%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO253+1 : TPTP v8.1.2. Bugfixed v6.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n027.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 23:22:46 EDT 2023 % Result : Theorem 8.26s 1.81s % Output : Proof 53.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.12 % Problem : GEO253+1 : TPTP v8.1.2. Bugfixed v6.4.0. % 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n027.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 20:18:23 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.11/1.08 Prover 4: Preprocessing ... % 3.11/1.10 Prover 1: Preprocessing ... % 3.11/1.11 Prover 6: Preprocessing ... % 3.11/1.11 Prover 0: Preprocessing ... % 3.11/1.11 Prover 2: Preprocessing ... % 3.11/1.11 Prover 5: Preprocessing ... % 3.11/1.11 Prover 3: Preprocessing ... % 6.09/1.54 Prover 5: Proving ... % 6.93/1.63 Prover 6: Constructing countermodel ... % 6.93/1.63 Prover 2: Proving ... % 7.25/1.66 Prover 3: Constructing countermodel ... % 7.25/1.68 Prover 1: Constructing countermodel ... % 7.91/1.75 Prover 3: gave up % 7.91/1.76 Prover 6: gave up % 7.91/1.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.91/1.76 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.26/1.81 Prover 2: proved (1191ms) % 8.26/1.81 % 8.26/1.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.26/1.81 % 8.26/1.82 Prover 5: stopped % 8.26/1.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.26/1.83 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.71/1.89 Prover 8: Preprocessing ... % 8.71/1.89 Prover 7: Preprocessing ... % 8.71/1.92 Prover 11: Preprocessing ... % 8.71/1.94 Prover 10: Preprocessing ... % 9.96/2.03 Prover 7: Warning: ignoring some quantifiers % 9.96/2.05 Prover 10: Warning: ignoring some quantifiers % 9.96/2.07 Prover 7: Constructing countermodel ... % 9.96/2.09 Prover 8: Warning: ignoring some quantifiers % 9.96/2.11 Prover 10: Constructing countermodel ... % 10.66/2.12 Prover 8: Constructing countermodel ... % 10.66/2.14 Prover 4: Constructing countermodel ... % 10.66/2.17 Prover 7: gave up % 10.66/2.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.27/2.21 Prover 10: gave up % 11.27/2.21 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.27/2.24 Prover 16: Preprocessing ... % 11.27/2.24 Prover 13: Preprocessing ... % 11.90/2.29 Prover 0: Proving ... % 11.90/2.30 Prover 8: gave up % 12.08/2.31 Prover 0: stopped % 12.08/2.31 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 12.18/2.33 Prover 16: Warning: ignoring some quantifiers % 12.18/2.34 Prover 13: Warning: ignoring some quantifiers % 12.18/2.35 Prover 19: Preprocessing ... % 12.18/2.35 Prover 16: Constructing countermodel ... % 12.18/2.36 Prover 13: Constructing countermodel ... % 12.92/2.46 Prover 13: gave up % 12.92/2.48 Prover 11: Constructing countermodel ... % 12.92/2.48 Prover 16: gave up % 13.52/2.52 Prover 19: Warning: ignoring some quantifiers % 13.52/2.53 Prover 19: Constructing countermodel ... % 52.47/8.00 Prover 11: Found proof (size 16) % 52.47/8.00 Prover 11: proved (6169ms) % 52.47/8.00 Prover 4: stopped % 52.47/8.00 Prover 1: stopped % 52.47/8.00 Prover 19: stopped % 52.47/8.01 % 52.47/8.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 52.47/8.01 % 52.47/8.01 % SZS output start Proof for theBenchmark % 52.95/8.01 Assumptions after simplification: % 52.95/8.01 --------------------------------- % 52.95/8.01 % 52.95/8.01 (apt_def) % 52.95/8.