%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO220+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 : n029.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 23:22:29 EDT 2023 % Result : Theorem 5.86s 1.46s % Output : Proof 8.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : GEO220+1 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.31 % Computer : n029.cluster.edu % 0.12/0.31 % Model : x86_64 x86_64 % 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.31 % Memory : 8042.1875MB % 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.31 % CPULimit : 300 % 0.12/0.31 % WCLimit : 300 % 0.12/0.31 % DateTime : Tue Aug 29 22:17:42 EDT 2023 % 0.12/0.31 % CPUTime : % 0.17/0.51 ________ _____ % 0.17/0.52 ___ __ \_________(_)________________________________ % 0.17/0.52 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.52 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.52 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.52 % 0.17/0.52 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.52 (2023-06-19) % 0.17/0.52 % 0.17/0.52 (c) Philipp Rümmer, 2009-2023 % 0.17/0.52 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.52 Amanda Stjerna. % 0.17/0.52 Free software under BSD-3-Clause. % 0.17/0.52 % 0.17/0.52 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.52 % 0.17/0.52 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.17/0.53 Running up to 7 provers in parallel. % 0.59/0.54 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.59/0.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.59/0.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.59/0.54 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.59/0.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.59/0.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.59/0.54 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.69/1.01 Prover 4: Preprocessing ... % 2.69/1.01 Prover 1: Preprocessing ... % 3.13/1.05 Prover 5: Preprocessing ... % 3.13/1.05 Prover 3: Preprocessing ... % 3.13/1.06 Prover 2: Preprocessing ... % 3.13/1.06 Prover 6: Preprocessing ... % 3.31/1.07 Prover 0: Preprocessing ... % 4.72/1.28 Prover 5: Proving ... % 4.72/1.31 Prover 2: Proving ... % 5.18/1.34 Prover 1: Constructing countermodel ... % 5.18/1.35 Prover 3: Constructing countermodel ... % 5.38/1.37 Prover 6: Constructing countermodel ... % 5.86/1.46 Prover 6: proved (917ms) % 5.86/1.46 % 5.86/1.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.86/1.46 % 5.86/1.46 Prover 3: proved (924ms) % 5.86/1.46 % 5.86/1.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.86/1.46 % 5.86/1.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.86/1.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.14/1.47 Prover 5: stopped % 6.14/1.47 Prover 2: stopped % 6.14/1.48 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.14/1.48 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.14/1.50 Prover 7: Preprocessing ... % 6.14/1.51 Prover 8: Preprocessing ... % 6.14/1.52 Prover 10: Preprocessing ... % 6.14/1.52 Prover 11: Preprocessing ... % 6.68/1.55 Prover 0: Proving ... % 6.68/1.55 Prover 4: Constructing countermodel ... % 6.68/1.56 Prover 0: stopped % 6.68/1.56 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.68/1.56 Prover 10: Warning: ignoring some quantifiers % 6.68/1.57 Prover 10: Constructing countermodel ... % 6.95/1.57 Prover 7: Warning: ignoring some quantifiers % 6.95/1.58 Prover 7: Constructing countermodel ... % 6.95/1.60 Prover 8: Warning: ignoring some quantifiers % 6.95/1.60 Prover 13: Preprocessing ... % 6.95/1.61 Prover 8: Constructing countermodel ... % 7.51/1.66 Prover 10: gave up % 7.69/1.68 Prover 1: Found proof (size 24) % 7.69/1.68 Prover 1: proved (1147ms) % 7.69/1.68 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.69/1.68 Prover 4: stopped % 7.69/1.68 Prover 8: stopped % 7.69/1.68 Prover 13: Warning: ignoring some quantifiers % 7.69/1.68 Prover 7: stopped % 7.69/1.69 Prover 13: Constructing countermodel ... % 7.69/1.70 Prover 13: stopped % 7.69/1.70 Prover 16: Preprocessing ... % 7.69/1.72 Prover 16: stopped % 8.23/1.76 Prover 11: Constructing countermodel ... % 8.23/1.78 Prover 11: stopped % 8.23/1.78 % 8.23/1.