%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO204+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 : n015.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 23:22:16 EDT 2023 % Result : Theorem 6.43s 1.65s % Output : Proof 8.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : GEO204+1 : TPTP v8.1.2. Released v3.3.0. % 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n015.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 22:29:56 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.65 ________ _____ % 0.21/0.65 ___ __ \_________(_)________________________________ % 0.21/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.65 % 0.21/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.65 (2023-06-19) % 0.21/0.65 % 0.21/0.65 (c) Philipp Rümmer, 2009-2023 % 0.21/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.65 Amanda Stjerna. % 0.21/0.65 Free software under BSD-3-Clause. % 0.21/0.65 % 0.21/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.65 % 0.21/0.66 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.67 Running up to 7 provers in parallel. % 0.21/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.21/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 2.69/1.11 Prover 4: Preprocessing ... % 2.69/1.11 Prover 1: Preprocessing ... % 2.69/1.15 Prover 6: Preprocessing ... % 2.69/1.15 Prover 2: Preprocessing ... % 2.69/1.15 Prover 0: Preprocessing ... % 2.69/1.15 Prover 5: Preprocessing ... % 2.69/1.15 Prover 3: Preprocessing ... % 3.76/1.39 Prover 5: Proving ... % 3.76/1.40 Prover 2: Proving ... % 3.76/1.41 Prover 1: Constructing countermodel ... % 3.76/1.43 Prover 6: Constructing countermodel ... % 3.76/1.43 Prover 3: Constructing countermodel ... % 5.85/1.56 Prover 4: Constructing countermodel ... % 6.01/1.60 Prover 0: Proving ... % 6.43/1.64 Prover 6: proved (942ms) % 6.43/1.64 % 6.43/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.43/1.65 % 6.68/1.66 Prover 0: stopped % 6.68/1.66 Prover 2: stopped % 6.68/1.66 Prover 3: stopped % 6.68/1.66 Prover 5: stopped % 6.68/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.68/1.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.68/1.67 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.68/1.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.68/1.67 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.68/1.70 Prover 10: Preprocessing ... % 6.68/1.71 Prover 13: Preprocessing ... % 6.68/1.71 Prover 8: Preprocessing ... % 6.68/1.71 Prover 7: Preprocessing ... % 6.68/1.73 Prover 11: Preprocessing ... % 7.24/1.74 Prover 10: Warning: ignoring some quantifiers % 7.24/1.75 Prover 7: Warning: ignoring some quantifiers % 7.24/1.76 Prover 10: Constructing countermodel ... % 7.24/1.76 Prover 7: Constructing countermodel ... % 7.24/1.77 Prover 13: Warning: ignoring some quantifiers % 7.58/1.79 Prover 13: Constructing countermodel ... % 7.58/1.81 Prover 8: Warning: ignoring some quantifiers % 7.58/1.82 Prover 10: