%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET803+4 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n016.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 : Thu Aug 31 15:26:30 EDT 2023 % Result : Theorem 7.63s 1.79s % Output : Proof 10.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET803+4 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n016.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sat Aug 26 15:44:57 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 % 2.48/1.11 Prover 1: Preprocessing ... % 2.48/1.11 Prover 4: Preprocessing ... % 3.10/1.14 Prover 5: Preprocessing ... % 3.10/1.14 Prover 2: Preprocessing ... % 3.10/1.14 Prover 3: Preprocessing ... % 3.10/1.14 Prover 6: Preprocessing ... % 3.10/1.14 Prover 0: Preprocessing ... % 4.42/1.48 Prover 5: Proving ... % 5.01/1.51 Prover 2: Proving ... % 6.83/1.66 Prover 3: Constructing countermodel ... % 6.83/1.66 Prover 6: Proving ... % 6.83/1.67 Prover 1: Constructing countermodel ... % 7.31/1.76 Prover 4: Constructing countermodel ... % 7.31/1.76 Prover 3: gave up % 7.31/1.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.63/1.78 Prover 1: gave up % 7.63/1.79 Prover 5: proved (1140ms) % 7.63/1.79 % 7.63/1.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.63/1.79 % 7.63/1.80 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.63/1.80 Prover 2: proved (1151ms) % 7.63/1.80 % 7.63/1.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.63/1.80 % 7.63/1.82 Prover 7: Preprocessing ... % 7.63/1.82 Prover 6: stopped % 7.63/1.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.63/1.83 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.63/1.83 Prover 0: Proving ... % 7.63/1.83 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.19/1.86 Prover 0: stopped % 8.19/1.87 Prover 8: Preprocessing ... % 8.40/1.88 Prover 7: Warning: ignoring some quantifiers % 8.40/1.88 Prover 10: Preprocessing ... % 8.40/1.88 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.40/1.89 Prover 7: Constructing countermodel ... % 8.40/1.91 Prover 13: Preprocessing ... % 8.40/1.91 Prover 11: Preprocessing ... % 8.40/1.93 Prover 16: Preprocessing ... % 8.82/1.95 Prover 10: Warning: ignoring some quantifiers % 8.98/1.96 Prover 10: Constructing countermodel ... % 8.98/1.97 Prover 13: Warning: ignoring some quantifiers % 8.98/1.99 Prover 13: Constructing countermodel ... % 8.98/1.99 Prover 16: Warning: ignoring some quantifiers % 8.98/2.01 Prover 8: Warning: ignoring some quantifiers % 8.98/2.01 Prover 16: Constructing countermodel ... % 9.49/2.02 Prover 8: Constructing countermodel ... % 9.49/2.09 Prover 7: Found proof (size 14) % 9.49/2.09 Prover 7: proved (331ms) % 9.49/2.09 Prover 8: stopped % 9.49/2.09 Prover 13: stopped % 9.49/2.09 Prover 4: stopped % 9.49/2.09 Prover 10: Found proof (size 14) % 9.49/2.09 Prover 10: proved (292ms) % 9.49/2.10 Prover 16: stopped % 9.49/2.15 Prover 11: Constructing countermodel ... % 9.49/2.16 Prover 11: stopped % 9.49/2.16 % 9.49/2.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.49/2.16 % 9.49/2.17 % SZS output start Proof for theBenchmark % 9.49/2.17 Assumptions after simplification: % 9.49/2.17 --------------------------------- % 9.49/2.17 % 9.49/2.17 (greatest) % 10.09/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) % 10.09/2.18 | ~ $i(v1) | ~ $i(v0) | ~ greatest(v2, v0, v1) | ~ member(v3, v1) | % 10.09/2.18 apply(v0, v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | % 10.09/2.18 ~ $i(v1) | ~ $i(v0) | ~ greatest(v2, v0, v1) | member(v2, v1)) & ? [v0: % 10.09/2.18 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 10.09/2.18 member(v2, v1) | greatest(v2, v0, v1) | ? [v3: $i] : ($i(v3) & member(v3, % 10.09/2.18 v1) & ~ apply(v0, v3, v2))) % 10.09/2.18 % 10.09/2.18 (max) % 10.09/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ $i(v3) | % 10.09/2.19 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ max(v2, v0, v1) | ~ apply(v0, v2, % 10.09/2.19 v3) | ~ member(v3, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 10.09/2.19 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ max(v2, v0, v1) | member(v2, v1)) & ? % 10.09/2.19 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 10.09/2.19 member(v2, v1) | max(v2, v0, v1) | ? [v3: $i] : ( ~ (v3 = v2) & $i(v3) & % 10.09/2.19 apply(v0, v2, v3) & member(v3, v1))) % 10.09/2.19 % 10.09/2.19 (thIV15) % 10.09/2.