%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO200+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n003.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 23:22:12 EDT 2023 % Result : Theorem 6.88s 1.60s % Output : Proof 10.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO200+1 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n003.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 18:58:11 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.62/0.64 Running up to 7 provers in parallel. % 0.62/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.62/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.62/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.62/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.62/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.62/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.62/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.51/1.01 Prover 1: Preprocessing ... % 2.51/1.02 Prover 4: Preprocessing ... % 2.51/1.05 Prover 5: Preprocessing ... % 2.51/1.06 Prover 2: Preprocessing ... % 2.51/1.06 Prover 6: Preprocessing ... % 2.51/1.06 Prover 0: Preprocessing ... % 2.51/1.06 Prover 3: Preprocessing ... % 3.94/1.27 Prover 2: Proving ... % 3.94/1.27 Prover 5: Proving ... % 3.94/1.28 Prover 3: Constructing countermodel ... % 3.94/1.28 Prover 1: Constructing countermodel ... % 3.94/1.31 Prover 6: Constructing countermodel ... % 5.46/1.41 Prover 4: Constructing countermodel ... % 5.46/1.42 Prover 3: gave up % 5.46/1.42 Prover 6: gave up % 5.46/1.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.46/1.42 Prover 0: Proving ... % 5.46/1.43 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.46/1.45 Prover 7: Preprocessing ... % 5.92/1.47 Prover 8: Preprocessing ... % 5.92/1.49 Prover 7: Warning: ignoring some quantifiers % 5.92/1.50 Prover 7: Constructing countermodel ... % 5.92/1.53 Prover 1: gave up % 5.92/1.54 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.92/1.55 Prover 9: Preprocessing ... % 6.63/1.56 Prover 8: Warning: ignoring some quantifiers % 6.63/1.57 Prover 8: Constructing countermodel ... % 6.88/1.60 Prover 5: proved (944ms) % 6.88/1.60 % 6.88/1.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.88/1.60 % 6.88/1.60 Prover 0: stopped % 6.88/1.60 Prover 2: stopped % 6.88/1.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.88/1.60 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.88/1.60 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.88/1.62 Prover 7: gave up % 6.88/1.62 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 6.88/1.62 Prover 11: Preprocessing ... % 7.16/1.63 Prover 13: Preprocessing ... % 7.16/1.63 Prover 8: gave up % 7.22/1.65 Prover 10: Preprocessing ... % 7.22/1.65 Prover 16: Preprocessing ... % 7.22/1.65 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 7.22/1.67 Prover 13: Warning: ignoring some quantifiers % 7.22/1.67 Prover 13: Constructing countermodel ... % 7.22/1.68 Prover 19: Preprocessing ... % 7.22/1.69 Prover 16: Warning: ignoring some quantifiers % 7.22/1.69 Prover 16: Constructing countermodel ... % 7.22/1.69 Prover 10: Warning: ignoring some quantifiers % 7.22/1.70 Prover 10: Constructing countermodel ... % 7.75/1.72 Prover 9: Constructing countermodel ... % 7.75/1.72 Prover 9: stopped % 8.18/1.77 Prover 10: gave up % 8.18/1.78 Prover 19: Warning: ignoring some quantifiers % 8.18/1.79 Prover 19: Constructing countermodel ... % 8.18/1.81 Prover 11: Constructing countermodel ... % 8.18/1.83 Prover 13: gave up % 8.18/1.84 Prover 16: gave up % 8.18/1.86 Prover 19: gave up % 9.96/2.04 Prover 4: Found proof (size 86) % 9.96/2.04 Prover 4: proved (1383ms) % 9.96/2.04 Prover 11: stopped % 9.96/2.04 % 9.96/2.