%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO205+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : 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 23:22:17 EDT 2023 % Result : Theorem 11.76s 2.35s % Output : Proof 20.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : GEO205+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.36 % Computer : n014.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Tue Aug 29 23:36:14 EDT 2023 % 0.14/0.36 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.28/1.06 Prover 4: Preprocessing ... % 2.28/1.06 Prover 1: Preprocessing ... % 2.71/1.10 Prover 0: Preprocessing ... % 2.71/1.10 Prover 3: Preprocessing ... % 2.71/1.11 Prover 6: Preprocessing ... % 2.71/1.11 Prover 5: Preprocessing ... % 2.71/1.11 Prover 2: Preprocessing ... % 4.25/1.35 Prover 2: Proving ... % 4.25/1.35 Prover 5: Proving ... % 4.75/1.37 Prover 6: Constructing countermodel ... % 4.75/1.38 Prover 1: Constructing countermodel ... % 4.75/1.40 Prover 3: Constructing countermodel ... % 5.43/1.50 Prover 1: gave up % 5.43/1.50 Prover 3: gave up % 5.43/1.50 Prover 6: gave up % 5.43/1.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.43/1.51 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.43/1.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.43/1.52 Prover 0: Proving ... % 5.43/1.54 Prover 4: Constructing countermodel ... % 5.43/1.56 Prover 8: Preprocessing ... % 5.43/1.57 Prover 9: Preprocessing ... % 5.43/1.57 Prover 7: Preprocessing ... % 5.43/1.62 Prover 7: Warning: ignoring some quantifiers % 6.39/1.64 Prover 7: Constructing countermodel ... % 6.39/1.66 Prover 8: Warning: ignoring some quantifiers % 6.39/1.67 Prover 8: Constructing countermodel ... % 7.04/1.70 Prover 7: gave up % 7.04/1.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.14/1.73 Prover 10: Preprocessing ... % 7.14/1.78 Prover 8: gave up % 7.14/1.79 Prover 10: Warning: ignoring some quantifiers % 7.14/1.79 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.14/1.80 Prover 10: Constructing countermodel ... % 7.85/1.83 Prover 11: Preprocessing ... % 7.85/1.83 Prover 9: Constructing countermodel ... % 7.85/1.87 Prover 10: gave up % 8.48/1.90 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 8.48/1.92 Prover 12: Preprocessing ... % 9.27/2.01 Prover 12: Proving ... % 9.39/2.04 Prover 11: Constructing countermodel ... % 11.76/2.35 Prover 0: proved (1707ms) % 11.76/2.35 % 11.76/2.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.76/2.35 % 11.76/2.35 Prover 5: stopped % 11.76/2.36 Prover 9: stopped % 11.76/2.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.76/2.37 Prover 2: stopped % 11.76/2.37 Prover 12: stopped % 11.76/2.37 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 11.76/2.37 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.76/2.38 Prover 13: Preprocessing ... % 11.76/2.39 Prover 16: Preprocessing ... % 11.76/2.40 Prover 19: Preprocessing ... % 11.76/2.41 Prover 13: Warning: ignoring some quantifiers % 11.76/2.41 Prover 13: Constructing countermodel ... % 12.42/2.43 Prover 16: Warning: ignoring some quantifiers % 12.42/2.43 Prover 16: Constructing countermodel ... % 12.42/2.47 Prover 19: Warning: ignoring some quantifiers % 12.42/2.47 Prover 13: gave up % 12.42/2.47 Prover 19: Constructing countermodel ... % 12.86/2.50 Prover 16: gave up % 12.86/2.50 Prover 19: gave up % 18.45/3.69 Prover 11: Found proof (size 187) % 18.45/3.69 Prover 11: proved (1899ms) % 18.45/3.71 Prover 4: stopped % 18.45/3.72 % 18.45/3.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.45/3.72 % 18.45/3.73 % SZS output start Proof for theBenchmark % 18.45/3.73 Assumptions after simplification: % 18.45/3.73 --------------------------------- % 18.45/3.73 % 18.45/3.73 (apart3) % 19.65/3.75 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 19.65/3.75 % 19.65/3.76 (ceq2) % 19.65/3.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 19.65/3.76 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 19.65/3.76 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 19.65/3.76 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 19.65/3.76 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 19.65/3.76 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 19.65/3.76 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.65/3.76 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 19.65/3.76 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 19.65/3.76 apart_point_and_line(v0, v2) = 0) % 19.65/3.76 % 19.65/3.76 (ceq3) % 19.65/3.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 19.65/3.77 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) % 19.65/3.77 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 19.65/3.77 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 19.65/3.77 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 19.65/3.77 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 19.65/3.77 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.65/3.77 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ % 19.65/3.77 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 19.65/3.77 convergent_lines(v0, v2) = 0) % 19.65/3.77 % 19.65/3.77 (ci1) % 19.92/3.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 19.92/3.77 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) & % 19.92/3.77 apart_point_and_line(v0, v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, % 19.92/3.77 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) % 19.92/3.77 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 19.92/3.77 line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 19.92/3.77 $i(v2))) % 19.92/3.77 % 19.92/3.77 (ci2) % 19.92/3.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 19.92/3.77 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) & % 19.92/3.77 apart_point_and_line(v1, v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, % 19.92/3.77 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) % 19.92/3.77 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 19.92/3.77 line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 19.92/3.77 $i(v2))) % 19.92/3.77 % 19.92/3.77 (ci3) % 19.92/3.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 19.92/3.78 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 19.92/3.78 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 19.92/3.78 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 19.92/3.78 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 19.92/3.78 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 19.92/3.78 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 19.92/3.78 % 19.92/3.78 (ci4) % 19.92/3.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 19.92/3.78 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 19.92/3.78 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 19.92/3.78 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 19.92/3.78 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 19.92/3.78 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 19.92/3.78 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 19.92/3.78 % 19.92/3.78 (con) % 19.92/3.79 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ? % 19.92/3.79 [v5: $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v3 = 0) & convergent_lines(v0, % 19.92/3.79 v1) = 0 & distinct_lines(v1, v2) = v3 & $i(v2) & $i(v1) & $i(v0) & ((v7 = % 19.92/3.79 0 & intersection_point(v0, v2) = v6 & intersection_point(v0, v1) = v5 & % 19.92/3.79 distinct_points(v5, v6) = 0 & $i(v6) & $i(v5)) | ( ~ (v4 = 0) & % 19.92/3.79 convergent_lines(v0, v2) = v4))) % 19.92/3.79 % 19.92/3.79 (cu1) % 19.92/3.