%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO225+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n010.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 23:22:33 EDT 2023 % Result : Theorem 10.69s 2.19s % Output : Proof 13.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO225+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n010.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Aug 29 22:25:03 EDT 2023 % 0.12/0.33 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 2.88/1.15 Prover 1: Preprocessing ... % 2.88/1.15 Prover 4: Preprocessing ... % 3.48/1.19 Prover 0: Preprocessing ... % 3.48/1.19 Prover 3: Preprocessing ... % 3.48/1.19 Prover 6: Preprocessing ... % 3.48/1.19 Prover 2: Preprocessing ... % 3.48/1.19 Prover 5: Preprocessing ... % 6.04/1.59 Prover 5: Proving ... % 6.04/1.60 Prover 2: Proving ... % 6.77/1.65 Prover 3: Constructing countermodel ... % 6.77/1.67 Prover 1: Constructing countermodel ... % 6.77/1.68 Prover 6: Proving ... % 7.22/1.74 Prover 3: gave up % 7.22/1.74 Prover 1: gave up % 7.22/1.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.22/1.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.97/1.83 Prover 7: Preprocessing ... % 8.23/1.85 Prover 8: Preprocessing ... % 8.23/1.91 Prover 7: Warning: ignoring some quantifiers % 8.23/1.93 Prover 7: Constructing countermodel ... % 8.96/1.98 Prover 0: Proving ... % 9.42/2.00 Prover 4: Constructing countermodel ... % 9.42/2.03 Prover 8: Warning: ignoring some quantifiers % 9.90/2.08 Prover 8: Constructing countermodel ... % 10.69/2.19 Prover 0: proved (1571ms) % 10.69/2.19 % 10.69/2.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.69/2.19 % 10.69/2.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.69/2.19 Prover 2: stopped % 10.69/2.19 Prover 5: stopped % 10.69/2.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.69/2.19 Prover 6: stopped % 10.97/2.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.97/2.21 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 10.97/2.21 Prover 8: gave up % 10.97/2.22 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 10.97/2.22 Prover 10: Preprocessing ... % 10.97/2.23 Prover 11: Preprocessing ... % 11.22/2.25 Prover 13: Preprocessing ... % 11.22/2.25 Prover 19: Preprocessing ... % 11.22/2.26 Prover 10: Warning: ignoring some quantifiers % 11.22/2.26 Prover 16: Preprocessing ... % 11.22/2.28 Prover 10: Constructing countermodel ... % 12.00/2.35 Prover 13: Warning: ignoring some quantifiers % 12.00/2.35 Prover 16: Warning: ignoring some quantifiers % 12.00/2.36 Prover 13: Constructing countermodel ... % 12.00/2.37 Prover 16: Constructing countermodel ... % 12.43/2.40 Prover 7: gave up % 12.43/2.42 Prover 10: gave up % 12.43/2.42 Prover 19: Warning: ignoring some quantifiers % 12.43/2.43 Prover 19: Constructing countermodel ... % 12.43/2.43 Prover 4: Found proof (size 46) % 12.43/2.43 Prover 4: proved (1807ms) % 12.43/2.43 Prover 16: stopped % 12.43/2.43 Prover 13: stopped % 12.43/2.43 Prover 19: stopped % 13.18/2.55 Prover 11: Constructing countermodel ... % 13.18/2.56 Prover 11: stopped % 13.18/2.56 % 13.18/2.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.18/2.56 % 13.18/2.57 % SZS output start Proof for theBenchmark % 13.18/2.58 Assumptions after simplification: % 13.18/2.58 --------------------------------- % 13.18/2.58 % 13.18/2.58 (a4) % 13.18/2.60 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 13.18/2.60 (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 13.18/2.60 apart_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] % 13.18/2.60 : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 13.18/2.60 incident_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 13.18/2.60 (incident_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] % 13.18/2.60 : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0: $i] : ! [v1: % 13.18/2.60 $i] : ( ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 13.18/2.60 [v2: int] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) % 13.18/2.60 % 13.18/2.60 (ci1) % 13.18/2.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 13.18/2.61 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 13.18/2.61 (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 13.18/2.61 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 13.18/2.61 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 13.18/2.61 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 13.18/2.61 apart_point_and_line(v0, v2) = v3 & $i(v2))) % 13.18/2.61 % 13.18/2.61 (ci2) % 13.18/2.