%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO172+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 : n022.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 23:21:49 EDT 2023 % Result : Theorem 9.83s 2.08s % Output : Proof 16.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : GEO172+1 : TPTP v8.1.2. Released v3.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n022.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 20:49:08 EDT 2023 % 0.13/0.35 % CPUTime : % 0.68/0.66 ________ _____ % 0.68/0.66 ___ __ \_________(_)________________________________ % 0.68/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.68/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.68/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.68/0.66 % 0.68/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.68/0.66 (2023-06-19) % 0.68/0.66 % 0.68/0.66 (c) Philipp Rümmer, 2009-2023 % 0.68/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.68/0.66 Amanda Stjerna. % 0.68/0.66 Free software under BSD-3-Clause. % 0.68/0.66 % 0.68/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.68/0.66 % 0.68/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.68/0.68 Running up to 7 provers in parallel. % 0.68/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.68/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.68/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.68/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.68/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.68/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.68/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.29/1.15 Prover 1: Preprocessing ... % 2.29/1.15 Prover 4: Preprocessing ... % 2.93/1.19 Prover 2: Preprocessing ... % 2.93/1.19 Prover 3: Preprocessing ... % 2.93/1.19 Prover 6: Preprocessing ... % 2.93/1.19 Prover 0: Preprocessing ... % 2.93/1.19 Prover 5: Preprocessing ... % 4.46/1.41 Prover 5: Proving ... % 4.46/1.42 Prover 2: Proving ... % 4.46/1.45 Prover 6: Constructing countermodel ... % 4.46/1.45 Prover 1: Constructing countermodel ... % 4.46/1.46 Prover 3: Constructing countermodel ... % 5.66/1.53 Prover 1: gave up % 5.66/1.53 Prover 3: gave up % 5.69/1.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.69/1.53 Prover 6: gave up % 5.69/1.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.69/1.54 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.69/1.55 Prover 4: Constructing countermodel ... % 5.69/1.55 Prover 0: Proving ... % 5.69/1.56 Prover 8: Preprocessing ... % 5.69/1.56 Prover 7: Preprocessing ... % 5.69/1.57 Prover 9: Preprocessing ... % 6.26/1.62 Prover 7: Warning: ignoring some quantifiers % 6.26/1.63 Prover 7: Constructing countermodel ... % 6.26/1.66 Prover 8: Warning: ignoring some quantifiers % 6.26/1.68 Prover 8: Constructing countermodel ... % 6.79/1.72 Prover 7: gave up % 6.79/1.72 Prover 8: gave up % 6.79/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.79/1.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.79/1.73 Prover 9: Constructing countermodel ... % 6.79/1.74 Prover 10: Preprocessing ... % 6.79/1.74 Prover 11: Preprocessing ... % 6.79/1.77 Prover 10: Warning: ignoring some quantifiers % 7.53/1.78 Prover 10: Constructing countermodel ... % 7.69/1.80 Prover 10: gave up % 7.69/1.81 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 7.87/1.84 Prover 12: Preprocessing ... % 7.87/1.89 Prover 11: Constructing countermodel ... % 8.50/1.94 Prover 12: Proving ... % 9.83/2.08 Prover 5: proved (1378ms) % 9.83/2.08 % 9.83/2.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.83/2.08 % 9.83/2.08 Prover 9: stopped % 9.83/2.08 Prover 0: stopped % 9.83/2.08 Prover 2: stopped % 9.83/2.09 Prover 12: stopped % 9.83/2.09 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.83/2.09 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.83/2.09 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 9.96/2.10 Prover 16: Preprocessing ... % 9.96/2.10 Prover 13: Preprocessing ... % 9.96/2.10 Prover 19: Preprocessing ... % 10.13/2.12 Prover 16: Warning: ignoring some quantifiers % 10.13/2.12 Prover 16: Constructing countermodel ... % 10.13/2.13 Prover 13: Warning: ignoring some quantifiers % 10.22/2.13 Prover 13: Constructing countermodel ... % 10.22/2.15 Prover 19: Warning: ignoring some quantifiers % 10.22/2.15 Prover 19: Constructing countermodel ... % 10.22/2.19 Prover 19: gave up % 10.86/2.23 Prover 16: gave up % 10.86/2.24 Prover 13: gave up % 15.25/3.03 Prover 11: Found proof (size 58) % 15.25/3.03 Prover 11: proved (1312ms) % 15.25/3.03 Prover 4: stopped % 15.25/3.03 % 15.25/3.