%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET790+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 : n011.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 15:26:27 EDT 2023 % Result : Theorem 6.85s 1.64s % Output : Proof 9.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SET790+4 : TPTP v8.1.2. Released v3.2.0. % 0.11/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.35 % Computer : n011.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Sat Aug 26 11:42:54 EDT 2023 % 0.15/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.95/1.10 Prover 1: Preprocessing ... % 2.95/1.10 Prover 4: Preprocessing ... % 3.10/1.14 Prover 6: Preprocessing ... % 3.10/1.14 Prover 5: Preprocessing ... % 3.10/1.14 Prover 3: Preprocessing ... % 3.10/1.14 Prover 2: Preprocessing ... % 3.10/1.14 Prover 0: Preprocessing ... % 5.39/1.44 Prover 5: Proving ... % 5.58/1.49 Prover 2: Proving ... % 6.28/1.61 Prover 6: Proving ... % 6.28/1.63 Prover 3: Constructing countermodel ... % 6.85/1.63 Prover 1: Constructing countermodel ... % 6.85/1.64 Prover 2: proved (1007ms) % 6.85/1.64 % 6.85/1.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.85/1.64 % 6.85/1.64 Prover 5: proved (1006ms) % 6.85/1.64 % 6.85/1.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.85/1.64 % 6.85/1.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.85/1.64 Prover 6: stopped % 6.85/1.65 Prover 3: stopped % 6.85/1.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.85/1.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.85/1.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.17/1.70 Prover 4: Constructing countermodel ... % 7.17/1.72 Prover 7: Preprocessing ... % 7.17/1.72 Prover 8: Preprocessing ... % 7.17/1.73 Prover 10: Preprocessing ... % 7.17/1.74 Prover 11: Preprocessing ... % 7.68/1.76 Prover 0: Proving ... % 7.83/1.77 Prover 0: stopped % 7.83/1.78 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.83/1.78 Prover 1: gave up % 7.83/1.79 Prover 7: Warning: ignoring some quantifiers % 7.83/1.80 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.83/1.81 Prover 10: Warning: ignoring some quantifiers % 8.23/1.83 Prover 7: Constructing countermodel ... % 8.23/1.84 Prover 10: Constructing countermodel ... % 8.50/1.86 Prover 13: Preprocessing ... % 8.50/1.86 Prover 16: Preprocessing ... % 8.50/1.90 Prover 13: Warning: ignoring some quantifiers % 8.50/1.92 Prover 8: Warning: ignoring some quantifiers % 8.50/1.92 Prover 13: Constructing countermodel ... % 8.50/1.92 Prover 16: Warning: ignoring some quantifiers % 8.50/1.93 Prover 8: Constructing countermodel ... % 8.50/1.94 Prover 16: Constructing countermodel ... % 8.50/1.97 Prover 7: Found proof (size 11) % 8.50/1.97 Prover 7: proved (327ms) % 8.50/1.97 Prover 8: stopped % 8.50/1.97 Prover 10: Found proof (size 11) % 8.50/1.97 Prover 10: proved (312ms) % 8.50/1.97 Prover 13: stopped % 8.50/1.97 Prover 4: stopped % 8.50/1.98 Prover 16: stopped % 9.39/2.03 Prover 11: Constructing countermodel ... % 9.39/2.04 Prover 11: stopped % 9.39/2.04 % 9.39/2.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.39/2.04 % 9.39/2.04 % SZS output start Proof for theBenchmark % 9.75/2.04 Assumptions after simplification: % 9.75/2.05 --------------------------------- % 9.75/2.05 % 9.75/2.05 (least) % 9.75/2.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) % 9.75/2.05 | ~ $i(v1) | ~ $i(v0) | ~ least(v2, v0, v1) | ~ member(v3, v1) | % 9.75/2.05 apply(v0, v2, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | % 9.75/2.05 ~ $i(v1) | ~ $i(v0) | ~ least(v2, v0, v1) | member(v2, v1)) & ? [v0: $i] % 9.75/2.05 : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 9.75/2.05 member(v2, v1) | least(v2, v0, v1) | ? [v3: $i] : ($i(v3) & member(v3, v1) % 9.75/2.05 & ~ apply(v0, v2, v3))) % 9.75/2.05 % 9.75/2.05 (order) % 9.75/2.