%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL953_8 : TPTP v9.3.1. Released v8.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n017.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 12:55:09 PM UTC 2026 % Result : Theorem 12.61s 2.46s % Output : Proof 17.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL953_8 : TPTP v9.3.1. Released v8.2.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.36 % Computer : n017.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Sat Sep 5 00:41:51 UTC 2026 % 0.10/0.36 % CPUTime : % 0.10/0.38 OpenJDK 64-Bit Server VM warning: Options -Xverify:none and -noverify were deprecated in JDK 13 and will likely be removed in a future release. % 0.66/0.72 ________ _____ % 0.66/0.72 ___ __ \_________(_)________________________________ % 0.66/0.72 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.66/0.72 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.66/0.72 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.66/0.72 % 0.66/0.72 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.66/0.72 (2023-06-19) % 0.66/0.72 % 0.66/0.72 (c) Philipp Rümmer, 2009-2023 % 0.66/0.72 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.66/0.72 Amanda Stjerna. % 0.66/0.72 Free software under BSD-3-Clause. % 0.66/0.72 % 0.66/0.72 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.66/0.72 % 0.66/0.72 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.66/0.74 Running up to 7 provers in parallel. % 0.66/0.75 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.66/0.76 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.66/0.76 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.66/0.76 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.66/0.76 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.66/0.76 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.66/0.76 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.19/1.29 Prover 4: Preprocessing ... % 4.01/1.30 Prover 1: Preprocessing ... % 4.01/1.31 Prover 5: Preprocessing ... % 4.01/1.31 Prover 6: Preprocessing ... % 4.01/1.31 Prover 2: Preprocessing ... % 4.01/1.31 Prover 0: Preprocessing ... % 4.01/1.33 Prover 3: Preprocessing ... % 6.38/1.65 Prover 5: Proving ... % 6.38/1.67 Prover 2: Proving ... % 8.70/1.96 Prover 3: Warning: ignoring some quantifiers % 8.70/1.96 Prover 3: Constructing countermodel ... % 8.70/1.98 Prover 1: Warning: ignoring some quantifiers % 8.70/1.99 Prover 4: Warning: ignoring some quantifiers % 8.70/1.99 Prover 6: Proving ... % 8.70/2.00 Prover 0: Proving ... % 8.70/2.04 Prover 1: Constructing countermodel ... % 9.92/2.08 Prover 4: Constructing countermodel ... % 12.61/2.45 Prover 2: proved (1698ms) % 12.61/2.45 % 12.61/2.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.61/2.46 % 12.61/2.46 Prover 3: stopped % 12.61/2.46 Prover 0: stopped % 12.61/2.47 Prover 6: stopped % 12.61/2.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.61/2.