % 15.18/2.86 | | | | | | | (64) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 15.18/2.86 | | | | | | | (unorthogonal_lines(all_38_1, all_38_3) = v2 & % 15.18/2.86 | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v1 & % 15.18/2.86 | | | | | | | distinct_lines(all_38_1, all_38_2) = v0 & ( ~ (v0 = 0) | % 15.18/2.86 | | | | | | | v2 = 0 | v1 = 0)) % 15.18/2.86 | | | | | | | % 15.18/2.86 | | | | | | | DELTA: instantiating (64) with fresh symbols all_194_0, all_194_1, % 15.18/2.86 | | | | | | | all_194_2 gives: % 15.18/2.86 | | | | | | | (65) unorthogonal_lines(all_38_1, all_38_3) = all_194_0 & % 15.18/2.86 | | | | | | | apart_point_and_line(all_38_4, all_38_2) = all_194_1 & % 15.18/2.86 | | | | | | | distinct_lines(all_38_1, all_38_2) = all_194_2 & ( ~ % 15.18/2.86 | | | | | | | (all_194_2 = 0) | all_194_0 = 0 | all_194_1 = 0) % 15.18/2.86 | | | | | | | % 15.18/2.86 | | | | | | | ALPHA: (65) implies: % 15.18/2.86 | | | | | | | (66) apart_point_and_line(all_38_4, all_38_2) = all_194_1 % 15.18/2.86 | | | | | | | % 15.18/2.86 | | | | | | | BETA: splitting (58) gives: % 15.18/2.86 | | | | | | | % 15.18/2.86 | | | | | | | Case 1: % 15.18/2.86 | | | | | | | | % 15.18/2.86 | | | | | | | | (67) all_49_0 = 0 % 15.18/2.86 | | | | | | | | % 15.18/2.86 | | | | | | | | REDUCE: (33), (67) imply: % 15.18/2.86 | | | | | | | | (68) $false % 15.18/2.86 | | | | | | | | % 15.18/2.86 | | | | | | | | CLOSE: (68) is inconsistent. % 15.18/2.86 | | | | | | | | % 15.18/2.86 | | | | | | | Case 2: % 15.18/2.86 | | | | | | | | % 15.18/2.86 | | | | | | | | (69) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 15.18/2.86 | | | | | | | | any] : (apart_point_and_line(all_38_4, all_38_2) = v3 % 15.18/2.86 | | | | | | | | & apart_point_and_line(all_38_5, all_38_1) = v2 & % 15.18/2.86 | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 & % 15.18/2.86 | | | | | | | | distinct_points(all_38_5, all_38_4) = v0 & ( ~ (v1 = % 15.18/2.86 | | | | | | | | 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 15.18/2.86 | | | | | | | | % 15.18/2.86 | | | | | | | | DELTA: instantiating (69) with fresh symbols all_204_0, % 15.18/2.86 | | | | | | | | all_204_1, all_204_2, all_204_3 gives: % 15.18/2.86 | | | | | | | | (70) apart_point_and_line(all_38_4, all_38_2) = all_204_0 & % 15.18/2.86 | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = all_204_1 & % 15.18/2.86 | | | | | | | | distinct_lines(all_38_1, all_38_2) = all_204_2 & % 15.18/2.86 | | | | | | | | distinct_points(all_38_5, all_38_4) = all_204_3 & ( ~ % 15.18/2.86 | | | | | | | | (all_204_2 = 0) | ~ (all_204_3 = 0) | all_204_0 = 0 | % 15.18/2.86 | | | | | | | | all_204_1 = 0) % 15.18/2.86 | | | | | | | | % 15.18/2.86 | | | | | | | | ALPHA: (70) implies: % 15.18/2.86 | | | | | | | | (71) apart_point_and_line(all_38_4, all_38_2) = all_204_0 % 15.18/2.86 | | | | | | | | % 15.18/2.86 | | | | | | | | BETA: splitting (61) gives: % 15.18/2.86 | | | | | | | | % 15.18/2.86 | | | | | | | | Case 1: % 15.18/2.86 | | | | | | | | | % 15.18/2.86 | | | | | | | | | (72) all_49_0 = 0 % 15.18/2.86 | | | | | | | | | % 15.18/2.86 | | | | | | | | | REDUCE: (33), (72) imply: % 15.18/2.86 | | | | | | | | | (73) $false % 15.18/2.86 | | | | | | | | | % 15.18/2.86 | | | | | | | | | CLOSE: (73) is inconsistent. % 15.18/2.86 | | | | | | | | | % 15.61/2.86 | | | | | | | | Case 2: % 15.61/2.86 | | | | | | | | | % 15.61/2.86 | | | | | | | | | (74) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 15.61/2.86 | | | | | | | | | any] : (apart_point_and_line(all_38_4, all_38_2) = % 15.61/2.86 | | | | | | | | | v2 & apart_point_and_line(all_38_5, all_38_1) = v3 & % 15.61/2.86 | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 & % 15.61/2.86 | | | | | | | | | distinct_points(all_38_4, all_38_5) = v0 & ( ~ (v1 = % 15.61/2.86 | | | | | | | | | 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 15.61/2.86 | | | | | | | | | % 15.61/2.86 | | | | | | | | | DELTA: instantiating (74) with fresh symbols all_209_0, % 15.61/2.86 | | | | | | | | | all_209_1, all_209_2, all_209_3 gives: % 15.61/2.86 | | | | | | | | | (75) apart_point_and_line(all_38_4, all_38_2) = all_209_1 & % 15.61/2.86 | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = all_209_0 & % 15.61/2.86 | | | | | | | | | distinct_lines(all_38_1, all_38_2) = all_209_2 & % 15.61/2.86 | | | | | | | | | distinct_points(all_38_4, all_38_5) = all_209_3 & ( ~ % 15.61/2.86 | | | | | | | | | (all_209_2 = 0) | ~ (all_209_3 = 0) | all_209_0 = 0 % 15.61/2.86 | | | | | | | | | | all_209_1 = 0) % 15.61/2.86 | | | | | | | | | % 15.61/2.86 | | | | | | | | | ALPHA: (75) implies: % 15.61/2.86 | | | | | | | | | (76) apart_point_and_line(all_38_4, all_38_2) = all_209_1 % 15.61/2.86 | | | | | | | | | % 15.61/2.86 | | | | | | | | | BETA: splitting (46) gives: % 15.61/2.86 | | | | | | | | | % 15.61/2.86 | | | | | | | | | Case 1: % 15.61/2.86 | | | | | | | | | | % 15.61/2.86 | | | | | | | | | | (77) all_53_0 = 0 % 15.61/2.86 | | | | | | | | | | % 15.61/2.86 | | | | | | | | | | REDUCE: (39), (77) imply: % 15.61/2.86 | | | | | | | | | | (78) $false % 15.61/2.86 | | | | | | | | | | % 15.61/2.86 | | | | | | | | | | CLOSE: (78) is inconsistent. % 15.61/2.86 | | | | | | | | | | % 15.61/2.86 | | | | | | | | | Case 2: % 15.61/2.86 | | | | | | | | | | % 15.61/2.86 | | | | | | | | | | (79) all_47_0 = 0 | ? [v0: any] : ? [v1: any] : % 15.61/2.86 | | | | | | | | | | (unorthogonal_lines(all_38_2, all_38_3) = v1 & % 15.61/2.86 | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v0 & % 15.61/2.86 | | | | | | | | | | (v1 = 0 | v0 = 0)) % 15.61/2.86 | | | | | | | | | | % 15.61/2.86 | | | | | | | | | | BETA: splitting (79) gives: % 15.61/2.86 | | | | | | | | | | % 15.61/2.86 | | | | | | | | | | Case 1: % 15.61/2.86 | | | | | | | | | | | % 15.61/2.86 | | | | | | | | | | | (80) all_47_0 = 0 % 15.61/2.86 | | | | | | | | | | | % 15.61/2.86 | | | | | | | | | | | REDUCE: (30), (80) imply: % 15.61/2.86 | | | | | | | | | | | (81) $false % 15.61/2.86 | | | | | | | | | | | % 15.61/2.86 | | | | | | | | | | | CLOSE: (81) is inconsistent. % 15.61/2.86 | | | | | | | | | | | % 15.61/2.86 | | | | | | | | | | Case 2: % 15.61/2.86 | | | | | | | | | | | % 15.61/2.86 | | | | | | | | | | | (82) ? [v0: any] : ? [v1: any] : % 15.61/2.86 | | | | | | | | | | | (unorthogonal_lines(all_38_2, all_38_3) = v1 & % 15.61/2.86 | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_2) = v0 & % 15.61/2.86 | | | | | | | | | | | (v1 = 0 | v0 = 0)) % 15.61/2.86 | | | | | | | | | | | % 