%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO248+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 23:22:44 EDT 2023 % Result : Theorem 9.52s 2.03s % Output : Proof 16.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : GEO248+3 : TPTP v8.1.2. Released v4.0.0. % 0.10/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n010.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 19:15:03 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 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. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.21/1.20 Prover 1: Preprocessing ... % 3.21/1.20 Prover 4: Preprocessing ... % 3.75/1.24 Prover 0: Preprocessing ... % 3.75/1.24 Prover 5: Preprocessing ... % 3.75/1.24 Prover 6: Preprocessing ... % 3.75/1.24 Prover 2: Preprocessing ... % 3.75/1.24 Prover 3: Preprocessing ... % 6.91/1.67 Prover 5: Proving ... % 7.53/1.81 Prover 2: Proving ... % 7.53/1.81 Prover 6: Constructing countermodel ... % 8.09/1.85 Prover 3: Constructing countermodel ... % 8.09/1.86 Prover 1: Constructing countermodel ... % 8.55/1.91 Prover 6: gave up % 8.55/1.93 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.55/1.93 Prover 3: gave up % 8.55/1.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.55/1.94 Prover 1: gave up % 8.55/1.97 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 9.52/2.03 Prover 2: proved (1410ms) % 9.52/2.03 % 9.52/2.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.52/2.03 % 9.52/2.04 Prover 5: stopped % 9.52/2.05 Prover 7: Preprocessing ... % 9.52/2.05 Prover 8: Preprocessing ... % 9.75/2.05 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.75/2.05 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.75/2.06 Prover 9: Preprocessing ... % 10.05/2.10 Prover 10: Preprocessing ... % 10.05/2.12 Prover 11: Preprocessing ... % 10.50/2.17 Prover 7: Warning: ignoring some quantifiers % 10.91/2.21 Prover 7: Constructing countermodel ... % 10.91/2.21 Prover 10: Warning: ignoring some quantifiers % 10.91/2.23 Prover 4: Constructing countermodel ... % 10.91/2.25 Prover 10: Constructing countermodel ... % 11.30/2.27 Prover 8: Warning: ignoring some quantifiers % 11.30/2.28 Prover 8: Constructing countermodel ... % 12.02/2.36 Prover 10: gave up % 12.02/2.36 Prover 0: Proving ... % 12.02/2.36 Prover 7: gave up % 12.02/2.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.02/2.37 Prover 0: stopped % 12.02/2.37 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 12.02/2.37 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 12.02/2.39 Prover 8: gave up % 12.35/2.41 Prover 16: Preprocessing ... % 12.35/2.41 Prover 19: Preprocessing ... % 12.35/2.41 Prover 13: Preprocessing ... % 12.79/2.53 Prover 16: Warning: ignoring some quantifiers % 12.79/2.53 Prover 13: Warning: ignoring some quantifiers % 13.50/2.56 Prover 16: Constructing countermodel ... % 13.50/2.56 Prover 13: Constructing countermodel ... % 13.89/2.61 Prover 19: Warning: ignoring some quantifiers % 13.89/2.61 Prover 11: Constructing countermodel ... % 13.89/2.63 Prover 19: Constructing countermodel ... % 13.89/2.63 Prover 9: Constructing countermodel ... % 13.89/2.66 Prover 9: stopped % 16.17/2.98 Prover 16: gave up % 16.17/2.99 Prover 13: gave up % 16.89/3.00 Prover 11: Found proof (size 35) % 16.89/3.00 Prover 11: proved (949ms) % 16.89/3.00 Prover 4: stopped % 16.89/3.00 Prover 19: stopped % 16.89/3.00 % 16.89/3.