%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO178+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 : n024.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 8.02s 1.78s % Output : Proof 10.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GEO178+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n024.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 19:33:53 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.59 ________ _____ % 0.20/0.59 ___ __ \_________(_)________________________________ % 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.59 (2023-06-19) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2023 % 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.59 Amanda Stjerna. % 0.20/0.59 Free software under BSD-3-Clause. % 0.20/0.59 % 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.59 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.61/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.61/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.61/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.61/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.61/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.61/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.61/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.92/1.12 Prover 4: Preprocessing ... % 2.92/1.12 Prover 1: Preprocessing ... % 3.46/1.16 Prover 5: Preprocessing ... % 3.46/1.16 Prover 0: Preprocessing ... % 3.46/1.16 Prover 6: Preprocessing ... % 3.46/1.16 Prover 2: Preprocessing ... % 3.46/1.17 Prover 3: Preprocessing ... % 6.52/1.56 Prover 2: Proving ... % 6.52/1.56 Prover 5: Proving ... % 6.81/1.62 Prover 6: Constructing countermodel ... % 7.14/1.66 Prover 3: Constructing countermodel ... % 7.14/1.68 Prover 1: Constructing countermodel ... % 8.02/1.78 Prover 6: proved (1143ms) % 8.02/1.78 % 8.02/1.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.02/1.78 % 8.02/1.78 Prover 2: stopped % 8.02/1.78 Prover 3: proved (1150ms) % 8.02/1.78 % 8.02/1.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.02/1.78 % 8.02/1.79 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.02/1.79 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.02/1.79 Prover 5: stopped % 8.02/1.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.02/1.84 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.68/1.87 Prover 8: Preprocessing ... % 8.68/1.87 Prover 7: Preprocessing ... % 8.68/1.89 Prover 10: Preprocessing ... % 8.68/1.89 Prover 11: Preprocessing ... % 8.68/1.91 Prover 1: Found proof (size 30) % 8.68/1.91 Prover 1: proved (1282ms) % 8.68/1.94 Prover 4: Constructing countermodel ... % 8.68/1.94 Prover 7: stopped % 8.68/1.94 Prover 10: stopped % 9.24/1.98 Prover 4: stopped % 9.24/1.99 Prover 11: stopped % 9.24/2.00 Prover 0: Proving ... % 9.73/2.01 Prover 0: stopped % 9.75/2.02 Prover 8: Warning: ignoring some quantifiers % 9.75/2.03 Prover 8: Constructing countermodel ... % 9.75/2.04 Prover 8: stopped % 9.75/2.04 % 9.75/2.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.75/2.04 % 9.75/2.05 % SZS output start Proof for theBenchmark % 9.75/2.05 Assumptions after simplification: % 9.75/2.05 --------------------------------- % 9.75/2.05 % 9.75/2.05 (ceq1) % 9.75/2.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 9.75/2.09 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~ % 9.75/2.09 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0) % 9.75/2.09 % 9.75/2.09 (ci1) % 9.75/2.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 9.75/2.09 ~ (apart_point_and_line(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 9.75/2.09 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 9.75/2.09 % 9.75/2.09 (ci2) % 9.75/2.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 9.75/2.09 ~ (apart_point_and_line(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 9.75/2.09 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 9.75/2.09 % 9.75/2.09 (con) % 9.75/2.10 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: % 9.75/2.10 any] : (line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = 0 & % 9.75/2.10 distinct_points(v2, v1) = v5 & distinct_points(v2, v0) = v4 & % 9.75/2.10 distinct_points(v0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v5 = % 9.75/2.10 0) | ~ (v4 = 0))) % 9.75/2.10 % 9.75/2.10 (con1) % 10.16/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 10.16/2.10 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: % 10.16/2.10 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & % 10.16/2.10 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | % 10.16/2.10 v6 = 0))) % 10.16/2.10 % 10.16/2.10 (function-axioms) % 10.16/2.11 