%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET804+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 : n012.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 15:26:31 EDT 2023 % Result : Theorem 7.46s 1.72s % Output : Proof 9.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET804+4 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n012.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 : Sat Aug 26 12:14:26 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.67/1.06 Prover 4: Preprocessing ... % 2.67/1.06 Prover 1: Preprocessing ... % 3.14/1.10 Prover 2: Preprocessing ... % 3.14/1.10 Prover 3: Preprocessing ... % 3.14/1.10 Prover 6: Preprocessing ... % 3.14/1.10 Prover 0: Preprocessing ... % 3.14/1.11 Prover 5: Preprocessing ... % 5.31/1.44 Prover 5: Proving ... % 5.31/1.48 Prover 2: Proving ... % 5.31/1.55 Prover 6: Proving ... % 6.05/1.58 Prover 1: Constructing countermodel ... % 6.05/1.59 Prover 3: Constructing countermodel ... % 7.21/1.69 Prover 1: gave up % 7.21/1.69 Prover 3: gave up % 7.21/1.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.21/1.70 Prover 0: Proving ... % 7.21/1.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.46/1.72 Prover 4: Constructing countermodel ... % 7.46/1.72 Prover 5: proved (1081ms) % 7.46/1.72 % 7.46/1.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.46/1.72 % 7.46/1.73 Prover 0: stopped % 7.46/1.73 Prover 2: stopped % 7.65/1.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.65/1.73 Prover 6: stopped % 7.65/1.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.65/1.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.65/1.75 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.65/1.75 Prover 7: Preprocessing ... % 7.65/1.75 Prover 8: Preprocessing ... % 7.65/1.79 Prover 16: Preprocessing ... % 7.65/1.79 Prover 11: Preprocessing ... % 7.65/1.80 Prover 10: Preprocessing ... % 7.65/1.80 Prover 13: Preprocessing ... % 8.29/1.83 Prover 7: Warning: ignoring some quantifiers % 8.29/1.84 Prover 16: Warning: ignoring some quantifiers % 8.29/1.84 Prover 7: Constructing countermodel ... % 8.29/1.85 Prover 13: Warning: ignoring some quantifiers % 8.29/1.85 Prover 16: Constructing countermodel ... % 8.29/1.85 Prover 10: Warning: ignoring some quantifiers % 8.29/1.86 Prover 10: Constructing countermodel ... % 8.29/1.87 Prover 13: Constructing countermodel ... % 8.83/1.91 Prover 8: Warning: ignoring some quantifiers % 8.83/1.92 Prover 8: Constructing countermodel ... % 9.45/2.00 Prover 10: Found proof (size 14) % 9.45/2.00 Prover 10: proved (269ms) % 9.45/2.00 Prover 7: stopped % 9.45/2.00 Prover 16: stopped % 9.45/2.00 Prover 13: Found proof (size 14) % 9.45/2.00 Prover 13: proved (254ms) % 9.45/2.00 Prover 8: stopped % 9.69/2.00 Prover 4: stopped % 9.80/2.05 Prover 11: Constructing countermodel ... % 9.80/2.06 Prover 11: stopped % 9.80/2.06 % 9.80/2.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.80/2.06 % 9.80/2.06 % SZS output start Proof for theBenchmark % 9.80/2.06 Assumptions after simplification: % 9.80/2.06 --------------------------------- % 9.80/2.06 % 9.80/2.06 (least) % 9.80/2.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) % 9.80/2.07 | ~ $i(v1) | ~ $i(v0) | ~ least(v2, v0, v1) | ~ member(v3, v1) | % 9.80/2.07 apply(v0, v2, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | % 9.80/2.07 ~ $i(v1) | ~ $i(v0) | ~ least(v2, v0, v1) | member(v2, v1)) & ? [v0: $i] % 9.80/2.07 : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 9.80/2.07 member(v2, v1) | least(v2, v0, v1) | ? [v3: $i] : ($i(v3) & member(v3, v1) % 9.80/2.07 & ~ apply(v0, v2, v3))) % 9.80/2.07 % 9.80/2.07 (min) % 9.80/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ $i(v3) | % 9.80/2.08 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ min(v2, v0, v1) | ~ apply(v0, v3, % 9.80/2.08 v2) | ~ member(v3, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 9.80/2.08 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ min(v2, v0, v1) | member(v2, v1)) & ? % 9.80/2.08 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 9.80/2.08 member(v2, v1) | min(v2, v0, v1) | ? [v3: $i] : ( ~ (v3 = v2) & $i(v3) & % 9.80/2.08 apply(v0, v3, v2) & member(v3, v1))) % 