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.25/3.03 % 15.25/3.04 % SZS output start Proof for theBenchmark % 15.25/3.04 Assumptions after simplification: % 15.25/3.04 --------------------------------- % 15.25/3.05 % 15.25/3.05 (apart3) % 15.77/3.09 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 15.77/3.09 % 15.77/3.09 (ceq3) % 15.91/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 15.91/3.10 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) % 15.91/3.10 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 15.91/3.10 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 15.91/3.10 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 15.91/3.10 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 15.91/3.10 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.91/3.10 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ % 15.91/3.10 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 15.91/3.10 convergent_lines(v0, v2) = 0) % 15.91/3.10 % 15.91/3.10 (ci3) % 15.91/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 15.91/3.10 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 15.91/3.10 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 15.91/3.10 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 15.91/3.10 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 15.91/3.10 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 15.91/3.10 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 15.91/3.10 % 15.91/3.10 (ci4) % 15.91/3.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 15.91/3.11 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 15.91/3.11 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 15.91/3.11 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 15.91/3.11 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 15.91/3.11 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 15.91/3.11 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 15.91/3.11 % 15.91/3.11 (con) % 15.91/3.11 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ? % 15.91/3.11 [v5: $i] : ( ~ (v4 = 0) & ~ (v3 = 0) & intersection_point(v0, v1) = v5 & % 15.91/3.11 apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3 & % 15.91/3.11 convergent_lines(v0, v1) = 0 & distinct_points(v2, v5) = 0 & $i(v5) & $i(v2) % 15.91/3.11 & $i(v1) & $i(v0)) % 15.91/3.11 % 15.91/3.11 (cu1) % 16.07/3.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 16.07/3.13 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 16.07/3.13 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 16.07/3.13 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 16.07/3.13 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 16.07/3.13 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, % 16.07/3.13 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 16.07/3.13 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, % 16.07/3.13 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ % 16.07/3.13 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 16.07/3.13 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 16.07/3.13 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0, % 16.07/3.13 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 16.07/3.13 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 16.07/3.13 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 16.07/3.13 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.07/3.13 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 16.07/3.13 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 16.07/3.13 