%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : DAT053_1 : TPTP v8.1.2. Released v5.0.0. % 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 : Wed Aug 30 22:19:02 EDT 2023 % Result : Theorem 7.92s 1.83s % Output : Proof 10.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : DAT053_1 : TPTP v8.1.2. Released v5.0.0. % 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.35 % Computer : n017.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 : Thu Aug 24 13:54:54 EDT 2023 % 0.15/0.35 % CPUTime : % 0.22/0.63 ________ _____ % 0.22/0.63 ___ __ \_________(_)________________________________ % 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.63 % 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.63 (2023-06-19) % 0.22/0.63 % 0.22/0.63 (c) Philipp Rümmer, 2009-2023 % 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.63 Amanda Stjerna. % 0.22/0.63 Free software under BSD-3-Clause. % 0.22/0.63 % 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.63 % 0.22/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.22/0.65 Running up to 7 provers in parallel. % 0.22/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.22/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 2.90/1.16 Prover 4: Preprocessing ... % 2.90/1.16 Prover 3: Preprocessing ... % 2.90/1.16 Prover 5: Preprocessing ... % 2.90/1.16 Prover 0: Preprocessing ... % 2.90/1.16 Prover 6: Preprocessing ... % 2.90/1.16 Prover 1: Preprocessing ... % 2.90/1.16 Prover 2: Preprocessing ... % 5.04/1.49 Prover 1: Constructing countermodel ... % 5.04/1.49 Prover 3: Constructing countermodel ... % 5.04/1.49 Prover 6: Constructing countermodel ... % 5.60/1.54 Prover 4: Constructing countermodel ... % 5.60/1.56 Prover 2: Proving ... % 5.96/1.60 Prover 5: Proving ... % 5.96/1.61 Prover 0: Proving ... % 7.30/1.82 Prover 6: proved (1164ms) % 7.30/1.83 % 7.92/1.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.92/1.83 % 7.92/1.83 Prover 3: stopped % 7.92/1.83 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.92/1.83 Prover 5: stopped % 7.92/1.84 Prover 2: stopped % 7.92/1.84 Prover 0: stopped % 7.92/1.84 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.92/1.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.92/1.84 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.92/1.84 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.27/1.88 Prover 7: Preprocessing ... % 8.27/1.88 Prover 10: Preprocessing ... % 8.27/1.88 Prover 8: Preprocessing ... % 8.27/1.90 Prover 11: Preprocessing ... % 8.27/1.90 Prover 13: Preprocessing ... % 8.27/2.01 Prover 8: Warning: ignoring some quantifiers % 8.99/2.02 Prover 8: Constructing countermodel ... % 8.99/2.02 Prover 10: Constructing countermodel ... % 8.99/2.03 Prover 7: Constructing countermodel ... % 9.31/2.07 Prover 13: Warning: ignoring some quantifiers % 9.31/2.08 Prover 13: Constructing countermodel ... % 9.72/2.14 Prover 11: Constructing countermodel ... % 10.22/2.18 Prover 10: Found proof (size 48) % 10.22/2.18 Prover 10: proved (342ms) % 10.22/2.18 Prover 8: stopped % 10.22/2.18 Prover 11: stopped % 10.22/2.18 Prover 13: stopped % 10.22/2.18 Prover 4: stopped % 10.22/2.18 Prover 1: stopped % 10.22/2.19 Prover 7: stopped % 10.22/2.19 % 10.22/2.