%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV412+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 : n017.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 22:56:14 EDT 2023 % Result : Theorem 6.48s 1.65s % Output : Proof 8.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWV412+1 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n017.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 : Tue Aug 29 08:25:43 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/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 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 % 2.28/1.10 Prover 1: Preprocessing ... % 2.28/1.10 Prover 4: Preprocessing ... % 2.98/1.14 Prover 3: Preprocessing ... % 2.98/1.14 Prover 6: Preprocessing ... % 2.98/1.14 Prover 2: Preprocessing ... % 2.98/1.14 Prover 5: Preprocessing ... % 2.98/1.14 Prover 0: Preprocessing ... % 5.21/1.50 Prover 6: Constructing countermodel ... % 5.21/1.50 Prover 1: Constructing countermodel ... % 5.91/1.54 Prover 5: Proving ... % 5.91/1.54 Prover 3: Constructing countermodel ... % 5.91/1.57 Prover 4: Constructing countermodel ... % 5.91/1.58 Prover 2: Proving ... % 6.48/1.63 Prover 0: Proving ... % 6.48/1.65 Prover 3: proved (1003ms) % 6.48/1.65 Prover 6: proved (1004ms) % 6.48/1.65 % 6.48/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.48/1.65 % 6.48/1.66 % 6.48/1.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.48/1.66 % 6.48/1.66 Prover 5: proved (1006ms) % 6.48/1.66 % 6.48/1.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.48/1.66 % 6.48/1.67 Prover 2: proved (1012ms) % 6.48/1.67 % 6.48/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.48/1.67 % 6.48/1.67 Prover 0: stopped % 6.48/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.48/1.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.48/1.67 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.48/1.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.48/1.67 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.20/1.69 Prover 7: Preprocessing ... % 7.34/1.71 Prover 13: Preprocessing ... % 7.34/1.71 Prover 8: Preprocessing ... % 7.34/1.71 Prover 11: Preprocessing ... % 7.42/1.72 Prover 1: Found proof (size 13) % 7.42/1.72 Prover 10: Preprocessing ... % 7.42/1.73 Prover 4: Found proof (size 14) % 7.42/1.74 Prover 1: proved (1103ms) % 7.42/1.74 Prover 4: proved (1092ms) % 7.42/1.75 Prover 10: stopped % 7.42/1.76 Prover 11: stopped % 7.42/1.77 Prover 13: stopped % 7.42/1.77 Prover 7: Warning: ignoring some quantifiers % 7.42/1.79 Prover 7: Constructing countermodel ... % 7.42/1.79 Prover 7: stopped % 7.42/1.80 Prover 8: Warning: ignoring some quantifiers % 7.42/1.81 Prover 8: Constructing countermodel ... % 7.42/1.82 Prover 8: stopped % 7.42/1.82 % 7.42/1.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.42/1.82 % 7.42/1.82 % SZS output start Proof for theBenchmark % 7.42/1.82 Assumptions after simplification: % 7.42/1.82 --------------------------------- % 7.42/1.82 % 7.42/1.82 (l48_co) % 7.42/1.85 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 7.42/1.85 int] : ( ~ (v5 = 0) & update_slb(v0, v3) = v4 & pair_in_list(v4, v1, v3) = % 7.42/1.85 v5 & pair_in_list(v0, v1, v2) = 0 & strictly_less_than(v2, v3) = 0 & % 7.42/1.85 strictly_less_than(v1, v3) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 7.42/1.85 % 7.42/1.85 (l48_li3839) % 7.42/1.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 7.42/1.85 int] : (v5 = 0 | ~ (update_slb(v0, v3) = v4) | ~ (pair_in_list(v4, v1, v3) % 7.42/1.85 = v5) | ~ (strictly_less_than(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 7.42/1.85 $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ (v6 = 0) & pair_in_list(v0, v1, v2) % 7.42/1.85 = v6)) % 7.42/1.85 % 7.42/1.85 (function-axioms) % 7.42/1.86 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 7.42/1.86 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 7.42/1.86 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 7.42/1.86 ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) % 7.42/1.86 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 7.42/1.86 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) & ! [v0: $i] % 7.42/1.86 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (remove_slb(v3, v2) % 7.42/1.86 = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 7.42/1.86 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.42/1.86 (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) & ! [v0: $i] % 7.42/1.86 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (pair(v3, v2) = v1) % 7.42/1.86 | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 7.42/1.86 [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ (insert_slb(v3, v2) = % 7.42/1.86 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 7.42/1.