%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO198+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 : n010.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 23:22:11 EDT 2023 % Result : Theorem 8.04s 1.87s % Output : Proof 9.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO198+2 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n010.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Tue Aug 29 21:46:48 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.73/1.10 Prover 4: Preprocessing ... % 2.73/1.10 Prover 1: Preprocessing ... % 2.73/1.14 Prover 3: Preprocessing ... % 2.73/1.14 Prover 0: Preprocessing ... % 2.73/1.14 Prover 6: Preprocessing ... % 2.73/1.14 Prover 2: Preprocessing ... % 2.73/1.14 Prover 5: Preprocessing ... % 3.97/1.33 Prover 5: Proving ... % 3.97/1.35 Prover 2: Proving ... % 4.68/1.37 Prover 1: Constructing countermodel ... % 4.68/1.37 Prover 6: Constructing countermodel ... % 4.68/1.39 Prover 3: Constructing countermodel ... % 5.27/1.48 Prover 1: gave up % 5.27/1.48 Prover 6: gave up % 5.47/1.49 Prover 3: gave up % 5.47/1.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.47/1.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.47/1.50 Prover 4: Constructing countermodel ... % 5.47/1.51 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.47/1.51 Prover 7: Preprocessing ... % 5.79/1.54 Prover 8: Preprocessing ... % 5.90/1.54 Prover 9: Preprocessing ... % 5.90/1.55 Prover 7: Warning: ignoring some quantifiers % 5.90/1.55 Prover 0: Proving ... % 5.90/1.56 Prover 7: Constructing countermodel ... % 6.44/1.65 Prover 8: Warning: ignoring some quantifiers % 6.44/1.66 Prover 8: Constructing countermodel ... % 6.84/1.73 Prover 8: gave up % 6.84/1.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.84/1.75 Prover 9: Constructing countermodel ... % 7.71/1.79 Prover 10: Preprocessing ... % 8.04/1.83 Prover 10: Warning: ignoring some quantifiers % 8.04/1.84 Prover 10: Constructing countermodel ... % 8.04/1.87 Prover 2: proved (1223ms) % 8.04/1.87 % 8.04/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.04/1.87 % 8.04/1.87 Prover 9: stopped % 8.04/1.87 Prover 0: stopped % 8.04/1.89 Prover 5: stopped % 8.04/1.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.04/1.90 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.04/1.90 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.04/1.90 Prover 13: Preprocessing ... % 8.04/1.90 Prover 11: Preprocessing ... % 8.04/1.90 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 8.57/1.93 Prover 16: Preprocessing ... % 8.57/1.93 Prover 19: Preprocessing ... % 8.57/1.97 Prover 13: Warning: ignoring some quantifiers % 8.57/1.97 Prover 16: Warning: ignoring some quantifiers % 8.57/1.97 Prover 13: Constructing countermodel ... % 8.57/1.97 Prover 16: Constructing countermodel ... % 9.12/2.00 Prover 19: Warning: ignoring some quantifiers % 9.12/2.01 Prover 19: Constructing countermodel ... % 9.12/2.01 Prover 7: Found proof (size 20) % 9.12/2.01 Prover 7: proved (531ms) % 9.12/2.01 Prover 13: stopped % 9.12/2.01 Prover 10: stopped % 9.12/2.01 Prover 16: stopped % 9.12/2.02 Prover 4: stopped % 9.12/2.02 Prover 19: stopped % 9.12/2.02 Prover 11: Constructing countermodel ... % 9.12/2.03 Prover 11: stopped % 9.12/2.03 % 9.12/2.