%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO214+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 : n023.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 23:22:24 EDT 2023 % Result : Theorem 13.81s 2.63s % Output : Proof 19.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO214+1 : TPTP v8.1.2. Released v3.3.0. % 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n023.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Tue Aug 29 20:27:09 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.54 ________ _____ % 0.19/0.54 ___ __ \_________(_)________________________________ % 0.19/0.54 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.54 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.54 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.54 % 0.19/0.54 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.54 (2023-06-19) % 0.19/0.54 % 0.19/0.54 (c) Philipp Rümmer, 2009-2023 % 0.19/0.54 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.54 Amanda Stjerna. % 0.19/0.54 Free software under BSD-3-Clause. % 0.19/0.54 % 0.19/0.54 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.54 % 0.19/0.54 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.55 Running up to 7 provers in parallel. % 0.53/0.56 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.53/0.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.53/0.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.53/0.56 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.53/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.53/0.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.53/0.57 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.47/0.98 Prover 1: Preprocessing ... % 2.47/0.98 Prover 4: Preprocessing ... % 2.90/1.04 Prover 3: Preprocessing ... % 2.90/1.04 Prover 5: Preprocessing ... % 2.90/1.04 Prover 6: Preprocessing ... % 2.90/1.04 Prover 0: Preprocessing ... % 2.90/1.04 Prover 2: Preprocessing ... % 5.20/1.36 Prover 5: Proving ... % 5.20/1.37 Prover 2: Proving ... % 5.20/1.43 Prover 1: Constructing countermodel ... % 5.20/1.43 Prover 3: Constructing countermodel ... % 5.20/1.44 Prover 6: Constructing countermodel ... % 6.52/1.58 Prover 3: gave up % 6.52/1.59 Prover 6: gave up % 6.52/1.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.52/1.61 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.52/1.61 Prover 1: gave up % 6.52/1.61 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 6.52/1.62 Prover 4: Constructing countermodel ... % 7.05/1.64 Prover 7: Preprocessing ... % 7.05/1.65 Prover 9: Preprocessing ... % 7.05/1.66 Prover 8: Preprocessing ... % 7.38/1.68 Prover 7: Warning: ignoring some quantifiers % 7.38/1.70 Prover 7: Constructing countermodel ... % 7.38/1.71 Prover 0: Proving ... % 7.96/1.77 Prover 7: gave up % 7.96/1.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.15/1.79 Prover 8: Warning: ignoring some quantifiers % 8.15/1.82 Prover 8: Constructing countermodel ... % 8.42/1.83 Prover 10: Preprocessing ... % 8.55/1.88 Prover 10: Warning: ignoring some quantifiers % 8.55/1.90 Prover 10: Constructing countermodel ... % 9.03/1.94 Prover 8: gave up % 9.03/1.94 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.03/1.96 Prover 10: gave up % 9.03/1.96 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 9.03/1.96 Prover 9: Constructing countermodel ... % 9.03/1.97 Prover 11: Preprocessing ... % 9.50/1.99 Prover 12: Preprocessing ... % 10.61/2.13 Prover 12: Proving ... % 11.24/2.28 Prover 11: Constructing countermodel ... % 13.81/2.62 Prover 0: proved (2066ms) % 13.81/2.62 % 13.81/2.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.81/2.63 % 13.81/2.63 Prover 9: stopped % 13.81/2.64 Prover 2: stopped % 13.81/2.