%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO200+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 : n002.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 23:22:13 EDT 2023 % Result : Theorem 21.68s 3.76s % Output : Proof 26.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GEO200+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n002.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 20:42:50 EDT 2023 % 0.13/0.36 % CPUTime : % 0.19/0.68 ________ _____ % 0.19/0.68 ___ __ \_________(_)________________________________ % 0.19/0.68 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.68 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.68 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.68 % 0.19/0.68 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.68 (2023-06-19) % 0.19/0.68 % 0.19/0.68 (c) Philipp Rümmer, 2009-2023 % 0.19/0.68 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.68 Amanda Stjerna. % 0.19/0.68 Free software under BSD-3-Clause. % 0.19/0.68 % 0.19/0.68 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.68 % 0.19/0.68 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.69 Running up to 7 provers in parallel. % 0.74/0.71 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.74/0.71 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.74/0.71 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.74/0.71 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.74/0.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.74/0.71 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.74/0.71 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.08/1.22 Prover 4: Preprocessing ... % 3.08/1.22 Prover 1: Preprocessing ... % 3.08/1.27 Prover 0: Preprocessing ... % 3.08/1.27 Prover 3: Preprocessing ... % 3.08/1.27 Prover 5: Preprocessing ... % 3.08/1.27 Prover 2: Preprocessing ... % 3.08/1.27 Prover 6: Preprocessing ... % 6.73/1.75 Prover 5: Proving ... % 6.73/1.76 Prover 2: Proving ... % 6.73/1.88 Prover 3: Constructing countermodel ... % 6.73/1.88 Prover 1: Constructing countermodel ... % 6.73/1.91 Prover 6: Constructing countermodel ... % 9.58/2.19 Prover 3: gave up % 10.27/2.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.27/2.26 Prover 6: gave up % 10.27/2.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.79/2.30 Prover 7: Preprocessing ... % 10.79/2.30 Prover 4: Constructing countermodel ... % 10.79/2.32 Prover 8: Preprocessing ... % 10.79/2.37 Prover 1: gave up % 10.79/2.38 Prover 0: Proving ... % 10.79/2.38 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 11.61/2.41 Prover 7: Warning: ignoring some quantifiers % 11.61/2.42 Prover 9: Preprocessing ... % 11.61/2.46 Prover 7: Constructing countermodel ... % 12.25/2.59 Prover 8: Warning: ignoring some quantifiers % 12.25/2.60 Prover 8: Constructing countermodel ... % 14.34/2.83 Prover 9: Constructing countermodel ... % 15.09/2.88 Prover 8: gave up % 15.22/2.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.36/2.98 Prover 10: Preprocessing ... % 15.99/3.07 Prover 10: Warning: ignoring some quantifiers % 15.99/3.08 Prover 10: Constructing countermodel ... % 17.21/3.26 Prover 7: gave up % 17.21/3.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 18.11/3.33 Prover 11: Preprocessing ... % 18.32/3.33 Prover 10: gave up % 18.43/3.35 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 18.43/3.40 Prover 12: Preprocessing ... % 20.25/3.62 Prover 12: Proving ... % 21.28/3.73 Prover 11: Constructing countermodel ... % 21.68/3.76 Prover 0: proved (3058ms) % 21.68/3.76 % 21.68/3.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.68/3.76 % 21.68/3.77 Prover 9: stopped % 21.68/3.78 Prover 5: stopped % 21.68/3.80 Prover 2: stopped % 21.68/3.80 Prover 12: stopped % 21.68/3.80 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 21.68/3.80 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 21.68/3.80 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 21.68/3.84 Prover 13: Preprocessing ... % 21.68/3.85 Prover 19: Preprocessing ... % 21.68/3.86 Prover 16: Preprocessing ... % 21.68/3.91 Prover 13: Warning: ignoring some quantifiers % 21.68/3.91 Prover 16: Warning: ignoring some quantifiers % 21.68/3.92 Prover 13: Constructing countermodel ... % 21.68/3.92 Prover 16: Constructing countermodel ... % 23.21/3.99 Prover 19: Warning: ignoring some quantifiers % 23.21/4.00 Prover 19: Constructing countermodel ... % 24.71/4.21 Prover 13: gave up % 25.25/4.25 Prover 4: Found proof (size 171) % 25.25/4.25 Prover 4: proved (3547ms) % 25.25/4.25 Prover 11: stopped % 25.25/4.25 Prover 16: stopped % 25.25/4.26 Prover 19: stopped % 25.25/4.26 % 25.25/4.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 25.25/4.26 % 25.25/4.28 % SZS output start Proof for theBenchmark % 25.25/4.29 Assumptions after simplification: % 25.25/4.29 --------------------------------- % 25.25/4.29 % 25.25/4.29 (apart1) % 25.56/4.33 ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 25.56/4.33 % 25.56/4.33 (apart4) % 25.56/4.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 25.56/4.34 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) % 25.56/4.34 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 25.56/4.34 distinct_points(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 25.56/4.34 ! [v3: int] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ % 25.56/4.34 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 25.56/4.34 distinct_points(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 25.56/4.34 [v3: int] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ % 25.56/4.34 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 25.56/4.34 distinct_points(v1, v2) = 0) % 25.56/4.34 % 25.56/4.34 (ax2) % 25.56/4.34 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_lines(v0, v1) = % 25.56/4.34 v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v0, v1) = 0) & ! [v0: $i] : % 25.56/4.34 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ~ % 25.56/4.34 $i(v1) | ~ $i(v0) | equal_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : % 25.56/4.34 ( ~ (equal_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 % 25.56/4.34 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 25.56/4.34 (distinct_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ % 25.56/4.34 (v2 = 0) & equal_lines(v0, v1) = v2)) % 25.56/4.34 % 25.56/4.34 (ci1) % 25.56/4.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 25.56/4.35 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 25.56/4.35 (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 25.56/4.35 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 25.56/4.35 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 25.56/4.35 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 25.56/4.35 apart_point_and_line(v0, v2) = v3 & $i(v2))) % 25.56/4.35 % 25.56/4.35 (ci2) % 25.56/4.