%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO194+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 : n014.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 23:22:07 EDT 2023 % Result : Theorem 20.89s 3.62s % Output : Proof 49.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : GEO194+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n014.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 21:47:15 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.23/1.18 Prover 1: Preprocessing ... % 3.23/1.18 Prover 4: Preprocessing ... % 3.23/1.22 Prover 3: Preprocessing ... % 3.23/1.22 Prover 5: Preprocessing ... % 3.23/1.22 Prover 0: Preprocessing ... % 3.23/1.22 Prover 6: Preprocessing ... % 3.23/1.22 Prover 2: Preprocessing ... % 6.34/1.68 Prover 5: Proving ... % 6.34/1.70 Prover 2: Proving ... % 7.28/1.77 Prover 1: Constructing countermodel ... % 7.28/1.78 Prover 6: Constructing countermodel ... % 7.28/1.78 Prover 3: Constructing countermodel ... % 8.55/1.94 Prover 3: gave up % 8.55/1.95 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.55/1.95 Prover 6: gave up % 8.55/1.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.55/2.01 Prover 8: Preprocessing ... % 8.55/2.04 Prover 7: Preprocessing ... % 8.55/2.09 Prover 4: Constructing countermodel ... % 8.55/2.10 Prover 7: Warning: ignoring some quantifiers % 8.55/2.12 Prover 7: Constructing countermodel ... % 8.55/2.13 Prover 0: Proving ... % 8.55/2.13 Prover 1: gave up % 8.55/2.13 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 9.66/2.16 Prover 8: Warning: ignoring some quantifiers % 9.66/2.19 Prover 8: Constructing countermodel ... % 9.66/2.19 Prover 9: Preprocessing ... % 11.90/2.41 Prover 8: gave up % 11.93/2.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.93/2.46 Prover 7: gave up % 11.93/2.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.93/2.49 Prover 10: Preprocessing ... % 11.93/2.50 Prover 9: Constructing countermodel ... % 12.65/2.50 Prover 11: Preprocessing ... % 12.65/2.53 Prover 10: Warning: ignoring some quantifiers % 12.65/2.56 Prover 10: Constructing countermodel ... % 14.89/2.89 Prover 11: Constructing countermodel ... % 14.89/2.90 Prover 10: gave up % 15.64/2.91 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 15.64/2.93 Prover 12: Preprocessing ... % 17.02/3.09 Prover 12: Proving ... % 20.89/3.61 Prover 0: proved (2964ms) % 20.89/3.61 % 20.89/3.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 20.89/3.62 % 20.89/3.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 20.89/3.62 Prover 5: stopped % 20.89/3.62 Prover 12: stopped % 20.89/3.62 Prover 2: stopped % 20.89/3.62 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 20.89/3.62 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 20.89/3.63 Prover 9: stopped % 20.89/3.65 Prover 19: Preprocessing ... % 20.89/3.65 Prover 16: Preprocessing ... % 20.89/3.65 Prover 13: Preprocessing ... % 21.41/3.68 Prover 16: Warning: ignoring some quantifiers % 21.41/3.68 Prover 16: Constructing countermodel ... % 21.41/3.69 Prover 13: Warning: ignoring some quantifiers % 21.41/3.69 Prover 13: Constructing countermodel ... % 21.41/3.75 Prover 19: Warning: ignoring some quantifiers % 21.41/3.76 Prover 19: Constructing countermodel ... % 22.65/3.87 Prover 19: gave up % 22.65/3.89 Prover 13: gave up % 25.25/4.25 Prover 16: gave up % 47.93/8.59 Prover 11: Found proof (size 171) % 47.93/8.59 Prover 11: proved (6127ms) % 47.93/8.59 Prover 4: stopped % 47.93/8.59 % 47.93/8.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 47.93/8.59 % 48.26/8.61 % SZS output start Proof for theBenchmark % 48.26/8.61 Assumptions after simplification: % 48.26/8.61 --------------------------------- % 48.26/8.61 % 48.26/8.61 (apart3) % 48.26/8.64 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 48.26/8.64 % 48.26/8.64 (ceq1) % 48.26/8.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 48.26/8.64 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ % 48.26/8.64 (distinct_points(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 48.26/8.64 int] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : % 48.26/8.65 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 48.26/8.65 (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) % 48.26/8.65 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) & ! [v0: % 48.26/8.65 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 48.26/8.65 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~ % 48.26/8.65 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0) % 48.26/8.65 % 48.26/8.65 (ceq2) % 48.26/8.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 48.26/8.65 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 48.26/8.65 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 48.26/8.65 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 48.26/8.65 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 48.26/8.65 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 48.26/8.65 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 48.26/8.65 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 48.26/8.65 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 48.26/8.65 apart_point_and_line(v0, v2) = 0) % 48.26/8.65 % 48.26/8.65 (ceq3) % 48.26/8.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 48.26/8.66 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) % 48.26/8.66 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 48.26/8.66 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 48.26/8.66 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 48.26/8.66 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 48.26/8.66 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 48.26/8.66 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ % 48.26/8.66 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 48.26/8.66 convergent_lines(v0, v2) = 0) % 48.26/8.66 % 48.26/8.66 (ci3) % 48.54/8.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 48.54/8.66 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 48.54/8.66 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 48.54/8.66 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 48.54/8.66 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 48.54/8.66 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 48.54/8.66 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 48.54/8.66 % 48.54/8.66 (ci4) % 48.54/8.