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 16.07/3.13 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 16.07/3.13 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 16.07/3.13 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 16.07/3.13 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.07/3.13 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 16.07/3.13 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 16.07/3.13 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 16.07/3.13 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 16.07/3.13 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 16.07/3.13 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 16.07/3.13 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~ % 16.07/3.13 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 16.07/3.13 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 16.07/3.13 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, % 16.07/3.13 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 16.07/3.13 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, % 16.07/3.13 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 16.07/3.13 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.07/3.13 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 16.07/3.13 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1, % 16.07/3.13 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i] % 16.07/3.13 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | % 16.07/3.13 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 16.07/3.13 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = % 16.07/3.13 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 16.07/3.13 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0, % 16.07/3.13 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 16.07/3.13 % 16.07/3.13 (function-axioms) % 16.07/3.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.07/3.14 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 16.07/3.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.07/3.14 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 16.07/3.14 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.07/3.14 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 16.07/3.14 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.07/3.14 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.07/3.14 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 16.07/3.14 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.07/3.14 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 16.07/3.14 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 16.07/3.14 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 16.07/3.14 (distinct_points(v3, v2) = v0)) % 16.07/3.14 % 16.07/3.14 Further assumptions not needed in the proof: % 16.07/3.14 -------------------------------------------- % 16.07/3.14 apart1, apart2, apart4, apart5, ax6, ceq1, ceq2, ci1, ci2 % 16.07/3.14 % 16.07/3.14 Those formulas are unsatisfiable: % 16.07/3.14 --------------------------------- % 16.07/3.14 % 16.07/3.14 Begin of proof % 16.07/3.14 | % 16.07/3.14 | ALPHA: (ci3) implies: % 16.07/3.14 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 16.07/3.14 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 16.07/3.14 | (( ~ (v4 = 0) & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 16.07/3.14 | convergent_lines(v0, v1) = v3))) % 16.07/3.14 | % 16.07/3.14 | ALPHA: (ci4) implies: % 16.07/3.14 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 16.07/3.14 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 16.07/3.14 | (( ~ (v4 = 0) & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 16.07/3.14 | convergent_lines(v0, v1) = v3))) % 16.07/3.14 | % 16.07/3.14 | ALPHA: (cu1) implies: % 16.07/3.14 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 16.07/3.14 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) % 16.07/3.14 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, % 16.07/3.14 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 16.07/3.14 | [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 16.07/3.14 | apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 16.07/3.15 | apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & % 16.07/3.15 | distinct_lines(v2, v3) = v6))) % 16.07/3.15 | % 16.07/3.15 | ALPHA: (ceq3) implies: % 16.07/3.15 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.07/3.15 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | % 16.07/3.15 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 16.07/3.15 | % 16.07/3.15 | ALPHA: (function-axioms) implies: % 16.07/3.15 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 16.07/3.15 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 16.07/3.15 | (convergent_lines(v3, v2) = v0)) % 16.07/3.15 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 16.07/3.15 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 16.07/3.15 | (apart_point_and_line(v3, v2) = v0)) % 16.07/3.15 | % 16.07/3.15 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 16.07/3.15 | all_17_3, all_17_4, all_17_5 gives: % 16.07/3.15 | (7) ~ (all_17_1 = 0) & ~ (all_17_2 = 0) & intersection_point(all_17_5, % 16.07/3.15 | all_17_4) = all_17_0 & apart_point_and_line(all_17_3, all_17_4) = % 16.07/3.15 | all_17_1 & apart_point_and_line(all_17_3, all_17_5) = all_17_2 & % 16.07/3.15 | convergent_lines(all_17_5, all_17_4) = 0 & distinct_points(all_17_3, % 16.07/3.15 | all_17_0) = 0 & $i(all_17_0) & $i(all_17_3) & $i(all_17_4) & % 16.07/3.15 | $i(all_17_5) % 16.07/3.15 | % 16.07/3.15 | ALPHA: (7) implies: % 16.07/3.15 | (8) ~ (all_17_2 = 0) % 16.07/3.15 | (9) ~ (all_17_1 = 0) % 16.07/3.15 | (10) $i(all_17_5) % 16.07/3.15 | (11) $i(all_17_4) % 16.07/3.15 | (12) $i(all_17_3) % 16.07/3.15 | (13) $i(all_17_0) % 16.07/3.15 | (14) distinct_points(all_17_3, all_17_0) = 0 % 16.07/3.15 | (15) convergent_lines(all_17_5, all_17_4) = 0 % 16.07/3.15 | (16) apart_point_and_line(all_17_3, all_17_5) = all_17_2 % 16.07/3.15 | (17) apart_point_and_line(all_17_3, all_17_4) = all_17_1 % 16.07/3.15 | (18) intersection_point(all_17_5, all_17_4) = all_17_0 % 16.07/3.15 | % 16.07/3.16 | GROUND_INST: instantiating (3) with all_17_3, all_17_0, all_17_4, all_17_5, % 16.07/3.16 | all_17_1, all_17_2, simplifying with (10), (11), (12), (13), % 16.07/3.16 | (14), (16), (17) gives: % 16.07/3.16 | (19) all_17_1 = 0 | all_17_2 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 16.07/3.16 | int] : ((v2 = 0 & apart_point_and_line(all_17_0, all_17_5) = 0) | % 16.07/3.16 | (v1 = 0 & apart_point_and_line(all_17_0, all_17_4) = 0) | ( ~ (v0 = % 16.07/3.16 | 0) & distinct_lines(all_17_4, all_17_5) = v0)) % 16.07/3.16 | % 16.07/3.16 | GROUND_INST: instantiating (2) with all_17_5, all_17_4, all_17_0, simplifying % 16.07/3.16 | with (10), (11), (18) gives: % 16.07/3.16 | (20) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 16.07/3.16 | apart_point_and_line(all_17_0, all_17_4) = v1) | ( ~ (v0 = 0) & % 16.07/3.16 | convergent_lines(all_17_5, all_17_4) = v0)) % 16.07/3.16 | % 16.07/3.16 | GROUND_INST: instantiating (1) with all_17_5, all_17_4, all_17_0, simplifying % 16.07/3.16 | with (10), (11), (18) gives: % 16.07/3.16 | (21) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 16.07/3.16 | apart_point_and_line(all_17_0, all_17_5) = v1) | ( ~ (v0 = 0) & % 16.07/3.16 | convergent_lines(all_17_5, all_17_4) = v0)) % 16.07/3.16 | % 16.07/3.16 | DELTA: instantiating (21) with fresh symbols all_24_0, all_24_1 gives: % 16.07/3.16 | (22) ( ~ (all_24_0 = 0) & apart_point_and_line(all_17_0, all_17_5) = % 16.07/3.16 | all_24_0) | ( ~ (all_24_1 = 0) & convergent_lines(all_17_5, % 16.07/3.16 | all_17_4) = all_24_1) % 16.07/3.16 | % 16.07/3.16 | DELTA: instantiating (20) with fresh symbols all_33_0, all_33_1 gives: % 16.07/3.16 | (23) ( ~ (all_33_0 = 0) & apart_point_and_line(all_17_0, all_17_4) = % 16.07/3.16 | all_33_0) | ( ~ (all_33_1 = 0) & convergent_lines(all_17_5, % 16.07/3.16 | all_17_4) = all_33_1) % 16.07/3.16 | % 16.07/3.16 | BETA: splitting (23) gives: % 16.07/3.16 | % 16.07/3.16 | Case 1: % 16.07/3.16 | | % 16.07/3.16 | | (24) ~ (all_33_0 = 