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 19.92/3.80 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 19.92/3.81 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 19.92/3.81 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 19.92/3.81 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 19.92/3.81 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, % 19.92/3.81 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 19.92/3.81 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, % 19.92/3.81 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ % 19.92/3.81 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 19.92/3.81 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 19.92/3.81 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0, % 19.92/3.81 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 19.92/3.81 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 19.92/3.81 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 19.92/3.81 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 19.92/3.81 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 19.92/3.81 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 19.92/3.81 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 19.92/3.81 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 19.92/3.81 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 19.92/3.81 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 19.92/3.81 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 19.92/3.81 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 19.92/3.81 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 19.92/3.81 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 19.92/3.81 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 19.92/3.81 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 19.92/3.81 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 19.92/3.81 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~ % 19.92/3.81 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 19.92/3.81 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 19.92/3.81 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, % 19.92/3.81 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 19.92/3.81 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, % 19.92/3.81 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 19.92/3.81 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 19.92/3.81 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 19.92/3.81 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1, % 19.92/3.81 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i] % 19.92/3.81 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | % 19.92/3.81 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 19.92/3.81 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = % 19.92/3.81 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 19.92/3.81 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0, % 19.92/3.81 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 19.92/3.81 % 19.92/3.81 (function-axioms) % 20.16/3.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.16/3.81 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 20.16/3.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.16/3.82 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 20.16/3.82 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 20.16/3.82 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 20.16/3.82 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.16/3.82 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.16/3.82 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 20.16/3.82 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 20.16/3.82 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 20.16/3.82 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 20.16/3.82 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 20.16/3.82 (distinct_points(v3, v2) = v0)) % 20.16/3.82 % 20.16/3.82 Further assumptions not needed in the proof: % 20.16/3.82 -------------------------------------------- % 20.16/3.82 apart1, apart2, apart4, apart5, ax6, ceq1 % 20.16/3.82 % 20.16/3.82 Those formulas are unsatisfiable: % 20.16/3.82 --------------------------------- % 20.16/3.82 % 20.16/3.82 Begin of proof % 20.16/3.82 | % 20.16/3.82 | ALPHA: (ci1) implies: % 20.16/3.82 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 20.16/3.82 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 20.16/3.82 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 20.16/3.82 | $i(v2))) % 20.16/3.82 | % 20.16/3.82 | ALPHA: (ci2) implies: % 20.16/3.82 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 20.16/3.82 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 20.16/3.82 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 20.16/3.82 | $i(v2))) % 20.16/3.82 | % 20.16/3.82 | ALPHA: (ci3) implies: % 20.16/3.82 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 20.16/3.82 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 20.16/3.82 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 20.16/3.82 | & $i(v2))) % 20.16/3.83 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 20.16/3.83 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 20.16/3.83 | (( ~ (v4 = 0) & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 20.16/3.83 | convergent_lines(v0, v1) = v3))) % 20.16/3.83 | % 20.16/3.83 | ALPHA: (ci4) implies: % 20.16/3.83 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 20.16/3.83 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 20.16/3.83 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 20.16/3.83 | & $i(v2))) % 20.16/3.83 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 20.16/3.83 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 20.16/3.83 | (( ~ (v4 = 0) & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 20.16/3.83 | convergent_lines(v0, v1) = v3))) % 20.16/3.83 | % 20.16/3.83 | ALPHA: (cu1) implies: % 20.16/3.83 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 20.16/3.83 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) % 20.16/3.83 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, % 20.16/3.83 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 20.16/3.83 | [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 20.16/3.83 | apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 20.16/3.83 | apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & % 20.16/3.83 | distinct_lines(v2, v3) = v6))) % 20.16/3.83 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 20.16/3.83 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 20.16/3.83 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 20.16/3.83 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 20.16/3.83 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 20.16/3.83 | apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & % 20.16/3.83 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 20.16/3.83 | v1) = v6))) % 20.16/3.83 | % 20.16/3.83 | ALPHA: (ceq2) implies: % 20.16/3.83 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 20.16/3.83 | (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 20.16/3.83 | (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 20.16/3.83 | ? [v5: int] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) % 20.16/3.83 | % 20.16/3.83 | ALPHA: (ceq3) implies: % 20.16/3.83 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 20.16/3.83 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | % 20.16/3.83 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 20.16/3.83 | % 20.16/3.83 | ALPHA: (function-axioms) implies: % 20.16/3.84 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 20.16/3.84 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 20.16/3.84 | (distinct_points(v3, v2) = v0)) % 20.16/3.84 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 20.16/3.84 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 20.16/3.84 | (distinct_lines(v3, v2) = v0)) % 20.16/3.84 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 20.16/3.84 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 20.16/3.84 | (convergent_lines(v3, v2) = v0)) % 20.16/3.84 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 20.16/3.84 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 20.16/3.84 | (apart_point_and_line(v3, v2) = v0)) % 20.16/3.84 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.16/3.84 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 20.16/3.84 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.16/3.84 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 20.16/3.84 | v0)) % 20.16/3.84 | % 20.16/3.84 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 20.16/3.84 | all_17_3, all_17_4, all_17_5, all_17_6, all_17_7 gives: % 20.16/3.84 | (17) ~ (all_17_4 = 0) & convergent_lines(all_17_7, all_17_6) = 0 & % 20.16/3.84 | distinct_lines(all_17_6, all_17_5) = all_17_4 & $i(all_17_5) & % 20.16/3.84 | $i(all_17_6) & $i(all_17_7) & ((all_17_0 = 0 & % 20.16/3.84 | intersection_point(all_17_7, all_17_5) = all_17_1 & % 20.16/3.84 | intersection_point(all_17_7, all_17_6) = all_17_2 & % 20.16/3.84 | distinct_points(all_17_2, all_17_1) = 0 & $i(all_17_1) & % 20.16/3.84 | $i(all_17_2)) | ( ~ (all_17_3 = 0) & convergent_lines(all_17_7, % 20.16/3.84 | all_17_5) = all_17_3)) % 20.16/3.84 | % 20.16/3.84 | ALPHA: (17) implies: % 20.16/3.84 | (18) ~ (all_17_4 = 0) % 20.16/3.84 | (19) $i(all_17_7) % 20.16/3.84 | (20) $i(all_17_6) % 20.16/3.84 | (21) $i(all_17_5) % 20.16/3.84 | (22) distinct_lines(all_17_6, all_17_5) = all_17_4 % 20.16/3.84 | (23) convergent_lines(all_17_7, all_17_6) = 0 % 20.16/3.84 | (24) (all_17_0 = 0 & intersection_point(all_17_7, all_17_5) = all_17_1 & % 20.16/3.84 | intersection_point(all_17_7, all_17_6) = all_17_2 & % 20.16/3.84 | distinct_points(all_17_2, all_17_1) = 0 & $i(all_17_1) & % 20.16/3.84 | $i(all_17_2)) | ( ~ (all_17_3 = 0) & convergent_lines(all_17_7, % 20.16/3.84 | all_17_5) = all_17_3) % 20.16/3.84 | % 20.16/3.84 | GROUND_INST: instantiating (10) with all_17_7, all_17_6, all_17_5, all_17_4, % 20.16/3.84 | simplifying with (19), (20), (21), (22), (23) gives: % 20.16/3.84 | (25) all_17_4 = 0 | convergent_lines(all_17_7, all_17_5) = 0 % 20.16/3.84 | % 20.16/3.84 | GROUND_INST: instantiating (5) with all_17_7, all_17_6, simplifying with (19), % 20.31/3.84 | (20), (23) gives: % 20.31/3.84 | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 20.31/3.84 | intersection_point(all_17_7, all_17_6) = v0 & % 20.31/3.84 | apart_point_and_line(v0, all_17_6) = v1 & $i(v0)) % 20.31/3.84 | % 20.31/3.85 | GROUND_INST: instantiating (3) with all_17_7, all_17_6, simplifying with (19), % 20.31/3.85 | (20), (23) gives: % 20.31/3.85 | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 20.31/3.85 | intersection_point(all_17_7, all_17_6) = v0 & % 20.31/3.85 | apart_point_and_line(v0, all_17_7) = v1 & $i(v0)) % 20.31/3.85 | % 20.31/3.85 | DELTA: instantiating (27) with fresh symbols all_24_0, all_24_1 gives: % 20.31/3.85 | (28) ~ (all_24_0 = 0) & intersection_point(all_17_7, all_17_6) = all_24_1 % 20.31/3.85 | & apart_point_and_line(all_24_1, all_17_7) = all_24_0 & $i(all_24_1) % 20.31/3.85 | % 20.31/3.85 | ALPHA: (28) implies: % 20.31/3.85 | (29) ~ (all_24_0 = 0) % 20.31/3.85 | (30) $i(all_24_1) % 20.31/3.85 | (31) apart_point_and_line(all_24_1, all_17_7) = all_24_0 % 20.31/3.85 | (32) intersection_point(all_17_7, all_17_6) = all_24_1 % 20.31/3.85 | % 20.31/3.85 | DELTA: instantiating (26) with fresh symbols all_26_0, all_26_1 gives: % 20.31/3.85 | (33) ~ (all_26_0 = 0) & intersection_point(all_17_7, all_17_6) = all_26_1 % 20.31/3.85 | & apart_point_and_line(all_26_1, all_17_6) = all_26_0 & $i(all_26_1) % 20.31/3.85 | % 20.31/3.85 | ALPHA: (33) implies: % 20.31/3.85 | (34) ~ (all_26_0 = 0) % 20.31/3.85 | (35) apart_point_and_line(all_26_1, all_17_6) = all_26_0 % 20.31/3.85 | (36) intersection_point(all_17_7, all_17_6) = all_26_1 % 20.31/3.85 | % 20.31/3.85 | BETA: splitting (25) gives: % 20.31/3.85 | % 20.31/3.85 | Case 1: % 20.31/3.85 | | % 20.31/3.85 | | (37) convergent_lines(all_17_7, all_17_5) = 0 % 20.31/3.85 | | % 20.31/3.85 | | BETA: splitting (24) gives: % 20.31/3.85 | | % 20.31/3.85 | | Case 1: % 20.31/3.85 | | | % 20.31/3.85 | | | (38) all_17_0 = 0 & intersection_point(all_17_7, all_17_5) = all_17_1 & % 20.31/3.85 | | | intersection_point(all_17_7, all_17_6) = all_17_2 & % 20.31/3.85 | | | distinct_points(all_17_2, all_17_1) = 0 & $i(all_17_1) & % 20.31/3.85 | | | $i(all_17_2) % 20.31/3.85 | | | % 20.31/3.85 | | | ALPHA: (38) implies: % 20.31/3.85 | | | (39) $i(all_17_1) % 20.31/3.85 | | | (40) distinct_points(all_17_2, all_17_1) = 0 % 20.31/3.85 | | | (41) intersection_point(all_17_7, all_17_6) = all_17_2 % 20.31/3.85 | | | (42) intersection_point(all_17_7, all_17_5) = all_17_1 % 20.31/3.85 | | | % 20.31/3.85 | | | GROUND_INST: instantiating (16) with all_24_1, all_26_1, all_17_6, % 20.31/3.85 | | | all_17_7, simplifying with (32), (36) gives: % 20.31/3.85 | | | (43) all_26_1 = all_24_1 % 20.31/3.85 | | | % 20.31/3.85 | | | GROUND_INST: instantiating (16) with all_17_2, all_26_1, all_17_6, % 20.31/3.85 | | | all_17_7, simplifying with (36), (41) gives: % 20.31/3.85 | | | (44) all_26_1 = all_17_2 % 20.31/3.85 | | | % 20.31/3.85 | | | COMBINE_EQS: (43), (44) imply: % 20.31/3.85 | | | (45) all_24_1 = all_17_2 % 20.31/3.85 | | | % 20.31/3.85 | | | SIMP: (45) implies: % 20.31/3.85 | | | (46) all_24_1 = all_17_2 % 20.31/3.85 | | | % 20.31/3.85 | | | REDUCE: (35), (44) imply: % 20.31/3.85 | | | (47) apart_point_and_line(all_17_2, all_17_6) = all_26_0 % 20.31/3.85 | | | % 20.31/3.85 | | | REDUCE: (31), (46) imply: % 20.31/3.85 | | | (48) apart_point_and_line(all_17_2, all_17_7) = all_24_0 % 20.31/3.85 | | | % 20.31/3.85 | | | REDUCE: (30), (46) imply: % 20.31/3.85 | | | (49) $i(all_17_2) % 20.31/3.85 | | | % 20.31/3.85 | | | GROUND_INST: instantiating (2) with all_17_2, all_17_1, simplifying with % 20.31/3.85 | | | (39), (40), (49) gives: % 20.31/3.85 | | | (50) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 20.31/3.85 | | | line_connecting(all_17_2, all_17_1) = v0 & % 20.31/3.85 | | | apart_point_and_line(all_17_1, v0) = v1 & $i(v0)) % 20.31/3.85 | | | % 20.31/3.85 | | | GROUND_INST: instantiating (1) with all_17_2, all_17_1, simplifying with % 20.31/3.85 | | | (39), (40), (49) gives: % 20.31/3.85 | | | (51) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 20.31/3.85 | | | line_connecting(all_17_2, all_17_1) = v0 & % 20.31/3.85 | | | apart_point_and_line(all_17_2, v0) = v1 & $i(v0)) % 20.31/3.85 | | | % 20.31/3.85 | | | GROUND_INST: instantiating (5) with all_17_7, all_17_5, simplifying with % 20.31/3.85 | | | (19), (21), (37) gives: % 20.31/3.85 | | | (52) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 20.31/3.85 | | | intersection_point(all_17_7, all_17_5) = v0 & % 20.31/3.85 | | | apart_point_and_line(v0, all_17_5) = v1 & $i(v0)) % 20.31/3.85 | | | % 20.31/3.85 | | | GROUND_INST: instantiating (3) with all_17_7, all_17_5, simplifying with % 20.31/3.85 | | | (19), (21), (37) gives: % 20.31/3.86 | | | (53) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 20.31/3.86 | | | intersection_point(all_17_7, all_17_5) = v0 & % 20.31/3.86 | | | apart_point_and_line(v0, all_17_7) = v1 & $i(v0)) % 20.31/3.86 | | | % 20.31/3.86 | | | GROUND_INST: instantiating (7) with all_17_2, all_17_1, all_17_7, % 20.31/3.86 | | | all_17_6, all_24_0, all_26_0, simplifying with (19), (20), % 20.31/3.86 | | | (39), (40), (47), (48), (49) gives: % 20.31/3.86 | | | (54) all_26_0 = 0 | all_24_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 20.31/3.86 | | | [v2: int] : ((v2 = 0 & apart_point_and_line(all_17_1, all_17_6) = % 20.31/3.86 | | | 0) | (v1 = 0 & apart_point_and_line(all_17_1, all_17_7) = 0) | % 20.31/3.86 | | | ( ~ (v0 = 0) & distinct_lines(all_17_7, all_17_6) = v0)) % 20.31/3.86 | | | % 20.31/3.86 | | | GROUND_INST: instantiating (7) with all_17_2, all_17_1, all_17_6, % 20.31/3.86 | | | all_17_7, all_26_0, all_24_0, simplifying with (19), (20), % 20.31/3.86 | | | (39), (40), (47), (48), (49) gives: % 20.31/3.86 | | | (55) all_26_0 = 0 | all_24_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 20.31/3.86 | | | [v2: int] : ((v2 = 0 & apart_point_and_line(all_17_1, all_17_7) = % 20.31/3.86 | | | 0) | (v1 = 0 & apart_point_and_line(all_17_1, all_17_6) = 0) | % 20.31/3.86 | | | ( ~ (v0 = 0) & distinct_lines(all_17_6, all_17_7) = v0)) % 20.31/3.86 | | | % 20.31/3.86 | | | GROUND_INST: instantiating (6) with all_17_7, all_17_5, all_17_1, % 20.31/3.86 | | | simplifying with (19), (21), (42) gives: % 20.31/3.86 | | | (56) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 20.31/3.86 | | | apart_point_and_line(all_17_1, all_17_5) = v1) | ( ~ (v0 = 0) % 20.31/3.86 | | | & convergent_lines(all_17_7, all_17_5) = v0)) % 20.31/3.86 | | | % 20.31/3.86 | | | GROUND_INST: instantiating (4) with all_17_7, all_17_5, all_17_1, % 20.31/3.86 | | | simplifying with (19), (21), (42) gives: % 20.31/3.86 | | | (57) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 20.31/3.86 | | | apart_point_and_line(all_17_1, all_17_7) = v1) | ( ~ (v0 = 0) % 20.31/3.86 | | | & convergent_lines(all_17_7, all_17_5) = v0)) % 20.31/3.86 | | | % 20.31/3.86 | | | DELTA: instantiating (57) with fresh symbols all_50_0, all_50_1 gives: % 20.31/3.86 | | | (58) ( ~ (all_50_0 = 0) & apart_point_and_line(all_17_1, all_17_7) = % 20.31/3.86 | | | all_50_0) | ( ~ (all_50_1 = 0) & convergent_lines(all_17_7, % 20.31/3.86 | | | all_17_5) = all_50_1) % 20.31/3.86 | | | % 20.31/3.86 | | | DELTA: instantiating (53) with fresh symbols all_51_0, all_51_1 gives: % 20.31/3.86 | | | (59) ~ (all_51_0 = 0) & intersection_point(all_17_7, all_17_5) = % 20.31/3.86 | | | all_51_1 & apart_point_and_line(all_51_1, all_17_7) = all_51_0 & % 20.31/3.86 | | | $i(all_51_1) % 20.31/3.86 | | | % 20.31/3.86 | | | ALPHA: (59) implies: % 20.31/3.86 | | | (60) ~ (all_51_0 = 0) % 20.31/3.86 | | | (61) $i(all_51_1) % 20.31/3.86 | | | (62) apart_point_and_line(all_51_1, all_17_7) = all_51_0 % 20.31/3.86 | | | (63) intersection_point(all_17_7, all_17_5) = all_51_1 % 20.31/3.86 | | | % 20.31/3.86 | | | DELTA: instantiating (51) with fresh symbols all_53_0, all_53_1 gives: % 20.31/3.86 | | | (64) ~ (all_53_0 = 0) & line_connecting(all_17_2, all_17_1) = all_53_1 % 20.31/3.86 | | | & apart_point_and_line(all_17_2, all_53_1) = all_53_0 & % 20.31/3.86 | | | $i(all_53_1) % 20.31/3.86 | | | % 20.31/3.86 | | | ALPHA: (64) implies: % 20.31/3.86 | | | (65) ~ (all_53_0 = 0) % 20.31/3.86 | | | (66) apart_point_and_line(all_17_2, all_53_1) = all_53_0 % 20.31/3.86 | | | (67) line_connecting(all_17_2, all_17_1) = all_53_1 % 20.31/3.86 | | | % 20.31/3.86 | | | DELTA: instantiating (52) with fresh symbols all_55_0, all_55_1 gives: % 20.31/3.86 | | | (68) ~ (all_55_0 = 0) & intersection_point(all_17_7, all_17_5) = % 20.31/3.86 | | | all_55_1 & apart_point_and_line(all_55_1, all_17_5) = all_55_0 & % 20.31/3.86 | | | $i(all_55_1) % 20.31/3.86 | | | % 20.31/3.86 | | | ALPHA: (68) implies: % 20.31/3.86 | | | (69) apart_point_and_line(all_55_1, all_17_5) = all_55_0 % 20.31/3.86 | | | (70) intersection_point(all_17_7, all_17_5) = all_55_1 % 20.31/3.86 | | | % 20.31/3.86 | | | DELTA: instantiating (50) with fresh symbols all_57_0, all_57_1 gives: % 20.31/3.86 | | | (71) ~ (all_57_0 = 0) & line_connecting(all_17_2, all_17_1) = all_57_1 % 20.31/3.86 | | | & apart_point_and_line(all_17_1, all_57_1) = all_57_0 & % 20.31/3.86 | | | $i(all_57_1) % 20.31/3.86 | | | % 20.31/3.86 | | | ALPHA: (71) implies: % 20.31/3.86 | | | (72) ~ (all_57_0 = 0) % 20.31/3.86 | | | (73) $i(all_57_1) % 20.31/3.86 | | | (74) apart_point_and_line(all_17_1, all_57_1) = all_57_0 % 20.31/3.86 | | | (75) line_connecting(all_17_2, all_17_1) = all_57_1 % 20.31/3.86 | | | % 20.31/3.86 | | | DELTA: instantiating (56) with fresh symbols all_59_0, all_59_1 gives: % 20.31/3.87 | | | (76) ( ~ (all_59_0 = 0) & apart_point_and_line(all_17_1, all_17_5) = % 20.31/3.87 | | | all_59_0) | ( ~ (all_59_1 = 0) & convergent_lines(all_17_7, % 20.31/3.87 | | | all_17_5) = all_59_1) % 20.31/3.87 | | | % 20.31/3.87 | | | BETA: splitting (76) gives: % 20.31/3.87 | | | % 20.31/3.87 | | | Case 1: % 20.31/3.87 | | | | % 20.31/3.87 | | | | (77) ~ (all_59_0 = 0) & apart_point_and_line(all_17_1, all_17_5) = % 20.31/3.87 | | | | all_59_0 % 20.31/3.87 | | | | % 20.31/3.87 | | | | ALPHA: (77) implies: % 20.31/3.87 | | | | (78) ~ (all_59_0 = 0) % 20.31/3.87 | | | | (79) apart_point_and_line(all_17_1, all_17_5) = all_59_0 % 20.31/3.87 | | | | % 20.31/3.87 | | | | BETA: splitting (58) gives: % 20.31/3.87 | | | | % 20.31/3.87 | | | | Case 1: % 20.31/3.87 | | | | | % 20.31/3.87 | | | | | (80) ~ (all_50_0 = 0) & apart_point_and_line(all_17_1, all_17_7) = % 20.31/3.87 | | | | | all_50_0 % 20.31/3.87 | | | | | % 20.31/3.87 | | | | | ALPHA: (80) implies: % 20.31/3.87 | | | | | (81) apart_point_and_line(all_17_1, all_17_7) = all_50_0 % 20.31/3.87 | | | | | % 20.31/3.87 | | | | | BETA: splitting (55) gives: % 20.31/3.87 | | | | | % 20.31/3.87 | | | | | Case 1: % 20.31/3.87 | | | | | | % 20.31/3.87 | | | | | | (82) all_26_0 = 0 % 20.31/3.87 | | | | | | % 20.31/3.87 | | | | | | REDUCE: (34), (82) imply: % 20.31/3.87 | | | | | | (83) $false % 20.31/3.87 | | | | | | % 20.31/3.87 | | | | | | CLOSE: (83) is inconsistent. % 20.31/3.87 | | | | | | % 20.31/3.87 | | | | | Case 2: % 20.31/3.87 | | | | | | % 20.31/3.87 | | | | | | (84) all_24_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : % 20.31/3.87 | | | | | | ((v2 = 0 & apart_point_and_line(all_17_1, all_17_7) = 0) | % 20.31/3.87 | | | | | | (v1 = 0 & apart_point_and_line(all_17_1, all_17_6) = 0) | % 20.31/3.87 | | | | | | ( ~ (v0 = 0) & distinct_lines(all_17_6, all_17_7) = v0)) % 20.31/3.87 | | | | | | % 20.31/3.87 | | | | | | BETA: splitting (54) gives: % 20.31/3.87 | | | | | | % 20.31/3.87 | | | | | | Case 1: % 20.31/3.87 | | | | | | | % 20.31/3.87 | | | | | | | (85) all_26_0 = 0 % 20.31/3.87 | | | | | | | % 20.31/3.87 | | | | | | | REDUCE: (34), (85) imply: % 20.31/3.87 | | | | | | | (86) $false % 20.31/3.87 | | | | | | | % 20.31/3.87 | | | | | | | CLOSE: (86) is inconsistent. % 20.31/3.87 | | | | | | | % 20.31/3.87 | | | | | | Case 2: % 20.31/3.87 | | | | | | | % 20.31/3.87 | | | | | | | (87) all_24_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] % 20.31/3.87 | | | | | | | : ((v2 = 0 & apart_point_and_line(all_17_1, all_17_6) = 0) % 20.31/3.87 | | | | | | | | (v1 = 0 & apart_point_and_line(all_17_1, all_17_7) = % 20.31/3.87 | | | | | | | 0) | ( ~ (v0 = 0) & distinct_lines(all_17_7, all_17_6) % 20.31/3.87 | | | | | | | = v0)) % 20.31/3.87 | | | | | | | % 20.31/3.87 | | | | | | | BETA: splitting (84) gives: % 20.31/3.87 | | | | | | | % 20.31/3.87 | | | | | | | Case 1: % 