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 9.75/2.06 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ apply(v0, v3, % 9.75/2.06 v4) | ~ apply(v0, v2, v3) | ~ member(v4, v1) | ~ member(v3, v1) | ~ % 9.75/2.06 member(v2, v1) | ~ order(v0, v1) | apply(v0, v2, v4)) & ! [v0: $i] : ! % 9.75/2.06 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ $i(v3) | ~ $i(v2) | ~ % 9.75/2.06 $i(v1) | ~ $i(v0) | ~ apply(v0, v3, v2) | ~ apply(v0, v2, v3) | ~ % 9.75/2.06 member(v3, v1) | ~ member(v2, v1) | ~ order(v0, v1)) & ! [v0: $i] : ! % 9.75/2.06 [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v2, % 9.75/2.06 v1) | ~ order(v0, v1) | apply(v0, v2, v2)) & ? [v0: $i] : ? [v1: $i] : % 9.75/2.06 ( ~ $i(v1) | ~ $i(v0) | order(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: % 9.75/2.06 $i] : ($i(v4) & $i(v3) & $i(v2) & (( ~ (v3 = v2) & apply(v0, v3, v2) & % 9.75/2.06 apply(v0, v2, v3) & member(v3, v1) & member(v2, v1)) | (apply(v0, v3, % 9.75/2.06 v4) & apply(v0, v2, v3) & member(v4, v1) & member(v3, v1) & % 9.75/2.06 member(v2, v1) & ~ apply(v0, v2, v4)) | (member(v2, v1) & ~ % 9.75/2.06 apply(v0, v2, v2))))) % 9.75/2.06 % 9.75/2.06 (thIV2) % 9.75/2.06 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & $i(v3) % 9.75/2.06 & $i(v2) & $i(v1) & $i(v0) & least(v3, v0, v1) & least(v2, v0, v1) & % 9.75/2.06 order(v0, v1)) % 9.75/2.06 % 9.75/2.06 Further assumptions not needed in the proof: % 9.75/2.06 -------------------------------------------- % 9.75/2.06 greatest, greatest_lower_bound, least_upper_bound, lower_bound, max, min, % 9.75/2.06 total_order, upper_bound % 9.75/2.06 % 9.75/2.06 Those formulas are unsatisfiable: % 9.75/2.06 --------------------------------- % 9.75/2.06 % 9.75/2.06 Begin of proof % 9.75/2.06 | % 9.75/2.07 | ALPHA: (least) implies: % 9.75/2.07 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 9.75/2.07 | $i(v0) | ~ least(v2, v0, v1) | member(v2, v1)) % 9.75/2.07 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 9.75/2.07 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ least(v2, v0, v1) | ~ member(v3, % 9.75/2.07 | v1) | apply(v0, v2, v3)) % 9.75/2.07 | % 9.75/2.07 | ALPHA: (order) implies: % 9.75/2.07 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 9.75/2.07 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ apply(v0, v3, v2) | % 9.75/2.07 | ~ apply(v0, v2, v3) | ~ member(v3, v1) | ~ member(v2, v1) | ~ % 9.75/2.07 | order(v0, v1)) % 9.75/2.07 | % 9.75/2.07 | DELTA: instantiating (thIV2) with fresh symbols all_18_0, all_18_1, all_18_2, % 9.75/2.07 | all_18_3 gives: % 9.75/2.07 | (4) ~ (all_18_0 = all_18_1) & $i(all_18_0) & $i(all_18_1) & $i(all_18_2) & % 9.75/2.07 | $i(all_18_3) & least(all_18_0, all_18_3, all_18_2) & least(all_18_1, % 9.75/2.07 | all_18_3, all_18_2) & order(all_18_3, all_18_2) % 9.75/2.07 | % 9.75/2.07 | ALPHA: (4) implies: % 9.75/2.07 | (5) ~ (all_18_0 = all_18_1) % 9.75/2.07 | (6) order(all_18_3, all_18_2) % 9.75/2.07 | (7) least(all_18_1, all_18_3, all_18_2) % 9.75/2.07 | (8) least(all_18_0, all_18_3, all_18_2) % 9.75/2.07 | (9) $i(all_18_3) % 9.75/2.07 | (10) $i(all_18_2) % 9.75/2.07 | (11) $i(all_18_1) % 9.75/2.07 | (12) $i(all_18_0) % 9.75/2.07 | % 9.75/2.08 | GROUND_INST: instantiating (1) with all_18_3, all_18_2, all_18_1, simplifying % 9.75/2.08 | with (7), (9), (10), (11) gives: % 9.75/2.08 | (13) member(all_18_1, all_18_2) % 9.75/2.08 | % 9.75/2.08 | GROUND_INST: instantiating (1) with all_18_3, all_18_2, all_18_0, simplifying % 9.75/2.08 | with (8), (9), (10), (12) gives: % 9.75/2.08 | (14) member(all_18_0, all_18_2) % 9.75/2.08 | % 9.75/2.08 | GROUND_INST: instantiating (2) with all_18_3, all_18_2, all_18_0, all_18_1, % 9.75/2.08 | simplifying with (8), (9), (10), (11), (12), (13) gives: % 9.75/2.08 | (15) apply(all_18_3, all_18_0, all_18_1) % 9.75/2.08 | % 9.75/2.08 | GROUND_INST: instantiating (2) with all_18_3, all_18_2, all_18_1, all_18_0, % 9.75/2.08 | simplifying with (7), (9), (10), (11), (12), (14) gives: % 9.75/2.08 | (16) apply(all_18_3, all_18_1, all_18_0) % 9.75/2.08 | % 9.75/2.08 | GROUND_INST: instantiating (3) with all_18_3, all_18_2, all_18_1, all_18_0, % 9.75/2.08 | simplifying with (6), (9), (10), (11), (12), (13), (14), (15), % 9.75/2.08 | (16) gives: % 9.75/2.08 | (17) all_18_0 = all_18_1 % 9.75/2.08 | % 9.75/2.08 | REDUCE: (5), (17) imply: % 9.75/2.08 | (18) $false % 9.75/2.08 | % 9.75/2.08 | CLOSE: (18) is inconsistent. % 9.75/2.08 | % 9.75/2.08 End of proof % 9.75/2.08 % SZS output end Proof for theBenchmark % 9.75/2.08 % 9.75/2.08 1467ms %------------------------------------------------------------------------------