15.61/2.86 | | | | | | | | | | | DELTA: instantiating (82) with fresh symbols all_225_0, % 15.61/2.86 | | | | | | | | | | | all_225_1 gives: % 15.61/2.86 | | | | | | | | | | | (83) unorthogonal_lines(all_38_2, all_38_3) = all_225_0 % 15.61/2.86 | | | | | | | | | | | & apart_point_and_line(all_38_4, all_38_2) = % 15.61/2.86 | | | | | | | | | | | all_225_1 & (all_225_0 = 0 | all_225_1 = 0) % 15.61/2.86 | | | | | | | | | | | % 15.61/2.86 | | | | | | | | | | | ALPHA: (83) implies: % 15.61/2.87 | | | | | | | | | | | (84) apart_point_and_line(all_38_4, all_38_2) = % 15.61/2.87 | | | | | | | | | | | all_225_1 % 15.61/2.87 | | | | | | | | | | | (85) unorthogonal_lines(all_38_2, all_38_3) = all_225_0 % 15.61/2.87 | | | | | | | | | | | (86) all_225_0 = 0 | all_225_1 = 0 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_45_0, all_194_1, % 15.61/2.87 | | | | | | | | | | | all_38_2, all_38_4, simplifying with (28), (66) % 15.61/2.87 | | | | | | | | | | | gives: % 15.61/2.87 | | | | | | | | | | | (87) all_194_1 = all_45_0 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_194_1, all_204_0, % 15.61/2.87 | | | | | | | | | | | all_38_2, all_38_4, simplifying with (66), (71) % 15.61/2.87 | | | | | | | | | | | gives: % 15.61/2.87 | | | | | | | | | | | (88) all_204_0 = all_194_1 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_194_1, all_209_1, % 15.61/2.87 | | | | | | | | | | | all_38_2, all_38_4, simplifying with (66), (76) % 15.61/2.87 | | | | | | | | | | | gives: % 15.61/2.87 | | | | | | | | | | | (89) all_209_1 = all_194_1 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_120_0, all_209_1, % 15.61/2.87 | | | | | | | | | | | all_38_2, all_38_4, simplifying with (52), (76) % 15.61/2.87 | | | | | | | | | | | gives: % 15.61/2.87 | | | | | | | | | | | (90) all_209_1 = all_120_0 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_204_0, all_225_1, % 15.61/2.87 | | | | | | | | | | | all_38_2, all_38_4, simplifying with (71), (84) % 15.61/2.87 | | | | | | | | | | | gives: % 15.61/2.87 | | | | | | | | | | | (91) all_225_1 = all_204_0 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_120_1, all_225_1, % 15.61/2.87 | | | | | | | | | | | all_38_2, all_38_4, simplifying with (51), (84) % 15.61/2.87 | | | | | | | | | | | gives: % 15.61/2.87 | | | | | | | | | | | (92) all_225_1 = all_120_1 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | GROUND_INST: instantiating (8) with all_51_0, all_225_0, % 15.61/2.87 | | | | | | | | | | | all_38_3, all_38_2, simplifying with (37), (85) % 15.61/2.87 | | | | | | | | | | | gives: % 15.61/2.87 | | | | | | | | | | | (93) all_225_0 = all_51_0 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | COMBINE_EQS: (91), (92) imply: % 15.61/2.87 | | | | | | | | | | | (94) all_204_0 = all_120_1 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | SIMP: (94) implies: % 15.61/2.87 | | | | | | | | | | | (95) all_204_0 = all_120_1 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | COMBINE_EQS: (89), (90) imply: % 15.61/2.87 | | | | | | | | | | | (96) all_194_1 = all_120_0 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | SIMP: (96) implies: % 15.61/2.87 | | | | | | | | | | | (97) all_194_1 = all_120_0 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | COMBINE_EQS: (88), (95) imply: % 15.61/2.87 | | | | | | | | | | | (98) all_194_1 = all_120_1 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | SIMP: (98) implies: % 15.61/2.87 | | | | | | | | | | | (99) all_194_1 = all_120_1 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | COMBINE_EQS: (87), (97) imply: % 15.61/2.87 | | | | | | | | | | | (100) all_120_0 = all_45_0 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | COMBINE_EQS: (97), (99) imply: % 15.61/2.87 | | | | | | | | | | | (101) all_120_0 = all_120_1 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | COMBINE_EQS: (100), (101) imply: % 15.61/2.87 | | | | | | | | | | | (102) all_120_1 = all_45_0 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | COMBINE_EQS: (92), (102) imply: % 15.61/2.87 | | | | | | | | | | | (103) all_225_1 = all_45_0 % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | BETA: splitting (86) gives: % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | Case 1: % 15.61/2.87 | | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | | (104) all_225_0 = 0 % 15.61/2.87 | | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | | COMBINE_EQS: (93), (104) imply: % 15.61/2.87 | | | | | | | | | | | | (105) all_51_0 = 0 % 15.61/2.87 | | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | | REDUCE: (36), (105) imply: % 15.61/2.87 | | | | | | | | | | | | (106) $false % 15.61/2.87 | | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | | CLOSE: (106) is inconsistent. % 15.61/2.87 | | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | Case 2: % 15.61/2.87 | | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | | (107) all_225_1 = 0 % 15.61/2.87 | | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | | COMBINE_EQS: (103), (107) imply: % 15.61/2.87 | | | | | | | | | | | | (108) all_45_0 = 0 % 15.61/2.87 | | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | | REDUCE: (27), (108) imply: % 15.61/2.87 | | | | | | | | | | | | (109) $false % 15.61/2.87 | | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | | CLOSE: (109) is inconsistent. % 15.61/2.87 | | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | | End of split % 15.61/2.87 | | | | | | | | | | | % 15.61/2.87 | | | | | | | | | | End of split % 15.61/2.87 | | | | | | | | | | % 15.61/2.87 | | | | | | | | | End of split % 15.61/2.87 | | | | | | | | | % 15.61/2.87 | | | | | | | | End of split % 15.61/2.87 | | | | | | | | % 15.61/2.87 | | | | | | | End of split % 15.61/2.87 | | | | | | | % 15.61/2.87 | | | | | | End of split % 15.61/2.87 | | | | | | % 15.61/2.87 | | | | | End of split % 15.61/2.87 | | | | | % 15.61/2.87 | | | | End of split % 15.61/2.87 | | | | % 15.61/2.87 | | | End of split % 15.61/2.87 | | | % 15.61/2.87 | | End of split % 15.61/2.87 | | % 15.61/2.87 | Case 2: % 15.61/2.87 | | % 15.61/2.87 | | (110) all_38_0 = 0 % 15.61/2.87 | | % 15.61/2.87 | | REDUCE: (10), (110) imply: % 15.61/2.87 | | (111) $false % 15.61/2.87 | | % 15.61/2.87 | | CLOSE: (111) is inconsistent. % 15.61/2.87 | | % 15.61/2.87 | End of split % 15.61/2.87 | % 15.61/2.87 End of proof % 15.61/2.87 % SZS output end Proof for theBenchmark % 15.61/2.87 % 15.61/2.87 2201ms %------------------------------------------------------------------------------