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 25.56/4.35 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 25.56/4.35 (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 25.56/4.35 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 25.56/4.35 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 25.56/4.35 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 25.56/4.35 apart_point_and_line(v1, v2) = v3 & $i(v2))) % 25.56/4.35 % 25.56/4.35 (con) % 25.56/4.35 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 25.56/4.35 = 0) & equal_lines(v2, v3) = v4 & line_connecting(v1, v0) = v3 & % 25.56/4.35 line_connecting(v0, v1) = v2 & distinct_points(v0, v1) = 0 & $i(v3) & $i(v2) % 25.56/4.35 & $i(v1) & $i(v0)) % 25.56/4.35 % 25.56/4.35 (con1) % 25.56/4.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 25.56/4.36 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: % 25.56/4.36 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & % 25.56/4.36 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | % 25.56/4.36 v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = % 25.56/4.36 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : % 25.56/4.36 ? [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & % 25.56/4.36 line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = % 25.56/4.36 0))) % 25.56/4.36 % 25.56/4.36 (cu1) % 25.78/4.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 25.78/4.37 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 25.78/4.37 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 25.78/4.37 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 25.78/4.37 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, % 25.78/4.37 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 25.78/4.37 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 25.78/4.37 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 25.78/4.37 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 25.78/4.37 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 25.78/4.37 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 25.78/4.37 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 % 25.78/4.38 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 25.78/4.38 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 25.78/4.38 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 25.78/4.38 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 25.78/4.38 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 25.78/4.38 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 25.78/4.38 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = % 25.78/4.38 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 25.78/4.38 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = % 25.78/4.38 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 25.78/4.38 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 25.78/4.38 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = % 25.78/4.38 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 % 25.78/4.38 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : % 25.78/4.38 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 25.78/4.38 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 25.78/4.38 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 25.78/4.38 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 25.78/4.38 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & % 25.78/4.38 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 25.78/4.38 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 25.78/4.38 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ % 25.78/4.38 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 25.78/4.38 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 25.78/4.38 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, % 25.78/4.38 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 25.78/4.38 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 25.78/4.38 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 25.78/4.38 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 25.78/4.38 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 25.78/4.38 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 25.78/4.38 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 25.78/4.38 % 25.78/4.38 (function-axioms) % 25.78/4.38 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 25.78/4.38 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 25.78/4.38 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 25.78/4.38 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.78/4.38 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 25.78/4.38 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 25.78/4.38 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 25.78/4.38 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 25.78/4.38 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.78/4.38 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 25.78/4.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 25.78/4.38 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 25.78/4.38 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.78/4.38 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 25.78/4.38 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 25.78/4.38 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 25.78/4.38 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 25.78/4.39 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 25.78/4.39 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 25.78/4.39 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 25.78/4.39 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 25.78/4.39 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 25.78/4.39 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 25.78/4.39 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.78/4.39 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 25.78/4.39 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 25.78/4.39 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 25.78/4.39 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 25.78/4.39 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.78/4.39 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 25.78/4.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 25.78/4.39 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 25.78/4.39 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 25.78/4.39 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 25.78/4.