%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO193+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n028.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 23:22:06 EDT 2023 % Result : Theorem 21.45s 3.57s % Output : Proof 51.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO193+3 : TPTP v8.1.2. Released v4.0.0. % 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n028.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 20:26:41 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.15/1.08 Prover 1: Preprocessing ... % 3.15/1.10 Prover 4: Preprocessing ... % 3.15/1.14 Prover 2: Preprocessing ... % 3.15/1.14 Prover 5: Preprocessing ... % 3.15/1.14 Prover 6: Preprocessing ... % 3.15/1.14 Prover 0: Preprocessing ... % 3.15/1.14 Prover 3: Preprocessing ... % 6.27/1.56 Prover 5: Proving ... % 6.27/1.57 Prover 2: Proving ... % 6.27/1.59 Prover 1: Constructing countermodel ... % 6.98/1.63 Prover 6: Constructing countermodel ... % 6.98/1.65 Prover 3: Constructing countermodel ... % 7.55/1.76 Prover 3: gave up % 8.24/1.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.24/1.85 Prover 7: Preprocessing ... % 8.24/1.85 Prover 6: gave up % 8.64/1.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.85/1.90 Prover 1: gave up % 8.85/1.90 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 8.85/1.92 Prover 4: Constructing countermodel ... % 8.85/1.93 Prover 8: Preprocessing ... % 8.85/1.94 Prover 7: Warning: ignoring some quantifiers % 8.85/1.95 Prover 9: Preprocessing ... % 8.85/1.95 Prover 0: Proving ... % 9.59/1.98 Prover 7: Constructing countermodel ... % 10.59/2.13 Prover 8: Warning: ignoring some quantifiers % 10.59/2.15 Prover 8: Constructing countermodel ... % 11.15/2.24 Prover 9: Constructing countermodel ... % 12.26/2.32 Prover 8: gave up % 12.26/2.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.26/2.34 Prover 7: gave up % 12.26/2.34 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.59/2.38 Prover 10: Preprocessing ... % 12.59/2.39 Prover 11: Preprocessing ... % 13.23/2.47 Prover 10: Warning: ignoring some quantifiers % 13.23/2.48 Prover 10: Constructing countermodel ... % 15.32/2.73 Prover 10: gave up % 15.32/2.74 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 15.32/2.75 Prover 11: Constructing countermodel ... % 15.55/2.77 Prover 12: Preprocessing ... % 16.45/2.88 Prover 12: Proving ... % 21.45/3.57 Prover 0: proved (2951ms) % 21.45/3.57 % 21.45/3.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.45/3.57 % 21.45/3.57 Prover 9: proved (1670ms) % 21.45/3.57 % 21.45/3.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.45/3.57 % 21.45/3.58 Prover 2: stopped % 21.45/3.58 Prover 12: stopped % 21.94/3.60 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 21.94/3.60 Prover 5: stopped % 21.94/3.60 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 21.94/3.60 Prover 13: Preprocessing ... % 21.94/3.60 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 21.94/3.63 Prover 13: Warning: ignoring some quantifiers % 21.94/3.63 Prover 16: Preprocessing ... % 21.94/3.63 Prover 19: Preprocessing ... % 21.94/3.63 Prover 13: Constructing countermodel ... % 21.94/3.67 Prover 16: Warning: ignoring some quantifiers % 21.94/3.68 Prover 16: Constructing countermodel ... % 22.89/3.73 Prover 19: Warning: ignoring some quantifiers % 22.89/3.74 Prover 19: Constructing countermodel ... % 23.61/3.85 Prover 13: gave up % 23.89/3.89 Prover 19: gave up % 28.01/4.53 Prover 16: gave up % 50.18/8.94 Prover 11: Found proof (size 176) % 50.18/8.94 Prover 11: proved (6607ms) % 50.18/8.95 Prover 4: stopped % 50.18/8.95 % 50.18/8.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 50.18/8.95 % 50.18/8.96 % SZS output start Proof for theBenchmark % 50.18/8.97 Assumptions after simplification: % 50.18/8.97 --------------------------------- % 50.18/8.97 % 50.18/8.97 (apart3) % 50.80/9.01 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 50.80/9.01 % 50.80/9.01 (ceq1) % 50.80/9.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 50.80/9.01 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ % 50.80/9.01 (distinct_points(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 50.80/9.02 int] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : % 50.80/9.02 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 50.80/9.02 (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) % 50.80/9.02 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) & ! [v0: % 50.80/9.02 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 50.80/9.02 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~ % 50.80/9.02 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0) % 50.80/9.02 % 50.80/9.02 (ceq3) % 50.80/9.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 50.80/9.02 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) % 50.80/9.02 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 50.80/9.02 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 50.80/9.02 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 50.80/9.02 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 50.80/9.02 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 50.80/9.02 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ % 50.80/9.02 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 50.80/9.02 convergent_lines(v0, v2) = 0) % 50.80/9.02 % 50.80/9.02 (ci3) % 50.80/9.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 50.80/9.02 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 50.80/9.02 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 50.80/9.02 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 50.80/9.02 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 50.80/9.02 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 50.80/9.02 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 50.80/9.02 % 50.80/9.02 (ci4) % 50.80/9.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 50.80/9.03 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 50.80/9.03 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 50.80/9.03 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 50.80/9.03 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 50.80/9.03 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 50.80/9.03 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 50.80/9.03 % 50.80/9.03 (con) % 50.80/9.03 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 50.80/9.03 int] : ( ~ (v5 = 0) & intersection_point(v2, v1) = v4 & % 50.80/9.03 intersection_point(v0, v1) = v3 & apart_point_and_line(v4, v0) = v5 & % 50.80/9.03 apart_point_and_line(v3, v2) = 0 & convergent_lines(v2, v1) = 0 & % 50.80/9.03 convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0 & $i(v4) & % 50.80/9.03 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 50.80/9.03 % 50.80/9.03 (cu1) % 50.98/9.