%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO179+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 : n012.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 1.61s % Output : Proof 8.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO179+2 : TPTP v8.1.2. Released v3.3.0. % 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n012.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Tue Aug 29 20:41:08 EDT 2023 % 0.13/0.33 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 2.21/1.06 Prover 1: Preprocessing ... % 2.21/1.06 Prover 4: Preprocessing ... % 2.90/1.10 Prover 2: Preprocessing ... % 2.90/1.10 Prover 0: Preprocessing ... % 2.90/1.10 Prover 6: Preprocessing ... % 2.90/1.10 Prover 5: Preprocessing ... % 2.90/1.10 Prover 3: Preprocessing ... % 3.59/1.35 Prover 6: Constructing countermodel ... % 3.59/1.35 Prover 1: Constructing countermodel ... % 3.59/1.35 Prover 5: Proving ... % 3.59/1.36 Prover 3: Constructing countermodel ... % 3.59/1.36 Prover 2: Proving ... % 4.44/1.43 Prover 4: Constructing countermodel ... % 5.44/1.47 Prover 0: Proving ... % 6.39/1.61 Prover 3: proved (980ms) % 6.39/1.61 % 6.39/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.39/1.61 % 6.39/1.61 Prover 6: stopped % 6.39/1.61 Prover 2: stopped % 6.39/1.61 Prover 5: stopped % 6.39/1.61 Prover 0: stopped % 6.39/1.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.39/1.61 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.39/1.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.39/1.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.39/1.62 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.68/1.66 Prover 8: Preprocessing ... % 6.68/1.67 Prover 13: Preprocessing ... % 6.68/1.67 Prover 10: Preprocessing ... % 6.68/1.67 Prover 11: Preprocessing ... % 6.68/1.68 Prover 7: Preprocessing ... % 7.13/1.70 Prover 10: Warning: ignoring some quantifiers % 7.13/1.71 Prover 10: Constructing countermodel ... % 7.13/1.72 Prover 13: Warning: ignoring some quantifiers % 7.13/1.72 Prover 13: Constructing countermodel ... % 7.13/1.73 Prover 7: Warning: ignoring some quantifiers % 7.13/1.74 Prover 8: Warning: ignoring some quantifiers % 7.13/1.74 Prover 8: Constructing countermodel ... % 7.59/1.77 Prover 7: Constructing countermodel ... % 7.59/1.78 Prover 10: gave up % 7.59/1.78 Prover 1: Found proof (size 51) % 7.59/1.78 Prover 1: proved (1165ms) % 7.59/1.79 Prover 13: stopped % 7.59/1.79 Prover 7: stopped % 7.59/1.79 Prover 8: stopped % 7.59/1.79 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.59/1.79 Prover 4: stopped % 7.59/1.81 Prover 16: Preprocessing ... % 7.59/1.82 Prover 16: stopped % 7.59/1.82 Prover 11: Constructing countermodel ... % 7.59/1.83 Prover 11: stopped % 7.59/1.83 % 7.59/1.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.59/1.83 % 7.59/1.84 % SZS output start Proof for theBenchmark % 7.59/1.84 Assumptions after simplification: % 7.59/1.84 --------------------------------- % 7.59/1.84 % 7.59/1.84 (apart1) % 8.15/1.87 ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0)) % 8.15/1.87 % 8.15/1.87 (ceq2) % 8.15/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.15/1.87 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | ~ % 8.15/1.87 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v0, v2) = 0) % 8.15/1.87 % 8.15/1.87 (con) % 8.15/1.88 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 8.15/1.88 any] : ? [v6: $i] : ? [v7: any] : (line_connecting(v2, v1) = v6 & % 8.15/1.88 line_connecting(v2, v0) = v4 & line_connecting(v0, v1) = v3 & % 8.15/1.88 apart_point_and_line(v2, v3) = 0 & distinct_lines(v3, v6) = v7 & % 8.15/1.88 distinct_lines(v3, v4) = v5 & distinct_points(v0, v1) = 0 & $i(v6) & $i(v4) % 8.15/1.88 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v7 = 0) | ~ (v5 = 0))) % 8.15/1.88 % 8.15/1.88 (con1) % 8.15/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.15/1.88 (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ~ % 8.15/1.88 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] % 8.15/1.88 : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & % 8.15/1.88 distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0)))) % 8.15/1.88 % 8.15/1.88 (function-axioms) % 8.15/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.15/1.88 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 8.15/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.15/1.89 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 8.15/1.89 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 8.15/1.89 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 8.15/1.89 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.15/1.89 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.15/1.89 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 8.15/1.89 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 8.15/1.89 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 8.15/1.89 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 8.15/1.89 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 8.15/1.89 (distinct_points(v3, v2) = v0)) % 8.15/1.89 % 8.15/1.89 Further assumptions not needed in the proof: % 8.15/1.89 -------------------------------------------- % 8.15/1.89 apart2, apart3, apart4, apart5, apart6, ceq1, ceq3, con2, cu1 % 8.15/1.89 % 8.15/1.89 Those formulas are unsatisfiable: % 8.15/1.89 --------------------------------- % 8.15/1.89 % 8.15/1.89 Begin of proof % 8.15/1.89 | % 8.15/1.89 | ALPHA: (function-axioms) implies: % 8.15/1.89 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.15/1.89 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 8.15/1.89 | (distinct_points(v3, v2) = v0)) % 8.15/1.89 | % 8.15/1.89 | DELTA: instantiating (con) with fresh symbols all_15_0, all_15_1, all_15_2, % 8.15/1.89 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7 gives: % 8.15/1.89 | (2) line_connecting(all_15_5, all_15_6) = all_15_1 & % 8.15/1.89 | line_connecting(all_15_5, all_15_7) = all_15_3 & % 8.15/1.89 | line_connecting(all_15_7, all_15_6) = all_15_4 & % 8.15/1.89 | apart_point_and_line(all_15_5, all_15_4) = 0 & distinct_lines(all_15_4, % 8.15/1.89 | all_15_1) = all_15_0 & distinct_lines(all_15_4, all_15_3) = all_15_2 % 8.15/1.89 | & distinct_points(all_15_7, all_15_6) = 0 & $i(all_15_1) & $i(all_15_3) % 8.15/1.89 | & $i(all_15_4) & $i(all_15_5) & $i(all_15_6) & $i(all_15_7) & ( ~ % 8.15/1.89 | (all_15_0 = 0) | ~ (all_15_2 = 0)) % 8.15/1.89 | % 8.15/1.89 | ALPHA: (2) implies: % 8.35/1.90 | (3) $i(all_15_7) % 8.35/1.90 | (4) $i(all_15_6) % 8.35/1.90 | (5) $i(all_15_5) % 8.35/1.90 | (6) $i(all_15_4) % 8.35/1.90 | (7) $i(all_15_3) % 8.35/1.90 | (8) $i(all_15_1) % 8.35/1.90 | (9) distinct_points(all_15_7, all_15_6) = 0 % 8.35/1.90 | (10) distinct_lines(all_15_4, all_15_3) = all_15_2 % 8.35/1.90 | (11) distinct_lines(all_15_4, all_15_1) = all_15_0 % 8.35/1.90 | (12) apart_point_and_line(all_15_5, all_15_4) = 0 % 8.35/1.90 | (13) line_connecting(all_15_7, all_15_6) = all_15_4 % 8.35/1.90 | (14) line_connecting(all_15_5, all_15_7) = all_15_3 % 8.35/1.90 | (15) line_connecting(all_15_5, all_15_6) = all_15_1 % 8.35/1.90 | (16) ~ (all_15_0 = 0) | ~ (all_15_2 = 0) % 8.35/1.90 | % 8.35/1.90 | GROUND_INST: instantiating (ceq2) with all_15_5, all_15_4, all_15_1, all_15_0, % 8.35/1.90 | simplifying with (5), (6), (8), (11), (12) gives: % 8.35/1.90 | (17) all_15_0 = 0 | apart_point_and_line(all_15_5, all_15_1) = 0 % 8.35/1.90 | % 8.35/1.90 | GROUND_INST: instantiating (ceq2) with all_15_5, all_15_4, all_15_3, all_15_2, % 8.35/1.90 | simplifying with (5), (6), (7), (10), (12) gives: % 8.35/1.90 | (18) all_15_2 = 0 | apart_point_and_line(all_15_5, all_15_3) = 0 % 8.35/1.90 | % 8.35/1.90 | GROUND_INST: instantiating (con1) with all_15_7, all_15_6, all_15_5, all_15_4, % 8.35/1.90 | simplifying with (3), (4), (5), (12), (13) gives: % 8.35/1.90 | (19) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 8.35/1.90 | (distinct_points(all_15_5, all_15_6) = v2 & distinct_points(all_15_5, % 8.35/1.90 | all_15_7) = v1 & distinct_points(all_15_7, all_15_6) = v0 & ( ~ % 8.35/1.90 | (v0 = 0) | (v2 = 0 & v1 = 0))) % 8.35/1.90 | % 8.35/1.90 | DELTA: instantiating (19) with fresh symbols all_22_0, all_22_1, all_22_2 % 8.35/1.90 | gives: % 8.35/1.91 | (20) distinct_points(all_15_5, all_15_6) = all_22_0 & % 8.35/1.91 | distinct_points(all_15_5, all_15_7) = all_22_1 & % 8.35/1.91 | distinct_points(all_15_7, all_15_6) = all_22_2 & ( ~ (all_22_2 = 0) | % 8.35/1.91 | (all_22_0 = 0 & all_22_1 = 0)) % 8.35/1.91 | % 8.35/1.91 | ALPHA: (20) implies: % 8.35/1.91 | (21) distinct_points(all_15_7, all_15_6) = all_22_2 % 8.35/1.91 | (22) distinct_points(all_15_5, all_15_7) = all_22_1 % 8.35/1.91 | (23) distinct_points(all_15_5, all_15_6) = all_22_0 % 8.35/1.91 | (24) ~ (all_22_2 = 0) | (all_22_0 = 0 & all_22_1 = 0) % 8.35/1.91 | % 8.35/1.91 | GROUND_INST: instantiating (1) with 0, all_22_2, all_15_6, all_15_7, % 8.35/1.91 | simplifying with (9), (21) gives: % 8.35/1.91 | (25) all_22_2 = 0 % 8.35/1.91 | % 8.35/1.91 | BETA: splitting (24) gives: % 8.35/1.91 | % 8.35/1.91 | Case 1: % 8.35/1.91 | | % 8.35/1.91 | | (26) ~ (all_22_2 = 0) % 8.35/1.91 | | % 8.35/1.91 | | REDUCE: (25), (26) imply: % 8.35/1.91 | | (27) $false % 8.35/1.91 | | % 8.35/1.91 | | CLOSE: (27) is inconsistent. % 8.35/1.91 | | % 8.35/1.91 | Case 2: % 8.35/1.91 | | % 8.35/1.91 | | (28) all_22_0 = 0 & all_22_1 = 0 % 8.35/1.91 | | % 8.35/1.91 | | ALPHA: (28) implies: % 8.35/1.91 | | (29) all_22_1 = 0 % 8.35/1.91 | | (30) all_22_0 = 0 % 8.35/1.91 | | % 8.35/1.91 | | REDUCE: (23), (30) imply: % 8.35/1.91 | | (31) distinct_points(all_15_5, all_15_6) = 0 % 8.35/1.91 | | % 8.35/1.91 | | REDUCE: (22), (29) imply: % 8.35/1.91 | | (32) distinct_points(all_15_5, all_15_7) = 0 % 8.35/1.91 | | % 8.35/1.91 | | BETA: splitting (16) gives: % 8.35/1.91 | | % 8.35/1.91 | | Case 1: % 8.35/1.91 | | | % 8.35/1.91 | | | (33) ~ (all_15_0 = 0) % 8.35/1.91 | | | % 8.35/1.91 | | | BETA: splitting (17) gives: % 8.35/1.91 | | | % 8.35/1.91 | | | Case 1: % 8.35/1.91 | | | | % 8.35/1.91 | | | | (34) apart_point_and_line(all_15_5, all_15_1) = 0 % 8.35/1.91 | | | | % 8.35/1.91 | | | | GROUND_INST: instantiating (con1) with all_15_5, all_15_6, all_15_5, % 8.35/1.91 | | | | all_15_1, simplifying with (4), (5), (15), (34) gives: % 