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v3 % 10.09/2.19 = v2) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & max(v3, v0, v1) & % 10.09/2.19 max(v2, v0, v1) & greatest(v4, v0, v1) & order(v0, v1)) % 10.09/2.19 % 10.09/2.19 Further assumptions not needed in the proof: % 10.09/2.19 -------------------------------------------- % 10.09/2.19 greatest_lower_bound, least, least_upper_bound, lower_bound, min, order, % 10.09/2.19 total_order, upper_bound % 10.09/2.19 % 10.09/2.19 Those formulas are unsatisfiable: % 10.09/2.19 --------------------------------- % 10.09/2.19 % 10.09/2.19 Begin of proof % 10.09/2.19 | % 10.09/2.19 | ALPHA: (max) implies: % 10.09/2.20 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 10.09/2.20 | $i(v0) | ~ max(v2, v0, v1) | member(v2, v1)) % 10.09/2.20 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 10.09/2.20 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ max(v2, v0, v1) | ~ % 10.09/2.20 | apply(v0, v2, v3) | ~ member(v3, v1)) % 10.09/2.20 | % 10.09/2.20 | ALPHA: (greatest) implies: % 10.09/2.20 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 10.09/2.20 | $i(v0) | ~ greatest(v2, v0, v1) | member(v2, v1)) % 10.09/2.20 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 10.09/2.20 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ greatest(v2, v0, v1) | ~ % 10.09/2.20 | member(v3, v1) | apply(v0, v3, v2)) % 10.09/2.20 | % 10.09/2.20 | DELTA: instantiating (thIV15) with fresh symbols all_22_0, all_22_1, all_22_2, % 10.09/2.20 | all_22_3, all_22_4 gives: % 10.09/2.20 | (5) ~ (all_22_1 = all_22_2) & $i(all_22_0) & $i(all_22_1) & $i(all_22_2) & % 10.09/2.20 | $i(all_22_3) & $i(all_22_4) & max(all_22_1, all_22_4, all_22_3) & % 10.09/2.20 | max(all_22_2, all_22_4, all_22_3) & greatest(all_22_0, all_22_4, % 10.09/2.20 | all_22_3) & order(all_22_4, all_22_3) % 10.09/2.20 | % 10.09/2.20 | ALPHA: (5) implies: % 10.09/2.21 | (6) ~ (all_22_1 = all_22_2) % 10.09/2.21 | (7) greatest(all_22_0, all_22_4, all_22_3) % 10.09/2.21 | (8) max(all_22_2, all_22_4, all_22_3) % 10.09/2.21 | (9) max(all_22_1, all_22_4, all_22_3) % 10.09/2.21 | (10) $i(all_22_4) % 10.09/2.21 | (11) $i(all_22_3) % 10.09/2.21 | (12) $i(all_22_2) % 10.09/2.21 | (13) $i(all_22_1) % 10.09/2.21 | (14) $i(all_22_0) % 10.09/2.21 | % 10.09/2.21 | GROUND_INST: instantiating (3) with all_22_4, all_22_3, all_22_0, simplifying % 10.09/2.21 | with (7), (10), (11), (14) gives: % 10.09/2.21 | (15) member(all_22_0, all_22_3) % 10.09/2.21 | % 10.09/2.21 | GROUND_INST: instantiating (1) with all_22_4, all_22_3, all_22_2, simplifying % 10.09/2.21 | with (8), (10), (11), (12) gives: % 10.09/2.21 | (16) member(all_22_2, all_22_3) % 10.09/2.21 | % 10.09/2.21 | GROUND_INST: instantiating (1) with all_22_4, all_22_3, all_22_1, simplifying % 10.09/2.21 | with (9), (10), (11), (13) gives: % 10.09/2.21 | (17) member(all_22_1, all_22_3) % 10.09/2.21 | % 10.09/2.21 | GROUND_INST: instantiating (4) with all_22_4, all_22_3, all_22_0, all_22_2, % 10.09/2.21 | simplifying with (7), (10), (11), (12), (14), (16) gives: % 10.09/2.21 | (18) apply(all_22_4, all_22_2, all_22_0) % 10.09/2.21 | % 10.09/2.21 | GROUND_INST: instantiating (4) with all_22_4, all_22_3, all_22_0, all_22_1, % 10.09/2.21 | simplifying with (7), (10), (11), (13), (14), (17) gives: % 10.09/2.21 | (19) apply(all_22_4, all_22_1, all_22_0) % 10.09/2.21 | % 10.09/2.21 | GROUND_INST: instantiating (2) with all_22_4, all_22_3, all_22_2, all_22_0, % 10.09/2.21 | simplifying with (8), (10), (11), (12), (14), (15), (18) gives: % 10.09/2.22 | (20) all_22_0 = all_22_2 % 10.09/2.22 | % 10.09/2.22 | GROUND_INST: instantiating (2) with all_22_4, all_22_3, all_22_1, all_22_0, % 10.09/2.22 | simplifying with (9), (10), (11), (13), (14), (15), (19) gives: % 10.09/2.22 | (21) all_22_0 = all_22_1 % 10.09/2.22 | % 10.09/2.22 | COMBINE_EQS: (20), (21) imply: % 10.09/2.22 | (22) all_22_1 = all_22_2 % 10.09/2.22 | % 10.09/2.22 | REDUCE: (6), (22) imply: % 10.09/2.22 | (23) $false % 10.09/2.22 | % 10.09/2.22 | CLOSE: (23) is inconsistent. % 10.09/2.22 | % 10.09/2.22 End of proof % 10.09/2.22 % SZS output end Proof for theBenchmark % 10.09/2.22 % 10.09/2.22 1601ms %------------------------------------------------------------------------------