%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO203+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 : n011.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 23:22:15 EDT 2023 % Result : Theorem 5.54s 1.44s % Output : Proof 7.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEO203+1 : TPTP v8.1.2. Released v3.3.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n011.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 21:47:11 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.39/1.03 Prover 1: Preprocessing ... % 2.39/1.03 Prover 4: Preprocessing ... % 2.39/1.07 Prover 2: Preprocessing ... % 2.39/1.07 Prover 6: Preprocessing ... % 2.39/1.07 Prover 0: Preprocessing ... % 2.39/1.07 Prover 5: Preprocessing ... % 2.39/1.07 Prover 3: Preprocessing ... % 4.31/1.28 Prover 5: Proving ... % 4.31/1.29 Prover 2: Proving ... % 4.31/1.34 Prover 3: Constructing countermodel ... % 4.93/1.35 Prover 1: Constructing countermodel ... % 4.93/1.36 Prover 6: Constructing countermodel ... % 5.54/1.43 Prover 2: proved (798ms) % 5.54/1.44 % 5.54/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.54/1.44 % 5.54/1.44 Prover 6: stopped % 5.66/1.45 Prover 3: stopped % 5.66/1.45 Prover 5: stopped % 5.66/1.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.66/1.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.66/1.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.66/1.47 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.66/1.49 Prover 0: Proving ... % 5.66/1.49 Prover 8: Preprocessing ... % 5.66/1.49 Prover 10: Preprocessing ... % 5.66/1.49 Prover 4: Constructing countermodel ... % 5.66/1.50 Prover 11: Preprocessing ... % 5.66/1.50 Prover 7: Preprocessing ... % 5.66/1.51 Prover 0: stopped % 5.66/1.51 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.16/1.54 Prover 13: Preprocessing ... % 6.16/1.55 Prover 7: Warning: ignoring some quantifiers % 6.16/1.56 Prover 7: Constructing countermodel ... % 6.16/1.56 Prover 10: Warning: ignoring some quantifiers % 6.50/1.57 Prover 10: Constructing countermodel ... % 6.50/1.60 Prover 13: Warning: ignoring some quantifiers % 6.50/1.61 Prover 8: Warning: ignoring some quantifiers % 6.50/1.62 Prover 13: Constructing countermodel ... % 6.50/1.62 Prover 8: Constructing countermodel ... % 6.50/1.64 Prover 1: Found proof (size 37) % 6.50/1.64 Prover 1: proved (1008ms) % 6.50/1.64 Prover 8: stopped % 6.50/1.64 Prover 7: stopped % 6.50/1.64 Prover 13: stopped % 6.50/1.64 Prover 10: stopped % 6.50/1.64 Prover 4: stopped % 7.32/1.69 Prover 11: Constructing countermodel ... % 7.32/1.70 Prover 11: stopped % 7.32/1.70 % 7.32/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.32/1.70 % 7.32/1.70 % SZS output start Proof for theBenchmark % 7.32/1.71 Assumptions after simplification: % 7.32/1.71 --------------------------------- % 7.32/1.71 % 7.32/1.71 (ci1) % 7.55/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 7.55/1.73 ~ (apart_point_and_line(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 7.55/1.73 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 7.55/1.73 % 7.55/1.73 (ci2) % 7.55/1.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 7.55/1.74 ~ (apart_point_and_line(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 7.55/1.74 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 7.55/1.74 % 7.55/1.74 (ci3) % 7.55/1.