0) & apart_point_and_line(all_17_0, all_17_4) = % 16.07/3.16 | | all_33_0 % 16.07/3.16 | | % 16.07/3.16 | | ALPHA: (24) implies: % 16.07/3.16 | | (25) ~ (all_33_0 = 0) % 16.07/3.16 | | (26) apart_point_and_line(all_17_0, all_17_4) = all_33_0 % 16.07/3.16 | | % 16.07/3.16 | | BETA: splitting (22) gives: % 16.07/3.16 | | % 16.07/3.16 | | Case 1: % 16.07/3.16 | | | % 16.07/3.16 | | | (27) ~ (all_24_0 = 0) & apart_point_and_line(all_17_0, all_17_5) = % 16.07/3.16 | | | all_24_0 % 16.07/3.16 | | | % 16.07/3.16 | | | ALPHA: (27) implies: % 16.07/3.16 | | | (28) ~ (all_24_0 = 0) % 16.07/3.16 | | | (29) apart_point_and_line(all_17_0, all_17_5) = all_24_0 % 16.07/3.16 | | | % 16.07/3.16 | | | BETA: splitting (19) gives: % 16.07/3.16 | | | % 16.07/3.16 | | | Case 1: % 16.07/3.16 | | | | % 16.07/3.16 | | | | (30) all_17_1 = 0 % 16.07/3.16 | | | | % 16.07/3.16 | | | | REDUCE: (9), (30) imply: % 16.07/3.16 | | | | (31) $false % 16.07/3.16 | | | | % 16.07/3.16 | | | | CLOSE: (31) is inconsistent. % 16.07/3.16 | | | | % 16.07/3.17 | | | Case 2: % 16.07/3.17 | | | | % 16.07/3.17 | | | | (32) all_17_2 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 16.07/3.17 | | | | = 0 & apart_point_and_line(all_17_0, all_17_5) = 0) | (v1 = % 16.07/3.17 | | | | 0 & apart_point_and_line(all_17_0, all_17_4) = 0) | ( ~ (v0 % 16.07/3.17 | | | | = 0) & distinct_lines(all_17_4, all_17_5) = v0)) % 16.07/3.17 | | | | % 16.07/3.17 | | | | BETA: splitting (32) gives: % 16.07/3.17 | | | | % 16.07/3.17 | | | | Case 1: % 16.07/3.17 | | | | | % 16.07/3.17 | | | | | (33) all_17_2 = 0 % 16.07/3.17 | | | | | % 16.07/3.17 | | | | | REDUCE: (8), (33) imply: % 16.07/3.17 | | | | | (34) $false % 16.07/3.17 | | | | | % 16.07/3.17 | | | | | CLOSE: (34) is inconsistent. % 16.07/3.17 | | | | | % 16.07/3.17 | | | | Case 2: % 16.07/3.17 | | | | | % 16.07/3.17 | | | | | (35) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & % 16.07/3.17 | | | | | apart_point_and_line(all_17_0, all_17_5) = 0) | (v1 = 0 & % 16.07/3.17 | | | | | apart_point_and_line(all_17_0, all_17_4) = 0) | ( ~ (v0 = % 16.07/3.17 | | | | | 0) & distinct_lines(all_17_4, all_17_5) = v0)) % 16.07/3.17 | | | | | % 16.07/3.17 | | | | | DELTA: instantiating (35) with fresh symbols all_96_0, all_96_1, % 16.07/3.17 | | | | | all_96_2 gives: % 16.07/3.17 | | | | | (36) (all_96_0 = 0 & apart_point_and_line(all_17_0, all_17_5) = 0) % 16.07/3.17 | | | | | | (all_96_1 = 0 & apart_point_and_line(all_17_0, all_17_4) = % 16.07/3.17 | | | | | 0) | ( ~ (all_96_2 = 0) & distinct_lines(all_17_4, all_17_5) % 16.07/3.17 | | | | | = all_96_2) % 16.07/3.17 | | | | | % 16.07/3.17 | | | | | BETA: splitting (36) gives: % 16.07/3.17 | | | | | % 16.07/3.17 | | | | | Case 1: % 16.07/3.17 | | | | | | % 16.07/3.17 | | | | | | (37) all_96_0 = 0 & apart_point_and_line(all_17_0, all_17_5) = 0 % 16.07/3.17 | | | | | | % 16.07/3.17 | | | | | | ALPHA: (37) implies: % 16.07/3.17 | | | | | | (38) apart_point_and_line(all_17_0, all_17_5) = 0 % 16.07/3.17 | | | | | | % 16.07/3.17 | | | | | | GROUND_INST: instantiating (6) with 0, all_24_0, all_17_5, all_17_0, % 16.07/3.17 | | | | | | simplifying with (29), (38) gives: % 16.07/3.17 | | | | | | (39) all_24_0 = 0 % 16.07/3.17 | | | | | | % 16.07/3.17 | | | | | | REDUCE: (28), (39) imply: % 16.07/3.17 | | | | | | (40) $false % 16.07/3.17 | | | | | | % 16.07/3.17 | | | | | | CLOSE: (40) is inconsistent. % 16.07/3.17 | | | | | | % 16.07/3.17 | | | | | Case 2: % 16.07/3.17 | | | | | | % 16.07/3.17 | | | | | | (41) (all_96_1 = 0 & apart_point_and_line(all_17_0, all_17_4) = % 16.07/3.17 | | | | | | 0) | ( ~ (all_96_2 = 0) & distinct_lines(all_17_4, % 16.07/3.17 | | | | | | all_17_5) = all_96_2) % 16.07/3.17 | | | | | | % 16.07/3.17 | | | | | | BETA: splitting (41) gives: % 16.07/3.17 | | | | | | % 16.07/3.17 | | | | | | Case 1: % 16.07/3.17 | | | | | | | % 16.07/3.17 | | | | | | | (42) all_96_1 = 0 & apart_point_and_line(all_17_0, all_17_4) = % 16.07/3.17 | | | | | | | 0 % 16.07/3.17 | | | | | | | % 16.07/3.17 | | | | | | | ALPHA: (42) implies: % 16.07/3.17 | | | | | | | (43) apart_point_and_line(all_17_0, all_17_4) = 0 % 16.07/3.17 | | | | | | | % 16.07/3.17 | | | | | | | GROUND_INST: instantiating (6) with 0, all_33_0, all_17_4, % 16.07/3.17 | | | | | | | all_17_0, simplifying with (26), (43) gives: % 16.07/3.17 | | | | | | | (44) all_33_0 = 0 % 16.07/3.17 | | | | | | | % 16.07/3.17 | | | | | | | REDUCE: (25), (44) imply: % 16.07/3.17 | | | | | | | (45) $false % 16.07/3.17 | | | | | | | % 16.07/3.17 | | | | | | | CLOSE: (45) is inconsistent. % 16.07/3.17 | | | | | | | % 16.07/3.17 | | | | | | Case 2: % 16.07/3.17 | | | | | | | % 16.07/3.17 | | | | | | | (46) ~ (all_96_2 = 0) & distinct_lines(all_17_4, all_17_5) = % 16.07/3.17 | | | | | | | all_96_2 % 16.07/3.17 | | | | | | | % 16.07/3.17 | | | | | | | ALPHA: (46) implies: % 16.07/3.17 | | | | | | | (47) ~ (all_96_2 = 0) % 16.07/3.17 | | | | | | | (48) distinct_lines(all_17_4, all_17_5) = all_96_2 % 16.07/3.17 | | | | | | | % 16.07/3.17 | | | | | | | GROUND_INST: instantiating (4) with all_17_5, all_17_4, all_17_5, % 16.07/3.17 | | | | | | | all_96_2, simplifying with (10), (11), (15), (48) % 16.07/3.17 | | | | | | | gives: % 16.07/3.17 | | | | | | | (49) all_96_2 = 0 | convergent_lines(all_17_5, all_17_5) = 0 % 16.07/3.17 | | | | | | | % 16.07/3.17 | | | | | | | BETA: splitting (49) gives: % 16.07/3.17 | | | | | | | % 16.07/3.17 | | | | | | | Case 1: % 16.07/3.17 | | | | | | | | % 16.07/3.17 | | | | | | | | (50) convergent_lines(all_17_5, all_17_5) = 0 % 16.07/3.17 | | | | | | | | % 16.07/3.17 | | | | | | | | GROUND_INST: instantiating (apart3) with all_17_5, simplifying % 16.07/3.17 | | | | | | | | with (10), (50) gives: % 16.07/3.17 | | | | | | | | (51) $false % 16.07/3.17 | | | | | | | | % 16.07/3.17 | | | | | | | | CLOSE: (51) is inconsistent. % 16.07/3.17 | | | | | | | | % 16.07/3.17 | | | | | | | Case 2: % 16.07/3.17 | | | | | | | | % 16.07/3.17 | | | | | | | | (52) all_96_2 = 0 % 16.07/3.17 | | | | | | | | % 16.07/3.17 | | | | | | | | REDUCE: (47), (52) imply: % 16.07/3.17 | | | | | | | | (53) $false % 16.07/3.17 | | | | | | | | % 16.07/3.17 | | | | | | | | CLOSE: (53) is inconsistent. % 16.07/3.17 | | | | | | | | % 16.07/3.17 | | | | | | | End of split % 16.07/3.17 | | | | | | | % 16.07/3.17 | | | | | | End of split % 16.07/3.17 | | | | | | % 16.07/3.17 | | | | | End of split % 16.07/3.17 | | | | | % 16.07/3.17 | | | | End of split % 16.07/3.17 | | | | % 16.07/3.17 | | | End of split % 16.07/3.17 | | | % 16.07/3.17 | | Case 2: % 16.07/3.17 | | | % 16.07/3.17 | | | (54) ~ (all_24_1 = 0) & convergent_lines(all_17_5, all_17_4) = % 16.07/3.17 | | | all_24_1 % 16.07/3.17 | | | % 16.07/3.17 | | | ALPHA: (54) implies: % 16.07/3.17 | | | (55) ~ (all_24_1 = 0) % 16.07/3.17 | | | (56) convergent_lines(all_17_5, all_17_4) = all_24_1 % 16.07/3.17 | | | % 16.07/3.17 | | | GROUND_INST: instantiating (5) with 0, all_24_1, all_17_4, all_17_5, % 16.07/3.17 | | | simplifying with (15), (56) gives: % 16.07/3.17 | | | (57) all_24_1 = 0 % 16.07/3.18 | | | % 16.07/3.18 | | | REDUCE: (55), (57) imply: % 16.07/3.18 | | | (58) $false % 16.07/3.18 | | | % 16.07/3.18 | | | CLOSE: (58) is inconsistent. % 16.07/3.18 | | | % 16.07/3.18 | | End of split % 16.07/3.18 | | % 16.07/3.18 | Case 2: % 16.07/3.18 | | % 16.07/3.18 | | (59) ~ (all_33_1 = 0) & convergent_lines(all_17_5, all_17_4) = all_33_1 % 16.07/3.18 | | % 16.07/3.18 | | ALPHA: (59) implies: % 16.07/3.18 | | (60) ~ (all_33_1 = 0) % 16.07/3.18 | | (61) convergent_lines(all_17_5, all_17_4) = all_33_1 % 16.07/3.18 | | % 16.07/3.18 | | GROUND_INST: instantiating (5) with 0, all_33_1, all_17_4, all_17_5, % 16.07/3.18 | | simplifying with (15), (61) gives: % 16.07/3.18 | | (62) all_33_1 = 0 % 16.07/3.18 | | % 16.07/3.18 | | REDUCE: (60), (62) imply: % 16.07/3.18 | | (63) $false % 16.07/3.18 | | % 16.07/3.18 | | CLOSE: (63) is inconsistent. % 16.07/3.18 | | % 16.07/3.18 | End of split % 16.07/3.18 | % 16.07/3.18 End of proof % 16.07/3.18 % SZS output end Proof for theBenchmark % 16.07/3.18 % 16.07/3.18 2514ms %------------------------------------------------------------------------------