%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO190+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n031.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 23:22:03 EDT 2023 % Result : Theorem 14.09s 2.58s % Output : Proof 14.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEO190+2 : TPTP v8.1.2. Released v3.3.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n031.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Tue Aug 29 22:18:11 EDT 2023 % 0.13/0.34 % CPUTime : % 0.54/0.60 ________ _____ % 0.54/0.60 ___ __ \_________(_)________________________________ % 0.54/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.54/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.54/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.54/0.60 % 0.54/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.54/0.60 (2023-06-19) % 0.54/0.60 % 0.54/0.60 (c) Philipp Rümmer, 2009-2023 % 0.54/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.54/0.60 Amanda Stjerna. % 0.54/0.60 Free software under BSD-3-Clause. % 0.54/0.60 % 0.54/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.54/0.60 % 0.54/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.54/0.61 Running up to 7 provers in parallel. % 0.72/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.72/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.72/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.72/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.72/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.72/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.72/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.43/1.02 Prover 1: Preprocessing ... % 2.43/1.02 Prover 4: Preprocessing ... % 2.43/1.05 Prover 6: Preprocessing ... % 2.43/1.05 Prover 2: Preprocessing ... % 2.43/1.05 Prover 3: Preprocessing ... % 2.43/1.05 Prover 5: Preprocessing ... % 2.43/1.05 Prover 0: Preprocessing ... % 4.44/1.26 Prover 5: Proving ... % 4.44/1.26 Prover 2: Proving ... % 4.44/1.27 Prover 6: Constructing countermodel ... % 4.60/1.29 Prover 1: Constructing countermodel ... % 4.60/1.29 Prover 3: Constructing countermodel ... % 5.05/1.37 Prover 4: Constructing countermodel ... % 5.05/1.41 Prover 0: Proving ... % 5.63/1.44 Prover 3: gave up % 5.63/1.46 Prover 6: gave up % 5.63/1.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.63/1.46 Prover 1: gave up % 5.63/1.46 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.63/1.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.08/1.49 Prover 7: Preprocessing ... % 6.08/1.50 Prover 8: Preprocessing ... % 6.08/1.51 Prover 9: Preprocessing ... % 6.84/1.58 Prover 7: Warning: ignoring some quantifiers % 6.84/1.59 Prover 7: Constructing countermodel ... % 6.84/1.62 Prover 8: Warning: ignoring some quantifiers % 7.16/1.62 Prover 8: Constructing countermodel ... % 7.38/1.69 Prover 9: Constructing countermodel ... % 7.38/1.72 Prover 7: gave up % 7.38/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.09/1.75 Prover 8: gave up % 8.09/1.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.09/1.76 Prover 10: Preprocessing ... % 8.09/1.78 Prover 11: Preprocessing ... % 8.54/1.80 Prover 10: Warning: ignoring some quantifiers % 8.54/1.81 Prover 10: Constructing countermodel ... % 8.98/1.87 Prover 10: gave up % 8.98/1.89 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 8.98/1.91 Prover 12: Preprocessing ... % 8.98/1.92 Prover 11: Constructing countermodel ... % 10.00/2.00 Prover 12: Proving ... % 14.09/2.58 Prover 11: Found proof (size 81) % 14.09/2.58 Prover 11: proved (830ms) % 14.09/2.58 Prover 9: stopped % 14.09/2.58 Prover 12: stopped % 14.09/2.58 Prover 2: stopped % 14.09/2.58 Prover 5: stopped % 14.09/2.58 Prover 0: stopped % 14.09/2.58 Prover 4: stopped % 14.09/2.58 % 14.09/2.