%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO179+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 : n003.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 23:21:54 EDT 2023 % Result : Theorem 6.39s 1.63s % Output : Proof 8.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO179+1 : TPTP v8.1.2. Released v3.3.0. % 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n003.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Tue Aug 29 19:01:56 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.62/1.13 Prover 1: Preprocessing ... % 2.84/1.13 Prover 4: Preprocessing ... % 2.84/1.17 Prover 5: Preprocessing ... % 2.84/1.17 Prover 2: Preprocessing ... % 2.84/1.17 Prover 3: Preprocessing ... % 2.84/1.17 Prover 0: Preprocessing ... % 2.84/1.17 Prover 6: Preprocessing ... % 4.42/1.40 Prover 2: Proving ... % 4.42/1.40 Prover 5: Proving ... % 4.42/1.43 Prover 3: Constructing countermodel ... % 4.92/1.43 Prover 1: Constructing countermodel ... % 4.92/1.43 Prover 6: Constructing countermodel ... % 5.93/1.60 Prover 0: Proving ... % 5.93/1.61 Prover 4: Constructing countermodel ... % 6.39/1.63 Prover 6: proved (996ms) % 6.39/1.63 Prover 3: proved (998ms) % 6.39/1.63 % 6.39/1.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.39/1.63 % 6.39/1.63 % 6.39/1.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.39/1.63 % 6.39/1.64 Prover 0: stopped % 6.39/1.64 Prover 2: stopped % 6.39/1.64 Prover 5: stopped % 6.39/1.65 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.39/1.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.39/1.65 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.39/1.65 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.39/1.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.60/1.68 Prover 7: Preprocessing ... % 6.60/1.68 Prover 8: Preprocessing ... % 6.60/1.69 Prover 11: Preprocessing ... % 6.60/1.69 Prover 13: Preprocessing ... % 6.60/1.69 Prover 10: Preprocessing ... % 6.60/1.72 Prover 7: Warning: ignoring some quantifiers % 6.60/1.72 Prover 7: Constructing countermodel ... % 7.12/1.73 Prover 10: Warning: ignoring some quantifiers % 7.12/1.73 Prover 10: Constructing countermodel ... % 7.12/1.74 Prover 13: Warning: ignoring some quantifiers % 7.12/1.76 Prover 13: Constructing countermodel ... % 7.43/1.77 Prover 10: gave up % 7.43/1.78 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.43/1.78 Prover 1: Found proof (size 55) % 7.43/1.78 Prover 1: proved (1153ms) % 7.43/1.78 Prover 13: stopped % 7.43/1.78 Prover 4: stopped % 7.43/1.79 Prover 7: stopped % 7.43/1.79 Prover 8: Warning: ignoring some quantifiers % 7.43/1.79 Prover 8: Constructing countermodel ... % 7.43/1.80 Prover 8: stopped % 7.43/1.80 Prover 16: Preprocessing ... % 7.43/1.81 Prover 16: stopped % 7.85/1.85 Prover 11: Constructing countermodel ... % 7.85/1.85 Prover 11: stopped % 7.85/1.85 % 7.85/1.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.85/1.86 % 7.85/1.86 % SZS output start Proof for theBenchmark % 7.85/1.87 Assumptions after simplification: % 7.85/1.87 --------------------------------- % 7.85/1.87 % 7.85/1.87 (apart5) % 7.85/1.