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.96/2.04 % 9.96/2.06 % SZS output start Proof for theBenchmark % 10.10/2.07 Assumptions after simplification: % 10.10/2.07 --------------------------------- % 10.10/2.07 % 10.10/2.07 (apart1) % 10.10/2.09 ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 10.10/2.09 % 10.10/2.09 (apart4) % 10.10/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 10.10/2.10 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) % 10.10/2.10 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 10.10/2.10 distinct_points(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 10.10/2.10 ! [v3: int] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ % 10.10/2.10 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 10.10/2.10 distinct_points(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 10.10/2.10 [v3: int] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ % 10.10/2.10 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 10.10/2.10 distinct_points(v1, v2) = 0) % 10.10/2.10 % 10.10/2.10 (ci1) % 10.10/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 10.10/2.10 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 10.10/2.10 (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 10.10/2.10 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 10.10/2.10 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 10.10/2.10 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 10.10/2.10 apart_point_and_line(v0, v2) = v3 & $i(v2))) % 10.10/2.10 % 10.10/2.10 (ci2) % 10.10/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 10.10/2.10 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 10.10/2.10 (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 10.10/2.10 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 10.10/2.10 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 10.10/2.10 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 10.10/2.10 apart_point_and_line(v1, v2) = v3 & $i(v2))) % 10.10/2.10 % 10.10/2.10 (con) % 10.10/2.11 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (line_connecting(v1, % 10.10/2.11 v0) = v3 & line_connecting(v0, v1) = v2 & distinct_lines(v2, v3) = 0 & % 10.10/2.11 distinct_points(v0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 10.10/2.11 % 10.10/2.11 (cu1) % 10.10/2.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 10.10/2.12 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 10.10/2.12 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 10.10/2.12 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 10.10/2.12 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, % 10.10/2.12 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 10.10/2.12 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 10.10/2.12 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 10.10/2.12 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 10.10/2.12 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 10.10/2.12 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 10.10/2.12 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 % 10.10/2.12 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 10.10/2.12 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 