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.09/2.58 % 14.09/2.59 % SZS output start Proof for theBenchmark % 14.58/2.59 Assumptions after simplification: % 14.58/2.59 --------------------------------- % 14.58/2.59 % 14.58/2.59 (apart1) % 14.58/2.62 ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 14.58/2.62 % 14.58/2.62 (apart4) % 14.58/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 14.58/2.62 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) % 14.58/2.62 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 14.58/2.62 distinct_points(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 14.58/2.62 ! [v3: int] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ % 14.58/2.62 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 14.58/2.62 distinct_points(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 14.58/2.62 [v3: int] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ % 14.58/2.62 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 14.58/2.62 distinct_points(v1, v2) = 0) % 14.58/2.62 % 14.58/2.62 (ceq2) % 14.58/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 14.58/2.62 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 14.58/2.62 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 14.58/2.62 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 14.58/2.62 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 14.58/2.62 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 14.58/2.62 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 14.58/2.62 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 14.58/2.62 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 14.58/2.62 apart_point_and_line(v0, v2) = 0) % 14.58/2.62 % 14.58/2.62 (con) % 14.58/2.63 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: % 14.58/2.63 $i] : ( ~ (v4 = 0) & line_connecting(v1, v0) = v5 & line_connecting(v0, v1) % 14.58/2.63 = v3 & apart_point_and_line(v2, v5) = 0 & apart_point_and_line(v2, v3) = v4 % 14.58/2.63 & distinct_points(v1, v2) = 0 & distinct_points(v0, v2) = 0 & % 14.58/2.63 distinct_points(v0, v1) = 0 & $i(v5) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 14.58/2.63 % 14.58/2.63 (con1) % 14.58/2.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 14.58/2.63 (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ~ % 14.58/2.63 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] % 14.58/2.63 : ((v6 = 0 & v5 = 0 & distinct_points(v2, v1) = 0 & distinct_points(v2, v0) % 14.58/2.63 = 0) | ( ~ (v4 = 0) & distinct_points(v0, v1) = v4))) % 14.58/2.63 % 14.58/2.63 (cu1) % 14.58/2.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 14.58/2.63 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 14.58/2.63 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 14.58/2.63 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 14.58/2.63 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 14.58/2.64 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, % 14.58/2.64 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 14.58/2.64 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, % 14.58/2.64 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ % 14.58/2.64 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 14.58/2.64 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 14.58/2.64 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0, % 14.58/2.64 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 14.58/2.64 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 14.58/2.64 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 14.58/2.64 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 14.58/2.64 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 14.58/2.64 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 14.58/2.64 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 14.58/2.64 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 