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.81/2.64 Prover 5: stopped % 13.81/2.64 Prover 12: stopped % 13.81/2.64 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 13.81/2.65 Prover 13: Preprocessing ... % 13.81/2.65 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 14.31/2.67 Prover 16: Preprocessing ... % 14.40/2.68 Prover 19: Preprocessing ... % 14.40/2.71 Prover 16: Warning: ignoring some quantifiers % 14.40/2.71 Prover 13: Warning: ignoring some quantifiers % 14.40/2.72 Prover 13: Constructing countermodel ... % 14.74/2.73 Prover 16: Constructing countermodel ... % 14.96/2.76 Prover 13: gave up % 14.96/2.77 Prover 19: Warning: ignoring some quantifiers % 14.96/2.78 Prover 16: gave up % 14.96/2.78 Prover 19: Constructing countermodel ... % 15.55/2.84 Prover 19: gave up % 18.27/3.34 Prover 11: Found proof (size 73) % 18.27/3.34 Prover 11: proved (1405ms) % 18.27/3.35 Prover 4: stopped % 18.27/3.35 % 18.27/3.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.27/3.35 % 18.27/3.36 % SZS output start Proof for theBenchmark % 18.27/3.36 Assumptions after simplification: % 18.27/3.36 --------------------------------- % 18.48/3.36 % 18.48/3.36 (apart3) % 18.48/3.39 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 18.48/3.39 % 18.48/3.39 (ax6) % 18.48/3.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 18.48/3.40 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 18.48/3.40 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 18.48/3.40 0) & convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! % 18.48/3.40 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ % 18.48/3.40 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 18.48/3.40 convergent_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 18.48/3.40 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 18.48/3.40 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 18.48/3.40 convergent_lines(v1, v2) = 0) % 18.48/3.40 % 18.48/3.40 (ci3) % 18.48/3.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 18.48/3.41 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 18.48/3.41 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 18.48/3.41 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 18.48/3.41 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 18.48/3.41 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 18.48/3.41 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 18.48/3.41 % 18.48/3.41 (ci4) % 18.48/3.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 18.48/3.41 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 18.48/3.41 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 18.48/3.41 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 18.48/3.41 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 18.48/3.41 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 18.48/3.41 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 18.48/3.41 % 18.48/3.41 (con) % 18.48/3.42 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 18.48/3.42 unorthogonal_lines(v1, v0) = v2 & unorthogonal_lines(v0, v1) = 0 & $i(v1) & % 18.48/3.42 $i(v0)) % 18.48/3.42 % 18.48/3.42 (cup1) % 18.48/3.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 18.48/3.43 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 18.48/3.43 (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 18.48/3.43 [v5: int] : ? [v6: int] : ((v6 = 0 & convergent_lines(v1, v2) = 0) | ( ~ % 18.48/3.43 (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0: $i] : ! [v1: $i] : % 18.48/3.43 ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = 0 | v3 = 0 | ~ % 18.48/3.43 (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | % 18.48/3.43 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ((v6 = 0 & % 18.48/3.43 apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, % 18.48/3.43 v2) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : % 18.48/3.43 ! [v4: int] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ % 18.48/3.43 (convergent_lines(v1, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 18.48/3.43 [v5: int] : ? [v6: int] : ((v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( % 18.48/3.43 ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0: $i] : ! [v1: $i] % 18.48/3.43 : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = % 18.48/3.43 v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 18.48/3.43 | ? [v4: int] : ? [v5: int] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | % 18.48/3.43 (v4 = 0 & apart_point_and_line(v0, v1) = 0))) & ! [v0: $i] : ! [v1: $i] % 18.48/3.43 : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = % 18.48/3.43 v3) | ~ (distinct_lines(v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 18.48/3.43 | ? [v4: int] : ? [v5: int] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | % 18.48/3.43 (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 18.48/3.43 % 18.48/3.43 (oac1) % 18.84/3.