10.10/2.12 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 10.10/2.12 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 10.10/2.12 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 10.10/2.12 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 10.10/2.12 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = % 10.10/2.12 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 10.10/2.12 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = % 10.10/2.12 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 10.10/2.12 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 10.10/2.12 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = % 10.10/2.12 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 % 10.10/2.12 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : % 10.10/2.12 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 10.10/2.12 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 10.10/2.12 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 10.10/2.12 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 10.10/2.12 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & % 10.10/2.12 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 10.10/2.12 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 10.10/2.12 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ % 10.10/2.12 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 10.10/2.12 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 10.10/2.12 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, % 10.10/2.12 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 10.10/2.12 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 10.10/2.12 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 10.10/2.12 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 10.10/2.12 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 10.10/2.12 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 10.10/2.12 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 10.10/2.12 % 10.10/2.12 (function-axioms) % 10.10/2.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.10/2.12 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 10.10/2.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.10/2.12 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 10.10/2.12 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 10.10/2.12 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 10.10/2.12 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.10/2.12 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.10/2.12 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 10.10/2.12 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 10.10/2.12 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 10.10/2.12 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 10.10/2.12 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 10.10/2.12 (distinct_points(v3, v2) = v0)) % 10.10/2.12 % 10.10/2.12 Further assumptions not needed in the proof: % 10.10/2.12 -------------------------------------------- % 10.10/2.12 apart2, apart3, apart5, ax6, ceq1, ceq2, ceq3, ci3, ci4 % 10.10/2.12 % 10.10/2.12 Those formulas are unsatisfiable: % 10.10/2.12 --------------------------------- % 10.10/2.12 % 10.10/2.12 Begin of proof % 10.10/2.12 | % 10.10/2.12 | ALPHA: (apart4) implies: % 10.10/2.12 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 10.10/2.12 | (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | % 10.10/2.12 