14.58/2.64 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 14.58/2.64 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 14.58/2.64 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 14.58/2.64 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 14.58/2.64 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 14.58/2.64 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 14.58/2.64 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 14.58/2.64 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 14.58/2.64 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 14.58/2.64 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~ % 14.58/2.64 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 14.58/2.64 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 14.58/2.64 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, % 14.58/2.64 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 14.58/2.64 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, % 14.58/2.64 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 14.58/2.64 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 14.58/2.64 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 14.58/2.64 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1, % 14.58/2.64 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i] % 14.58/2.64 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | % 14.58/2.64 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 14.58/2.64 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = % 14.58/2.64 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 14.58/2.64 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0, % 14.58/2.64 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 14.58/2.64 % 14.58/2.64 (function-axioms) % 14.58/2.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.58/2.64 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 14.58/2.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.58/2.64 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 14.58/2.64 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 14.58/2.64 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 14.58/2.64 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.58/2.64 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.58/2.64 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 14.58/2.64 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 14.58/2.64 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 14.58/2.64 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 14.58/2.64 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 14.58/2.64 (distinct_points(v3, v2) = v0)) % 14.58/2.64 % 14.58/2.64 Further assumptions not needed in the proof: % 14.58/2.64 -------------------------------------------- % 14.58/2.64 apart2, apart3, apart5, apart6, ceq1, ceq3, con2 % 14.58/2.64 % 14.58/2.64 Those formulas are unsatisfiable: % 14.58/2.64 --------------------------------- % 14.58/2.64 % 14.58/2.64 Begin of proof % 14.58/2.64 | % 14.58/2.64 | ALPHA: (apart4) implies: % 14.58/2.64 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 14.58/2.64 | (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | % 14.58/2.64 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0) % 14.58/2.64 | % 14.58/2.64 | ALPHA: (cu1) implies: % 14.58/2.64 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 14.58/2.64 | (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ % 14.58/2.64 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: % 14.58/2.64 | int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & % 14.58/2.64 | apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 14.58/2.64 | apart_point_and_line(v1, v2) = 0) | (v5 = 0 & % 14.58/2.64 | apart_point_and_line(v0, v3) = 0) | (v4 = 0 & % 14.58/2.64 | apart_point_and_line(v0, v2) = 0))) % 14.58/2.64 