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.61/2.47 Prover 5: stopped % 12.61/2.47 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.61/2.47 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.61/2.47 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.38/2.54 Prover 7: Preprocessing ... % 13.38/2.58 Prover 13: Preprocessing ... % 13.38/2.58 Prover 7: Warning: ignoring some quantifiers % 13.38/2.59 Prover 7: Constructing countermodel ... % 14.16/2.60 Prover 11: Preprocessing ... % 14.16/2.61 Prover 8: Preprocessing ... % 14.16/2.63 Prover 10: Preprocessing ... % 14.16/2.66 Prover 13: Warning: ignoring some quantifiers % 14.16/2.67 Prover 13: Constructing countermodel ... % 15.01/2.72 Prover 10: Warning: ignoring some quantifiers % 15.01/2.74 Prover 10: Constructing countermodel ... % 15.75/2.82 Prover 8: Warning: ignoring some quantifiers % 15.75/2.83 Prover 8: Constructing countermodel ... % 16.54/2.90 Prover 10: Found proof (size 12) % 16.54/2.90 Prover 10: proved (441ms) % 16.54/2.91 Prover 7: stopped % 16.54/2.91 Prover 4: stopped % 16.54/2.91 Prover 11: Warning: ignoring some quantifiers % 16.54/2.91 Prover 13: stopped % 16.54/2.91 Prover 1: stopped % 16.54/2.91 Prover 8: stopped % 16.54/2.94 Prover 11: Constructing countermodel ... % 16.54/2.95 Prover 11: stopped % 16.54/2.95 % 16.54/2.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.54/2.95 % 16.54/2.95 % SZS output start Proof for theBenchmark % 16.54/2.96 Assumptions after simplification: % 16.54/2.96 --------------------------------- % 16.54/2.96 % 16.54/2.96 (l28_zfmisc_1) % 16.54/3.01 $ki_world($ki_local_world) & ! [v0: $ki_world] : ! [v1: $i] : ! [v2: $i] : % 16.54/3.01 ! [v3: $ki_world] : ! [v4: $i] : ! [v5: $ki_world] : ! [v6: $ki_world] : ( % 16.54/3.01 ~ (singleton(v1) = v2) | ~ $ki_world(v6) | ~ $ki_world(v5) | ~ % 16.54/3.01 $ki_world(v3) | ~ $ki_world(v0) | ~ $i(v4) | ~ $i(v1) | ~ % 16.54/3.01 $ki_exists_in_world_$i(v3, v4) | ~ $ki_exists_in_world_$i(v0, v1) | ~ % 16.54/3.01 $ki_accessible(v5, v6) | ~ $ki_accessible(v3, v5) | ~ $ki_accessible(v0, % 16.54/3.01 v3) | ~ $ki_accessible($ki_local_world, v0) | disjoint(v6, v2, v4) | ? % 16.54/3.01 [v7: $ki_world] : ($ki_world(v7) & $ki_accessible(v5, v7) & ! [v8: % 16.54/3.01 $ki_world] : ( ~ $ki_world(v8) | ~ $ki_accessible(v7, v8) | in(v8, v1, % 16.54/3.01 v4)))) % 16.54/3.01 % 16.54/3.01 (verify) % 16.54/3.02 $ki_world($ki_local_world) & ? [v0: $ki_world] : ? [v1: $i] : ? [v2: $i] : % 16.54/3.02 ? [v3: $ki_world] : ? [v4: $i] : ? [v5: $ki_world] : ? [v6: $ki_world] : % 16.54/3.02 (singleton(v1) = v2 & $ki_world(v6) & $ki_world(v5) & $ki_world(v3) & % 16.54/3.02 $ki_world(v0) & $i(v4) & $i(v2) & $i(v1) & $ki_exists_in_world_$i(v3, v4) & % 16.54/3.02 $ki_exists_in_world_$i(v0, v1) & $ki_accessible(v5, v6) & $ki_accessible(v3, % 16.54/3.02 v5) & $ki_accessible(v0, v3) & $ki_accessible($ki_local_world, v0) & ~ % 16.54/3.02 disjoint(v6, v2, v4) & ! [v7: $ki_world] : ( ~ $ki_world(v7) | ~ % 16.54/3.02 $ki_accessible(v5, v7) | ? [v8: $ki_world] : ($ki_world(v8) & % 16.54/3.02 $ki_accessible(v7, v8) & ~ in(v8, v1, v4)))) % 16.54/3.02 % 16.54/3.02 Further assumptions