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 50.98/9.04 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 50.98/9.04 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 50.98/9.04 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 50.98/9.04 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 50.98/9.04 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, % 50.98/9.04 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 50.98/9.04 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, % 50.98/9.04 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ % 50.98/9.04 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 50.98/9.04 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 50.98/9.04 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0, % 50.98/9.04 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 50.98/9.04 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 50.98/9.04 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 50.98/9.04 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 50.98/9.04 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 50.98/9.04 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 50.98/9.04 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 50.98/9.04 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 50.98/9.04 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 50.98/9.04 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 50.98/9.04 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 50.98/9.04 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 50.98/9.04 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 50.98/9.04 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 50.98/9.04 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 50.98/9.04 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 50.98/9.04 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 50.98/9.04 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~ % 50.98/9.04 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 50.98/9.04 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 50.98/9.04 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, % 50.98/9.04 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 50.98/9.04 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, % 50.98/9.04 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 50.98/9.04 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 50.98/9.04 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 50.98/9.04 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1, % 50.98/9.04 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i] % 50.98/9.04 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | % 50.98/9.04 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 50.98/9.04 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = % 50.98/9.04 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 50.98/9.04 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0, % 50.98/9.04 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 50.98/9.04 % 50.98/9.04 (function-axioms) % 50.98/9.05 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 50.98/9.05 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 50.98/9.05 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 50.98/9.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 50.98/9.05 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 50.98/9.05 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 50.98/9.05 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 50.98/9.05 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 50.98/9.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 50.98/9.05 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 50.98/9.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 50.98/9.05 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 50.98/9.05 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 50.98/9.05 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 50.98/9.05 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 50.98/9.05 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 50.98/9.05 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 50.98/9.05 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 50.98/9.05 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 50.98/9.05 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 50.98/9.05 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 50.98/9.05 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 50.98/9.05 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 50.98/9.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 50.98/9.05 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 50.98/9.05 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 50.98/9.05 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 50.98/9.05 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 50.98/9.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 50.98/9.05 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 50.98/9.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 50.98/9.05 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 50.98/9.05 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 50.98/9.05 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 50.98/9.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 50.98/9.05 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 50.98/9.05 % 50.98/9.05 Further assumptions not needed in the proof: % 50.98/9.05 -------------------------------------------- % 50.98/9.05 a3, a4, a5, apart1, apart2, apart4, apart5, ax1, ax2, ax6, ceq2, ci1, ci2, % 50.98/9.05 coipo1, con1, cotno1, couo1, cp1, cp2, cup1, int1, oac1, occu1, ooc1, ooc2, % 50.98/9.05 orth1, ouo1, p1, par1 % 50.98/9.05 % 50.98/9.05 Those formulas are unsatisfiable: % 50.98/9.05 --------------------------------- % 50.98/9.05 % 50.98/9.05 Begin of proof % 50.98/9.05 | % 50.98/9.05 | ALPHA: (ci3) implies: % 50.98/9.05 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 50.98/9.05 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 50.98/9.05 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 50.98/9.05 | & $i(v2))) % 50.98/9.06 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 50.98/9.06 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 50.98/9.06 | (( ~ (v4 = 0) & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 50.98/9.06 | convergent_lines(v0, v1) = v3))) % 50.98/9.06 | % 50.98/9.06 | ALPHA: (ci4) implies: % 50.98/9.06 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 50.98/9.06 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 50.98/9.06 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 50.98/9.06 | & $i(v2))) % 50.98/9.06 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 50.98/9.06 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 50.98/9.06 | (( ~ (v4 = 0) & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 50.98/9.06 | convergent_lines(v0, v1) = v3))) % 50.98/9.06 | % 50.98/9.06 | ALPHA: (cu1) implies: % 50.98/9.06 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 50.98/9.06 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 50.98/9.06 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 50.98/9.06 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 