%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWX000_1 : TPTP v9.1.0. Released v9.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n004.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 : Sun Apr 6 10:08:52 AM UTC 2025 % Result : Theorem 10.83s 2.12s % Output : Proof 12.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWX000_1 : TPTP v9.1.0. Released v9.1.0. % 0.07/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n004.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sun Apr 6 03:06:53 EDT 2025 % 0.12/0.33 % CPUTime : % 0.48/0.60 ________ _____ % 0.48/0.60 ___ __ \_________(_)________________________________ % 0.48/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.48/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.48/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.48/0.60 % 0.48/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.48/0.60 (2023-06-19) % 0.48/0.60 % 0.48/0.60 (c) Philipp Rümmer, 2009-2023 % 0.48/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.48/0.60 Amanda Stjerna. % 0.48/0.60 Free software under BSD-3-Clause. % 0.48/0.60 % 0.48/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.48/0.60 % 0.48/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.48/0.62 Running up to 7 provers in parallel. % 0.48/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.48/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.48/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.48/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.48/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.48/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.48/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.63/1.20 Prover 4: Preprocessing ... % 3.63/1.20 Prover 0: Preprocessing ... % 3.63/1.20 Prover 2: Preprocessing ... % 3.63/1.20 Prover 6: Preprocessing ... % 3.63/1.20 Prover 1: Preprocessing ... % 3.63/1.21 Prover 3: Preprocessing ... % 3.63/1.22 Prover 5: Preprocessing ... % 8.59/1.82 Prover 0: Proving ... % 8.59/1.82 Prover 5: Proving ... % 8.59/1.83 Prover 1: Warning: ignoring some quantifiers % 8.59/1.84 Prover 4: Constructing countermodel ... % 8.59/1.85 Prover 1: Constructing countermodel ... % 8.59/1.86 Prover 3: Warning: ignoring some quantifiers % 8.94/1.87 Prover 3: Constructing countermodel ... % 8.94/1.90 Prover 6: Proving ... % 9.81/2.03 Prover 2: Proving ... % 10.83/2.11 Prover 0: proved (1492ms) % 10.83/2.12 % 10.83/2.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.83/2.12 % 10.83/2.12 Prover 5: stopped % 10.83/2.12 Prover 6: stopped % 10.83/2.13 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.83/2.13 Prover 2: stopped % 10.83/2.13 Prover 3: proved (1499ms) % 10.83/2.13 % 10.83/2.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.83/2.14 % 10.83/2.14 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.83/2.14 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.83/2.14 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.83/2.