gave up % 7.58/1.82 Prover 7: gave up % 7.58/1.82 Prover 8: Constructing countermodel ... % 7.58/1.82 Prover 1: Found proof (size 67) % 7.58/1.82 Prover 1: proved (1144ms) % 7.58/1.83 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.58/1.83 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 7.58/1.83 Prover 4: stopped % 7.58/1.83 Prover 13: stopped % 7.58/1.84 Prover 8: stopped % 8.02/1.85 Prover 16: Preprocessing ... % 8.02/1.85 Prover 19: Preprocessing ... % 8.16/1.86 Prover 16: stopped % 8.50/1.92 Prover 11: Constructing countermodel ... % 8.50/1.92 Prover 19: Warning: ignoring some quantifiers % 8.50/1.93 Prover 11: stopped % 8.50/1.93 Prover 19: Constructing countermodel ... % 8.50/1.93 Prover 19: stopped % 8.50/1.93 % 8.50/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.50/1.93 % 8.50/1.95 % SZS output start Proof for theBenchmark % 8.50/1.95 Assumptions after simplification: % 8.50/1.95 --------------------------------- % 8.50/1.95 % 8.50/1.95 (apart4) % 8.50/1.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.50/1.99 (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | ~ % 8.50/1.99 $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v1, v2) = 0) % 8.50/1.99 % 8.50/1.99 (ceq1) % 8.50/1.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.50/1.99 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~ % 8.50/1.99 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0) % 8.50/1.99 % 8.50/1.99 (ci1) % 8.50/2.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 8.50/2.00 ~ (apart_point_and_line(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 8.50/2.00 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 8.50/2.00 % 8.50/2.00 (ci2) % 8.50/2.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 8.50/2.00 ~ (apart_point_and_line(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 8.50/2.00 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 8.50/2.00 % 8.50/2.00 (con) % 8.50/2.00 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: any] : ? % 8.50/2.00 [v5: $i] : ? [v6: $i] : ? [v7: any] : ( ~ (v3 = 0) & line_connecting(v0, v2) % 8.50/2.00 = v6 & line_connecting(v0, v1) = v5 & distinct_lines(v5, v6) = v7 & % 8.50/2.00 distinct_points(v1, v2) = v3 & distinct_points(v0, v2) = v4 & % 8.50/2.00 distinct_points(v0, v1) = 0 & $i(v6) & $i(v5) & $i(v2) & $i(v1) & $i(v0) & ( % 8.50/2.00 ~ (v4 = 0) | v7 = 0)) % 8.50/2.00 % 8.50/2.00 (cu1) % 8.50/2.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.50/2.00 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 8.50/2.00 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 8.50/2.00 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 8.50/2.00 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 8.50/2.00 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 8.50/2.00 % 8.50/2.00 (function-axioms) % 8.50/2.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.50/2.01 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 8.50/2.