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) % 10.10/2.12 | % 10.10/2.12 | ALPHA: (ci1) implies: % 10.10/2.13 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 10.10/2.13 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 10.10/2.13 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 10.10/2.13 | $i(v2))) % 10.40/2.13 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 10.40/2.13 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 10.40/2.13 | (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( % 10.40/2.13 | ~ (v4 = 0) | ~ (v3 = 0)))) % 10.40/2.13 | % 10.40/2.13 | ALPHA: (ci2) implies: % 10.40/2.13 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 10.40/2.13 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 10.40/2.13 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 10.40/2.13 | $i(v2))) % 10.40/2.13 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 10.40/2.13 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 10.40/2.13 | (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( % 10.40/2.13 | ~ (v4 = 0) | ~ (v3 = 0)))) % 10.40/2.13 | % 10.40/2.13 | ALPHA: (cu1) implies: % 10.40/2.13 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 10.40/2.13 | (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ % 10.40/2.13 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 10.40/2.13 | any] : ? [v6: any] : ? [v7: any] : (apart_point_and_line(v1, v3) % 10.40/2.13 | = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, % 10.40/2.13 | v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | % 10.40/2.13 | v5 = 0 | v4 = 0))) % 10.40/2.13 | % 10.40/2.13 | ALPHA: (function-axioms) implies: % 10.40/2.13 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.40/2.13 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 10.40/2.13 | (distinct_points(v3, v2) = v0)) % 10.40/2.13 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.40/2.13 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 10.40/2.13 | (apart_point_and_line(v3, v2) = v0)) % 10.40/2.13 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.40/2.13 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 10.40/2.13 | % 10.40/2.13 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 10.40/2.13 | all_17_3 gives: % 10.40/2.13 | (10) line_connecting(all_17_2, all_17_3) = all_17_0 & % 10.40/2.13 | line_connecting(all_17_3, all_17_2) = all_17_1 & % 10.40/2.13 | distinct_lines(all_17_1, all_17_0) = 0 & distinct_points(all_17_3, % 10.40/2.13 | all_17_2) = 0 & $i(all_17_0) & $i(all_17_1) & $i(all_17_2) & % 10.40/2.13 | $i(all_17_3) % 10.40/2.13 | % 10.40/2.13 | ALPHA: (10) implies: % 10.40/2.13 | (11) $i(all_17_3) % 10.40/2.14 | (12) $i(all_17_2) % 10.40/2.14 | (13) $i(all_17_1) % 10.40/2.14 | (14) $i(all_17_0) % 10.40/2.14 | (15) distinct_points(all_17_3, all_17_2) = 0 % 10.40/2.14 | (16) distinct_lines(all_17_1, all_17_0) = 0 % 10.40/2.14 | (17) line_connecting(all_17_3, all_17_2) = all_17_1 % 10.40/2.14 | (18) line_connecting(all_17_2, all_17_3) = all_17_0 % 10.40/2.14 | % 10.40/2.14 | GROUND_INST: instantiating (4) with all_17_3, all_17_2, simplifying with (11), % 10.40/2.14 | (12), (15) gives: % 10.40/2.14 | (19) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_3, % 10.40/2.14 | all_17_2) = v0 & apart_point_and_line(all_17_2, v0) = v1 & $i(v0)) % 10.40/2.14 | % 10.40/2.14 | GROUND_INST: instantiating (2) with all_17_3, all_17_2, simplifying with (11), % 10.40/2.14 | (12), (15) gives: % 10.40/2.14 | (20) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_17_3, % 10.40/2.14 | all_17_2) = v0 & apart_point_and_line(all_17_3, v0) = v1 & $i(v0)) % 10.40/2.14 | % 10.40/2.14 | GROUND_INST: instantiating (6) with all_17_3, all_17_2, all_17_1, all_17_0, % 10.40/2.14 | simplifying with (11), (12), (13), (14), (15), (16) gives: % 10.40/2.14 | (21) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 10.40/2.14 | (apart_point_and_line(all_17_2, all_17_0) = v3 & % 10.40/2.14 | apart_point_and_line(all_17_2, all_17_1) = v2 & % 10.40/2.14 | apart_point_and_line(all_17_3, all_17_0) = v1 & % 10.40/2.14 | apart_point_and_line(all_17_3, all_17_1) = v0 & (v3 = 0 | v2 = 0 | % 10.40/2.14 | v1 = 0 | v0 = 0)) % 10.40/2.14 | % 10.40/2.14 | GROUND_INST: instantiating (5) with all_17_3, all_17_2, all_17_1, simplifying % 10.40/2.14 | with (11), (12), (17) gives: % 10.40/2.14 | (22) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_2, % 10.40/2.14 | all_17_1) = v1 & distinct_points(all_17_3, all_17_2) = v0 & ( ~ % 10.40/2.14 | (v1 = 0) | ~ (v0 = 0))) % 10.40/2.14 | % 10.40/2.14 | GROUND_INST: instantiating (3) with all_17_3, all_17_2, all_17_1, simplifying % 10.40/2.14 | with (11), (12), (17) gives: % 10.40/2.14 | (23) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_3, % 10.40/2.14 | all_17_1) = v1 & distinct_points(all_17_3, all_17_2) = v0 & ( ~ % 10.40/2.14 | (v1 = 0) | ~ (v0 = 0))) % 10.40/2.14 | % 10.40/2.14 | GROUND_INST: instantiating (5) with all_17_2, all_17_3, all_17_0, simplifying % 10.40/2.14 | with (11), (12), (18) gives: % 10.40/2.14 | (24) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_3, % 10.40/2.14 | all_17_0) = v1 & distinct_points(all_17_2, all_17_3) = v0 & ( ~ % 10.40/2.14 | (v1 = 0) | ~ (v0 = 0))) % 10.40/2.14 | % 10.40/2.14 | GROUND_INST: instantiating (3) with all_17_2, all_17_3, all_17_0, simplifying % 10.40/2.14 | with (11), (12), (18) gives: % 10.40/2.14 | (25) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_17_2, % 10.40/2.14 | all_17_0) = v1 & distinct_points(all_17_2, all_17_3) = v0 & ( ~ % 10.40/2.14 | (v1 = 0) | ~ (v0 = 0))) % 10.40/2.14 | % 10.40/2.14 | DELTA: instantiating (25) with fresh symbols all_24_0, all_24_1 gives: % 10.40/2.14 | (26) apart_point_and_line(all_17_2, all_17_0) = all_24_0 & % 10.40/2.14 | distinct_points(all_17_2, all_17_3) = all_24_1 & ( ~ (all_24_0 = 0) | % 10.40/2.14 | ~ (all_24_1 = 0)) % 10.40/2.14 | % 10.40/2.14 | ALPHA: (26) implies: % 10.40/2.14 | (27) distinct_points(all_17_2, all_17_3) = all_24_1 % 10.40/2.15 | (28) apart_point_and_line(all_17_2, all_17_0) = all_24_0 % 10.40/2.15 | (29) ~ (all_24_0 = 0) | ~ (all_24_1 = 0) % 10.40/2.15 | % 10.40/2.15 | DELTA: instantiating (22) with fresh symbols all_26_0, all_26_1 gives: % 10.40/2.15 | (30) apart_point_and_line(all_17_2, all_17_1) = all_26_0 & % 10.40/2.15 | distinct_points(all_17_3, all_17_2) = all_26_1 & ( ~ (all_26_0 = 0) | % 10.40/2.15 | ~ (all_26_1 = 0)) % 10.40/2.15 | % 10.40/2.15 | ALPHA: (30) implies: % 10.40/2.15 | (31) distinct_points(all_17_3, all_17_2) = all_26_1 % 10.40/2.15 | (32) apart_point_and_line(all_17_2, all_17_1) = all_26_0 % 10.40/2.15 | % 10.40/2.15 | DELTA: instantiating (24) with fresh symbols all_28_0, all_28_1 gives: % 10.40/2.15 | (33) apart_point_and_line(all_17_3, all_17_0) = all_28_0 & % 10.40/2.15 | distinct_points(all_17_2, all_17_3) = all_28_1 & ( ~ (all_28_0 = 0) | % 10.40/2.15 | ~ (all_28_1 = 0)) % 10.40/2.15 | % 10.40/2.15 | ALPHA: (33) implies: % 10.40/2.15 | (34) distinct_points(all_17_2, all_17_3) = all_28_1 % 10.40/2.15 | (35) apart_point_and_line(all_17_3, all_17_0) = all_28_0 % 10.40/2.15 | (36) ~ (all_28_0 = 0) | ~ (all_28_1 = 0) % 10.40/2.15 | % 10.40/2.15 | DELTA: instantiating (23) with fresh symbols all_30_0, all_30_1 gives: % 10.40/2.15 | (37) apart_point_and_line(all_17_3, all_17_1) = all_30_0 & % 10.40/2.15 | distinct_points(all_17_3, all_17_2) = all_30_1 & ( ~ (all_30_0 = 0) | % 10.40/2.15 | ~ (all_30_1 = 0)) % 10.40/2.15 | % 10.40/2.15 | ALPHA: (37) implies: % 10.40/2.15 | (38) distinct_points(all_17_3, all_17_2) = all_30_1 % 10.40/2.15 | (39) apart_point_and_line(all_17_3, all_17_1) = all_30_0 % 10.40/2.15 | % 10.40/2.15 | DELTA: instantiating (20) with fresh symbols all_32_0, all_32_1 gives: % 10.40/2.15 | (40) ~ (all_32_0 = 0) & line_connecting(all_17_3, all_17_2) = all_32_1 & % 10.40/2.15 | apart_point_and_line(all_17_3, all_32_1) = all_32_0 & $i(all_32_1) % 10.40/2.15 | % 10.40/2.15 | ALPHA: (40) implies: % 10.40/2.15 | (41) ~ (all_32_0 = 0) % 10.40/2.15 | (42) apart_point_and_line(all_17_3, all_32_1) = all_32_0 % 10.40/2.15 | (43) line_connecting(all_17_3, all_17_2) = all_32_1 % 10.40/2.15 | % 10.40/2.15 | DELTA: instantiating (19) with fresh symbols all_34_0, all_34_1 gives: % 10.40/2.15 | (44) ~ (all_34_0 = 0) & line_connecting(all_17_3, all_17_2) = all_34_1 & % 10.40/2.15 | apart_point_and_line(all_17_2, all_34_1) = all_34_0 & $i(all_34_1) % 10.40/2.15 | % 10.40/2.15 | ALPHA: (44) implies: % 10.40/2.15 | (45) ~ (all_34_0 = 0) % 10.40/2.15 | (46) apart_point_and_line(all_17_2, all_34_1) = all_34_0 % 10.40/2.15 | (47) line_connecting(all_17_3, all_17_2) = all_34_1 % 10.40/2.15 | % 10.40/2.15 | DELTA: instantiating (21) with fresh symbols all_36_0, all_36_1, all_36_2, % 10.40/2.15 | all_36_3 gives: % 10.40/2.15 | (48) apart_point_and_line(all_17_2, all_17_0) = all_36_0 & % 10.40/2.15 | apart_point_and_line(all_17_2, all_17_1) = all_36_1 & % 10.40/2.15 | apart_point_and_line(all_17_3, all_17_0) = all_36_2 & % 10.40/2.15 | apart_point_and_line(all_17_3, all_17_1) = all_36_3 & (all_36_0 = 0 | % 10.40/2.15 | all_36_1 = 0 | all_36_2 = 0 | all_36_3 = 0) % 10.40/2.15 | % 10.40/2.15 | ALPHA: (48) implies: % 10.40/2.15 | (49) apart_point_and_line(all_17_3, all_17_1) = all_36_3 % 10.40/2.15 | (50) apart_point_and_line(all_17_3, all_17_0) = all_36_2 % 10.40/2.15 | (51) apart_point_and_line(all_17_2, all_17_1) = all_36_1 % 10.40/2.15 | (52) apart_point_and_line(all_17_2, all_17_0) = all_36_0 % 10.40/2.15 | (53) all_36_0 = 0 | all_36_1 = 0 | all_36_2 = 0 | all_36_3 = 0 % 10.40/2.15 | % 10.40/2.15 | GROUND_INST: instantiating (7) with 0, all_30_1, all_17_2, all_17_3, % 10.40/2.15 | simplifying with (15), (38) gives: % 10.40/2.15 | (54) all_30_1 = 0 % 10.40/2.15 | % 10.40/2.15 | GROUND_INST: instantiating (7) with all_26_1, all_30_1, all_17_2, all_17_3, % 10.40/2.15 | simplifying with (31), (38) gives: % 10.40/2.15 | (55) all_30_1 = all_26_1 % 10.40/2.15 | % 10.40/2.15 | GROUND_INST: instantiating (7) with all_24_1, all_28_1, all_17_3, all_17_2, % 10.40/2.15 | simplifying with (27), (34) gives: % 10.40/2.15 | (56) all_28_1 = all_24_1 % 10.40/2.15 | % 10.40/2.15 | GROUND_INST: instantiating (8) with all_30_0, all_36_3, all_17_1, all_17_3, % 10.40/2.15 | simplifying with (39), (49) gives: % 10.40/2.15 | (57) all_36_3 = all_30_0 % 10.40/2.15 | % 10.40/2.15 | GROUND_INST: instantiating (8) with all_28_0, all_36_2, all_17_0, all_17_3, % 10.40/2.15 | simplifying