9.80/2.08 % 9.80/2.08 (thIV16) % 9.80/2.08 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v3 % 9.80/2.08 = v2) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & min(v3, v0, v1) & % 9.80/2.08 min(v2, v0, v1) & least(v4, v0, v1) & order(v0, v1)) % 9.80/2.08 % 9.80/2.08 Further assumptions not needed in the proof: % 9.80/2.08 -------------------------------------------- % 9.80/2.08 greatest, greatest_lower_bound, least_upper_bound, lower_bound, max, order, % 9.80/2.08 total_order, upper_bound % 9.80/2.08 % 9.80/2.08 Those formulas are unsatisfiable: % 9.80/2.08 --------------------------------- % 9.80/2.08 % 9.80/2.08 Begin of proof % 9.80/2.08 | % 9.80/2.08 | ALPHA: (min) implies: % 9.80/2.08 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 9.80/2.08 | $i(v0) | ~ min(v2, v0, v1) | member(v2, v1)) % 9.80/2.09 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 9.80/2.09 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ min(v2, v0, v1) | ~ % 9.80/2.09 | apply(v0, v3, v2) | ~ member(v3, v1)) % 9.80/2.09 | % 9.80/2.09 | ALPHA: (least) implies: % 9.80/2.09 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 9.80/2.09 | $i(v0) | ~ least(v2, v0, v1) | member(v2, v1)) % 9.80/2.09 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 9.80/2.09 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ least(v2, v0, v1) | ~ member(v3, % 9.80/2.09 | v1) | apply(v0, v2, v3)) % 9.80/2.09 | % 9.80/2.09 | DELTA: instantiating (thIV16) with fresh symbols all_22_0, all_22_1, all_22_2, % 9.80/2.09 | all_22_3, all_22_4 gives: % 9.80/2.09 | (5) ~ (all_22_1 = all_22_2) & $i(all_22_0) & $i(all_22_1) & $i(all_22_2) & % 9.80/2.09 | $i(all_22_3) & $i(all_22_4) & min(all_22_1, all_22_4, all_22_3) & % 9.80/2.09 | min(all_22_2, all_22_4, all_22_3) & least(all_22_0, all_22_4, all_22_3) % 9.80/2.09 | & order(all_22_4, all_22_3) % 9.80/2.09 | % 9.80/2.09 | ALPHA: (5) implies: % 9.80/2.09 | (6) ~ (all_22_1 = all_22_2) % 9.80/2.09 | (7) least(all_22_0, all_22_4, all_22_3) % 9.80/2.09 | (8) min(all_22_2, all_22_4, all_22_3) % 9.80/2.09 | (9) min(all_22_1, all_22_4, all_22_3) % 9.80/2.09 | (10) $i(all_22_4) % 9.80/2.09 | (11) $i(all_22_3) % 9.80/2.09 | (12) $i(all_22_2) % 9.80/2.09 | (13) $i(all_22_1) % 9.80/2.09 | (14) $i(all_22_0) % 9.80/2.09 | % 9.80/2.09 | GROUND_INST: instantiating (3) with all_22_4, all_22_3, all_22_0, simplifying % 9.80/2.09 | with (7), (10), (11), (14) gives: % 9.80/2.09 | (15) member(all_22_0, all_22_3) % 9.80/2.09 | % 9.80/2.09 | GROUND_INST: instantiating (1) with all_22_4, all_22_3, all_22_2, simplifying % 9.80/2.09 | with (8), (10), (11), (12) gives: % 9.80/2.10 | (16) member(all_22_2, all_22_3) % 9.80/2.10 | % 9.80/2.10 | GROUND_INST: instantiating (1) with all_22_4, all_22_3, all_22_1, simplifying % 9.80/2.10 | with (9), (10), (11), (13) gives: % 9.80/2.10 | (17) member(all_22_1, all_22_3) % 9.80/2.10 | % 9.80/2.10 | GROUND_INST: instantiating (4) with all_22_4, all_22_3, all_22_0, all_22_2, % 9.80/2.10 | simplifying with (7), (10), (11), (12), (14), (16) gives: % 9.80/2.10 | (18) apply(all_22_4, all_22_0, all_22_2) % 9.80/2.10 | % 9.80/2.10 | GROUND_INST: instantiating (4) with all_22_4, all_22_3, all_22_0, all_22_1, % 9.80/2.10 | simplifying with (7), (10), (11), (13), (14), (17) gives: % 9.80/2.10 | (19) apply(all_22_4, all_22_0, all_22_1) % 9.80/2.10 | % 9.80/2.10 | GROUND_INST: instantiating (2) with all_22_4, all_22_3, all_22_2, all_22_0, % 9.80/2.10 | simplifying with (8), (10), (11), (12), (14), (15), (18) gives: % 9.80/2.10 | (20) all_22_0 = all_22_2 % 9.80/2.10 | % 9.80/2.10 | GROUND_INST: instantiating (2) with all_22_4, all_22_3, all_22_1, all_22_0, % 9.80/2.10 | simplifying with (9), (10), (11), (13), (14), (15), (19) gives: % 9.80/2.10 | (21) all_22_0 = all_22_1 % 9.80/2.10 | % 9.80/2.10 | COMBINE_EQS: (20), (21) imply: % 9.80/2.10 | (22) all_22_1 = all_22_2 % 9.80/2.10 | % 9.80/2.10 | REDUCE: (6), (22) imply: % 9.80/2.10 | (23) $false % 9.80/2.10 | % 9.80/2.10 | CLOSE: (23) is inconsistent. % 9.80/2.10 | % 9.80/2.10 End of proof % 9.80/2.10 % SZS output end Proof for theBenchmark % 9.80/2.10 % 9.80/2.10 1487ms %------------------------------------------------------------------------------