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.12/2.03 % 9.12/2.03 % SZS output start Proof for theBenchmark % 9.12/2.04 Assumptions after simplification: % 9.12/2.04 --------------------------------- % 9.12/2.04 % 9.12/2.04 (apart1) % 9.51/2.04 ! [v0: $i] : ( ~ $i(v0) | ~ distinct_points(v0, v0)) % 9.51/2.04 % 9.51/2.04 (ceq3) % 9.51/2.04 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ convergent_lines(v0, % 9.51/2.04 v1) | distinct_lines(v0, v1)) % 9.51/2.04 % 9.51/2.04 (con) % 9.59/2.06 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 9.59/2.06 (intersection_point(v0, v2) = v4 & intersection_point(v0, v1) = v3 & $i(v4) & % 9.59/2.06 $i(v3) & $i(v2) & $i(v1) & $i(v0) & apart_point_and_line(v4, v1) & % 9.59/2.06 convergent_lines(v2, v1) & convergent_lines(v0, v2) & convergent_lines(v0, % 9.59/2.06 v1) & ~ apart_point_and_line(v3, v2)) % 9.59/2.06 % 9.59/2.06 (con2) % 9.59/2.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 9.59/2.07 (intersection_point(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 9.59/2.07 apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1) | % 9.59/2.07 distinct_points(v2, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 9.59/2.07 $i] : ( ~ (intersection_point(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 9.59/2.07 $i(v0) | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1) | % 9.59/2.07 distinct_points(v2, v3)) % 9.59/2.07 % 9.59/2.07 (cu1) % 9.59/2.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) % 9.59/2.07 | ~ $i(v1) | ~ $i(v0) | ~ distinct_lines(v2, v3) | ~ distinct_points(v0, % 9.59/2.07 v1) | apart_point_and_line(v1, v3) | apart_point_and_line(v1, v2) | % 9.59/2.07 apart_point_and_line(v0, v3) | apart_point_and_line(v0, v2)) % 9.59/2.07 % 9.59/2.07 Further assumptions not needed in the proof: % 9.59/2.07 -------------------------------------------- % 9.59/2.07 apart2, apart3, apart4, apart5, apart6, ceq1, ceq2, con1 % 9.59/2.07 % 9.59/2.07 Those formulas are unsatisfiable: % 9.59/2.07 --------------------------------- % 9.59/2.07 % 9.59/2.07 Begin of proof % 9.59/2.07 | % 9.59/2.07 | ALPHA: (con2) implies: % 9.59/2.07 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 9.59/2.07 | (intersection_point(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 9.59/2.07 | | ~ apart_point_and_line(v2, v0) | ~ convergent_lines(v0, v1) | % 9.59/2.07 | distinct_points(v2, v3)) % 9.59/2.07 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 9.59/2.07 | (intersection_point(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 9.59/2.07 | | ~ apart_point_and_line(v2, v1) | ~ convergent_lines(v0, v1) | % 9.59/2.07 | distinct_points(v2, v3)) % 9.59/2.07 | % 9.59/2.07 | DELTA: instantiating (con) with fresh symbols all_20_0, all_20_1, all_20_2, % 9.59/2.07 | all_20_3, all_20_4 gives: % 9.59/2.08 | (3) intersection_point(all_20_4, all_20_2) = all_20_0 & % 9.59/2.08 | intersection_point(all_20_4, all_20_3) = all_20_1 & $i(all_20_0) & % 9.59/2.08 | $i(all_20_1) & $i(all_20_2) & $i(all_20_3) & $i(all_20_4) & % 9.59/2.08 | apart_point_and_line(all_20_0, all_20_3) & convergent_lines(all_20_2, % 9.59/2.08 | all_20_3) & convergent_lines(all_20_4, all_20_2) & % 9.59/2.08 | convergent_lines(all_20_4, all_20_3) & ~ % 9.59/2.08 | apart_point_and_line(all_20_1, all_20_2) % 9.59/2.08 | % 9.59/2.08 | ALPHA: (3) implies: % 9.59/2.08 | (4) ~ apart_point_and_line(all_20_1, all_20_2) % 9.59/2.08 | (5) convergent_lines(all_20_4, all_20_3) % 9.59/2.08 | (6) convergent_lines(all_20_4, all_20_2) % 9.59/2.08 | (7) apart_point_and_line(all_20_0, all_20_3) % 9.59/2.08 | (8) $i(all_20_4) % 