8.35/1.91 | | | | (35) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 8.35/1.91 | | | | (distinct_points(all_15_5, all_15_5) = v1 & % 8.35/1.91 | | | | distinct_points(all_15_5, all_15_6) = v2 & % 8.35/1.91 | | | | distinct_points(all_15_5, all_15_6) = v0 & ( ~ (v0 = 0) | (v2 % 8.35/1.91 | | | | = 0 & v1 = 0))) % 8.35/1.91 | | | | % 8.35/1.91 | | | | DELTA: instantiating (35) with fresh symbols all_48_0, all_48_1, % 8.35/1.91 | | | | all_48_2 gives: % 8.35/1.92 | | | | (36) distinct_points(all_15_5, all_15_5) = all_48_1 & % 8.35/1.92 | | | | distinct_points(all_15_5, all_15_6) = all_48_0 & % 8.35/1.92 | | | | distinct_points(all_15_5, all_15_6) = all_48_2 & ( ~ (all_48_2 = % 8.35/1.92 | | | | 0) | (all_48_0 = 0 & all_48_1 = 0)) % 8.35/1.92 | | | | % 8.35/1.92 | | | | ALPHA: (36) implies: % 8.35/1.92 | | | | (37) distinct_points(all_15_5, all_15_6) = all_48_2 % 8.35/1.92 | | | | (38) distinct_points(all_15_5, all_15_6) = all_48_0 % 8.35/1.92 | | | | (39) distinct_points(all_15_5, all_15_5) = all_48_1 % 8.35/1.92 | | | | (40) ~ (all_48_2 = 0) | (all_48_0 = 0 & all_48_1 = 0) % 8.35/1.92 | | | | % 8.35/1.92 | | | | GROUND_INST: instantiating (1) with 0, all_48_0, all_15_6, all_15_5, % 8.35/1.92 | | | | simplifying with (31), (38) gives: % 8.35/1.92 | | | | (41) all_48_0 = 0 % 8.35/1.92 | | | | % 8.35/1.92 | | | | GROUND_INST: instantiating (1) with all_48_2, all_48_0, all_15_6, % 8.35/1.92 | | | | all_15_5, simplifying with (37), (38) gives: % 8.35/1.92 | | | | (42) all_48_0 = all_48_2 % 8.35/1.92 | | | | % 8.35/1.92 | | | | COMBINE_EQS: (41), (42) imply: % 8.35/1.92 | | | | (43) all_48_2 = 0 % 8.35/1.92 | | | | % 8.35/1.92 | | | | BETA: splitting (40) gives: % 8.35/1.92 | | | | % 8.35/1.92 | | | | Case 1: % 8.35/1.92 | | | | | % 8.35/1.92 | | | | | (44) ~ (all_48_2 = 0) % 8.35/1.92 | | | | | % 8.35/1.92 | | | | | REDUCE: (43), (44) imply: % 8.35/1.92 | | | | | (45) $false % 8.35/1.92 | | | | | % 8.35/1.92 | | | | | CLOSE: (45) is inconsistent. % 8.35/1.92 | | | | | % 8.35/1.92 | | | | Case 2: % 8.35/1.92 | | | | | % 8.35/1.92 | | | | | (46) all_48_0 = 0 & all_48_1 = 0 % 8.35/1.92 | | | | | % 8.35/1.92 | | | | | ALPHA: (46) implies: % 8.35/1.92 | | | | | (47) all_48_1 = 0 % 8.35/1.92 | | | | | % 8.35/1.92 | | | | | REDUCE: (39), (47) imply: % 8.35/1.92 | | | | | (48) distinct_points(all_15_5, all_15_5) = 0 % 8.35/1.92 | | | | | % 8.35/1.92 | | | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying with % 8.35/1.92 | | | | | (5), (48) gives: % 8.35/1.92 | | | | | (49) $false % 8.35/1.92 | | | | | % 8.35/1.92 | | | | | CLOSE: (49) is inconsistent. % 8.35/1.92 | | | | | % 8.35/1.92 | | | | End of split % 8.35/1.92 | | | | % 8.35/1.92 | | | Case 2: % 8.35/1.92 | | | | % 8.35/1.92 | | | | (50) all_15_0 = 0 % 8.35/1.92 | | | | % 8.35/1.92 | | | | REDUCE: (33), (50) imply: % 8.35/1.92 | | | | (51) $false % 8.35/1.92 | | | | % 8.35/1.92 | | | | CLOSE: (51) is inconsistent. % 8.35/1.92 | | | | % 8.35/1.92 | | | End of split % 8.35/1.92 | | | % 8.35/1.92 | | Case 2: % 8.35/1.92 | | | % 8.35/1.92 | | | (52) ~ (all_15_2 = 0) % 8.35/1.92 | | | % 8.35/1.92 | | | BETA: splitting (18) gives: % 8.35/1.92 | | | % 8.35/1.92 | | | Case 1: % 8.35/1.92 | | | | % 8.35/1.92 | | | | (53) apart_point_and_line(all_15_5, all_15_3) = 0 % 8.35/1.92 | | | | % 8.35/1.92 | | | | GROUND_INST: instantiating (con1) with all_15_5, all_15_7, all_15_5, % 8.35/1.92 | | | | all_15_3, simplifying