50.98/9.06 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 50.98/9.06 | apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & % 50.98/9.06 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 50.98/9.06 | v1) = v6))) % 50.98/9.06 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 50.98/9.06 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 50.98/9.06 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 50.98/9.06 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 50.98/9.06 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 50.98/9.06 | apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & % 50.98/9.06 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 50.98/9.06 | v1) = v6))) % 50.98/9.06 | % 50.98/9.06 | ALPHA: (ceq1) implies: % 50.98/9.06 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 50.98/9.06 | (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, % 50.98/9.06 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 50.98/9.06 | distinct_points(v0, v2) = 0) % 50.98/9.06 | % 50.98/9.06 | ALPHA: (ceq3) implies: % 50.98/9.06 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 50.98/9.06 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | % 50.98/9.06 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 50.98/9.06 | % 50.98/9.06 | ALPHA: (function-axioms) implies: % 50.98/9.06 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 50.98/9.06 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 50.98/9.06 | (distinct_points(v3, v2) = v0)) % 50.98/9.06 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 50.98/9.06 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 50.98/9.06 | (distinct_lines(v3, v2) = v0)) % 50.98/9.06 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 50.98/9.06 | : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 50.98/9.06 | (convergent_lines(v3, v2) = v0)) % 50.98/9.06 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 50.98/9.06 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 50.98/9.06 | (apart_point_and_line(v3, v2) = v0)) % 50.98/9.07 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 50.98/9.07 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 50.98/9.07 | v0)) % 50.98/9.07 | % 50.98/9.07 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 50.98/9.07 | all_38_3, all_38_4, all_38_5 gives: % 50.98/9.07 | (14) ~ (all_38_0 = 0) & intersection_point(all_38_3, all_38_4) = all_38_1 % 50.98/9.07 | & intersection_point(all_38_5, all_38_4) = all_38_2 & % 50.98/9.07 | apart_point_and_line(all_38_1, all_38_5) = all_38_0 & % 50.98/9.07 | apart_point_and_line(all_38_2, all_38_3) = 0 & % 50.98/9.07 | convergent_lines(all_38_3, all_38_4) = 0 & convergent_lines(all_38_5, % 50.98/9.07 | all_38_3) = 0 & convergent_lines(all_38_5, all_38_4) = 0 & % 50.98/9.07 | $i(all_38_1) & $i(all_38_2) & $i(all_38_3) & $i(all_38_4) & % 50.98/9.07 | $i(all_38_5) % 50.98/9.07 | % 50.98/9.07 | ALPHA: (14) implies: % 50.98/9.07 | (15) ~ (all_38_0 = 0) % 50.98/9.07 | (16) $i(all_38_5) % 50.98/9.07 | (17) $i(all_38_4) % 50.98/9.07 | (18) $i(all_38_3) % 50.98/9.07 | (19) convergent_lines(all_38_5, all_38_4) = 0 % 50.98/9.07 | (20) convergent_lines(all_38_5, all_38_3) = 0 % 50.98/9.07 | (21) convergent_lines(all_38_3, all_38_4) = 0 % 50.98/9.07 | (22) apart_point_and_line(all_38_2, all_38_3) = 0 % 50.98/9.07 | (23) apart_point_and_line(all_38_1, all_38_5) = all_38_0 % 50.98/9.07 | (24) intersection_point(all_38_5, all_38_4) = all_38_2 % 50.98/9.07 | (25) intersection_point(all_38_3, all_38_4) = all_38_1 % 50.98/9.07 | % 50.98/9.07 | GROUND_INST: instantiating (3) with all_38_5, all_38_4, simplifying with (16), % 50.98/9.07 | (17), (19) gives: % 50.98/9.07 | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 50.98/9.07 | intersection_point(all_38_5, all_38_4) = v0 & % 50.98/9.07 | apart_point_and_line(v0, all_38_4) = v1 & $i(v0)) % 50.98/9.07 | % 50.98/9.07 | GROUND_INST: instantiating (1) with all_38_5, all_38_4, simplifying with (16), % 50.98/9.07 | (17), (19) gives: % 50.98/9.07 | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 50.98/9.07 | intersection_point(all_38_5, all_38_4) = v0 & % 50.98/9.07 | apart_point_and_line(v0, all_38_5) = v1 & $i(v0)) % 50.98/9.07 | % 50.98/9.07 | GROUND_INST: instantiating (3) with all_38_5, all_38_3, simplifying with (16), % 50.98/9.07 | (18), (20) gives: % 50.98/9.07 | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 50.98/9.07 | intersection_point(all_38_5, all_38_3) = v0 & % 50.98/9.07 | apart_point_and_line(v0, all_38_3) = v1 & $i(v0)) % 50.98/9.07 | % 50.98/9.07 | GROUND_INST: instantiating (1) with all_38_5, all_38_3, simplifying with (16), % 50.98/9.07 | (18), (20) gives: % 50.98/9.07 | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 50.98/9.07 | intersection_point(all_38_5, all_38_3) = v0 & % 50.98/9.07 | apart_point_and_line(v0, all_38_5) = v1 & $i(v0)) % 50.98/9.07 | % 50.98/9.07 | GROUND_INST: instantiating (3) with all_38_3, all_38_4, simplifying with (17), % 50.98/9.07 | (18), (21) gives: % 50.98/9.07 | (30) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 50.98/9.07 | intersection_point(all_38_3, all_38_4) = v0 & % 50.98/9.07 | apart_point_and_line(v0, all_38_4) = v1 & $i(v0)) % 50.98/9.07 | % 50.98/9.07 | GROUND_INST: instantiating (1) with all_38_3, all_38_4, simplifying with (17), % 50.98/9.07 | (18), (21) gives: % 51.19/9.08 | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 51.19/9.08 | intersection_point(all_38_3, all_38_4) = v0 & % 51.19/9.08 | apart_point_and_line(v0, all_38_3) = v1 & $i(v0)) % 51.19/9.08 | % 51.19/9.08 | GROUND_INST: instantiating (4) with all_38_5, all_38_4, all_38_2, simplifying % 51.19/9.08 | with (16), (17), (24) gives: % 51.19/9.08 | (32) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 51.19/9.08 | apart_point_and_line(all_38_2, all_38_4) = v1) | ( ~ (v0 = 0) & % 51.19/9.08 | convergent_lines(all_38_5, all_38_4) = v0)) % 51.19/9.08 | % 51.19/9.08 | GROUND_INST: instantiating (2) with all_38_5, all_38_4, all_38_2, simplifying % 51.19/9.08 | with (16), (17), (24) gives: % 51.19/9.08 | (33) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 51.19/9.08 | apart_point_and_line(all_38_2, all_38_5) = v1) | ( ~ (v0 = 0) & % 51.19/9.08 | convergent_lines(all_38_5, all_38_4) = v0)) % 51.19/9.08 | % 51.19/9.08 | GROUND_INST: instantiating (4) with all_38_3, all_38_4, all_38_1, simplifying % 51.19/9.08 | with (17), (18), (25) gives: % 51.19/9.08 | (34) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 51.19/9.08 | apart_point_and_line(all_38_1, all_38_4) = v1) | ( ~ (v0 = 0) & % 51.19/9.08 | convergent_lines(all_38_3, all_38_4) = v0)) % 51.19/9.08 | % 51.19/9.08 | GROUND_INST: instantiating (2) with all_38_3, all_38_4, all_38_1, simplifying % 51.19/9.08 | with (17), (18), (25) gives: % 51.19/9.08 | (35) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 51.19/9.08 | apart_point_and_line(all_38_1, all_38_3) = v1) | ( ~ (v0 = 0) & % 51.19/9.08 | convergent_lines(all_38_3, all_38_4) = v0)) % 51.19/9.08 | % 