%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO170+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n008.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 23:21:48 EDT 2023 % Result : Theorem 6.18s 1.53s % Output : Proof 7.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO170+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.33 % Computer : n008.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Tue Aug 29 19:56:32 EDT 2023 % 0.16/0.34 % CPUTime : % 0.19/0.58 ________ _____ % 0.19/0.58 ___ __ \_________(_)________________________________ % 0.19/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.58 % 0.19/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.58 (2023-06-19) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2023 % 0.19/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.58 Amanda Stjerna. % 0.19/0.58 Free software under BSD-3-Clause. % 0.19/0.58 % 0.19/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.07/1.00 Prover 1: Preprocessing ... % 2.07/1.00 Prover 4: Preprocessing ... % 2.58/1.04 Prover 2: Preprocessing ... % 2.58/1.04 Prover 6: Preprocessing ... % 2.58/1.04 Prover 5: Preprocessing ... % 2.58/1.04 Prover 0: Preprocessing ... % 2.58/1.04 Prover 3: Preprocessing ... % 4.22/1.27 Prover 5: Proving ... % 4.22/1.28 Prover 2: Proving ... % 4.22/1.28 Prover 1: Constructing countermodel ... % 4.22/1.28 Prover 6: Constructing countermodel ... % 4.22/1.29 Prover 3: Constructing countermodel ... % 4.70/1.43 Prover 4: Constructing countermodel ... % 4.70/1.43 Prover 0: Proving ... % 6.18/1.53 Prover 3: proved (911ms) % 6.18/1.53 % 6.18/1.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.18/1.53 % 6.18/1.53 Prover 5: proved (910ms) % 6.18/1.53 % 6.18/1.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.18/1.53 % 6.18/1.54 Prover 2: proved (915ms) % 6.18/1.54 % 6.18/1.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.18/1.54 % 6.18/1.54 Prover 0: stopped % 6.18/1.55 Prover 6: stopped % 6.18/1.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.18/1.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.18/1.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.18/1.56 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.18/1.56 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.18/1.59 Prover 11: Preprocessing ... % 6.18/1.59 Prover 7: Preprocessing ... % 6.18/1.59 Prover 10: Preprocessing ... % 6.18/1.60 Prover 13: Preprocessing ... % 6.18/1.60 Prover 8: Preprocessing ... % 6.18/1.61 Prover 1: Found proof (size 44) % 6.18/1.61 Prover 1: proved (1010ms) % 6.18/1.61 Prover 4: stopped % 6.18/1.61 Prover 10: stopped % 6.18/1.62 Prover 7: stopped % 6.90/1.62 Prover 13: stopped % 6.90/1.64 Prover 11: stopped % 7.07/1.67 Prover 8: Warning: ignoring some quantifiers % 7.07/1.67 Prover 8: Constructing countermodel ... % 7.07/1.68 Prover 8: stopped % 7.07/1.68 % 7.07/1.