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 14.58/2.64 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 14.58/2.64 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 14.58/2.64 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 14.58/2.64 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 14.58/2.64 | apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & % 14.58/2.64 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 14.58/2.64 | v1) = v6))) % 14.58/2.64 | % 14.58/2.64 | ALPHA: (ceq2) implies: % 14.58/2.64 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 14.58/2.64 | (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, % 14.58/2.64 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v1, % 14.58/2.64 | v2) = 0) % 14.58/2.64 | % 14.58/2.64 | ALPHA: (function-axioms) implies: % 14.58/2.65 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.58/2.65 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 14.58/2.65 | (distinct_points(v3, v2) = v0)) % 14.58/2.65 | % 14.58/2.65 | DELTA: instantiating (con) with fresh symbols all_15_0, all_15_1, all_15_2, % 14.58/2.65 | all_15_3, all_15_4, all_15_5 gives: % 14.58/2.65 | (6) ~ (all_15_1 = 0) & line_connecting(all_15_4, all_15_5) = all_15_0 & % 14.58/2.65 | line_connecting(all_15_5, all_15_4) = all_15_2 & % 14.58/2.65 | apart_point_and_line(all_15_3, all_15_0) = 0 & % 14.58/2.65 | apart_point_and_line(all_15_3, all_15_2) = all_15_1 & % 14.58/2.65 | distinct_points(all_15_4, all_15_3) = 0 & distinct_points(all_15_5, % 14.58/2.65 | all_15_3) = 0 & distinct_points(all_15_5, all_15_4) = 0 & % 14.58/2.65 | $i(all_15_0) & $i(all_15_2) & $i(all_15_3) & $i(all_15_4) & % 14.58/2.65 | $i(all_15_5) % 14.58/2.65 | % 14.58/2.65 | ALPHA: (6) implies: % 14.58/2.65 | (7) ~ (all_15_1 = 0) % 14.58/2.65 | (8) $i(all_15_5) % 14.58/2.65 | (9) $i(all_15_4) % 14.58/2.65 | (10) $i(all_15_3) % 14.58/2.65 | (11) $i(all_15_2) % 14.58/2.65 | (12) $i(all_15_0) % 14.58/2.65 | (13) distinct_points(all_15_5, all_15_4) = 0 % 14.58/2.65 | (14) apart_point_and_line(all_15_3, all_15_2) = all_15_1 % 14.58/2.65 | (15) apart_point_and_line(all_15_3, all_15_0) = 0 % 14.58/2.65 | (16) line_connecting(all_15_5, all_15_4) = all_15_2 % 14.58/2.65 | (17) line_connecting(all_15_4, all_15_5) = all_15_0 % 14.58/2.65 | % 14.58/2.65 | GROUND_INST: instantiating (3) with all_15_3, all_15_3, all_15_2, all_15_2, % 14.58/2.65 | all_15_1, all_15_1, simplifying with (10), (11), (14) gives: % 14.58/2.65 | (18) all_15_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 14.58/2.65 | int] : ((v3 = 0 & apart_point_and_line(all_15_3, all_15_2) = 0) | % 14.58/2.65 | (v2 = 0 & apart_point_and_line(all_15_3, all_15_2) = 0) | ( ~ (v1 = % 14.58/2.65 | 0) & distinct_lines(all_15_2, all_15_2) = v1) | ( ~ (v0 = 0) & % 14.58/2.65 | distinct_points(all_15_3, all_15_3) = v0)) % 14.58/2.65 | % 14.58/2.65 | GROUND_INST: instantiating (4) with all_15_3, all_15_0, all_15_2, all_15_1, % 14.58/2.65 | simplifying with (10), (11), (12), (14), (15) gives: % 14.58/2.65 | (19) all_15_1 = 0 | distinct_lines(all_15_0, all_15_2) = 0 % 14.58/2.65 | % 14.58/2.65 | BETA: splitting (19) gives: % 14.58/2.65 | % 14.58/2.65 | Case 1: % 14.58/2.65 | | % 14.58/2.65 | | (20) distinct_lines(all_15_0, all_15_2) = 0 % 14.58/2.65 | | % 14.58/2.65 | | BETA: splitting (18) gives: % 14.58/2.65 | | % 14.58/2.65 | | Case 1: % 14.58/2.65 | | | % 14.58/2.65 | | | (21) all_15_1 = 0 % 14.58/2.65 | | | % 14.58/2.65 | | | REDUCE: (7), (21) imply: % 14.58/2.65 | | | (22) $false % 14.58/2.65 | | | % 14.58/2.65 | | | CLOSE: (22) is inconsistent. % 14.58/2.65 | | | % 14.58/2.65 | | Case 2: % 14.58/2.65 | | | % 14.58/2.65 | | | % 14.58/2.65 | | | GROUND_INST: instantiating (2) with all_15_5, all_15_4, all_15_0, % 14.58/2.65 | | | all_15_2, simplifying with (8), (9), (11), (12), (13), (20) % 