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.89/3.00 % 16.89/3.00 % SZS output start Proof for theBenchmark % 16.89/3.00 Assumptions after simplification: % 16.89/3.00 --------------------------------- % 16.89/3.00 % 16.89/3.00 (a2_defns) % 16.89/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.89/3.03 (left_apart_point(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ~ $i(v1) | % 16.89/3.03 ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & right_apart_point(v0, v1) = v4)) & % 16.89/3.03 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (right_apart_point(v0, % 16.89/3.03 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 16.89/3.03 = 0) & left_apart_point(v0, v3) = v4 & reverse_line(v1) = v3 & $i(v3))) % 16.89/3.03 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (left_apart_point(v0, v2) = 0) % 16.89/3.03 | ~ (reverse_line(v1) = v2) | ~ $i(v1) | ~ $i(v0) | right_apart_point(v0, % 16.89/3.03 v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (right_apart_point(v0, v1) = 0) % 16.89/3.03 | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (left_apart_point(v0, v2) = 0 & % 16.89/3.03 reverse_line(v1) = v2 & $i(v2))) % 16.89/3.03 % 16.89/3.03 (a6_defns) % 16.89/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 16.89/3.04 (apart_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : % 16.89/3.04 ? [v4: int] : ( ~ (v4 = 0) & ~ (v3 = 0) & left_apart_point(v0, v1) = v3 & % 16.89/3.04 right_apart_point(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 16.89/3.04 int] : (v2 = 0 | ~ (left_apart_point(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 16.89/3.04 | ? [v3: int] : ? [v4: int] : ((v4 = 0 & right_apart_point(v0, v1) = 0) | % 16.89/3.04 ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3))) & ! [v0: $i] : ! % 16.89/3.04 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (right_apart_point(v0, v1) = v2) | ~ % 16.89/3.04 $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & % 16.89/3.04 left_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, % 16.89/3.04 v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 16.89/3.04 (left_apart_point(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? % 16.89/3.04 [v4: int] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) & ~ % 16.89/3.04 (v2 = 0) & right_apart_point(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] % 16.89/3.04 : ! [v2: any] : ( ~ (right_apart_point(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 16.89/3.04 | ? [v3: int] : ? [v4: int] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) % 16.89/3.04 | ( ~ (v3 = 0) & ~ (v2 = 0) & left_apart_point(v0, v1) = v3))) & ! [v0: % 16.89/3.04 $i] : ! [v1: $i] : ( ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ % 16.89/3.04 $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & right_apart_point(v0, v1) % 16.89/3.04 = 0) | (v2 = 0 & left_apart_point(v0, v1) = 0))) % 16.89/3.04 % 16.89/3.04 (ax10_basics) % 16.89/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (left_apart_point(v0, v2) = 0) | % 16.89/3.04 ~ (reverse_line(v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: % 16.89/3.04 $i] : ( ~ (left_apart_point(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)) % 16.89/3.04 % 16.89/3.04 (con) % 16.89/3.04 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 16.89/3.04 = 0) & parallel_lines(v2, v0) = v3 & incident_point_and_line(v1, v3) = 0 & % 16.89/3.04 apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = 0 & % 16.89/3.04 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 16.89/3.04 % 16.89/3.04 (function-axioms) % 16.89/3.05 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 16.89/3.05 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_on_line(v5, v4, % 16.89/3.05 v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0: % 16.89/3.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.89/3.05 : ! [v4: $i] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ % 16.89/3.05 (before_on_line(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.89/3.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 16.89/3.05 (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) & % 16.89/3.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.89/3.05 (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) & ! [v0: % 16.89/3.05 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.89/3.05 (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = % 16.89/3.05 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 16.89/3.05 ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 16.89/3.05 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 16.89/3.05 [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 16.89/3.05 (distinct_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 16.89/3.05 ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 16.89/3.05 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.89/3.