%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO180+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 : n009.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 23:21:55 EDT 2023 % Result : Theorem 12.43s 2.49s % Output : Proof 19.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO180+1 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n009.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Aug 29 21:19:35 EDT 2023 % 0.12/0.33 % CPUTime : % 0.46/0.62 ________ _____ % 0.46/0.62 ___ __ \_________(_)________________________________ % 0.46/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.46/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.46/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.46/0.62 % 0.46/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.46/0.62 (2023-06-19) % 0.46/0.62 % 0.46/0.62 (c) Philipp Rümmer, 2009-2023 % 0.46/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.46/0.62 Amanda Stjerna. % 0.46/0.62 Free software under BSD-3-Clause. % 0.46/0.62 % 0.46/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.46/0.62 % 0.46/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.66/0.64 Running up to 7 provers in parallel. % 0.66/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.66/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.66/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.66/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.66/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.66/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.66/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.42/1.15 Prover 4: Preprocessing ... % 2.42/1.15 Prover 1: Preprocessing ... % 2.82/1.20 Prover 5: Preprocessing ... % 2.82/1.20 Prover 2: Preprocessing ... % 2.82/1.20 Prover 6: Preprocessing ... % 2.82/1.20 Prover 3: Preprocessing ... % 2.82/1.20 Prover 0: Preprocessing ... % 4.92/1.45 Prover 5: Proving ... % 5.55/1.53 Prover 1: Constructing countermodel ... % 5.55/1.54 Prover 2: Proving ... % 5.55/1.55 Prover 6: Constructing countermodel ... % 5.77/1.57 Prover 3: Constructing countermodel ... % 6.61/1.70 Prover 1: gave up % 6.61/1.70 Prover 4: Constructing countermodel ... % 6.61/1.70 Prover 6: gave up % 6.61/1.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.61/1.72 Prover 3: gave up % 6.61/1.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.14/1.74 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 7.14/1.75 Prover 7: Preprocessing ... % 7.14/1.76 Prover 8: Preprocessing ... % 7.36/1.78 Prover 0: Proving ... % 7.36/1.78 Prover 9: Preprocessing ... % 7.36/1.80 Prover 7: Warning: ignoring some quantifiers % 7.36/1.85 Prover 7: Constructing countermodel ... % 8.17/1.92 Prover 8: Warning: ignoring some quantifiers % 8.17/1.94 Prover 8: Constructing countermodel ... % 8.91/1.99 Prover 7: gave up % 8.91/1.99 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.28/2.03 Prover 10: Preprocessing ... % 9.48/2.07 Prover 8: gave up % 9.48/2.08 Prover 10: Warning: ignoring some quantifiers % 9.48/2.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.48/2.09 Prover 10: Constructing countermodel ... % 9.48/2.10 Prover 9: Constructing countermodel ... % 10.10/2.14 Prover 10: gave up % 10.10/2.14 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 10.10/2.15 Prover 11: Preprocessing ... % 10.52/2.18 Prover 12: Preprocessing ... % 11.81/2.40 Prover 12: Proving ... % 12.43/2.48 Prover 9: proved (742ms) % 12.43/2.49 % 12.43/2.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.43/2.49 % 12.43/2.49 Prover 0: proved (1838ms) % 12.43/2.49 % 12.43/2.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.43/2.49 % 12.43/2.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.43/2.49 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 12.81/2.50 Prover 5: stopped % 12.81/2.50 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 12.81/2.50 Prover 2: stopped % 12.81/2.50 Prover 12: stopped % 12.81/2.51 Prover 16: Preprocessing ... % 12.81/2.52 Prover 11: Constructing countermodel ... % 12.81/2.53 Prover 13: Preprocessing ... % 12.81/2.54 Prover 19: Preprocessing ... % 13.25/2.57 Prover 16: Warning: ignoring some quantifiers % 13.25/2.58 Prover 16: Constructing countermodel ... % 13.25/2.59 Prover 13: Warning: ignoring some quantifiers % 13.61/2.60 Prover 13: Constructing countermodel ... % 13.61/2.62 Prover 19: Warning: ignoring some quantifiers % 13.61/2.62 Prover 19: Constructing countermodel ... % 13.96/2.67 Prover 19: gave up % 13.96/2.72 Prover 13: gave up % 14.71/2.78 Prover 16: gave up % 18.75/3.45 Prover 11: Found proof (size 137) % 18.75/3.45 Prover 11: proved (1365ms) % 18.75/3.45 Prover 4: stopped % 18.75/3.45 % 18.75/3.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.75/3.45 % 18.75/3.48 % SZS output start Proof for theBenchmark % 18.75/3.48 Assumptions after simplification: % 18.75/3.48 --------------------------------- % 18.75/3.48 % 18.75/3.48 (ceq1) % 19.07/3.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 19.07/3.52 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ % 19.07/3.52 (distinct_points(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 19.07/3.52 int] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : % 19.07/3.52 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 19.07/3.52 (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) % 19.07/3.52 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) & ! [v0: % 19.07/3.52 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 19.07/3.52 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~ % 19.07/3.52 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0) % 19.07/3.52 % 19.07/3.52 (ceq2) % 19.07/3.