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 7.85/1.89 (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | ~ $i(v2) % 7.85/1.89 | ~ $i(v1) | ~ $i(v0) | distinct_lines(v1, v2) = 0) % 7.85/1.89 % 7.85/1.89 (ceq1) % 7.85/1.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 7.85/1.90 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~ % 7.85/1.90 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0) % 7.85/1.90 % 7.85/1.90 (ceq2) % 7.85/1.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 7.85/1.90 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | ~ % 7.85/1.90 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v0, v2) = 0) % 7.85/1.90 % 7.85/1.90 (ci1) % 7.85/1.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 7.85/1.90 ~ (apart_point_and_line(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 7.85/1.90 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 7.85/1.90 % 7.85/1.90 (ci2) % 7.85/1.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 7.85/1.90 ~ (apart_point_and_line(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 7.85/1.90 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 7.85/1.90 % 7.85/1.90 (con) % 8.11/1.91 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 8.11/1.91 any] : ? [v6: $i] : ? [v7: any] : (line_connecting(v2, v1) = v6 & % 8.11/1.91 line_connecting(v2, v0) = v4 & line_connecting(v0, v1) = v3 & % 8.11/1.91 apart_point_and_line(v2, v3) = 0 & distinct_lines(v3, v6) = v7 & % 8.11/1.91 distinct_lines(v3, v4) = v5 & distinct_points(v0, v1) = 0 & $i(v6) & $i(v4) % 8.11/1.91 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v7 = 0) | ~ (v5 = 0))) % 8.11/1.91 % 8.11/1.91 (cu1) % 8.11/1.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.11/1.91 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 8.11/1.91 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 8.11/1.91 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 8.11/1.91 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 8.11/1.91 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 8.11/1.91 % 8.11/1.91 (function-axioms) % 8.11/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.11/1.92 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 8.11/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.11/1.92 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 8.11/1.92 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 8.11/1.92 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 8.11/1.92 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.11/1.92 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.11/1.92 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 8.11/1.92 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 8.11/1.92 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 8.11/1.92 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 8.11/1.92 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 8.11/1.92 (distinct_points(v3, v2) = v0)) % 8.11/1.92 % 8.11/1.92 Further assumptions not needed in