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.22/2.19 % 10.22/2.20 % SZS output start Proof for theBenchmark % 10.22/2.20 Assumptions after simplification: % 10.22/2.20 --------------------------------- % 10.22/2.20 % 10.22/2.20 (ax3) % 10.52/2.22 ! [v0: record] : ! [v1: int] : ( ~ (length(v0) = v1) | ~ record(v0) | ~ % 10.52/2.22 isrecord(v0) | ? [v2: record] : (next(v0) = v2 & length(v2) = $sum(v1, -1) % 10.52/2.22 & record(v2))) % 10.52/2.22 % 10.52/2.22 (ax5) % 10.52/2.22 ! [v0: record] : ! [v1: record] : ( ~ (split1(v0) = v1) | ~ record(v0) | ~ % 10.52/2.22 isrecord(v0) | isrecord(v1)) % 10.52/2.22 % 10.52/2.22 (ax8) % 10.52/2.22 ! [v0: record] : ! [v1: record] : ( ~ (split1(v0) = v1) | ~ record(v0) | ~ % 10.52/2.23 isrecord(v0) | ? [v2: record] : ? [v3: record] : ? [v4: record] : ? [v5: % 10.52/2.23 record] : (next(v0) = v2 & record(v2) & ( ~ isrecord(v2) | (v5 = v3 & % 10.52/2.23 split1(v4) = v3 & next(v2) = v4 & next(v1) = v3 & record(v4) & % 10.52/2.23 record(v3))))) % 10.52/2.23 % 10.52/2.23 (co1) % 10.52/2.23 record(b) & record(a) & ? [v0: record] : ? [v1: record] : ? [v2: int] : ? % 10.52/2.23 [v3: int] : ? [v4: record] : ? [v5: int] : ? [v6: int] : ( ~ % 10.52/2.23 ($difference(v6, $product(2, v5)) = -1) & ~ (v6 = $product(2, v5)) & % 10.52/2.23 split1(b) = v4 & split1(a) = v1 & next(v0) = a & next(b) = v0 & length(v4) = % 10.52/2.23 v5 & length(v1) = v2 & length(b) = v6 & length(a) = v3 & record(v4) & % 10.52/2.23 record(v1) & record(v0) & isrecord(v0) & isrecord(b) & ($difference(v3, % 10.52/2.23 $product(2, v2)) = -1 | v3 = $product(2, v2))) % 10.52/2.23 % 10.52/2.23 (function-axioms) % 10.52/2.23 ! [v0: record] : ! [v1: record] : ! [v2: record] : (v1 = v0 | ~ % 10.52/2.23 (split2(v2) = v1) | ~ (split2(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! % 10.52/2.23 [v2: record] : (v1 = v0 | ~ (data(v2) = v1) | ~ (data(v2) = v0)) & ! [v0: % 10.52/2.23 record] : ! [v1: record] : ! [v2: record] : (v1 = v0 | ~ (split1(v2) = % 10.52/2.23 v1) | ~ (split1(v2) = v0)) & ! [v0: record] : ! [v1: record] : ! [v2: % 10.52/2.23 record] : (v1 = v0 | ~ (next(v2) = v1) | ~ (next(v2) = v0)) & ! [v0: int] % 10.52/2.23 : ! [v1: int] : ! [v2: record] : (v1 = v0 | ~ (length(v2) = v1) | ~ % 10.52/2.23 (length(v2) = v0)) % 10.52/2.23 % 10.52/2.23 Further assumptions not needed in the proof: % 10.52/2.23 -------------------------------------------- % 10.52/2.23 ax1, ax10, ax11, ax12, ax13, ax2, ax4, ax6, ax7, ax9 % 10.52/2.23 % 10.52/2.23 Those formulas are unsatisfiable: % 10.52/2.23 --------------------------------- % 10.52/2.23 % 10.52/2.23 Begin of proof % 10.52/2.24 | % 10.52/2.24 | ALPHA: (co1) implies: % 10.52/2.24 | (1) record(b) % 10.52/2.24 | (2) ? [v0: record] : ? [v1: record] : ? [v2: int] : ? [v3: int] : ? % 10.52/2.24 | [v4: record] : ? [v5: int] : ? [v6: int] : ( ~ ($difference(v6, % 10.52/2.24 | $product(2, v5)) = -1) & ~ (v6 = $product(2, v5)) & split1(b) = % 10.52/2.24 | v4 & split1(a) = v1 & next(v0) = a & next(b) = v0 & length(v4) = v5 & % 10.52/2.24 | length(v1) = v2 & length(b) = v6 & length(a) = v3 & record(v4) & % 10.52/2.24 | record(v1) & record(v0) & isrecord(v0) & isrecord(b) & % 10.52/2.24 | ($difference(v3, $product(2, v2)) = -1 | v3 = $product(2, v2))) % 10.52/2.24 | % 10.52/2.24 | ALPHA: (function-axioms) implies: % 10.52/2.24 | (3) ! [v0: int] : ! [v1: int] : ! [v2: record] : (v1 = v0 | ~ % 10.52/2.24 | (length(v2) = v1) | ~ (length(v2) = v0)) % 10.52/2.24 | (4) ! [v0: record] : ! [v1: record] : ! [v2: record] : (v1 = v0 | ~ % 10.52/2.24 | (next(v2) = v1) | ~ (next(v2) = v0)) % 10.72/2.24 | (5) ! [v0: record] : ! [v1: record] : ! [v2: record] : (v1 = v0 | ~ % 10.72/2.24 | (split1(v2) = v1) | ~ (split1(v2) = v0)) % 10.72/2.24 | % 10.72/2.24 | DELTA: instantiating (2) with fresh symbols all_19_0, all_19_1, all_19_2, % 10.72/2.24 | all_19_3, all_19_4, all_19_5, all_19_6 gives: % 10.72/2.25 | (6) ~ ($difference(all_19_0, $product(2, all_19_1)) = -1) & ~ (all_19_0 = % 10.72/2.25 | $product(2, all_19_1)) & split1(b) = all_19_2 & split1(a) = all_19_5 % 10.72/2.25 | & next(all_19_6) = a & next(b) = all_19_6 & length(all_19_2) = all_19_1 % 10.72/2.25 | & length(all_19_5) = all_19_4 & length(b) = all_19_0 & length(a) = % 10.72/2.25 | all_19_3 & record(all_19_2) & record(all_19_5) & record(all_19_6) & % 10.72/2.25 | isrecord(all_19_6) & isrecord(b) & ($difference(all_19_3, $product(2, % 10.72/2.25 | all_19_4)) = -1 | all_19_3 = $product(2, all_19_4)) % 10.72/2.25 | % 10.72/2.25 | ALPHA: (6) implies: % 10.72/2.25 | (7) ~ (all_19_0 = $product(2, all_19_1)) % 10.72/2.25 | (8) ~ ($difference(all_19_0, $product(2, all_19_1)) = -1) % 10.72/2.25 | (9) isrecord(b) % 10.72/2.25 | (10) isrecord(all_19_6) % 10.72/2.25 | (11) record(all_19_2) % 10.72/2.25 | (12) length(a) = all_19_3 % 10.72/2.25 | (13) length(b) = all_19_0 % 10.72/2.25 | (14) length(all_19_5) = all_19_4 % 10.72/2.25 | (15) length(all_19_2) = all_19_1 % 10.72/2.25 | (16) next(b) = all_19_6 % 10.72/2.25 | (17) next(all_19_6) = a % 10.72/2.25 | (18) split1(a) = all_19_5 % 10.72/2.25 | (19) split1(b) = all_19_2 % 10.72/2.25 | (20) $difference(all_19_3, $product(2, all_19_4)) = -1 | all_19_3 = % 10.72/2.25 | $product(2, all_19_4) % 10.72/2.25 | % 10.72/2.25 | GROUND_INST: instantiating (ax3) with b, all_19_0, simplifying with (1), (9), % 10.72/2.25 | (13) gives: % 10.72/2.25 | (21) ? [v0: record] : (next(b) = v0 & length(v0) = $sum(all_19_0, -1) & % 10.72/2.25 | record(v0)) % 10.72/2.25 | % 10.72/2.25 | GROUND_INST: instantiating (ax5) with b, all_19_2, simplifying with (1), (9), % 10.72/2.25 | (19) gives: % 10.72/2.25 | (22) isrecord(all_19_2) % 10.72/2.25 | % 10.72/2.25 | GROUND_INST: instantiating (ax8) with b, all_19_2, simplifying with (1), (9), % 10.72/2.25 | (19) gives: % 10.72/2.26 | (23) ? [v0: record] : ? [v1: record] : ? [v2: record] : ? [v3: record] % 10.72/2.26 | : (next(b) = v0 & record(v0) & ( ~ isrecord(v0) | (v3 = v1 & % 10.72/2.26 | split1(v2) = v1 & next(v0) = v2 & next(all_19_2) = v1 & % 10.72/2.26 | record(v2) & record(v1)))) % 10.72/2.26 | % 10.72/2.26 | DELTA: instantiating (21) with fresh symbol all_28_0 gives: % 10.72/2.26 | (24) next(b) = all_28_0 & length(all_28_0) = $sum(all_19_0, -1) & % 10.72/2.26 | record(all_28_0) % 10.72/2.26 | % 10.72/2.26 | ALPHA: (24) implies: % 10.72/2.26 | (25) record(all_28_0) % 10.72/2.26 | (26) length(all_28_0) = $sum(all_19_0, -1) % 10.72/2.26 | (27) next(b) = all_28_0 % 10.72/2.26 | % 10.72/2.26 | DELTA: instantiating (23) with fresh symbols