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 25.78/4.39 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 25.78/4.39 % 25.78/4.39 Further assumptions not needed in the proof: % 25.78/4.39 -------------------------------------------- % 25.78/4.39 a3, a4, a5, apart2, apart3, apart5, ax1, ax6, ceq1, ceq2, ceq3, ci3, ci4, % 25.78/4.39 coipo1, cotno1, couo1, cp1, cp2, cup1, int1, oac1, occu1, ooc1, ooc2, orth1, % 25.78/4.39 ouo1, p1, par1 % 25.78/4.39 % 25.78/4.39 Those formulas are unsatisfiable: % 25.78/4.39 --------------------------------- % 25.78/4.39 % 25.78/4.39 Begin of proof % 25.78/4.39 | % 25.78/4.39 | ALPHA: (apart4) implies: % 25.78/4.39 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 25.78/4.39 | (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | % 25.78/4.39 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) % 25.78/4.39 | % 25.78/4.39 | ALPHA: (ci1) implies: % 25.78/4.39 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 25.78/4.39 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 25.78/4.39 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 25.78/4.39 | $i(v2))) % 25.78/4.39 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 25.78/4.39 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 25.78/4.39 | (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( % 25.78/4.39 | ~ (v4 = 0) | ~ (v3 = 0)))) % 25.78/4.39 | % 25.78/4.39 | ALPHA: (ci2) implies: % 25.78/4.40 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 25.78/4.40 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 25.78/4.40 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 25.78/4.40 | $i(v2))) % 25.78/4.40 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 25.78/4.40 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 25.78/4.40 | (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( % 25.78/4.40 | ~ (v4 = 0) | ~ (v3 = 0)))) % 25.78/4.40 | % 25.78/4.40 | ALPHA: (cu1) implies: % 25.78/4.40 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 25.78/4.40 | (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ % 25.78/4.40 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 25.78/4.40 | any] : ? [v6: any] : ? [v7: any] : (apart_point_and_line(v1, v3) % 25.78/4.40 | = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, % 25.78/4.40 | v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | % 25.78/4.40 | v5 = 0 | v4 = 0))) % 25.78/4.40 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 25.78/4.40 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) % 25.78/4.40 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, % 25.78/4.40 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 25.78/4.40 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v1, % 25.78/4.40 | v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, % 25.78/4.40 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 25.78/4.41 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 25.78/4.41 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) % 25.78/4.41 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) % 25.78/4.41 | = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] % 25.78/4.41 | : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & % 25.78/4.41 | apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & % 25.78/4.41 | ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 25.78/4.41 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 25.78/4.41 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 25.78/4.41 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 25.78/4.41 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 25.78/4.41 | [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 25.78/4.41 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 25.78/4.41 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 25.78/4.41 | | v8 = 0))) % 25.78/4.41 | % 25.78/4.41 | ALPHA: (con1) implies: % 25.78/4.41 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 25.78/4.41 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? % 25.78/4.41 | [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & % 25.78/4.41 | line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) % 25.78/4.41 | | v5 = 0))) % 25.78/4.41 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 25.78/4.41 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 25.78/4.41 | [v5: any] : ? [v6: any] : (point(v1) = v4 & point(v0) = v3 & % 25.78/4.41 | line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ % 25.78/4.41 | (v4 = 0) | ~ (v3 = 0) | v6 = 0))) % 25.78/4.41 | % 25.78/4.41 | ALPHA: (ax2) implies: % 25.78/4.41 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 25.78/4.41 | (equal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 25.78/4.41 | distinct_lines(v0, v1) = 0) % 25.78/4.41 | % 25.78/4.41 | ALPHA: (function-axioms) implies: % 25.78/4.42 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 25.78/4.42 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 25.78/4.42 | (distinct_points(v3, v2) = v0)) % 25.78/4.42 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 25.78/4.42 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 25.78/4.42 | (apart_point_and_line(v3, v2) = v0)) % 25.78/4.42 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.78/4.42 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 25.78/4.42 | % 25.78/4.42 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 25.78/4.42 | all_38_3, all_38_4 gives: % 25.78/4.42 | (16) ~ (all_38_0 = 0) & equal_lines(all_38_2, all_38_1) = all_38_0 & % 25.78/4.42 | line_connecting(all_38_3, all_38_4) = all_38_1 & % 25.78/4.42 | line_connecting(all_38_4, all_38_3) = all_38_2 & % 25.78/4.42 | distinct_points(all_38_4, all_38_3) = 0 & $i(all_38_1) & $i(all_38_2) % 25.78/4.42 | & $i(all_38_3) & $i(all_38_4) % 25.78/4.42 | % 25.78/4.42 | ALPHA: (16) implies: % 25.78/4.42 | (17) ~ (all_38_0 = 0) % 25.78/4.42 | (18) $i(all_38_4) % 25.78/4.42 | (19) $i(all_38_3) % 25.78/4.42 | (20) $i(all_38_2) % 25.78/4.42 | (21) $i(all_38_1) % 25.78/4.42 | (22) distinct_points(all_38_4, all_38_3) = 0 % 25.78/4.42 | (23) line_connecting(all_38_4, all_38_3) = all_38_2 % 25.78/4.42 | (24) line_connecting(all_38_3, all_38_4) = all_38_1 % 25.78/4.42 | (25) equal_lines(all_38_2, all_38_1) = all_38_0 % 25.78/4.42 | % 25.78/4.42 | GROUND_INST: instantiating (10) with all_38_4, all_38_3, simplifying with % 25.78/4.43 | (18), (19), (22) gives: % 25.78/4.43 | (26) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 25.78/4.43 | (point(all_38_3) = v1 & point(all_38_4) = v0 & line(v2) = v3 & % 25.78/4.43 | line_connecting(all_38_4, all_38_3) = v2 & $i(v2) & ( ~ (v1 = 0) | % 25.78/4.43 | ~ (v0 = 0) | v3 = 0)) % 25.78/4.43 | % 25.78/4.43 | GROUND_INST: instantiating (4) with all_38_4, all_38_3, simplifying with (18), % 25.78/4.43 | (19), (22) gives: % 25.78/4.43 | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_4, % 25.78/4.43 | all_38_3) = v0 & apart_point_and_line(all_38_3, v0) = v1 & $i(v0)) % 25.78/4.43 | % 25.78/4.43 | GROUND_INST: instantiating (2) with all_38_4, all_38_3, simplifying with (18), % 25.78/4.43 | (19), (22) gives: % 