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 19.07/3.53 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 19.07/3.53 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 19.07/3.53 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 19.07/3.53 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 19.07/3.53 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 19.07/3.53 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 19.07/3.53 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 19.07/3.53 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 19.07/3.53 apart_point_and_line(v0, v2) = 0) % 19.07/3.53 % 19.07/3.53 (ci1) % 19.07/3.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 19.07/3.53 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) & % 19.07/3.53 apart_point_and_line(v0, v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, % 19.07/3.53 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) % 19.07/3.53 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 19.07/3.53 line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 19.07/3.53 $i(v2))) % 19.07/3.53 % 19.07/3.53 (ci2) % 19.07/3.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 19.07/3.54 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) & % 19.07/3.54 apart_point_and_line(v1, v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, % 19.07/3.54 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) % 19.07/3.54 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 19.07/3.54 line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 19.07/3.54 $i(v2))) % 19.07/3.54 % 19.07/3.54 (con) % 19.07/3.54 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 19.07/3.54 int] : ( ~ (v5 = 0) & line_connecting(v2, v1) = v4 & line_connecting(v0, v1) % 19.07/3.54 = v3 & apart_point_and_line(v2, v3) = 0 & apart_point_and_line(v0, v4) = v5 % 19.07/3.54 & distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 19.07/3.54 % 19.07/3.54 (cu1) % 19.07/3.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 19.07/3.56 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 19.07/3.56 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 19.07/3.56 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 19.07/3.56 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 19.07/3.56 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, % 19.07/3.56 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 19.07/3.56 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, % 19.07/3.56 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ % 19.07/3.56 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 19.07/3.56 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 19.07/3.56 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0, % 19.07/3.56 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 19.07/3.56 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 19.07/3.56 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 19.07/3.56 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 19.07/3.56 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 19.07/3.56 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 19.07/3.56 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 19.07/3.56 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 19.07/3.56 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 19.07/3.56 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 19.07/3.56 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 19.07/3.56 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 19.07/3.56 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 19.07/3.56 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 19.07/3.56 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 19.07/3.56 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 19.07/3.56 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 19.07/3.56 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~ % 19.07/3.56 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 19.07/3.56 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 19.07/3.56 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, % 19.07/3.56 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 19.07/3.56 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, % 19.07/3.56 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 19.07/3.56 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 19.07/3.56 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 19.07/3.56 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1, % 19.07/3.56 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i] % 19.07/3.56 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | % 19.07/3.56 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 19.07/3.56 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = % 19.07/3.56 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 19.07/3.56 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0, % 19.07/3.56 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 19.07/3.57 % 19.07/3.57 (function-axioms) % 19.07/3.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.07/3.57 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 19.07/3.