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.21/2.24 Prover 1: Found proof (size 39) % 11.21/2.24 Prover 1: proved (1615ms) % 11.21/2.24 Prover 4: stopped % 11.85/2.26 Prover 8: Preprocessing ... % 11.85/2.26 Prover 11: Preprocessing ... % 11.85/2.26 Prover 7: Preprocessing ... % 11.85/2.27 Prover 10: Preprocessing ... % 11.85/2.27 Prover 13: Preprocessing ... % 12.15/2.30 Prover 7: stopped % 12.15/2.30 Prover 10: stopped % 12.15/2.30 Prover 11: stopped % 12.15/2.33 Prover 13: stopped % 12.45/2.39 Prover 8: Warning: ignoring some quantifiers % 12.45/2.40 Prover 8: Constructing countermodel ... % 12.76/2.41 Prover 8: stopped % 12.76/2.41 % 12.76/2.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.76/2.41 % 12.76/2.41 % SZS output start Proof for theBenchmark % 12.76/2.41 Assumptions after simplification: % 12.76/2.41 --------------------------------- % 12.76/2.41 % 12.76/2.41 (formula_5_unnamed_formula) % 12.76/2.43 ! [v0: int] : ! [v1: int] : ! [v2: general] : ! [v3: general] : ! [v4: % 12.76/2.43 int] : (v4 = 0 | ~ ($lesseq(0, v0)) | ~ (sqrt(v2, v3) = v4) | ~ % 12.76/2.43 (f__integer__(v1) = v3) | ~ (f__integer__(v0) = v2) | ? [v5: int] : ? % 12.76/2.43 [v6: int] : ($product($sum(v0, 1), $sum(v0, 1)) = v6 & $product(v0, v0) = v5 % 12.76/2.43 & ( ~ ($lesseq(1, $difference(v6, v1))) | ~ ($lesseq(v5, v1))))) & ! % 12.76/2.43 [v0: int] : ! [v1: int] : ! [v2: general] : ! [v3: general] : ( ~ (sqrt(v2, % 12.76/2.43 v3) = 0) | ~ (f__integer__(v1) = v3) | ~ (f__integer__(v0) = v2) | % 12.76/2.43 ($lesseq(0, v0) & ? [v4: int] : ? [v5: int] : ($lesseq(1, $difference(v5, % 12.76/2.43 v1)) & $lesseq(v4, v1) & $product($sum(v0, 1), $sum(v0, 1)) = v5 & % 12.76/2.43 $product(v0, v0) = v4))) % 12.76/2.43 % 12.76/2.43 (formula_6_unnamed_formula) % 12.76/2.43 ? [v0: int] : ? [v1: int] : ? [v2: general] : ? [v3: general] : ? [v4: % 12.76/2.43 int] : ? [v5: general] : ? [v6: general] : ? [v7: int] : ( ~ (v7 = 0) & % 12.76/2.43 $lesseq(-1, $difference(v1, v4)) & sqrt(v5, v6) = v7 & sqrt(v2, v3) = 0 & % 12.76/2.43 f__integer__($sum(v1, 1)) = v6 & f__integer__(v1) = v3 & % 12.76/2.43 f__integer__($sum(v0, 1)) = v5 & f__integer__(v0) = v2 & $product($sum(v0, % 12.76/2.43 1), $sum(v0, 1)) = v4 & general(v6) & general(v5) & general(v3) & % 12.76/2.43 general(v2)) % 12.76/2.43 % 12.76/2.43 Further assumptions not needed in the proof: % 12.76/2.43 -------------------------------------------- % 12.76/2.43 antisymmetric_ordering_ax, f__integer__def_ax, f__symbolic__def_ax, % 12.76/2.43 formula_0_unnamed_formula, formula_1_completed_definition_of_composite_1, % 12.76/2.43 formula_2_completed_definition_of_sqrtb_1, % 12.76/2.43 formula_3_completed_definition_of_composite_1, % 12.76/2.43 formula_4_completed_definition_of_prime_1, general_universe_ax, % 12.76/2.43 maximal_element_ax, minimal_element_ax, numeral_ordering_ax, % 12.76/2.43 numerals_less_than_symbols_ax, p__greater__def_ax, p__greater_equal__def_ax, % 