25.78/4.43 | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_4, % 25.78/4.43 | all_38_3) = v0 & apart_point_and_line(all_38_4, v0) = v1 & $i(v0)) % 25.78/4.43 | % 25.78/4.43 | GROUND_INST: instantiating (11) with all_38_4, all_38_3, all_38_2, simplifying % 25.78/4.43 | with (18), (19), (23) gives: % 25.78/4.43 | (29) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 25.78/4.43 | (point(all_38_3) = v1 & point(all_38_4) = v0 & line(all_38_2) = v3 & % 25.78/4.43 | distinct_points(all_38_4, all_38_3) = v2 & ( ~ (v2 = 0) | ~ (v1 = % 25.78/4.43 | 0) | ~ (v0 = 0) | v3 = 0)) % 25.78/4.43 | % 25.78/4.43 | GROUND_INST: instantiating (5) with all_38_4, all_38_3, all_38_2, simplifying % 25.78/4.43 | with (18), (19), (23) gives: % 25.78/4.43 | (30) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_3, % 25.78/4.43 | all_38_2) = v1 & distinct_points(all_38_4, all_38_3) = v0 & ( ~ % 25.78/4.43 | (v1 = 0) | ~ (v0 = 0))) % 25.78/4.43 | % 25.78/4.43 | GROUND_INST: instantiating (3) with all_38_4, all_38_3, all_38_2, simplifying % 25.78/4.43 | with (18), (19), (23) gives: % 25.78/4.43 | (31) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_4, % 25.78/4.43 | all_38_2) = v1 & distinct_points(all_38_4, all_38_3) = v0 & ( ~ % 25.78/4.44 | (v1 = 0) | ~ (v0 = 0))) % 25.78/4.44 | % 25.78/4.44 | GROUND_INST: instantiating (11) with all_38_3, all_38_4, all_38_1, simplifying % 25.78/4.44 | with (18), (19), (24) gives: % 25.78/4.44 | (32) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 25.78/4.44 | (point(all_38_3) = v0 & point(all_38_4) = v1 & line(all_38_1) = v3 & % 25.78/4.44 | distinct_points(all_38_3, all_38_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = % 25.78/4.44 | 0) | ~ (v0 = 0) | v3 = 0)) % 25.78/4.44 | % 25.78/4.44 | GROUND_INST: instantiating (5) with all_38_3, all_38_4, all_38_1, simplifying % 25.78/4.44 | with (18), (19), (24) gives: % 25.78/4.44 | (33) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_4, % 25.78/4.44 | all_38_1) = v1 & distinct_points(all_38_3, all_38_4) = v0 & ( ~ % 25.78/4.44 | (v1 = 0) | ~ (v0 = 0))) % 25.78/4.44 | % 25.78/4.44 | GROUND_INST: instantiating (3) with all_38_3, all_38_4, all_38_1, simplifying % 25.78/4.44 | with (18), (19), (24) gives: % 25.78/4.44 | (34) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_3, % 25.78/4.44 | all_38_1) = v1 & distinct_points(all_38_3, all_38_4) = v0 & ( ~ % 25.78/4.44 | (v1 = 0) | ~ (v0 = 0))) % 25.78/4.44 | % 25.78/4.44 | GROUND_INST: instantiating (12) with all_38_2, all_38_1, all_38_0, simplifying % 25.78/4.44 | with (20), (21), (25) gives: % 25.78/4.44 | (35) all_38_0 = 0 | distinct_lines(all_38_2, all_38_1) = 0 % 25.78/4.44 | % 25.78/4.44 | DELTA: instantiating (34) with fresh symbols all_47_0, all_47_1 gives: % 25.78/4.44 | (36) apart_point_and_line(all_38_3, all_38_1) = all_47_0 & % 25.78/4.44 | distinct_points(all_38_3, all_38_4) = all_47_1 & ( ~ (all_47_0 = 0) | % 25.78/4.44 | ~ (all_47_1 = 0)) % 25.78/4.44 | % 25.78/4.44 | ALPHA: (36) implies: % 25.78/4.44 | (37) distinct_points(all_38_3, all_38_4) = all_47_1 % 25.78/4.44 | (38) apart_point_and_line(all_38_3, all_38_1) = all_47_0 % 25.78/4.44 | (39) ~ (all_47_0 = 0) | ~ (all_47_1 = 0) % 25.78/4.44 | % 25.78/4.44 | DELTA: instantiating (33) with fresh symbols all_49_0, all_49_1 gives: % 25.78/4.44 | (40) apart_point_and_line(all_38_4, all_38_1) = all_49_0 & % 25.78/4.44 | distinct_points(all_38_3, all_38_4) = all_49_1 & ( ~ (all_49_0 = 0) | % 25.78/4.44 | ~ (all_49_1 = 0)) % 25.78/4.44 | % 25.78/4.44 | ALPHA: (40) implies: % 25.78/4.44 | (41) distinct_points(all_38_3, all_38_4) = all_49_1 % 25.78/4.44 | (42) apart_point_and_line(all_38_4, all_38_1) = all_49_0 % 25.78/4.44 | (43) ~ (all_49_0 = 0) | ~ (all_49_1 = 0) % 26.17/4.44 | % 26.17/4.44 | DELTA: instantiating (27) with fresh symbols all_51_0, all_51_1 gives: % 26.17/4.44 | (44) ~ (all_51_0 = 0) & line_connecting(all_38_4, all_38_3) = all_51_1 & % 26.17/4.44 | apart_point_and_line(all_38_3, all_51_1) = all_51_0 & $i(all_51_1) % 26.17/4.44 | % 26.17/4.44 | ALPHA: (44) implies: % 26.17/4.45 | (45) $i(all_51_1) % 26.17/4.45 | (46) apart_point_and_line(all_38_3, all_51_1) = all_51_0 % 26.17/4.45 | (47) line_connecting(all_38_4, all_38_3) = all_51_1 % 26.17/4.45 | % 26.17/4.45 | DELTA: instantiating (31) with fresh symbols all_53_0, all_53_1 gives: % 26.17/4.45 | (48) apart_point_and_line(all_38_4, all_38_2) = all_53_0 & % 26.17/4.45 | distinct_points(all_38_4, all_38_3) = all_53_1 & ( ~ (all_53_0 = 0) | % 26.17/4.45 | ~ (all_53_1 = 0)) % 26.17/4.45 | % 26.17/4.45 | ALPHA: (48) implies: % 26.17/4.45 | (49) distinct_points(all_38_4, all_38_3) = all_53_1 % 26.17/4.45 | (50) apart_point_and_line(all_38_4, all_38_2) = all_53_0 % 26.17/4.45 | % 26.17/4.45 | DELTA: instantiating (28) with fresh symbols all_55_0, all_55_1 gives: % 26.17/4.45 | (51) ~ (all_55_0 = 0) & line_connecting(all_38_4, all_38_3) = all_55_1 & % 26.17/4.45 | apart_point_and_line(all_38_4, all_55_1) = all_55_0 & $i(all_55_1) % 26.17/4.45 | % 26.17/4.45 | ALPHA: (51) implies: % 26.17/4.45 | (52) ~ (all_55_0 = 0) % 26.17/4.45 | (53) apart_point_and_line(all_38_4, all_55_1) = all_55_0 % 26.17/4.45 | (54) line_connecting(all_38_4, all_38_3) = all_55_1 % 26.17/4.45 | % 26.17/4.45 | DELTA: instantiating (30) with fresh symbols all_57_0, all_57_1 gives: % 26.17/4.45 | (55) apart_point_and_line(all_38_3, all_38_2) = all_57_0 & % 26.17/4.45 | distinct_points(all_38_4, all_38_3) = all_57_1 & ( ~ (all_57_0 = 0) | % 26.17/4.45 | ~ (all_57_1 = 0)) % 26.17/4.45 | % 26.17/4.45 | ALPHA: (55) implies: % 26.17/4.45 | (56) distinct_points(all_38_4, all_38_3) = all_57_1 % 26.17/4.45 | (57) apart_point_and_line(all_38_3, all_38_2) = all_57_0 % 26.17/4.45 | (58) ~ (all_57_0 = 0) | ~ (all_57_1 = 0) % 26.17/4.45 | % 26.17/4.45 | DELTA: instantiating (26) with fresh symbols all_59_0, all_59_1, all_59_2, % 26.17/4.45 | all_59_3 gives: % 26.17/4.45 | (59) point(all_38_3) = all_59_2 & point(all_38_4) = all_59_3 & % 26.17/4.45 | line(all_59_1) = all_59_0 & line_connecting(all_38_4, all_38_3) = % 26.17/4.45 | all_59_1 & $i(all_59_1) & ( ~ (all_59_2 = 0) | ~ (all_59_3 = 0) | % 26.17/4.45 | all_59_0 = 0) % 26.17/4.45 | % 26.17/4.45 | ALPHA: (59) implies: % 26.17/4.45 | (60) line_connecting(all_38_4, all_38_3) = all_59_1 % 26.17/4.45 | % 26.17/4.45 | DELTA: instantiating (32) with fresh symbols all_61_0, all_61_1, all_61_2, % 26.17/4.45 | all_61_3 gives: % 26.17/4.45 | (61) point(all_38_3) = all_61_3 & point(all_38_4) = all_61_2 & % 26.17/4.45 | line(all_38_1) = all_61_0 & distinct_points(all_38_3, all_38_4) = % 26.17/4.45 | all_61_1 & ( ~ (all_61_1 = 0) | ~ (all_61_2 = 0) | ~ (all_61_3 = 0) % 26.17/4.45 | | all_61_0 = 0) % 26.17/4.45 | % 26.17/4.45 | ALPHA: (61) implies: % 26.17/4.45 | (62) distinct_points(all_38_3, all_38_4) = all_61_1 % 26.17/4.45 | % 