the proof: % 8.11/1.92 -------------------------------------------- % 8.11/1.92 apart1, apart2, apart3, apart4, ax6, ceq3, ci3, ci4 % 8.11/1.92 % 8.11/1.92 Those formulas are unsatisfiable: % 8.11/1.92 --------------------------------- % 8.11/1.92 % 8.11/1.92 Begin of proof % 8.11/1.92 | % 8.11/1.92 | ALPHA: (function-axioms) implies: % 8.11/1.92 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.11/1.92 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 8.11/1.92 | (distinct_points(v3, v2) = v0)) % 8.11/1.92 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.11/1.92 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 8.11/1.92 | (apart_point_and_line(v3, v2) = v0)) % 8.11/1.92 | % 8.11/1.92 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 8.11/1.92 | all_17_3, all_17_4, all_17_5, all_17_6, all_17_7 gives: % 8.11/1.93 | (3) line_connecting(all_17_5, all_17_6) = all_17_1 & % 8.11/1.93 | line_connecting(all_17_5, all_17_7) = all_17_3 & % 8.11/1.93 | line_connecting(all_17_7, all_17_6) = all_17_4 & % 8.11/1.93 | apart_point_and_line(all_17_5, all_17_4) = 0 & distinct_lines(all_17_4, % 8.11/1.93 | all_17_1) = all_17_0 & distinct_lines(all_17_4, all_17_3) = all_17_2 % 8.11/1.93 | & distinct_points(all_17_7, all_17_6) = 0 & $i(all_17_1) & $i(all_17_3) % 8.11/1.93 | & $i(all_17_4) & $i(all_17_5) & $i(all_17_6) & $i(all_17_7) & ( ~ % 8.11/1.93 | (all_17_0 = 0) | ~ (all_17_2 = 0)) % 8.11/1.93 | % 8.11/1.93 | ALPHA: (3) implies: % 8.11/1.93 | (4) $i(all_17_7) % 8.11/1.93 | (5) $i(all_17_6) % 8.11/1.93 | (6) $i(all_17_5) % 8.11/1.93 | (7) $i(all_17_4) % 8.11/1.93 | (8) $i(all_17_3) % 8.11/1.93 | (9) $i(all_17_1) % 8.11/1.93 | (10) distinct_points(all_17_7, all_17_6) = 0 % 8.11/1.93 | (11) distinct_lines(all_17_4, all_17_3) = all_17_2 % 8.11/1.93 | (12) distinct_lines(all_17_4, all_17_1) = all_17_0 % 8.11/1.93 | (13) apart_point_and_line(all_17_5, all_17_4) = 0 % 8.11/1.93 | (14) line_connecting(all_17_7, all_17_6) = all_17_4 % 8.11/1.93 | (15) line_connecting(all_17_5, all_17_7) = all_17_3 % 8.11/1.93 | (16) line_connecting(all_17_5, all_17_6) = all_17_1 % 8.11/1.93 | (17) ~ (all_17_0 = 0) | ~ (all_17_2 = 0) % 8.11/1.93 | % 8.11/1.93 | GROUND_INST: instantiating (ceq2) with all_17_5, all_17_4, all_17_1, all_17_0, % 8.11/1.93 | simplifying with (6), (7), (9), (12), (13) gives: % 8.11/1.93 | (18) all_17_0 = 0 | apart_point_and_line(all_17_5, all_17_1) = 0 % 8.11/1.93 | % 8.11/1.93 | GROUND_INST: instantiating (ceq2) with all_17_5, all_17_4, all_17_3, all_17_2, % 8.11/1.93 | simplifying with (6), (7), (8), (11), (13) gives: % 8.11/1.93 | (19) all_17_2 = 0 | apart_point_and_line(all_17_5, all_17_3) = 0 % 8.11/1.93 | % 8.11/1.93 | BETA: splitting (17) gives: % 8.11/1.93 | % 8.11/1.93 | Case 1: % 8.11/1.93 | | % 8.11/1.93 | | (20) ~ (all_17_0 = 0) % 8.11/1.93 | | % 8.11/1.93 | | BETA: splitting (18) gives: % 8.11/1.93 | | % 8.11/1.93 | | Case 1: % 8.11/1.93 | | | % 8.11/1.93 | | | (21) apart_point_and_line(all_17_5, all_17_1) = 0 % 8.11/1.93 | | | % 8.11/1.94 | | | GROUND_INST: instantiating (ci1) with