14.58/2.65 | | | gives: % 14.58/2.65 | | | (23) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = % 14.58/2.65 | | | 0 & apart_point_and_line(all_15_4, all_15_2) = 0) | (v2 = 0 & % 14.58/2.65 | | | apart_point_and_line(all_15_4, all_15_0) = 0) | (v1 = 0 & % 14.58/2.65 | | | apart_point_and_line(all_15_5, all_15_2) = 0) | (v0 = 0 & % 14.58/2.65 | | | apart_point_and_line(all_15_5, all_15_0) = 0)) % 14.58/2.65 | | | % 14.58/2.65 | | | DELTA: instantiating (23) with fresh symbols all_43_0, all_43_1, all_43_2, % 14.58/2.65 | | | all_43_3 gives: % 14.58/2.66 | | | (24) (all_43_0 = 0 & apart_point_and_line(all_15_4, all_15_2) = 0) | % 14.58/2.66 | | | (all_43_1 = 0 & apart_point_and_line(all_15_4, all_15_0) = 0) | % 14.58/2.66 | | | (all_43_2 = 0 & apart_point_and_line(all_15_5, all_15_2) = 0) | % 14.58/2.66 | | | (all_43_3 = 0 & apart_point_and_line(all_15_5, all_15_0) = 0) % 14.58/2.66 | | | % 14.58/2.66 | | | BETA: splitting (24) gives: % 14.58/2.66 | | | % 14.58/2.66 | | | Case 1: % 14.58/2.66 | | | | % 14.58/2.66 | | | | (25) (all_43_0 = 0 & apart_point_and_line(all_15_4, all_15_2) = 0) | % 14.58/2.66 | | | | (all_43_1 = 0 & apart_point_and_line(all_15_4, all_15_0) = 0) % 14.58/2.66 | | | | % 14.58/2.66 | | | | BETA: splitting (25) gives: % 14.58/2.66 | | | | % 14.58/2.66 | | | | Case 1: % 14.58/2.66 | | | | | % 14.58/2.66 | | | | | (26) all_43_0 = 0 & apart_point_and_line(all_15_4, all_15_2) = 0 % 14.58/2.66 | | | | | % 14.58/2.66 | | | | | ALPHA: (26) implies: % 14.58/2.66 | | | | | (27) apart_point_and_line(all_15_4, all_15_2) = 0 % 14.58/2.66 | | | | | % 14.58/2.66 | | | | | GROUND_INST: instantiating (con1) with all_15_5, all_15_4, all_15_4, % 14.58/2.66 | | | | | all_15_2, simplifying with (8), (9), (16), (27) gives: % 14.58/2.66 | | | | | (28) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & v1 = 0 % 14.58/2.66 | | | | | & distinct_points(all_15_4, all_15_4) = 0 & % 14.58/2.66 | | | | | distinct_points(all_15_4, all_15_5) = 0) | ( ~ (v0 = 0) & % 14.58/2.66 | | | | | distinct_points(all_15_5, all_15_4) = v0)) % 14.58/2.66 | | | | | % 14.58/2.66 | | | | | DELTA: instantiating (28) with fresh symbols all_118_0, all_118_1, % 14.58/2.66 | | | | | all_118_2 gives: % 14.58/2.66 | | | | | (29) (all_118_0 = 0 & all_118_1 = 0 & distinct_points(all_15_4, % 14.58/2.66 | | | | | all_15_4) = 0 & distinct_points(all_15_4, all_15_5) = 0) | % 14.58/2.66 | | | | | ( ~ (all_118_2 = 0) & distinct_points(all_15_5, all_15_4) = % 14.58/2.66 | | | | | all_118_2) % 14.58/2.66 | | | | | % 14.58/2.66 | | | | | BETA: splitting (29) gives: % 14.58/2.66 | | | | | % 14.58/2.66 | | | | | Case 1: % 14.58/2.66 | | | | | | % 14.58/2.66 | | | | | | (30) all_118_0 = 0 & all_118_1 = 0 & distinct_points(all_15_4, % 14.58/2.66 | | | | | | all_15_4) = 0 & distinct_points(all_15_4, all_15_5) = 0 % 14.58/2.66 | | | | | | % 14.58/2.66 | | | | | | ALPHA: (30) implies: % 14.58/2.66 | | | | | | (31) distinct_points(all_15_4, all_15_4) = 0 % 14.58/2.66 | | | | | | % 14.58/2.66 | | | | | | GROUND_INST: instantiating (apart1) with all_15_4, simplifying with % 14.58/2.66 | | | | | | (9), (31) gives: % 14.58/2.66 | | | | | | (32) $false % 14.58/2.66 | | | | | | % 14.58/2.66 | | | | | | CLOSE: (32) is inconsistent. % 14.58/2.66 | | | | | | % 14.58/2.66 | | | | | Case 2: % 14.58/2.66 | | | | | | % 14.58/2.66 | | | | | | (33) ~ (all_118_2 = 0) & distinct_points(all_15_5, all_15_4) = % 14.58/2.66 | | | | | | all_118_2 % 14.58/2.66 | | | | | | % 14.58/2.66 | | | | | | ALPHA: (33) implies: % 14.58/2.66 | | | | | | (34) ~ (all_118_2 = 0) % 14.58/2.66 | | | | | | (35) distinct_points(all_15_5, all_15_4) = all_118_2 % 14.58/2.66 | | | | | | % 14.58/2.66 | | | | | | GROUND_INST: instantiating (5) with 0, all_118_2, all_15_4, % 14.58/2.66 | | | | | | all_15_5, simplifying