51.19/9.08 | DELTA: instantiating (32) with fresh symbols all_53_0, all_53_1 gives: % 51.19/9.08 | (36) ( ~ (all_53_0 = 0) & apart_point_and_line(all_38_2, all_38_4) = % 51.19/9.08 | all_53_0) | ( ~ (all_53_1 = 0) & convergent_lines(all_38_5, % 51.19/9.08 | all_38_4) = all_53_1) % 51.19/9.08 | % 51.19/9.08 | DELTA: instantiating (31) with fresh symbols all_54_0, all_54_1 gives: % 51.19/9.08 | (37) ~ (all_54_0 = 0) & intersection_point(all_38_3, all_38_4) = all_54_1 % 51.19/9.08 | & apart_point_and_line(all_54_1, all_38_3) = all_54_0 & $i(all_54_1) % 51.19/9.08 | % 51.19/9.08 | ALPHA: (37) implies: % 51.19/9.08 | (38) $i(all_54_1) % 51.19/9.08 | (39) apart_point_and_line(all_54_1, all_38_3) = all_54_0 % 51.19/9.08 | (40) intersection_point(all_38_3, all_38_4) = all_54_1 % 51.19/9.08 | % 51.19/9.08 | DELTA: instantiating (29) with fresh symbols all_56_0, all_56_1 gives: % 51.19/9.08 | (41) ~ (all_56_0 = 0) & intersection_point(all_38_5, all_38_3) = all_56_1 % 51.19/9.08 | & apart_point_and_line(all_56_1, all_38_5) = all_56_0 & $i(all_56_1) % 51.19/9.08 | % 51.19/9.08 | ALPHA: (41) implies: % 51.19/9.08 | (42) ~ (all_56_0 = 0) % 51.19/9.08 | (43) apart_point_and_line(all_56_1, all_38_5) = all_56_0 % 51.19/9.08 | (44) intersection_point(all_38_5, all_38_3) = all_56_1 % 51.19/9.08 | % 51.19/9.08 | DELTA: instantiating (26) with fresh symbols all_58_0, all_58_1 gives: % 51.19/9.08 | (45) ~ (all_58_0 = 0) & intersection_point(all_38_5, all_38_4) = all_58_1 % 51.19/9.08 | & apart_point_and_line(all_58_1, all_38_4) = all_58_0 & $i(all_58_1) % 51.19/9.08 | % 51.19/9.08 | ALPHA: (45) implies: % 51.19/9.08 | (46) ~ (all_58_0 = 0) % 51.19/9.08 | (47) $i(all_58_1) % 51.19/9.08 | (48) apart_point_and_line(all_58_1, all_38_4) = all_58_0 % 51.19/9.08 | (49) intersection_point(all_38_5, all_38_4) = all_58_1 % 51.19/9.08 | % 51.19/9.08 | DELTA: instantiating (30) with fresh symbols all_60_0, all_60_1 gives: % 51.19/9.08 | (50) ~ (all_60_0 = 0) & intersection_point(all_38_3, all_38_4) = all_60_1 % 51.19/9.08 | & apart_point_and_line(all_60_1, all_38_4) = all_60_0 & $i(all_60_1) % 51.19/9.08 | % 51.19/9.08 | ALPHA: (50) implies: % 51.19/9.08 | (51) apart_point_and_line(all_60_1, all_38_4) = all_60_0 % 51.19/9.08 | (52) intersection_point(all_38_3, all_38_4) = all_60_1 % 51.19/9.08 | % 51.19/9.08 | DELTA: instantiating (28) with fresh symbols all_62_0, all_62_1 gives: % 51.19/9.08 | (53) ~ (all_62_0 = 0) & intersection_point(all_38_5, all_38_3) = all_62_1 % 51.19/9.08 | & apart_point_and_line(all_62_1, all_38_3) = all_62_0 & $i(all_62_1) % 51.19/9.08 | % 51.19/9.08 | ALPHA: (53) implies: % 51.19/9.08 | (54) $i(all_62_1) % 51.19/9.08 | (55) intersection_point(all_38_5, all_38_3) = all_62_1 % 51.19/9.08 | % 51.19/9.08 | DELTA: instantiating (27) with fresh symbols all_64_0, all_64_1 gives: % 51.19/9.09 | (56) ~ (all_64_0 = 0) & intersection_point(all_38_5, all_38_4) = all_64_1 % 51.19/9.09 | & apart_point_and_line(all_64_1, all_38_5) = all_64_0 & $i(all_64_1) % 51.19/9.09 | % 51.19/9.09 | ALPHA: (56) implies: % 51.19/9.09 | (57) apart_point_and_line(all_64_1, all_38_5) = all_64_0 % 51.19/9.09 | (58) intersection_point(all_38_5, all_38_4) = all_64_1 % 51.19/9.09 | % 51.19/9.09 | DELTA: instantiating (35) with fresh symbols all_66_0, all_66_1 gives: % 51.19/9.09 | (59) ( ~ (all_66_0 = 0) & apart_point_and_line(all_38_1, all_38_3) = % 51.19/9.09 | all_66_0) | ( ~ (all_66_1 = 0) & convergent_lines(all_38_3, % 51.19/9.09 | all_38_4) = all_66_1) % 51.19/9.09 | % 51.19/9.09 | DELTA: instantiating (34) with fresh symbols all_67_0, all_67_1 gives: % 51.19/9.09 | (60) ( ~ (all_67_0 = 0) & apart_point_and_line(all_38_1, all_38_4) = % 51.19/9.09 | all_67_0) | ( ~ (all_67_1 = 0) & convergent_lines(all_38_3, % 51.19/9.09 | all_38_4) = all_67_1) % 51.19/9.09 | % 51.19/9.09 | DELTA: instantiating (33) with fresh symbols all_68_0, all_68_1 gives: % 51.19/9.09 | (61) ( ~ (all_68_0 = 0) & apart_point_and_line(all_38_2, all_38_5) = % 51.19/9.09 | all_68_0) | ( ~ (all_68_1 = 0) & convergent_lines(all_38_5, % 51.19/9.09 | all_38_4) = all_68_1) % 51.19/9.09 | % 51.19/9.09 | BETA: splitting (59) gives: % 51.19/9.09 | % 51.19/9.09 | Case 1: % 51.19/9.09 | | % 51.19/9.09 | | (62) ~ (all_66_0 = 0) & apart_point_and_line(all_38_1, all_38_3) = % 51.19/9.09 | | all_66_0 % 51.19/9.09 | | % 51.19/9.09 | | ALPHA: (62) implies: % 51.19/9.09 | | (63) ~ (all_66_0 = 0) % 51.19/9.09 | | (64) apart_point_and_line(all_38_1, all_38_3) = all_66_0 % 51.19/9.09 | | % 51.19/9.09 | | BETA: splitting (61) gives: % 51.19/9.09 | | % 51.19/9.09 | | Case 1: % 51.19/9.09 | | | % 51.19/9.09 | | | (65) ~ (all_68_0 = 0) & apart_point_and_line(all_38_2, all_38_5) = % 51.19/9.09 | | | all_68_0 % 51.19/9.09 | | | % 51.19/9.09 | | | ALPHA: (65) implies: % 51.19/9.09 | | | (66) ~ (all_68_0 = 0) % 51.19/9.09 | | | (67) apart_point_and_line(all_38_2, all_38_5) = all_68_0 % 51.19/9.09 | | | % 51.19/9.09 | | | BETA: splitting (36) gives: % 51.19/9.09 | | | % 51.19/9.09 | | | Case 1: % 51.19/9.09 | | | | % 51.19/9.09 | | | | (68) ~ (all_53_0 = 0) & apart_point_and_line(all_38_2, all_38_4) = % 51.19/9.09 | | | | all_53_0 % 51.19/9.09 | | | | % 51.19/9.09 | | | | ALPHA: (68) implies: % 51.19/9.09 | | | | (69) apart_point_and_line(all_38_2, all_38_4) = all_53_0 % 51.19/9.09 | | | | % 51.19/9.09 | | | | BETA: splitting (60) gives: % 51.19/9.09 | | | | % 51.19/9.09 | | | | Case 1: % 51.19/9.09 | | | | | % 51.19/9.09 | | | | | (70) ~ (all_67_0 = 0) & apart_point_and_line(all_38_1, all_38_4) = % 51.19/9.09 | | | | | all_67_0 % 51.19/9.09 | | | | | % 51.19/9.09 | | | | | ALPHA: (70) implies: % 51.19/9.09 | | | | | (71) ~ (all_67_0 = 0) % 51.19/9.09 | | | | | (72) apart_point_and_line(all_38_1, all_38_4) = all_67_0 % 51.19/9.09 | | | | | % 51.19/9.09 | | | | | GROUND_INST: instantiating (13) with all_38_2, all_64_1, all_38_4, % 51.19/9.09 | | | | | all_38_5, simplifying with (24), (58) gives: % 51.19/9.09 | | | | | (73) all_64_1 = all_38_2 % 51.19/9.09 | | | | | % 51.19/9.09 | | | | | GROUND_INST: instantiating (13) with all_58_1, all_64_1, all_38_4, % 51.19/9.09 | | | | | all_38_5, simplifying with (49), (58) gives: % 51.19/9.09 | | | | | (74) all_64_1 = all_58_1 % 51.19/9.09 | | | | | % 51.19/9.09 | | | | | GROUND_INST: instantiating (13) with all_56_1, all_62_1, all_38_3, % 51.19/9.09 | | | | | all_38_5, simplifying with (44), (55) gives: % 51.19/9.09 | | | | | (75) all_62_1 = all_56_1 % 51.19/9.09 | | | | | % 51.19/9.09 | | | | | GROUND_INST: instantiating (13) with all_38_1, all_60_1, all_38_4, % 51.19/9.09 | | | | | all_38_3, simplifying with (25), (52) gives: % 51.19/9.09 | | | | | (76) all_60_1 = all_38_1 % 51.19/9.09 | | | | | % 51.19/9.09 | | | | | GROUND_INST: instantiating (13) with all_54_1, all_60_1, all_38_4, % 51.19/9.09 | | | | | all_38_3, simplifying with (40), (52) gives: % 51.19/9.09 | | | | | (77) all_60_1 = all_54_1 % 51.19/9.09 | | | | | % 51.19/9.09 | | | | | COMBINE_EQS: (73), (74) imply: % 51.19/9.09 | | | | | (78) all_58_1 = all_38_2 % 51.19/9.09 | | | | | % 