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.07/1.68 % 7.07/1.68 % SZS output start Proof for theBenchmark % 7.07/1.69 Assumptions after simplification: % 7.07/1.69 --------------------------------- % 7.07/1.69 % 7.07/1.69 (apart1) % 7.07/1.71 ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 7.07/1.71 % 7.07/1.71 (con) % 7.07/1.72 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ? % 7.07/1.72 [v5: $i] : ( ~ (v4 = 0) & ~ (v3 = 0) & line_connecting(v0, v1) = v5 & % 7.07/1.72 apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = v3 & % 7.07/1.72 distinct_lines(v2, v5) = 0 & distinct_points(v0, v1) = 0 & $i(v5) & $i(v2) & % 7.07/1.72 $i(v1) & $i(v0)) % 7.07/1.72 % 7.07/1.72 (con1) % 7.07/1.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 7.07/1.72 (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ~ % 7.07/1.72 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] % 7.07/1.72 : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & % 7.07/1.72 distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0)))) % 7.07/1.72 % 7.07/1.72 (cu1) % 7.07/1.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 7.07/1.72 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 7.07/1.72 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 7.07/1.72 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 7.07/1.72 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 7.07/1.72 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 7.07/1.72 % 7.07/1.72 (function-axioms) % 7.44/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.44/1.73 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 7.44/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.44/1.73 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 7.44/1.73 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 7.44/1.73 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 7.44/1.73 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 7.44/1.73 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.44/1.73 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 7.44/1.73 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 7.44/1.73 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 7.44/1.73 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 7.44/1.73 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 7.44/1.73 (distinct_points(v3, v2) = v0)) % 7.44/1.73 % 7.44/1.73 Further assumptions not needed in the proof: % 7.44/1.73 -------------------------------------------- % 7.44/1.73 apart2, apart3, apart4, apart5, apart6, ceq1, ceq2, ceq3, con2 % 7.44/1.73 % 7.44/1.73 Those formulas are unsatisfiable: % 7.44/1.73 --------------------------------- % 7.44/1.73 % 7.44/1.73 Begin of proof % 7.44/1.73 | % 7.44/1.73 | ALPHA: (function-axioms) implies: % 7.44/1.73 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 7.44/1.73 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 7.44/1.73 | (distinct_points(v3, v2) = v0)) % 7.44/1.74 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 7.44/1.74 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 7.44/1.74 | (apart_point_and_line(v3, v2) = v0)) % 7.44/1.74 | % 7.44/1.74 | DELTA: instantiating (con) with fresh symbols all_15_0, all_15_1, all_15_2, % 7.44/1.74 | all_15_3, all_15_4, all_15_5 gives: % 7.44/1.74 | (3) ~ (all_15_1 = 0) & ~ (all_15_2 = 0) & line_connecting(all_15_5, % 7.44/1.74 | all_15_4) = all_15_0 & apart_point_and_line(all_15_4, all_15_3) = % 7.44/1.74 | all_15_1 & apart_point_and_line(all_15_5, all_15_3) = all_15_2 & % 7.44/1.74 | distinct_lines(all_15_3, all_15_0) = 