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 10.16/2.11 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 10.16/2.11 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.16/2.11 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.16/2.11 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 10.16/2.11 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.16/2.11 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 10.16/2.11 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.16/2.11 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.16/2.11 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 10.16/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.16/2.11 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 10.16/2.11 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.16/2.11 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 10.16/2.11 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 10.16/2.11 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 10.16/2.11 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 10.16/2.11 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 10.16/2.11 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 10.16/2.11 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 10.16/2.11 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 10.16/2.11 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 10.16/2.11 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.16/2.11 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.16/2.11 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 10.16/2.11 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.16/2.11 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 10.16/2.11 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.16/2.11 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.16/2.11 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 10.16/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.16/2.11 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 10.16/2.11 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.16/2.11 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 10.16/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 10.16/2.11 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 10.16/2.12 % 10.16/2.12 Further assumptions not needed in the proof: % 10.16/2.12 -------------------------------------------- % 10.16/2.12 a3, a4, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ax6, ceq2, ceq3, % 10.16/2.12 ci3, ci4, coipo1, cotno1, couo1, cp1, cp2, cu1, cup1, int1, oac1, occu1, ooc1, % 10.16/2.12 ooc2, orth1, ouo1, p1, par1 % 10.16/2.12 % 10.16/2.12 Those formulas are unsatisfiable: % 10.16/2.12 --------------------------------- % 10.16/2.12 % 10.16/2.12 Begin of proof % 10.16/2.12 | % 10.16/2.12 | ALPHA: (function-axioms) implies: % 10.16/2.12 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.16/2.12 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 10.16/2.12 | (distinct_points(v3, v2) = v0)) % 10.16/2.12 | % 10.16/2.12 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 10.16/2.12 | all_38_3, all_38_4, all_38_5 gives: % 10.16/2.12 | (2) line_connecting(all_38_5, all_38_4) = all_38_2 & % 10.16/2.12 | apart_point_and_line(all_38_3, all_38_2) = 0 & % 10.16/2.12 | distinct_points(all_38_3, all_38_4) = all_38_0 & % 10.16/2.12 | distinct_points(all_38_3, all_38_5) = all_38_1 & % 10.16/2.12 | distinct_points(all_38_5, all_38_4) = 0 & $i(all_38_2) & $i(all_38_3) & % 10.16/2.12 | $i(all_38_4) & $i(all_38_5) & ( ~ (all_38_0 = 0) | ~ (all_38_1 = 0)) % 10.16/2.12 | % 10.16/2.12 | ALPHA: (2) implies: % 10.16/2.12 | (3) $i(all_38_5) % 10.16/2.12 | (4) $i(all_38_4) % 10.16/2.12 | (5) $i(all_38_3) % 10.16/2.12 | (6) $i(all_38_2) % 10.16/2.12 | (7) distinct_points(all_38_5, all_38_4) = 0 % 10.16/2.12 | (8) distinct_points(all_38_3, all_38_5) = all_38_1 % 10.16/2.12 | (9) distinct_points(all_38_3, all_38_4) = all_38_0 % 10.16/2.12 | (10) apart_point_and_line(all_38_3, all_38_2) = 0 % 10.16/2.12 | (11) line_connecting(all_38_5, all_38_4) = all_38_2 % 10.16/2.12 | (12) ~ (all_38_0 = 0) | ~ (all_38_1 = 0) % 10.16/2.12 | % 10.16/2.12 | GROUND_INST: instantiating (ceq1) with all_38_3, all_38_2, all_38_4, all_38_0, % 10.16/2.12 | simplifying with (4), (5), (6), (9), (10) gives: % 10.16/2.12 | (13) all_38_0 = 0 | apart_point_and_line(all_38_4, all_38_2) = 0 % 10.16/2.12 | % 10.16/2.13 | GROUND_INST: instantiating (ceq1) with all_38_3, all_38_2, all_38_5, all_38_1, % 10.16/2.13 | simplifying with (3), (5), (6), (8), (10) gives: % 10.16/2.13 | (14) all_38_1 = 0 | apart_point_and_line(all_38_5, all_38_2) = 0 % 10.16/2.13 | % 