with (35), (50) gives: % 10.40/2.16 | (58) all_36_2 = all_28_0 % 10.40/2.16 | % 10.40/2.16 | GROUND_INST: instantiating (8) with all_26_0, all_36_1, all_17_1, all_17_2, % 10.40/2.16 | simplifying with (32), (51) gives: % 10.40/2.16 | (59) all_36_1 = all_26_0 % 10.40/2.16 | % 10.40/2.16 | GROUND_INST: instantiating (8) with all_24_0, all_36_0, all_17_0, all_17_2, % 10.40/2.16 | simplifying with (28), (52) gives: % 10.40/2.16 | (60) all_36_0 = all_24_0 % 10.40/2.16 | % 10.40/2.16 | GROUND_INST: instantiating (9) with all_17_1, all_34_1, all_17_2, all_17_3, % 10.40/2.16 | simplifying with (17), (47) gives: % 10.40/2.16 | (61) all_34_1 = all_17_1 % 10.40/2.16 | % 10.40/2.16 | GROUND_INST: instantiating (9) with all_32_1, all_34_1, all_17_2, all_17_3, % 10.40/2.16 | simplifying with (43), (47) gives: % 10.40/2.16 | (62) all_34_1 = all_32_1 % 10.40/2.16 | % 10.40/2.16 | COMBINE_EQS: (61), (62) imply: % 10.40/2.16 | (63) all_32_1 = all_17_1 % 10.40/2.16 | % 10.40/2.16 | SIMP: (63) implies: % 10.55/2.16 | (64) all_32_1 = all_17_1 % 10.55/2.16 | % 10.55/2.16 | COMBINE_EQS: (54), (55) imply: % 10.55/2.16 | (65) all_26_1 = 0 % 10.55/2.16 | % 10.55/2.16 | REDUCE: (46), (61) imply: % 10.55/2.16 | (66) apart_point_and_line(all_17_2, all_17_1) = all_34_0 % 10.55/2.16 | % 10.55/2.16 | REDUCE: (42), (64) imply: % 10.55/2.16 | (67) apart_point_and_line(all_17_3, all_17_1) = all_32_0 % 10.55/2.16 | % 10.55/2.16 | GROUND_INST: instantiating (8) with all_30_0, all_32_0, all_17_1, all_17_3, % 10.55/2.16 | simplifying with (39), (67) gives: % 10.55/2.16 | (68) all_32_0 = all_30_0 % 10.55/2.16 | % 10.55/2.16 | GROUND_INST: instantiating (8) with all_26_0, all_34_0, all_17_1, all_17_2, % 10.55/2.16 | simplifying with (32), (66) gives: % 10.55/2.16 | (69) all_34_0 = all_26_0 % 10.55/2.16 | % 10.55/2.16 | REDUCE: (45), (69) imply: % 10.55/2.16 | (70) ~ (all_26_0 = 0) % 10.55/2.16 | % 10.55/2.16 | REDUCE: (41), (68) imply: % 10.55/2.16 | (71) ~ (all_30_0 = 0) % 10.55/2.16 | % 10.55/2.16 | GROUND_INST: instantiating (1) with all_17_3, all_17_2, all_17_3, all_24_1, % 10.55/2.16 | simplifying with (11), (12), (15), (27) gives: % 10.55/2.16 | (72) all_24_1 = 0 | distinct_points(all_17_3, all_17_3) = 0 % 10.55/2.16 | % 10.55/2.16 | BETA: splitting (29) gives: % 10.55/2.16 | % 10.55/2.16 | Case 1: % 10.55/2.16 | | % 10.55/2.16 | | (73) ~ (all_24_0 = 0) % 10.55/2.16 | | % 10.55/2.16 | | BETA: splitting (53) gives: % 10.55/2.16 | | % 10.55/2.16 | | Case 1: % 10.55/2.16 | | | % 10.55/2.16 | | | (74) all_36_0 = 0 % 10.55/2.16 | | | % 10.55/2.16 | | | COMBINE_EQS: (60), (74) imply: % 10.55/2.16 | | | (75) all_24_0 = 0 % 10.55/2.16 | | | % 10.55/2.16 | | | REDUCE: (73), (75) imply: % 10.55/2.16 | | | (76) $false % 10.55/2.16 | | | % 10.55/2.16 | | | CLOSE: (76) is inconsistent. % 10.55/2.16 | | | % 10.55/2.16 | | Case 2: % 10.55/2.16 | | | % 10.55/2.16 | | | (77) all_36_1 = 0 | all_36_2 = 0 | all_36_3 = 0 % 10.55/2.16 | | | % 10.55/2.16 | | | BETA: splitting (36) gives: % 10.55/2.16 | | | % 10.55/2.16 | | | Case 1: % 10.55/2.16 | | | | % 10.55/2.16 | | | | (78) ~ (all_28_0 = 0) % 10.55/2.16 | | | | % 10.55/2.16 | | | | BETA: splitting (77) gives: % 10.55/2.16 | | | | % 10.55/2.16 | | | | Case 1: % 10.55/2.16 | | | | | % 10.55/2.16 | | | | | (79) all_36_1 = 0 % 10.55/2.16 | | | | | % 10.55/2.16 | | | | | COMBINE_EQS: (59), (79) imply: % 10.55/2.16 | | | | | (80) all_26_0 = 0 % 10.55/2.16 | | | | | % 10.55/2.16 | | | | | REDUCE: (70), (80) imply: % 10.55/2.16 | | | | | (81) $false % 10.55/2.16 | | | | | % 10.55/2.16 | | | | | CLOSE: (81) is inconsistent. % 10.55/2.16 | | | | | % 10.55/2.16 | | | | Case 2: % 10.55/2.16 | | | | | % 10.55/2.16 | | | | | (82) all_36_2 = 0 | all_36_3 = 0 % 10.55/2.16 | | | | | % 10.55/2.16 | | | | | BETA: splitting (82) gives: % 10.55/2.16 | | | | | % 10.55/2.16 | | | | | Case 1: % 10.55/2.16 | | | | | | % 10.55/2.16 | | | | | | (83) all_36_2 = 0 % 10.55/2.16 | | | | | | % 10.55/2.16 | | | | | | COMBINE_EQS: (58), (83) imply: % 10.55/2.17 | | | | | | (84) all_28_0 = 0 % 10.55/2.17 | | | | | | % 10.55/2.17 | | | | | | SIMP: (84) implies: % 10.55/2.17 | | | | | | (85) all_28_0 = 0 % 10.55/2.17 | | | | | | % 10.55/2.17 | | | | | | REDUCE: (78), (85) imply: % 10.55/2.17 | | | | | | (86) $false % 10.55/2.17 | | | | | | % 10.55/2.17 | | | | | | CLOSE: (86) is inconsistent. % 10.55/2.17 | | | | | | % 10.55/2.17 | | | | | Case 2: % 10.55/2.17 | | | | | | % 10.55/2.17 | | | | | | (87) all_36_3 = 0 % 10.55/2.17 | | | | | | % 10.55/2.17 | | | | | | COMBINE_EQS: (57), (87) imply: % 10.55/2.17 | | | | | | (88) all_30_0 = 0 % 10.55/2.17 | | | | | | % 10.55/2.17 | | | | | | REDUCE: (71), (88) imply: % 10.55/2.17 | | | | | | (89) $false % 10.55/2.17 | | | | | | % 10.55/2.17 | | | | | | CLOSE: (89) is inconsistent. % 10.55/2.17 | | | | | | % 10.55/2.17 | | | | | End of split % 10.55/2.17 | | | | | % 10.55/2.17 | | | | End of split % 10.55/2.17 | | | | % 10.55/2.17 | | | Case 2: % 10.55/2.17 | | | | % 10.55/2.17 | | | | (90) ~ (all_28_1 = 0) % 10.55/2.17 | | | | % 10.55/2.17 | | | | REDUCE: (56), (90) imply: % 10.55/2.17 | | | | (91) ~ (all_24_1 = 0) % 10.55/2.17 | | | | % 10.55/2.17 | | | | REF_CLOSE: (11), (72), (91), (apart1) are inconsistent by sub-proof #1. % 10.55/2.17 | | | | % 10.55/2.17 | | | End of split % 10.55/2.17 | | | % 10.55/2.17 | | End of split % 10.55/2.17 | | % 10.55/2.17 | Case 2: % 10.55/2.17 | | % 10.55/2.17 | | (92) ~ (all_24_1 = 0) % 10.55/2.17 | | % 10.55/2.17 | | REF_CLOSE: (11), (72), (92), (apart1) are inconsistent by sub-proof #1. % 10.55/2.17 | | % 10.55/2.17 | End of split % 10.55/2.17 | % 10.55/2.17 End of proof % 10.55/2.17 % 10.55/2.17 Sub-proof #1 shows that the following formulas are inconsistent: % 10.55/2.17 ---------------------------------------------------------------- % 10.55/2.17 (1) all_24_1 = 0 | distinct_points(all_17_3, all_17_3) = 0 % 10.55/2.17 (2) ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 10.55/2.17 (3) $i(all_17_3) % 10.55/2.17 (4) ~ (all_24_1 = 0) % 10.55/2.17 % 10.55/2.17 Begin of proof % 10.55/2.17 | % 10.55/2.17 | BETA: splitting (1) gives: % 10.55/2.17 | % 10.55/2.17 | Case 1: % 10.55/2.17 | | % 10.55/2.17 | | (5) distinct_points(all_17_3, all_17_3) = 0 % 10.55/2.17 | | % 10.55/2.17 | | GROUND_INST: instantiating (2) with all_17_3, simplifying with (3), (5) % 10.55/2.17 | | gives: % 10.55/2.17 | | (6) $false % 10.55/2.17 | | % 10.55/2.17 | | CLOSE: (6) is inconsistent. % 10.55/2.17 | | % 10.55/2.17 | Case 2: % 10.55/2.17 | | % 10.55/2.17 | | (7) all_24_1 = 0 % 10.55/2.17 | | % 10.55/2.17 | | REDUCE: (4), (7) imply: % 10.55/2.17 | | (8) $false % 10.55/2.17 | | % 10.55/2.17 | | CLOSE: (8) is inconsistent. % 10.55/2.17 | | % 10.55/2.17 | End of split % 10.55/2.17 | % 10.55/2.17 End of proof % 10.55/2.17 % SZS output end Proof for theBenchmark % 10.55/2.17 % 10.55/2.17 1547ms %------------------------------------------------------------------------------