12.76/2.43 p__is_integer__def_ax, p__is_symbolic__def_ax, p__less__def_ax, % 12.76/2.43 strongly_connected_ordering_ax, transitive_ordering_ax % 12.76/2.43 % 12.76/2.43 Those formulas are unsatisfiable: % 12.76/2.43 --------------------------------- % 12.76/2.43 % 12.76/2.43 Begin of proof % 12.76/2.43 | % 12.76/2.43 | ALPHA: (formula_5_unnamed_formula) implies: % 12.76/2.43 | (1) ! [v0: int] : ! [v1: int] : ! [v2: general] : ! [v3: general] : ( ~ % 12.76/2.43 | (sqrt(v2, v3) = 0) | ~ (f__integer__(v1) = v3) | ~ % 12.76/2.43 | (f__integer__(v0) = v2) | ($lesseq(0, v0) & ? [v4: int] : ? [v5: % 12.76/2.43 | int] : ($lesseq(1, $difference(v5, v1)) & $lesseq(v4, v1) & % 12.76/2.43 | $product($sum(v0, 1), $sum(v0, 1)) = v5 & $product(v0, v0) = % 12.76/2.43 | v4))) % 12.76/2.44 | (2) ! [v0: int] : ! [v1: int] : ! [v2: general] : ! [v3: general] : ! % 12.76/2.44 | [v4: int] : (v4 = 0 | ~ ($lesseq(0, v0)) | ~ (sqrt(v2, v3) = v4) | ~ % 12.76/2.44 | (f__integer__(v1) = v3) | ~ (f__integer__(v0) = v2) | ? [v5: int] : % 12.76/2.44 | ? [v6: int] : ($product($sum(v0, 1), $sum(v0, 1)) = v6 & % 12.76/2.44 | $product(v0, v0) = v5 & ( ~ ($lesseq(1, $difference(v6, v1))) | ~ % 12.76/2.44 | ($lesseq(v5, v1))))) % 12.76/2.44 | % 12.76/2.44 | DELTA: instantiating (formula_6_unnamed_formula) with fresh symbols all_27_0, % 12.76/2.44 | all_27_1, all_27_2, all_27_3, all_27_4, all_27_5, all_27_6, all_27_7 % 12.76/2.44 | gives: % 12.76/2.44 | (3) ~ (all_27_0 = 0) & $lesseq(-1, $difference(all_27_6, all_27_3)) & % 12.76/2.44 | sqrt(all_27_2, all_27_1) = all_27_0 & sqrt(all_27_5, all_27_4) = 0 & % 12.76/2.44 | f__integer__($sum(all_27_6, 1)) = all_27_1 & f__integer__(all_27_6) = % 12.76/2.44 | all_27_4 & f__integer__($sum(all_27_7, 1)) = all_27_2 & % 12.76/2.44 | f__integer__(all_27_7) = all_27_5 & $product($sum(all_27_7, 1), % 12.76/2.44 | $sum(all_27_7, 1)) = all_27_3 & general(all_27_1) & general(all_27_2) % 12.76/2.44 | & general(all_27_4) & general(all_27_5) % 12.76/2.44 | % 12.76/2.44 | ALPHA: (3) implies: % 12.76/2.44 | (4) ~ (all_27_0 = 0) % 12.76/2.44 | (5) $lesseq(-1, $difference(all_27_6, all_27_3)) % 12.76/2.44 | (6) $product($sum(all_27_7, 1), $sum(all_27_7, 1)) = all_27_3 % 12.76/2.44 | (7) f__integer__(all_27_7) = all_27_5 % 12.76/2.44 | (8) f__integer__($sum(all_27_7, 1)) = all_27_2 % 12.76/2.44 | (9) f__integer__(all_27_6) = all_27_4 % 12.76/2.44 | (10) f__integer__($sum(all_27_6, 1)) = all_27_1 % 12.76/2.44 | (11) sqrt(all_27_5, all_27_4) = 0 % 12.76/2.44 | (12) sqrt(all_27_2, all_27_1) = all_27_0 % 12.76/2.44 | % 12.76/2.44 | GROUND_INST: instantiating (1) with all_27_7, all_27_6, all_27_5, all_27_4, % 12.76/2.44 | simplifying with (7), (9), (11) gives: % 12.76/2.44 | (13) $lesseq(0, all_27_7) & ? [v0: int] : ? [v1: int] : ($lesseq(1, % 12.76/2.44 | $difference(v1, all_27_6)) & $lesseq(v0, all_27_6) & % 12.76/2.44 | $product($sum(all_27_7, 1), $sum(all_27_7, 1)) = v1 & % 