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 18.84/3.45 (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | % 18.84/3.45 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: % 18.84/3.45 int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | % 18.84/3.45 (v7 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 18.84/3.45 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, % 18.84/3.45 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 18.84/3.45 ! [v4: any] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ % 18.84/3.45 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 18.84/3.45 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 18.84/3.45 convergent_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 18.84/3.45 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0, % 18.84/3.45 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0: % 18.84/3.45 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 18.84/3.45 (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ~ % 18.84/3.45 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] % 18.84/3.45 : ? [v8: int] : ((v8 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v7 = % 18.84/3.45 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v6 = 0) & % 18.84/3.45 unorthogonal_lines(v0, v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, % 18.84/3.45 v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : % 18.84/3.45 ! [v4: any] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, % 18.84/3.45 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 18.84/3.45 int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & v4 = 0 & % 18.84/3.45 unorthogonal_lines(v1, v2) = 0) | (v7 = 0 & v3 = 0 & % 18.84/3.45 unorthogonal_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v0, % 18.84/3.45 v1) = v6) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0: % 18.84/3.45 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, % 18.84/3.45 v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) % 18.84/3.45 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 18.84/3.45 ((v7 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 18.84/3.45 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 18.84/3.45 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : % 18.84/3.45 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ % 18.84/3.46 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 18.84/3.46 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 18.84/3.46 convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 18.84/3.46 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 18.84/3.46 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] % 18.84/3.46 : ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 18.84/3.46 (unorthogonal_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 18.84/3.46 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 18.84/3.46 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 18.84/3.46 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 18.84/3.46 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 18.84/3.46 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ % 18.84/3.46 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 18.84/3.46 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 18.84/3.46 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 18.84/3.46 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 18.84/3.46 unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 18.84/3.46 $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 18.84/3.46 (convergent_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 18.84/3.46 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 18.84/3.46 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 18.84/3.46 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 18.84/3.46 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : % 18.84/3.46 ! [v2: $i] : ! [v3: any] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ % 18.84/3.46 (convergent_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 18.84/3.46 [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 18.84/3.46 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 18.84/3.46 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 18.84/3.46 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 18.84/3.46 $i] : ! [v3: any] : ( ~ (convergent_lines(v1, v2) = v3) | ~ % 18.84/3.46 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 18.84/3.46 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 18.84/3.46 unorthogonal_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 18.84/3.46 unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 % 18.84/3.46 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] % 18.84/3.46 : ! [v2: $i] : ! [v3: any] : ( ~ (convergent_lines(v0, v2) = v3) | ~ % 18.84/3.46 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 18.84/3.46 int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 18.84/3.46 unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 % 18.84/3.46 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 18.84/3.46 unorthogonal_lines(v0, v1) = v4))) % 18.84/3.46 % 18.84/3.46 (occu1) % 18.84/3.46 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 18.84/3.46 (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 18.84/3.46 convergent_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 18.84/3.46 (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 18.84/3.46 unorthogonal_lines(v0, v1) = 0) % 18.84/3.46 % 18.84/3.46 (function-axioms) % 18.84/3.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.84/3.46 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 18.84/3.46 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 18.84/3.46 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 18.84/3.46 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 18.84/3.46 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 18.84/3.46 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 18.84/3.46 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 18.84/3.46 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 18.84/3.46 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 18.84/3.46 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 18.84/3.46 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.84/3.46 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 18.84/3.46 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 18.84/3.46 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 18.84/3.46 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 18.84/3.46 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 18.84/3.46 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 18.84/3.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 18.84/3.46 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 18.84/3.46 v0)) % 18.84/3.46 % 18.84/3.46 Further assumptions not needed in the proof: % 18.84/3.46 -------------------------------------------- % 18.84/3.46 apart1, apart2, apart4, apart5, ceq1, ceq2, ceq3, ci1, ci2, cp1, cp2, cu1, ooc1, % 18.84/3.46 ooc2, ouo1 % 18.84/3.46 % 18.84/3.46 Those formulas are unsatisfiable: % 18.84/3.46 --------------------------------- % 18.84/3.46 % 18.84/3.46 Begin of proof % 18.84/3.47 | % 18.84/3.47 | ALPHA: (ax6) implies: % 18.84/3.47 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 18.84/3.47 | (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | % 18.84/3.47 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 18.84/3.47 | % 18.84/3.47 | ALPHA: (ci3) implies: % 18.84/3.47 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 18.84/3.47 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 18.84/3.47 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 18.84/3.47 | & $i(v2))) % 18.84/3.47 | % 18.84/3.47 | ALPHA: (ci4) implies: % 18.84/3.47 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 18.84/3.47 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 18.84/3.47 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 18.84/3.47 | & $i(v2))) % 18.84/3.47 | % 18.84/3.47 | ALPHA: (cup1) implies: % 18.84/3.47 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : % 18.84/3.47 | (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 18.84/3.47 | (apart_point_and_line(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 18.84/3.47 | $i(v0) | ? [v5: int] : ? [v6: int] : ((v6 = 0 & % 18.84/3.47 | convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, % 18.84/3.47 | v2) = v5))) % 19.02/3.47 | % 19.02/3.47 | ALPHA: (occu1) implies: % 19.02/3.47 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 19.02/3.47 | (unorthogonal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 19.02/3.47 | convergent_lines(v0, v1) = 0) % 19.02/3.47 | % 19.02/3.47 | ALPHA: (oac1) implies: % 19.02/3.48 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 19.02/3.48 | (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = % 19.02/3.48 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: % 19.02/3.48 | int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v6 = 0 & % 19.02/3.48 | unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | % 19.02/3.48 | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & % 19.02/3.48 | convergent_lines(v0, v1) = v4))) % 19.02/3.48 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 19.02/3.48 | (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = % 19.02/3.48 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: % 19.02/3.48 | int] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & v3 = 0 & % 19.02/3.48 | convergent_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & % 19.02/3.48 | unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | % 19.02/3.48 | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) % 19.02/3.48 | % 19.02/3.48 | ALPHA: (function-axioms) implies: % 19.02/3.48 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 19.02/3.48 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 19.02/3.48 | (convergent_lines(v3, v2) = v0)) % 19.02/3.48 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 19.02/3.48 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 19.02/3.48 | v0)) % 19.02/3.48 | % 19.02/3.48 | DELTA: instantiating (con) with fresh symbols all_25_0, all_25_1, all_25_2 % 19.02/3.48 | gives: % 19.02/3.48 | (10) ~ (all_25_0 = 0) & unorthogonal_lines(all_25_1, all_25_2) = all_25_0 % 19.02/3.48 | & unorthogonal_lines(all_25_2, all_25_1) = 0 & $i(all_25_1) & % 19.02/3.48 | $i(all_25_2) % 19.02/3.48 | % 19.02/3.48 | ALPHA: (10) implies: % 19.02/3.48 | (11) ~ (all_25_0 = 0) % 19.02/3.48 | (12) $i(all_25_2) % 19.02/3.48 | (13) $i(all_25_1) % 19.02/3.48 | (14) unorthogonal_lines(all_25_2, all_25_1) = 0 % 19.02/3.48 | (15) unorthogonal_lines(all_25_1, all_25_2) = all_25_0 % 19.02/3.48 | % 19.02/3.49 | GROUND_INST: instantiating (6) with all_25_2, all_25_1, all_25_1, 0, % 19.02/3.49 | simplifying with (12), (13), (14) gives: % 19.02/3.49 | (16) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 19.02/3.49 | v2 = 0 & unorthogonal_lines(all_25_1, all_25_1) = 0 & % 19.02/3.49 | convergent_lines(all_25_1, all_25_1) = 0) | (v1 = 0 & % 19.02/3.49 | convergent_lines(all_25_2, all_25_1) = 0) | ( ~ (v0 = 0) & % 19.02/3.49 | convergent_lines(all_25_2, all_25_1) = v0)) % 19.02/3.49 | % 19.02/3.49 | GROUND_INST: instantiating (7) with all_25_2, all_25_1, all_25_2, all_25_0, % 19.02/3.49 | simplifying with (12), (13), (14), (15) gives: % 19.02/3.49 | (17) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 19.02/3.49 | all_25_0 = 0 & convergent_lines(all_25_1, all_25_2) = 0) | (v2 = 0 % 19.02/3.49 | & v1 = 0 & unorthogonal_lines(all_25_2, all_25_2) = 0 & % 19.02/3.49 | convergent_lines(all_25_2, all_25_2) = 0) | ( ~ (v0 = 0) & % 19.02/3.49 | convergent_lines(all_25_2, all_25_1) = v0)) % 19.02/3.49 | % 19.02/3.49 | GROUND_INST: instantiating (5) with all_25_1, all_25_2, all_25_0, simplifying % 19.02/3.49 | with (12), (13), (15) gives: % 19.02/3.49 | (18) all_25_0 = 0 | convergent_lines(all_25_1, all_25_2) = 0 % 19.02/3.49 | % 19.02/3.49 | DELTA: instantiating (16) with fresh symbols all_32_0, all_32_1, all_32_2, % 19.02/3.49 | all_32_3 gives: % 19.02/3.49 | (19) (all_32_0 = 0 & all_32_1 = 0 & unorthogonal_lines(all_25_1, all_25_1) % 19.02/3.49 | = 0 & convergent_lines(all_25_1, all_25_1) = 0) | (all_32_2 = 0 & % 19.02/3.49 | convergent_lines(all_25_2, all_25_1) = 0) | ( ~ (all_32_3 = 0) & % 19.02/3.49 | convergent_lines(all_25_2, all_25_1) = all_32_3) % 19.02/3.49 | % 19.02/3.49 | DELTA: instantiating (17) with fresh symbols all_34_0, all_34_1, all_34_2, % 19.02/3.49 | all_34_3 gives: % 19.02/3.49 | (20) (all_34_0 = 0 & all_25_0 = 0 & convergent_lines(all_25_1, all_25_2) = % 19.02/3.49 | 0) | (all_34_1 = 0 & all_34_2 = 0 & unorthogonal_lines(all_25_2, % 19.02/3.49 | all_25_2) = 0 & convergent_lines(all_25_2, all_25_2) = 0) | ( ~ % 19.02/3.49 | (all_34_3 = 0) & convergent_lines(all_25_2, all_25_1) = all_34_3) % 19.02/3.49 | % 19.02/3.49 | BETA: splitting (18) gives: % 19.02/3.49 | % 19.02/3.49 | Case 1: % 19.02/3.49 | | % 19.02/3.49 | | (21) convergent_lines(all_25_1, all_25_2) = 0 % 19.02/3.49 | | % 19.02/3.49 | | GROUND_INST: instantiating (3) with all_25_1, all_25_2, simplifying with % 19.02/3.49 | | (12), (13), (21) gives: % 19.02/3.50 | | (22) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 19.02/3.50 | | intersection_point(all_25_1, all_25_2) = v0 & % 19.02/3.50 | | apart_point_and_line(v0, all_25_2) = v1 & $i(v0)) % 19.02/3.50 | | % 19.02/3.50 | | GROUND_INST: instantiating (2) with all_25_1, all_25_2, simplifying with % 19.02/3.50 | | (12), (13), (21) gives: % 19.02/3.50 | | (23) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 19.02/3.50 | | intersection_point(all_25_1, all_25_2) = v0 & % 19.02/3.50 | | apart_point_and_line(v0, all_25_1) = v1 & $i(v0)) % 19.02/3.50 | | % 19.02/3.50 | | DELTA: instantiating (23) with fresh symbols all_43_0, all_43_1 gives: % 19.02/3.50 | | (24) ~ (all_43_0 = 0) & intersection_point(all_25_1, all_25_2) = % 19.02/3.50 | | all_43_1 & apart_point_and_line(all_43_1, all_25_1) = all_43_0 & % 19.02/3.50 | | $i(all_43_1) % 19.02/3.50 | | % 19.02/3.50 | | ALPHA: (24) implies: % 19.02/3.50 | | (25) ~ (all_43_0 = 0) % 19.02/3.50 | | (26) apart_point_and_line(all_43_1, all_25_1) = all_43_0 % 19.02/3.50 | | (27) intersection_point(all_25_1, all_25_2) = all_43_1 % 19.02/3.50 | | % 19.02/3.50 | | DELTA: instantiating (22) with fresh symbols all_45_0, all_45_1 gives: % 19.02/3.50 | | (28) ~ (all_45_0 = 0) & intersection_point(all_25_1, all_25_2) = % 19.02/3.50 | | all_45_1 & apart_point_and_line(all_45_1, all_25_2) = all_45_0 & % 19.02/3.50 | | $i(all_45_1) % 19.02/3.50 | | % 19.02/3.50 | | ALPHA: (28) implies: % 19.02/3.50 | | (29) ~ (all_45_0 = 0) % 19.02/3.50 | | (30) $i(all_45_1) % 19.02/3.50 | | (31) apart_point_and_line(all_45_1, all_25_2) = all_45_0 % 19.02/3.50 | | (32) intersection_point(all_25_1, all_25_2) = all_45_1 % 19.02/3.50 | | % 19.02/3.50 | | GROUND_INST: instantiating (9) with all_43_1, all_45_1, all_25_2, all_25_1, % 19.02/3.50 | | simplifying with (27), (32) gives: % 19.02/3.50 | | (33) all_45_1 = all_43_1 % 19.02/3.50 | | % 19.02/3.50 | | REDUCE: (31), (33) imply: % 19.02/3.50 | | (34) apart_point_and_line(all_43_1, all_25_2) = all_45_0 % 19.02/3.50 | | % 19.02/3.50 | | REDUCE: (30), (33) imply: % 19.02/3.50 | | (35) $i(all_43_1) % 19.02/3.50 | | % 19.02/3.50 | | GROUND_INST: instantiating (4) with all_43_1, all_25_2, all_25_1, all_45_0, % 19.02/3.50 | | all_43_0, simplifying with (12), (13), (26), (34), (35) gives: % 19.02/3.51 | | (36) all_45_0 = 0 | all_43_0 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 % 19.02/3.51 | | & convergent_lines(all_25_2, all_25_1) = 0) | ( ~ (v0 = 0) & % 19.02/3.51 | | distinct_lines(all_25_2, all_25_1) = v0)) % 19.02/3.51 | | % 19.02/3.51 | | BETA: splitting (19) gives: % 19.02/3.51 | | % 19.02/3.51 | | Case 1: % 19.02/3.51 | | | % 19.02/3.51 | | | (37) all_32_0 = 0 & all_32_1 = 0 & unorthogonal_lines(all_25_1, % 19.02/3.51 | | | all_25_1) = 0 & convergent_lines(all_25_1, all_25_1) = 0 % 19.02/3.51 | | | % 19.02/3.51 | | | ALPHA: (37) implies: % 19.02/3.51 | | | (38) convergent_lines(all_25_1, all_25_1) = 0 % 19.02/3.51 | | | % 19.02/3.51 | | | GROUND_INST: instantiating (apart3) with all_25_1, simplifying with (13), % 19.02/3.51 | | | (38) gives: % 19.02/3.51 | | | (39) $false % 19.02/3.51 | | | % 19.02/3.51 | | | CLOSE: (39) is inconsistent. % 19.02/3.51 | | | % 19.02/3.51 | | Case 2: % 19.02/3.51 | | | % 19.02/3.51 | | | (40) (all_32_2 = 0 & convergent_lines(all_25_2, all_25_1) = 0) | ( ~ % 19.02/3.51 | | | (all_32_3 = 0) & convergent_lines(all_25_2, all_25_1) = % 19.02/3.51 | | | all_32_3) % 19.02/3.51 | | | % 19.02/3.51 | | | BETA: splitting (40) gives: % 19.02/3.51 | | | % 19.02/3.51 | | | Case 1: % 19.02/3.51 | | | | % 19.02/3.51 | | | | (41) all_32_2 = 0 & convergent_lines(all_25_2, all_25_1) = 0 % 19.02/3.51 | | | | % 19.02/3.51 | | | | ALPHA: (41) implies: % 19.02/3.51 | | | | (42) convergent_lines(all_25_2, all_25_1) = 0 % 19.02/3.51 | | | | % 19.02/3.51 | | | | BETA: splitting (20) gives: % 19.02/3.51 | | | | % 19.02/3.51 | | | | Case 1: % 19.02/3.51 | | | | | % 19.02/3.51 | | | | | (43) all_34_0 = 0 & all_25_0 = 0 & convergent_lines(all_25_1, % 19.02/3.51 | | | | | all_25_2) = 0 % 19.02/3.51 | | | | | % 19.02/3.51 | | | | | ALPHA: (43) implies: % 19.02/3.51 | | | | | (44) all_25_0 = 0 % 19.02/3.51 | | | | | % 19.02/3.51 | | | | | REDUCE: (11), (44) imply: % 19.02/3.51 | | | | | (45) $false % 19.02/3.51 | | | | | % 19.02/3.51 | | | | | CLOSE: (45) is inconsistent. % 19.02/3.51 | | | | | % 19.02/3.51 | | | | Case 2: % 19.02/3.51 | | | | | % 19.02/3.51 | | | | | (46) (all_34_1 = 0 & all_34_2 = 0 & unorthogonal_lines(all_25_2, % 19.02/3.51 | | | | | all_25_2) = 0 & convergent_lines(all_25_2, all_25_2) = 0) % 19.02/3.51 | | | | | | ( ~ (all_34_3 = 0) & convergent_lines(all_25_2, all_25_1) = % 19.02/3.51 | | | | | all_34_3) % 19.02/3.51 | | | | | % 19.02/3.51 | | | | | BETA: splitting (46) gives: % 19.02/3.51 | | | | | % 19.02/3.51 | | | | | Case 1: % 19.02/3.51 | | | | | | % 19.02/3.51 | | | | | | (47) all_34_1 = 0 & all_34_2 = 0 & unorthogonal_lines(all_25_2, % 19.02/3.51 | | | | | | all_25_2) = 0 & convergent_lines(all_25_2, all_25_2) = 0 % 19.02/3.51 | | | | | | % 19.02/3.51 | | | | | | ALPHA: (47) implies: % 19.02/3.51 | | | | | | (48) convergent_lines(all_25_2, all_25_2) = 0 % 19.02/3.51 | | | | | | % 19.02/3.51 | | | | | | GROUND_INST: instantiating (apart3) with all_25_2, simplifying with % 19.02/3.51 | | | | | | (12), (48) gives: % 19.02/3.51 | | | | | | (49) $false % 19.02/3.51 | | | | | | % 19.02/3.51 | | | | | | CLOSE: (49) is inconsistent. % 19.02/3.51 | | | | | | % 19.02/3.52 | | | | | Case 2: % 19.02/3.52 | | | | | | % 19.02/3.52 | | | | | | (50) ~ (all_34_3 = 0) & convergent_lines(all_25_2, all_25_1) = % 19.02/3.52 | | | | | | all_34_3 % 19.02/3.52 | | | | | | % 19.02/3.52 | | | | | | ALPHA: (50) implies: % 19.02/3.52 | | | | | | (51) ~ (all_34_3 = 0) % 19.02/3.52 | | | | | | (52) convergent_lines(all_25_2, all_25_1) = all_34_3 % 19.02/3.52 | | | | | | % 19.02/3.52 | | | | | | GROUND_INST: instantiating (8) with 0, all_34_3, all_25_1, all_25_2, % 19.02/3.52 | | | | | | simplifying with (42), (52) gives: % 19.02/3.52 | | | | | | (53) all_34_3 = 0 % 19.02/3.52 | | | | | | % 19.02/3.52 | | | | | | REDUCE: (51), (53) imply: % 19.02/3.52 | | | | | | (54) $false % 19.02/3.52 | | | | | | % 19.02/3.52 | | | | | | CLOSE: (54) is inconsistent. % 19.02/3.52 | | | | | | % 19.02/3.52 | | | | | End of split % 19.02/3.52 | | | | | % 19.02/3.52 | | | | End of split % 19.02/3.52 | | | | % 19.02/3.52 | | | Case 2: % 19.02/3.52 | | | | % 19.02/3.52 | | | | (55) ~ (all_32_3 = 0) & convergent_lines(all_25_2, all_25_1) = % 19.02/3.52 | | | | all_32_3 % 19.02/3.52 | | | | % 19.02/3.52 | | | | ALPHA: (55) implies: % 19.02/3.52 | | | | (56) ~ (all_32_3 = 0) % 19.02/3.52 | | | | (57) convergent_lines(all_25_2, all_25_1) = all_32_3 % 19.02/3.52 | | | | % 19.02/3.52 | | | | BETA: splitting (36) gives: % 19.02/3.52 | | | | % 19.02/3.52 | | | | Case 1: % 19.02/3.52 | | | | | % 19.02/3.52 | | | | | (58) all_45_0 = 0 % 19.02/3.52 | | | | | % 19.02/3.52 | | | | | REDUCE: (29), (58) imply: % 19.02/3.52 | | | | | (59) $false % 19.02/3.52 | | | | | % 19.02/3.52 | | | | | CLOSE: (59) is inconsistent. % 19.02/3.52 | | | | | % 19.02/3.52 | | | | Case 2: % 19.02/3.52 | | | | | % 19.02/3.52 | | | | | (60) all_43_0 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 & % 19.02/3.52 | | | | | convergent_lines(all_25_2, all_25_1) = 0) | ( ~ (v0 = 0) & % 19.02/3.52 | | | | | distinct_lines(all_25_2, all_25_1) = v0)) % 19.02/3.52 | | | | | % 19.02/3.52 | | | | | BETA: splitting (60) gives: % 19.02/3.52 | | | | | % 19.02/3.52 | | | | | Case 1: % 19.02/3.52 | | | | | | % 19.02/3.52 | | | | | | (61) all_43_0 = 0 % 19.02/3.52 | | | | | | % 19.02/3.52 | | | | | | REDUCE: (25), (61) imply: % 19.02/3.52 | | | | | | (62) $false % 19.02/3.52 | | | | | | % 19.02/3.52 | | | | | | CLOSE: (62) is inconsistent. % 19.02/3.52 | | | | | | % 19.02/3.52 | | | | | Case 2: % 19.02/3.52 | | | | | | % 19.02/3.52 | | | | | | (63) ? [v0: int] : ? [v1: int] : ((v1 = 0 & % 19.02/3.52 | | | | | | convergent_lines(all_25_2, all_25_1) = 0) | ( ~ (v0 = 0) % 19.02/3.52 | | | | | | & distinct_lines(all_25_2, all_25_1) = v0)) % 19.02/3.52 | | | | | | % 19.02/3.52 | | | | | | DELTA: instantiating (63) with fresh symbols all_117_0, all_117_1 % 19.02/3.52 | | | | | | gives: % 19.02/3.52 | | | | | | (64) (all_117_0 = 0 & convergent_lines(all_25_2, all_25_1) = 0) | % 19.02/3.52 | | | | | | ( ~ (all_117_1 = 0) & distinct_lines(all_25_2, all_25_1) = % 19.02/3.52 | | | | | | all_117_1) % 19.02/3.52 | | | | | | % 19.02/3.52 | | | | | | BETA: splitting (64) gives: % 19.02/3.52 | | | | | | % 19.02/3.52 | | | | | | Case 1: % 19.02/3.52 | | | | | | | % 19.02/3.52 | | | | | | | (65) all_117_0 = 0 & convergent_lines(all_25_2, all_25_1) = 0 % 19.02/3.52 | | | | | | | % 19.02/3.52 | | | | | | | ALPHA: (65) implies: % 19.02/3.52 | | | | | | | (66) convergent_lines(all_25_2, all_25_1) = 0 % 19.02/3.52 | | | | | | | % 19.02/3.52 | | | | | | | GROUND_INST: instantiating (8) with 0, all_32_3, all_25_1, % 19.02/3.52 | | | | | | | all_25_2, simplifying with (57), (66) gives: % 19.02/3.52 | | | | | | | (67) all_32_3 = 0 % 19.02/3.52 | | | | | | | % 19.02/3.52 | | | | | | | REDUCE: (56), (67) imply: % 19.02/3.52 | | | | | | | (68) $false % 19.02/3.52 | | | | | | | % 19.02/3.52 | | | | | | | CLOSE: (68) is inconsistent. % 19.02/3.52 | | | | | | | % 19.02/3.52 | | | | | | Case 2: % 19.02/3.52 | | | | | | | % 19.02/3.52 | | | | | | | % 19.02/3.52 | | | | | | | GROUND_INST: instantiating (1) with all_25_1, all_25_2, all_25_1, % 19.02/3.52 | | | | | | | all_32_3, simplifying with (12), (13), (21), (57) % 19.02/3.52 | | | | | | | gives: % 19.02/3.52 | | | | | | | (69) all_32_3 = 0 | convergent_lines(all_25_1, all_25_1) = 0 % 19.02/3.52 | | | | | | | % 19.02/3.52 | | | | | | | BETA: splitting (69) gives: % 19.02/3.52 | | | | | | | % 19.02/3.52 | | | | | | | Case 1: % 19.02/3.52 | | | | | | | | % 19.02/3.53 | | | | | | | | (70) convergent_lines(all_25_1, all_25_1) = 0 % 19.02/3.53 | | | | | | | | % 19.02/3.53 | | | | | | | | GROUND_INST: instantiating (apart3) with all_25_1, simplifying % 19.02/3.53 | | | | | | | | with (13), (70) gives: % 19.02/3.53 | | | | | | | | (71) $false % 19.02/3.53 | | | | | | | | % 19.02/3.53 | | | | | | | | CLOSE: (71) is inconsistent. % 19.02/3.53 | | | | | | | | % 19.02/3.53 | | | | | | | Case 2: % 19.02/3.53 | | | | | | | | % 19.02/3.53 | | | | | | | | (72) all_32_3 = 0 % 19.02/3.53 | | | | | | | | % 19.02/3.53 | | | | | | | | REDUCE: (56), (72) imply: % 19.02/3.53 | | | | | | | | (73) $false % 19.02/3.53 | | | | | | | | % 19.02/3.53 | | | | | | | | CLOSE: (73) is inconsistent. % 19.02/3.53 | | | | | | | | % 19.02/3.53 | | | | | | | End of split % 19.02/3.53 | | | | | | | % 19.02/3.53 | | | | | | End of split % 19.02/3.53 | | | | | | % 19.02/3.53 | | | | | End of split % 19.02/3.53 | | | | | % 19.02/3.53 | | | | End of split % 19.02/3.53 | | | | % 19.02/3.53 | | | End of split % 19.02/3.53 | | | % 19.02/3.53 | | End of split % 19.02/3.53 | | % 19.02/3.53 | Case 2: % 19.02/3.53 | | % 19.02/3.53 | | (74) all_25_0 = 0 % 19.02/3.53 | | % 19.02/3.53 | | REDUCE: (11), (74) imply: % 19.02/3.53 | | (75) $false % 19.02/3.53 | | % 19.02/3.53 | | CLOSE: (75) is inconsistent. % 19.02/3.53 | | % 19.02/3.53 | End of split % 19.02/3.53 | % 19.02/3.53 End of proof % 19.02/3.53 % SZS output end Proof for theBenchmark % 19.02/3.53 % 19.02/3.53 2991ms %------------------------------------------------------------------------------