20.31/3.87 | | | | | | | | % 20.31/3.87 | | | | | | | | (88) all_24_0 = 0 % 20.31/3.87 | | | | | | | | % 20.31/3.87 | | | | | | | | REDUCE: (29), (88) imply: % 20.31/3.87 | | | | | | | | (89) $false % 20.31/3.87 | | | | | | | | % 20.31/3.87 | | | | | | | | CLOSE: (89) is inconsistent. % 20.31/3.87 | | | | | | | | % 20.31/3.87 | | | | | | | Case 2: % 20.31/3.87 | | | | | | | | % 20.31/3.87 | | | | | | | | (90) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & % 20.31/3.87 | | | | | | | | apart_point_and_line(all_17_1, all_17_7) = 0) | (v1 % 20.31/3.87 | | | | | | | | = 0 & apart_point_and_line(all_17_1, all_17_6) = 0) % 20.31/3.87 | | | | | | | | | ( ~ (v0 = 0) & distinct_lines(all_17_6, all_17_7) = % 20.31/3.87 | | | | | | | | v0)) % 20.31/3.87 | | | | | | | | % 20.31/3.87 | | | | | | | | DELTA: instantiating (90) with fresh symbols all_126_0, % 20.31/3.87 | | | | | | | | all_126_1, all_126_2 gives: % 20.31/3.87 | | | | | | | | (91) (all_126_0 = 0 & apart_point_and_line(all_17_1, % 20.31/3.87 | | | | | | | | all_17_7) = 0) | (all_126_1 = 0 & % 20.31/3.87 | | | | | | | | apart_point_and_line(all_17_1, all_17_6) = 0) | ( ~ % 20.31/3.87 | | | | | | | | (all_126_2 = 0) & distinct_lines(all_17_6, all_17_7) = % 20.31/3.87 | | | | | | | | all_126_2) % 20.31/3.87 | | | | | | | | % 20.31/3.87 | | | | | | | | BETA: splitting (87) gives: % 20.31/3.87 | | | | | | | | % 20.31/3.87 | | | | | | | | Case 1: % 20.31/3.87 | | | | | | | | | % 20.31/3.87 | | | | | | | | | (92) all_24_0 = 0 % 20.31/3.87 | | | | | | | | | % 20.31/3.87 | | | | | | | | | REDUCE: (29), (92) imply: % 20.31/3.87 | | | | | | | | | (93) $false % 20.31/3.87 | | | | | | | | | % 20.31/3.87 | | | | | | | | | CLOSE: (93) is inconsistent. % 20.31/3.87 | | | | | | | | | % 20.31/3.87 | | | | | | | | Case 2: % 20.31/3.87 | | | | | | | | | % 20.31/3.87 | | | | | | | | | % 20.31/3.87 | | | | | | | | | GROUND_INST: instantiating (15) with all_53_1, all_57_1, % 20.31/3.87 | | | | | | | | | all_17_1, all_17_2, simplifying with (67), (75) % 20.31/3.87 | | | | | | | | | gives: % 20.31/3.87 | | | | | | | | | (94) all_57_1 = all_53_1 % 20.31/3.87 | | | | | | | | | % 20.31/3.87 | | | | | | | | | GROUND_INST: instantiating (16) with all_17_1, all_55_1, % 20.31/3.87 | | | | | | | | | all_17_5, all_17_7, simplifying with (42), (70) % 20.31/3.87 | | | | | | | | | gives: % 20.31/3.87 | | | | | | | | | (95) all_55_1 = all_17_1 % 20.31/3.87 | | | | | | | | | % 20.31/3.87 | | | | | | | | | GROUND_INST: instantiating (16) with all_51_1, all_55_1, % 20.31/3.87 | | | | | | | | | all_17_5, all_17_7, simplifying with (63), (70) % 20.31/3.87 | | | | | | | | | gives: % 20.31/3.88 | | | | | | | | | (96) all_55_1 = all_51_1 % 20.31/3.88 | | | | | | | | | % 20.31/3.88 | | | | | | | | | COMBINE_EQS: (95), (96) imply: % 20.31/3.88 | | | | | | | | | (97) all_51_1 = all_17_1 % 20.31/3.88 | | | | | | | | | % 20.31/3.88 | | | | | | | | | SIMP: (97) implies: % 20.31/3.88 | | | | | | | | | (98) all_51_1 = all_17_1 % 20.31/3.88 | | | | | | | | | % 20.31/3.88 | | | | | | | | | REDUCE: (69), (95) imply: % 20.31/3.88 | | | | | | | | | (99) apart_point_and_line(all_17_1, all_17_5) = all_55_0 % 20.31/3.88 | | | | | | | | | % 20.31/3.88 | | | | | | | | | REDUCE: (62), (98) imply: % 20.31/3.88 | | | | | | | | | (100) apart_point_and_line(all_17_1, all_17_7) = all_51_0 % 20.31/3.88 | | | | | | | | | % 20.31/3.88 | | | | | | | | | REDUCE: (74), (94) imply: % 20.31/3.88 | | | | | | | | | (101) apart_point_and_line(all_17_1, all_53_1) = all_57_0 % 20.31/3.88 | | | | | | | | | % 20.31/3.88 | | | | | | | | | REDUCE: (73), (94) imply: % 20.31/3.88 | | | | | | | | | (102) $i(all_53_1) % 20.31/3.88 | | | | | | | | | % 20.31/3.88 | | | | | | | | | GROUND_INST: instantiating (14) with all_50_0, all_51_0, % 20.31/3.88 | | | | | | | | | all_17_7, all_17_1, simplifying with (81), (100) % 20.31/3.88 | | | | | | | | | gives: % 20.31/3.88 | | | | | | | | | (103) all_51_0 = all_50_0 % 20.31/3.88 | | | | | | | | | % 20.31/3.88 | | | | | | | | | GROUND_INST: instantiating (14) with all_59_0, all_55_0, % 20.31/3.88 | | | | | | | | | all_17_5, all_17_1, simplifying with (79), (99) % 20.31/3.88 | | | | | | | | | gives: % 20.31/3.88 | | | | | | | | | (104) all_59_0 = all_55_0 % 20.31/3.88 | | | | | | | | | % 20.31/3.88 | | | | | | | | | REDUCE: (78), (104) imply: % 20.31/3.88 | | | | | | | | | (105) ~ (all_55_0 = 0) % 20.31/3.88 | | | | | | | | | % 20.31/3.88 | | | | | | | | | REDUCE: (60), (103) imply: % 20.31/3.88 | | | | | | | | | (106) ~ (all_50_0 = 0) % 20.31/3.88 | | | | | | | | | % 20.31/3.88 | | | | | | | | | GROUND_INST: instantiating (7) with all_17_2, all_17_1, % 20.31/3.88 | | | | | | | | | all_53_1, all_17_6, all_53_0, all_26_0, % 20.31/3.88 | | | | | | | | | simplifying with (20), (39), (40), (47), (49), % 20.31/3.88 | | | | | | | | | (66), (102) gives: % 20.31/3.88 | | | | | | | | | (107) all_53_0 = 0 | all_26_0 = 0 | ? [v0: int] : ? [v1: % 20.31/3.88 | | | | | | | | | int] : ? [v2: int] : ((v2 = 0 & % 20.31/3.88 | | | | | | | | | apart_point_and_line(all_17_1, all_17_6) = 0) | % 20.31/3.88 | | | | | | | | | (v1 = 0 & apart_point_and_line(all_17_1, all_53_1) % 20.31/3.88 | | | | | | | | | = 0) | ( ~ (v0 = 0) & distinct_lines(all_53_1, % 20.31/3.88 | | | | | | | | | all_17_6) = v0)) % 20.31/3.88 | | | | | | | | | % 20.31/3.88 | | | | | | | | | GROUND_INST: instantiating (8) with all_17_2, all_17_1, % 20.31/3.88 | | | | | | | | | all_17_6, all_17_7, all_26_0, all_50_0, % 20.31/3.88 | | | | | | | | | simplifying with (19), (20), (39), (47), (49), % 20.31/3.88 | | | | | | | | | (81) gives: % 20.31/3.88 | | | | | | | | | (108) all_50_0 = 0 | all_26_0 = 0 | ? [v0: int] : ? [v1: % 20.31/3.88 | | | | | | | | | int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 20.31/3.88 | | | | | | | | | apart_point_and_line(all_17_1, all_17_6) = 0) | % 20.31/3.88 | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_2, all_17_7) % 20.31/3.88 | | | | | | | | | = 0) | ( ~ (v1 = 0) & distinct_lines(all_17_6, % 20.31/3.88 | | | | | | | | | all_17_7) = v1) | ( ~ (v0 = 0) & % 20.31/3.88 | | | | | | | | | distinct_points(all_17_2, all_17_1) = v0)) % 20.31/3.88 | | | | | | | | | % 20.31/3.88 | | | | | | | | | GROUND_INST: instantiating (9) with all_17_1, all_17_6, % 20.31/3.88 | | | | | | | | | all_17_5, all_17_4, all_55_0, simplifying with % 20.31/3.88 | | | | | | | | | (20), (21), (22), (39), (99) gives: % 20.31/3.88 | | | | | | | | | (109) all_55_0 = 0 | all_17_4 = 0 | ? [v0: int] : ( ~ (v0 % 20.31/3.88 | | | | | | | | | = 0) & apart_point_and_line(all_17_1, all_17_6) = % 20.31/3.88 | | | | | | | | | v0) % 20.31/3.88 | | | | | | | | | % 20.31/3.88 | | | | | | | | | BETA: splitting (109) gives: % 20.31/3.88 | | | | | | | | | % 20.31/3.88 | | | | | | | | | Case 1: % 20.31/3.88 | | | | | | | | | | % 20.31/3.88 | | | | | | | | | | (110) all_55_0 = 0 % 20.31/3.88 | | | | | | | | | | % 20.31/3.88 | | | | | | | | | | REDUCE: (105), (110) imply: % 20.31/3.88 | | | | | | | | | | (111) $false % 20.31/3.88 | | | | | | | | | | % 20.31/3.88 | | | | | | | | | | CLOSE: (111) is inconsistent. % 20.31/3.88 | | | | | | | | | | % 20.31/3.88 | | | | | | | | | Case 2: % 20.31/3.88 | | | | | | | | | | % 20.31/3.88 | | | | | | | | | | (112) all_17_4 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 20.31/3.89 | | | | | | | | | | apart_point_and_line(all_17_1, all_17_6) = v0) % 20.31/3.89 | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | BETA: splitting (107) gives: % 20.31/3.89 | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | Case 1: % 20.31/3.89 | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | (113) all_53_0 = 0 % 20.31/3.89 | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | REDUCE: (65), (113) imply: % 20.31/3.89 | | | | | | | | | | | (114) $false % 20.31/3.89 | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | CLOSE: (114) is inconsistent. % 20.31/3.89 | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | Case 2: % 20.31/3.89 | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | (115) all_26_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 20.31/3.89 | | | | | | | | | | | [v2: int] : ((v2 = 0 & % 20.31/3.89 | | | | | | | | | | | apart_point_and_line(all_17_1, all_17_6) = 0) % 20.31/3.89 | | | | | | | | | | | | (v1 = 0 & apart_point_and_line(all_17_1, % 20.31/3.89 | | | | | | | | | | | all_53_1) = 0) | ( ~ (v0 = 0) & % 20.31/3.89 | | | | | | | | | | | distinct_lines(all_53_1, all_17_6) = v0)) % 20.31/3.89 | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | BETA: splitting (108) gives: % 20.31/3.89 | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | Case 1: % 20.31/3.89 | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | (116) all_50_0 = 0 % 20.31/3.89 | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | REDUCE: (106), (116) imply: % 20.31/3.89 | | | | | | | | | | | | (117) $false % 20.31/3.89 | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | CLOSE: (117) is inconsistent. % 20.31/3.89 | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | Case 2: % 20.31/3.89 | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | (118) all_26_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 20.31/3.89 | | | | | | | | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 20.31/3.89 | | | | | | | | | | | | apart_point_and_line(all_17_1, all_17_6) = 0) % 20.31/3.89 | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_2, % 20.31/3.89 | | | | | | | | | | | | all_17_7) = 0) | ( ~ (v1 = 0) & % 20.31/3.89 | | | | | | | | | | | | distinct_lines(all_17_6, all_17_7) = v1) | ( ~ % 20.31/3.89 | | | | | | | | | | | | (v0 = 0) & distinct_points(all_17_2, all_17_1) % 20.31/3.89 | | | | | | | | | | | | = v0)) % 20.31/3.89 | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | BETA: splitting (112) gives: % 20.31/3.89 | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | Case 1: % 20.31/3.89 | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | (119) all_17_4 = 0 % 20.31/3.89 | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | REDUCE: (18), (119) imply: % 20.31/3.89 | | | | | | | | | | | | | (120) $false % 20.31/3.89 | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | CLOSE: (120) is inconsistent. % 20.31/3.89 | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | Case 2: % 20.31/3.89 | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | (121) ? [v0: int] : ( ~ (v0 = 0) & % 20.31/3.89 | | | | | | | | | | | | | apart_point_and_line(all_17_1, all_17_6) = v0) % 20.31/3.89 | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | DELTA: instantiating (121) with fresh symbol all_372_0 % 20.31/3.89 | | | | | | | | | | | | | gives: % 20.31/3.89 | | | | | | | | | | | | | (122) ~ (all_372_0 = 0) & % 20.31/3.89 | | | | | | | | | | | | | apart_point_and_line(all_17_1, all_17_6) = % 20.31/3.89 | | | | | | | | | | | | | all_372_0 % 20.31/3.89 | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | ALPHA: (122) implies: % 20.31/3.89 | | | | | | | | | | | | | (123) ~ (all_372_0 = 0) % 20.31/3.89 | | | | | | | | | | | | | (124) apart_point_and_line(all_17_1, all_17_6) = % 20.31/3.89 | | | | | | | | | | | | | all_372_0 % 20.31/3.89 | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | BETA: splitting (115) gives: % 20.31/3.89 | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | Case 1: % 20.31/3.89 | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | (125) all_26_0 = 0 % 20.31/3.89 | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | REDUCE: (34), (125) imply: % 20.31/3.89 | | | | | | | | | | | | | | (126) $false % 20.31/3.89 | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | CLOSE: (126) is inconsistent. % 20.31/3.89 | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | Case 2: % 20.31/3.89 | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | (127) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 20.31/3.89 | | | | | | | | | | | | | | = 0 & apart_point_and_line(all_17_1, all_17_6) % 20.31/3.89 | | | | | | | | | | | | | | = 0) | (v1 = 0 & % 20.31/3.89 | | | | | | | | | | | | | | apart_point_and_line(all_17_1, all_53_1) = 0) % 20.31/3.89 | | | | | | | | | | | | | | | ( ~ (v0 = 0) & distinct_lines(all_53_1, % 20.31/3.89 | | | | | | | | | | | | | | all_17_6) = v0)) % 20.31/3.89 | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | DELTA: instantiating (127) with fresh symbols all_425_0, % 20.31/3.89 | | | | | | | | | | | | | | all_425_1, all_425_2 gives: % 20.31/3.89 | | | | | | | | | | | | | | (128) (all_425_0 = 0 & apart_point_and_line(all_17_1, % 20.31/3.89 | | | | | | | | | | | | | | all_17_6) = 0) | (all_425_1 = 0 & % 20.31/3.89 | | | | | | | | | | | | | | apart_point_and_line(all_17_1, all_53_1) = 0) | % 20.31/3.89 | | | | | | | | | | | | | | ( ~ (all_425_2 = 0) & distinct_lines(all_53_1, % 20.31/3.89 | | | | | | | | | | | | | | all_17_6) = all_425_2) % 20.31/3.89 | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | BETA: splitting (118) gives: % 20.31/3.89 | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | Case 1: % 20.31/3.89 | | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | | (129) all_26_0 = 0 % 20.31/3.89 | | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | | REDUCE: (34), (129) imply: % 20.31/3.89 | | | | | | | | | | | | | | | (130) $false % 20.31/3.89 | | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | | CLOSE: (130) is inconsistent. % 20.31/3.89 | | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | Case 2: % 20.31/3.89 | | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | | (131) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 20.31/3.89 | | | | | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 20.31/3.89 | | | | | | | | | | | | | | | apart_point_and_line(all_17_1, all_17_6) = 0) % 20.31/3.89 | | | | | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_17_2, % 20.31/3.89 | | | | | | | | | | | | | | | all_17_7) = 0) | ( ~ (v1 = 0) & % 20.31/3.89 | | | | | | | | | | | | | | | distinct_lines(all_17_6, all_17_7) = v1) | ( ~ % 20.31/3.89 | | | | | | | | | | | | | | | (v0 = 0) & distinct_points(all_17_2, all_17_1) % 20.31/3.89 | | | | | | | | | | | | | | | = v0)) % 20.31/3.89 | | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | | DELTA: instantiating (131) with fresh symbols all_461_0, % 20.31/3.89 | | | | | | | | | | | | | | | all_461_1, all_461_2, all_461_3 gives: % 20.31/3.89 | | | | | | | | | | | | | | | (132) (all_461_0 = 0 & apart_point_and_line(all_17_1, % 20.31/3.89 | | | | | | | | | | | | | | | all_17_6) = 0) | (all_461_1 = 0 & % 20.31/3.89 | | | | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_7) = 0) | % 20.31/3.89 | | | | | | | | | | | | | | | ( ~ (all_461_2 = 0) & distinct_lines(all_17_6, % 20.31/3.89 | | | | | | | | | | | | | | | all_17_7) = all_461_2) | ( ~ (all_461_3 = 0) & % 20.31/3.89 | | | | | | | | | | | | | | | distinct_points(all_17_2, all_17_1) = all_461_3) % 20.31/3.89 | | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | | BETA: splitting (91) gives: % 20.31/3.89 | | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | | Case 1: % 20.31/3.89 | | | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | | | (133) all_126_0 = 0 & apart_point_and_line(all_17_1, % 20.31/3.89 | | | | | | | | | | | | | | | | all_17_7) = 0 % 20.31/3.89 | | | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | | | ALPHA: (133) implies: % 20.31/3.89 | | | | | | | | | | | | | | | | (134) apart_point_and_line(all_17_1, all_17_7) = 0 % 20.31/3.89 | | | | | | | | | | | | | | | | % 20.31/3.89 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_50_0, all_17_7, % 20.31/3.89 | | | | | | | | | | | | | | | | all_17_1, simplifying with (81), (134) gives: % 20.31/3.90 | | | | | | | | | | | | | | | | (135) all_50_0 = 0 % 20.31/3.90 | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | REDUCE: (106), (135) imply: % 20.31/3.90 | | | | | | | | | | | | | | | | (136) $false % 20.31/3.90 | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | CLOSE: (136) is inconsistent. % 20.31/3.90 | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | Case 2: % 20.31/3.90 | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | (137) (all_126_1 = 0 & apart_point_and_line(all_17_1, % 20.31/3.90 | | | | | | | | | | | | | | | | all_17_6) = 0) | ( ~ (all_126_2 = 0) & % 20.31/3.90 | | | | | | | | | | | | | | | | distinct_lines(all_17_6, all_17_7) = all_126_2) % 20.31/3.90 | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | BETA: splitting (137) gives: % 20.31/3.90 | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | Case 1: % 20.31/3.90 | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | (138) all_126_1 = 0 & apart_point_and_line(all_17_1, % 20.31/3.90 | | | | | | | | | | | | | | | | | all_17_6) = 0 % 20.31/3.90 | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | ALPHA: (138) implies: % 20.31/3.90 | | | | | | | | | | | | | | | | | (139) apart_point_and_line(all_17_1, all_17_6) = 0 % 20.31/3.90 | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (123), (124), (139) are inconsistent by % 20.31/3.90 | | | | | | | | | | | | | | | | | sub-proof #1. % 20.31/3.90 | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | Case 2: % 20.31/3.90 | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | (140) ~ (all_126_2 = 0) & distinct_lines(all_17_6, % 20.31/3.90 | | | | | | | | | | | | | | | | | all_17_7) = all_126_2 % 20.31/3.90 | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | ALPHA: (140) implies: % 20.31/3.90 | | | | | | | | | | | | | | | | | (141) distinct_lines(all_17_6, all_17_7) = all_126_2 % 20.31/3.90 | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | BETA: splitting (132) gives: % 20.31/3.90 | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | Case 1: % 20.31/3.90 | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | (142) (all_461_0 = 0 & apart_point_and_line(all_17_1, % 20.31/3.90 | | | | | | | | | | | | | | | | | | all_17_6) = 0) | (all_461_1 = 0 & % 20.31/3.90 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_17_2, all_17_7) = 0) % 20.31/3.90 | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives: % 20.31/3.90 | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | Case 1: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | (143) all_461_0 = 0 & apart_point_and_line(all_17_1, % 20.31/3.90 | | | | | | | | | | | | | | | | | | | all_17_6) = 0 % 20.31/3.90 | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | (144) apart_point_and_line(all_17_1, all_17_6) = 0 % 20.31/3.90 | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (123), (124), (144) are inconsistent by % 20.31/3.90 | | | | | | | | | | | | | | | | | | | sub-proof #1. % 20.31/3.90 | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | Case 2: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | (145) all_461_1 = 0 & apart_point_and_line(all_17_2, % 20.31/3.90 | | | | | | | | | | | | | | | | | | | all_17_7) = 0 % 20.31/3.90 | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | ALPHA: (145) implies: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | (146) apart_point_and_line(all_17_2, all_17_7) = 0 % 20.31/3.90 | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_24_0, 0, all_17_7, % 20.31/3.90 | | | | | | | | | | | | | | | | | | | all_17_2, simplifying with (48), (146) gives: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | (147) all_24_0 = 0 % 20.31/3.90 | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | REDUCE: (29), (147) imply: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | (148) $false % 20.31/3.90 | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | CLOSE: (148) is inconsistent. % 20.31/3.90 | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | End of split % 20.31/3.90 | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | Case 2: % 20.31/3.90 | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | (149) ( ~ (all_461_2 = 0) & distinct_lines(all_17_6, % 20.31/3.90 | | | | | | | | | | | | | | | | | | all_17_7) = all_461_2) | ( ~ (all_461_3 = 0) & % 20.31/3.90 | | | | | | | | | | | | | | | | | | distinct_points(all_17_2, all_17_1) = all_461_3) % 20.31/3.90 | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives: % 20.31/3.90 | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | Case 1: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | (150) ~ (all_461_2 = 0) & distinct_lines(all_17_6, % 20.31/3.90 | | | | | | | | | | | | | | | | | | | all_17_7) = all_461_2 % 20.31/3.90 | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | ALPHA: (150) implies: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | (151) ~ (all_461_2 = 0) % 20.31/3.90 | | | | | | | | | | | | | | | | | | | (152) distinct_lines(all_17_6, all_17_7) = all_461_2 % 20.31/3.90 | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | Case 1: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | (153) all_425_0 = 0 & apart_point_and_line(all_17_1, % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | all_17_6) = 0 % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | (154) apart_point_and_line(all_17_1, all_17_6) = 0 % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (123), (124), (154) are inconsistent by % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | Case 2: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | (155) (all_425_1 = 0 & apart_point_and_line(all_17_1, % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | all_53_1) = 0) | ( ~ (all_425_2 = 0) & % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | distinct_lines(all_53_1, all_17_6) = all_425_2) % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | Case 1: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | (156) all_425_1 = 0 & apart_point_and_line(all_17_1, % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | all_53_1) = 0 % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | (157) apart_point_and_line(all_17_1, all_53_1) = 0 % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_57_0, 0, all_53_1, % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | all_17_1, simplifying with (101), (157) gives: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | (158) all_57_0 = 0 % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (158) imply: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | (159) $false % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | CLOSE: (159) is inconsistent. % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | Case 2: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_126_2, all_461_2, % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | all_17_7, all_17_6, simplifying with (141), (152) % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | gives: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | (160) all_461_2 = all_126_2 % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | REDUCE: (151), (160) imply: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | (161) ~ (all_126_2 = 0) % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_17_7, all_17_6, % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | all_17_7, all_126_2, simplifying with (19), (20), % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | (23), (141) gives: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | (162) all_126_2 = 0 | convergent_lines(all_17_7, % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | all_17_7) = 0 % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | Case 1: % 20.31/3.90 | | | | | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | | (163) convergent_lines(all_17_7, all_17_7) = 0 % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_17_7, simplifying % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | | with (19), (163) gives: % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | | (164) $false % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (164) is inconsistent. % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | Case 2: % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | | (165) all_126_2 = 0 % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (165) imply: % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | | (166) $false % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (166) is inconsistent. % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | End of split % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | End of split % 20.31/3.91 | | | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | | | End of split % 20.31/3.91 | | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | | Case 2: % 20.31/3.91 | | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | | | (167) ~ (all_461_3 = 0) & distinct_points(all_17_2, % 20.31/3.91 | | | | | | | | | | | | | | | | | | | all_17_1) = all_461_3 % 20.31/3.91 | | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | | | ALPHA: (167) implies: % 20.31/3.91 | | | | | | | | | | | | | | | | | | | (168) ~ (all_461_3 = 0) % 20.31/3.91 | | | | | | | | | | | | | | | | | | | (169) distinct_points(all_17_2, all_17_1) = all_461_3 % 20.31/3.91 | | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_461_3, all_17_1, % 20.31/3.91 | | | | | | | | | | | | | | | | | | | all_17_2, simplifying with (40), (169) gives: % 20.31/3.91 | | | | | | | | | | | | | | | | | | | (170) all_461_3 = 0 % 20.31/3.91 | | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | | | REDUCE: (168), (170) imply: % 20.31/3.91 | | | | | | | | | | | | | | | | | | | (171) $false % 20.31/3.91 | | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | | | CLOSE: (171) is inconsistent. % 20.31/3.91 | | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | | End of split % 20.31/3.91 | | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | | End of split % 20.31/3.91 | | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | | End of split % 20.31/3.91 | | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | | End of split % 20.31/3.91 | | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | | End of split % 20.31/3.91 | | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | | End of split % 20.31/3.91 | | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | | End of split % 20.31/3.91 | | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | | End of split % 20.31/3.91 | | | | | | | | | | | % 20.31/3.91 | | | | | | | | | | End of split % 20.31/3.91 | | | | | | | | | | % 20.31/3.91 | | | | | | | | | End of split % 20.31/3.91 | | | | | | | | | % 20.31/3.91 | | | | | | | | End of split % 20.31/3.91 | | | | | | | | % 20.31/3.91 | | | | | | | End of split % 20.31/3.91 | | | | | | | % 20.31/3.91 | | | | | | End of split % 20.31/3.91 | | | | | | % 20.31/3.91 | | | | | End of split % 20.31/3.91 | | | | | % 20.31/3.91 | | | | Case 2: % 20.31/3.91 | | | | | % 20.31/3.91 | | | | | (172) ~ (all_50_1 = 0) & convergent_lines(all_17_7, all_17_5) = % 20.31/3.91 | | | | | all_50_1 % 20.31/3.91 | | | | | % 20.31/3.91 | | | | | ALPHA: (172) implies: % 20.31/3.91 | | | | | (173) ~ (all_50_1 = 0) % 20.31/3.91 | | | | | (174) convergent_lines(all_17_7, all_17_5) = all_50_1 % 20.31/3.91 | | | | | % 20.31/3.91 | | | | | GROUND_INST: instantiating (13) with 0, all_50_1, all_17_5, all_17_7, % 20.31/3.91 | | | | | simplifying with (37), (174) gives: % 20.31/3.91 | | | | | (175) all_50_1 = 0 % 20.31/3.91 | | | | | % 20.31/3.91 | | | | | REDUCE: (173), (175) imply: % 20.31/3.91 | | | | | (176) $false % 20.31/3.91 | | | | | % 20.31/3.91 | | | | | CLOSE: (176) is inconsistent. % 20.31/3.91 | | | | | % 20.31/3.91 | | | | End of split % 20.31/3.91 | | | | % 20.31/3.91 | | | Case 2: % 20.31/3.91 | | | | % 20.31/3.91 | | | | (177) ~ (all_59_1 = 0) & convergent_lines(all_17_7, all_17_5) = % 20.31/3.91 | | | | all_59_1 % 20.31/3.91 | | | | % 20.31/3.91 | | | | ALPHA: (177) implies: % 20.31/3.91 | | | | (178) ~ (all_59_1 = 0) % 20.31/3.91 | | | | (179) convergent_lines(all_17_7, all_17_5) = all_59_1 % 20.31/3.91 | | | | % 20.31/3.91 | | | | GROUND_INST: instantiating (13) with 0, all_59_1, all_17_5, all_17_7, % 20.31/3.91 | | | | simplifying with (37), (179) gives: % 20.31/3.91 | | | | (180) all_59_1 = 0 % 20.31/3.91 | | | | % 20.31/3.91 | | | | REDUCE: (178), (180) imply: % 20.31/3.91 | | | | (181) $false % 20.31/3.91 | | | | % 20.31/3.91 | | | | CLOSE: (181) is inconsistent. % 20.31/3.91 | | | | % 20.31/3.91 | | | End of split % 20.31/3.91 | | | % 20.31/3.91 | | Case 2: % 20.31/3.91 | | | % 20.31/3.91 | | | (182) ~ (all_17_3 = 0) & convergent_lines(all_17_7, all_17_5) = % 20.31/3.91 | | | all_17_3 % 20.31/3.91 | | | % 20.31/3.91 | | | ALPHA: (182) implies: % 20.31/3.91 | | | (183) ~ (all_17_3 = 0) % 20.31/3.91 | | | (184) convergent_lines(all_17_7, all_17_5) = all_17_3 % 20.31/3.91 | | | % 20.31/3.91 | | | GROUND_INST: instantiating (13) with 0, all_17_3, all_17_5, all_17_7, % 20.31/3.91 | | | simplifying with (37), (184) gives: % 20.31/3.91 | | | (185) all_17_3 = 0 % 20.31/3.91 | | | % 20.31/3.91 | | | REDUCE: (183), (185) imply: % 20.31/3.91 | | | (186) $false % 20.31/3.91 | | | % 20.31/3.91 | | | CLOSE: (186) is inconsistent. % 20.31/3.91 | | | % 20.31/3.91 | | End of split % 20.31/3.91 | | % 20.31/3.91 | Case 2: % 20.31/3.91 | | % 20.31/3.91 | | (187) all_17_4 = 0 % 20.31/3.91 | | % 20.31/3.91 | | REDUCE: (18), (187) imply: % 20.31/3.91 | | (188) $false % 20.31/3.91 | | % 20.31/3.91 | | CLOSE: (188) is inconsistent. % 20.31/3.91 | | % 20.31/3.91 | End of split % 20.31/3.91 | % 20.31/3.91 End of proof % 20.31/3.91 % 20.31/3.91 Sub-proof #1 shows that the following formulas are inconsistent: % 20.31/3.91 ---------------------------------------------------------------- % 20.31/3.91 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.31/3.91 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 20.31/3.91 (apart_point_and_line(v3, v2) = v0)) % 20.31/3.91 (2) apart_point_and_line(all_17_1, all_17_6) = all_372_0 % 20.31/3.91 (3) apart_point_and_line(all_17_1, all_17_6) = 0 % 20.31/3.91 (4) ~ (all_372_0 = 0) % 20.31/3.91 % 20.31/3.91 Begin of proof % 20.31/3.91 | % 20.31/3.91 | GROUND_INST: instantiating (1) with 0, all_372_0, all_17_6, all_17_1, % 20.31/3.91 | simplifying with (2), (3) gives: % 20.31/3.91 | (5) all_372_0 = 0 % 20.31/3.91 | % 20.31/3.91 | REDUCE: (4), (5) imply: % 20.31/3.91 | (6) $false % 20.31/3.91 | % 20.31/3.91 | CLOSE: (6) is inconsistent. % 20.31/3.91 | % 20.31/3.91 End of proof % 20.31/3.91 % SZS output end Proof for theBenchmark % 20.31/3.91 % 20.31/3.91 3289ms %------------------------------------------------------------------------------