51.19/9.09 | | | | | COMBINE_EQS: (76), (77) imply: % 51.19/9.09 | | | | | (79) all_54_1 = all_38_1 % 51.19/9.09 | | | | | % 51.19/9.09 | | | | | SIMP: (79) implies: % 51.19/9.09 | | | | | (80) all_54_1 = all_38_1 % 51.19/9.09 | | | | | % 51.19/9.09 | | | | | REDUCE: (57), (73) imply: % 51.19/9.09 | | | | | (81) apart_point_and_line(all_38_2, all_38_5) = all_64_0 % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | REDUCE: (51), (76) imply: % 51.19/9.10 | | | | | (82) apart_point_and_line(all_38_1, all_38_4) = all_60_0 % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | REDUCE: (48), (78) imply: % 51.19/9.10 | | | | | (83) apart_point_and_line(all_38_2, all_38_4) = all_58_0 % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | REDUCE: (39), (80) imply: % 51.19/9.10 | | | | | (84) apart_point_and_line(all_38_1, all_38_3) = all_54_0 % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | REDUCE: (54), (75) imply: % 51.19/9.10 | | | | | (85) $i(all_56_1) % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | REDUCE: (47), (78) imply: % 51.19/9.10 | | | | | (86) $i(all_38_2) % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | REDUCE: (38), (80) imply: % 51.19/9.10 | | | | | (87) $i(all_38_1) % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | GROUND_INST: instantiating (12) with all_68_0, all_64_0, all_38_5, % 51.19/9.10 | | | | | all_38_2, simplifying with (67), (81) gives: % 51.19/9.10 | | | | | (88) all_68_0 = all_64_0 % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | GROUND_INST: instantiating (12) with all_53_0, all_58_0, all_38_4, % 51.19/9.10 | | | | | all_38_2, simplifying with (69), (83) gives: % 51.19/9.10 | | | | | (89) all_58_0 = all_53_0 % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | GROUND_INST: instantiating (12) with all_67_0, all_60_0, all_38_4, % 51.19/9.10 | | | | | all_38_1, simplifying with (72), (82) gives: % 51.19/9.10 | | | | | (90) all_67_0 = all_60_0 % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | GROUND_INST: instantiating (12) with all_66_0, all_54_0, all_38_3, % 51.19/9.10 | | | | | all_38_1, simplifying with (64), (84) gives: % 51.19/9.10 | | | | | (91) all_66_0 = all_54_0 % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | REDUCE: (66), (88) imply: % 51.19/9.10 | | | | | (92) ~ (all_64_0 = 0) % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | REDUCE: (71), (90) imply: % 51.19/9.10 | | | | | (93) ~ (all_60_0 = 0) % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | REDUCE: (63), (91) imply: % 51.19/9.10 | | | | | (94) ~ (all_54_0 = 0) % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | REDUCE: (46), (89) imply: % 51.19/9.10 | | | | | (95) ~ (all_53_0 = 0) % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | GROUND_INST: instantiating (6) with all_38_2, all_38_1, all_38_4, % 51.19/9.10 | | | | | all_38_5, all_53_0, all_38_0, simplifying with (16), % 51.19/9.10 | | | | | (17), (23), (69), (86), (87) gives: % 51.19/9.10 | | | | | (96) all_53_0 = 0 | all_38_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 51.19/9.10 | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 51.19/9.10 | | | | | apart_point_and_line(all_38_1, all_38_4) = 0) | (v2 = 0 & % 51.19/9.10 | | | | | apart_point_and_line(all_38_2, all_38_5) = 0) | ( ~ (v1 = % 51.19/9.10 | | | | | 0) & distinct_lines(all_38_4, all_38_5) = v1) | ( ~ (v0 % 51.19/9.10 | | | | | = 0) & distinct_points(all_38_2, all_38_1) = v0)) % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | GROUND_INST: instantiating (5) with all_38_2, all_38_1, all_38_4, % 51.19/9.10 | | | | | all_38_5, all_64_0, all_60_0, simplifying with (16), % 51.19/9.10 | | | | | (17), (81), (82), (86), (87) gives: % 51.19/9.10 | | | | | (97) all_64_0 = 0 | all_60_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 51.19/9.10 | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 51.19/9.10 | | | | | apart_point_and_line(all_38_1, all_38_5) = 0) | (v2 = 0 & % 51.19/9.10 | | | | | apart_point_and_line(all_38_2, all_38_4) = 0) | ( ~ (v1 = % 51.19/9.10 | | | | | 0) & distinct_lines(all_38_4, all_38_5) = v1) | ( ~ (v0 % 51.19/9.10 | | | | | = 0) & distinct_points(all_38_2, all_38_1) = v0)) % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | GROUND_INST: instantiating (7) with all_38_2, all_38_3, all_38_1, % 51.19/9.10 | | | | | all_54_0, simplifying with (18), (22), (84), (86), (87) % 51.19/9.10 | | | | | gives: % 51.19/9.10 | | | | | (98) all_54_0 = 0 | distinct_points(all_38_2, all_38_1) = 0 % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | GROUND_INST: instantiating (5) with all_56_1, all_38_2, all_38_4, % 51.19/9.10 | | | | | all_38_5, all_56_0, all_53_0, simplifying with (16), % 51.19/9.10 | | | | | (17), (43), (69), (85), (86) gives: % 51.19/9.10 | | | | | (99) all_56_0 = 0 | all_53_0 = 0 | ? [v0: int] : ? [v1: int] : ? % 51.19/9.10 | | | | | [v2: int] : ? [v3: int] : ((v3 = 0 & % 51.19/9.10 | | | | | apart_point_and_line(all_38_2, all_38_5) = 0) | (v2 = 0 & % 51.19/9.10 | | | | | apart_point_and_line(all_56_1, all_38_4) = 0) | ( ~ (v1 = % 51.19/9.10 | | | | | 0) & distinct_lines(all_38_4, all_38_5) = v1) | ( ~ (v0 % 51.19/9.10 | | | | | = 0) & distinct_points(all_56_1, all_38_2) = v0)) % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | BETA: splitting (98) gives: % 51.19/9.10 | | | | | % 51.19/9.10 | | | | | Case 1: % 51.19/9.10 | | | | | | % 51.19/9.10 | | | | | | (100) distinct_points(all_38_2, all_38_1) = 0 % 51.19/9.10 | | | | | | % 51.19/9.10 | | | | | | BETA: splitting (96) gives: % 51.19/9.10 | | | | | | % 51.19/9.10 | | | | | | Case 1: % 51.19/9.10 | | | | | | | % 51.19/9.10 | | | | | | | (101) all_53_0 = 0 % 51.19/9.10 | | | | | | | % 51.19/9.10 | | | | | | | REDUCE: (95), (101) imply: % 51.19/9.11 | | | | | | | (102) $false % 51.19/9.11 | | | | | | | % 51.19/9.11 | | | | | | | CLOSE: (102) is inconsistent. % 51.19/9.11 | | | | | | | % 51.19/9.11 | | | | | | Case 2: % 51.19/9.11 | | | | | | | % 51.19/9.11 | | | | | | | (103) all_38_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] % 51.19/9.11 | | | | | | | : ? [v3: int] : ((v3 = 0 & % 51.19/9.11 | | | | | | | apart_point_and_line(all_38_1, all_38_4) = 0) | (v2 = % 51.19/9.11 | | | | | | | 0 & apart_point_and_line(all_38_2, all_38_5) = 0) | ( % 51.19/9.11 | | | | | | | ~ (v1 = 0) & distinct_lines(all_38_4, all_38_5) = v1) % 51.19/9.11 | | | | | | | | ( ~ (v0 = 0) & distinct_points(all_38_2, all_38_1) = % 51.19/9.11 | | | | | | | v0)) % 51.19/9.11 | | | | | | | % 51.19/9.11 | | | | | | | BETA: splitting (97) gives: % 51.19/9.11 | | | | | | | % 51.19/9.11 | | | | | | | Case 1: % 51.19/9.11 | | | | | | | | % 51.19/9.11 | | | | | | | | (104) all_64_0 = 0 % 51.19/9.11 | | | | | | | | % 51.19/9.11 | | | | | | | | REDUCE: (92), (104) imply: % 51.19/9.11 | | | | | | | | (105) $false % 51.19/9.11 | | | | | | | | % 51.19/9.11 | | | | | | | | CLOSE: (105) is inconsistent. % 51.19/9.11 | | | | | | | | % 51.19/9.11 | | | | | | | Case 2: % 51.19/9.11 | | | | | | | | % 51.19/9.11 | | | | | | | | (106) all_60_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 51.19/9.11 | | | | | | | | int] : ? [v3: int] : ((v3 = 0 & % 51.19/9.11 | | | | | | | | apart_point_and_line(all_38_1, all_38_5) = 0) | (v2 % 51.19/9.11 | | | | | | | | = 0 & apart_point_and_line(all_38_2, all_38_4) = 0) % 51.19/9.11 | | | | | | | | | ( ~ (v1 = 0) & distinct_lines(all_38_4, all_38_5) = % 51.19/9.11 | | | | | | | | v1) | ( ~ (v0 = 0) & distinct_points(all_38_2, % 51.19/9.11 | | | | | | | | all_38_1) = v0)) % 51.19/9.11 | | | | | | | | % 51.19/9.11 | | | | | | | | BETA: splitting (99) gives: % 51.19/9.11 | | | | | | | | % 51.19/9.11 | | | | | | | | Case 1: % 51.19/9.11 | | | | | | | | | % 51.19/9.11 | | | | | | | | | (107) all_56_0 = 0 % 51.19/9.11 | | | | | | | | | % 51.19/9.11 | | | | | | | | | REDUCE: (42), (107) imply: % 51.19/9.11 | | | | | | | | | (108) $false % 51.19/9.11 | | | | | | | | | % 51.19/9.11 | | | | | | | | | CLOSE: (108) is inconsistent. % 51.19/9.11 | | | | | | | | | % 51.19/9.11 | | | | | | | | Case 2: % 51.19/9.11 | | | | | | | | | % 51.19/9.11 | | | | | | | | | (109) all_53_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 51.19/9.11 | | | | | | | | | int] : ? [v3: int] : ((v3 = 0 & % 51.19/9.11 | | | | | | | | | apart_point_and_line(all_38_2, all_38_5) = 0) | % 51.19/9.11 | | | | | | | | | (v2 = 0 & apart_point_and_line(all_56_1, all_38_4) % 51.19/9.11 | | | | | | | | | = 0) | ( ~ (v1 = 0) & distinct_lines(all_38_4, % 51.19/9.11 | | | | | | | | | all_38_5) = v1) | ( ~ (v0 = 0) & % 51.19/9.11 | | | | | | | | | distinct_points(all_56_1, all_38_2) = v0)) % 51.19/9.11 | | | | | | | | | % 51.19/9.11 | | | | | | | | | BETA: splitting (103) gives: % 51.19/9.11 | | | | | | | | | % 51.19/9.11 | | | | | | | | | Case 1: % 51.19/9.11 | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | (110) all_38_0 = 0 % 51.19/9.11 | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | REDUCE: (15), (110) imply: % 51.19/9.11 | | | | | | | | | | (111) $false % 51.19/9.11 | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | CLOSE: (111) is inconsistent. % 51.19/9.11 | | | | | | | | | | % 51.19/9.11 | | | | | | | | | Case 2: % 51.19/9.11 | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | (112) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 51.19/9.11 | | | | | | | | | | [v3: int] : ((v3 = 0 & % 51.19/9.11 | | | | | | | | | | apart_point_and_line(all_38_1, all_38_4) = 0) | % 51.19/9.11 | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_2, % 51.19/9.11 | | | | | | | | | | all_38_5) = 0) | ( ~ (v1 = 0) & % 51.19/9.11 | | | | | | | | | | distinct_lines(all_38_4, all_38_5) = v1) | ( ~ % 51.19/9.11 | | | | | | | | | | (v0 = 0) & distinct_points(all_38_2, all_38_1) % 51.19/9.11 | | | | | | | | | | = v0)) % 51.19/9.11 | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | DELTA: instantiating (112) with fresh symbols all_804_0, % 51.19/9.11 | | | | | | | | | | all_804_1, all_804_2, all_804_3 gives: % 51.19/9.11 | | | | | | | | | | (113) (all_804_0 = 0 & apart_point_and_line(all_38_1, % 51.19/9.11 | | | | | | | | | | all_38_4) = 0) | (all_804_1 = 0 & % 51.19/9.11 | | | | | | | | | | apart_point_and_line(all_38_2, all_38_5) = 0) | ( % 51.19/9.11 | | | | | | | | | | ~ (all_804_2 = 0) & distinct_lines(all_38_4, % 51.19/9.11 | | | | | | | | | | all_38_5) = all_804_2) | ( ~ (all_804_3 = 0) & % 51.19/9.11 | | | | | | | | | | distinct_points(all_38_2, all_38_1) = all_804_3) % 51.19/9.11 | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | BETA: splitting (106) gives: % 51.19/9.11 | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | Case 1: % 51.19/9.11 | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | (114) all_60_0 = 0 % 51.19/9.11 | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | REDUCE: (93), (114) imply: % 51.19/9.11 | | | | | | | | | | | (115) $false % 51.19/9.11 | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | CLOSE: (115) is inconsistent. % 51.19/9.11 | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | Case 2: % 51.19/9.11 | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | (116) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 51.19/9.11 | | | | | | | | | | | [v3: int] : ((v3 = 0 & % 51.19/9.11 | | | | | | | | | | | apart_point_and_line(all_38_1, all_38_5) = 0) % 51.19/9.11 | | | | | | | | | | | | (v2 = 0 & apart_point_and_line(all_38_2, % 51.19/9.11 | | | | | | | | | | | all_38_4) = 0) | ( ~ (v1 = 0) & % 51.19/9.11 | | | | | | | | | | | distinct_lines(all_38_4, all_38_5) = v1) | ( ~ % 51.19/9.11 | | | | | | | | | | | (v0 = 0) & distinct_points(all_38_2, all_38_1) % 51.19/9.11 | | | | | | | | | | | = v0)) % 51.19/9.11 | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | DELTA: instantiating (116) with fresh symbols all_808_0, % 51.19/9.11 | | | | | | | | | | | all_808_1, all_808_2, all_808_3 gives: % 51.19/9.11 | | | | | | | | | | | (117) (all_808_0 = 0 & apart_point_and_line(all_38_1, % 51.19/9.11 | | | | | | | | | | | all_38_5) = 0) | (all_808_1 = 0 & % 51.19/9.11 | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_4) = 0) | % 51.19/9.11 | | | | | | | | | | | ( ~ (all_808_2 = 0) & distinct_lines(all_38_4, % 51.19/9.11 | | | | | | | | | | | all_38_5) = all_808_2) | ( ~ (all_808_3 = 0) & % 51.19/9.11 | | | | | | | | | | | distinct_points(all_38_2, all_38_1) = all_808_3) % 51.19/9.11 | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | BETA: splitting (117) gives: % 51.19/9.11 | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | Case 1: % 51.19/9.11 | | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | | (118) (all_808_0 = 0 & apart_point_and_line(all_38_1, % 51.19/9.11 | | | | | | | | | | | | all_38_5) = 0) | (all_808_1 = 0 & % 51.19/9.11 | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_4) = 0) % 51.19/9.11 | | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | | BETA: splitting (118) gives: % 51.19/9.11 | | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | | Case 1: % 51.19/9.11 | | | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | | | (119) all_808_0 = 0 & apart_point_and_line(all_38_1, % 51.19/9.11 | | | | | | | | | | | | | all_38_5) = 0 % 51.19/9.11 | | | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | | | ALPHA: (119) implies: % 51.19/9.11 | | | | | | | | | | | | | (120) apart_point_and_line(all_38_1, all_38_5) = 0 % 51.19/9.11 | | | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_38_0, 0, all_38_5, % 51.19/9.11 | | | | | | | | | | | | | all_38_1, simplifying with (23), (120) gives: % 51.19/9.11 | | | | | | | | | | | | | (121) all_38_0 = 0 % 51.19/9.11 | | | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | | | REDUCE: (15), (121) imply: % 51.19/9.11 | | | | | | | | | | | | | (122) $false % 51.19/9.11 | | | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | | | CLOSE: (122) is inconsistent. % 51.19/9.11 | | | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | | Case 2: % 51.19/9.11 | | | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | | | (123) all_808_1 = 0 & apart_point_and_line(all_38_2, % 51.19/9.11 | | | | | | | | | | | | | all_38_4) = 0 % 51.19/9.11 | | | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | | | ALPHA: (123) implies: % 51.19/9.11 | | | | | | | | | | | | | (124) apart_point_and_line(all_38_2, all_38_4) = 0 % 51.19/9.11 | | | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_53_0, 0, all_38_4, % 51.19/9.11 | | | | | | | | | | | | | all_38_2, simplifying with (69), (124) gives: % 51.19/9.11 | | | | | | | | | | | | | (125) all_53_0 = 0 % 51.19/9.11 | | | | | | | | | | | | | % 51.19/9.11 | | | | | | | | | | | | | REDUCE: (95), (125) imply: % 51.19/9.12 | | | | | | | | | | | | | (126) $false % 51.19/9.12 | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | CLOSE: (126) is inconsistent. % 51.19/9.12 | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | End of split % 51.19/9.12 | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | Case 2: % 51.19/9.12 | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | (127) ( ~ (all_808_2 = 0) & distinct_lines(all_38_4, % 51.19/9.12 | | | | | | | | | | | | all_38_5) = all_808_2) | ( ~ (all_808_3 = 0) & % 51.19/9.12 | | | | | | | | | | | | distinct_points(all_38_2, all_38_1) = all_808_3) % 51.19/9.12 | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | BETA: splitting (127) gives: % 51.19/9.12 | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | Case 1: % 51.19/9.12 | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | (128) ~ (all_808_2 = 0) & distinct_lines(all_38_4, % 51.19/9.12 | | | | | | | | | | | | | all_38_5) = all_808_2 % 51.19/9.12 | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | ALPHA: (128) implies: % 51.19/9.12 | | | | | | | | | | | | | (129) ~ (all_808_2 = 0) % 51.19/9.12 | | | | | | | | | | | | | (130) distinct_lines(all_38_4, all_38_5) = all_808_2 % 51.19/9.12 | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | BETA: splitting (113) gives: % 51.19/9.12 | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | Case 1: % 51.19/9.12 | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | (131) (all_804_0 = 0 & apart_point_and_line(all_38_1, % 51.19/9.12 | | | | | | | | | | | | | | all_38_4) = 0) | (all_804_1 = 0 & % 51.19/9.12 | | | | | | | | | | | | | | apart_point_and_line(all_38_2, all_38_5) = 0) % 51.19/9.12 | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | BETA: splitting (131) gives: % 51.19/9.12 | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | Case 1: % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | (132) all_804_0 = 0 & apart_point_and_line(all_38_1, % 51.19/9.12 | | | | | | | | | | | | | | | all_38_4) = 0 % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | ALPHA: (132) implies: % 51.19/9.12 | | | | | | | | | | | | | | | (133) apart_point_and_line(all_38_1, all_38_4) = 0 % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_60_0, 0, all_38_4, % 51.19/9.12 | | | | | | | | | | | | | | | all_38_1, simplifying with (82), (133) gives: % 51.19/9.12 | | | | | | | | | | | | | | | (134) all_60_0 = 0 % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | REDUCE: (93), (134) imply: % 51.19/9.12 | | | | | | | | | | | | | | | (135) $false % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | CLOSE: (135) is inconsistent. % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | Case 2: % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | (136) all_804_1 = 0 & apart_point_and_line(all_38_2, % 51.19/9.12 | | | | | | | | | | | | | | | all_38_5) = 0 % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | ALPHA: (136) implies: % 51.19/9.12 | | | | | | | | | | | | | | | (137) apart_point_and_line(all_38_2, all_38_5) = 0 % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_64_0, 0, all_38_5, % 51.19/9.12 | | | | | | | | | | | | | | | all_38_2, simplifying with (81), (137) gives: % 51.19/9.12 | | | | | | | | | | | | | | | (138) all_64_0 = 0 % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | REDUCE: (92), (138) imply: % 51.19/9.12 | | | | | | | | | | | | | | | (139) $false % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | CLOSE: (139) is inconsistent. % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | End of split % 51.19/9.12 | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | Case 2: % 51.19/9.12 | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | (140) ( ~ (all_804_2 = 0) & distinct_lines(all_38_4, % 51.19/9.12 | | | | | | | | | | | | | | all_38_5) = all_804_2) | ( ~ (all_804_3 = 0) & % 51.19/9.12 | | | | | | | | | | | | | | distinct_points(all_38_2, all_38_1) = all_804_3) % 51.19/9.12 | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | BETA: splitting (140) gives: % 51.19/9.12 | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | Case 1: % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | (141) ~ (all_804_2 = 0) & distinct_lines(all_38_4, % 51.19/9.12 | | | | | | | | | | | | | | | all_38_5) = all_804_2 % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | ALPHA: (141) implies: % 51.19/9.12 | | | | | | | | | | | | | | | (142) distinct_lines(all_38_4, all_38_5) = all_804_2 % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | BETA: splitting (109) gives: % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | Case 1: % 51.19/9.12 | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | | (143) all_53_0 = 0 % 51.19/9.12 | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | | REDUCE: (95), (143) imply: % 51.19/9.12 | | | | | | | | | | | | | | | | (144) $false % 51.19/9.12 | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | | CLOSE: (144) is inconsistent. % 51.19/9.12 | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | Case 2: % 51.19/9.12 | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_804_2, all_808_2, % 51.19/9.12 | | | | | | | | | | | | | | | | all_38_5, all_38_4, simplifying with (130), (142) % 51.19/9.12 | | | | | | | | | | | | | | | | gives: % 51.19/9.12 | | | | | | | | | | | | | | | | (145) all_808_2 = all_804_2 % 51.19/9.12 | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | | REDUCE: (129), (145) imply: % 51.19/9.12 | | | | | | | | | | | | | | | | (146) ~ (all_804_2 = 0) % 51.19/9.12 | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_38_5, all_38_4, % 51.19/9.12 | | | | | | | | | | | | | | | | all_38_5, all_804_2, simplifying with (16), (17), % 51.19/9.12 | | | | | | | | | | | | | | | | (19), (142) gives: % 51.19/9.12 | | | | | | | | | | | | | | | | (147) all_804_2 = 0 | convergent_lines(all_38_5, % 51.19/9.12 | | | | | | | | | | | | | | | | all_38_5) = 0 % 51.19/9.12 | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | | BETA: splitting (147) gives: % 51.19/9.12 | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | | Case 1: % 51.19/9.12 | | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | | | (148) convergent_lines(all_38_5, all_38_5) = 0 % 51.19/9.12 | | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_38_5, simplifying % 51.19/9.12 | | | | | | | | | | | | | | | | | with (16), (148) gives: % 51.19/9.12 | | | | | | | | | | | | | | | | | (149) $false % 51.19/9.12 | | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | | | CLOSE: (149) is inconsistent. % 51.19/9.12 | | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | | Case 2: % 51.19/9.12 | | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | | | (150) all_804_2 = 0 % 51.19/9.12 | | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | | | REDUCE: (146), (150) imply: % 51.19/9.12 | | | | | | | | | | | | | | | | | (151) $false % 51.19/9.12 | | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | | | CLOSE: (151) is inconsistent. % 51.19/9.12 | | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | | End of split % 51.19/9.12 | | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | End of split % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | Case 2: % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | (152) ~ (all_804_3 = 0) & distinct_points(all_38_2, % 51.19/9.12 | | | | | | | | | | | | | | | all_38_1) = all_804_3 % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | ALPHA: (152) implies: % 51.19/9.12 | | | | | | | | | | | | | | | (153) ~ (all_804_3 = 0) % 51.19/9.12 | | | | | | | | | | | | | | | (154) distinct_points(all_38_2, all_38_1) = all_804_3 % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_804_3, all_38_1, % 51.19/9.12 | | | | | | | | | | | | | | | all_38_2, simplifying with (100), (154) gives: % 51.19/9.12 | | | | | | | | | | | | | | | (155) all_804_3 = 0 % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | REDUCE: (153), (155) imply: % 51.19/9.12 | | | | | | | | | | | | | | | (156) $false % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | | CLOSE: (156) is inconsistent. % 51.19/9.12 | | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | | End of split % 51.19/9.12 | | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | End of split % 51.19/9.12 | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | Case 2: % 51.19/9.12 | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | (157) ~ (all_808_3 = 0) & distinct_points(all_38_2, % 51.19/9.12 | | | | | | | | | | | | | all_38_1) = all_808_3 % 51.19/9.12 | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | ALPHA: (157) implies: % 51.19/9.12 | | | | | | | | | | | | | (158) ~ (all_808_3 = 0) % 51.19/9.12 | | | | | | | | | | | | | (159) distinct_points(all_38_2, all_38_1) = all_808_3 % 51.19/9.12 | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_808_3, all_38_1, % 51.19/9.12 | | | | | | | | | | | | | all_38_2, simplifying with (100), (159) gives: % 51.19/9.12 | | | | | | | | | | | | | (160) all_808_3 = 0 % 51.19/9.12 | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | REDUCE: (158), (160) imply: % 51.19/9.12 | | | | | | | | | | | | | (161) $false % 51.19/9.12 | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | | CLOSE: (161) is inconsistent. % 51.19/9.12 | | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | | End of split % 51.19/9.12 | | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | | End of split % 51.19/9.12 | | | | | | | | | | | % 51.19/9.12 | | | | | | | | | | End of split % 51.19/9.12 | | | | | | | | | | % 51.19/9.12 | | | | | | | | | End of split % 51.19/9.12 | | | | | | | | | % 51.19/9.12 | | | | | | | | End of split % 51.19/9.12 | | | | | | | | % 51.19/9.12 | | | | | | | End of split % 51.19/9.12 | | | | | | | % 51.19/9.12 | | | | | | End of split % 51.19/9.12 | | | | | | % 51.19/9.12 | | | | | Case 2: % 51.19/9.12 | | | | | | % 51.19/9.12 | | | | | | (162) all_54_0 = 0 % 51.19/9.12 | | | | | | % 51.19/9.12 | | | | | | REDUCE: (94), (162) imply: % 51.19/9.12 | | | | | | (163) $false % 51.19/9.12 | | | | | | % 51.19/9.12 | | | | | | CLOSE: (163) is inconsistent. % 51.19/9.12 | | | | | | % 51.19/9.12 | | | | | End of split % 51.19/9.12 | | | | | % 51.19/9.12 | | | | Case 2: % 51.19/9.12 | | | | | % 51.19/9.12 | | | | | (164) ~ (all_67_1 = 0) & convergent_lines(all_38_3, all_38_4) = % 51.19/9.12 | | | | | all_67_1 % 51.19/9.12 | | | | | % 51.19/9.12 | | | | | ALPHA: (164) implies: % 51.19/9.12 | | | | | (165) ~ (all_67_1 = 0) % 51.19/9.12 | | | | | (166) convergent_lines(all_38_3, all_38_4) = all_67_1 % 51.19/9.12 | | | | | % 51.19/9.12 | | | | | GROUND_INST: instantiating (11) with 0, all_67_1, all_38_4, all_38_3, % 51.19/9.12 | | | | | simplifying with (21), (166) gives: % 51.19/9.12 | | | | | (167) all_67_1 = 0 % 51.19/9.12 | | | | | % 51.19/9.12 | | | | | REDUCE: (165), (167) imply: % 51.19/9.12 | | | | | (168) $false % 51.19/9.12 | | | | | % 51.19/9.12 | | | | | CLOSE: (168) is inconsistent. % 51.19/9.12 | | | | | % 51.19/9.12 | | | | End of split % 51.19/9.12 | | | | % 51.19/9.12 | | | Case 2: % 51.19/9.12 | | | | % 51.19/9.12 | | | | (169) ~ (all_53_1 = 0) & convergent_lines(all_38_5, all_38_4) = % 51.19/9.12 | | | | all_53_1 % 51.19/9.12 | | | | % 51.19/9.12 | | | | ALPHA: (169) implies: % 51.19/9.12 | | | | (170) ~ (all_53_1 = 0) % 51.19/9.13 | | | | (171) convergent_lines(all_38_5, all_38_4) = all_53_1 % 51.19/9.13 | | | | % 51.19/9.13 | | | | GROUND_INST: instantiating (11) with 0, all_53_1, all_38_4, all_38_5, % 51.19/9.13 | | | | simplifying with (19), (171) gives: % 51.19/9.13 | | | | (172) all_53_1 = 0 % 51.19/9.13 | | | | % 51.19/9.13 | | | | REDUCE: (170), (172) imply: % 51.19/9.13 | | | | (173) $false % 51.19/9.13 | | | | % 51.19/9.13 | | | | CLOSE: (173) is inconsistent. % 51.19/9.13 | | | | % 51.19/9.13 | | | End of split % 51.19/9.13 | | | % 51.19/9.13 | | Case 2: % 51.19/9.13 | | | % 51.19/9.13 | | | (174) ~ (all_68_1 = 0) & convergent_lines(all_38_5, all_38_4) = % 51.19/9.13 | | | all_68_1 % 51.19/9.13 | | | % 51.19/9.13 | | | ALPHA: (174) implies: % 51.19/9.13 | | | (175) ~ (all_68_1 = 0) % 51.19/9.13 | | | (176) convergent_lines(all_38_5, all_38_4) = all_68_1 % 51.19/9.13 | | | % 51.19/9.13 | | | GROUND_INST: instantiating (11) with 0, all_68_1, all_38_4, all_38_5, % 51.19/9.13 | | | simplifying with (19), (176) gives: % 51.19/9.13 | | | (177) all_68_1 = 0 % 51.19/9.13 | | | % 51.19/9.13 | | | REDUCE: (175), (177) imply: % 51.19/9.13 | | | (178) $false % 51.19/9.13 | | | % 51.19/9.13 | | | CLOSE: (178) is inconsistent. % 51.19/9.13 | | | % 51.19/9.13 | | End of split % 51.19/9.13 | | % 51.19/9.13 | Case 2: % 51.19/9.13 | | % 51.19/9.13 | | (179) ~ (all_66_1 = 0) & convergent_lines(all_38_3, all_38_4) = all_66_1 % 51.19/9.13 | | % 51.19/9.13 | | ALPHA: (179) implies: % 51.19/9.13 | | (180) ~ (all_66_1 = 0) % 51.19/9.13 | | (181) convergent_lines(all_38_3, all_38_4) = all_66_1 % 51.19/9.13 | | % 51.19/9.13 | | GROUND_INST: instantiating (11) with 0, all_66_1, all_38_4, all_38_3, % 51.19/9.13 | | simplifying with (21), (181) gives: % 51.19/9.13 | | (182) all_66_1 = 0 % 51.19/9.13 | | % 51.19/9.13 | | REDUCE: (180), (182) imply: % 51.19/9.13 | | (183) $false % 51.19/9.13 | | % 51.19/9.13 | | CLOSE: (183) is inconsistent. % 51.19/9.13 | | % 51.19/9.13 | End of split % 51.19/9.13 | % 51.19/9.13 End of proof % 51.19/9.13 % SZS output end Proof for theBenchmark % 51.19/9.13 % 51.19/9.13 8529ms %------------------------------------------------------------------------------