10.16/2.13 | GROUND_INST: instantiating (con1) with all_38_5, all_38_4, all_38_2, % 10.16/2.13 | simplifying with (3), (4), (11) gives: % 10.16/2.13 | (15) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 10.16/2.13 | (point(all_38_4) = v1 & point(all_38_5) = v0 & line(all_38_2) = v3 & % 10.16/2.13 | distinct_points(all_38_5, all_38_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = % 10.16/2.13 | 0) | ~ (v0 = 0) | v3 = 0)) % 10.16/2.13 | % 10.16/2.13 | DELTA: instantiating (15) with fresh symbols all_45_0, all_45_1, all_45_2, % 10.16/2.13 | all_45_3 gives: % 10.16/2.13 | (16) point(all_38_4) = all_45_2 & point(all_38_5) = all_45_3 & % 10.16/2.13 | line(all_38_2) = all_45_0 & distinct_points(all_38_5, all_38_4) = % 10.16/2.13 | all_45_1 & ( ~ (all_45_1 = 0) | ~ (all_45_2 = 0) | ~ (all_45_3 = 0) % 10.16/2.13 | | all_45_0 = 0) % 10.16/2.13 | % 10.16/2.13 | ALPHA: (16) implies: % 10.16/2.13 | (17) distinct_points(all_38_5, all_38_4) = all_45_1 % 10.16/2.13 | % 10.16/2.13 | GROUND_INST: instantiating (1) with 0, all_45_1, all_38_4, all_38_5, % 10.16/2.13 | simplifying with (7), (17) gives: % 10.16/2.13 | (18) all_45_1 = 0 % 10.16/2.13 | % 10.16/2.13 | BETA: splitting (12) gives: % 10.16/2.13 | % 10.16/2.13 | Case 1: % 10.16/2.13 | | % 10.16/2.13 | | (19) ~ (all_38_0 = 0) % 10.16/2.13 | | % 10.16/2.13 | | BETA: splitting (13) gives: % 10.16/2.13 | | % 10.16/2.13 | | Case 1: % 10.16/2.13 | | | % 10.16/2.13 | | | (20) apart_point_and_line(all_38_4, all_38_2) = 0 % 10.16/2.13 | | | % 10.16/2.13 | | | GROUND_INST: instantiating (ci2) with all_38_5, all_38_4, all_38_2, % 10.16/2.13 | | | simplifying with (3), (4), (11), (20) gives: % 10.16/2.13 | | | (21) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_5, all_38_4) % 10.16/2.13 | | | = v0) % 10.16/2.13 | | | % 10.16/2.13 | | | DELTA: instantiating (21) with fresh symbol all_67_0 gives: % 10.16/2.13 | | | (22) ~ (all_67_0 = 0) & distinct_points(all_38_5, all_38_4) = all_67_0 % 10.16/2.13 | | | % 10.16/2.13 | | | ALPHA: (22) implies: % 10.16/2.13 | | | (23) ~ (all_67_0 = 0) % 10.16/2.13 | | | (24) distinct_points(all_38_5, all_38_4) = all_67_0 % 10.16/2.13 | | | % 10.16/2.13 | | | GROUND_INST: instantiating (1) with 0, all_67_0, all_38_4, all_38_5, % 10.16/2.13 | | | simplifying with (7), (24) gives: % 10.16/2.13 | | | (25) all_67_0 = 0 % 10.16/2.13 | | | % 10.16/2.13 | | | REDUCE: (23), (25) imply: % 10.16/2.13 | | | (26) $false % 10.16/2.13 | | | % 10.16/2.13 | | | CLOSE: (26) is inconsistent. % 10.16/2.13 | | | % 10.16/2.13 | | Case 2: % 10.16/2.13 | | | % 10.16/2.13 | | | (27) all_38_0 = 0 % 10.16/2.13 | | | % 10.16/2.13 | | | REDUCE: (19), (27) imply: % 10.16/2.13 | | | (28) $false % 10.16/2.13 | | | % 10.16/2.13 | | | CLOSE: (28) is inconsistent. % 10.16/2.13 | | | % 10.16/2.13 | | End of split % 10.16/2.13 | | % 10.16/2.13 | Case 2: % 10.16/2.13 | | % 10.16/2.13 | | (29) ~ (all_38_1 = 0) % 10.16/2.13 | | % 10.16/2.13 | | BETA: splitting (14) gives: % 10.16/2.13 | | % 10.16/2.13 | | Case 1: % 10.16/2.13 | | | % 10.16/2.13 | | | (30) apart_point_and_line(all_38_5, all_38_2) = 0 % 10.16/2.13 | | | % 10.16/2.13 | | | GROUND_INST: instantiating (ci1) with all_38_5, all_38_4, all_38_2, % 10.16/2.13 | | | simplifying with (3), (4), (11), (30) gives: % 10.16/2.13 | | | (31) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_5, all_38_4) % 10.16/2.13 | | | = v0) % 10.16/2.14 | | | % 10.16/2.14 | | | DELTA: instantiating (31) with fresh symbol all_67_0 gives: % 10.16/2.14 | | | (32) ~ (all_67_0 = 0) & distinct_points(all_38_5, all_38_4) = all_67_0 % 10.16/2.14 | | | % 10.16/2.14 | | | ALPHA: (32) implies: % 10.16/2.14 | | | (33) ~ (all_67_0 = 0) % 10.16/2.14 | | | (34) distinct_points(all_38_5, all_38_4) = all_67_0 % 10.16/2.14 | | | % 10.16/2.14 | | | GROUND_INST: instantiating (1) with 0, all_67_0, all_38_4, all_38_5, % 10.16/2.14 | | | simplifying with (7), (34) gives: % 10.16/2.14 | | | (35) all_67_0 = 0 % 10.16/2.14 | | | % 10.16/2.14 | | | REDUCE: (33), (35) imply: % 10.16/2.14 | | | (36) $false % 10.16/2.14 | | | % 10.16/2.14 | | | CLOSE: (36) is inconsistent. % 10.16/2.14 | | | % 10.16/2.14 | | Case 2: % 10.16/2.14 | | | % 10.16/2.14 | | | (37) all_38_1 = 0 % 10.16/2.14 | | | % 10.16/2.14 | | | REDUCE: (29), (37) imply: % 10.16/2.14 | | | (38) $false % 10.16/2.14 | | | % 10.16/2.14 | | | CLOSE: (38) is inconsistent. % 10.16/2.14 | | | % 10.16/2.14 | | End of split % 10.16/2.14 | | % 10.16/2.14 | End of split % 10.16/2.14 | % 10.16/2.14 End of proof % 10.16/2.14 % SZS output end Proof for theBenchmark % 10.16/2.14 % 10.16/2.14 1540ms %------------------------------------------------------------------------------