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ % 7.42/1.86 (strictly_less_than(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 7.42/1.86 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.42/1.86 (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) & ! [v0: % 7.42/1.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 7.42/1.86 ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) = v0)) % 7.42/1.86 % 7.42/1.86 Further assumptions not needed in the proof: % 7.42/1.86 -------------------------------------------- % 7.42/1.86 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, % 7.42/1.86 bottom_smallest, reflexivity, stricly_smaller_definition, totality, transitivity % 7.42/1.86 % 7.42/1.86 Those formulas are unsatisfiable: % 7.42/1.86 --------------------------------- % 7.42/1.86 % 7.42/1.86 Begin of proof % 7.42/1.86 | % 7.42/1.86 | ALPHA: (function-axioms) implies: % 7.42/1.86 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 7.42/1.86 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = % 7.42/1.86 | v1) | ~ (pair_in_list(v4, v3, v2) = v0)) % 7.42/1.86 | % 7.42/1.86 | DELTA: instantiating (l48_co) with fresh symbols all_24_0, all_24_1, all_24_2, % 7.42/1.86 | all_24_3, all_24_4, all_24_5 gives: % 7.42/1.86 | (2) ~ (all_24_0 = 0) & update_slb(all_24_5, all_24_2) = all_24_1 & % 7.42/1.86 | pair_in_list(all_24_1, all_24_4, all_24_2) = all_24_0 & % 7.42/1.86 | pair_in_list(all_24_5, all_24_4, all_24_3) = 0 & % 7.42/1.86 | strictly_less_than(all_24_3, all_24_2) = 0 & % 7.42/1.86 | strictly_less_than(all_24_4, all_24_2) = 0 & $i(all_24_1) & % 7.42/1.86 | $i(all_24_2) & $i(all_24_3) & $i(all_24_4) & $i(all_24_5) % 7.42/1.86 | % 7.42/1.86 | ALPHA: (2) implies: % 8.11/1.87 | (3) ~ (all_24_0 = 0) % 8.11/1.87 | (4) $i(all_24_5) % 8.11/1.87 | (5) $i(all_24_4) % 8.11/1.87 | (6) $i(all_24_3) % 8.11/1.87 | (7) $i(all_24_2) % 8.11/1.87 | (8) strictly_less_than(all_24_3, all_24_2) = 0 % 8.11/1.87 | (9) pair_in_list(all_24_5, all_24_4, all_24_3) = 0 % 8.11/1.87 | (10) pair_in_list(all_24_1, all_24_4, all_24_2) = all_24_0 % 8.11/1.87 | (11) update_slb(all_24_5, all_24_2) = all_24_1 % 8.11/1.87 | % 8.11/1.87 | GROUND_INST: instantiating (l48_li3839) with all_24_5, all_24_4, all_24_3, % 8.11/1.87 | all_24_2, all_24_1, all_24_0, simplifying with (4), (5), (6), % 8.11/1.87 | (7), (8), (10), (11) gives: % 8.11/1.87 | (12) all_24_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & pair_in_list(all_24_5, % 8.11/1.87 | all_24_4, all_24_3) = v0) % 8.11/1.87 | % 8.11/1.87 | BETA: splitting (12) gives: % 8.11/1.87 | % 8.11/1.87 | Case 1: % 8.11/1.87 | | % 8.11/1.87 | | (13) all_24_0 = 0 % 8.11/1.87 | | % 8.11/1.87 | | REDUCE: (3), (13) imply: % 8.11/1.87 | | (14) $false % 8.11/1.87 | | % 8.11/1.87 | | CLOSE: (14) is inconsistent. % 8.11/1.87 | | % 8.11/1.87 | Case 2: % 8.11/1.87 | | % 8.11/1.87 | | (15) ? [v0: int] : ( ~ (v0 = 0) & pair_in_list(all_24_5, all_24_4, % 8.11/1.87 | | all_24_3) = v0) % 8.11/1.87 | | % 8.11/1.87 | | DELTA: instantiating (15) with fresh symbol all_39_0 gives: % 8.11/1.87 | | (16) ~ (all_39_0 = 0) & pair_in_list(all_24_5, all_24_4, all_24_3) = % 8.11/1.87 | | all_39_0 % 8.11/1.87 | | % 8.11/1.87 | | ALPHA: (16) implies: % 8.11/1.87 | | (17) ~ (all_39_0 = 0) % 8.11/1.87 | | (18) pair_in_list(all_24_5, all_24_4, all_24_3) = all_39_0 % 8.11/1.87 | | % 8.11/1.87 | | GROUND_INST: instantiating (1) with 0, all_39_0, all_24_3, all_24_4, % 8.11/1.87 | | all_24_5, simplifying with (9), (18) gives: % 8.11/1.87 | | (19) all_39_0 = 0 % 8.11/1.87 | | % 8.11/1.87 | | REDUCE: (17), (19) imply: % 8.11/1.87 | | (20) $false % 8.11/1.87 | | % 8.11/1.87 | | CLOSE: (20) is inconsistent. % 8.11/1.87 | | % 8.11/1.87 | End of split % 8.11/1.87 | % 8.11/1.87 End of proof % 8.11/1.87 % SZS output end Proof for theBenchmark % 8.11/1.87 % 8.11/1.87 1260ms %------------------------------------------------------------------------------