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 48.54/8.66 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 48.54/8.66 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 48.54/8.66 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 48.54/8.66 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 48.54/8.66 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 48.54/8.66 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 48.54/8.66 % 48.54/8.66 (con) % 48.54/8.66 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 48.54/8.66 int] : ( ~ (v5 = 0) & intersection_point(v0, v2) = v4 & % 48.54/8.66 intersection_point(v0, v1) = v3 & apart_point_and_line(v4, v1) = v5 & % 48.54/8.66 apart_point_and_line(v3, v2) = 0 & convergent_lines(v2, v1) = 0 & % 48.54/8.66 convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0 & $i(v4) & % 48.54/8.67 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 48.54/8.67 % 48.54/8.67 (cu1) % 48.54/8.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 48.54/8.68 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 48.54/8.68 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 48.54/8.68 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 48.54/8.68 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 48.54/8.68 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, % 48.54/8.68 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 48.54/8.68 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, % 48.54/8.68 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ % 48.54/8.68 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 48.54/8.68 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 48.54/8.68 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0, % 48.54/8.68 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 48.54/8.68 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 48.54/8.68 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 48.54/8.68 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 48.54/8.68 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 48.54/8.68 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 48.54/8.68 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 48.54/8.68 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 48.54/8.68 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 48.54/8.68 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 48.54/8.68 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 48.54/8.68 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 48.54/8.68 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 48.54/8.68 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 48.54/8.68 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 48.54/8.68 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 48.54/8.68 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 48.54/8.68 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~ % 48.54/8.68 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 48.54/8.68 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 48.54/8.68 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, % 48.54/8.68 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 48.54/8.68 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, % 48.54/8.68 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 48.54/8.68 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 48.54/8.68 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 48.54/8.68 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1, % 48.54/8.68 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i] % 48.54/8.68 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | % 48.54/8.68 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 48.54/8.68 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = % 48.54/8.68 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 48.54/8.68 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0, % 48.54/8.68 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 48.54/8.68 % 48.54/8.68 (function-axioms) % 48.54/8.68 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 48.54/8.68 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 48.54/8.68 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 48.54/8.68 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 48.54/8.68 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 48.54/8.68 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 48.54/8.68 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 48.54/8.68 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 48.54/8.68 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 48.54/8.68 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 48.54/8.68 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 48.54/8.68 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 48.54/8.68 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 48.54/8.68 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 48.54/8.68 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 48.54/8.68 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 48.54/8.68 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 48.54/8.68 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 48.54/8.68 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 48.54/8.68 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 48.54/8.68 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 48.54/8.68 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 48.54/8.68 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 48.54/8.68 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 48.54/8.68 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 48.54/8.68 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 48.54/8.68 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 48.54/8.68 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 48.54/8.68 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 48.54/8.68 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 48.54/8.68 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 48.54/8.68 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 48.54/8.68 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 48.54/8.68 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 48.54/8.68 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 48.54/8.68 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 48.54/8.68 % 48.54/8.68 Further assumptions not needed in the proof: % 48.54/8.68 -------------------------------------------- % 48.54/8.68 a3, a4, a5, apart1, apart2, apart4, apart5, ax1, ax2, ax6, ci1, ci2, coipo1, % 48.54/8.68 con1, cotno1, couo1, cp1, cp2, cup1, int1, oac1, occu1, ooc1, ooc2, orth1, ouo1, % 48.54/8.68 p1, par1 % 48.54/8.68 % 48.54/8.68 Those formulas are unsatisfiable: % 48.54/8.68 --------------------------------- % 48.54/8.68 % 48.54/8.68 Begin of proof % 48.54/8.68 | % 48.54/8.69 | ALPHA: (ci3) implies: % 48.54/8.69 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 48.54/8.69 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 48.54/8.69 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 48.54/8.69 | & $i(v2))) % 48.54/8.69 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 48.54/8.69 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 48.54/8.69 | (( ~ (v4 = 0) & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 48.54/8.69 | convergent_lines(v0, v1) = v3))) % 48.54/8.69 | % 48.54/8.69 | ALPHA: (ci4) implies: % 48.54/8.69 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 48.54/8.69 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 48.54/8.69 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 48.54/8.69 | & $i(v2))) % 48.54/8.69 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 48.54/8.69 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 48.54/8.69 | (( ~ (v4 = 0) & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 48.54/8.69 | convergent_lines(v0, v1) = v3))) % 48.54/8.69 | % 48.54/8.69 | ALPHA: (cu1) implies: % 48.54/8.69 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 48.54/8.69 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 48.54/8.69 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 48.54/8.69 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 48.54/8.69 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 48.54/8.69 | apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & % 48.54/8.69 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 48.54/8.69 | v1) = v6))) % 48.54/8.69 | % 48.54/8.69 | ALPHA: (ceq1) implies: % 48.54/8.69 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 48.54/8.69 | (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, % 48.54/8.69 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 48.54/8.69 | distinct_points(v0, v2) = 0) % 48.54/8.69 | % 48.54/8.69 | ALPHA: (ceq2) implies: % 48.54/8.69 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 48.54/8.69 | (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, % 48.54/8.69 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v1, % 48.54/8.69 | v2) = 0) % 48.54/8.69 | % 48.54/8.69 | ALPHA: (ceq3) implies: % 48.54/8.69 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 48.54/8.69 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | % 48.54/8.69 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 48.54/8.69 | % 48.54/8.69 | ALPHA: (function-axioms) implies: % 48.54/8.70 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 48.54/8.70 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 48.54/8.70 | (distinct_points(v3, v2) = v0)) % 48.54/8.70 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 48.54/8.70 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 48.54/8.70 | (distinct_lines(v3, v2) = v0)) % 48.54/8.70 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 48.54/8.70 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 48.54/8.70 | (convergent_lines(v3, v2) = v0)) % 48.54/8.70 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 48.54/8.70 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 48.54/8.70 | (apart_point_and_line(v3, v2) = v0)) % 48.54/8.70 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 48.54/8.70 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 48.54/8.70 | v0)) % 48.54/8.70 | % 48.54/8.70 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 48.54/8.70 | all_38_3, all_38_4, all_38_5 gives: % 48.54/8.70 | (14) ~ (all_38_0 = 0) & intersection_point(all_38_5, all_38_3) = all_38_1 % 48.54/8.70 | & intersection_point(all_38_5, all_38_4) = all_38_2 & % 48.54/8.70 | apart_point_and_line(all_38_1, all_38_4) = all_38_0 & % 48.54/8.70 | apart_point_and_line(all_38_2, all_38_3) = 0 & % 48.54/8.70 | convergent_lines(all_38_3, all_38_4) = 0 & convergent_lines(all_38_5, % 48.54/8.70 | all_38_3) = 0 & convergent_lines(all_38_5, all_38_4) = 0 & % 48.54/8.70 | $i(all_38_1) & $i(all_38_2) & $i(all_38_3) & $i(all_38_4) & % 48.54/8.70 | $i(all_38_5) % 48.54/8.70 | % 48.54/8.70 | ALPHA: (14) implies: % 48.54/8.70 | (15) ~ (all_38_0 = 0) % 48.54/8.70 | (16) $i(all_38_5) % 48.54/8.70 | (17) $i(all_38_4) % 48.54/8.70 | (18) $i(all_38_3) % 48.54/8.70 | (19) convergent_lines(all_38_5, all_38_4) = 0 % 48.54/8.70 | (20) convergent_lines(all_38_5, all_38_3) = 0 % 48.54/8.70 | (21) convergent_lines(all_38_3, all_38_4) = 0 % 48.54/8.70 | (22) apart_point_and_line(all_38_2, all_38_3) = 0 % 48.54/8.70 | (23) apart_point_and_line(all_38_1, all_38_4) = all_38_0 % 48.54/8.70 | (24) intersection_point(all_38_5, all_38_4) = all_38_2 % 48.54/8.70 | (25) intersection_point(all_38_5, all_38_3) = all_38_1 % 48.54/8.70 | % 48.54/8.70 | GROUND_INST: instantiating (3) with all_38_5, all_38_4, simplifying with (16), % 48.54/8.70 | (17), (19) gives: % 48.54/8.70 | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 48.54/8.70 | intersection_point(all_38_5, all_38_4) = v0 & % 48.54/8.70 | apart_point_and_line(v0, all_38_4) = v1 & $i(v0)) % 48.54/8.70 | % 48.54/8.70 | GROUND_INST: instantiating (1) with all_38_5, all_38_4, simplifying with (16), % 48.54/8.70 | (17), (19) gives: % 48.54/8.70 | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 48.54/8.70 | intersection_point(all_38_5, all_38_4) = v0 & % 48.54/8.70 | apart_point_and_line(v0, all_38_5) = v1 & $i(v0)) % 48.54/8.70 | % 48.54/8.70 | GROUND_INST: instantiating (3) with all_38_5, all_38_3, simplifying with (16), % 48.54/8.70 | (18), (20) gives: % 48.54/8.71 | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 48.54/8.71 | intersection_point(all_38_5, all_38_3) = v0 & % 48.54/8.71 | apart_point_and_line(v0, all_38_3) = v1 & $i(v0)) % 48.54/8.71 | % 48.54/8.71 | GROUND_INST: instantiating (1) with all_38_5, all_38_3, simplifying with (16), % 48.54/8.71 | (18), (20) gives: % 48.54/8.71 | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 48.54/8.71 | intersection_point(all_38_5, all_38_3) = v0 & % 48.54/8.71 | apart_point_and_line(v0, all_38_5) = v1 & $i(v0)) % 48.54/8.71 | % 48.54/8.71 | GROUND_INST: instantiating (3) with all_38_3, all_38_4, simplifying with (17), % 48.54/8.71 | (18), (21) gives: % 48.54/8.71 | (30) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 48.54/8.71 | intersection_point(all_38_3, all_38_4) = v0 & % 48.54/8.71 | apart_point_and_line(v0, all_38_4) = v1 & $i(v0)) % 48.54/8.71 | % 48.54/8.71 | GROUND_INST: instantiating (1) with all_38_3, all_38_4, simplifying with (17), % 48.54/8.71 | (18), (21) gives: % 48.54/8.71 | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 48.54/8.71 | intersection_point(all_38_3, all_38_4) = v0 & % 48.54/8.71 | apart_point_and_line(v0, all_38_3) = v1 & $i(v0)) % 48.54/8.71 | % 48.54/8.71 | GROUND_INST: instantiating (4) with all_38_5, all_38_4, all_38_2, simplifying % 48.54/8.71 | with (16), (17), (24) gives: % 48.54/8.71 | (32) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 48.54/8.71 | apart_point_and_line(all_38_2, all_38_4) = v1) | ( ~ (v0 = 0) & % 48.54/8.71 | convergent_lines(all_38_5, all_38_4) = v0)) % 48.54/8.71 | % 48.54/8.71 | GROUND_INST: instantiating (2) with all_38_5, all_38_4, all_38_2, simplifying % 48.54/8.71 | with (16), (17), (24) gives: % 48.54/8.71 | (33) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 48.54/8.71 | apart_point_and_line(all_38_2, all_38_5) = v1) | ( ~ (v0 = 0) & % 48.54/8.71 | convergent_lines(all_38_5, all_38_4) = v0)) % 48.54/8.71 | % 48.54/8.71 | GROUND_INST: instantiating (4) with all_38_5, all_38_3, all_38_1, simplifying % 48.54/8.71 | with (16), (18), (25) gives: % 48.54/8.71 | (34) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 48.54/8.71 | apart_point_and_line(all_38_1, all_38_3) = v1) | ( ~ (v0 = 0) & % 48.54/8.71 | convergent_lines(all_38_5, all_38_3) = v0)) % 48.54/8.71 | % 48.54/8.71 | GROUND_INST: instantiating (2) with all_38_5, all_38_3, all_38_1, simplifying % 48.54/8.71 | with (16), (18), (25) gives: % 48.54/8.71 | (35) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 48.54/8.71 | apart_point_and_line(all_38_1, all_38_5) = v1) | ( ~ (v0 = 0) & % 48.54/8.71 | convergent_lines(all_38_5, all_38_3) = v0)) % 48.54/8.71 | % 48.54/8.71 | DELTA: instantiating (32) with fresh symbols all_53_0, all_53_1 gives: % 48.54/8.71 | (36) ( ~ (all_53_0 = 0) & apart_point_and_line(all_38_2, all_38_4) = % 48.54/8.71 | all_53_0) | ( ~ (all_53_1 = 0) & convergent_lines(all_38_5, % 48.54/8.71 | all_38_4) = all_53_1) % 48.54/8.71 | % 48.54/8.71 | DELTA: instantiating (31) with fresh symbols all_54_0, all_54_1 gives: % 48.54/8.71 | (37) ~ (all_54_0 = 0) & intersection_point(all_38_3, all_38_4) = all_54_1 % 48.54/8.71 | & apart_point_and_line(all_54_1, all_38_3) = all_54_0 & $i(all_54_1) % 48.54/8.71 | % 48.54/8.71 | ALPHA: (37) implies: % 48.54/8.71 | (38) ~ (all_54_0 = 0) % 48.54/8.71 | (39) apart_point_and_line(all_54_1, all_38_3) = all_54_0 % 48.54/8.71 | (40) intersection_point(all_38_3, all_38_4) = all_54_1 % 48.54/8.71 | % 48.54/8.71 | DELTA: instantiating (29) with fresh symbols all_56_0, all_56_1 gives: % 48.54/8.71 | (41) ~ (all_56_0 = 0) & intersection_point(all_38_5, all_38_3) = all_56_1 % 48.54/8.71 | & apart_point_and_line(all_56_1, all_38_5) = all_56_0 & $i(all_56_1) % 48.54/8.71 | % 48.54/8.71 | ALPHA: (41) implies: % 48.54/8.71 | (42) $i(all_56_1) % 48.54/8.71 | (43) apart_point_and_line(all_56_1, all_38_5) = all_56_0 % 48.54/8.71 | (44) intersection_point(all_38_5, all_38_3) = all_56_1 % 48.54/8.71 | % 48.54/8.71 | DELTA: instantiating (26) with fresh symbols all_58_0, all_58_1 gives: % 48.54/8.72 | (45) ~ (all_58_0 = 0) & intersection_point(all_38_5, all_38_4) = all_58_1 % 48.54/8.72 | & apart_point_and_line(all_58_1, all_38_4) = all_58_0 & $i(all_58_1) % 48.54/8.72 | % 48.54/8.72 | ALPHA: (45) implies: % 48.54/8.72 | (46) ~ (all_58_0 = 0) % 48.54/8.72 | (47) $i(all_58_1) % 48.54/8.72 | (48) apart_point_and_line(all_58_1, all_38_4) = all_58_0 % 48.54/8.72 | (49) intersection_point(all_38_5, all_38_4) = all_58_1 % 48.54/8.72 | % 48.54/8.72 | DELTA: instantiating (30) with fresh symbols all_60_0, all_60_1 gives: % 48.54/8.72 | (50) ~ (all_60_0 = 0) & intersection_point(all_38_3, all_38_4) = all_60_1 % 48.54/8.72 | & apart_point_and_line(all_60_1, all_38_4) = all_60_0 & $i(all_60_1) % 48.54/8.72 | % 48.54/8.72 | ALPHA: (50) implies: % 48.54/8.72 | (51) ~ (all_60_0 = 0) % 48.54/8.72 | (52) $i(all_60_1) % 48.54/8.72 | (53) apart_point_and_line(all_60_1, all_38_4) = all_60_0 % 48.54/8.72 | (54) intersection_point(all_38_3, all_38_4) = all_60_1 % 48.54/8.72 | % 48.54/8.72 | DELTA: instantiating (28) with fresh symbols all_62_0, all_62_1 gives: % 48.54/8.72 | (55) ~ (all_62_0 = 0) & intersection_point(all_38_5, all_38_3) = all_62_1 % 48.54/8.72 | & apart_point_and_line(all_62_1, all_38_3) = all_62_0 & $i(all_62_1) % 48.54/8.72 | % 48.54/8.72 | ALPHA: (55) implies: % 48.54/8.72 | (56) apart_point_and_line(all_62_1, all_38_3) = all_62_0 % 48.54/8.72 | (57) intersection_point(all_38_5, all_38_3) = all_62_1 % 48.54/8.72 | % 48.54/8.72 | DELTA: instantiating (27) with fresh symbols all_64_0, all_64_1 gives: % 48.54/8.72 | (58) ~ (all_64_0 = 0) & intersection_point(all_38_5, all_38_4) = all_64_1 % 48.54/8.72 | & apart_point_and_line(all_64_1, all_38_5) = all_64_0 & $i(all_64_1) % 48.54/8.72 | % 48.54/8.72 | ALPHA: (58) implies: % 48.54/8.72 | (59) apart_point_and_line(all_64_1, all_38_5) = all_64_0 % 48.54/8.72 | (60) intersection_point(all_38_5, all_38_4) = all_64_1 % 48.54/8.72 | % 48.54/8.72 | DELTA: instantiating (35) with fresh symbols all_66_0, all_66_1 gives: % 48.54/8.72 | (61) ( ~ (all_66_0 = 0) & apart_point_and_line(all_38_1, all_38_5) = % 48.54/8.72 | all_66_0) | ( ~ (all_66_1 = 0) & convergent_lines(all_38_5, % 48.54/8.72 | all_38_3) = all_66_1) % 48.54/8.72 | % 48.54/8.72 | DELTA: instantiating (34) with fresh symbols all_67_0, all_67_1 gives: % 48.54/8.72 | (62) ( ~ (all_67_0 = 0) & apart_point_and_line(all_38_1, all_38_3) = % 48.54/8.72 | all_67_0) | ( ~ (all_67_1 = 0) & convergent_lines(all_38_5, % 48.54/8.72 | all_38_3) = all_67_1) % 48.54/8.72 | % 48.54/8.72 | DELTA: instantiating (33) with fresh symbols all_68_0, all_68_1 gives: % 48.54/8.72 | (63) ( ~ (all_68_0 = 0) & apart_point_and_line(all_38_2, all_38_5) = % 48.54/8.72 | all_68_0) | ( ~ (all_68_1 = 0) & convergent_lines(all_38_5, % 48.54/8.72 | all_38_4) = all_68_1) % 48.54/8.72 | % 48.54/8.72 | BETA: splitting (61) gives: % 48.54/8.72 | % 48.54/8.72 | Case 1: % 48.54/8.72 | | % 48.54/8.72 | | (64) ~ (all_66_0 = 0) & apart_point_and_line(all_38_1, all_38_5) = % 48.54/8.72 | | all_66_0 % 48.54/8.72 | | % 48.54/8.72 | | ALPHA: (64) implies: % 48.54/8.72 | | (65) ~ (all_66_0 = 0) % 48.54/8.72 | | (66) apart_point_and_line(all_38_1, all_38_5) = all_66_0 % 48.54/8.72 | | % 48.54/8.72 | | BETA: splitting (63) gives: % 48.54/8.72 | | % 48.54/8.72 | | Case 1: % 48.54/8.72 | | | % 48.54/8.72 | | | (67) ~ (all_68_0 = 0) & apart_point_and_line(all_38_2, all_38_5) = % 48.54/8.72 | | | all_68_0 % 48.54/8.72 | | | % 48.54/8.72 | | | ALPHA: (67) implies: % 48.54/8.72 | | | (68) ~ (all_68_0 = 0) % 48.54/8.72 | | | (69) apart_point_and_line(all_38_2, all_38_5) = all_68_0 % 48.54/8.72 | | | % 48.54/8.72 | | | BETA: splitting (36) gives: % 48.54/8.72 | | | % 48.54/8.72 | | | Case 1: % 48.54/8.72 | | | | % 48.54/8.72 | | | | (70) ~ (all_53_0 = 0) & apart_point_and_line(all_38_2, all_38_4) = % 48.54/8.72 | | | | all_53_0 % 48.54/8.72 | | | | % 48.54/8.72 | | | | ALPHA: (70) implies: % 48.54/8.72 | | | | (71) apart_point_and_line(all_38_2, all_38_4) = all_53_0 % 48.54/8.72 | | | | % 48.54/8.72 | | | | BETA: splitting (62) gives: % 48.54/8.72 | | | | % 48.54/8.72 | | | | Case 1: % 48.54/8.72 | | | | | % 48.54/8.72 | | | | | (72) ~ (all_67_0 = 0) & apart_point_and_line(all_38_1, all_38_3) = % 48.54/8.72 | | | | | all_67_0 % 48.54/8.72 | | | | | % 48.54/8.72 | | | | | ALPHA: (72) implies: % 48.54/8.72 | | | | | (73) ~ (all_67_0 = 0) % 48.54/8.72 | | | | | (74) apart_point_and_line(all_38_1, all_38_3) = all_67_0 % 48.54/8.72 | | | | | % 48.54/8.72 | | | | | GROUND_INST: instantiating (13) with all_38_2, all_64_1, all_38_4, % 48.54/8.73 | | | | | all_38_5, simplifying with (24), (60) gives: % 48.54/8.73 | | | | | (75) all_64_1 = all_38_2 % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | GROUND_INST: instantiating (13) with all_58_1, all_64_1, all_38_4, % 48.54/8.73 | | | | | all_38_5, simplifying with (49), (60) gives: % 48.54/8.73 | | | | | (76) all_64_1 = all_58_1 % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | GROUND_INST: instantiating (13) with all_38_1, all_62_1, all_38_3, % 48.54/8.73 | | | | | all_38_5, simplifying with (25), (57) gives: % 48.54/8.73 | | | | | (77) all_62_1 = all_38_1 % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | GROUND_INST: instantiating (13) with all_56_1, all_62_1, all_38_3, % 48.54/8.73 | | | | | all_38_5, simplifying with (44), (57) gives: % 48.54/8.73 | | | | | (78) all_62_1 = all_56_1 % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | GROUND_INST: instantiating (13) with all_54_1, all_60_1, all_38_4, % 48.54/8.73 | | | | | all_38_3, simplifying with (40), (54) gives: % 48.54/8.73 | | | | | (79) all_60_1 = all_54_1 % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | COMBINE_EQS: (75), (76) imply: % 48.54/8.73 | | | | | (80) all_58_1 = all_38_2 % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | COMBINE_EQS: (77), (78) imply: % 48.54/8.73 | | | | | (81) all_56_1 = all_38_1 % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | REDUCE: (59), (75) imply: % 48.54/8.73 | | | | | (82) apart_point_and_line(all_38_2, all_38_5) = all_64_0 % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | REDUCE: (56), (77) imply: % 48.54/8.73 | | | | | (83) apart_point_and_line(all_38_1, all_38_3) = all_62_0 % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | REDUCE: (53), (79) imply: % 48.54/8.73 | | | | | (84) apart_point_and_line(all_54_1, all_38_4) = all_60_0 % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | REDUCE: (48), (80) imply: % 48.54/8.73 | | | | | (85) apart_point_and_line(all_38_2, all_38_4) = all_58_0 % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | REDUCE: (43), (81) imply: % 48.54/8.73 | | | | | (86) apart_point_and_line(all_38_1, all_38_5) = all_56_0 % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | REDUCE: (52), (79) imply: % 48.54/8.73 | | | | | (87) $i(all_54_1) % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | REDUCE: (47), (80) imply: % 48.54/8.73 | | | | | (88) $i(all_38_2) % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | REDUCE: (42), (81) imply: % 48.54/8.73 | | | | | (89) $i(all_38_1) % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | GROUND_INST: instantiating (12) with all_68_0, all_64_0, all_38_5, % 48.54/8.73 | | | | | all_38_2, simplifying with (69), (82) gives: % 48.54/8.73 | | | | | (90) all_68_0 = all_64_0 % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | GROUND_INST: instantiating (12) with all_53_0, all_58_0, all_38_4, % 48.54/8.73 | | | | | all_38_2, simplifying with (71), (85) gives: % 48.54/8.73 | | | | | (91) all_58_0 = all_53_0 % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | GROUND_INST: instantiating (12) with all_66_0, all_56_0, all_38_5, % 48.54/8.73 | | | | | all_38_1, simplifying with (66), (86) gives: % 48.54/8.73 | | | | | (92) all_66_0 = all_56_0 % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | GROUND_INST: instantiating (12) with all_67_0, all_62_0, all_38_3, % 48.54/8.73 | | | | | all_38_1, simplifying with (74), (83) gives: % 48.54/8.73 | | | | | (93) all_67_0 = all_62_0 % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | REDUCE: (68), (90) imply: % 48.54/8.73 | | | | | (94) ~ (all_64_0 = 0) % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | REDUCE: (73), (93) imply: % 48.54/8.73 | | | | | (95) ~ (all_62_0 = 0) % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | REDUCE: (65), (92) imply: % 48.54/8.73 | | | | | (96) ~ (all_56_0 = 0) % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | REDUCE: (46), (91) imply: % 48.54/8.73 | | | | | (97) ~ (all_53_0 = 0) % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | GROUND_INST: instantiating (7) with all_38_2, all_38_3, all_38_4, % 48.54/8.73 | | | | | all_53_0, simplifying with (17), (18), (22), (71), (88) % 48.54/8.73 | | | | | gives: % 48.54/8.73 | | | | | (98) all_53_0 = 0 | distinct_lines(all_38_3, all_38_4) = 0 % 48.54/8.73 | | | | | % 48.54/8.73 | | | | | GROUND_INST: instantiating (5) with all_38_2, all_38_1, all_38_4, % 48.54/8.73 | | | | | all_38_5, all_53_0, all_56_0, simplifying with (16), % 48.54/8.73 | | | | | (17), (71), (86), (88), (89) gives: % 48.54/8.74 | | | | | (99) all_56_0 = 0 | all_53_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 48.54/8.74 | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 48.54/8.74 | | | | | apart_point_and_line(all_38_1, all_38_4) = 0) | (v2 = 0 & % 48.54/8.74 | | | | | apart_point_and_line(all_38_2, all_38_5) = 0) | ( ~ (v1 = % 48.54/8.74 | | | | | 0) & distinct_lines(all_38_4, all_38_5) = v1) | ( ~ (v0 % 48.54/8.74 | | | | | = 0) & distinct_points(all_38_2, all_38_1) = v0)) % 48.54/8.74 | | | | | % 48.54/8.74 | | | | | GROUND_INST: instantiating (6) with all_38_2, all_38_3, all_38_1, % 48.54/8.74 | | | | | all_62_0, simplifying with (18), (22), (83), (88), (89) % 48.54/8.74 | | | | | gives: % 48.54/8.74 | | | | | (100) all_62_0 = 0 | distinct_points(all_38_2, all_38_1) = 0 % 48.54/8.74 | | | | | % 48.54/8.74 | | | | | GROUND_INST: instantiating (5) with all_54_1, all_38_1, all_38_3, % 48.54/8.74 | | | | | all_38_4, all_54_0, all_38_0, simplifying with (17), % 48.54/8.74 | | | | | (18), (23), (39), (87), (89) gives: % 48.54/8.74 | | | | | (101) all_54_0 = 0 | all_38_0 = 0 | ? [v0: int] : ? [v1: int] : % 48.54/8.74 | | | | | ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 48.54/8.74 | | | | | apart_point_and_line(all_38_1, all_38_3) = 0) | (v2 = 0 & % 48.54/8.74 | | | | | apart_point_and_line(all_54_1, all_38_4) = 0) | ( ~ (v1 = % 48.54/8.74 | | | | | 0) & distinct_lines(all_38_3, all_38_4) = v1) | ( ~ (v0 % 48.54/8.74 | | | | | = 0) & distinct_points(all_54_1, all_38_1) = v0)) % 48.54/8.74 | | | | | % 48.54/8.74 | | | | | BETA: splitting (100) gives: % 48.54/8.74 | | | | | % 48.54/8.74 | | | | | Case 1: % 48.54/8.74 | | | | | | % 48.54/8.74 | | | | | | (102) distinct_points(all_38_2, all_38_1) = 0 % 48.54/8.74 | | | | | | % 48.54/8.74 | | | | | | BETA: splitting (99) gives: % 48.54/8.74 | | | | | | % 48.54/8.74 | | | | | | Case 1: % 48.54/8.74 | | | | | | | % 48.54/8.74 | | | | | | | (103) all_56_0 = 0 % 48.54/8.74 | | | | | | | % 48.54/8.74 | | | | | | | REDUCE: (96), (103) imply: % 48.54/8.74 | | | | | | | (104) $false % 48.54/8.74 | | | | | | | % 48.54/8.74 | | | | | | | CLOSE: (104) is inconsistent. % 48.54/8.74 | | | | | | | % 48.54/8.74 | | | | | | Case 2: % 48.54/8.74 | | | | | | | % 48.54/8.74 | | | | | | | (105) all_53_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] % 48.54/8.74 | | | | | | | : ? [v3: int] : ((v3 = 0 & % 48.54/8.74 | | | | | | | apart_point_and_line(all_38_1, all_38_4) = 0) | (v2 = % 48.54/8.74 | | | | | | | 0 & apart_point_and_line(all_38_2, all_38_5) = 0) | ( % 48.54/8.74 | | | | | | | ~ (v1 = 0) & distinct_lines(all_38_4, all_38_5) = v1) % 48.54/8.74 | | | | | | | | ( ~ (v0 = 0) & distinct_points(all_38_2, all_38_1) = % 48.54/8.74 | | | | | | | v0)) % 48.54/8.74 | | | | | | | % 48.54/8.74 | | | | | | | BETA: splitting (98) gives: % 48.54/8.74 | | | | | | | % 48.54/8.74 | | | | | | | Case 1: % 48.54/8.74 | | | | | | | | % 48.54/8.74 | | | | | | | | (106) distinct_lines(all_38_3, all_38_4) = 0 % 48.54/8.74 | | | | | | | | % 48.54/8.74 | | | | | | | | BETA: splitting (105) gives: % 48.54/8.74 | | | | | | | | % 48.54/8.74 | | | | | | | | Case 1: % 48.54/8.74 | | | | | | | | | % 48.54/8.74 | | | | | | | | | (107) all_53_0 = 0 % 48.54/8.74 | | | | | | | | | % 48.54/8.74 | | | | | | | | | REDUCE: (97), (107) imply: % 48.54/8.74 | | | | | | | | | (108) $false % 48.54/8.74 | | | | | | | | | % 48.54/8.74 | | | | | | | | | CLOSE: (108) is inconsistent. % 48.54/8.74 | | | | | | | | | % 48.54/8.74 | | | | | | | | Case 2: % 48.54/8.74 | | | | | | | | | % 48.54/8.74 | | | | | | | | | (109) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 48.54/8.74 | | | | | | | | | int] : ((v3 = 0 & apart_point_and_line(all_38_1, % 48.54/8.74 | | | | | | | | | all_38_4) = 0) | (v2 = 0 & % 48.54/8.74 | | | | | | | | | apart_point_and_line(all_38_2, all_38_5) = 0) | ( % 48.54/8.74 | | | | | | | | | ~ (v1 = 0) & distinct_lines(all_38_4, all_38_5) = % 48.54/8.74 | | | | | | | | | v1) | ( ~ (v0 = 0) & distinct_points(all_38_2, % 48.54/8.74 | | | | | | | | | all_38_1) = v0)) % 48.54/8.74 | | | | | | | | | % 48.54/8.74 | | | | | | | | | DELTA: instantiating (109) with fresh symbols all_431_0, % 48.54/8.74 | | | | | | | | | all_431_1, all_431_2, all_431_3 gives: % 48.54/8.74 | | | | | | | | | (110) (all_431_0 = 0 & apart_point_and_line(all_38_1, % 48.54/8.74 | | | | | | | | | all_38_4) = 0) | (all_431_1 = 0 & % 48.54/8.74 | | | | | | | | | apart_point_and_line(all_38_2, all_38_5) = 0) | ( ~ % 48.54/8.74 | | | | | | | | | (all_431_2 = 0) & distinct_lines(all_38_4, % 48.54/8.74 | | | | | | | | | all_38_5) = all_431_2) | ( ~ (all_431_3 = 0) & % 48.54/8.74 | | | | | | | | | distinct_points(all_38_2, all_38_1) = all_431_3) % 48.54/8.74 | | | | | | | | | % 48.54/8.74 | | | | | | | | | BETA: splitting (101) gives: % 48.54/8.74 | | | | | | | | | % 48.54/8.74 | | | | | | | | | Case 1: % 48.54/8.74 | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | (111) all_54_0 = 0 % 48.54/8.75 | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | REDUCE: (38), (111) imply: % 48.54/8.75 | | | | | | | | | | (112) $false % 48.54/8.75 | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | CLOSE: (112) is inconsistent. % 48.54/8.75 | | | | | | | | | | % 48.54/8.75 | | | | | | | | | Case 2: % 48.54/8.75 | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | (113) all_38_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 48.54/8.75 | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 48.54/8.75 | | | | | | | | | | apart_point_and_line(all_38_1, all_38_3) = 0) | % 48.54/8.75 | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_54_1, % 48.54/8.75 | | | | | | | | | | all_38_4) = 0) | ( ~ (v1 = 0) & % 48.54/8.75 | | | | | | | | | | distinct_lines(all_38_3, all_38_4) = v1) | ( ~ % 48.54/8.75 | | | | | | | | | | (v0 = 0) & distinct_points(all_54_1, all_38_1) % 48.54/8.75 | | | | | | | | | | = v0)) % 48.54/8.75 | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | BETA: splitting (110) gives: % 48.54/8.75 | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | Case 1: % 48.54/8.75 | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | (114) (all_431_0 = 0 & apart_point_and_line(all_38_1, % 48.54/8.75 | | | | | | | | | | | all_38_4) = 0) | (all_431_1 = 0 & % 48.54/8.75 | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_5) = 0) % 48.54/8.75 | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | BETA: splitting (114) gives: % 48.54/8.75 | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | Case 1: % 48.54/8.75 | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | (115) all_431_0 = 0 & apart_point_and_line(all_38_1, % 48.54/8.75 | | | | | | | | | | | | all_38_4) = 0 % 48.54/8.75 | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | ALPHA: (115) implies: % 48.54/8.75 | | | | | | | | | | | | (116) apart_point_and_line(all_38_1, all_38_4) = 0 % 48.54/8.75 | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_38_0, 0, all_38_4, % 48.54/8.75 | | | | | | | | | | | | all_38_1, simplifying with (23), (116) gives: % 48.54/8.75 | | | | | | | | | | | | (117) all_38_0 = 0 % 48.54/8.75 | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | REDUCE: (15), (117) imply: % 48.54/8.75 | | | | | | | | | | | | (118) $false % 48.54/8.75 | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | CLOSE: (118) is inconsistent. % 48.54/8.75 | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | Case 2: % 48.54/8.75 | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | (119) all_431_1 = 0 & apart_point_and_line(all_38_2, % 48.54/8.75 | | | | | | | | | | | | all_38_5) = 0 % 48.54/8.75 | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | ALPHA: (119) implies: % 48.54/8.75 | | | | | | | | | | | | (120) apart_point_and_line(all_38_2, all_38_5) = 0 % 48.54/8.75 | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_64_0, 0, all_38_5, % 48.54/8.75 | | | | | | | | | | | | all_38_2, simplifying with (82), (120) gives: % 48.54/8.75 | | | | | | | | | | | | (121) all_64_0 = 0 % 48.54/8.75 | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | REDUCE: (94), (121) imply: % 48.54/8.75 | | | | | | | | | | | | (122) $false % 48.54/8.75 | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | CLOSE: (122) is inconsistent. % 48.54/8.75 | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | End of split % 48.54/8.75 | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | Case 2: % 48.54/8.75 | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | (123) ( ~ (all_431_2 = 0) & distinct_lines(all_38_4, % 48.54/8.75 | | | | | | | | | | | all_38_5) = all_431_2) | ( ~ (all_431_3 = 0) & % 48.54/8.75 | | | | | | | | | | | distinct_points(all_38_2, all_38_1) = all_431_3) % 48.54/8.75 | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | BETA: splitting (123) gives: % 48.54/8.75 | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | Case 1: % 48.54/8.75 | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | (124) ~ (all_431_2 = 0) & distinct_lines(all_38_4, % 48.54/8.75 | | | | | | | | | | | | all_38_5) = all_431_2 % 48.54/8.75 | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | ALPHA: (124) implies: % 48.54/8.75 | | | | | | | | | | | | (125) ~ (all_431_2 = 0) % 48.54/8.75 | | | | | | | | | | | | (126) distinct_lines(all_38_4, all_38_5) = all_431_2 % 48.54/8.75 | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | BETA: splitting (113) gives: % 48.54/8.75 | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | Case 1: % 48.54/8.75 | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | (127) all_38_0 = 0 % 48.54/8.75 | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | REDUCE: (15), (127) imply: % 48.54/8.75 | | | | | | | | | | | | | (128) $false % 48.54/8.75 | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | CLOSE: (128) is inconsistent. % 48.54/8.75 | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | Case 2: % 48.54/8.75 | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | (129) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 48.54/8.75 | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 48.54/8.75 | | | | | | | | | | | | | apart_point_and_line(all_38_1, all_38_3) = 0) % 48.54/8.75 | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_54_1, % 48.54/8.75 | | | | | | | | | | | | | all_38_4) = 0) | ( ~ (v1 = 0) & % 48.54/8.75 | | | | | | | | | | | | | distinct_lines(all_38_3, all_38_4) = v1) | ( ~ % 48.54/8.75 | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_54_1, all_38_1) % 48.54/8.75 | | | | | | | | | | | | | = v0)) % 48.54/8.75 | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | DELTA: instantiating (129) with fresh symbols all_732_0, % 48.54/8.75 | | | | | | | | | | | | | all_732_1, all_732_2, all_732_3 gives: % 48.54/8.75 | | | | | | | | | | | | | (130) (all_732_0 = 0 & apart_point_and_line(all_38_1, % 48.54/8.75 | | | | | | | | | | | | | all_38_3) = 0) | (all_732_1 = 0 & % 48.54/8.75 | | | | | | | | | | | | | apart_point_and_line(all_54_1, all_38_4) = 0) | % 48.54/8.75 | | | | | | | | | | | | | ( ~ (all_732_2 = 0) & distinct_lines(all_38_3, % 48.54/8.75 | | | | | | | | | | | | | all_38_4) = all_732_2) | ( ~ (all_732_3 = 0) & % 48.54/8.75 | | | | | | | | | | | | | distinct_points(all_54_1, all_38_1) = all_732_3) % 48.54/8.75 | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | BETA: splitting (130) gives: % 48.54/8.75 | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | Case 1: % 48.54/8.75 | | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | | (131) (all_732_0 = 0 & apart_point_and_line(all_38_1, % 48.54/8.75 | | | | | | | | | | | | | | all_38_3) = 0) | (all_732_1 = 0 & % 48.54/8.75 | | | | | | | | | | | | | | apart_point_and_line(all_54_1, all_38_4) = 0) % 48.54/8.75 | | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | | BETA: splitting (131) gives: % 48.54/8.75 | | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | | Case 1: % 48.54/8.75 | | | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | | | (132) all_732_0 = 0 & apart_point_and_line(all_38_1, % 48.54/8.75 | | | | | | | | | | | | | | | all_38_3) = 0 % 48.54/8.75 | | | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | | | ALPHA: (132) implies: % 48.54/8.75 | | | | | | | | | | | | | | | (133) apart_point_and_line(all_38_1, all_38_3) = 0 % 48.54/8.75 | | | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_62_0, 0, all_38_3, % 48.54/8.75 | | | | | | | | | | | | | | | all_38_1, simplifying with (83), (133) gives: % 48.54/8.75 | | | | | | | | | | | | | | | (134) all_62_0 = 0 % 48.54/8.75 | | | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | | | REDUCE: (95), (134) imply: % 48.54/8.75 | | | | | | | | | | | | | | | (135) $false % 48.54/8.75 | | | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | | | CLOSE: (135) is inconsistent. % 48.54/8.75 | | | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | | Case 2: % 48.54/8.75 | | | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | | | (136) all_732_1 = 0 & apart_point_and_line(all_54_1, % 48.54/8.75 | | | | | | | | | | | | | | | all_38_4) = 0 % 48.54/8.75 | | | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | | | ALPHA: (136) implies: % 48.54/8.75 | | | | | | | | | | | | | | | (137) apart_point_and_line(all_54_1, all_38_4) = 0 % 48.54/8.75 | | | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_60_0, 0, all_38_4, % 48.54/8.75 | | | | | | | | | | | | | | | all_54_1, simplifying with (84), (137) gives: % 48.54/8.75 | | | | | | | | | | | | | | | (138) all_60_0 = 0 % 48.54/8.75 | | | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | | | REDUCE: (51), (138) imply: % 48.54/8.75 | | | | | | | | | | | | | | | (139) $false % 48.54/8.75 | | | | | | | | | | | | | | | % 48.54/8.75 | | | | | | | | | | | | | | | CLOSE: (139) is inconsistent. % 48.54/8.75 | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | End of split % 48.54/8.76 | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | Case 2: % 48.54/8.76 | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | (140) ( ~ (all_732_2 = 0) & distinct_lines(all_38_3, % 48.54/8.76 | | | | | | | | | | | | | | all_38_4) = all_732_2) | ( ~ (all_732_3 = 0) & % 48.54/8.76 | | | | | | | | | | | | | | distinct_points(all_54_1, all_38_1) = all_732_3) % 48.54/8.76 | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | BETA: splitting (140) gives: % 48.54/8.76 | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | Case 1: % 48.54/8.76 | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | | (141) ~ (all_732_2 = 0) & distinct_lines(all_38_3, % 48.54/8.76 | | | | | | | | | | | | | | | all_38_4) = all_732_2 % 48.54/8.76 | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | | ALPHA: (141) implies: % 48.54/8.76 | | | | | | | | | | | | | | | (142) ~ (all_732_2 = 0) % 48.54/8.76 | | | | | | | | | | | | | | | (143) distinct_lines(all_38_3, all_38_4) = all_732_2 % 48.54/8.76 | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_732_2, all_38_4, % 48.54/8.76 | | | | | | | | | | | | | | | all_38_3, simplifying with (106), (143) gives: % 48.54/8.76 | | | | | | | | | | | | | | | (144) all_732_2 = 0 % 48.54/8.76 | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | | REDUCE: (142), (144) imply: % 48.54/8.76 | | | | | | | | | | | | | | | (145) $false % 48.54/8.76 | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | | CLOSE: (145) is inconsistent. % 48.54/8.76 | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | Case 2: % 48.54/8.76 | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_38_5, all_38_4, % 48.54/8.76 | | | | | | | | | | | | | | | all_38_5, all_431_2, simplifying with (16), (17), % 48.54/8.76 | | | | | | | | | | | | | | | (19), (126) gives: % 48.54/8.76 | | | | | | | | | | | | | | | (146) all_431_2 = 0 | convergent_lines(all_38_5, % 48.54/8.76 | | | | | | | | | | | | | | | all_38_5) = 0 % 48.54/8.76 | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | | BETA: splitting (146) gives: % 48.54/8.76 | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | | Case 1: % 48.54/8.76 | | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | | | (147) convergent_lines(all_38_5, all_38_5) = 0 % 48.54/8.76 | | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_38_5, simplifying % 48.54/8.76 | | | | | | | | | | | | | | | | with (16), (147) gives: % 48.54/8.76 | | | | | | | | | | | | | | | | (148) $false % 48.54/8.76 | | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | | | CLOSE: (148) is inconsistent. % 48.54/8.76 | | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | | Case 2: % 48.54/8.76 | | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | | | (149) all_431_2 = 0 % 48.54/8.76 | | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | | | REDUCE: (125), (149) imply: % 48.54/8.76 | | | | | | | | | | | | | | | | (150) $false % 48.54/8.76 | | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | | | CLOSE: (150) is inconsistent. % 48.54/8.76 | | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | | End of split % 48.54/8.76 | | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | | End of split % 48.54/8.76 | | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | | End of split % 48.54/8.76 | | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | End of split % 48.54/8.76 | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | Case 2: % 48.54/8.76 | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | (151) ~ (all_431_3 = 0) & distinct_points(all_38_2, % 48.54/8.76 | | | | | | | | | | | | all_38_1) = all_431_3 % 48.54/8.76 | | | | | | | | | | | | % 48.54/8.76 | | | | | | | | | | | | ALPHA: (151) implies: % 49.04/8.76 | | | | | | | | | | | | (152) ~ (all_431_3 = 0) % 49.04/8.76 | | | | | | | | | | | | (153) distinct_points(all_38_2, all_38_1) = all_431_3 % 49.04/8.76 | | | | | | | | | | | | % 49.04/8.76 | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_431_3, all_38_1, % 49.04/8.76 | | | | | | | | | | | | all_38_2, simplifying with (102), (153) gives: % 49.04/8.76 | | | | | | | | | | | | (154) all_431_3 = 0 % 49.04/8.76 | | | | | | | | | | | | % 49.04/8.76 | | | | | | | | | | | | REDUCE: (152), (154) imply: % 49.04/8.76 | | | | | | | | | | | | (155) $false % 49.04/8.76 | | | | | | | | | | | | % 49.04/8.76 | | | | | | | | | | | | CLOSE: (155) is inconsistent. % 49.04/8.76 | | | | | | | | | | | | % 49.04/8.76 | | | | | | | | | | | End of split % 49.04/8.76 | | | | | | | | | | | % 49.04/8.76 | | | | | | | | | | End of split % 49.04/8.76 | | | | | | | | | | % 49.04/8.76 | | | | | | | | | End of split % 49.04/8.76 | | | | | | | | | % 49.04/8.76 | | | | | | | | End of split % 49.04/8.76 | | | | | | | | % 49.04/8.76 | | | | | | | Case 2: % 49.04/8.76 | | | | | | | | % 49.04/8.76 | | | | | | | | (156) all_53_0 = 0 % 49.04/8.76 | | | | | | | | % 49.04/8.76 | | | | | | | | REDUCE: (97), (156) imply: % 49.04/8.76 | | | | | | | | (157) $false % 49.04/8.76 | | | | | | | | % 49.04/8.76 | | | | | | | | CLOSE: (157) is inconsistent. % 49.04/8.76 | | | | | | | | % 49.04/8.76 | | | | | | | End of split % 49.04/8.76 | | | | | | | % 49.04/8.76 | | | | | | End of split % 49.04/8.76 | | | | | | % 49.04/8.76 | | | | | Case 2: % 49.04/8.76 | | | | | | % 49.04/8.76 | | | | | | (158) all_62_0 = 0 % 49.04/8.76 | | | | | | % 49.04/8.76 | | | | | | REDUCE: (95), (158) imply: % 49.04/8.76 | | | | | | (159) $false % 49.04/8.76 | | | | | | % 49.04/8.76 | | | | | | CLOSE: (159) is inconsistent. % 49.04/8.76 | | | | | | % 49.04/8.76 | | | | | End of split % 49.04/8.76 | | | | | % 49.04/8.76 | | | | Case 2: % 49.04/8.76 | | | | | % 49.04/8.76 | | | | | (160) ~ (all_67_1 = 0) & convergent_lines(all_38_5, all_38_3) = % 49.04/8.76 | | | | | all_67_1 % 49.04/8.76 | | | | | % 49.04/8.76 | | | | | ALPHA: (160) implies: % 49.04/8.76 | | | | | (161) ~ (all_67_1 = 0) % 49.04/8.76 | | | | | (162) convergent_lines(all_38_5, all_38_3) = all_67_1 % 49.04/8.76 | | | | | % 49.04/8.76 | | | | | GROUND_INST: instantiating (11) with 0, all_67_1, all_38_3, all_38_5, % 49.04/8.76 | | | | | simplifying with (20), (162) gives: % 49.04/8.76 | | | | | (163) all_67_1 = 0 % 49.04/8.76 | | | | | % 49.04/8.76 | | | | | REDUCE: (161), (163) imply: % 49.04/8.76 | | | | | (164) $false % 49.04/8.76 | | | | | % 49.04/8.76 | | | | | CLOSE: (164) is inconsistent. % 49.04/8.76 | | | | | % 49.04/8.76 | | | | End of split % 49.04/8.76 | | | | % 49.04/8.76 | | | Case 2: % 49.04/8.76 | | | | % 49.04/8.76 | | | | (165) ~ (all_53_1 = 0) & convergent_lines(all_38_5, all_38_4) = % 49.04/8.76 | | | | all_53_1 % 49.04/8.76 | | | | % 49.04/8.76 | | | | ALPHA: (165) implies: % 49.04/8.76 | | | | (166) ~ (all_53_1 = 0) % 49.04/8.76 | | | | (167) convergent_lines(all_38_5, all_38_4) = all_53_1 % 49.04/8.76 | | | | % 49.04/8.76 | | | | GROUND_INST: instantiating (11) with 0, all_53_1, all_38_4, all_38_5, % 49.04/8.76 | | | | simplifying with (19), (167) gives: % 49.04/8.76 | | | | (168) all_53_1 = 0 % 49.04/8.76 | | | | % 49.04/8.76 | | | | REDUCE: (166), (168) imply: % 49.04/8.76 | | | | (169) $false % 49.04/8.76 | | | | % 49.04/8.76 | | | | CLOSE: (169) is inconsistent. % 49.04/8.76 | | | | % 49.04/8.76 | | | End of split % 49.04/8.76 | | | % 49.04/8.76 | | Case 2: % 49.04/8.76 | | | % 49.04/8.76 | | | (170) ~ (all_68_1 = 0) & convergent_lines(all_38_5, all_38_4) = % 49.04/8.76 | | | all_68_1 % 49.04/8.76 | | | % 49.04/8.76 | | | ALPHA: (170) implies: % 49.04/8.76 | | | (171) ~ (all_68_1 = 0) % 49.04/8.76 | | | (172) convergent_lines(all_38_5, all_38_4) = all_68_1 % 49.04/8.76 | | | % 49.04/8.76 | | | GROUND_INST: instantiating (11) with 0, all_68_1, all_38_4, all_38_5, % 49.04/8.76 | | | simplifying with (19), (172) gives: % 49.04/8.76 | | | (173) all_68_1 = 0 % 49.04/8.76 | | | % 49.04/8.76 | | | REDUCE: (171), (173) imply: % 49.04/8.76 | | | (174) $false % 49.04/8.76 | | | % 49.04/8.76 | | | CLOSE: (174) is inconsistent. % 49.04/8.76 | | | % 49.04/8.76 | | End of split % 49.04/8.76 | | % 49.04/8.76 | Case 2: % 49.04/8.76 | | % 49.04/8.76 | | (175) ~ (all_66_1 = 0) & convergent_lines(all_38_5, all_38_3) = all_66_1 % 49.04/8.76 | | % 49.04/8.76 | | ALPHA: (175) implies: % 49.04/8.76 | | (176) ~ (all_66_1 = 0) % 49.04/8.76 | | (177) convergent_lines(all_38_5, all_38_3) = all_66_1 % 49.04/8.76 | | % 49.04/8.76 | | GROUND_INST: instantiating (11) with 0, all_66_1, all_38_3, all_38_5, % 49.04/8.76 | | simplifying with (20), (177) gives: % 49.04/8.76 | | (178) all_66_1 = 0 % 49.04/8.76 | | % 49.04/8.76 | | REDUCE: (176), (178) imply: % 49.04/8.76 | | (179) $false % 49.04/8.76 | | % 49.04/8.76 | | CLOSE: (179) is inconsistent. % 49.04/8.76 | | % 49.04/8.76 | End of split % 49.04/8.76 | % 49.04/8.76 End of proof % 49.04/8.77 % SZS output end Proof for theBenchmark % 49.04/8.77 % 49.04/8.77 8132ms %------------------------------------------------------------------------------