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.50/2.01 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 8.50/2.01 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 8.50/2.01 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 8.50/2.01 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.50/2.01 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.50/2.01 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 8.50/2.01 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 8.50/2.01 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 8.50/2.01 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 8.50/2.01 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 8.50/2.01 (distinct_points(v3, v2) = v0)) % 8.50/2.01 % 8.50/2.01 Further assumptions not needed in the proof: % 8.50/2.01 -------------------------------------------- % 8.50/2.01 apart1, apart2, apart3, apart5, ax6, ceq2, ceq3, ci3, ci4 % 8.50/2.01 % 8.50/2.01 Those formulas are unsatisfiable: % 8.50/2.01 --------------------------------- % 8.50/2.01 % 8.50/2.01 Begin of proof % 8.50/2.01 | % 8.50/2.01 | ALPHA: (function-axioms) implies: % 8.50/2.01 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.50/2.01 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 8.50/2.01 | (distinct_points(v3, v2) = v0)) % 8.50/2.01 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.50/2.01 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 8.50/2.01 | (apart_point_and_line(v3, v2) = v0)) % 8.50/2.01 | % 8.50/2.01 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 8.50/2.01 | all_17_3, all_17_4, all_17_5, all_17_6, all_17_7 gives: % 8.50/2.01 | (3) ~ (all_17_4 = 0) & line_connecting(all_17_7, all_17_5) = all_17_1 & % 8.50/2.01 | line_connecting(all_17_7, all_17_6) = all_17_2 & % 8.50/2.01 | distinct_lines(all_17_2, all_17_1) = all_17_0 & % 8.50/2.01 | distinct_points(all_17_6, all_17_5) = all_17_4 & % 8.50/2.01 | distinct_points(all_17_7, all_17_5) = all_17_3 & % 8.50/2.01 | distinct_points(all_17_7, all_17_6) = 0 & $i(all_17_1) & $i(all_17_2) & % 8.50/2.01 | $i(all_17_5) & $i(all_17_6) & $i(all_17_7) & ( ~ (all_17_3 = 0) | % 8.50/2.01 | all_17_0 = 0) % 8.50/2.01 | % 8.50/2.01 | ALPHA: (3) implies: % 8.50/2.01 | (4) ~ (all_17_4 = 0) % 8.50/2.01 | (5) $i(all_17_7) % 8.50/2.01 | (6) $i(all_17_6) % 8.50/2.01 | (7) $i(all_17_5) % 8.50/2.01 | (8) $i(all_17_2) % 8.50/2.01 | (9) $i(all_17_1) % 8.50/2.02 | (10) distinct_points(all_17_7, all_17_6) = 0 % 8.50/2.02 | (11) distinct_points(all_17_7, all_17_5) = all_17_3 % 8.50/2.02 | (12) distinct_points(all_17_6, all_17_5) = all_17_4 % 8.50/2.02 | (13) distinct_lines(all_17_2, all_17_1) = all_17_0 % 8.50/2.02 | (14) line_connecting(all_17_7, all_17_6) = all_17_2 % 8.50/2.02 | (15) line_connecting(all_17_7, all_17_5) = all_17_1 % 8.50/2.02 | (16) ~ (all_17_3 = 0) | all_17_0 = 0 % 8.50/2.02 | % 8.50/2.02 | GROUND_INST: instantiating (apart4) with all_17_7, all_17_6, all_17_5, % 8.50/2.02 | all_17_3, simplifying