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.23/1.78 % 8.23/1.78 % SZS output start Proof for theBenchmark % 8.23/1.78 Assumptions after simplification: % 8.23/1.78 --------------------------------- % 8.23/1.78 % 8.23/1.78 (con) % 8.23/1.81 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ( ~ % 8.23/1.81 (v4 = 0) & ~ (v3 = 0) & unorthogonal_lines(v0, v2) = v4 & % 8.23/1.81 unorthogonal_lines(v0, v1) = v3 & convergent_lines(v1, v2) = 0 & $i(v2) & % 8.23/1.81 $i(v1) & $i(v0)) % 8.23/1.81 % 8.23/1.81 (cotno1) % 8.23/1.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 8.23/1.81 (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | % 8.23/1.81 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: % 8.23/1.81 any] : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 & % 8.23/1.81 convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & % 8.23/1.81 convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 % 8.23/1.81 = 0) | (v5 = 0 & v3 = 0)))) % 8.23/1.81 % 8.23/1.82 (couo1) % 8.23/1.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 8.23/1.82 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 8.23/1.82 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 8.23/1.82 [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) % 8.23/1.82 % 8.23/1.82 (function-axioms) % 8.23/1.82 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.55/1.82 [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ % 8.55/1.82 (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 8.55/1.82 : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 8.55/1.82 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 8.55/1.82 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 8.55/1.83 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.55/1.83 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.55/1.83 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 8.55/1.83 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.55/1.83 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 8.55/1.83 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.55/1.83 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.55/1.83 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 8.55/1.83 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 8.55/1.83 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 8.55/1.83 v0)) % 8.55/1.83 % 8.55/1.83 Further assumptions not needed in the proof: % 8.55/1.83 -------------------------------------------- % 8.55/1.83 apart1, apart2, apart3, apart4, apart5, ax6, ceq1, ceq2, ceq3, ci1, ci2, ci3, % 8.55/1.83 ci4, coipo1, cu1 % 8.55/1.83 % 8.55/1.83 Those formulas are unsatisfiable: % 8.55/1.83 --------------------------------- % 8.55/1.83 % 8.55/1.83 Begin of proof % 8.55/1.83 | % 8.55/1.83 | ALPHA: (function-axioms) implies: % 8.55/1.83 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.55/1.83 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 8.55/1.83 | (convergent_lines(v3, v2) = v0)) % 8.55/1.83 | % 8.55/1.83 | DELTA: instantiating (con) with fresh symbols all_20_0, all_20_1, all_20_2, % 8.55/1.83 | all_20_3, all_20_4 gives: % 8.55/1.83 | (2) ~ (all_20_0 = 0) & ~ (all_20_1 = 0) & unorthogonal_lines(all_20_4, % 8.55/1.83 | all_20_2) = all_20_0 & unorthogonal_lines(all_20_4, all_20_3) = % 8.55/1.83 | all_20_1 & convergent_lines(all_20_3, all_20_2) = 0 & $i(all_20_2) & % 8.55/1.83 | $i(all_20_3) & $i(all_20_4) % 8.55/1.83 | % 8.55/1.83 | ALPHA: (2) implies: % 8.55/1.83 | (3) ~ (all_20_1 = 0) % 8.55/1.83 | (4) ~ (all_20_0 = 0) % 8.55/1.83 | (5) $i(all_20_4) % 8.55/1.83 | (6) $i(all_20_3) % 8.55/1.83 | (7) $i(all_20_2) % 8.55/1.83 | (8) convergent_lines(all_20_3, all_20_2) = 0 % 8.55/1.83 | (9) unorthogonal_lines(all_20_4, all_20_3) = all_20_1 % 8.55/1.84 | (10) unorthogonal_lines(all_20_4, all_20_2) = all_20_0 % 8.55/1.84 | % 8.55/1.84 | GROUND_INST: instantiating (couo1) with all_20_4, all_20_3, all_20_2, % 8.55/1.84 | all_20_1, all_20_0, simplifying with (5), (6), (7), (9), (10) % 8.55/1.84 | gives: % 8.55/1.84 | (11) all_20_0 = 0 | all_20_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 8.55/1.84 | convergent_lines(all_20_3, all_20_2) = v0) % 8.55/1.84 | % 8.55/1.84 | GROUND_INST: instantiating (cotno1) with all_20_4, all_20_3, all_20_2, % 8.55/1.84 | all_20_1, all_20_0, simplifying with (5), (6), (7), (9), (10) % 8.55/1.84 | gives: % 8.55/1.84 | (12) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 8.55/1.84 | (unorthogonal_lines(all_20_3, all_20_2) = v3 & % 8.55/1.84 | convergent_lines(all_20_3, all_20_2) = v2 & % 8.55/1.84 | convergent_lines(all_20_4, all_20_2) = v1 & % 8.55/1.84 | convergent_lines(all_20_4, all_20_3) = v0 & ( ~ (v3 = 0) | ~ (v2 = % 8.55/1.84 | 0) | (v1 = 0 & all_20_0 = 0) | (v0 = 0 & all_20_1 = 0))) % 8.55/1.84 | % 8.55/1.84 | DELTA: instantiating (12) with fresh symbols all_29_0, all_29_1, all_29_2, % 8.55/1.84 | all_29_3 gives: % 8.55/1.84 | (13) unorthogonal_lines(all_20_3, all_20_2) = all_29_0 & % 8.55/1.84 | convergent_lines(all_20_3, all_20_2) = all_29_1 & % 8.55/1.84 | convergent_lines(all_20_4, all_20_2) = all_29_2 & % 8.55/1.84 | convergent_lines(all_20_4, all_20_3) = all_29_3 & ( ~ (all_29_0 = 0) | % 8.55/1.84 | ~ (all_29_1 = 0) | (all_29_2 = 0 & all_20_0 = 0) | (all_29_3 = 0 & % 8.55/1.84 | all_20_1 = 0)) % 8.55/1.84 | % 8.55/1.84 | ALPHA: (13) implies: % 8.55/1.84 | (14) convergent_lines(all_20_3, all_20_2) = all_29_1 % 8.55/1.84 | % 8.55/1.84 | BETA: splitting (11) gives: % 8.55/1.84 | % 8.55/1.84 | Case 1: % 8.55/1.84 | | % 8.55/1.84 | | (15) all_20_0 = 0 % 8.55/1.84 | | % 8.55/1.84 | | REDUCE: (4), (15) imply: % 8.55/1.84 | | (16) $false % 8.55/1.84 | | % 8.55/1.84 | | CLOSE: (16) is inconsistent. % 8.55/1.84 | | % 8.55/1.84 | Case 2: % 8.55/1.84 | | % 8.55/1.84 | | (17) all_20_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 8.55/1.84 | | convergent_lines(all_20_3, all_20_2) = v0) % 8.55/1.84 | | % 8.55/1.84 | | BETA: splitting (17) gives: % 8.55/1.84 | | % 8.55/1.84 | | Case 1: % 8.55/1.84 | | | % 8.55/1.84 | | | (18) all_20_1 = 0 % 8.55/1.84 | | | % 8.55/1.84 | | | REDUCE: (3), (18) imply: % 8.55/1.84 | | | (19) $false % 8.55/1.84 | | | % 8.55/1.84 | | | CLOSE: (19) is inconsistent. % 8.55/1.84 | | | % 8.55/1.84 | | Case 2: % 8.55/1.84 | | | % 8.55/1.84 | | | (20) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_20_3, all_20_2) % 8.55/1.84 | | | = v0) % 8.55/1.84 | | | % 8.55/1.85 | | | DELTA: instantiating (20) with fresh symbol all_67_0 gives: % 8.55/1.85 | | | (21) ~ (all_67_0 = 0) & convergent_lines(all_20_3, all_20_2) = % 8.55/1.85 | | | all_67_0 % 8.55/1.85 | | | % 8.55/1.85 | | | ALPHA: (21) implies: % 8.55/1.85 | | | (22) ~ (all_67_0 = 0) % 8.55/1.85 | | | (23) convergent_lines(all_20_3, all_20_2) = all_67_0 % 8.55/1.85 | | | % 8.55/1.85 | | | GROUND_INST: instantiating (1) with 0, all_67_0, all_20_2, all_20_3, % 8.55/1.85 | | | simplifying with (8), (23) gives: % 8.55/1.85 | | | (24) all_67_0 = 0 % 8.55/1.85 | | | % 8.55/1.85 | | | GROUND_INST: instantiating (1) with all_29_1, all_67_0, all_20_2, % 8.55/1.85 | | | all_20_3, simplifying with (14), (23) gives: % 8.55/1.85 | | | (25) all_67_0 = all_29_1 % 8.55/1.85 | | | % 8.55/1.85 | | | COMBINE_EQS: (24), (25) imply: % 8.55/1.85 | | | (26) all_29_1 = 0 % 8.55/1.85 | | | % 8.55/1.85 | | | REDUCE: (22), (24) imply: % 8.55/1.85 | | | (27) $false % 8.55/1.85 | | | % 8.55/1.85 | | | CLOSE: (27) is inconsistent. % 8.55/1.85 | | | % 8.55/1.85 | | End of split % 8.55/1.85 | | % 8.55/1.85 | End of split % 8.55/1.85 | % 8.55/1.85 End of proof % 8.55/1.85 % SZS output end Proof for theBenchmark % 8.55/1.85 % 8.55/1.85 1331ms %------------------------------------------------------------------------------