26.17/4.45 | DELTA: instantiating (29) with fresh symbols all_63_0, all_63_1, all_63_2, % 26.17/4.45 | all_63_3 gives: % 26.17/4.45 | (63) point(all_38_3) = all_63_2 & point(all_38_4) = all_63_3 & % 26.17/4.45 | line(all_38_2) = all_63_0 & distinct_points(all_38_4, all_38_3) = % 26.17/4.45 | all_63_1 & ( ~ (all_63_1 = 0) | ~ (all_63_2 = 0) | ~ (all_63_3 = 0) % 26.17/4.45 | | all_63_0 = 0) % 26.17/4.45 | % 26.17/4.45 | ALPHA: (63) implies: % 26.17/4.45 | (64) distinct_points(all_38_4, all_38_3) = all_63_1 % 26.17/4.45 | % 26.17/4.45 | BETA: splitting (35) gives: % 26.17/4.45 | % 26.17/4.45 | Case 1: % 26.17/4.45 | | % 26.17/4.45 | | (65) distinct_lines(all_38_2, all_38_1) = 0 % 26.17/4.45 | | % 26.17/4.45 | | GROUND_INST: instantiating (13) with all_53_1, all_57_1, all_38_3, all_38_4, % 26.17/4.45 | | simplifying with (49), (56) gives: % 26.17/4.46 | | (66) all_57_1 = all_53_1 % 26.17/4.46 | | % 26.17/4.46 | | GROUND_INST: instantiating (13) with 0, all_63_1, all_38_3, all_38_4, % 26.17/4.46 | | simplifying with (22), (64) gives: % 26.17/4.46 | | (67) all_63_1 = 0 % 26.17/4.46 | | % 26.17/4.46 | | GROUND_INST: instantiating (13) with all_57_1, all_63_1, all_38_3, all_38_4, % 26.17/4.46 | | simplifying with (56), (64) gives: % 26.17/4.46 | | (68) all_63_1 = all_57_1 % 26.17/4.46 | | % 26.17/4.46 | | GROUND_INST: instantiating (13) with all_49_1, all_61_1, all_38_4, all_38_3, % 26.17/4.46 | | simplifying with (41), (62) gives: % 26.17/4.46 | | (69) all_61_1 = all_49_1 % 26.17/4.46 | | % 26.17/4.46 | | GROUND_INST: instantiating (13) with all_47_1, all_61_1, all_38_4, all_38_3, % 26.17/4.46 | | simplifying with (37), (62) gives: % 26.17/4.46 | | (70) all_61_1 = all_47_1 % 26.17/4.46 | | % 26.17/4.46 | | GROUND_INST: instantiating (15) with all_38_2, all_55_1, all_38_3, all_38_4, % 26.17/4.46 | | simplifying with (23), (54) gives: % 26.17/4.46 | | (71) all_55_1 = all_38_2 % 26.17/4.46 | | % 26.17/4.46 | | GROUND_INST: instantiating (15) with all_55_1, all_59_1, all_38_3, all_38_4, % 26.17/4.46 | | simplifying with (54), (60) gives: % 26.17/4.46 | | (72) all_59_1 = all_55_1 % 26.17/4.46 | | % 26.17/4.46 | | GROUND_INST: instantiating (15) with all_51_1, all_59_1, all_38_3, all_38_4, % 26.17/4.46 | | simplifying with (47), (60) gives: % 26.17/4.46 | | (73) all_59_1 = all_51_1 % 26.17/4.46 | | % 26.17/4.46 | | COMBINE_EQS: (67), (68) imply: % 26.17/4.46 | | (74) all_57_1 = 0 % 26.17/4.46 | | % 26.17/4.46 | | SIMP: (74) implies: % 26.17/4.46 | | (75) all_57_1 = 0 % 26.17/4.46 | | % 26.17/4.46 | | COMBINE_EQS: (69), (70) imply: % 26.17/4.46 | | (76) all_49_1 = all_47_1 % 26.17/4.46 | | % 26.17/4.46 | | SIMP: (76) implies: % 26.17/4.46 | | (77) all_49_1 = all_47_1 % 26.17/4.46 | | % 26.17/4.46 | | COMBINE_EQS: (72), (73) imply: % 26.17/4.46 | | (78) all_55_1 = all_51_1 % 26.17/4.46 | | % 26.17/4.46 | | SIMP: (78) implies: % 26.17/4.46 | | (79) all_55_1 = all_51_1 % 26.17/4.46 | | % 26.17/4.46 | | COMBINE_EQS: (66), (75) imply: % 26.17/4.46 | | (80) all_53_1 = 0 % 26.17/4.46 | | % 26.17/4.46 | | COMBINE_EQS: (71), (79) imply: % 26.17/4.46 | | (81) all_51_1 = all_38_2 % 26.17/4.46 | | % 26.17/4.46 | | REDUCE: (46), (81) imply: % 26.17/4.46 | | (82) apart_point_and_line(all_38_3, all_38_2) = all_51_0 % 26.17/4.46 | | % 26.17/4.46 | | REDUCE: (53), (71) imply: % 26.17/4.46 | | (83) apart_point_and_line(all_38_4, all_38_2) = all_55_0 % 26.17/4.46 | | % 26.17/4.46 | | BETA: splitting (58) gives: % 26.17/4.46 | | % 26.17/4.46 | | Case 1: % 26.17/4.46 | | | % 26.17/4.46 | | | (84) ~ (all_57_0 = 0) % 26.17/4.46 | | | % 26.17/4.46 | | | GROUND_INST: instantiating (14) with all_53_0, all_55_0, all_38_2, % 26.17/4.46 | | | all_38_4, simplifying with (50), (83) gives: % 26.17/4.46 | | | (85) all_55_0 = all_53_0 % 26.17/4.46 | | | % 26.17/4.46 | | | GROUND_INST: instantiating (14) with all_57_0, all_51_0, all_38_2, % 26.17/4.46 | | | all_38_3, simplifying with (57), (82) gives: % 26.17/4.46 | | | (86) all_57_0 = all_51_0 % 26.17/4.46 | | | % 26.17/4.46 | | | REDUCE: (84), (86) imply: % 26.17/4.46 | | | (87) ~ (all_51_0 = 0) % 26.17/4.46 | | | % 26.17/4.46 | | | REDUCE: (52), (85) imply: % 26.17/4.46 | | | (88) ~ (all_53_0 = 0) % 26.17/4.46 | | | % 26.17/4.46 | | | GROUND_INST: instantiating (1) with all_38_4, all_38_3, all_38_4, % 26.17/4.46 | | | all_47_1, simplifying with (18), (19), (22), (37) gives: % 26.17/4.46 | | | (89) all_47_1 = 0 | distinct_points(all_38_4, all_38_4) = 0 % 26.17/4.46 | | | % 26.17/4.46 | | | GROUND_INST: instantiating (6) with all_38_4, all_38_3, all_38_2, % 26.17/4.46 | | | all_38_1, simplifying with (18), (19), (20), (21), (22), (65) % 26.17/4.46 | | | gives: % 26.17/4.46 | | | (90) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 26.17/4.46 | | | (apart_point_and_line(all_38_3, all_38_1) = v3 & % 26.17/4.46 | | | apart_point_and_line(all_38_3, all_38_2) = v2 & % 26.17/4.46 | | | apart_point_and_line(all_38_4, all_38_1) = v1 & % 26.17/4.46 | | | apart_point_and_line(all_38_4, all_38_2) = v0 & (v3 = 0 | v2 = 0 % 26.17/4.46 | | | | v1 = 0 | v0 = 0)) % 26.17/4.46 | | | % 26.17/4.46 | | | GROUND_INST: instantiating (7) with all_38_4, all_38_3, all_38_2, % 26.17/4.47 | | | all_38_2, all_53_0, all_53_0, simplifying with (18), (19), % 26.17/4.47 | | | (20), (22), (50) gives: % 26.17/4.47 | | | (91) all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.17/4.47 | | | (apart_point_and_line(all_38_3, all_38_2) = v2 & % 26.17/4.47 | | | apart_point_and_line(all_38_3, all_38_2) = v1 & % 26.17/4.47 | | | distinct_lines(all_38_2, all_38_2) = v0 & ( ~ (v0 = 0) | v2 = 0 % 26.17/4.47 | | | | v1 = 0)) % 26.17/4.47 | | | % 26.17/4.47 | | | GROUND_INST: instantiating (8) with all_38_4, all_38_4, all_38_2, % 26.17/4.47 | | | all_38_1, all_53_0, all_53_0, simplifying with (18), (20), % 26.17/4.47 | | | (21), (50), (65) gives: % 26.17/4.47 | | | (92) all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.17/4.47 | | | (apart_point_and_line(all_38_4, all_38_1) = v2 & % 26.17/4.47 | | | apart_point_and_line(all_38_4, all_38_1) = v1 & % 26.17/4.47 | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ (v0 = 0) | v2 = 0 % 26.17/4.47 | | | | v1 = 0)) % 26.17/4.47 | | | % 26.17/4.47 | | | GROUND_INST: instantiating (8) with all_38_3, all_38_3, all_38_2, % 26.17/4.47 | | | all_38_1, all_51_0, all_51_0, simplifying with (19), (20), % 26.17/4.47 | | | (21), (65), (82) gives: % 26.17/4.47 | | | (93) all_51_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.17/4.47 | | | (apart_point_and_line(all_38_3, all_38_1) = v2 & % 26.17/4.47 | | | apart_point_and_line(all_38_3, all_38_1) = v1 & % 26.17/4.47 | | | distinct_points(all_38_3, all_38_3) = v0 & ( ~ (v0 = 0) | v2 = 0 % 26.17/4.47 | | | | v1 = 0)) % 26.17/4.47 | | | % 26.17/4.47 | | | GROUND_INST: instantiating (9) with all_38_3, all_38_3, all_38_2, % 