all_31_0, all_31_1, all_31_2, % 10.72/2.26 | all_31_3 gives: % 10.72/2.26 | (28) next(b) = all_31_3 & record(all_31_3) & ( ~ isrecord(all_31_3) | % 10.72/2.26 | (all_31_0 = all_31_2 & split1(all_31_1) = all_31_2 & next(all_31_3) % 10.72/2.26 | = all_31_1 & next(all_19_2) = all_31_2 & record(all_31_1) & % 10.72/2.26 | record(all_31_2))) % 10.72/2.26 | % 10.72/2.26 | ALPHA: (28) implies: % 10.72/2.26 | (29) next(b) = all_31_3 % 10.72/2.26 | (30) ~ isrecord(all_31_3) | (all_31_0 = all_31_2 & split1(all_31_1) = % 10.72/2.26 | all_31_2 & next(all_31_3) = all_31_1 & next(all_19_2) = all_31_2 & % 10.72/2.26 | record(all_31_1) & record(all_31_2)) % 10.72/2.26 | % 10.72/2.26 | GROUND_INST: instantiating (4) with all_19_6, all_31_3, b, simplifying with % 10.72/2.26 | (16), (29) gives: % 10.72/2.26 | (31) all_31_3 = all_19_6 % 10.72/2.26 | % 10.72/2.26 | GROUND_INST: instantiating (4) with all_28_0, all_31_3, b, simplifying with % 10.72/2.26 | (27), (29) gives: % 10.72/2.26 | (32) all_31_3 = all_28_0 % 10.72/2.26 | % 10.72/2.26 | COMBINE_EQS: (31), (32) imply: % 10.72/2.26 | (33) all_28_0 = all_19_6 % 10.72/2.26 | % 10.72/2.26 | REDUCE: (26), (33) imply: % 10.72/2.26 | (34) length(all_19_6) = $sum(all_19_0, -1) % 10.72/2.26 | % 10.72/2.26 | REDUCE: (25), (33) imply: % 10.72/2.26 | (35) record(all_19_6) % 10.72/2.26 | % 10.72/2.26 | BETA: splitting (30) gives: % 10.72/2.26 | % 10.72/2.26 | Case 1: % 10.72/2.26 | | % 10.72/2.26 | | (36) ~ isrecord(all_31_3) % 10.72/2.26 | | % 10.72/2.26 | | REDUCE: (31), (36) imply: % 10.72/2.26 | | (37) ~ isrecord(all_19_6) % 10.72/2.26 | | % 10.72/2.26 | | PRED_UNIFY: (10), (37) imply: % 10.72/2.26 | | (38) $false % 10.72/2.26 | | % 10.72/2.26 | | CLOSE: (38) is inconsistent. % 10.72/2.26 | | % 10.72/2.26 | Case 2: % 10.72/2.26 | | % 10.72/2.27 | | (39) isrecord(all_31_3) % 10.72/2.27 | | (40) all_31_0 = all_31_2 & split1(all_31_1) = all_31_2 & next(all_31_3) = % 10.72/2.27 | | all_31_1 & next(all_19_2) = all_31_2 & record(all_31_1) & % 10.72/2.27 | | record(all_31_2) % 10.72/2.27 | | % 10.72/2.27 | | ALPHA: (40) implies: % 10.72/2.27 | | (41) next(all_19_2) = all_31_2 % 10.72/2.27 | | (42) next(all_31_3) = all_31_1 % 10.72/2.27 | | (43) split1(all_31_1) = all_31_2 % 10.72/2.27 | | % 10.72/2.27 | | REDUCE: (31), (42) imply: % 10.72/2.27 | | (44) next(all_19_6) = all_31_1 % 10.72/2.27 | | % 10.72/2.27 | | GROUND_INST: instantiating (4) with a, all_31_1, all_19_6, simplifying with % 10.72/2.27 | | (17), (44) gives: % 10.72/2.27 | | (45) all_31_1 = a % 10.72/2.27 | | % 10.72/2.27 | | REDUCE: (43), (45) imply: % 10.72/2.27 | | (46) split1(a) = all_31_2 % 10.72/2.27 | | % 10.72/2.27 | | GROUND_INST: instantiating (5) with all_19_5, all_31_2, a, simplifying with % 10.72/2.27 | | (18), (46) gives: % 10.72/2.27 | | (47) all_31_2 = all_19_5 % 10.72/2.27 | | % 10.72/2.27 | | REDUCE: (41), (47) imply: % 10.72/2.27 | | (48) next(all_19_2) = all_19_5 % 10.72/2.27 | | % 10.72/2.27 | | GROUND_INST: instantiating (ax3) with all_19_2, all_19_1, simplifying with % 10.72/2.27 | | (11), (15), (22) gives: % 10.72/2.27 | | (49) ? [v0: record] : (next(all_19_2) = v0 & length(v0) = $sum(all_19_1, % 10.72/2.27 | | -1) & record(v0)) % 10.72/2.27 | | % 10.72/2.27 | | GROUND_INST: instantiating (ax3) with all_19_6, $sum(all_19_0, -1), % 10.72/2.27 | | simplifying with (10), (34), (35) gives: % 10.72/2.27 | | (50) ? [v0: record] : (next(all_19_6) = v0 & length(v0) = $sum(all_19_0, % 10.72/2.27 | | -2) & record(v0)) % 10.72/2.27 | | % 10.72/2.27 | | DELTA: instantiating (50) with fresh symbol all_56_0 gives: % 10.72/2.27 | | (51) next(all_19_6) = all_56_0 & length(all_56_0) = $sum(all_19_0, -2) & % 10.72/2.27 | | record(all_56_0) % 10.72/2.27 | | % 10.72/2.27 | | ALPHA: (51) implies: % 10.72/2.27 | | (52) length(all_56_0) = $sum(all_19_0, -2) % 10.72/2.27 | | (53) next(all_19_6) = all_56_0 % 10.72/2.27 | | % 10.72/2.27 | | DELTA: instantiating (49) with fresh symbol all_58_0 gives: % 10.72/2.27 | | (54) next(all_19_2) = all_58_0 & length(all_58_0) = $sum(all_19_1, -1) & % 10.72/2.27 | | record(all_58_0) % 10.72/2.27 | | % 10.72/2.27 | | ALPHA: (54) implies: % 10.72/2.27 | | (55) length(all_58_0) = $sum(all_19_1, -1) % 10.72/2.27 | | (56) next(all_19_2) = all_58_0 % 10.72/2.27 | | % 10.72/2.27 | | GROUND_INST: instantiating (4) with a, all_56_0, all_19_6, simplifying with % 10.72/2.27 | | (17), (53) gives: % 10.72/2.27 | | (57) all_56_0 = a % 10.72/2.27 | | % 10.72/2.27 | | GROUND_INST: instantiating (4) with all_19_5, all_58_0, all_19_2, % 10.72/2.27 | | simplifying with (48), (56) gives: % 10.72/2.27 | | (58) all_58_0 = all_19_5 % 10.72/2.27 | | % 10.72/2.27 | | REDUCE: (55), (58) imply: % 10.72/2.27 | | (59) length(all_19_5) = $sum(all_19_1, -1) % 10.72/2.27 | | % 10.72/2.27 | | REDUCE: (52), (57) imply: % 10.72/2.27 | | (60) length(a) = $sum(all_19_0, -2) % 10.72/2.27 | | % 10.72/2.28 | | GROUND_INST: instantiating (3) with all_19_3, $sum(all_19_0, -2), a, % 10.72/2.28 | | simplifying with (12), (60) gives: % 10.72/2.28 | | (61) $difference(all_19_0, all_19_3) = 2 % 10.72/2.28 | | % 10.72/2.28 | | GROUND_INST: instantiating (3) with all_19_4, $sum(all_19_1, -1), all_19_5, % 10.72/2.28 | | simplifying with (14), (59) gives: % 10.72/2.28 | | (62) $difference(all_19_1, all_19_4) = 1 % 10.72/2.28 | | % 10.72/2.28 | | REDUCE: (8), (61), (62) imply: % 10.72/2.28 | | (63) ~ ($difference(all_19_3, $product(2, all_19_4)) = -1) % 10.72/2.28 | | % 10.72/2.28 | | REDUCE: (7), (61), (62) imply: % 10.72/2.28 | | (64) ~ (all_19_3 = $product(2, all_19_4)) % 10.72/2.28 | | % 10.72/2.28 | | BETA: splitting (20) gives: % 10.72/2.28 | | % 10.72/2.28 | | Case 1: % 10.72/2.28 | | | % 10.72/2.28 | | | (65) all_19_3 = $product(2, all_19_4) % 10.72/2.28 | | | % 10.72/2.28 | | | REDUCE: (64), (65) imply: % 10.72/2.28 | | | (66) $false % 10.72/2.28 | | | % 10.72/2.28 | | | CLOSE: (66) is inconsistent. % 10.72/2.28 | | | % 10.72/2.28 | | Case 2: % 10.72/2.28 | | | % 10.72/2.28 | | | (67) $difference(all_19_3, $product(2, all_19_4)) = -1 % 10.72/2.28 | | | % 10.72/2.28 | | | REDUCE: (63), (67) imply: % 10.72/2.28 | | | (68) $false % 10.72/2.28 | | | % 10.72/2.28 | | | CLOSE: (68) is inconsistent. % 10.72/2.28 | | | % 10.72/2.28 | | End of split % 10.72/2.28 | | % 10.72/2.28 | End of split % 10.72/2.28 | % 10.72/2.28 End of proof % 10.72/2.28 % SZS output end Proof for theBenchmark % 10.72/2.28 % 10.72/2.28 1644ms %------------------------------------------------------------------------------