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 13.18/2.61 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 13.18/2.61 (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 13.18/2.61 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 13.18/2.61 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 13.18/2.61 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 13.18/2.61 apart_point_and_line(v1, v2) = v3 & $i(v2))) % 13.18/2.61 % 13.18/2.61 (con) % 13.18/2.61 ? [v0: $i] : ? [v1: $i] : (point(v1) = 0 & point(v0) = 0 & % 13.18/2.61 distinct_points(v0, v1) = 0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: int] : % 13.18/2.61 (v3 = 0 | ~ (line(v2) = v3) | ~ $i(v2)) & ! [v2: $i] : ( ~ % 13.18/2.61 (incident_point_and_line(v1, v2) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 % 13.18/2.61 = 0) & incident_point_and_line(v0, v2) = v3)) & ! [v2: $i] : ( ~ % 13.18/2.61 (incident_point_and_line(v0, v2) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 % 13.18/2.61 = 0) & incident_point_and_line(v1, v2) = v3))) % 13.18/2.61 % 13.18/2.61 (con1) % 13.18/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 13.18/2.62 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: % 13.18/2.62 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & % 13.18/2.62 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | % 13.18/2.62 v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = % 13.18/2.62 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : % 13.18/2.62 ? [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & % 13.18/2.62 line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = % 13.18/2.62 0))) % 13.18/2.62 % 13.18/2.62 (cu1) % 13.18/2.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 13.18/2.63 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 13.18/2.63 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 13.18/2.63 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 13.18/2.63 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, % 13.18/2.63 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 13.18/2.63 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 13.18/2.63 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 13.18/2.63 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 13.18/2.63 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 13.18/2.63 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 13.18/2.63 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 % 13.18/2.63 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 13.18/2.63 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 13.18/2.63 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 13.18/2.63 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 13.18/2.63 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 13.18/2.63 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 13.18/2.63 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = % 13.18/2.63 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 13.18/2.63 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = % 13.18/2.63 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 13.18/2.63 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 13.18/2.63 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = % 13.18/2.63 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 % 13.18/2.63 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : % 13.18/2.63 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 13.18/2.63 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 13.18/2.63 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 13.18/2.63 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 13.18/2.63 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & % 13.18/2.63 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 13.18/2.63 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 13.18/2.63 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ % 13.18/2.63 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 13.18/2.63 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 13.66/2.63 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, % 13.66/2.63 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 13.66/2.63 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 13.66/2.63 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 13.66/2.63 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 13.66/2.63 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 13.66/2.63 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 13.66/2.63 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 13.66/2.63 % 13.66/2.63 (function-axioms) % 13.66/2.64 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.66/2.64 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 13.66/2.64 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.66/2.64 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.66/2.64 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 13.66/2.64 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.66/2.64 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 13.66/2.64 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.66/2.64 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.66/2.64 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 13.66/2.