26.17/4.47 | | | all_38_2, all_51_0, all_51_0, simplifying with (19), (20), % 26.17/4.47 | | | (82) gives: % 26.17/4.47 | | | (94) all_51_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.17/4.47 | | | [v3: any] : (apart_point_and_line(all_38_3, all_38_2) = v3 & % 26.17/4.47 | | | apart_point_and_line(all_38_3, all_38_2) = v2 & % 26.17/4.47 | | | distinct_lines(all_38_2, all_38_2) = v1 & % 26.17/4.47 | | | distinct_points(all_38_3, all_38_3) = v0 & ( ~ (v1 = 0) | ~ (v0 % 26.17/4.47 | | | = 0) | v3 = 0 | v2 = 0)) % 26.17/4.47 | | | % 26.17/4.47 | | | DELTA: instantiating (90) with fresh symbols all_91_0, all_91_1, all_91_2, % 26.17/4.47 | | | all_91_3 gives: % 26.17/4.47 | | | (95) apart_point_and_line(all_38_3, all_38_1) = all_91_0 & % 26.17/4.47 | | | apart_point_and_line(all_38_3, all_38_2) = all_91_1 & % 26.17/4.47 | | | apart_point_and_line(all_38_4, all_38_1) = all_91_2 & % 26.17/4.47 | | | apart_point_and_line(all_38_4, all_38_2) = all_91_3 & (all_91_0 = % 26.17/4.47 | | | 0 | all_91_1 = 0 | all_91_2 = 0 | all_91_3 = 0) % 26.17/4.47 | | | % 26.17/4.47 | | | ALPHA: (95) implies: % 26.17/4.47 | | | (96) apart_point_and_line(all_38_4, all_38_2) = all_91_3 % 26.17/4.47 | | | (97) apart_point_and_line(all_38_4, all_38_1) = all_91_2 % 26.17/4.47 | | | (98) apart_point_and_line(all_38_3, all_38_2) = all_91_1 % 26.17/4.47 | | | (99) apart_point_and_line(all_38_3, all_38_1) = all_91_0 % 26.17/4.47 | | | (100) all_91_0 = 0 | all_91_1 = 0 | all_91_2 = 0 | all_91_3 = 0 % 26.17/4.47 | | | % 26.17/4.47 | | | BETA: splitting (91) gives: % 26.17/4.47 | | | % 26.17/4.47 | | | Case 1: % 26.17/4.47 | | | | % 26.17/4.47 | | | | (101) all_53_0 = 0 % 26.17/4.47 | | | | % 26.17/4.47 | | | | REDUCE: (88), (101) imply: % 26.17/4.47 | | | | (102) $false % 26.17/4.47 | | | | % 26.17/4.47 | | | | CLOSE: (102) is inconsistent. % 26.17/4.47 | | | | % 26.17/4.47 | | | Case 2: % 26.17/4.47 | | | | % 26.17/4.47 | | | | (103) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.17/4.47 | | | | (apart_point_and_line(all_38_3, all_38_2) = v2 & % 26.17/4.47 | | | | apart_point_and_line(all_38_3, all_38_2) = v1 & % 26.17/4.47 | | | | distinct_lines(all_38_2, all_38_2) = v0 & ( ~ (v0 = 0) | v2 = % 26.17/4.47 | | | | 0 | v1 = 0)) % 26.17/4.47 | | | | % 26.17/4.47 | | | | DELTA: instantiating (103) with fresh symbols all_100_0, all_100_1, % 26.17/4.47 | | | | all_100_2 gives: % 26.17/4.47 | | | | (104) apart_point_and_line(all_38_3, all_38_2) = all_100_0 & % 26.17/4.47 | | | | apart_point_and_line(all_38_3, all_38_2) = all_100_1 & % 26.17/4.47 | | | | distinct_lines(all_38_2, all_38_2) = all_100_2 & ( ~ (all_100_2 % 26.17/4.47 | | | | = 0) | all_100_0 = 0 | all_100_1 = 0) % 26.17/4.47 | | | | % 26.17/4.47 | | | | ALPHA: (104) implies: % 26.17/4.47 | | | | (105) apart_point_and_line(all_38_3, all_38_2) = all_100_1 % 26.17/4.47 | | | | (106) apart_point_and_line(all_38_3, all_38_2) = all_100_0 % 26.17/4.47 | | | | % 26.17/4.47 | | | | BETA: splitting (92) gives: % 26.17/4.47 | | | | % 26.17/4.47 | | | | Case 1: % 26.17/4.47 | | | | | % 26.17/4.47 | | | | | (107) all_53_0 = 0 % 26.17/4.47 | | | | | % 26.17/4.47 | | | | | REDUCE: (88), (107) imply: % 26.17/4.47 | | | | | (108) $false % 26.17/4.47 | | | | | % 26.17/4.47 | | | | | CLOSE: (108) is inconsistent. % 26.17/4.47 | | | | | % 26.17/4.47 | | | | Case 2: % 26.17/4.47 | | | | | % 26.17/4.47 | | | | | (109) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.17/4.48 | | | | | (apart_point_and_line(all_38_4, all_38_1) = v2 & % 26.17/4.48 | | | | | apart_point_and_line(all_38_4, all_38_1) = v1 & % 26.17/4.48 | | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ (v0 = 0) | % 26.17/4.48 | | | | | v2 = 0 | v1 = 0)) % 26.17/4.48 | | | | | % 26.17/4.48 | | | | | DELTA: instantiating (109) with fresh symbols all_114_0, all_114_1, % 26.17/4.48 | | | | | all_114_2 gives: % 26.17/4.48 | | | | | (110) apart_point_and_line(all_38_4, all_38_1) = all_114_0 & % 26.17/4.48 | | | | | apart_point_and_line(all_38_4, all_38_1) = all_114_1 & % 26.17/4.48 | | | | | distinct_points(all_38_4, all_38_4) = all_114_2 & ( ~ % 26.17/4.48 | | | | | (all_114_2 = 0) | all_114_0 = 0 | all_114_1 = 0) % 26.17/4.48 | | | | | % 26.17/4.48 | | | | | ALPHA: (110) implies: % 26.17/4.48 | | | | | (111) apart_point_and_line(all_38_4, all_38_1) = all_114_1 % 26.17/4.48 | | | | | (112) apart_point_and_line(all_38_4, all_38_1) = all_114_0 % 26.17/4.48 | | | | | % 26.31/4.48 | | | | | BETA: splitting (93) gives: % 26.31/4.48 | | | | | % 26.31/4.48 | | | | | Case 1: % 26.31/4.48 | | | | | | % 26.31/4.48 | | | | | | (113) all_51_0 = 0 % 26.31/4.48 | | | | | | % 26.31/4.48 | | | | | | REDUCE: (87), (113) imply: % 26.31/4.48 | | | | | | (114) $false % 26.31/4.48 | | | | | | % 26.31/4.48 | | | | | | CLOSE: (114) is inconsistent. % 26.31/4.48 | | | | | | % 26.31/4.48 | | | | | Case 2: % 26.31/4.48 | | | | | | % 26.31/4.48 | | | | | | (115) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.31/4.48 | | | | | | (apart_point_and_line(all_38_3, all_38_1) = v2 & % 26.31/4.48 | | | | | | apart_point_and_line(all_38_3, all_38_1) = v1 & % 26.31/4.48 | | | | | | distinct_points(all_38_3, all_38_3) = v0 & ( ~ (v0 = 0) | % 26.31/4.48 | | | | | | v2 = 0 | v1 = 0)) % 26.31/4.48 | | | | | | % 26.31/4.48 | | | | | | DELTA: instantiating (115) with fresh symbols all_124_0, all_124_1, % 26.31/4.48 | | | | | | all_124_2 gives: % 26.31/4.48 | | | | | | (116) apart_point_and_line(all_38_3, all_38_1) = all_124_0 & % 26.31/4.48 | | | | | | apart_point_and_line(all_38_3, all_38_1) = all_124_1 & % 26.31/4.48 | | | | | | distinct_points(all_38_3, all_38_3) = all_124_2 & ( ~ % 26.31/4.48 | | | | | | (all_124_2 = 0) | all_124_0 = 0 | all_124_1 = 0) % 26.31/4.48 | | | | | | % 26.31/4.48 | | | | | | ALPHA: (116) implies: % 26.31/4.48 | | | | | | (117) apart_point_and_line(all_38_3, all_38_1) = all_124_1 % 26.31/4.48 | | | | | | (118) apart_point_and_line(all_38_3, all_38_1) = all_124_0 % 26.31/4.48 | | | | | | % 26.31/4.48 | | | | | | BETA: splitting (94) gives: % 26.31/4.48 | | | | | | % 26.31/4.48 | | | | | | Case 1: % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | (119) all_51_0 = 0 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | REDUCE: (87), (119) imply: % 26.31/4.48 | | | | | | | (120) $false % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | CLOSE: (120) is inconsistent. % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | Case 2: % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | (121) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] % 26.31/4.48 | | | | | | | : (apart_point_and_line(all_38_3, all_38_2) = v3 & % 26.31/4.48 | | | | | | | apart_point_and_line(all_38_3, all_38_2) = v2 & % 26.31/4.48 | | | | | | | distinct_lines(all_38_2, all_38_2) = v1 & % 26.31/4.48 | | | | | | | distinct_points(all_38_3, all_38_3) = v0 & ( ~ (v1 = 0) % 26.31/4.48 | | | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | DELTA: instantiating (121) with fresh symbols all_129_0, % 26.31/4.48 | | | | | | | all_129_1, all_129_2, all_129_3 gives: % 26.31/4.48 | | | | | | | (122) apart_point_and_line(all_38_3, all_38_2) = all_129_0 & % 26.31/4.48 | | | | | | | apart_point_and_line(all_38_3, all_38_2) = all_129_1 & % 26.31/4.48 | | | | | | | distinct_lines(all_38_2, all_38_2) = all_129_2 & % 26.31/4.48 | | | | | | | distinct_points(all_38_3, all_38_3) = all_129_3 & ( ~ % 26.31/4.48 | | | | | | | (all_129_2 = 0) | ~ (all_129_3 = 0) | all_129_0 = 0 | % 26.31/4.48 | | | | | | | all_129_1 = 0) % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | ALPHA: (122) implies: % 26.31/4.48 | | | | | | | (123) apart_point_and_line(all_38_3, all_38_2) = all_129_1 % 26.31/4.48 | | | | | | | (124) apart_point_and_line(all_38_3, all_38_2) = all_129_0 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | GROUND_INST: instantiating (14) with all_53_0, all_91_3, all_38_2, % 26.31/4.48 | | | | | | | all_38_4, simplifying with (50), (96) gives: % 26.31/4.48 | | | | | | | (125) all_91_3 = all_53_0 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | GROUND_INST: instantiating (14) with all_49_0, all_114_0, % 26.31/4.48 | | | | | | | all_38_1, all_38_4, simplifying with (42), (112) % 26.31/4.48 | | | | | | | gives: % 26.31/4.48 | | | | | | | (126) all_114_0 = all_49_0 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | GROUND_INST: instantiating (14) with all_114_1, all_114_0, % 26.31/4.48 | | | | | | | all_38_1, all_38_4, simplifying with (111), (112) % 26.31/4.48 | | | | | | | gives: % 26.31/4.48 | | | | | | | (127) all_114_0 = all_114_1 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | GROUND_INST: instantiating (14) with all_91_2, all_114_0, % 26.31/4.48 | | | | | | | all_38_1, all_38_4, simplifying with (97), (112) % 26.31/4.48 | | | | | | | gives: % 26.31/4.48 | | | | | | | (128) all_114_0 = all_91_2 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | GROUND_INST: instantiating (14) with all_51_0, all_100_1, % 26.31/4.48 | | | | | | | all_38_2, all_38_3, simplifying with (82), (105) % 26.31/4.48 | | | | | | | gives: % 26.31/4.48 | | | | | | | (129) all_100_1 = all_51_0 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | GROUND_INST: instantiating (14) with all_91_1, all_129_1, % 26.31/4.48 | | | | | | | all_38_2, all_38_3, simplifying with (98), (123) % 26.31/4.48 | | | | | | | gives: % 26.31/4.48 | | | | | | | (130) all_129_1 = all_91_1 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | GROUND_INST: instantiating (14) with all_129_1, all_129_0, % 26.31/4.48 | | | | | | | all_38_2, all_38_3, simplifying with (123), (124) % 26.31/4.48 | | | | | | | gives: % 26.31/4.48 | | | | | | | (131) all_129_0 = all_129_1 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | GROUND_INST: instantiating (14) with all_100_0, all_129_0, % 26.31/4.48 | | | | | | | all_38_2, all_38_3, simplifying with (106), (124) % 26.31/4.48 | | | | | | | gives: % 26.31/4.48 | | | | | | | (132) all_129_0 = all_100_0 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | GROUND_INST: instantiating (14) with all_100_1, all_129_0, % 26.31/4.48 | | | | | | | all_38_2, all_38_3, simplifying with (105), (124) % 26.31/4.48 | | | | | | | gives: % 26.31/4.48 | | | | | | | (133) all_129_0 = all_100_1 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | GROUND_INST: instantiating (14) with all_91_0, all_124_1, % 26.31/4.48 | | | | | | | all_38_1, all_38_3, simplifying with (99), (117) % 26.31/4.48 | | | | | | | gives: % 26.31/4.48 | | | | | | | (134) all_124_1 = all_91_0 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | GROUND_INST: instantiating (14) with all_47_0, all_124_0, % 26.31/4.48 | | | | | | | all_38_1, all_38_3, simplifying with (38), (118) % 26.31/4.48 | | | | | | | gives: % 26.31/4.48 | | | | | | | (135) all_124_0 = all_47_0 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | GROUND_INST: instantiating (14) with all_124_1, all_124_0, % 26.31/4.48 | | | | | | | all_38_1, all_38_3, simplifying with (117), (118) % 26.31/4.48 | | | | | | | gives: % 26.31/4.48 | | | | | | | (136) all_124_0 = all_124_1 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | COMBINE_EQS: (131), (132) imply: % 26.31/4.48 | | | | | | | (137) all_129_1 = all_100_0 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | SIMP: (137) implies: % 26.31/4.48 | | | | | | | (138) all_129_1 = all_100_0 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | COMBINE_EQS: (132), (133) imply: % 26.31/4.48 | | | | | | | (139) all_100_0 = all_100_1 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | COMBINE_EQS: (130), (138) imply: % 26.31/4.48 | | | | | | | (140) all_100_0 = all_91_1 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | SIMP: (140) implies: % 26.31/4.48 | | | | | | | (141) all_100_0 = all_91_1 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | COMBINE_EQS: (135), (136) imply: % 26.31/4.48 | | | | | | | (142) all_124_1 = all_47_0 % 26.31/4.48 | | | | | | | % 26.31/4.48 | | | | | | | SIMP: (142) implies: % 26.31/4.49 | | | | | | | (143) all_124_1 = all_47_0 % 26.31/4.49 | | | | | | | % 26.31/4.49 | | | | | | | COMBINE_EQS: (134), (143) imply: % 26.31/4.49 | | | | | | | (144) all_91_0 = all_47_0 % 26.31/4.49 | | | | | | | % 26.31/4.49 | | | | | | | COMBINE_EQS: (127), (128) imply: % 26.31/4.49 | | | | | | | (145) all_114_1 = all_91_2 % 26.31/4.49 | | | | | | | % 26.31/4.49 | | | | | | | COMBINE_EQS: (126), (127) imply: % 26.31/4.49 | | | | | | | (146) all_114_1 = all_49_0 % 26.31/4.49 | | | | | | | % 26.31/4.49 | | | | | | | COMBINE_EQS: (145), (146) imply: % 26.31/4.49 | | | | | | | (147) all_91_2 = all_49_0 % 26.31/4.49 | | | | | | | % 26.31/4.49 | | | | | | | SIMP: (147) implies: % 26.31/4.49 | | | | | | | (148) all_91_2 = all_49_0 % 26.31/4.49 | | | | | | | % 26.31/4.49 | | | | | | | COMBINE_EQS: (139), (141) imply: % 26.31/4.49 | | | | | | | (149) all_100_1 = all_91_1 % 26.31/4.49 | | | | | | | % 26.31/4.49 | | | | | | | SIMP: (149) implies: % 26.31/4.49 | | | | | | | (150) all_100_1 = all_91_1 % 26.31/4.49 | | | | | | | % 26.31/4.49 | | | | | | | COMBINE_EQS: (129), (150) imply: % 26.31/4.49 | | | | | | | (151) all_91_1 = all_51_0 % 26.31/4.49 | | | | | | | % 26.31/4.49 | | | | | | | BETA: splitting (39) gives: % 26.31/4.49 | | | | | | | % 26.31/4.49 | | | | | | | Case 1: % 26.31/4.49 | | | | | | | | % 26.31/4.49 | | | | | | | | (152) ~ (all_47_0 = 0) % 26.31/4.49 | | | | | | | | % 26.31/4.49 | | | | | | | | BETA: splitting (100) gives: % 26.31/4.49 | | | | | | | | % 26.31/4.49 | | | | | | | | Case 1: % 26.31/4.49 | | | | | | | | | % 26.31/4.49 | | | | | | | | | (153) all_91_0 = 0 % 26.31/4.49 | | | | | | | | | % 