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.07/3.57 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 19.07/3.57 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 19.07/3.57 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 19.07/3.57 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 19.07/3.57 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.07/3.57 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 19.07/3.57 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 19.07/3.57 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 19.07/3.57 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 19.07/3.57 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 19.07/3.57 (distinct_points(v3, v2) = v0)) % 19.07/3.57 % 19.07/3.57 Further assumptions not needed in the proof: % 19.07/3.57 -------------------------------------------- % 19.07/3.57 apart1, apart2, apart3, apart4, apart5, ax6, ceq3, ci3, ci4 % 19.07/3.57 % 19.07/3.57 Those formulas are unsatisfiable: % 19.07/3.57 --------------------------------- % 19.07/3.57 % 19.07/3.57 Begin of proof % 19.07/3.57 | % 19.07/3.57 | ALPHA: (ci1) implies: % 19.07/3.58 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 19.07/3.58 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 19.07/3.58 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 19.07/3.58 | $i(v2))) % 19.07/3.58 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 19.07/3.58 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ % 19.38/3.58 | (v4 = 0) & apart_point_and_line(v0, v2) = v4) | ( ~ (v3 = 0) & % 19.38/3.58 | distinct_points(v0, v1) = v3))) % 19.38/3.58 | % 19.38/3.58 | ALPHA: (ci2) implies: % 19.38/3.58 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 19.38/3.58 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 19.38/3.58 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 19.38/3.58 | $i(v2))) % 19.38/3.58 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 19.38/3.58 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ % 19.38/3.58 | (v4 = 0) & apart_point_and_line(v1, v2) = v4) | ( ~ (v3 = 0) & % 19.38/3.58 | distinct_points(v0, v1) = v3))) % 19.38/3.58 | % 19.38/3.58 | ALPHA: (cu1) implies: % 19.38/3.59 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 19.38/3.59 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) % 19.38/3.59 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, % 19.38/3.59 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 19.38/3.59 | [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 19.38/3.59 | apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 19.38/3.59 | apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & % 19.38/3.59 | distinct_lines(v2, v3) = v6))) % 19.38/3.59 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 19.38/3.59 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 19.38/3.59 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 19.38/3.59 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 19.38/3.59 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 19.38/3.59 | apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & % 19.38/3.59 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 19.38/3.59 | v1) = v6))) % 19.38/3.59 | % 19.38/3.59 | ALPHA: (ceq1) implies: % 19.38/3.59 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 19.38/3.59 | (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, % 19.38/3.59 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 19.38/3.59 | distinct_points(v0, v2) = 0) % 19.38/3.59 | % 19.38/3.59 | ALPHA: (ceq2) implies: % 19.38/3.59 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 19.38/3.59 | (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) % 19.38/3.59 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v0, v2) = % 19.38/3.60 | 0) % 19.38/3.60 | % 19.38/3.60 | ALPHA: (function-axioms) implies: % 19.38/3.60 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 19.38/3.60 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 19.38/3.60 | (distinct_points(v3, v2) = v0)) % 19.38/3.60 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 19.38/3.60 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 19.38/3.60 | (distinct_lines(v3, v2) = v0)) % 19.38/3.60 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 19.38/3.60 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 19.38/3.60 | (apart_point_and_line(v3, v2) = v0)) % 19.38/3.60 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.38/3.60 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 19.38/3.60 | % 19.38/3.60 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 19.38/3.60 | all_17_3, all_17_4, all_17_5 gives: % 19.38/3.60 | (13) ~ (all_17_0 = 0) & line_connecting(all_17_3, all_17_4) = all_17_1 & % 19.38/3.60 | line_connecting(all_17_5, all_17_4) = all_17_2 & % 19.38/3.60 | apart_point_and_line(all_17_3, all_17_2) = 0 & % 19.38/3.60 | apart_point_and_line(all_17_5, all_17_1) = all_17_0 & % 19.38/3.60 | distinct_points(all_17_5, all_17_4) = 0 & $i(all_17_1) & $i(all_17_2) % 19.38/3.60 | & $i(all_17_3) & $i(all_17_4) & $i(all_17_5) % 19.38/3.60 | % 19.38/3.60 | ALPHA: (13) implies: % 19.38/3.60 | (14) ~ (all_17_0 = 0) % 19.38/3.60 | (15) $i(all_17_5) % 19.38/3.60 | (16) $i(all_17_4) % 19.38/3.60 | (17) $i(all_17_3) % 19.38/3.60 | (18) $i(all_17_1) % 19.38/3.61 | (19) distinct_points(all_17_5, all_17_4) = 0 % 19.38/3.61 | (20) apart_point_and_line(all_17_5, all_17_1) = all_17_0 % 19.38/3.61 | (21) apart_point_and_line(all_17_3, all_17_2) = 0 % 19.38/3.61 | (22) line_connecting(all_17_5, all_17_4) = all_17_2 % 19.38/3.61 | (23) line_connecting(all_17_3, all_17_4) = all_17_1 % 19.38/3.61 | % 19.38/3.61 | GROUND_INST: instantiating (3) with all_17_5, all_17_4, simplifying with (15), % 19.38/3.61 | (16), (19) gives: % 19.38/3.61 | (24) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5, % 19.38/3.61 | all_17_4) = v0 & apart_point_and_line(all_17_4, v0) = v1 & $i(v0)) % 19.38/3.61 | % 19.38/3.61 | GROUND_INST: instantiating (1) with all_17_5, all_17_4, simplifying with (15), % 19.38/3.61 | (16), (19) gives: % 19.38/3.61 | (25) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_5, % 19.38/3.61 | all_17_4) = v0 & apart_point_and_line(all_17_5, v0) = v1 & $i(v0)) % 19.38/3.61 | % 19.38/3.61 | GROUND_INST: instantiating (4) with all_17_5, all_17_4, all_17_2, simplifying % 19.38/3.61 | with (15), (16), (22) gives: % 19.38/3.61 | (26) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 19.38/3.61 | apart_point_and_line(all_17_4, all_17_2) = v1) | ( ~ (v0 = 0) & % 19.38/3.61 | distinct_points(all_17_5, all_17_4) = v0)) % 19.38/3.61 | % 19.38/3.61 | GROUND_INST: instantiating (2) with all_17_5, all_17_4, all_17_2, simplifying % 19.38/3.61 | with (15), (16), (22) gives: % 19.38/3.61 | (27) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 19.38/3.61 | apart_point_and_line(all_17_5, all_17_2) = v1) | ( ~ (v0 = 0) & % 19.38/3.61 | distinct_points(all_17_5, all_17_4) = v0)) % 19.38/3.62 | % 19.38/3.62 | GROUND_INST: instantiating (4) with all_17_3, all_17_4, all_17_1, simplifying % 19.38/3.62 | with (16), (17), (23) gives: % 19.38/3.62 | (28) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 19.38/3.62 | apart_point_and_line(all_17_4, all_17_1) = v1) | ( ~ (v0 = 0) & % 19.38/3.62 | distinct_points(all_17_3, all_17_4) = v0)) % 19.38/3.62 | % 19.38/3.62 | GROUND_INST: instantiating (2) with all_17_3, all_17_4, all_17_1, simplifying % 19.38/3.62 | with (16), (17), (23) gives: % 19.38/3.62 | (29) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 19.38/3.62 | apart_point_and_line(all_17_3, all_17_1) = v1) | ( ~ (v0 = 0) & % 19.38/3.62 | distinct_points(all_17_3, all_17_4) = v0)) % 19.38/3.62 | % 19.38/3.62 | DELTA: instantiating (29) with fresh symbols all_24_0, all_24_1 gives: % 19.38/3.62 | (30) ( ~ (all_24_0 = 0) & apart_point_and_line(all_17_3, all_17_1) = % 19.38/3.62 | all_24_0) | ( ~ (all_24_1 = 0) & distinct_points(all_17_3, all_17_4) % 19.38/3.62 | = all_24_1) % 19.38/3.62 | % 19.38/3.62 | DELTA: instantiating (28) with fresh symbols all_25_0, all_25_1 gives: % 19.38/3.62 | (31) ( ~ (all_25_0 = 0) & apart_point_and_line(all_17_4, all_17_1) = % 19.38/3.62 | all_25_0) | ( ~ (all_25_1 = 0) & distinct_points(all_17_3, all_17_4) % 19.38/3.62 | = all_25_1) % 19.38/3.62 | % 19.38/3.62 | DELTA: instantiating (27) with fresh symbols all_26_0, all_26_1 gives: % 19.38/3.62 | (32) ( ~ (all_26_0 = 0) & apart_point_and_line(all_17_5, all_17_2) = % 19.38/3.62 | all_26_0) | ( ~ (all_26_1 = 0) & distinct_points(all_17_5, all_17_4) % 19.38/3.62 | = all_26_1) % 19.38/3.63 | % 19.38/3.63 | DELTA: instantiating (26) with fresh symbols all_27_0, all_27_1 gives: % 19.38/3.63 | (33) ( ~ (all_27_0 = 0) & apart_point_and_line(all_17_4, all_17_2) = % 19.38/3.63 | all_27_0) | ( ~ (all_27_1 = 0) & distinct_points(all_17_5, all_17_4) % 19.38/3.63 | = all_27_1) % 19.38/3.63 | % 19.38/3.63 | DELTA: instantiating (25) with fresh symbols all_28_0, all_28_1 gives: % 19.38/3.63 | (34) ~ (all_28_0 = 0) & line_connecting(all_17_5, all_17_4) = all_28_1 & % 19.38/3.63 | apart_point_and_line(all_17_5, all_28_1) = all_28_0 & $i(all_28_1) % 19.38/3.63 | % 19.38/3.63 | ALPHA: (34) implies: % 19.38/3.63 | (35) ~ (all_28_0 = 0) % 19.38/3.63 | (36) $i(all_28_1) % 19.38/3.63 | (37) apart_point_and_line(all_17_5, all_28_1) = all_28_0 % 19.38/3.63 | (38) line_connecting(all_17_5, all_17_4) = all_28_1 % 19.38/3.63 | % 19.38/3.63 | DELTA: instantiating (24) with fresh symbols all_30_0, all_30_1 gives: % 19.38/3.63 | (39) ~ (all_30_0 = 0) & line_connecting(all_17_5, all_17_4) = all_30_1 & % 19.38/3.63 | apart_point_and_line(all_17_4, all_30_1) = all_30_0 & $i(all_30_1) % 19.38/3.63 | % 19.38/3.63 | ALPHA: (39) implies: % 19.38/3.63 | (40) ~ (all_30_0 = 0) % 19.38/3.63 | (41) apart_point_and_line(all_17_4, all_30_1) = all_30_0 % 19.38/3.63 | (42) line_connecting(all_17_5, all_17_4) = all_30_1 % 19.38/3.63 | % 19.38/3.63 | BETA: splitting (33) gives: % 19.38/3.63 | % 19.38/3.63 | Case 1: % 19.38/3.63 | | % 19.38/3.63 | | (43) ~ (all_27_0 = 0) & apart_point_and_line(all_17_4, all_17_2) = % 19.38/3.63 | | all_27_0 % 19.38/3.63 | | % 19.38/3.63 | | ALPHA: (43) implies: % 19.38/3.63 | | (44) apart_point_and_line(all_17_4, all_17_2) = all_27_0 % 19.38/3.63 | | % 19.38/3.63 | | BETA: splitting (32) gives: % 19.38/3.63 | | % 19.38/3.63 | | Case 1: % 19.38/3.63 | | | % 19.38/3.64 | | | (45) ~ (all_26_0 = 0) & apart_point_and_line(all_17_5, all_17_2) = % 19.38/3.64 | | | all_26_0 % 19.38/3.64 | | | % 19.38/3.64 | | | ALPHA: (45) implies: % 19.38/3.64 | | | (46) apart_point_and_line(all_17_5, all_17_2) = all_26_0 % 19.38/3.64 | | | % 19.38/3.64 | | | GROUND_INST: instantiating (12) with all_17_2, all_30_1, all_17_4, % 19.38/3.64 | | | all_17_5, simplifying with (22), (42) gives: % 19.38/3.64 | | | (47) all_30_1 = all_17_2 % 19.38/3.64 | | | % 19.38/3.64 | | | GROUND_INST: instantiating (12) with all_28_1, all_30_1, all_17_4, % 19.38/3.64 | | | all_17_5, simplifying with (38), (42) gives: % 19.38/3.64 | | | (48) all_30_1 = all_28_1 % 19.38/3.64 | | | % 19.38/3.64 | | | COMBINE_EQS: (47), (48) imply: % 19.38/3.64 | | | (49) all_28_1 = all_17_2 % 19.38/3.64 | | | % 19.38/3.64 | | | REDUCE: (41), (47) imply: % 19.38/3.64 | | | (50) apart_point_and_line(all_17_4, all_17_2) = all_30_0 % 19.38/3.64 | | | % 19.38/3.64 | | | REDUCE: (37), (49) imply: % 19.38/3.64 | | | (51) apart_point_and_line(all_17_5, all_17_2) = all_28_0 % 19.38/3.64 | | | % 19.38/3.64 | | | REDUCE: (36), (49) imply: % 19.38/3.64 | | | (52) $i(all_17_2) % 19.38/3.64 | | | % 19.38/3.64 | | | GROUND_INST: instantiating (11) with all_26_0, all_28_0, all_17_2, % 19.38/3.64 | | | all_17_5, simplifying with (46), (51) gives: % 19.38/3.64 | | | (53) all_28_0 = all_26_0 % 19.38/3.64 | | | % 19.38/3.64 | | | GROUND_INST: instantiating (11) with all_27_0, all_30_0, all_17_2, % 19.38/3.64 | | | all_17_4, simplifying with (44), (50) gives: % 19.38/3.64 | | | (54) all_30_0 = all_27_0 % 19.38/3.64 | | | % 19.38/3.64 | | | REDUCE: (40), (54) imply: % 19.38/3.64 | | | (55) ~ (all_27_0 = 0) % 19.38/3.64 | | | % 19.38/3.64 | | | REDUCE: (35), (53) imply: % 19.38/3.64 | | | (56) ~ (all_26_0 = 0) % 19.38/3.64 | | | % 19.38/3.64 | | | GROUND_INST: instantiating (5) with all_17_5, all_17_4, all_17_2, % 19.38/3.65 | | | all_17_1, all_26_0, all_17_0, simplifying with (15), (16), % 19.38/3.65 | | | (18), (19), (20), (46), (52) gives: % 19.38/3.65 | | | (57) all_26_0 = 0 | all_17_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 19.38/3.65 | | | [v2: int] : ((v2 = 0 & apart_point_and_line(all_17_4, all_17_1) = % 19.38/3.65 | | | 0) | (v1 = 0 & apart_point_and_line(all_17_4, all_17_2) = 0) | % 19.38/3.65 | | | ( ~ (v0 = 0) & distinct_lines(all_17_2, all_17_1) = v0)) % 19.38/3.65 | | | % 19.38/3.65 | | | GROUND_INST: instantiating (7) with all_17_3, all_17_2, all_17_4, % 19.38/3.65 | | | all_27_0, simplifying with (16), (17), (21), (44), (52) % 19.38/3.65 | | | gives: % 19.38/3.65 | | | (58) all_27_0 = 0 | distinct_points(all_17_3, all_17_4) = 0 % 19.38/3.65 | | | % 19.38/3.65 | | | GROUND_INST: instantiating (6) with all_17_5, all_17_4, all_17_2, % 19.38/3.65 | | | all_17_1, all_17_0, all_27_0, simplifying with (15), (16), % 19.38/3.65 | | | (18), (20), (44), (52) gives: % 19.38/3.65 | | | (59) all_27_0 = 0 | all_17_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 19.38/3.65 | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 19.38/3.65 | | | apart_point_and_line(all_17_4, all_17_1) = 0) | (v2 = 0 & % 19.38/3.65 | | | apart_point_and_line(all_17_5, all_17_2) = 0) | ( ~ (v1 = 0) & % 19.38/3.65 | | | distinct_lines(all_17_2, all_17_1) = v1) | ( ~ (v0 = 0) & % 19.38/3.65 | | | distinct_points(all_17_5, all_17_4) = v0)) % 19.38/3.65 | | | % 19.38/3.65 | | | BETA: splitting (30) gives: % 19.38/3.65 | | | % 19.38/3.65 | | | Case 1: % 19.38/3.65 | | | | % 19.38/3.65 | | | | (60) ~ (all_24_0 = 0) & apart_point_and_line(all_17_3, all_17_1) = % 19.38/3.65 | | | | all_24_0 % 19.38/3.65 | | | | % 19.38/3.65 | | | | ALPHA: (60) implies: % 19.38/3.66 | | | | (61) ~ (all_24_0 = 0) % 19.38/3.66 | | | | (62) apart_point_and_line(all_17_3, all_17_1) = all_24_0 % 19.38/3.66 | | | | % 19.38/3.66 | | | | BETA: splitting (58) gives: % 19.38/3.66 | | | | % 19.38/3.66 | | | | Case 1: % 19.38/3.66 | | | | | % 19.38/3.66 | | | | | (63) distinct_points(all_17_3, all_17_4) = 0 % 19.38/3.66 | | | | | % 19.38/3.66 | | | | | BETA: splitting (31) gives: % 19.38/3.66 | | | | | % 19.38/3.66 | | | | | Case 1: % 19.38/3.66 | | | | | | % 19.38/3.66 | | | | | | (64) ~ (all_25_0 = 0) & apart_point_and_line(all_17_4, all_17_1) % 19.38/3.66 | | | | | | = all_25_0 % 19.38/3.66 | | | | | | % 19.38/3.66 | | | | | | ALPHA: (64) implies: % 19.38/3.66 | | | | | | (65) ~ (all_25_0 = 0) % 19.38/3.66 | | | | | | (66) apart_point_and_line(all_17_4, all_17_1) = all_25_0 % 19.38/3.66 | | | | | | % 19.38/3.66 | | | | | | BETA: splitting (59) gives: % 19.38/3.66 | | | | | | % 19.38/3.66 | | | | | | Case 1: % 19.38/3.66 | | | | | | | % 19.38/3.66 | | | | | | | (67) all_27_0 = 0 % 19.38/3.66 | | | | | | | % 19.38/3.66 | | | | | | | REDUCE: (55), (67) imply: % 19.76/3.66 | | | | | | | (68) $false % 19.76/3.66 | | | | | | | % 19.76/3.66 | | | | | | | CLOSE: (68) is inconsistent. % 19.76/3.66 | | | | | | | % 19.76/3.66 | | | | | | Case 2: % 19.76/3.66 | | | | | | | % 19.76/3.66 | | | | | | | (69) all_17_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] % 19.76/3.66 | | | | | | | : ? [v3: int] : ((v3 = 0 & apart_point_and_line(all_17_4, % 19.76/3.66 | | | | | | | all_17_1) = 0) | (v2 = 0 & % 19.76/3.66 | | | | | | | apart_point_and_line(all_17_5, all_17_2) = 0) | ( ~ % 19.76/3.66 | | | | | | | (v1 = 0) & distinct_lines(all_17_2, all_17_1) = v1) | % 19.76/3.66 | | | | | | | ( ~ (v0 = 0) & distinct_points(all_17_5, all_17_4) = % 19.76/3.66 | | | | | | | v0)) % 19.76/3.66 | | | | | | | % 19.76/3.66 | | | | | | | BETA: splitting (57) gives: % 19.76/3.66 | | | | | | | % 19.76/3.66 | | | | | | | Case 1: % 19.76/3.66 | | | | | | | | % 19.76/3.66 | | | | | | | | (70) all_26_0 = 0 % 19.76/3.66 | | | | | | | | % 19.76/3.66 | | | | | | | | REDUCE: (56), (70) imply: % 19.76/3.66 | | | | | | | | (71) $false % 19.76/3.66 | | | | | | | | % 19.76/3.66 | | | | | | | | CLOSE: (71) is inconsistent. % 19.76/3.66 | | | | | | | | % 19.76/3.66 | | | | | | | Case 2: % 19.76/3.66 | | | | | | | | % 19.76/3.66 | | | | | | | | (72) all_17_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 19.76/3.66 | | | | | | | | int] : ((v2 = 0 & apart_point_and_line(all_17_4, % 19.76/3.66 | | | | | | | | all_17_1) = 0) | (v1 = 0 & % 19.76/3.66 | | | | | | | | apart_point_and_line(all_17_4, all_17_2) = 0) | ( ~ % 19.76/3.66 | | | | | | | | (v0 = 0) & distinct_lines(all_17_2, all_17_1) = v0)) % 19.76/3.66 | | | | | | | | % 19.76/3.66 | | | | | | | | BETA: splitting (69) gives: % 19.76/3.66 | | | | | | | | % 19.76/3.66 | | | | | | | | Case 1: % 19.76/3.66 | | | | | | | | | % 19.76/3.66 | | | | | | | | | (73) all_17_0 = 0 % 19.76/3.66 | | | | | | | | | % 19.76/3.66 | | | | | | | | | REDUCE: (14), (73) imply: % 19.76/3.66 | | | | | | | | | (74) $false % 19.76/3.66 | | | | | | | | | % 19.76/3.66 | | | | | | | | | CLOSE: (74) is inconsistent. % 19.76/3.66 | | | | | | | | | % 19.76/3.66 | | | | | | | | Case 2: % 19.76/3.66 | | | | | | | | | % 19.76/3.67 | | | | | | | | | (75) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 19.76/3.67 | | | | | | | | | int] : ((v3 = 0 & apart_point_and_line(all_17_4, % 19.76/3.67 | | | | | | | | | all_17_1) = 0) | (v2 = 0 & % 19.76/3.67 | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = 0) | ( % 19.76/3.67 | | | | | | | | | ~ (v1 = 0) & distinct_lines(all_17_2, all_17_1) = % 19.76/3.67 | | | | | | | | | v1) | ( ~ (v0 = 0) & distinct_points(all_17_5, % 