0 & distinct_points(all_15_5, % 7.44/1.74 | all_15_4) = 0 & $i(all_15_0) & $i(all_15_3) & $i(all_15_4) & % 7.44/1.74 | $i(all_15_5) % 7.44/1.74 | % 7.44/1.74 | ALPHA: (3) implies: % 7.44/1.74 | (4) ~ (all_15_2 = 0) % 7.44/1.74 | (5) ~ (all_15_1 = 0) % 7.44/1.74 | (6) $i(all_15_5) % 7.44/1.74 | (7) $i(all_15_4) % 7.44/1.74 | (8) $i(all_15_3) % 7.44/1.74 | (9) $i(all_15_0) % 7.44/1.74 | (10) distinct_points(all_15_5, all_15_4) = 0 % 7.44/1.74 | (11) distinct_lines(all_15_3, all_15_0) = 0 % 7.44/1.74 | (12) apart_point_and_line(all_15_5, all_15_3) = all_15_2 % 7.44/1.74 | (13) apart_point_and_line(all_15_4, all_15_3) = all_15_1 % 7.44/1.74 | (14) line_connecting(all_15_5, all_15_4) = all_15_0 % 7.44/1.74 | % 7.44/1.74 | GROUND_INST: instantiating (cu1) with all_15_5, all_15_4, all_15_3, all_15_0, % 7.44/1.74 | simplifying with (6), (7), (8), (9), (10), (11) gives: % 7.44/1.74 | (15) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 7.44/1.74 | (apart_point_and_line(all_15_4, all_15_0) = v3 & % 7.44/1.74 | apart_point_and_line(all_15_4, all_15_3) = v2 & % 7.44/1.74 | apart_point_and_line(all_15_5, all_15_0) = v1 & % 7.44/1.74 | apart_point_and_line(all_15_5, all_15_3) = v0 & (v3 = 0 | v2 = 0 | % 7.44/1.74 | v1 = 0 | v0 = 0)) % 7.44/1.74 | % 7.44/1.74 | DELTA: instantiating (15) with fresh symbols all_22_0, all_22_1, all_22_2, % 7.44/1.74 | all_22_3 gives: % 7.44/1.74 | (16) apart_point_and_line(all_15_4, all_15_0) = all_22_0 & % 7.44/1.74 | apart_point_and_line(all_15_4, all_15_3) = all_22_1 & % 7.44/1.74 | apart_point_and_line(all_15_5, all_15_0) = all_22_2 & % 7.44/1.74 | apart_point_and_line(all_15_5, all_15_3) = all_22_3 & (all_22_0 = 0 | % 7.44/1.74 | all_22_1 = 0 | all_22_2 = 0 | all_22_3 = 0) % 7.44/1.75 | % 7.44/1.75 | ALPHA: (16) implies: % 7.44/1.75 | (17) apart_point_and_line(all_15_5, all_15_3) = all_22_3 % 7.44/1.75 | (18) apart_point_and_line(all_15_5, all_15_0) = all_22_2 % 7.44/1.75 | (19) apart_point_and_line(all_15_4, all_15_3) = all_22_1 % 7.44/1.75 | (20) apart_point_and_line(all_15_4, all_15_0) = all_22_0 % 7.44/1.75 | (21) all_22_0 = 0 | all_22_1 = 0 | all_22_2 = 0 | all_22_3 = 0 % 7.44/1.75 | % 7.44/1.75 | GROUND_INST: instantiating (2) with all_15_2, all_22_3, all_15_3, all_15_5, % 7.44/1.75 | simplifying with (12), (17) gives: % 7.44/1.75 | (22) all_22_3 = all_15_2 % 7.44/1.75 | % 7.44/1.75 | GROUND_INST: instantiating (2) with all_15_1, all_22_1, all_15_3, all_15_4, % 7.44/1.75 | simplifying with (13), (19) gives: % 7.44/1.75 | (23) all_22_1 = all_15_1 % 7.44/1.75 | % 7.44/1.75 | BETA: splitting (21) gives: % 7.44/1.75 | % 7.44/1.75 | Case 1: % 7.44/1.75 | | % 7.44/1.75 | | (24) all_22_0 = 0 % 7.44/1.75 | | % 7.44/1.75 | | REDUCE: (20), (24) imply: % 7.44/1.75 | | (25) apart_point_and_line(all_15_4, all_15_0) = 0 % 7.44/1.75 | | % 7.44/1.75 | | GROUND_INST: instantiating (con1) with all_15_5, all_15_4, all_15_4, % 7.44/1.75 | | all_15_0, simplifying with (6), (7), (14), (25) gives: % 7.44/1.75 | | (26) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 7.44/1.75 | | (distinct_points(all_15_4, all_15_4) = v2 & % 7.44/1.75 | | distinct_points(all_15_4, all_15_5) = v1 & % 7.44/1.75 | | distinct_points(all_15_5, all_15_4) = v0 & ( ~ (v0 = 0) | (v2 = 0 % 7.44/1.75 | | & v1 = 0))) % 7.44/1.75 | | % 7.44/1.75 | | DELTA: instantiating (26) with fresh symbols all_40_0, all_40_1, all_40_2 % 7.44/1.75 | | gives: % 7.44/1.75 | | (27) distinct_points(all_15_4, all_15_4) = all_40_0 & % 7.44/1.75 | | distinct_points(all_15_4, all_15_5) = all_40_1 & % 7.44/1.75 | | distinct_points(all_15_5, all_15_4) = all_40_2 & ( ~ (all_40_2 = 0) % 7.44/1.75 | | | (all_40_0 = 0 & all_40_1 = 0)) % 7.44/1.75 | | % 7.44/1.75 | | ALPHA: (27) implies: % 7.44/1.75 | | (28) distinct_points(all_15_5, all_15_4) = all_40_2 % 7.44/1.75 | | (29) distinct_points(all_15_4, all_15_4) = all_40_0 % 7.44/1.75 | | (30) ~ (all_40_2 = 0) | (all_40_0 = 0 & all_40_1 = 0) % 7.44/1.75 | | % 7.44/1.75 | | GROUND_INST: instantiating (1) with 0, all_40_2, all_15_4, all_15_5, % 7.44/1.75 | | simplifying with (10), (28) gives: % 7.44/1.75 | | (31) all_40_2 = 0 % 7.44/1.75 | | % 7.44/1.75 | | BETA: splitting (30) gives: % 7.44/1.75 | | % 7.44/1.75 | | Case 1: % 7.44/1.75 | | | % 7.44/1.75 | | | (32) ~ (all_40_2 = 0) % 7.44/1.75 | | | % 7.44/1.75 | | | REDUCE: (31), (32) imply: % 7.44/1.75 | | | (33) $false % 7.44/1.75 | | | % 7.44/1.75 | | | CLOSE: (33) is inconsistent. % 7.44/1.75 | | | % 7.44/1.75 | | Case 2: % 7.44/1.75 | | | % 7.44/1.75 | | | (34) all_40_0 = 0 & all_40_1 = 0 % 7.44/1.75 | | | % 7.44/1.75 | | | ALPHA: (34) implies: % 7.44/1.76 | | | (35) all_40_0 = 0 % 7.44/1.76 | | | % 7.44/1.76 | | | REDUCE: (29), (35) imply: % 7.44/1.76 | | | (36) distinct_points(all_15_4, all_15_4) = 0 % 7.44/1.76 | | | % 7.44/1.76 | | | GROUND_INST: instantiating (apart1) with all_15_4, simplifying with (7), % 7.44/1.76 | | | (36) gives: % 7.44/1.76 | | | (37) $false % 7.44/1.76 | | | % 7.44/1.76 | | | CLOSE: (37) is inconsistent. % 7.44/1.76 | | | % 7.44/1.76 | | End of split % 7.44/1.76 | | % 7.44/1.76 | Case 2: % 7.44/1.76 | | % 7.44/1.76 | | (38) all_22_1 = 0 | all_22_2 = 0 | all_22_3 = 0 % 7.44/1.76 | | % 7.44/1.76 | | BETA: splitting (38) gives: % 7.44/1.76 | | % 7.44/1.76 | | Case 1: % 7.44/1.76 | | | % 7.44/1.76 | | | (39) all_22_1 = 0 % 7.44/1.76 | | | % 7.44/1.76 | | | COMBINE_EQS: (23), (39) imply: % 7.44/1.76 | | | (40) all_15_1 = 0 % 7.44/1.76 | | | % 7.44/1.76 | | | REDUCE: (5), (40) imply: % 7.44/1.76 | | | (41) $false % 7.44/1.76 | | | % 7.44/1.76 | | | CLOSE: (41) is inconsistent. % 7.44/1.76 | | | % 7.44/1.76 | | Case 2: % 7.44/1.76 | | | % 7.44/1.76 | | | (42) all_22_2 = 0 | all_22_3 = 0 % 7.44/1.76 | | | % 7.44/1.76 | | | BETA: splitting (42) gives: % 7.44/1.76 | | | % 7.44/1.76 | | | Case 1: % 7.44/1.76 | | | | % 7.44/1.76 | | | | (43) all_22_2 = 0 % 7.44/1.76 | | | | % 7.44/1.76 | | | | REDUCE: (18), (43) imply: % 7.44/1.76 | | | | (44) apart_point_and_line(all_15_5, all_15_0) = 0 % 7.44/1.76 | | | | % 7.44/1.76 | | | | GROUND_INST: instantiating (con1) with all_15_5, all_15_4, all_15_5, % 7.44/1.76 | | | | all_15_0, simplifying with (6), (7), (14), (44) gives: % 7.44/1.76 | | | | (45) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 7.44/1.76 | | | | (distinct_points(all_15_5, all_15_4) = v2 & % 7.44/1.76 | | | | distinct_points(all_15_5, all_15_4) = v0 & % 7.44/1.76 | | | | distinct_points(all_15_5, all_15_5) = v1 & ( ~ (v0 = 0) | (v2 % 7.44/1.76 | | | | = 0 & v1 = 0))) % 7.44/1.76 | | | | % 7.44/1.76 | | | | DELTA: instantiating (45) with fresh symbols all_48_0, all_48_1, % 7.44/1.76 | | | | all_48_2 gives: % 7.44/1.76 | | | | (46) distinct_points(all_15_5, all_15_4) = all_48_0 & % 7.44/1.76 | | | | distinct_points(all_15_5, all_15_4) = all_48_2 & % 7.44/1.76 | | | | distinct_points(all_15_5, all_15_5) = all_48_1 & ( ~ (all_48_2 = % 7.44/1.76 | | | | 0) | (all_48_0 = 0 & all_48_1 = 0)) % 7.44/1.76 | | | | % 7.44/1.76 | | | | ALPHA: (46) implies: % 7.44/1.76 | | | | (47) distinct_points(all_15_5, all_15_5) = all_48_1 % 7.44/1.76 | | | | (48) distinct_points(all_15_5, all_15_4) = all_48_2 % 7.44/1.76 | | | | (49) distinct_points(all_15_5, all_15_4) = all_48_0 % 7.44/1.76 | | | | (50) ~ (all_48_2 = 0) | (all_48_0 = 0 & all_48_1 = 0) % 7.44/1.76 | | | | % 7.44/1.76 | | | | GROUND_INST: instantiating (1) with 0, all_48_0, all_15_4, all_15_5, % 7.44/1.76 | | | | simplifying with (10), (49) gives: % 7.44/1.76 | | | | (51) all_48_0 = 0 % 7.44/1.76 | | | | % 7.44/1.76 | | | | GROUND_INST: instantiating (1) with all_48_2, all_48_0, all_15_4, % 7.44/1.76 | | | | all_15_5, simplifying with (48), (49) gives: % 7.44/1.76 | | | | (52) all_48_0 = all_48_2 % 7.44/1.76 | | | | % 7.44/1.76 | | | | COMBINE_EQS: (51), (52) imply: % 7.44/1.76 | | | | (53) all_48_2 = 0 % 7.44/1.76 | | | | % 7.44/1.76 | | | | BETA: splitting (50) gives: % 7.44/1.76 | | | | % 7.44/1.76 | | | | Case 1: % 7.44/1.76 | | | | | % 7.44/1.76 | | | | | (54) ~ (all_48_2 = 0) % 7.44/1.76 | | | | | % 7.44/1.76 | | | | | REDUCE: (53), (54) imply: % 7.44/1.76 | | | | | (55) $false % 7.44/1.76 | | | | | % 7.44/1.76 | | | | | CLOSE: (55) is inconsistent. % 7.44/1.76 | | | | | % 7.44/1.76 | | | | Case 2: % 7.44/1.76 | | | | | % 7.44/1.76 | | | | | (56) all_48_0 = 0 & all_48_1 = 0 % 7.44/1.76 | | | | | % 7.44/1.76 | | | | | ALPHA: (56) implies: % 7.44/1.76 | | | | | (57) all_48_1 = 0 % 7.44/1.76 | | | | | % 7.44/1.76 | | | | | REDUCE: (47), (57) imply: % 7.44/1.76 | | | | | (58) distinct_points(all_15_5, all_15_5) = 0 % 7.44/1.76 | | | | | % 7.44/1.76 | | | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying with % 7.44/1.76 | | | | | (6), (58) gives: % 7.44/1.76 | | | | | (59) $false % 7.44/1.76 | | | | | % 7.44/1.76 | | | | | CLOSE: (59) is inconsistent. % 7.44/1.76 | | | | | % 7.44/1.76 | | | | End of split % 7.44/1.76 | | | | % 7.44/1.76 | | | Case 2: % 7.44/1.76 | | | | % 7.44/1.76 | | | | (60) all_22_3 = 0 % 7.44/1.76 | | | | % 7.44/1.76 | | | | COMBINE_EQS: (22), (60) imply: % 7.44/1.76 | | | | (61) all_15_2 = 0 % 7.44/1.76 | | | | % 7.44/1.76 | | | | SIMP: (61) implies: % 7.44/1.76 | | | | (62) all_15_2 = 0 % 7.44/1.76 | | | | % 7.44/1.77 | | | | REDUCE: (4), (62) imply: % 7.44/1.77 | | | | (63) $false % 7.44/1.77 | | | | % 7.44/1.77 | | | | CLOSE: (63) is inconsistent. % 7.44/1.77 | | | | % 7.44/1.77 | | | End of split % 7.44/1.77 | | | % 7.44/1.77 | | End of split % 7.44/1.77 | | % 7.44/1.77 | End of split % 7.44/1.77 | % 7.44/1.77 End of proof % 7.44/1.77 % SZS output end Proof for theBenchmark % 7.44/1.77 % 7.44/1.77 1180ms %------------------------------------------------------------------------------