with (13), (35) gives: % 14.58/2.66 | | | | | | (36) all_118_2 = 0 % 14.58/2.66 | | | | | | % 14.58/2.66 | | | | | | REDUCE: (34), (36) imply: % 14.58/2.66 | | | | | | (37) $false % 14.58/2.66 | | | | | | % 14.58/2.66 | | | | | | CLOSE: (37) is inconsistent. % 14.58/2.66 | | | | | | % 14.58/2.66 | | | | | End of split % 14.58/2.66 | | | | | % 14.58/2.66 | | | | Case 2: % 14.58/2.66 | | | | | % 14.58/2.66 | | | | | (38) all_43_1 = 0 & apart_point_and_line(all_15_4, all_15_0) = 0 % 14.58/2.66 | | | | | % 14.58/2.66 | | | | | ALPHA: (38) implies: % 14.58/2.66 | | | | | (39) apart_point_and_line(all_15_4, all_15_0) = 0 % 14.58/2.66 | | | | | % 14.92/2.66 | | | | | GROUND_INST: instantiating (con1) with all_15_4, all_15_5, all_15_4, % 14.92/2.66 | | | | | all_15_0, simplifying with (8), (9), (17), (39) gives: % 14.92/2.66 | | | | | (40) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & v1 = 0 % 14.92/2.66 | | | | | & distinct_points(all_15_4, all_15_4) = 0 & % 14.92/2.66 | | | | | distinct_points(all_15_4, all_15_5) = 0) | ( ~ (v0 = 0) & % 14.92/2.66 | | | | | distinct_points(all_15_4, all_15_5) = v0)) % 14.92/2.66 | | | | | % 14.92/2.66 | | | | | DELTA: instantiating (40) with fresh symbols all_118_0, all_118_1, % 14.92/2.66 | | | | | all_118_2 gives: % 14.92/2.66 | | | | | (41) (all_118_0 = 0 & all_118_1 = 0 & distinct_points(all_15_4, % 14.92/2.66 | | | | | all_15_4) = 0 & distinct_points(all_15_4, all_15_5) = 0) | % 14.92/2.66 | | | | | ( ~ (all_118_2 = 0) & distinct_points(all_15_4, all_15_5) = % 14.92/2.66 | | | | | all_118_2) % 14.92/2.66 | | | | | % 14.92/2.66 | | | | | BETA: splitting (41) gives: % 14.92/2.66 | | | | | % 14.92/2.66 | | | | | Case 1: % 14.92/2.66 | | | | | | % 14.92/2.66 | | | | | | (42) all_118_0 = 0 & all_118_1 = 0 & distinct_points(all_15_4, % 14.92/2.66 | | | | | | all_15_4) = 0 & distinct_points(all_15_4, all_15_5) = 0 % 14.92/2.66 | | | | | | % 14.92/2.66 | | | | | | ALPHA: (42) implies: % 14.92/2.66 | | | | | | (43) distinct_points(all_15_4, all_15_4) = 0 % 14.92/2.66 | | | | | | % 14.92/2.66 | | | | | | GROUND_INST: instantiating (apart1) with all_15_4, simplifying with % 14.92/2.66 | | | | | | (9), (43) gives: % 14.92/2.66 | | | | | | (44) $false % 14.92/2.66 | | | | | | % 14.92/2.66 | | | | | | CLOSE: (44) is inconsistent. % 14.92/2.66 | | | | | | % 14.92/2.66 | | | | | Case 2: % 14.92/2.66 | | | | | | % 14.92/2.66 | | | | | | (45) ~ (all_118_2 = 0) & distinct_points(all_15_4, all_15_5) = % 14.92/2.66 | | | | | | all_118_2 % 14.92/2.66 | | | | | | % 14.92/2.66 | | | | | | ALPHA: (45) implies: % 14.92/2.66 | | | | | | (46) ~ (all_118_2 = 0) % 14.92/2.66 | | | | | | (47) distinct_points(all_15_4, all_15_5) = all_118_2 % 14.92/2.66 | | | | | | % 14.92/2.67 | | | | | | GROUND_INST: instantiating (1) with all_15_5, all_15_4, all_15_5, % 14.92/2.67 | | | | | | all_118_2, simplifying with (8), (9), (13), (47) gives: % 14.93/2.67 | | | | | | (48) all_118_2 = 0 | distinct_points(all_15_5, all_15_5) = 0 % 14.93/2.67 | | | | | | % 14.93/2.67 | | | | | | BETA: splitting (48) gives: % 14.93/2.67 | | | | | | % 14.93/2.67 | | | | | | Case 1: % 14.93/2.67 | | | | | | | % 14.93/2.67 | | | | | | | (49) distinct_points(all_15_5, all_15_5) = 0 % 14.93/2.67 | | | | | | | % 14.93/2.67 | | | | | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying % 14.93/2.67 | | | | | | | with (8), (49) gives: % 14.93/2.67 | | | | | | | (50) $false % 14.93/2.67 | | | | | | | % 14.93/2.67 | | | | | | | CLOSE: (50) is inconsistent. % 14.93/2.67 | | | | | | | % 14.93/2.67 | | | | | | Case 2: % 14.93/2.67 | | | | | | | % 14.93/2.67 | | | | | | | (51) all_118_2 = 0 % 14.93/2.67 | | | | | | | % 14.93/2.67 | | | | | | | REDUCE: (46), (51) imply: % 14.93/2.67 | | | | | | | (52) $false % 14.93/2.67 | | | | | | | % 14.93/2.67 | | | | | | | CLOSE: (52) is