with (5), (6), (7), (10), (11) gives: % 8.50/2.02 | (17) all_17_3 = 0 | distinct_points(all_17_6, all_17_5) = 0 % 8.50/2.02 | % 8.50/2.02 | BETA: splitting (16) gives: % 8.50/2.02 | % 8.50/2.02 | Case 1: % 8.50/2.02 | | % 8.50/2.02 | | (18) ~ (all_17_3 = 0) % 8.50/2.02 | | % 8.50/2.02 | | BETA: splitting (17) gives: % 8.50/2.02 | | % 8.50/2.02 | | Case 1: % 8.50/2.02 | | | % 8.50/2.02 | | | (19) distinct_points(all_17_6, all_17_5) = 0 % 8.50/2.02 | | | % 8.50/2.02 | | | GROUND_INST: instantiating (1) with all_17_4, 0, all_17_5, all_17_6, % 8.50/2.02 | | | simplifying with (12), (19) gives: % 8.50/2.02 | | | (20) all_17_4 = 0 % 8.50/2.02 | | | % 8.50/2.02 | | | REDUCE: (4), (20) imply: % 8.50/2.02 | | | (21) $false % 8.50/2.02 | | | % 8.50/2.02 | | | CLOSE: (21) is inconsistent. % 8.50/2.02 | | | % 8.50/2.02 | | Case 2: % 8.50/2.02 | | | % 8.50/2.02 | | | (22) all_17_3 = 0 % 8.50/2.02 | | | % 8.50/2.02 | | | REDUCE: (18), (22) imply: % 8.50/2.02 | | | (23) $false % 8.50/2.02 | | | % 8.50/2.02 | | | CLOSE: (23) is inconsistent. % 8.50/2.02 | | | % 8.50/2.02 | | End of split % 8.50/2.02 | | % 8.50/2.02 | Case 2: % 8.50/2.02 | | % 8.50/2.02 | | (24) all_17_3 = 0 % 8.50/2.02 | | (25) all_17_0 = 0 % 8.50/2.02 | | % 8.50/2.02 | | REDUCE: (13), (25) imply: % 8.50/2.02 | | (26) distinct_lines(all_17_2, all_17_1) = 0 % 8.50/2.02 | | % 8.50/2.02 | | REDUCE: (11), (24) imply: % 8.50/2.02 | | (27) distinct_points(all_17_7, all_17_5) = 0 % 8.50/2.02 | | % 8.50/2.02 | | GROUND_INST: instantiating (cu1) with all_17_7, all_17_6, all_17_2, % 8.50/2.02 | | all_17_1, simplifying with (5), (6), (8), (9), (10), (26) % 8.50/2.02 | | gives: % 8.50/2.02 | | (28) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 8.50/2.02 | | (apart_point_and_line(all_17_6, all_17_1) = v3 & % 8.50/2.02 | | apart_point_and_line(all_17_6, all_17_2) = v2 & % 8.50/2.02 | | apart_point_and_line(all_17_7, all_17_1) = v1 & % 8.50/2.02 | | apart_point_and_line(all_17_7, all_17_2) = v0 & (v3 = 0 | v2 = 0 | % 8.50/2.02 | | v1 = 0 | v0 = 0)) % 8.50/2.02 | | % 8.50/2.02 | | GROUND_INST: instantiating (cu1) with all_17_7, all_17_5, all_17_2, % 8.50/2.02 | | all_17_1, simplifying with (5), (7), (8), (9), (26), (27) % 8.50/2.02 | | gives: % 8.50/2.03 | | (29) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 8.50/2.03 | | (apart_point_and_line(all_17_5, all_17_1) = v3 & % 8.50/2.03 | | apart_point_and_line(all_17_5, all_17_2) = v2 & % 8.50/2.03 | | apart_point_and_line(all_17_7, all_17_1) = v1 & % 8.50/2.03 | | apart_point_and_line(all_17_7, all_17_2) = v0 & (v3 = 0 | v2 = 0 | % 8.50/2.03 | | v1 = 0 | v0 = 0)) % 8.50/2.03 | | % 8.50/2.03 | | DELTA: instantiating (29) with fresh symbols all_31_0, all_31_1, all_31_2, % 8.50/2.03 | | all_31_3 gives: % 8.50/2.03 | | (30) apart_point_and_line(all_17_5, all_17_1) = all_31_0 & % 8.50/2.03 | | apart_point_and_line(all_17_5, all_17_2) = all_31_1 & % 8.50/2.03 | | apart_point_and_line(all_17_7, all_17_1) = all_31_2 & % 8.50/2.03 | | apart_point_and_line(all_17_7, all_17_2) = all_31_3 & (all_31_0 = 0 % 8.50/2.03 | | | all_31_1 = 0 | all_31_2 = 0 | all_31_3 = 0) % 8.50/2.03 | | % 8.50/2.03 | | ALPHA: (30) implies: % 8.50/2.03 | | (31) apart_point_and_line(all_17_7, all_17_2) = all_31_3 % 8.50/2.03 | | (32) apart_point_and_line(all_17_7, all_17_1) = all_31_2 % 8.50/2.03 | | % 8.50/2.03 | | DELTA: instantiating (28) with fresh symbols all_33_0, all_33_1, all_33_2, % 8.50/2.03 | | all_33_3 gives: % 8.50/2.03 | | (33) apart_point_and_line(all_17_6, all_17_1) = all_33_0 & % 8.50/2.03 | | apart_point_and_line(all_17_6, all_17_2) = all_33_1 & % 8.50/2.03 | | apart_point_and_line(all_17_7, all_17_1) = all_33_2 & % 8.50/2.03 | | apart_point_and_line(all_17_7, all_17_2) = all_33_3 & (all_33_0 = 0 % 8.50/2.03 | | | all_33_1 = 0 | all_33_2 = 0 | all_33_3 = 0) % 8.50/2.03 | | % 8.50/2.03 | | ALPHA: (33) implies: % 8.50/2.03 | | (34) apart_point_and_line(all_17_7, all_17_2) = all_33_3 % 8.50/2.03 | | (35) apart_point_and_line(all_17_7, all_17_1) = all_33_2 % 8.50/2.03 | | (36) apart_point_and_line(all_17_6, all_17_2) = all_33_1 % 8.50/2.03 | | (37) apart_point_and_line(all_17_6, all_17_1) = all_33_0 % 8.50/2.03 | | (38) all_33_0 = 0 | all_33_1 = 0 | all_33_2 = 0 | all_33_3 = 0 % 8.50/2.03 | | % 8.50/2.03 | | GROUND_INST: instantiating (2) with all_31_3, all_33_3, all_17_2, all_17_7, % 8.50/2.03 | | simplifying with (31), (34) gives: % 8.50/2.03 | | (39) all_33_3 = all_31_3 % 8.50/2.03 | | % 8.50/2.03 | | GROUND_INST: instantiating (2) with all_31_2, all_33_2, all_17_1, all_17_7, % 8.50/2.03 | | simplifying with (32), (35) gives: % 8.50/2.03 | | (40) all_33_2 = all_31_2 % 8.50/2.03 | | % 8.50/2.03 | | BETA: splitting (38) gives: % 8.50/2.03 | | % 8.50/2.03 | | Case 1: % 8.50/2.03 | | | % 8.50/2.03 | | | (41) all_33_0 = 0 % 8.50/2.03 | | | % 8.50/2.03 | | | REDUCE: (37), (41) imply: % 8.50/2.03 | | | (42) apart_point_and_line(all_17_6, all_17_1) = 0 % 8.50/2.03 | | | % 8.50/2.03 | | | GROUND_INST: instantiating (ceq1) with all_17_6, all_17_1, all_17_5, % 8.50/2.03 | | | all_17_4, simplifying with (6), (7), (9), (12), (42) gives: % 8.50/2.03 | | | (43) all_17_4 = 0 | apart_point_and_line(all_17_5, all_17_1) = 0 % 8.50/2.03 | | | % 8.50/2.03 | | | BETA: splitting (43) gives: % 8.50/2.03 | | | % 8.50/2.03 | | | Case 1: % 8.50/2.03 | | | | % 8.50/2.03 | | | | (44) apart_point_and_line(all_17_5, all_17_1) = 0 % 8.50/2.03 | | | | % 8.50/2.03 | | | | GROUND_INST: instantiating (ci2) with all_17_7, all_17_5, all_17_1, % 8.50/2.03 | | | | simplifying with (5), (7), (15), (44) gives: % 8.50/2.03 | | | | (45) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_17_7, % 8.50/2.03 | | | | all_17_5) = v0) % 8.50/2.03 | | | | % 8.50/2.03 | | | | DELTA: instantiating (45) with fresh symbol all_51_0 gives: % 8.50/2.03 | | | | (46) ~ (all_51_0 = 0) & distinct_points(all_17_7, all_17_5) = % 8.50/2.03 | | | | all_51_0 % 8.50/2.03 | | | | % 8.50/2.03 | | | | ALPHA: (46) implies: % 8.50/2.03 | | | | (47) ~ (all_51_0 = 0) % 8.50/2.03 | | | | (48) distinct_points(all_17_7, all_17_5) = all_51_0 % 8.50/2.03 | | | | % 8.50/2.03 | | | | GROUND_INST: instantiating (1) with 0, all_51_0, all_17_5, all_17_7, % 8.50/2.03 | | | | simplifying with (27), (48) gives: % 8.50/2.03 | | | | (49) all_51_0 = 0 % 8.50/2.03 | | | | % 8.50/2.03 | | | | REDUCE: (47), (49) imply: % 8.50/2.03 | | | | (50) $false % 8.50/2.03 | | | | % 8.50/2.03 | | | | CLOSE: (50) is inconsistent. % 8.50/2.03 | | | | % 8.50/2.03 | | | Case 2: % 8.50/2.03 | | | | % 8.50/2.03 | | | | (51) all_17_4 = 0 % 8.50/2.03 | | | | % 8.50/2.03 | | | | REDUCE: (4), (51) imply: % 8.50/2.03 | | | | (52) $false % 8.50/2.04 | | | | % 8.50/2.04 | | | | CLOSE: (52) is inconsistent. % 8.50/2.04 | | | | % 8.50/2.04 | | | End of split % 8.50/2.04 | | | % 8.50/2.04 | | Case 2: % 8.50/2.04 | | | % 8.50/2.04 | | | (53) all_33_1 = 0 | all_33_2 = 0 | all_33_3 = 0 % 8.50/2.04 | | | % 8.50/2.04 | | | BETA: splitting (53) gives: % 8.50/2.04 | | | % 8.50/2.04 | | | Case 1: % 8.50/2.04 | | | | % 8.50/2.04 | | | | (54) all_33_1 = 0 % 8.50/2.04 | | | | % 8.50/2.04 | | | | REDUCE: (36), (54) imply: % 8.50/2.04 | | | | (55) apart_point_and_line(all_17_6, all_17_2) = 0 % 8.50/2.04 | | | | % 8.50/2.04 | | | | GROUND_INST: instantiating (ci2) with all_17_7, all_17_6, all_17_2, % 8.50/2.04 | | | | simplifying with (5), (6), (14), (55) gives: % 8.50/2.04 | | | | (56) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_17_7, % 8.50/2.04 | | | | all_17_6) = v0) % 8.50/2.04 | | | | % 8.50/2.04 | | | | DELTA: instantiating (56) with fresh symbol all_72_0 gives: % 8.50/2.04 | | | | (57) ~ (all_72_0 = 0) & distinct_points(all_17_7, all_17_6) = % 8.50/2.04 | | | | all_72_0 % 8.50/2.04 | | | | % 8.50/2.04 | | | | ALPHA: (57) implies: % 8.50/2.04 | | | | (58) ~ (all_72_0 = 0) % 8.50/2.04 | | | | (59) distinct_points(all_17_7, all_17_6) = all_72_0 % 8.50/2.04 | | | | % 8.50/2.04 | | | | GROUND_INST: instantiating (1) with 0, all_72_0, all_17_6, all_17_7, % 8.50/2.04 | | | | simplifying with (10), (59) gives: % 8.50/2.04 | | | | (60) all_72_0 = 0 % 8.50/2.04 | | | | % 8.50/2.04 | | | | REDUCE: (58), (60) imply: % 8.50/2.04 | | | | (61) $false % 8.50/2.04 | | | | % 8.50/2.04 | | | | CLOSE: (61) is inconsistent. % 8.50/2.04 | | | | % 8.50/2.04 | | | Case 2: % 8.50/2.04 | | | | % 8.50/2.04 | | | | (62) all_33_2 = 0 | all_33_3 = 0 % 8.50/2.04 | | | | % 8.50/2.04 | | | | BETA: splitting (62) gives: % 8.50/2.04 | | | | % 8.50/2.04 | | | | Case 1: % 8.50/2.04 | | | | | % 8.50/2.04 | | | | | (63) all_33_2 = 0 % 8.50/2.04 | | | | | % 8.50/2.04 | | | | | COMBINE_EQS: (40), (63) imply: % 8.50/2.04 | | | | | (64) all_31_2 = 0 % 8.50/2.04 | | | | | % 8.50/2.04 | | | | | REDUCE: (32), (64) imply: % 8.50/2.04 | | | | | (65) apart_point_and_line(all_17_7, all_17_1) = 0 % 8.50/2.04 | | | | | % 8.50/2.04 | | | | | GROUND_INST: instantiating (ci1) with