not needed in the proof: % 16.54/3.02 -------------------------------------------- % 16.54/3.02 $ki_exists_in_world_$i_nonempty, antisymmetry_r2_hidden, mrel_reflexive, % 16.54/3.02 rc1_xboole_0, rc2_xboole_0, symmetry_r1_xboole_0 % 16.54/3.02 % 16.54/3.02 Those formulas are unsatisfiable: % 16.54/3.02 --------------------------------- % 16.54/3.02 % 16.54/3.02 Begin of proof % 16.54/3.02 | % 16.54/3.02 | ALPHA: (l28_zfmisc_1) implies: % 17.20/3.03 | (1) ! [v0: $ki_world] : ! [v1: $i] : ! [v2: $i] : ! [v3: $ki_world] : % 17.20/3.03 | ! [v4: $i] : ! [v5: $ki_world] : ! [v6: $ki_world] : ( ~ % 17.20/3.03 | (singleton(v1) = v2) | ~ $ki_world(v6) | ~ $ki_world(v5) | ~ % 17.20/3.03 | $ki_world(v3) | ~ $ki_world(v0) | ~ $i(v4) | ~ $i(v1) | ~ % 17.20/3.03 | $ki_exists_in_world_$i(v3, v4) | ~ $ki_exists_in_world_$i(v0, v1) | % 17.20/3.03 | ~ $ki_accessible(v5, v6) | ~ $ki_accessible(v3, v5) | ~ % 17.20/3.03 | $ki_accessible(v0, v3) | ~ $ki_accessible($ki_local_world, v0) | % 17.20/3.03 | disjoint(v6, v2, v4) | ? [v7: $ki_world] : ($ki_world(v7) & % 17.20/3.03 | $ki_accessible(v5, v7) & ! [v8: $ki_world] : ( ~ $ki_world(v8) | % 17.20/3.03 | ~ $ki_accessible(v7, v8) | in(v8, v1, v4)))) % 17.20/3.03 | % 17.20/3.03 | ALPHA: (verify) implies: % 17.20/3.04 | (2) ? [v0: $ki_world] : ? [v1: $i] : ? [v2: $i] : ? [v3: $ki_world] : % 17.20/3.04 | ? [v4: $i] : ? [v5: $ki_world] : ? [v6: $ki_world] : (singleton(v1) = % 17.20/3.04 | v2 & $ki_world(v6) & $ki_world(v5) & $ki_world(v3) & $ki_world(v0) & % 17.20/3.04 | $i(v4) & $i(v2) & $i(v1) & $ki_exists_in_world_$i(v3, v4) & % 17.20/3.04 | $ki_exists_in_world_$i(v0, v1) & $ki_accessible(v5, v6) & % 17.20/3.04 | $ki_accessible(v3, v5) & $ki_accessible(v0, v3) & % 17.20/3.04 | $ki_accessible($ki_local_world, v0) & ~ disjoint(v6, v2, v4) & ! % 17.20/3.04 | [v7: $ki_world] : ( ~ $ki_world(v7) | ~ $ki_accessible(v5, v7) | ? % 17.20/3.04 | [v8: $ki_world] : ($ki_world(v8) & $ki_accessible(v7, v8) & ~ % 17.20/3.04 | in(v8, v1, v4)))) % 17.20/3.04 | % 17.20/3.04 | DELTA: instantiating (2) with fresh symbols all_17_0, all_17_1, all_17_2, % 17.20/3.04 | all_17_3, all_17_4, all_17_5, all_17_6 gives: % 17.20/3.05 | (3) singleton(all_17_5) = all_17_4 & $ki_world(all_17_0) & % 17.20/3.05 | $ki_world(all_17_1) & $ki_world(all_17_3) & $ki_world(all_17_6) & % 17.20/3.05 | $i(all_17_2) & $i(all_17_4) & $i(all_17_5) & % 17.20/3.05 | $ki_exists_in_world_$i(all_17_3, all_17_2) & % 17.20/3.05 | $ki_exists_in_world_$i(all_17_6, all_17_5) & $ki_accessible(all_17_1, % 17.20/3.05 | all_17_0) & $ki_accessible(all_17_3, all_17_1) & % 17.20/3.05 | $ki_accessible(all_17_6, all_17_3) & $ki_accessible($ki_local_world, % 17.20/3.05 | all_17_6) & ~ disjoint(all_17_0, all_17_4, all_17_2) & ! [v0: % 17.20/3.05 | $ki_world] : ( ~ $ki_world(v0) | ~ $ki_accessible(all_17_1, v0) | ? % 17.20/3.05 | [v1: $ki_world] : ($ki_world(v1) & $ki_accessible(v0, v1) & ~ in(v1, % 17.20/3.05 | all_17_5, all_17_2))) % 17.20/3.05 | % 17.20/3.05 | ALPHA: (3) implies: % 17.20/3.05 | (4) ~ disjoint(all_17_0, all_17_4, all_17_2) % 