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.89/3.05 (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! % 16.89/3.05 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.89/3.05 $i] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ % 16.89/3.05 (incident_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 16.89/3.05 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.89/3.05 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 16.89/3.05 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.89/3.05 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 16.89/3.05 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.89/3.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.89/3.05 (equally_directed_opposite_lines(v3, v2) = v1) | ~ % 16.89/3.05 (equally_directed_opposite_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 16.89/3.05 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.89/3.05 (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) = % 16.89/3.05 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 16.89/3.05 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ % 16.89/3.05 (left_convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.89/3.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.89/3.05 (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) = % 16.89/3.05 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 16.89/3.05 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ % 16.89/3.05 (left_apart_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.89/3.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.89/3.05 (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0)) & ! % 16.89/3.05 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.89/3.05 $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ % 16.89/3.05 (unequally_directed_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 16.89/3.05 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.89/3.05 (unequally_directed_opposite_lines(v3, v2) = v1) | ~ % 16.89/3.05 (unequally_directed_opposite_lines(v3, v2) = v0)) & ! [v0: % 16.89/3.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 16.89/3.05 ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 16.89/3.05 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (line(v2) = v1) | ~ % 16.89/3.05 (line(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 16.89/3.05 (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 16.89/3.05 % 16.89/3.05 Further assumptions not needed in the proof: % 16.89/3.05 -------------------------------------------- % 16.89/3.05 a1_defns, a3_defns, a4_defns, a5_defns, a7_defns, a8_defns, a9_defns, % 16.89/3.05 ax10_cons_objs, ax11_basics, ax1_basics, ax1_cons_objs, ax1_subs, ax1_uniq_cons, % 16.89/3.05 ax2_basics, ax2_cons_objs, ax2_subs, ax2_uniq_cons, ax3_basics, ax3_cons_objs, % 16.89/3.05 ax3_subs, ax4_basics, ax4_cons_objs, ax4_defns, ax5_basics, ax5_cons_objs, % 16.89/3.05 ax6_basics, ax6_cons_objs, ax7_basics, ax7_cons_objs, ax8_basics, ax8_cons_objs, % 16.89/3.05 ax9_basics, ax9_cons_objs % 16.89/3.05 % 16.89/3.05 Those formulas are unsatisfiable: % 16.89/3.05 --------------------------------- % 16.89/3.05 % 16.89/3.05 Begin of proof % 16.89/3.05 | % 16.89/3.05 | ALPHA: (a2_defns) implies: % 16.89/3.05 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (right_apart_point(v0, v1) = 0) | ~ % 16.89/3.05 | $i(v1) | ~ $i(v0) | ? [v2: $i] : (left_apart_point(v0, v2) = 0 & % 16.89/3.06 | reverse_line(v1) = v2 & $i(v2))) % 16.89/3.06 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 16.89/3.06 | (right_apart_point(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 