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.66/2.64 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 13.66/2.64 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.66/2.64 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 13.66/2.64 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 13.66/2.64 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 13.66/2.64 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 13.66/2.64 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 13.66/2.64 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 13.66/2.64 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 13.66/2.64 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 13.66/2.64 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 13.66/2.64 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.66/2.64 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.66/2.64 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 13.66/2.64 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.66/2.64 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 13.66/2.64 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 13.66/2.64 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.66/2.64 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 13.66/2.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.66/2.64 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 13.66/2.64 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 13.66/2.64 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 13.66/2.64 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 13.66/2.64 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 13.66/2.64 % 13.66/2.64 Further assumptions not needed in the proof: % 13.66/2.64 -------------------------------------------- % 13.66/2.64 a3, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ax6, ceq1, ceq2, ceq3, % 13.66/2.64 ci3, ci4, coipo1, cotno1, couo1, cp1, cp2, cup1, int1, oac1, occu1, ooc1, ooc2, % 13.66/2.64 orth1, ouo1, p1, par1 % 13.66/2.64 % 13.66/2.64 Those formulas are unsatisfiable: % 13.66/2.64 --------------------------------- % 13.66/2.64 % 13.66/2.64 Begin of proof % 13.66/2.64 | % 13.66/2.64 | ALPHA: (ci1) implies: % 13.66/2.64 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 13.66/2.64 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 13.66/2.64 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 13.66/2.64 | $i(v2))) % 13.66/2.64 | % 13.66/2.64 | ALPHA: (ci2) implies: % 13.66/2.64 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 13.66/2.64 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 13.66/2.64 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 13.66/2.64 | $i(v2))) % 13.66/2.64 | % 13.66/2.64 | ALPHA: (cu1) implies: % 13.66/2.65 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 13.66/2.65 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 13.66/2.65 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 13.66/2.65 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 13.66/2.65 | [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 13.66/2.65 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 13.66/2.65 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 13.66/2.65 | | v8 = 0))) % 13.66/2.65 | % 13.66/2.65 | ALPHA: (con1) implies: % 13.66/2.65 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 13.66/2.65 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? % 13.66/2.65 | [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & % 13.66/2.65 | line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) % 13.66/2.65 | | v5 = 0))) % 13.66/2.65 | % 13.66/2.65 | ALPHA: (a4) implies: % 13.66/2.65 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 13.66/2.65 | (apart_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 13.66/2.65 | incident_point_and_line(v0, v1) = 0) % 13.66/2.65 | % 13.66/2.65 | ALPHA: (function-axioms) implies: % 13.66/2.65 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.66/2.65 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 13.66/2.65 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.66/2.65 | ! [v3: $i] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ % 13.66/2.65 | (incident_point_and_line(v3, v2) = v0)) % 13.66/2.65 | % 13.66/2.65 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1 gives: % 13.66/2.65 | (8) point(all_38_0) = 0 & point(all_38_1) = 0 & distinct_points(all_38_1, % 13.66/2.65 | all_38_0) = 0 & $i(all_38_0) & $i(all_38_1) & ! [v0: $i] : ! [v1: % 13.66/2.65 | int] : (v1 = 0 | ~ (line(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ % 13.66/2.65 | (incident_point_and_line(all_38_0, v0) = 0) | ~ $i(v0) | ? [v1: % 13.66/2.65 | int] : ( ~ (v1 = 0) & incident_point_and_line(all_38_1, v0) = v1)) % 13.66/2.65 | & ! [v0: $i] : ( ~ (incident_point_and_line(all_38_1, v0) = 0) | ~ % 13.66/2.65 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 13.66/2.65 | incident_point_and_line(all_38_0, v0) = v1)) % 13.66/2.65 | % 13.66/2.65 | ALPHA: (8) implies: % 13.66/2.65 | (9) $i(all_38_1) % 13.66/2.65 | (10) $i(all_38_0) % 13.66/2.65 | (11) distinct_points(all_38_1, all_38_0) = 0 % 13.66/2.65 | (12) ! [v0: $i] : ( ~ (incident_point_and_line(all_38_0, v0) = 0) | ~ % 13.66/2.65 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 13.66/2.65 | incident_point_and_line(all_38_1, v0) = v1)) % 13.66/2.65 | % 13.66/2.66 | GROUND_INST: instantiating (4) with all_38_1, all_38_0, simplifying with (9), % 13.66/2.66 | (10), (11) gives: % 13.66/2.66 | (13) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 13.66/2.66 | (point(all_38_0) = v1 & point(all_38_1) = v0 & line(v2) = v3 & % 13.66/2.66 | line_connecting(all_38_1, all_38_0) = v2 & $i(v2) & ( ~ (v1 = 0) | % 13.66/2.66 | ~ (v0 = 0) | v3 = 0)) % 13.66/2.66 | % 13.66/2.66 | GROUND_INST: instantiating (2) with all_38_1, all_38_0, simplifying with (9), % 13.66/2.66 | (10), (11) gives: % 13.66/2.66 | (14) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_1, % 13.66/2.66 | all_38_0) = v0 & apart_point_and_line(all_38_0, v0) = v1 & $i(v0)) % 13.66/2.66 | % 13.66/2.66 | GROUND_INST: instantiating (1) with all_38_1, all_38_0, simplifying with (9), % 13.66/2.66 | (10), (11) gives: % 13.66/2.66 | (15) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_1, % 13.66/2.66 | all_38_0) = v0 & apart_point_and_line(all_38_1, v0) = v1 & $i(v0)) % 13.66/2.66 | % 13.66/2.66 | DELTA: instantiating (14) with fresh symbols all_48_0, all_48_1 gives: % 13.66/2.66 | (16) ~ (all_48_0 = 0) & line_connecting(all_38_1, all_38_0) = all_48_1 & % 13.66/2.66 | apart_point_and_line(all_38_0, all_48_1) = all_48_0 & $i(all_48_1) % 13.66/2.66 | % 13.66/2.66 | ALPHA: (16) implies: % 13.66/2.66 | (17) ~ (all_48_0 = 0) % 13.66/2.66 | (18) apart_point_and_line(all_38_0, all_48_1) = all_48_0 % 13.66/2.66 | (19) line_connecting(all_38_1, all_38_0) = all_48_1 % 13.66/2.66 | % 13.66/2.66 | DELTA: instantiating (15) with fresh symbols all_50_0, all_50_1 gives: % 13.66/2.66 | (20) ~ (all_50_0 = 0) & line_connecting(all_38_1, all_38_0) = all_50_1 & % 13.66/2.66 | apart_point_and_line(all_38_1, all_50_1) = all_50_0 & $i(all_50_1) % 13.66/2.66 | % 13.66/2.66 | ALPHA: (20) implies: % 13.66/2.66 | (21) ~ (all_50_0 = 0) % 13.66/2.66 | (22) $i(all_50_1) % 13.66/2.66 | (23) apart_point_and_line(all_38_1, all_50_1) = all_50_0 % 13.66/2.66 | (24) line_connecting(all_38_1, all_38_0) = all_50_1 % 13.66/2.66 | % 13.66/2.66 | DELTA: instantiating (13) with fresh symbols all_52_0, all_52_1, all_52_2, % 13.66/2.66 | all_52_3 gives: % 13.66/2.66 | (25) point(all_38_0) = all_52_2 & point(all_38_1) = all_52_3 & % 13.66/2.66 | line(all_52_1) = all_52_0 & line_connecting(all_38_1, all_38_0) = % 13.66/2.66 | all_52_1 & $i(all_52_1) & ( ~ (all_52_2 = 0) | ~ (all_52_3 = 0) | % 13.66/2.66 | all_52_0 = 0) % 13.66/2.66 | % 13.66/2.66 | ALPHA: (25) implies: % 13.66/2.66 | (26) line_connecting(all_38_1, all_38_0) = all_52_1 % 13.66/2.66 | % 13.66/2.66 | GROUND_INST: instantiating (6) with all_50_1, all_52_1, all_38_0, all_38_1, % 13.66/2.66 | simplifying with (24), (26) gives: % 13.66/2.66 | (27) all_52_1 = all_50_1 % 13.66/2.66 | % 13.66/2.66 | GROUND_INST: instantiating (6) with all_48_1, all_52_1, all_38_0, all_38_1, % 13.66/2.66 | simplifying with (19), (26) gives: % 13.66/2.66 | (28) all_52_1 = all_48_1 % 13.66/2.66 | % 13.66/2.66 | COMBINE_EQS: (27), (28) imply: % 13.66/2.66 | (29) all_50_1 = all_48_1 % 13.66/2.66 | % 13.66/2.66 | REDUCE: (23), (29) imply: % 13.66/2.66 | (30) apart_point_and_line(all_38_1, all_48_1) = all_50_0 % 13.66/2.66 | % 13.66/2.66 | REDUCE: (22), (29) imply: % 13.66/2.66 | (31) $i(all_48_1) % 13.66/2.66 | % 13.66/2.66 | GROUND_INST: instantiating (5) with all_38_1, all_48_1, all_50_0, simplifying % 13.66/2.66 | with (9), (30), (31) gives: % 13.66/2.67 | (32) all_50_0 = 0 | incident_point_and_line(all_38_1, all_48_1) = 0 % 13.66/2.67 | % 13.66/2.67 | GROUND_INST: instantiating (3) with all_38_0, all_38_1, all_48_1, all_48_1, % 13.66/2.67 | all_48_0, all_50_0, simplifying with (9), (10), (18), (30), (31) % 13.66/2.67 | gives: % 13.66/2.67 | (33) all_50_0 = 0 | all_48_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 13.66/2.67 | any] : ? [v3: any] : (apart_point_and_line(all_38_0, all_48_1) = v2 % 13.66/2.67 | & apart_point_and_line(all_38_1, all_48_1) = v3 & % 13.66/2.67 | distinct_lines(all_48_1, all_48_1) = v1 & distinct_points(all_38_0, % 13.66/2.67 | all_38_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 13.66/2.67 | % 13.66/2.67 | GROUND_INST: instantiating (5) with all_38_0, all_48_1, all_48_0, simplifying % 13.66/2.67 | with (10), (18), (31) gives: % 13.66/2.67 | (34) all_48_0 = 0 | incident_point_and_line(all_38_0, all_48_1) = 0 % 13.66/2.67 | % 13.66/2.67 | BETA: splitting (34) gives: % 13.66/2.67 | % 13.66/2.67 | Case 1: % 13.66/2.67 | | % 13.66/2.67 | | (35) incident_point_and_line(all_38_0, all_48_1) = 0 % 13.66/2.67 | | % 13.66/2.67 | | BETA: splitting (32) gives: % 13.66/2.67 | | % 13.66/2.67 | | Case 1: % 13.66/2.67 | | | % 13.66/2.67 | | | (36) incident_point_and_line(all_38_1, all_48_1) = 0 % 13.66/2.67 | | | % 13.66/2.67 | | | BETA: splitting (33) gives: % 13.66/2.67 | | | % 13.66/2.67 | | | Case 1: % 13.66/2.67 | | | | % 13.66/2.67 | | | | (37) all_50_0 = 0 % 13.66/2.67 | | | | % 13.66/2.67 | | | | REDUCE: (21), (37) imply: % 13.66/2.67 | | | | (38) $false % 13.66/2.67 | | | | % 13.66/2.67 | | | | CLOSE: (38) is inconsistent. % 13.66/2.67 | | | | % 13.66/2.67 | | | Case 2: % 13.66/2.67 | | | | % 13.66/2.67 | | | | (39) all_48_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 13.66/2.67 | | | | [v3: any] : (apart_point_and_line(all_38_0, all_48_1) = v2 & % 13.66/2.67 | | | | apart_point_and_line(all_38_1, all_48_1) = v3 & % 13.66/2.67 | | | | distinct_lines(all_48_1, all_48_1) = v1 & % 13.66/2.67 | | | | distinct_points(all_38_0, all_38_1) = v0 & ( ~ (v1 = 0) | ~ % 13.66/2.67 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 13.66/2.67 | | | | % 13.66/2.67 | | | | BETA: splitting (39) gives: % 13.66/2.67 | | | | % 13.66/2.67 | | | | Case 1: % 13.66/2.67 | | | | | % 13.66/2.67 | | | | | (40) all_48_0 = 0 % 13.66/2.67 | | | | | % 13.66/2.67 | | | | | REDUCE: (17), (40) imply: % 13.66/2.67 | | | | | (41) $false % 13.66/2.67 | | | | | % 13.66/2.67 | | | | | CLOSE: (41) is inconsistent. % 13.66/2.67 | | | | | % 13.66/2.67 | | | | Case 2: % 13.66/2.67 | | | | | % 13.66/2.67 | | | | | % 13.66/2.67 | | | | | GROUND_INST: instantiating (12) with all_48_1, simplifying with (31), % 13.66/2.67 | | | | | (35) gives: % 13.66/2.67 | | | | | (42) ? [v0: int] : ( ~ (v0 = 0) & % 13.66/2.67 | | | | | incident_point_and_line(all_38_1, all_48_1) = v0) % 13.66/2.67 | | | | | % 13.66/2.67 | | | | | DELTA: instantiating (42) with fresh symbol all_133_0 gives: % 13.66/2.67 | | | | | (43) ~ (all_133_0 = 0) & incident_point_and_line(all_38_1, % 13.66/2.67 | | | | | all_48_1) = all_133_0 % 13.66/2.67 | | | | | % 13.66/2.67 | | | | | ALPHA: (43) implies: % 13.66/2.67 | | | | | (44) ~ (all_133_0 = 0) % 13.66/2.67 | | | | | (45) incident_point_and_line(all_38_1, all_48_1) = all_133_0 % 13.66/2.67 | | | | | % 13.66/2.67 | | | | | GROUND_INST: instantiating (7) with 0, all_133_0, all_48_1, all_38_1, % 13.66/2.67 | | | | | simplifying with (36), (45) gives: % 13.66/2.67 | | | | | (46) all_133_0 = 0 % 13.66/2.67 | | | | | % 13.66/2.67 | | | | | REDUCE: (44), (46) imply: % 13.66/2.67 | | | | | (47) $false % 13.66/2.67 | | | | | % 13.66/2.67 | | | | | CLOSE: (47) is inconsistent. % 13.66/2.67 | | | | | % 13.66/2.67 | | | | End of split % 13.66/2.67 | | | | % 13.66/2.67 | | | End of split % 13.66/2.67 | | | % 13.66/2.67 | | Case 2: % 13.66/2.67 | | | % 13.66/2.67 | | | (48) all_50_0 = 0 % 13.66/2.68 | | | % 13.66/2.68 | | | REDUCE: (21), (48) imply: % 13.66/2.68 | | | (49) $false % 13.66/2.68 | | | % 13.66/2.68 | | | CLOSE: (49) is inconsistent. % 13.66/2.68 | | | % 13.66/2.68 | | End of split % 13.66/2.68 | | % 13.66/2.68 | Case 2: % 13.66/2.68 | | % 13.66/2.68 | | (50) all_48_0 = 0 % 13.66/2.68 | | % 13.66/2.68 | | REDUCE: (17), (50) imply: % 13.66/2.68 | | (51) $false % 13.66/2.68 | | % 13.66/2.68 | | CLOSE: (51) is inconsistent. % 13.66/2.68 | | % 13.66/2.68 | End of split % 13.66/2.68 | % 13.66/2.68 End of proof % 13.66/2.68 % SZS output end Proof for theBenchmark % 13.66/2.68 % 13.66/2.68 2080ms %------------------------------------------------------------------------------