17.20/3.05 | (5) $ki_accessible($ki_local_world, all_17_6) % 17.20/3.05 | (6) $ki_accessible(all_17_6, all_17_3) % 17.20/3.05 | (7) $ki_accessible(all_17_3, all_17_1) % 17.20/3.05 | (8) $ki_accessible(all_17_1, all_17_0) % 17.20/3.05 | (9) $ki_exists_in_world_$i(all_17_6, all_17_5) % 17.20/3.05 | (10) $ki_exists_in_world_$i(all_17_3, all_17_2) % 17.20/3.05 | (11) $i(all_17_5) % 17.20/3.05 | (12) $i(all_17_2) % 17.20/3.05 | (13) $ki_world(all_17_6) % 17.20/3.05 | (14) $ki_world(all_17_3) % 17.20/3.05 | (15) $ki_world(all_17_1) % 17.20/3.05 | (16) $ki_world(all_17_0) % 17.20/3.05 | (17) singleton(all_17_5) = all_17_4 % 17.20/3.06 | (18) ! [v0: $ki_world] : ( ~ $ki_world(v0) | ~ $ki_accessible(all_17_1, % 17.20/3.06 | v0) | ? [v1: $ki_world] : ($ki_world(v1) & $ki_accessible(v0, v1) % 17.20/3.06 | & ~ in(v1, all_17_5, all_17_2))) % 17.20/3.06 | % 17.20/3.06 | GROUND_INST: instantiating (1) with all_17_6, all_17_5, all_17_4, all_17_3, % 17.20/3.06 | all_17_2, all_17_1, all_17_0, simplifying with (4), (5), (6), % 17.20/3.06 | (7), (8), (9), (10), (11), (12), (13), (14), (15), (16), (17) % 17.20/3.06 | gives: % 17.20/3.06 | (19) ? [v0: $ki_world] : ($ki_world(v0) & $ki_accessible(all_17_1, v0) & % 17.20/3.06 | ! [v1: $ki_world] : ( ~ $ki_world(v1) | ~ $ki_accessible(v0, v1) | % 17.20/3.06 | in(v1, all_17_5, all_17_2))) % 17.20/3.06 | % 17.20/3.06 | DELTA: instantiating (19) with fresh symbol all_30_0 gives: % 17.20/3.06 | (20) $ki_world(all_30_0) & $ki_accessible(all_17_1, all_30_0) & ! [v0: % 17.20/3.06 | $ki_world] : ( ~ $ki_world(v0) | ~ $ki_accessible(all_30_0, v0) | % 17.20/3.06 | in(v0, all_17_5, all_17_2)) % 17.20/3.06 | % 17.20/3.06 | ALPHA: (20) implies: % 17.20/3.06 | (21) $ki_accessible(all_17_1, all_30_0) % 17.20/3.06 | (22) $ki_world(all_30_0) % 17.20/3.06 | (23) ! [v0: $ki_world] : ( ~ $ki_world(v0) | ~ $ki_accessible(all_30_0, % 17.20/3.06 | v0) | in(v0, all_17_5, all_17_2)) % 17.20/3.06 | % 17.20/3.06 | GROUND_INST: instantiating (18) with all_30_0, simplifying with (21), (22) % 17.20/3.06 | gives: % 17.20/3.07 | (24) ? [v0: $ki_world] : ($ki_world(v0) & $ki_accessible(all_30_0, v0) & % 17.20/3.07 | ~ in(v0, all_17_5, all_17_2)) % 17.20/3.07 | % 17.20/3.07 | DELTA: instantiating (24) with fresh symbol all_40_0 gives: % 17.20/3.07 | (25) $ki_world(all_40_0) & $ki_accessible(all_30_0, all_40_0) & ~ % 17.20/3.07 | in(all_40_0, all_17_5, all_17_2) % 17.20/3.07 | % 17.20/3.07 | ALPHA: (25) implies: % 17.20/3.07 | (26) ~ in(all_40_0, all_17_5, all_17_2) % 17.20/3.07 | (27) $ki_accessible(all_30_0, all_40_0) % 17.20/3.07 | (28) $ki_world(all_40_0) % 17.20/3.07 | % 17.20/3.07 | GROUND_INST: instantiating (23) with all_40_0, simplifying with (26), (27), % 17.20/3.07 | (28) gives: % 17.20/3.07 | (29) $false % 17.20/3.07 | % 17.20/3.07 | CLOSE: (29) is inconsistent. % 17.20/3.07 | % 17.20/3.07 End of proof % 17.20/3.07 % SZS output end Proof for theBenchmark % 17.20/3.07 % 17.20/3.07 2350ms %------------------------------------------------------------------------------