16.89/3.06 | $i] : ? [v4: int] : ( ~ (v4 = 0) & left_apart_point(v0, v3) = v4 & % 16.89/3.06 | reverse_line(v1) = v3 & $i(v3))) % 16.89/3.06 | % 16.89/3.06 | ALPHA: (a6_defns) implies: % 16.89/3.06 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (apart_point_and_line(v0, v1) = 0) | ~ % 16.89/3.06 | $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & % 16.89/3.06 | right_apart_point(v0, v1) = 0) | (v2 = 0 & left_apart_point(v0, % 16.89/3.06 | v1) = 0))) % 16.89/3.06 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 16.89/3.06 | (apart_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 16.89/3.06 | int] : ? [v4: int] : ( ~ (v4 = 0) & ~ (v3 = 0) & % 16.89/3.06 | left_apart_point(v0, v1) = v3 & right_apart_point(v0, v1) = v4)) % 16.89/3.06 | % 16.89/3.06 | ALPHA: (ax10_basics) implies: % 16.89/3.06 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (left_apart_point(v0, v1) = 0) | ~ % 16.89/3.06 | $i(v1) | ~ $i(v0)) % 16.89/3.06 | % 16.89/3.06 | ALPHA: (function-axioms) implies: % 16.89/3.06 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 16.89/3.06 | (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 16.89/3.06 | % 16.89/3.06 | DELTA: instantiating (con) with fresh symbols all_39_0, all_39_1, all_39_2, % 16.89/3.06 | all_39_3, all_39_4 gives: % 16.89/3.06 | (7) ~ (all_39_0 = 0) & parallel_lines(all_39_2, all_39_4) = all_39_1 & % 16.89/3.06 | incident_point_and_line(all_39_3, all_39_1) = 0 & % 16.89/3.06 | apart_point_and_line(all_39_3, all_39_2) = all_39_0 & % 16.89/3.06 | apart_point_and_line(all_39_4, all_39_2) = 0 & $i(all_39_1) & % 16.89/3.06 | $i(all_39_2) & $i(all_39_3) & $i(all_39_4) % 16.89/3.06 | % 16.89/3.06 | ALPHA: (7) implies: % 16.89/3.06 | (8) ~ (all_39_0 = 0) % 16.89/3.06 | (9) $i(all_39_4) % 16.89/3.06 | (10) $i(all_39_3) % 16.89/3.06 | (11) $i(all_39_2) % 16.89/3.06 | (12) apart_point_and_line(all_39_4, all_39_2) = 0 % 16.89/3.06 | (13) apart_point_and_line(all_39_3, all_39_2) = all_39_0 % 16.89/3.06 | % 16.89/3.06 | GROUND_INST: instantiating (3) with all_39_4, all_39_2, simplifying with (9), % 16.89/3.06 | (11), (12) gives: % 16.89/3.06 | (14) ? [v0: int] : ? [v1: int] : ((v1 = 0 & right_apart_point(all_39_4, % 16.89/3.06 | all_39_2) = 0) | (v0 = 0 & left_apart_point(all_39_4, all_39_2) % 16.89/3.06 | = 0)) % 16.89/3.06 | % 16.89/3.06 | GROUND_INST: instantiating (4) with all_39_3, all_39_2, all_39_0, simplifying % 16.89/3.06 | with (10), (11), (13) gives: % 16.89/3.06 | (15) all_39_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 16.89/3.06 | 0) & left_apart_point(all_39_3, all_39_2) = v0 & % 16.89/3.06 | right_apart_point(all_39_3, all_39_2) = v1) % 16.89/3.06 | % 16.89/3.06 | DELTA: instantiating (14) with fresh symbols all_46_0, all_46_1 gives: % 16.89/3.06 | (16) (all_46_0 = 0 & right_apart_point(all_39_4, all_39_2) = 0) | (all_46_1 % 16.89/3.06 | = 0 & left_apart_point(all_39_4, all_39_2) = 0) % 16.89/3.06 | % 16.89/3.06 | BETA: splitting (15) gives: % 16.89/3.06 | % 16.89/3.06 | Case 1: % 16.89/3.06 | | % 16.89/3.06 | | (17) all_39_0 = 0 % 16.89/3.06 | | % 16.89/3.07 | | REDUCE: (8), (17) imply: % 16.89/3.07 | | (18) $false % 16.89/3.07 | | % 16.89/3.07 | | CLOSE: (18) is inconsistent. % 16.89/3.07 | | % 16.89/3.07 | Case 2: % 16.89/3.07 | | % 16.89/3.07 | | (19) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 16.89/3.07 | | left_apart_point(all_39_3, all_39_2) = v0 & % 16.89/3.07 | | right_apart_point(all_39_3, all_39_2) = v1) % 16.89/3.07 | | % 16.89/3.07 | | DELTA: instantiating (19) with fresh symbols all_49_0, all_49_1 gives: % 16.89/3.07 | | (20) ~ (all_49_0 = 0) & ~ (all_49_1 = 0) & left_apart_point(all_39_3, % 16.89/3.07 | | all_39_2) = all_49_1 & right_apart_point(all_39_3, all_39_2) = % 16.89/3.07 | | all_49_0 % 16.89/3.07 | | % 16.89/3.07 | | ALPHA: (20) implies: % 16.89/3.07 | | (21) ~ (all_49_0 = 0) % 16.89/3.07 | | (22) right_apart_point(all_39_3, all_39_2) = all_49_0 % 16.89/3.07 | | % 16.89/3.07 | | GROUND_INST: instantiating (2) with all_39_3, all_39_2, all_49_0, % 16.89/3.07 | | simplifying with (10), (11), (22) gives: % 16.89/3.07 | | (23) all_49_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 16.89/3.07 | | left_apart_point(all_39_3, v0) = v1 & reverse_line(all_39_2) = v0 % 16.89/3.07 | | & $i(v0)) % 16.89/3.07 | | % 16.89/3.07 | | BETA: splitting (16) gives: % 16.89/3.07 | | % 16.89/3.07 | | Case 1: % 16.89/3.07 | | | % 16.89/3.07 | | | (24) all_46_0 = 0 & right_apart_point(all_39_4, all_39_2) = 0 % 16.89/3.07 | | | % 16.89/3.07 | | | ALPHA: (24) implies: % 16.89/3.07 | | | (25) right_apart_point(all_39_4, all_39_2) = 0 % 16.89/3.07 | | | % 16.89/3.07 | | | BETA: splitting (23) gives: % 16.89/3.07 | | | % 16.89/3.07 | | | Case 1: % 16.89/3.07 | | | | % 16.89/3.07 | | | | (26) all_49_0 = 0 % 16.89/3.07 | | | | % 16.89/3.07 | | | | REDUCE: (21), (26) imply: % 16.89/3.07 | | | | (27) $false % 16.89/3.07 | | | | % 16.89/3.07 | | | | CLOSE: (27) is inconsistent. % 16.89/3.07 | | | | % 16.89/3.07 | | | Case 2: % 16.89/3.07 | | | | % 16.89/3.07 | | | | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 16.89/3.07 | | | | left_apart_point(all_39_3, v0) = v1 & reverse_line(all_39_2) = % 16.89/3.07 | | | | v0 & $i(v0)) % 16.89/3.07 | | | | % 16.89/3.07 | | | | DELTA: instantiating (28) with fresh symbols all_62_0, all_62_1 gives: % 16.89/3.07 | | | | (29) ~ (all_62_0 = 0) & left_apart_point(all_39_3, all_62_1) = % 16.89/3.07 | | | | all_62_0 & reverse_line(all_39_2) = all_62_1 & $i(all_62_1) % 16.89/3.07 | | | | % 16.89/3.07 | | | | ALPHA: (29) implies: % 16.89/3.07 | | | | (30) reverse_line(all_39_2) = all_62_1 % 16.89/3.07 | | | | % 16.89/3.07 | | | | GROUND_INST: instantiating (1) with all_39_4, all_39_2, simplifying with % 16.89/3.07 | | | | (9), (11), (25) gives: % 16.89/3.07 | | | | (31) ? [v0: $i] : (left_apart_point(all_39_4, v0) = 0 & % 16.89/3.07 | | | | reverse_line(all_39_2) = v0 & $i(v0)) % 16.89/3.07 | | | | % 16.89/3.07 | | | | DELTA: instantiating (31) with fresh symbol all_75_0 gives: % 16.89/3.07 | | | | (32) left_apart_point(all_39_4, all_75_0) = 0 & % 16.89/3.07 | | | | reverse_line(all_39_2) = all_75_0 & $i(all_75_0) % 16.89/3.07 | | | | % 16.89/3.07 | | | | ALPHA: (32) implies: % 16.89/3.07 | | | | (33) $i(all_75_0) % 16.89/3.07 | | | | (34) reverse_line(all_39_2) = all_75_0 % 16.89/3.07 | | | | (35) left_apart_point(all_39_4, all_75_0) = 0 % 16.89/3.07 | | | | % 16.89/3.07 | | | | GROUND_INST: instantiating (6) with all_62_1, all_75_0, all_39_2, % 16.89/3.07 | | | | simplifying with (30), (34) gives: % 16.89/3.07 | | | | (36) all_75_0 = all_62_1 % 16.89/3.07 | | | | % 16.89/3.07 | | | | REDUCE: (35), (36) imply: % 16.89/3.07 | | | | (37) left_apart_point(all_39_4, all_62_1) = 0 % 16.89/3.07 | | | | % 16.89/3.07 | | | | REDUCE: (33), (36) imply: % 16.89/3.07 | | | | (38) $i(all_62_1) % 16.89/3.07 | | | | % 16.89/3.07 | | | | GROUND_INST: instantiating (5) with all_39_4, all_62_1, simplifying with % 16.89/3.07 | | | | (9), (37), (38) gives: % 16.89/3.07 | | | | (39) $false % 16.89/3.07 | | | | % 16.89/3.07 | | | | CLOSE: (39) is inconsistent. % 16.89/3.07 | | | | % 16.89/3.07 | | | End of split % 16.89/3.07 | | | % 16.89/3.07 | | Case 2: % 16.89/3.07 | | | % 16.89/3.07 | | | (40) all_46_1 = 0 & left_apart_point(all_39_4, all_39_2) = 0 % 16.89/3.07 | | | % 16.89/3.07 | | | ALPHA: (40) implies: % 16.89/3.08 | | | (41) left_apart_point(all_39_4, all_39_2) = 0 % 16.89/3.08 | | | % 16.89/3.08 | | | GROUND_INST: instantiating (5) with all_39_4, all_39_2, simplifying with % 16.89/3.08 | | | (9), (11), (41) gives: % 16.89/3.08 | | | (42) $false % 16.89/3.08 | | | % 16.89/3.08 | | | CLOSE: (42) is inconsistent. % 16.89/3.08 | | | % 16.89/3.08 | | End of split % 16.89/3.08 | | % 16.89/3.08 | End of split % 16.89/3.08 | % 16.89/3.08 End of proof % 16.89/3.08 % SZS output end Proof for theBenchmark % 16.89/3.08 % 16.89/3.08 2476ms %------------------------------------------------------------------------------