all_17_7, all_17_5, all_17_1, % 8.50/2.04 | | | | | simplifying with (5), (7), (15), (65) gives: % 8.50/2.04 | | | | | (66) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_17_7, % 8.50/2.04 | | | | | all_17_5) = v0) % 8.50/2.04 | | | | | % 8.50/2.04 | | | | | DELTA: instantiating (66) with fresh symbol all_79_0 gives: % 8.50/2.04 | | | | | (67) ~ (all_79_0 = 0) & distinct_points(all_17_7, all_17_5) = % 8.50/2.04 | | | | | all_79_0 % 8.50/2.04 | | | | | % 8.50/2.04 | | | | | ALPHA: (67) implies: % 8.50/2.04 | | | | | (68) ~ (all_79_0 = 0) % 8.50/2.04 | | | | | (69) distinct_points(all_17_7, all_17_5) = all_79_0 % 8.50/2.04 | | | | | % 8.50/2.04 | | | | | GROUND_INST: instantiating (1) with 0, all_79_0, all_17_5, all_17_7, % 8.50/2.04 | | | | | simplifying with (27), (69) gives: % 8.50/2.04 | | | | | (70) all_79_0 = 0 % 8.50/2.04 | | | | | % 8.50/2.04 | | | | | REDUCE: (68), (70) imply: % 8.50/2.04 | | | | | (71) $false % 8.50/2.04 | | | | | % 8.50/2.04 | | | | | CLOSE: (71) is inconsistent. % 8.50/2.04 | | | | | % 8.50/2.04 | | | | Case 2: % 8.50/2.04 | | | | | % 8.50/2.04 | | | | | (72) all_33_3 = 0 % 8.50/2.04 | | | | | % 8.50/2.04 | | | | | COMBINE_EQS: (39), (72) imply: % 8.50/2.04 | | | | | (73) all_31_3 = 0 % 8.50/2.04 | | | | | % 8.50/2.04 | | | | | SIMP: (73) implies: % 8.50/2.04 | | | | | (74) all_31_3 = 0 % 8.50/2.04 | | | | | % 8.50/2.04 | | | | | REDUCE: (31), (74) imply: % 8.50/2.04 | | | | | (75) apart_point_and_line(all_17_7, all_17_2) = 0 % 8.50/2.04 | | | | | % 8.50/2.04 | | | | | GROUND_INST: instantiating (ci1) with all_17_7, all_17_6, all_17_2, % 8.50/2.04 | | | | | simplifying with (5), (6), (14), (75) gives: % 8.50/2.04 | | | | | (76) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_17_7, % 8.50/2.04 | | | | | all_17_6) = v0) % 8.50/2.04 | | | | | % 8.50/2.04 | | | | | DELTA: instantiating (76) with fresh symbol all_79_0 gives: % 8.50/2.04 | | | | | (77) ~ (all_79_0 = 0) & distinct_points(all_17_7, all_17_6) = % 8.50/2.04 | | | | | all_79_0 % 8.50/2.04 | | | | | % 8.50/2.04 | | | | | ALPHA: (77) implies: % 8.50/2.04 | | | | | (78) ~ (all_79_0 = 0) % 8.50/2.04 | | | | | (79) distinct_points(all_17_7, all_17_6) = all_79_0 % 8.50/2.04 | | | | | % 8.50/2.05 | | | | | GROUND_INST: instantiating (1) with 0, all_79_0, all_17_6, all_17_7, % 8.50/2.05 | | | | | simplifying with (10), (79) gives: % 8.50/2.05 | | | | | (80) all_79_0 = 0 % 8.50/2.05 | | | | | % 8.50/2.05 | | | | | REDUCE: (78), (80) imply: % 8.50/2.05 | | | | | (81) $false % 8.50/2.05 | | | | | % 8.50/2.05 | | | | | CLOSE: (81) is inconsistent. % 8.50/2.05 | | | | | % 8.50/2.05 | | | | End of split % 8.50/2.05 | | | | % 8.50/2.05 | | | End of split % 8.50/2.05 | | | % 8.50/2.05 | | End of split % 8.50/2.05 | | % 8.50/2.05 | End of split % 8.50/2.05 | % 8.50/2.05 End of proof % 8.50/2.05 % SZS output end Proof for theBenchmark % 8.50/2.05 % 8.50/2.05 1390ms %------------------------------------------------------------------------------