inconsistent. % 14.93/2.67 | | | | | | | % 14.93/2.67 | | | | | | End of split % 14.93/2.67 | | | | | | % 14.93/2.67 | | | | | End of split % 14.93/2.67 | | | | | % 14.93/2.67 | | | | End of split % 14.93/2.67 | | | | % 14.93/2.67 | | | Case 2: % 14.93/2.67 | | | | % 14.93/2.67 | | | | (53) (all_43_2 = 0 & apart_point_and_line(all_15_5, all_15_2) = 0) | % 14.93/2.67 | | | | (all_43_3 = 0 & apart_point_and_line(all_15_5, all_15_0) = 0) % 14.93/2.67 | | | | % 14.93/2.67 | | | | BETA: splitting (53) gives: % 14.93/2.67 | | | | % 14.93/2.67 | | | | Case 1: % 14.93/2.67 | | | | | % 14.93/2.67 | | | | | (54) all_43_2 = 0 & apart_point_and_line(all_15_5, all_15_2) = 0 % 14.93/2.67 | | | | | % 14.93/2.67 | | | | | ALPHA: (54) implies: % 14.93/2.67 | | | | | (55) apart_point_and_line(all_15_5, all_15_2) = 0 % 14.93/2.67 | | | | | % 14.93/2.67 | | | | | GROUND_INST: instantiating (con1) with all_15_5, all_15_4, all_15_5, % 14.93/2.67 | | | | | all_15_2, simplifying with (8), (9), (16), (55) gives: % 14.93/2.67 | | | | | (56) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & v1 = 0 % 14.93/2.67 | | | | | & distinct_points(all_15_5, all_15_4) = 0 & % 14.93/2.67 | | | | | distinct_points(all_15_5, all_15_5) = 0) | ( ~ (v0 = 0) & % 14.93/2.67 | | | | | distinct_points(all_15_5, all_15_4) = v0)) % 14.93/2.67 | | | | | % 14.93/2.67 | | | | | DELTA: instantiating (56) with fresh symbols all_118_0, all_118_1, % 14.93/2.67 | | | | | all_118_2 gives: % 14.93/2.67 | | | | | (57) (all_118_0 = 0 & all_118_1 = 0 & distinct_points(all_15_5, % 14.93/2.67 | | | | | all_15_4) = 0 & distinct_points(all_15_5, all_15_5) = 0) | % 14.93/2.67 | | | | | ( ~ (all_118_2 = 0) & distinct_points(all_15_5, all_15_4) = % 14.93/2.67 | | | | | all_118_2) % 14.93/2.67 | | | | | % 14.93/2.67 | | | | | BETA: splitting (57) gives: % 14.93/2.67 | | | | | % 14.93/2.67 | | | | | Case 1: % 14.93/2.67 | | | | | | % 14.93/2.67 | | | | | | (58) all_118_0 = 0 & all_118_1 = 0 & distinct_points(all_15_5, % 14.93/2.67 | | | | | | all_15_4) = 0 & distinct_points(all_15_5, all_15_5) = 0 % 14.93/2.67 | | | | | | % 14.93/2.67 | | | | | | ALPHA: (58) implies: % 14.93/2.67 | | | | | | (59) distinct_points(all_15_5, all_15_5) = 0 % 14.93/2.67 | | | | | | % 14.93/2.67 | | | | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying with % 14.93/2.67 | | | | | | (8), (59) gives: % 14.93/2.67 | | | | | | (60) $false % 14.93/2.67 | | | | | | % 14.93/2.67 | | | | | | CLOSE: (60) is inconsistent. % 14.93/2.67 | | | | | | % 14.93/2.67 | | | | | Case 2: % 14.93/2.67 | | | | | | % 14.93/2.67 | | | | | | (61) ~ (all_118_2 = 0) & distinct_points(all_15_5, all_15_4) = % 14.93/2.67 | | | | | | all_118_2 % 14.93/2.67 | | | | | | % 14.93/2.67 | | | | | | ALPHA: (61) implies: % 14.93/2.67 | | | | | | (62) ~ (all_118_2 = 0) % 14.93/2.67 | | | | | | (63) distinct_points(all_15_5, all_15_4) = all_118_2 % 14.93/2.67 | | | | | | % 14.93/2.67 | | | | | | GROUND_INST: instantiating (5) with 0, all_118_2, all_15_4, % 14.93/2.67 | | | | | | all_15_5, simplifying with (13), (63) gives: % 14.93/2.67 | | | | | | (64) all_118_2 = 0 % 14.93/2.67 | | | | | | % 14.93/2.67 | | | | | | REDUCE: (62), (64) imply: % 14.93/2.67 | | | | | | (65) $false % 14.93/2.67 | | | | | | % 14.93/2.67 | | | | | | CLOSE: (65) is inconsistent. % 14.93/2.67 | | | | | | % 14.93/2.67 | | | | | End of split % 14.93/2.67 | | | | | % 14.93/2.67 | | | | Case 2: % 14.93/2.67 | | | | | % 14.93/2.67 | | | | | (66) all_43_3 = 0 & apart_point_and_line(all_15_5, all_15_0) = 0 % 14.93/2.67 | | | | | % 14.93/2.67 | | | | | ALPHA: (66) implies: % 14.93/2.67 | | | | | (67) apart_point_and_line(all_15_5, all_15_0) = 0 % 14.93/2.67 | | | | | % 14.93/2.67 | | | | | GROUND_INST: instantiating (con1) with all_15_4, all_15_5, all_15_5, % 14.93/2.67 | | | | | all_15_0, simplifying