with (3), (5), (14), (53) gives: % 8.35/1.92 | | | | (54) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 8.35/1.92 | | | | (distinct_points(all_15_5, all_15_5) = v1 & % 8.35/1.92 | | | | distinct_points(all_15_5, all_15_7) = v2 & % 8.35/1.92 | | | | distinct_points(all_15_5, all_15_7) = v0 & ( ~ (v0 = 0) | (v2 % 8.35/1.92 | | | | = 0 & v1 = 0))) % 8.35/1.92 | | | | % 8.35/1.92 | | | | DELTA: instantiating (54) with fresh symbols all_48_0, all_48_1, % 8.35/1.92 | | | | all_48_2 gives: % 8.35/1.92 | | | | (55) distinct_points(all_15_5, all_15_5) = all_48_1 & % 8.35/1.92 | | | | distinct_points(all_15_5, all_15_7) = all_48_0 & % 8.35/1.92 | | | | distinct_points(all_15_5, all_15_7) = all_48_2 & ( ~ (all_48_2 = % 8.35/1.92 | | | | 0) | (all_48_0 = 0 & all_48_1 = 0)) % 8.35/1.92 | | | | % 8.35/1.92 | | | | ALPHA: (55) implies: % 8.35/1.92 | | | | (56) distinct_points(all_15_5, all_15_7) = all_48_2 % 8.35/1.92 | | | | (57) distinct_points(all_15_5, all_15_7) = all_48_0 % 8.35/1.92 | | | | (58) distinct_points(all_15_5, all_15_5) = all_48_1 % 8.35/1.92 | | | | (59) ~ (all_48_2 = 0) | (all_48_0 = 0 & all_48_1 = 0) % 8.35/1.92 | | | | % 8.35/1.93 | | | | GROUND_INST: instantiating (1) with 0, all_48_0, all_15_7, all_15_5, % 8.35/1.93 | | | | simplifying with (32), (57) gives: % 8.35/1.93 | | | | (60) all_48_0 = 0 % 8.35/1.93 | | | | % 8.35/1.93 | | | | GROUND_INST: instantiating (1) with all_48_2, all_48_0, all_15_7, % 8.35/1.93 | | | | all_15_5, simplifying with (56), (57) gives: % 8.35/1.93 | | | | (61) all_48_0 = all_48_2 % 8.35/1.93 | | | | % 8.35/1.93 | | | | COMBINE_EQS: (60), (61) imply: % 8.35/1.93 | | | | (62) all_48_2 = 0 % 8.35/1.93 | | | | % 8.35/1.93 | | | | SIMP: (62) implies: % 8.35/1.93 | | | | (63) all_48_2 = 0 % 8.35/1.93 | | | | % 8.35/1.93 | | | | BETA: splitting (59) gives: % 8.35/1.93 | | | | % 8.35/1.93 | | | | Case 1: % 8.35/1.93 | | | | | % 8.35/1.93 | | | | | (64) ~ (all_48_2 = 0) % 8.35/1.93 | | | | | % 8.35/1.93 | | | | | REDUCE: (63), (64) imply: % 8.35/1.93 | | | | | (65) $false % 8.35/1.93 | | | | | % 8.35/1.93 | | | | | CLOSE: (65) is inconsistent. % 8.35/1.93 | | | | | % 8.35/1.93 | | | | Case 2: % 8.35/1.93 | | | | | % 8.35/1.93 | | | | | (66) all_48_0 = 0 & all_48_1 = 0 % 8.35/1.93 | | | | | % 8.35/1.93 | | | | | ALPHA: (66) implies: % 8.35/1.93 | | | | | (67) all_48_1 = 0 % 8.35/1.93 | | | | | % 8.35/1.93 | | | | | REDUCE: (58), (67) imply: % 8.35/1.93 | | | | | (68) distinct_points(all_15_5, all_15_5) = 0 % 8.35/1.93 | | | | | % 8.35/1.93 | | | | | GROUND_INST: instantiating (apart1) with all_15_5, simplifying with % 8.35/1.93 | | | | | (5), (68) gives: % 8.35/1.93 | | | | | (69) $false % 8.35/1.93 | | | | | % 8.35/1.93 | | | | | CLOSE: (69) is inconsistent. % 8.35/1.93 | | | | | % 8.35/1.93 | | | | End of split % 8.35/1.93 | | | | % 8.35/1.93 | | | Case 2: % 8.35/1.93 | | | | % 8.35/1.93 | | | | (70) all_15_2 = 0 % 8.35/1.93 | | | | % 8.35/1.93 | | | | REDUCE: (52), (70) imply: % 8.35/1.93 | | | | (71) $false % 8.35/1.93 | | | | % 8.35/1.93 | | | | CLOSE: (71) is inconsistent. % 8.35/1.93 | | | | % 8.35/1.93 | | | End of split % 8.35/1.93 | | | % 8.35/1.93 | | End of split % 8.35/1.93 | | % 8.35/1.93 | End of split % 8.35/1.93 | % 8.35/1.93 End of proof % 8.35/1.93 % SZS output end Proof for theBenchmark % 8.35/1.93 % 8.35/1.93 1333ms %------------------------------------------------------------------------------