26.31/4.49 | | | | | | | | | COMBINE_EQS: (144), (153) imply: % 26.31/4.49 | | | | | | | | | (154) all_47_0 = 0 % 26.31/4.49 | | | | | | | | | % 26.31/4.49 | | | | | | | | | SIMP: (154) implies: % 26.31/4.49 | | | | | | | | | (155) all_47_0 = 0 % 26.31/4.49 | | | | | | | | | % 26.31/4.49 | | | | | | | | | REDUCE: (152), (155) imply: % 26.31/4.49 | | | | | | | | | (156) $false % 26.31/4.49 | | | | | | | | | % 26.31/4.49 | | | | | | | | | CLOSE: (156) is inconsistent. % 26.31/4.49 | | | | | | | | | % 26.31/4.49 | | | | | | | | Case 2: % 26.31/4.49 | | | | | | | | | % 26.31/4.49 | | | | | | | | | (157) all_91_1 = 0 | all_91_2 = 0 | all_91_3 = 0 % 26.31/4.49 | | | | | | | | | % 26.31/4.49 | | | | | | | | | BETA: splitting (157) gives: % 26.31/4.49 | | | | | | | | | % 26.31/4.49 | | | | | | | | | Case 1: % 26.31/4.49 | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | (158) all_91_1 = 0 % 26.31/4.49 | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | COMBINE_EQS: (151), (158) imply: % 26.31/4.49 | | | | | | | | | | (159) all_51_0 = 0 % 26.31/4.49 | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | SIMP: (159) implies: % 26.31/4.49 | | | | | | | | | | (160) all_51_0 = 0 % 26.31/4.49 | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | REDUCE: (87), (160) imply: % 26.31/4.49 | | | | | | | | | | (161) $false % 26.31/4.49 | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | CLOSE: (161) is inconsistent. % 26.31/4.49 | | | | | | | | | | % 26.31/4.49 | | | | | | | | | Case 2: % 26.31/4.49 | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | (162) all_91_2 = 0 | all_91_3 = 0 % 26.31/4.49 | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | BETA: splitting (162) gives: % 26.31/4.49 | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | Case 1: % 26.31/4.49 | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | (163) all_91_2 = 0 % 26.31/4.49 | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | COMBINE_EQS: (148), (163) imply: % 26.31/4.49 | | | | | | | | | | | (164) all_49_0 = 0 % 26.31/4.49 | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | SIMP: (164) implies: % 26.31/4.49 | | | | | | | | | | | (165) all_49_0 = 0 % 26.31/4.49 | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | BETA: splitting (43) gives: % 26.31/4.49 | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | Case 1: % 26.31/4.49 | | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | | (166) ~ (all_49_0 = 0) % 26.31/4.49 | | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | | REDUCE: (165), (166) imply: % 26.31/4.49 | | | | | | | | | | | | (167) $false % 26.31/4.49 | | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | | CLOSE: (167) is inconsistent. % 26.31/4.49 | | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | Case 2: % 26.31/4.49 | | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | | (168) ~ (all_49_1 = 0) % 26.31/4.49 | | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | | REDUCE: (77), (168) imply: % 26.31/4.49 | | | | | | | | | | | | (169) ~ (all_47_1 = 0) % 26.31/4.49 | | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | | REF_CLOSE: (18), (89), (169), (apart1) are inconsistent by % 26.31/4.49 | | | | | | | | | | | | sub-proof #1. % 26.31/4.49 | | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | End of split % 26.31/4.49 | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | Case 2: % 26.31/4.49 | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | (170) all_91_3 = 0 % 26.31/4.49 | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | COMBINE_EQS: (125), (170) imply: % 26.31/4.49 | | | | | | | | | | | (171) all_53_0 = 0 % 26.31/4.49 | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | SIMP: (171) implies: % 26.31/4.49 | | | | | | | | | | | (172) all_53_0 = 0 % 26.31/4.49 | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | REDUCE: (88), (172) imply: % 26.31/4.49 | | | | | | | | | | | (173) $false % 26.31/4.49 | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | | CLOSE: (173) is inconsistent. % 26.31/4.49 | | | | | | | | | | | % 26.31/4.49 | | | | | | | | | | End of split % 26.31/4.49 | | | | | | | | | | % 26.31/4.49 | | | | | | | | | End of split % 26.31/4.49 | | | | | | | | | % 26.31/4.49 | | | | | | | | End of split % 26.31/4.49 | | | | | | | | % 26.31/4.49 | | | | | | | Case 2: % 26.31/4.49 | | | | | | | | % 26.31/4.49 | | | | | | | | (174) ~ (all_47_1 = 0) % 26.31/4.49 | | | | | | | | % 26.31/4.49 | | | | | | | | REF_CLOSE: (18), (89), (174), (apart1) are inconsistent by % 26.31/4.49 | | | | | | | | sub-proof #1. % 26.31/4.49 | | | | | | | | % 26.31/4.49 | | | | | | | End of split % 26.31/4.49 | | | | | | | % 26.31/4.49 | | | | | | End of split % 26.31/4.49 | | | | | | % 26.31/4.49 | | | | | End of split % 26.31/4.49 | | | | | % 26.31/4.49 | | | | End of split % 26.31/4.49 | | | | % 26.31/4.49 | | | End of split % 26.31/4.49 | | | % 26.31/4.49 | | Case 2: % 26.31/4.49 | | | % 26.31/4.49 | | | (175) ~ (all_57_1 = 0) % 26.31/4.49 | | | % 26.31/4.49 | | | REDUCE: (75), (175) imply: % 26.31/4.49 | | | (176) $false % 26.31/4.49 | | | % 26.31/4.49 | | | CLOSE: (176) is inconsistent. % 26.31/4.49 | | | % 26.31/4.49 | | End of split % 26.31/4.49 | | % 26.31/4.49 | Case 2: % 26.31/4.49 | | % 26.31/4.49 | | (177) all_38_0 = 0 % 26.31/4.49 | | % 26.31/4.49 | | REDUCE: (17), (177) imply: % 26.31/4.49 | | (178) $false % 26.31/4.49 | | % 26.31/4.49 | | CLOSE: (178) is inconsistent. % 26.31/4.49 | | % 26.31/4.49 | End of split % 26.31/4.49 | % 26.31/4.49 End of proof % 26.31/4.49 % 26.31/4.49 Sub-proof #1 shows that the following formulas are inconsistent: % 26.31/4.49 ---------------------------------------------------------------- % 26.31/4.49 (1) all_47_1 = 0 | distinct_points(all_38_4, all_38_4) = 0 % 26.31/4.49 (2) ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 26.31/4.49 (3) $i(all_38_4) % 26.31/4.49 (4) ~ (all_47_1 = 0) % 26.31/4.49 % 26.31/4.49 Begin of proof % 26.31/4.49 | % 26.31/4.49 | BETA: splitting (1) gives: % 26.31/4.49 | % 26.31/4.49 | Case 1: % 26.31/4.49 | | % 26.31/4.49 | | (5) distinct_points(all_38_4, all_38_4) = 0 % 26.31/4.49 | | % 26.31/4.49 | | GROUND_INST: instantiating (2) with all_38_4, simplifying with (3), (5) % 26.31/4.49 | | gives: % 26.31/4.50 | | (6) $false % 26.31/4.50 | | % 26.31/4.50 | | CLOSE: (6) is inconsistent. % 26.31/4.50 | | % 26.31/4.50 | Case 2: % 26.31/4.50 | | % 26.31/4.50 | | (7) all_47_1 = 0 % 26.31/4.50 | | % 26.31/4.50 | | REDUCE: (4), (7) imply: % 26.31/4.50 | | (8) $false % 26.31/4.50 | | % 26.31/4.50 | | CLOSE: (8) is inconsistent. % 26.31/4.50 | | % 26.31/4.50 | End of split % 26.31/4.50 | % 26.31/4.50 End of proof % 26.31/4.50 % SZS output end Proof for theBenchmark % 26.31/4.50 % 26.31/4.50 3818ms %------------------------------------------------------------------------------