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 52.95/8.04 (reverse_line(v1) = v2) | ~ (left_apart_point(v0, v2) = v3) | ~ $i(v1) | % 52.95/8.04 ~ $i(v0) | ? [v4: int] : ? [v5: int] : ((v5 = 0 & left_apart_point(v0, v1) % 52.95/8.04 = 0) | ( ~ (v4 = 0) & apart_point_and_line(v0, v1) = v4))) & ! [v0: $i] % 52.95/8.04 : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (reverse_line(v1) = v2) | ~ % 52.95/8.05 (left_apart_point(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? % 52.95/8.05 [v5: int] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v4 = 0) & ~ % 52.95/8.05 (v3 = 0) & left_apart_point(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] % 52.95/8.05 : ! [v2: int] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ~ $i(v1) % 52.95/8.05 | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & ~ % 52.95/8.05 (v3 = 0) & reverse_line(v1) = v4 & left_apart_point(v0, v4) = v5 & % 52.95/8.05 left_apart_point(v0, v1) = v3 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! % 52.95/8.05 [v2: int] : (v2 = 0 | ~ (left_apart_point(v0, v1) = v2) | ~ $i(v1) | ~ % 52.95/8.05 $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ((v5 = 0 & % 52.95/8.05 reverse_line(v1) = v4 & left_apart_point(v0, v4) = 0 & $i(v4)) | ( ~ (v3 % 52.95/8.05 = 0) & apart_point_and_line(v0, v1) = v3))) & ! [v0: $i] : ! [v1: % 52.95/8.05 $i] : ! [v2: any] : ( ~ (left_apart_point(v0, v1) = v2) | ~ $i(v1) | ~ % 52.95/8.05 $i(v0) | ? [v3: $i] : ? [v4: int] : ? [v5: int] : ((v5 = 0 & % 52.95/8.05 apart_point_and_line(v0, v1) = 0) | ( ~ (v4 = 0) & ~ (v2 = 0) & % 52.95/8.05 reverse_line(v1) = v3 & left_apart_point(v0, v3) = v4 & $i(v3)))) & ! % 52.95/8.05 [v0: $i] : ! [v1: $i] : ( ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v1) | % 52.95/8.05 ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 & % 52.95/8.05 reverse_line(v1) = v3 & left_apart_point(v0, v3) = 0 & $i(v3)) | (v2 = 0 % 52.95/8.05 & left_apart_point(v0, v1) = 0))) % 52.95/8.05 % 52.95/8.05 (con) % 52.95/8.05 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: % 52.95/8.05 int] : ( ~ (v5 = 0) & ~ (v4 = 0) & parallel_through_point(v2, v0) = v3 & % 52.95/8.05 apart_point_and_line(v1, v3) = v4 & apart_point_and_line(v1, v2) = v5 & % 52.95/8.05 apart_point_and_line(v0, v2) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 52.95/8.05 % 52.95/8.05 (oag10) % 52.95/8.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (reverse_line(v1) = v2) | ~ % 52.95/8.05 (left_apart_point(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! % 52.95/8.05 [v1: $i] : ( ~ (left_apart_point(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)) % 52.95/8.05 % 52.95/8.05 Further assumptions not needed in the proof: % 52.95/8.05 -------------------------------------------- % 52.95/8.05 bet_def, bf_def, con_def, div_def, oag1, oag11, oag2, oag3, oag4, oag5, oag6, % 52.95/8.05 oag7, oag8, oag9, oagco1, oagco10, oagco2, oagco3, oagco4, oagco5, oagco6, % 52.95/8.05 oagco7, oagco8, oagco9, oagsub1, oagsub2, oagsub3, oaguc1, oaguc2 % 52.95/8.05 % 52.95/8.05 Those formulas are unsatisfiable: % 52.95/8.05 --------------------------------- % 52.95/8.05 % 52.95/8.05 Begin of proof % 52.95/8.05 | % 52.95/8.05 | ALPHA: (apt_def) implies: % 52.95/8.05 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (apart_point_and_line(v0, v1) = 0) | ~ % 52.95/8.05 | $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] : ((v4 % 52.95/8.05 | = 0 & reverse_line(v1) = v3 & left_apart_point(v0, v3) = 0 & % 52.95/8.05 | $i(v3)) | (v2 = 0 & left_apart_point(v0, v1) = 0))) % 52.95/8.06 | % 52.95/8.06 | ALPHA: (oag10) implies: % 52.95/8.06 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (left_apart_point(v0, v1) = 0) | ~ % 52.95/8.06 | $i(v1) | ~ $i(v0)) % 52.95/8.06 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (reverse_line(v1) = v2) | % 52.95/8.06 | ~ (left_apart_point(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 52.95/8.06 | % 52.95/8.06 | DELTA: instantiating (con) with fresh symbols all_34_0, all_34_1, all_34_2, % 52.95/8.06 | all_34_3, all_34_4, all_34_5 gives: % 52.95/8.06 | (4) ~ (all_34_0 = 0) & ~ (all_34_1 = 0) & % 52.95/8.06 | parallel_through_point(all_34_3, all_34_5) = all_34_2 & % 52.95/8.06 | apart_point_and_line(all_34_4, all_34_2) = all_34_1 & % 52.95/8.06 | apart_point_and_line(all_34_4, all_34_3) = all_34_0 & % 52.95/8.06 | apart_point_and_line(all_34_5, all_34_3) = 0 & $i(all_34_2) & % 52.95/8.06 | $i(all_34_3) & $i(all_34_4) & $i(all_34_5) % 52.95/8.06 | % 52.95/8.06 | ALPHA: (4) implies: % 52.95/8.06 | (5) $i(all_34_5) % 52.95/8.06 | (6) $i(all_34_3) % 52.95/8.06 | (7) apart_point_and_line(all_34_5, all_34_3) = 0 % 52.95/8.06 | % 53.21/8.06 | GROUND_INST: instantiating (1) with all_34_5, all_34_3, simplifying with (5), % 53.21/8.06 | (6), (7) gives: % 53.21/8.06 | (8) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v2 = 0 & % 53.21/8.06 | reverse_line(all_34_3) = v1 & left_apart_point(all_34_5, v1) = 0 & % 53.21/8.06 | $i(v1)) | (v0 = 0 & left_apart_point(all_34_5, all_34_3) = 0)) % 53.21/8.06 | % 53.21/8.06 | DELTA: instantiating (8) with fresh symbols all_45_0, all_45_1, all_45_2 % 53.21/8.06 | gives: % 53.21/8.06 | (9) (all_45_0 = 0 & reverse_line(all_34_3) = all_45_1 & % 53.21/8.06 | left_apart_point(all_34_5, all_45_1) = 0 & $i(all_45_1)) | (all_45_2 % 53.21/8.06 | = 0 & left_apart_point(all_34_5, all_34_3) = 0) % 53.21/8.06 | % 53.21/8.06 | BETA: splitting (9) gives: % 53.21/8.06 | % 53.21/8.06 | Case 1: % 53.21/8.06 | | % 53.21/8.06 | | (10) all_45_0 = 0 & reverse_line(all_34_3) = all_45_1 & % 53.21/8.06 | | left_apart_point(all_34_5, all_45_1) = 0 & $i(all_45_1) % 53.21/8.06 | | % 53.21/8.06 | | ALPHA: (10) implies: % 53.21/8.06 | | (11) left_apart_point(all_34_5, all_45_1) = 0 % 53.21/8.06 | | (12) reverse_line(all_34_3) = all_45_1 % 53.21/8.06 | | % 53.21/8.06 | | GROUND_INST: instantiating (3) with all_34_5, all_34_3, all_45_1, % 53.21/8.06 | | simplifying with (5), (6), (11), (12) gives: % 53.21/8.06 | | (13) $false % 53.21/8.07 | | % 53.21/8.07 | | CLOSE: (13) is inconsistent. % 53.21/8.07 | | % 53.21/8.07 | Case 2: % 53.21/8.07 | | % 53.21/8.07 | | (14) all_45_2 = 0 & left_apart_point(all_34_5, all_34_3) = 0 % 53.21/8.07 | | % 53.21/8.07 | | ALPHA: (14) implies: % 53.21/8.07 | | (15) left_apart_point(all_34_5, all_34_3) = 0 % 53.21/8.07 | | % 53.21/8.07 | | GROUND_INST: instantiating (2) with all_34_5, all_34_3, simplifying with % 53.21/8.07 | | (5), (6), (15) gives: % 53.21/8.07 | | (16) $false % 53.21/8.07 | | % 53.21/8.07 | | CLOSE: (16) is inconsistent. % 53.21/8.07 | | % 53.21/8.07 | End of split % 53.21/8.07 | % 53.21/8.07 End of proof % 53.21/8.07 % SZS output end Proof for theBenchmark % 53.21/8.07 % 53.21/8.07 7465ms %------------------------------------------------------------------------------