with (8), (9), (17), (67) gives: % 14.93/2.67 | | | | | (68) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & v1 = 0 % 14.93/2.67 | | | | | & distinct_points(all_15_5, all_15_4) = 0 & % 14.93/2.67 | | | | | distinct_points(all_15_5, all_15_5) = 0) | ( ~ (v0 = 0) & % 14.93/2.67 | | | | | distinct_points(all_15_4, all_15_5) = v0)) % 14.93/2.67 | | | | | % 14.93/2.67 | | | | | DELTA: instantiating (68) with fresh symbols all_118_0, all_118_1, % 14.93/2.67 | | | | | all_118_2 gives: % 14.93/2.67 | | | | | (69) (all_118_0 = 0 & all_118_1 = 0 & distinct_points(all_15_5, % 14.93/2.67 | | | | | all_15_4) = 0 & distinct_points(all_15_5, all_15_5) = 0) | % 14.93/2.67 | | | | | ( ~ (all_118_2 = 0) & distinct_points(all_15_4, all_15_5) = % 14.93/2.67 | | | | | all_118_2) % 14.93/2.67 | | | | | % 14.93/2.67 | | | | | BETA: splitting (69) gives: % 14.93/2.67 | | | | | % 14.93/2.67 | | | | | Case 1: % 14.93/2.67 | | | | | | % 14.93/2.67 | | | | | | (70) all_118_0 = 0 & all_118_1 = 0 & distinct_points(all_15_5, % 14.93/2.67 | | | | | | all_15_4) = 0 & distinct_points(all_15_5, all_15_5) = 0 % 14.93/2.68 | | | | | | % 14.93/2.68 | | | | | | ALPHA: (70) implies: % 14.93/2.68 | | | | | | (71) distinct_points(all_15_5, all_15_5) = 0 % 14.93/2.68 | | | | | | % 14.93/2.68 | | | | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying with % 14.93/2.68 | | | | | | (8), (71) gives: % 14.93/2.68 | | | | | | (72) $false % 14.93/2.68 | | | | | | % 14.93/2.68 | | | | | | CLOSE: (72) is inconsistent. % 14.93/2.68 | | | | | | % 14.93/2.68 | | | | | Case 2: % 14.93/2.68 | | | | | | % 14.93/2.68 | | | | | | (73) ~ (all_118_2 = 0) & distinct_points(all_15_4, all_15_5) = % 14.93/2.68 | | | | | | all_118_2 % 14.93/2.68 | | | | | | % 14.93/2.68 | | | | | | ALPHA: (73) implies: % 14.93/2.68 | | | | | | (74) ~ (all_118_2 = 0) % 14.93/2.68 | | | | | | (75) distinct_points(all_15_4, all_15_5) = all_118_2 % 14.93/2.68 | | | | | | % 14.93/2.68 | | | | | | GROUND_INST: instantiating (1) with all_15_5, all_15_4, all_15_5, % 14.93/2.68 | | | | | | all_118_2, simplifying with (8), (9), (13), (75) gives: % 14.93/2.68 | | | | | | (76) all_118_2 = 0 | distinct_points(all_15_5, all_15_5) = 0 % 14.93/2.68 | | | | | | % 14.93/2.68 | | | | | | BETA: splitting (76) gives: % 14.93/2.68 | | | | | | % 14.93/2.68 | | | | | | Case 1: % 14.93/2.68 | | | | | | | % 14.93/2.68 | | | | | | | (77) distinct_points(all_15_5, all_15_5) = 0 % 14.93/2.68 | | | | | | | % 14.93/2.68 | | | | | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying % 14.93/2.68 | | | | | | | with (8), (77) gives: % 14.93/2.68 | | | | | | | (78) $false % 14.93/2.68 | | | | | | | % 14.93/2.68 | | | | | | | CLOSE: (78) is inconsistent. % 14.93/2.68 | | | | | | | % 14.93/2.68 | | | | | | Case 2: % 14.93/2.68 | | | | | | | % 14.93/2.68 | | | | | | | (79) all_118_2 = 0 % 14.93/2.68 | | | | | | | % 14.93/2.68 | | | | | | | REDUCE: (74), (79) imply: % 14.93/2.68 | | | | | | | (80) $false % 14.93/2.68 | | | | | | | % 14.93/2.68 | | | | | | | CLOSE: (80) is inconsistent. % 14.93/2.68 | | | | | | | % 14.93/2.68 | | | | | | End of split % 14.93/2.68 | | | | | | % 14.93/2.68 | | | | | End of split % 14.93/2.68 | | | | | % 14.93/2.68 | | | | End of split % 14.93/2.68 | | | | % 14.93/2.68 | | | End of split % 14.93/2.68 | | | % 14.93/2.68 | | End of split % 14.93/2.68 | | % 14.93/2.68 | Case 2: % 14.93/2.68 | | % 14.93/2.68 | | (81) all_15_1 = 0 % 14.93/2.68 | | % 14.93/2.68 | | REDUCE: (7), (81) imply: % 14.93/2.68 | | (82) $false % 14.93/2.68 | | % 14.93/2.68 | | CLOSE: (82) is inconsistent. % 14.93/2.68 | | % 14.93/2.68 | End of split % 14.93/2.68 | % 14.93/2.68 End of proof % 14.93/2.68 % SZS output end Proof for theBenchmark % 14.93/2.68 % 14.93/2.68 2078ms %------------------------------------------------------------------------------