9.59/2.08 | (9) $i(all_20_3) % 9.59/2.08 | (10) $i(all_20_2) % 9.59/2.08 | (11) $i(all_20_1) % 9.59/2.08 | (12) $i(all_20_0) % 9.59/2.08 | (13) intersection_point(all_20_4, all_20_3) = all_20_1 % 9.59/2.08 | (14) intersection_point(all_20_4, all_20_2) = all_20_0 % 9.59/2.08 | % 9.59/2.08 | GROUND_INST: instantiating (ceq3) with all_20_4, all_20_2, simplifying with % 9.59/2.08 | (6), (8), (10) gives: % 9.59/2.08 | (15) distinct_lines(all_20_4, all_20_2) % 9.59/2.08 | % 9.59/2.08 | GROUND_INST: instantiating (2) with all_20_4, all_20_3, all_20_0, all_20_1, % 9.59/2.08 | simplifying with (5), (7), (8), (9), (12), (13) gives: % 9.59/2.08 | (16) distinct_points(all_20_0, all_20_1) % 9.59/2.08 | % 9.59/2.08 | GROUND_INST: instantiating (apart1) with all_20_1, simplifying with (11) % 9.59/2.08 | gives: % 9.59/2.08 | (17) ~ distinct_points(all_20_1, all_20_1) % 9.59/2.08 | % 9.59/2.08 | GROUND_INST: instantiating (cu1) with all_20_0, all_20_1, all_20_4, all_20_2, % 9.59/2.08 | simplifying with (4), (8), (10), (11), (12), (15), (16) gives: % 9.59/2.08 | (18) apart_point_and_line(all_20_0, all_20_2) | % 9.59/2.08 | apart_point_and_line(all_20_0, all_20_4) | % 9.59/2.08 | apart_point_and_line(all_20_1, all_20_4) % 9.59/2.08 | % 9.59/2.08 | BETA: splitting (18) gives: % 9.59/2.08 | % 9.59/2.08 | Case 1: % 9.59/2.08 | | % 9.59/2.08 | | (19) apart_point_and_line(all_20_0, all_20_2) % 9.59/2.08 | | % 9.59/2.08 | | GROUND_INST: instantiating (2) with all_20_4, all_20_2, all_20_0, all_20_0, % 9.59/2.08 | | simplifying with (6), (8), (10), (12), (14), (19) gives: % 9.59/2.09 | | (20) distinct_points(all_20_0, all_20_0) % 9.59/2.09 | | % 9.59/2.09 | | GROUND_INST: instantiating (apart1) with all_20_0, simplifying with (12), % 9.59/2.09 | | (20) gives: % 9.59/2.09 | | (21) $false % 9.59/2.09 | | % 9.59/2.09 | | CLOSE: (21) is inconsistent. % 9.59/2.09 | | % 9.59/2.09 | Case 2: % 9.59/2.09 | | % 9.59/2.09 | | (22) apart_point_and_line(all_20_0, all_20_4) | % 9.59/2.09 | | apart_point_and_line(all_20_1, all_20_4) % 9.59/2.09 | | % 9.59/2.09 | | BETA: splitting (22) gives: % 9.59/2.09 | | % 9.59/2.09 | | Case 1: % 9.59/2.09 | | | % 9.59/2.09 | | | (23) apart_point_and_line(all_20_0, all_20_4) % 9.59/2.09 | | | % 9.59/2.09 | | | GROUND_INST: instantiating (1) with all_20_4, all_20_2, all_20_0, % 9.59/2.09 | | | all_20_0, simplifying with (6), (8), (10), (12), (14), (23) % 9.59/2.09 | | | gives: % 9.59/2.09 | | | (24) distinct_points(all_20_0, all_20_0) % 9.59/2.09 | | | % 9.59/2.09 | | | GROUND_INST: instantiating (apart1) with all_20_0, simplifying with (12), % 9.59/2.09 | | | (24) gives: % 9.59/2.09 | | | (25) $false % 9.59/2.09 | | | % 9.59/2.09 | | | CLOSE: (25) is inconsistent. % 9.59/2.09 | | | % 9.59/2.09 | | Case 2: % 9.59/2.09 | | | % 9.59/2.09 | | | (26) apart_point_and_line(all_20_1, all_20_4) % 9.59/2.09 | | | % 9.59/2.09 | | | GROUND_INST: instantiating (1) with all_20_4, all_20_3, all_20_1, % 9.59/2.09 | | | all_20_1, simplifying with (5), (8), (9), (11), (13), (17), % 9.59/2.09 | | | (26) gives: % 9.59/2.09 | | | (27) $false % 9.59/2.09 | | | % 9.59/2.09 | | | CLOSE: (27) is inconsistent. % 9.59/2.09 | | | % 9.59/2.09 | | End of split % 9.59/2.09 | | % 9.59/2.09 | End of split % 9.59/2.09 | % 9.59/2.09 End of proof % 9.59/2.09 % SZS output end Proof for theBenchmark % 9.59/2.09 % 9.59/2.09 1472ms %------------------------------------------------------------------------------