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 7.55/1.74 v2) | ~ (apart_point_and_line(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 7.55/1.74 [v3: int] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 7.55/1.74 % 7.55/1.74 (con) % 7.55/1.74 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 7.55/1.74 $i] : (intersection_point(v0, v2) = v4 & intersection_point(v0, v1) = v3 & % 7.55/1.74 line_connecting(v3, v4) = v5 & convergent_lines(v0, v2) = 0 & % 7.55/1.74 convergent_lines(v0, v1) = 0 & distinct_lines(v5, v0) = 0 & % 7.55/1.74 distinct_points(v3, v4) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 7.55/1.74 $i(v0)) % 7.55/1.74 % 7.55/1.74 (cu1) % 7.55/1.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 7.55/1.75 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 7.55/1.75 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 7.55/1.75 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 7.55/1.75 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 7.55/1.75 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 7.55/1.75 % 7.55/1.75 (function-axioms) % 7.55/1.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.55/1.75 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 7.55/1.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.55/1.75 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 7.55/1.75 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 7.55/1.75 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 7.55/1.75 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 7.55/1.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.55/1.75 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 7.55/1.75 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 7.55/1.75 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 7.55/1.75 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 7.55/1.75 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 7.55/1.75 (distinct_points(v3, v2) = v0)) % 7.55/1.75 % 7.55/1.75 Further assumptions not needed in the proof: % 7.55/1.75 -------------------------------------------- % 7.55/1.75 apart1, apart2, apart3, apart4, apart5, ax6, ceq1, ceq2, ceq3, ci4 % 7.55/1.75 % 7.55/1.75 Those formulas are unsatisfiable: % 7.55/1.75 --------------------------------- % 7.55/1.75 % 7.55/1.75 Begin of proof % 7.55/1.76 | % 7.55/1.76 | ALPHA: (function-axioms) implies: % 7.55/1.76 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 7.55/1.76 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 7.55/1.76 | (distinct_points(v3, v2) = v0)) % 7.55/1.76 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 7.55/1.76 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 7.55/1.76 | (convergent_lines(v3, v2) = v0)) % 7.55/1.76 | % 7.55/1.76 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 7.55/1.76 | all_17_3, all_17_4, all_17_5 gives: % 7.55/1.76 | (3) intersection_point(all_17_5, all_17_3) = all_17_1 & % 7.55/1.76 | intersection_point(all_17_5, all_17_4) = all_17_2 & % 7.55/1.76 | line_connecting(all_17_2, all_17_1) = all_17_0 & % 7.55/1.76 | convergent_lines(all_17_5, all_17_3) = 0 & convergent_lines(all_17_5, % 7.55/1.76 | all_17_4) = 0 & distinct_lines(all_17_0, all_17_5) = 0 & % 7.55/1.76 | distinct_points(all_17_2, all_17_1) = 0 & $i(all_17_0) & $i(all_17_1) & % 7.55/1.76 | $i(all_17_2) & $i(all_17_3) & $i(all_17_4) & $i(all_17_5) % 7.55/1.76 | % 7.55/1.76 | ALPHA: (3) implies: % 7.55/1.77 | (4) $i(all_17_5) % 7.55/1.77 | (5) $i(all_17_4) % 7.55/1.77 | (6) $i(all_17_3) % 7.55/1.77 | (7) $i(all_17_2) % 7.55/1.77 | (8) $i(all_17_1) % 7.55/1.77 | (9) $i(all_17_0) % 7.55/1.77 | (10) distinct_points(all_17_2, all_17_1) = 0 % 7.55/1.77 | (11) distinct_lines(all_17_0, all_17_5) = 0 % 7.55/1.77 | (12) convergent_lines(all_17_5, all_17_4) = 0 % 7.55/1.77 | (13) convergent_lines(all_17_5, all_17_3) = 0 % 7.55/1.77 | (14) line_connecting(all_17_2, all_17_1) = all_17_0 % 7.55/1.77 | (15) intersection_point(all_17_5, all_17_4) = all_17_2 % 7.55/1.77 | (16) intersection_point(all_17_5, all_17_3) = all_17_1 % 7.55/1.77 | % 7.55/1.77 | GROUND_INST: instantiating (cu1) with all_17_2, all_17_1, all_17_0, all_17_5, % 7.55/1.77 | simplifying with (4), (7), (8), (9), (10), (11) gives: % 7.55/1.77 | (17) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 7.55/1.77 | (apart_point_and_line(all_17_1, all_17_0) = v2 & % 7.55/1.77 | apart_point_and_line(all_17_1, all_17_5) = v3 & % 7.55/1.77 | apart_point_and_line(all_17_2, all_17_0) = v0 & % 7.55/1.77 | apart_point_and_line(all_17_2, all_17_5) = v1 & (v3 = 0 | v2 = 0 | % 7.55/1.77 | v1 = 0 | v0 = 0)) % 7.55/1.77 | % 7.55/1.77 | DELTA: instantiating (17) with fresh symbols all_24_0, all_24_1, all_24_2, % 7.55/1.77 | all_24_3 gives: % 7.55/1.77 | (18) apart_point_and_line(all_17_1, all_17_0) = all_24_1 & % 7.55/1.77 | apart_point_and_line(all_17_1, all_17_5) = all_24_0 & % 7.55/1.77 | apart_point_and_line(all_17_2, all_17_0) = all_24_3 & % 7.55/1.77 | apart_point_and_line(all_17_2, all_17_5) = all_24_2 & (all_24_0 = 0 | % 7.55/1.77 | all_24_1 = 0 | all_24_2 = 0 | all_24_3 = 0) % 7.55/1.77 | % 7.55/1.77 | ALPHA: (18) implies: % 7.55/1.77 | (19) apart_point_and_line(all_17_2, all_17_5) = all_24_2 % 7.55/1.77 | (20) apart_point_and_line(all_17_2, all_17_0) = all_24_3 % 7.55/1.77 | (21) apart_point_and_line(all_17_1, all_17_5) = all_24_0 % 7.55/1.77 | (22) apart_point_and_line(all_17_1, all_17_0) = all_24_1 % 7.55/1.77 | (23) all_24_0 = 0 | all_24_1 = 0 | all_24_2 = 0 | all_24_3 = 0 % 7.55/1.77 | % 7.55/1.77 | BETA: splitting (23) gives: % 7.55/1.77 | % 7.55/1.78 | Case 1: % 7.55/1.78 | | % 7.55/1.78 | | (24) all_24_0 = 0 % 7.55/1.78 | | % 7.55/1.78 | | REDUCE: (21), (24) imply: % 7.55/1.78 | | (25) apart_point_and_line(all_17_1, all_17_5) = 0 % 7.55/1.78 | | % 7.55/1.78 | | GROUND_INST: instantiating (ci3) with all_17_5, all_17_3, all_17_1, % 7.55/1.78 | | simplifying with (4), (6), (16), (25) gives: % 7.55/1.78 | | (26) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_17_5, all_17_3) = % 7.55/1.78 | | v0) % 7.55/1.78 | | % 7.55/1.78 | | DELTA: instantiating (26) with fresh symbol all_38_0 gives: % 7.55/1.78 | | (27) ~ (all_38_0 = 0) & convergent_lines(all_17_5, all_17_3) = all_38_0 % 7.55/1.78 | | % 7.55/1.78 | | ALPHA: (27) implies: % 7.55/1.78 | | (28) ~ (all_38_0 = 0) % 7.55/1.78 | | (29) convergent_lines(all_17_5, all_17_3) = all_38_0 % 7.55/1.78 | | % 7.55/1.78 | | GROUND_INST: instantiating (2) with 0, all_38_0, all_17_3, all_17_5, % 7.55/1.78 | | simplifying with (13), (29) gives: % 7.55/1.78 | | (30) all_38_0 = 0 % 7.55/1.78 | | % 7.55/1.78 | | REDUCE: (28), (30) imply: % 7.55/1.78 | | (31) $false % 7.55/1.78 | | % 7.55/1.78 | | CLOSE: (31) is inconsistent. % 7.55/1.78 | | % 7.55/1.78 | Case 2: % 7.55/1.78 | | % 7.55/1.78 | | (32) all_24_1 = 0 | all_24_2 = 0 | all_24_3 = 0 % 7.55/1.78 | | % 7.55/1.78 | | BETA: splitting (32) gives: % 7.55/1.78 | | % 7.55/1.78 | | Case 1: % 7.55/1.78 | | | % 7.55/1.78 | | | (33) all_24_1 = 0 % 7.55/1.78 | | | % 7.55/1.78 | | | REDUCE: (22), (33) imply: % 7.55/1.78 | | | (34) apart_point_and_line(all_17_1, all_17_0) = 0 % 7.55/1.78 | | | % 7.55/1.78 | | | GROUND_INST: instantiating (ci2) with all_17_2, all_17_1, all_17_0, % 7.55/1.78 | | | simplifying with (7), (8), (14), (34) gives: % 7.55/1.78 | | | (35) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_17_2, all_17_1) % 7.55/1.78 | | | = v0) % 7.55/1.78 | | | % 7.55/1.78 | | | DELTA: instantiating (35) with fresh symbol all_45_0 gives: % 7.55/1.78 | | | (36) ~ (all_45_0 = 0) & distinct_points(all_17_2, all_17_1) = all_45_0 % 7.55/1.78 | | | % 7.55/1.78 | | | ALPHA: (36) implies: % 7.55/1.78 | | | (37) ~ (all_45_0 = 0) % 7.55/1.78 | | | (38) distinct_points(all_17_2, all_17_1) = all_45_0 % 7.55/1.78 | | | % 7.55/1.78 | | | GROUND_INST: instantiating (1) with 0, all_45_0, all_17_1, all_17_2, % 7.55/1.78 | | | simplifying with (10), (38) gives: % 7.55/1.78 | | | (39) all_45_0 = 0 % 7.55/1.78 | | | % 7.55/1.78 | | | REDUCE: (37), (39) imply: % 7.55/1.79 | | | (40) $false % 7.55/1.79 | | | % 7.55/1.79 | | | CLOSE: (40) is inconsistent. % 7.55/1.79 | | | % 7.55/1.79 | | Case 2: % 7.55/1.79 | | | % 7.55/1.79 | | | (41) all_24_2 = 0 | all_24_3 = 0 % 7.55/1.79 | | | % 7.55/1.79 | | | BETA: splitting (41) gives: % 7.55/1.79 | | | % 7.55/1.79 | | | Case 1: % 7.55/1.79 | | | | % 7.55/1.79 | | | | (42) all_24_2 = 0 % 7.55/1.79 | | | | % 7.55/1.79 | | | | REDUCE: (19), (42) imply: % 7.55/1.79 | | | | (43) apart_point_and_line(all_17_2, all_17_5) = 0 % 7.55/1.79 | | | | % 7.55/1.79 | | | | GROUND_INST: instantiating (ci3) with all_17_5, all_17_4, all_17_2, % 7.55/1.79 | | | | simplifying with (4), (5), (15), (43) gives: % 7.55/1.79 | | | | (44) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_17_5, % 7.55/1.79 | | | | all_17_4) = v0) % 7.55/1.79 | | | | % 7.55/1.79 | | | | DELTA: instantiating (44) with fresh symbol all_52_0 gives: % 7.55/1.79 | | | | (45) ~ (all_52_0 = 0) & convergent_lines(all_17_5, all_17_4) = % 7.55/1.79 | | | | all_52_0 % 7.55/1.79 | | | | % 7.55/1.79 | | | | ALPHA: (45) implies: % 7.55/1.79 | | | | (46) ~ (all_52_0 = 0) % 7.55/1.79 | | | | (47) convergent_lines(all_17_5, all_17_4) = all_52_0 % 7.55/1.79 | | | | % 7.55/1.79 | | | | GROUND_INST: instantiating (2) with 0, all_52_0, all_17_4, all_17_5, % 7.55/1.79 | | | | simplifying with (12), (47) gives: % 7.55/1.79 | | | | (48) all_52_0 = 0 % 7.55/1.79 | | | | % 7.55/1.79 | | | | REDUCE: (46), (48) imply: % 7.55/1.79 | | | | (49) $false % 7.55/1.79 | | | | % 7.55/1.79 | | | | CLOSE: (49) is inconsistent. % 7.55/1.79 | | | | % 7.55/1.79 | | | Case 2: % 7.55/1.79 | | | | % 7.55/1.79 | | | | (50) all_24_3 = 0 % 7.55/1.79 | | | | % 7.55/1.79 | | | | REDUCE: (20), (50) imply: % 7.55/1.79 | | | | (51) apart_point_and_line(all_17_2, all_17_0) = 0 % 7.55/1.79 | | | | % 7.55/1.79 | | | | GROUND_INST: instantiating (ci1) with all_17_2, all_17_1, all_17_0, % 7.55/1.79 | | | | simplifying with (7), (8), (14), (51) gives: % 7.55/1.79 | | | | (52) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_17_2, % 7.55/1.79 | | | | all_17_1) = v0) % 7.55/1.79 | | | | % 7.55/1.79 | | | | DELTA: instantiating (52) with fresh symbol all_52_0 gives: % 7.55/1.79 | | | | (53) ~ (all_52_0 = 0) & distinct_points(all_17_2, all_17_1) = % 7.55/1.79 | | | | all_52_0 % 7.55/1.79 | | | | % 7.55/1.79 | | | | ALPHA: (53) implies: % 7.55/1.79 | | | | (54) ~ (all_52_0 = 0) % 7.55/1.79 | | | | (55) distinct_points(all_17_2, all_17_1) = all_52_0 % 7.55/1.79 | | | | % 7.55/1.79 | | | | GROUND_INST: instantiating (1) with 0, all_52_0, all_17_1, all_17_2, % 7.55/1.79 | | | | simplifying with (10), (55) gives: % 7.55/1.79 | | | | (56) all_52_0 = 0 % 7.55/1.79 | | | | % 7.55/1.79 | | | | REDUCE: (54), (56) imply: % 7.55/1.79 | | | | (57) $false % 7.55/1.79 | | | | % 7.55/1.79 | | | | CLOSE: (57) is inconsistent. % 7.55/1.79 | | | | % 7.55/1.79 | | | End of split % 7.55/1.79 | | | % 7.55/1.79 | | End of split % 7.55/1.79 | | % 7.55/1.79 | End of split % 7.55/1.79 | % 7.55/1.79 End of proof % 7.55/1.79 % SZS output end Proof for theBenchmark % 7.55/1.79 % 7.55/1.79 1185ms %------------------------------------------------------------------------------