all_17_5, all_17_6, all_17_1, % 8.11/1.94 | | | simplifying with (5), (6), (16), (21) gives: % 8.11/1.94 | | | (22) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_17_5, all_17_6) % 8.11/1.94 | | | = v0) % 8.11/1.94 | | | % 8.11/1.94 | | | DELTA: instantiating (22) with fresh symbol all_35_0 gives: % 8.11/1.94 | | | (23) ~ (all_35_0 = 0) & distinct_points(all_17_5, all_17_6) = all_35_0 % 8.11/1.94 | | | % 8.11/1.94 | | | ALPHA: (23) implies: % 8.11/1.94 | | | (24) ~ (all_35_0 = 0) % 8.11/1.94 | | | (25) distinct_points(all_17_5, all_17_6) = all_35_0 % 8.11/1.94 | | | % 8.11/1.94 | | | GROUND_INST: instantiating (ceq1) with all_17_5, all_17_1, all_17_6, % 8.11/1.94 | | | all_35_0, simplifying with (5), (6), (9), (21), (25) gives: % 8.11/1.94 | | | (26) all_35_0 = 0 | apart_point_and_line(all_17_6, all_17_1) = 0 % 8.11/1.94 | | | % 8.11/1.94 | | | GROUND_INST: instantiating (ceq1) with all_17_5, all_17_4, all_17_6, % 8.11/1.94 | | | all_35_0, simplifying with (5), (6), (7), (13), (25) gives: % 8.11/1.94 | | | (27) all_35_0 = 0 | apart_point_and_line(all_17_6, all_17_4) = 0 % 8.11/1.94 | | | % 8.11/1.94 | | | BETA: splitting (27) gives: % 8.11/1.94 | | | % 8.11/1.94 | | | Case 1: % 8.11/1.94 | | | | % 8.11/1.94 | | | | (28) apart_point_and_line(all_17_6, all_17_4) = 0 % 8.11/1.94 | | | | % 8.11/1.94 | | | | BETA: splitting (26) gives: % 8.11/1.94 | | | | % 8.11/1.94 | | | | Case 1: % 8.11/1.94 | | | | | % 8.11/1.94 | | | | | % 8.11/1.94 | | | | | GROUND_INST: instantiating (ci2) with all_17_7, all_17_6, all_17_4, % 8.11/1.94 | | | | | simplifying with (4), (5), (14), (28) gives: % 8.11/1.94 | | | | | (29) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_17_7, % 8.11/1.94 | | | | | all_17_6) = v0) % 8.11/1.94 | | | | | % 8.11/1.94 | | | | | DELTA: instantiating (29) with fresh symbol all_59_0 gives: % 8.11/1.94 | | | | | (30) ~ (all_59_0 = 0) & distinct_points(all_17_7, all_17_6) = % 8.11/1.94 | | | | | all_59_0 % 8.11/1.94 | | | | | % 8.11/1.94 | | | | | ALPHA: (30) implies: % 8.11/1.94 | | | | | (31) ~ (all_59_0 = 0) % 8.11/1.94 | | | | | (32) distinct_points(all_17_7, all_17_6) = all_59_0 % 8.11/1.94 | | | | | % 8.11/1.94 | | | | | GROUND_INST: instantiating (1) with 0, all_59_0, all_17_6, all_17_7, % 8.11/1.94 | | | | | simplifying with (10), (32) gives: % 8.11/1.94 | | | | | (33) all_59_0 = 0 % 8.11/1.94 | | | | | % 8.11/1.94 | | | | | REDUCE: (31), (33) imply: % 8.11/1.94 | | | | | (34) $false % 8.11/1.94 | | | | | % 8.11/1.94 | | | | | CLOSE: (34) is inconsistent. % 8.11/1.94 | | | | | % 8.11/1.94 | | | | Case 2: % 8.11/1.94 | | | | | % 8.11/1.94 | | | | | (35) all_35_0 = 0 % 8.11/1.94 | | | | | % 8.11/1.94 | | | | | REDUCE: (24), (35) imply: % 8.11/1.94 | | | | | (36) $false % 8.11/1.94 | | | | | % 8.11/1.94 | | | | | CLOSE: (36) is inconsistent. % 8.11/1.94 | | | | | % 8.11/1.94 | | | | End of split % 8.11/1.94 | | | | % 8.11/1.94 | | | Case 2: % 8.11/1.94 | | | | % 8.11/1.94 | | | | (37) all_35_0 = 0 % 8.11/1.94 | | | | % 8.11/1.94 | | | | REDUCE: (24), (37) imply: % 8.11/1.94 | | | | (38) $false % 8.11/1.94 | | | | % 8.11/1.94 | | | | CLOSE: (38) is inconsistent. % 8.11/1.94 | | | | % 8.11/1.94 | | | End of split % 8.11/1.94 | | | % 8.11/1.94 | | Case 2: % 8.11/1.94 | | | % 8.11/1.94 | | | (39) all_17_0 = 0 % 8.11/1.94 | | | % 8.11/1.94 | | | REDUCE: (20), (39) imply: % 8.11/1.94 | | | (40) $false % 8.11/1.94 | | | % 8.11/1.94 | | | CLOSE: (40) is inconsistent. % 8.11/1.94 | | | % 8.11/1.94 | | End of split % 8.11/1.94 | | % 8.11/1.94 | Case 2: % 8.11/1.94 | | % 8.11/1.95 | | (41) all_17_0 = 0 % 8.11/1.95 | | (42) ~ (all_17_2 = 0) % 8.11/1.95 | | % 8.11/1.95 | | REDUCE: (12), (41) imply: % 8.11/1.95 | | (43) distinct_lines(all_17_4, all_17_1) = 0 % 8.11/1.95 | | % 8.11/1.95 | | BETA: splitting (19) gives: % 8.11/1.95 | | % 8.11/1.95 | | Case 1: % 8.11/1.95 | | | % 8.11/1.95 | | | (44) apart_point_and_line(all_17_5, all_17_3) = 0 % 8.11/1.95 | | | % 8.11/1.95 | | | GROUND_INST: instantiating (apart5) with all_17_4, all_17_1, all_17_3, % 8.11/1.95 | | | all_17_2, simplifying with (7), (8), (9), (11), (43) gives: % 8.11/1.95 | | | (45) all_17_2 = 0 | distinct_lines(all_17_1, all_17_3) = 0 % 8.11/1.95 | | | % 8.11/1.95 | | | GROUND_INST: instantiating (cu1) with all_17_7, all_17_6, all_17_4, % 8.11/1.95 | | | all_17_1, simplifying with (4), (5), (7), (9), (10), (43) % 8.11/1.95 | | | gives: % 8.11/1.95 | | | (46) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 8.11/1.95 | | | (apart_point_and_line(all_17_6, all_17_1) = v3 & % 8.11/1.95 | | | apart_point_and_line(all_17_6, all_17_4) = v2 & % 8.11/1.95 | | | apart_point_and_line(all_17_7, all_17_1) = v1 & % 8.11/1.95 | | | apart_point_and_line(all_17_7, all_17_4) = v0 & (v3 = 0 | v2 = 0 % 8.11/1.95 | | | | v1 = 0 | v0 = 0)) % 8.11/1.95 | | | % 8.11/1.95 | | | GROUND_INST: instantiating (ci1) with all_17_5, all_17_7, all_17_3, % 8.11/1.95 | | | simplifying with (4), (6), (15), (44) gives: % 8.11/1.95 | | | (47) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_17_5, all_17_7) % 8.11/1.95 | | | = v0) % 8.11/1.95 | | | % 8.11/1.95 | | | DELTA: instantiating (47) with fresh symbol all_35_0 gives: % 8.11/1.95 | | | (48) ~ (all_35_0 = 0) & distinct_points(all_17_5, all_17_7) = all_35_0 % 8.11/1.95 | | | % 8.11/1.95 | | | ALPHA: (48) implies: % 8.11/1.95 | | | (49) ~ (all_35_0 = 0) % 8.11/1.95 | | | (50) distinct_points(all_17_5, all_17_7) = all_35_0 % 8.11/1.95 | | | % 8.11/1.95 | | | DELTA: instantiating (46) with fresh symbols all_37_0, all_37_1, all_37_2, % 8.11/1.95 | | | all_37_3 gives: % 8.11/1.95 | | | (51) apart_point_and_line(all_17_6, all_17_1) = all_37_0 & % 8.11/1.95 | | | apart_point_and_line(all_17_6, all_17_4) = all_37_1 & % 8.11/1.95 | | | apart_point_and_line(all_17_7, all_17_1) = all_37_2 & % 8.11/1.95 | | | apart_point_and_line(all_17_7, all_17_4) = all_37_3 & (all_37_0 = % 8.11/1.95 | | | 0 | all_37_1 = 0 | all_37_2 = 0 | all_37_3 = 0) % 8.11/1.95 | | | % 8.11/1.95 | | | ALPHA: (51) implies: % 8.11/1.95 | | | (52) apart_point_and_line(all_17_7, all_17_4) = all_37_3 % 8.11/1.95 | | | % 8.11/1.95 | | | BETA: splitting (45) gives: % 8.11/1.95 | | | % 8.11/1.95 | | | Case 1: % 8.11/1.95 | | | | % 8.11/1.95 | | | | % 8.11/1.95 | | | | GROUND_INST: instantiating (ceq1) with all_17_5, all_17_4, all_17_7, % 8.11/1.95 | | | | all_35_0, simplifying with (4), (6), (7), (13), (50) gives: % 8.11/1.95 | | | | (53) all_35_0 = 0 | apart_point_and_line(all_17_7, all_17_4) = 0 % 8.11/1.95 | | | | % 8.11/1.95 | | | | BETA: splitting (53) gives: % 8.11/1.95 | | | | % 8.11/1.95 | | | | Case 1: % 8.11/1.95 | | | | | % 8.11/1.95 | | | | | (54) apart_point_and_line(all_17_7, all_17_4) = 0 % 8.11/1.95 | | | | | % 8.11/1.95 | | | | | GROUND_INST: instantiating (2) with all_37_3, 0, all_17_4, all_17_7, % 8.11/1.95 | | | | | simplifying with (52), (54) gives: % 8.11/1.95 | | | | | (55) all_37_3 = 0 % 8.11/1.95 | | | | | % 8.11/1.95 | | | | | GROUND_INST: instantiating (ci1) with all_17_7, all_17_6, all_17_4, % 8.11/1.95 | | | | | simplifying with (4), (5), (14), (54) gives: % 8.11/1.96 | | | | | (56) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_17_7, % 8.11/1.96 | | | | | all_17_6) = v0) % 8.11/1.96 | | | | | % 8.11/1.96 | | | | | DELTA: instantiating (56) with fresh symbol all_67_0 gives: % 8.11/1.96 | | | | | (57) ~ (all_67_0 = 0) & distinct_points(all_17_7, all_17_6) = % 8.11/1.96 | | | | | all_67_0 % 8.11/1.96 | | | | | % 8.11/1.96 | | | | | ALPHA: (57) implies: % 8.11/1.96 | | | | | (58) ~ (all_67_0 = 0) % 8.11/1.96 | | | | | (59) distinct_points(all_17_7, all_17_6) = all_67_0 % 8.11/1.96 | | | | | % 8.11/1.96 | | | | | GROUND_INST: instantiating (1) with 0, all_67_0, all_17_6, all_17_7, % 8.11/1.96 | | | | | simplifying with (10), (59) gives: % 8.11/1.96 | | | | | (60) all_67_0 = 0 % 8.11/1.96 | | | | | % 8.11/1.96 | | | | | REDUCE: (58), (60) imply: % 8.11/1.96 | | | | | (61) $false % 8.11/1.96 | | | | | % 8.11/1.96 | | | | | CLOSE: (61) is inconsistent. % 8.11/1.96 | | | | | % 8.11/1.96 | | | | Case 2: % 8.11/1.96 | | | | | % 8.11/1.96 | | | | | (62) all_35_0 = 0 % 8.11/1.96 | | | | | % 8.11/1.96 | | | | | REDUCE: (49), (62) imply: % 8.11/1.96 | | | | | (63) $false % 8.11/1.96 | | | | | % 8.11/1.96 | | | | | CLOSE: (63) is inconsistent. % 8.11/1.96 | | | | | % 8.11/1.96 | | | | End of split % 8.11/1.96 | | | | % 8.11/1.96 | | | Case 2: % 8.11/1.96 | | | | % 8.11/1.96 | | | | (64) all_17_2 = 0 % 8.11/1.96 | | | | % 8.11/1.96 | | | | REDUCE: (42), (64) imply: % 8.11/1.96 | | | | (65) $false % 8.11/1.96 | | | | % 8.11/1.96 | | | | CLOSE: (65) is inconsistent. % 8.11/1.96 | | | | % 8.11/1.96 | | | End of split % 8.11/1.96 | | | % 8.11/1.96 | | Case 2: % 8.11/1.96 | | | % 8.11/1.96 | | | (66) all_17_2 = 0 % 8.11/1.96 | | | % 8.11/1.96 | | | REDUCE: (42), (66) imply: % 8.11/1.96 | | | (67) $false % 8.11/1.96 | | | % 8.11/1.96 | | | CLOSE: (67) is inconsistent. % 8.11/1.96 | | | % 8.11/1.96 | | End of split % 8.11/1.96 | | % 8.11/1.96 | End of split % 8.11/1.96 | % 8.11/1.96 End of proof % 8.11/1.96 % SZS output end Proof for theBenchmark % 8.11/1.96 % 8.11/1.96 1348ms %------------------------------------------------------------------------------