19.76/3.67 | | | | | | | | | all_17_4) = v0)) % 19.76/3.67 | | | | | | | | | % 19.76/3.67 | | | | | | | | | DELTA: instantiating (75) with fresh symbols all_186_0, % 19.76/3.67 | | | | | | | | | all_186_1, all_186_2, all_186_3 gives: % 19.76/3.67 | | | | | | | | | (76) (all_186_0 = 0 & apart_point_and_line(all_17_4, % 19.76/3.67 | | | | | | | | | all_17_1) = 0) | (all_186_1 = 0 & % 19.76/3.67 | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = 0) | ( ~ % 19.76/3.67 | | | | | | | | | (all_186_2 = 0) & distinct_lines(all_17_2, all_17_1) % 19.76/3.67 | | | | | | | | | = all_186_2) | ( ~ (all_186_3 = 0) & % 19.76/3.67 | | | | | | | | | distinct_points(all_17_5, all_17_4) = all_186_3) % 19.76/3.67 | | | | | | | | | % 19.76/3.67 | | | | | | | | | BETA: splitting (72) gives: % 19.76/3.67 | | | | | | | | | % 19.76/3.67 | | | | | | | | | Case 1: % 19.76/3.67 | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | (77) all_17_0 = 0 % 19.76/3.67 | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | REDUCE: (14), (77) imply: % 19.76/3.67 | | | | | | | | | | (78) $false % 19.76/3.67 | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | CLOSE: (78) is inconsistent. % 19.76/3.67 | | | | | | | | | | % 19.76/3.67 | | | | | | | | | Case 2: % 19.76/3.67 | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | (79) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = % 19.76/3.67 | | | | | | | | | | 0 & apart_point_and_line(all_17_4, all_17_1) = % 19.76/3.67 | | | | | | | | | | 0) | (v1 = 0 & apart_point_and_line(all_17_4, % 19.76/3.67 | | | | | | | | | | all_17_2) = 0) | ( ~ (v0 = 0) & % 19.76/3.67 | | | | | | | | | | distinct_lines(all_17_2, all_17_1) = v0)) % 19.76/3.67 | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | DELTA: instantiating (79) with fresh symbols all_194_0, % 19.76/3.67 | | | | | | | | | | all_194_1, all_194_2 gives: % 19.76/3.67 | | | | | | | | | | (80) (all_194_0 = 0 & apart_point_and_line(all_17_4, % 19.76/3.67 | | | | | | | | | | all_17_1) = 0) | (all_194_1 = 0 & % 19.76/3.67 | | | | | | | | | | apart_point_and_line(all_17_4, all_17_2) = 0) | ( % 19.76/3.67 | | | | | | | | | | ~ (all_194_2 = 0) & distinct_lines(all_17_2, % 19.76/3.67 | | | | | | | | | | all_17_1) = all_194_2) % 19.76/3.67 | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | BETA: splitting (76) gives: % 19.76/3.67 | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | Case 1: % 19.76/3.67 | | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | | (81) (all_186_0 = 0 & apart_point_and_line(all_17_4, % 19.76/3.67 | | | | | | | | | | | all_17_1) = 0) | (all_186_1 = 0 & % 19.76/3.67 | | | | | | | | | | | apart_point_and_line(all_17_5, all_17_2) = 0) % 19.76/3.67 | | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | | BETA: splitting (81) gives: % 19.76/3.67 | | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | | Case 1: % 19.76/3.67 | | | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | | | (82) all_186_0 = 0 & apart_point_and_line(all_17_4, % 19.76/3.67 | | | | | | | | | | | | all_17_1) = 0 % 19.76/3.67 | | | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | | | ALPHA: (82) implies: % 19.76/3.67 | | | | | | | | | | | | (83) apart_point_and_line(all_17_4, all_17_1) = 0 % 19.76/3.67 | | | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | | | REF_CLOSE: (11), (65), (66), (83) are inconsistent by % 19.76/3.67 | | | | | | | | | | | | sub-proof #1. % 19.76/3.67 | | | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | | Case 2: % 19.76/3.67 | | | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | | | (84) all_186_1 = 0 & apart_point_and_line(all_17_5, % 19.76/3.67 | | | | | | | | | | | | all_17_2) = 0 % 19.76/3.67 | | | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | | | ALPHA: (84) implies: % 19.76/3.67 | | | | | | | | | | | | (85) apart_point_and_line(all_17_5, all_17_2) = 0 % 19.76/3.67 | | | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_26_0, 0, all_17_2, % 19.76/3.67 | | | | | | | | | | | | all_17_5, simplifying with (46), (85) gives: % 19.76/3.67 | | | | | | | | | | | | (86) all_26_0 = 0 % 19.76/3.67 | | | | | | | | | | | | % 19.76/3.67 | | | | | | | | | | | | REDUCE: (56), (86) imply: % 19.76/3.67 | | | | | | | | | | | | (87) $false % 19.76/3.68 | | | | | | | | | | | | % 19.76/3.68 | | | | | | | | | | | | CLOSE: (87) is inconsistent. % 19.76/3.68 | | | | | | | | | | | | % 19.76/3.68 | | | | | | | | | | | End of split % 19.76/3.68 | | | | | | | | | | | % 19.76/3.68 | | | | | | | | | | Case 2: % 19.76/3.68 | | | | | | | | | | | % 19.76/3.68 | | | | | | | | | | | (88) ( ~ (all_186_2 = 0) & distinct_lines(all_17_2, % 19.76/3.68 | | | | | | | | | | | all_17_1) = all_186_2) | ( ~ (all_186_3 = 0) & % 19.76/3.68 | | | | | | | | | | | distinct_points(all_17_5, all_17_4) = all_186_3) % 19.76/3.68 | | | | | | | | | | | % 19.76/3.68 | | | | | | | | | | | BETA: splitting (88) gives: % 19.76/3.68 | | | | | | | | | | | % 19.76/3.68 | | | | | | | | | | | Case 1: % 19.76/3.68 | | | | | | | | | | | | % 19.76/3.68 | | | | | | | | | | | | (89) ~ (all_186_2 = 0) & distinct_lines(all_17_2, % 19.76/3.68 | | | | | | | | | | | | all_17_1) = all_186_2 % 19.76/3.68 | | | | | | | | | | | | % 19.76/3.68 | | | | | | | | | | | | ALPHA: (89) implies: % 19.84/3.68 | | | | | | | | | | | | (90) distinct_lines(all_17_2, all_17_1) = all_186_2 % 19.84/3.68 | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | BETA: splitting (80) gives: % 19.84/3.68 | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | Case 1: % 19.84/3.68 | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | (91) all_194_0 = 0 & apart_point_and_line(all_17_4, % 19.84/3.68 | | | | | | | | | | | | | all_17_1) = 0 % 19.84/3.68 | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | ALPHA: (91) implies: % 19.84/3.68 | | | | | | | | | | | | | (92) apart_point_and_line(all_17_4, all_17_1) = 0 % 19.84/3.68 | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | REF_CLOSE: (11), (65), (66), (92) are inconsistent by % 19.84/3.68 | | | | | | | | | | | | | sub-proof #1. % 19.84/3.68 | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | Case 2: % 19.84/3.68 | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | (93) (all_194_1 = 0 & apart_point_and_line(all_17_4, % 19.84/3.68 | | | | | | | | | | | | | all_17_2) = 0) | ( ~ (all_194_2 = 0) & % 19.84/3.68 | | | | | | | | | | | | | distinct_lines(all_17_2, all_17_1) = all_194_2) % 19.84/3.68 | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | BETA: splitting (93) gives: % 19.84/3.68 | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | Case 1: % 19.84/3.68 | | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | | (94) all_194_1 = 0 & apart_point_and_line(all_17_4, % 19.84/3.68 | | | | | | | | | | | | | | all_17_2) = 0 % 19.84/3.68 | | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | | ALPHA: (94) implies: % 19.84/3.68 | | | | | | | | | | | | | | (95) apart_point_and_line(all_17_4, all_17_2) = 0 % 19.84/3.68 | | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_27_0, 0, all_17_2, % 19.84/3.68 | | | | | | | | | | | | | | all_17_4, simplifying with (44), (95) gives: % 19.84/3.68 | | | | | | | | | | | | | | (96) all_27_0 = 0 % 19.84/3.68 | | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | | REDUCE: (55), (96) imply: % 19.84/3.68 | | | | | | | | | | | | | | (97) $false % 19.84/3.68 | | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | | CLOSE: (97) is inconsistent. % 19.84/3.68 | | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | Case 2: % 19.84/3.68 | | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | | (98) ~ (all_194_2 = 0) & distinct_lines(all_17_2, % 19.84/3.68 | | | | | | | | | | | | | | all_17_1) = all_194_2 % 19.84/3.68 | | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | | ALPHA: (98) implies: % 19.84/3.68 | | | | | | | | | | | | | | (99) ~ (all_194_2 = 0) % 19.84/3.68 | | | | | | | | | | | | | | (100) distinct_lines(all_17_2, all_17_1) = all_194_2 % 19.84/3.68 | | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_186_2, all_194_2, % 19.84/3.68 | | | | | | | | | | | | | | all_17_1, all_17_2, simplifying with (90), (100) % 19.84/3.68 | | | | | | | | | | | | | | gives: % 19.84/3.68 | | | | | | | | | | | | | | (101) all_194_2 = all_186_2 % 19.84/3.68 | | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | | REDUCE: (99), (101) imply: % 19.84/3.68 | | | | | | | | | | | | | | (102) ~ (all_186_2 = 0) % 19.84/3.68 | | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_17_3, all_17_2, % 19.84/3.68 | | | | | | | | | | | | | | all_17_1, all_186_2, simplifying with (17), (18), % 19.84/3.68 | | | | | | | | | | | | | | (21), (52), (90) gives: % 19.84/3.68 | | | | | | | | | | | | | | (103) all_186_2 = 0 | apart_point_and_line(all_17_3, % 19.84/3.68 | | | | | | | | | | | | | | all_17_1) = 0 % 19.84/3.68 | | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | | BETA: splitting (103) gives: % 19.84/3.68 | | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | | Case 1: % 19.84/3.68 | | | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | | | (104) apart_point_and_line(all_17_3, all_17_1) = 0 % 19.84/3.68 | | | | | | | | | | | | | | | % 19.84/3.68 | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_24_0, 0, all_17_1, % 19.84/3.68 | | | | | | | | | | | | | | | all_17_3, simplifying with (62), (104) gives: % 19.84/3.69 | | | | | | | | | | | | | | | (105) all_24_0 = 0 % 19.84/3.69 | | | | | | | | | | | | | | | % 19.84/3.69 | | | | | | | | | | | | | | | REDUCE: (61), (105) imply: % 19.84/3.69 | | | | | | | | | | | | | | | (106) $false % 19.84/3.69 | | | | | | | | | | | | | | | % 19.84/3.69 | | | | | | | | | | | | | | | CLOSE: (106) is inconsistent. % 19.84/3.69 | | | | | | | | | | | | | | | % 19.84/3.69 | | | | | | | | | | | | | | Case 2: % 19.84/3.69 | | | | | | | | | | | | | | | % 19.84/3.69 | | | | | | | | | | | | | | | (107) all_186_2 = 0 % 19.84/3.69 | | | | | | | | | | | | | | | % 19.84/3.69 | | | | | | | | | | | | | | | REDUCE: (102), (107) imply: % 19.84/3.69 | | | | | | | | | | | | | | | (108) $false % 19.84/3.69 | | | | | | | | | | | | | | | % 19.84/3.69 | | | | | | | | | | | | | | | CLOSE: (108) is inconsistent. % 19.84/3.69 | | | | | | | | | | | | | | | % 19.84/3.69 | | | | | | | | | | | | | | End of split % 19.84/3.69 | | | | | | | | | | | | | | % 19.84/3.69 | | | | | | | | | | | | | End of split % 19.84/3.69 | | | | | | | | | | | | | % 19.84/3.69 | | | | | | | | | | | | End of split % 19.84/3.69 | | | | | | | | | | | | % 19.84/3.69 | | | | | | | | | | | Case 2: % 19.84/3.69 | | | | | | | | | | | | % 19.84/3.69 | | | | | | | | | | | | (109) ~ (all_186_3 = 0) & distinct_points(all_17_5, % 19.84/3.69 | | | | | | | | | | | | all_17_4) = all_186_3 % 19.84/3.69 | | | | | | | | | | | | % 19.84/3.69 | | | | | | | | | | | | ALPHA: (109) implies: % 19.84/3.69 | | | | | | | | | | | | (110) ~ (all_186_3 = 0) % 19.84/3.69 | | | | | | | | | | | | (111) distinct_points(all_17_5, all_17_4) = all_186_3 % 19.84/3.69 | | | | | | | | | | | | % 19.84/3.69 | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_186_3, all_17_4, % 19.84/3.69 | | | | | | | | | | | | all_17_5, simplifying with (19), (111) gives: % 19.84/3.69 | | | | | | | | | | | | (112) all_186_3 = 0 % 19.84/3.69 | | | | | | | | | | | | % 19.84/3.69 | | | | | | | | | | | | REDUCE: (110), (112) imply: % 19.84/3.69 | | | | | | | | | | | | (113) $false % 19.84/3.69 | | | | | | | | | | | | % 19.84/3.69 | | | | | | | | | | | | CLOSE: (113) is inconsistent. % 19.84/3.69 | | | | | | | | | | | | % 19.84/3.69 | | | | | | | | | | | End of split % 19.84/3.69 | | | | | | | | | | | % 19.84/3.69 | | | | | | | | | | End of split % 19.84/3.69 | | | | | | | | | | % 19.84/3.69 | | | | | | | | | End of split % 19.84/3.69 | | | | | | | | | % 19.84/3.69 | | | | | | | | End of split % 19.84/3.69 | | | | | | | | % 19.84/3.69 | | | | | | | End of split % 19.84/3.69 | | | | | | | % 19.84/3.69 | | | | | | End of split % 19.84/3.69 | | | | | | % 19.84/3.69 | | | | | Case 2: % 19.84/3.69 | | | | | | % 19.84/3.69 | | | | | | (114) ~ (all_25_1 = 0) & distinct_points(all_17_3, all_17_4) = % 19.84/3.69 | | | | | | all_25_1 % 19.84/3.69 | | | | | | % 19.84/3.69 | | | | | | ALPHA: (114) implies: % 19.84/3.69 | | | | | | (115) ~ (all_25_1 = 0) % 19.84/3.69 | | | | | | (116) distinct_points(all_17_3, all_17_4) = all_25_1 % 19.84/3.69 | | | | | | % 19.84/3.69 | | | | | | GROUND_INST: instantiating (9) with 0, all_25_1, all_17_4, all_17_3, % 19.84/3.69 | | | | | | simplifying with (63), (116) gives: % 19.84/3.69 | | | | | | (117) all_25_1 = 0 % 19.84/3.69 | | | | | | % 19.84/3.69 | | | | | | REDUCE: (115), (117) imply: % 19.84/3.69 | | | | | | (118) $false % 19.84/3.69 | | | | | | % 19.84/3.69 | | | | | | CLOSE: (118) is inconsistent. % 19.84/3.69 | | | | | | % 19.84/3.69 | | | | | End of split % 19.84/3.69 | | | | | % 19.84/3.69 | | | | Case 2: % 19.84/3.69 | | | | | % 19.84/3.69 | | | | | (119) all_27_0 = 0 % 19.84/3.69 | | | | | % 19.84/3.69 | | | | | REDUCE: (55), (119) imply: % 19.84/3.69 | | | | | (120) $false % 19.84/3.69 | | | | | % 19.84/3.69 | | | | | CLOSE: (120) is inconsistent. % 19.84/3.69 | | | | | % 19.84/3.69 | | | | End of split % 19.84/3.69 | | | | % 19.84/3.69 | | | Case 2: % 19.84/3.69 | | | | % 19.84/3.69 | | | | (121) ~ (all_24_1 = 0) & distinct_points(all_17_3, all_17_4) = % 19.84/3.69 | | | | all_24_1 % 19.84/3.69 | | | | % 19.84/3.69 | | | | ALPHA: (121) implies: % 19.84/3.69 | | | | (122) ~ (all_24_1 = 0) % 19.84/3.69 | | | | (123) distinct_points(all_17_3, all_17_4) = all_24_1 % 19.84/3.69 | | | | % 19.84/3.69 | | | | BETA: splitting (58) gives: % 19.84/3.69 | | | | % 19.84/3.69 | | | | Case 1: % 19.84/3.69 | | | | | % 19.84/3.69 | | | | | (124) distinct_points(all_17_3, all_17_4) = 0 % 19.84/3.69 | | | | | % 19.84/3.69 | | | | | GROUND_INST: instantiating (9) with 0, all_24_1, all_17_4, all_17_3, % 19.84/3.69 | | | | | simplifying with (123), (124) gives: % 19.84/3.69 | | | | | (125) all_24_1 = 0 % 19.84/3.69 | | | | | % 19.84/3.69 | | | | | REDUCE: (122), (125) imply: % 19.84/3.69 | | | | | (126) $false % 19.84/3.69 | | | | | % 19.84/3.69 | | | | | CLOSE: (126) is inconsistent. % 19.84/3.69 | | | | | % 19.84/3.69 | | | | Case 2: % 19.84/3.69 | | | | | % 19.84/3.69 | | | | | (127) all_27_0 = 0 % 19.84/3.69 | | | | | % 19.84/3.69 | | | | | REDUCE: (55), (127) imply: % 19.84/3.69 | | | | | (128) $false % 19.84/3.69 | | | | | % 19.84/3.69 | | | | | CLOSE: (128) is inconsistent. % 19.84/3.69 | | | | | % 19.84/3.69 | | | | End of split % 19.84/3.69 | | | | % 19.84/3.69 | | | End of split % 19.84/3.69 | | | % 19.84/3.69 | | Case 2: % 19.84/3.69 | | | % 19.84/3.69 | | | (129) ~ (all_26_1 = 0) & distinct_points(all_17_5, all_17_4) = % 19.84/3.69 | | | all_26_1 % 19.84/3.69 | | | % 19.84/3.69 | | | ALPHA: (129) implies: % 19.84/3.69 | | | (130) ~ (all_26_1 = 0) % 19.84/3.70 | | | (131) distinct_points(all_17_5, all_17_4) = all_26_1 % 19.84/3.70 | | | % 19.84/3.70 | | | GROUND_INST: instantiating (9) with 0, all_26_1, all_17_4, all_17_5, % 19.84/3.70 | | | simplifying with (19), (131) gives: % 19.84/3.70 | | | (132) all_26_1 = 0 % 19.84/3.70 | | | % 19.84/3.70 | | | REDUCE: (130), (132) imply: % 19.84/3.70 | | | (133) $false % 19.84/3.70 | | | % 19.84/3.70 | | | CLOSE: (133) is inconsistent. % 19.84/3.70 | | | % 19.84/3.70 | | End of split % 19.84/3.70 | | % 19.84/3.70 | Case 2: % 19.84/3.70 | | % 19.84/3.70 | | (134) ~ (all_27_1 = 0) & distinct_points(all_17_5, all_17_4) = all_27_1 % 19.84/3.70 | | % 19.84/3.70 | | ALPHA: (134) implies: % 19.84/3.70 | | (135) ~ (all_27_1 = 0) % 19.84/3.70 | | (136) distinct_points(all_17_5, all_17_4) = all_27_1 % 19.84/3.70 | | % 19.84/3.70 | | GROUND_INST: instantiating (9) with 0, all_27_1, all_17_4, all_17_5, % 19.84/3.70 | | simplifying with (19), (136) gives: % 19.84/3.70 | | (137) all_27_1 = 0 % 19.84/3.70 | | % 19.84/3.70 | | REDUCE: (135), (137) imply: % 19.84/3.70 | | (138) $false % 19.84/3.70 | | % 19.84/3.70 | | CLOSE: (138) is inconsistent. % 19.84/3.70 | | % 19.84/3.70 | End of split % 19.84/3.70 | % 19.84/3.70 End of proof % 19.84/3.70 % 19.84/3.70 Sub-proof #1 shows that the following formulas are inconsistent: % 19.84/3.70 ---------------------------------------------------------------- % 19.84/3.70 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 19.84/3.70 ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 19.84/3.70 (apart_point_and_line(v3, v2) = v0)) % 19.84/3.70 (2) apart_point_and_line(all_17_4, all_17_1) = all_25_0 % 19.84/3.70 (3) apart_point_and_line(all_17_4, all_17_1) = 0 % 19.84/3.70 (4) ~ (all_25_0 = 0) % 19.84/3.70 % 19.84/3.70 Begin of proof % 19.84/3.70 | % 19.84/3.70 | GROUND_INST: instantiating (1) with 0, all_25_0, all_17_1, all_17_4, % 19.84/3.70 | simplifying with (2), (3) gives: % 19.84/3.70 | (5) all_25_0 = 0 % 19.84/3.70 | % 19.84/3.70 | REDUCE: (4), (5) imply: % 19.84/3.70 | (6) $false % 19.84/3.70 | % 19.84/3.70 | CLOSE: (6) is inconsistent. % 19.84/3.70 | % 19.84/3.70 End of proof % 19.84/3.70 % SZS output end Proof for theBenchmark % 19.84/3.70 % 19.84/3.70 3076ms %------------------------------------------------------------------------------