12.76/2.44 | $product(all_27_7, all_27_7) = v0) % 12.76/2.44 | % 12.76/2.44 | ALPHA: (13) implies: % 12.76/2.44 | (14) ? [v0: int] : ? [v1: int] : ($lesseq(1, $difference(v1, all_27_6)) & % 12.76/2.44 | $lesseq(v0, all_27_6) & $product($sum(all_27_7, 1), $sum(all_27_7, % 12.76/2.44 | 1)) = v1 & $product(all_27_7, all_27_7) = v0) % 12.76/2.44 | % 12.76/2.44 | GROUND_INST: instantiating (2) with $sum(all_27_7, 1), $sum(all_27_6, 1), % 12.76/2.44 | all_27_2, all_27_1, all_27_0, simplifying with (8), (10), (12) % 12.76/2.44 | gives: % 12.76/2.44 | (15) all_27_0 = 0 | ~ ($lesseq(-1, all_27_7)) | ? [v0: int] : ? [v1: % 12.76/2.44 | int] : ($product($sum(all_27_7, 2), $sum(all_27_7, 2)) = v1 & % 12.76/2.44 | $product($sum(all_27_7, 1), $sum(all_27_7, 1)) = v0 & ( ~ % 12.76/2.44 | ($lesseq(2, $difference(v1, all_27_6))) | ~ ($lesseq(-1, % 12.76/2.44 | $difference(all_27_6, v0))))) % 12.76/2.44 | % 12.76/2.44 | DELTA: instantiating (14) with fresh symbols all_47_0, all_47_1 gives: % 12.76/2.44 | (16) $lesseq(1, $difference(all_47_0, all_27_6)) & $lesseq(all_47_1, % 12.76/2.44 | all_27_6) & $product($sum(all_27_7, 1), $sum(all_27_7, 1)) = % 12.76/2.44 | all_47_0 & $product(all_27_7, all_27_7) = all_47_1 % 12.76/2.44 | % 12.76/2.44 | ALPHA: (16) implies: % 12.76/2.44 | (17) $lesseq(all_47_1, all_27_6) % 12.76/2.44 | (18) $lesseq(1, $difference(all_47_0, all_27_6)) % 12.76/2.44 | (19) $product(all_27_7, all_27_7) = all_47_1 % 12.76/2.44 | (20) $product($sum(all_27_7, 1), $sum(all_27_7, 1)) = all_47_0 % 12.76/2.44 | % 12.76/2.44 | THEORY_AXIOM GroebnerMultiplication: % 12.76/2.44 | (21) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ % 12.76/2.44 | ($product($sum(v0, 1), $sum(v0, 1)) = v2) | ~ ($product($sum(v0, % 12.76/2.44 | 1), $sum(v0, 1)) = v1)) % 12.76/2.44 | % 12.76/2.44 | GROUND_INST: instantiating (21) with all_27_7, all_27_3, all_47_0, simplifying % 12.76/2.44 | with (6), (20) gives: % 12.76/2.45 | (22) all_47_0 = all_27_3 % 12.76/2.45 | % 12.76/2.45 | THEORY_AXIOM GroebnerMultiplication: % 12.76/2.45 | (23) ! [v0: int] : ! [v1: int] : ! [v2: int] : ($sum($difference(v2, % 12.76/2.45 | v1), $product(2, v0)) = -1 | ~ ($product($sum(v0, 1), $sum(v0, % 12.76/2.45 | 1)) = v1) | ~ ($product(v0, v0) = v2)) % 12.76/2.45 | % 12.76/2.45 | GROUND_INST: instantiating (23) with all_27_7, all_27_3, all_47_1, simplifying % 12.76/2.45 | with (6), (19) gives: % 12.76/2.45 | (24) $sum($difference(all_47_1, all_27_3), $product(2, all_27_7)) = -1 % 12.76/2.45 | % 12.76/2.45 | REDUCE: (18), (22) imply: % 12.76/2.45 | (25) $lesseq(1, $difference(all_27_3, all_27_6)) % 12.76/2.45 | % 12.76/2.45 | REDUCE: (17), (24) imply: % 12.76/2.45 | (26) $lesseq(-1, $sum($difference(all_27_6, all_27_3), $product(2, % 12.76/2.45 | all_27_7))) % 12.76/2.45 | % 12.76/2.45 | ANTI_SYMM: (5), (25) imply: % 12.76/2.45 | (27) $difference(all_27_3, all_27_6) = 1 % 12.76/2.45 | % 12.76/2.45 | REDUCE: (26), (27) imply: % 12.76/2.45 | (28) $lesseq(0, all_27_7) % 12.76/2.45 | % 12.76/2.45 | SIMP: (28) implies: % 12.76/2.45 | (29) $lesseq(0, all_27_7) % 12.76/2.45 | % 12.76/2.45 | REDUCE: (6), (27) imply: % 12.76/2.45 | (30) $product($sum(all_27_7, 1), $sum(all_27_7, 1)) = $sum(all_27_6, 1) % 12.76/2.45 | % 12.76/2.45 | BETA: splitting (15) gives: % 12.76/2.45 | % 12.76/2.45 | Case 1: % 12.76/2.45 | | % 12.76/2.45 | | (31) $lesseq(all_27_7, -2) % 12.76/2.45 | | % 12.76/2.45 | | COMBINE_INEQS: (29), (31) imply: % 12.76/2.45 | | (32) $false % 12.76/2.45 | | % 12.76/2.45 | | CLOSE: (32) is inconsistent. % 12.76/2.45 | | % 12.76/2.45 | Case 2: % 12.76/2.45 | | % 12.76/2.45 | | (33) all_27_0 = 0 | ? [v0: int] : ? [v1: int] : % 12.76/2.45 | | ($product($sum(all_27_7, 2), $sum(all_27_7, 2)) = v1 & % 12.76/2.45 | | $product($sum(all_27_7, 1), $sum(all_27_7, 1)) = v0 & ( ~ % 12.76/2.45 | | ($lesseq(2, $difference(v1, all_27_6))) | ~ ($lesseq(-1, % 12.76/2.45 | | $difference(all_27_6, v0))))) % 12.76/2.45 | | % 12.76/2.45 | | BETA: splitting (33) gives: % 12.76/2.45 | | % 12.76/2.45 | | Case 1: % 12.76/2.45 | | | % 12.76/2.45 | | | (34) all_27_0 = 0 % 12.76/2.45 | | | % 12.76/2.45 | | | REDUCE: (4), (34) imply: % 12.76/2.45 | | | (35) $false % 12.76/2.45 | | | % 12.76/2.45 | | | CLOSE: (35) is inconsistent. % 12.76/2.45 | | | % 12.76/2.45 | | Case 2: % 12.76/2.45 | | | % 12.76/2.45 | | | (36) ? [v0: int] : ? [v1: int] : ($product($sum(all_27_7, 2), % 12.76/2.45 | | | $sum(all_27_7, 2)) = v1 & $product($sum(all_27_7, 1), % 12.76/2.45 | | | $sum(all_27_7, 1)) = v0 & ( ~ ($lesseq(2, $difference(v1, % 12.76/2.45 | | | all_27_6))) | ~ ($lesseq(-1, $difference(all_27_6, % 12.76/2.45 | | | v0))))) % 12.76/2.45 | | | % 12.76/2.45 | | | DELTA: instantiating (36) with fresh symbols all_66_0, all_66_1 gives: % 12.76/2.45 | | | (37) $product($sum(all_27_7, 2), $sum(all_27_7, 2)) = all_66_0 & % 12.76/2.45 | | | $product($sum(all_27_7, 1), $sum(all_27_7, 1)) = all_66_1 & ( ~ % 12.76/2.45 | | | ($lesseq(2, $difference(all_66_0, all_27_6))) | ~ ($lesseq(-1, % 12.76/2.45 | | | $difference(all_27_6, all_66_1)))) % 12.76/2.45 | | | % 12.76/2.45 | | | ALPHA: (37) implies: % 12.76/2.45 | | | (38) $product($sum(all_27_7, 1), $sum(all_27_7, 1)) = all_66_1 % 12.76/2.45 | | | (39) $product($sum(all_27_7, 2), $sum(all_27_7, 2)) = all_66_0 % 12.76/2.45 | | | (40) ~ ($lesseq(2, $difference(all_66_0, all_27_6))) | ~ ($lesseq(-1, % 12.76/2.45 | | | $difference(all_27_6, all_66_1))) % 12.76/2.45 | | | % 12.76/2.45 | | | THEORY_AXIOM GroebnerMultiplication: % 12.76/2.45 | | | (41) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : % 12.76/2.45 | | | ($difference($difference(v3, v2), $product(2, v0)) = 3 | ~ % 12.76/2.45 | | | ($product($sum(v0, 2), $sum(v0, 2)) = v3) | ~ % 12.76/2.45 | | | ($product($sum(v0, 1), $sum(v0, 1)) = v2) | ~ % 12.76/2.45 | | | ($product($sum(v0, 1), $sum(v0, 1)) = $sum(v1, 1))) % 12.76/2.45 | | | % 12.76/2.45 | | | GROUND_INST: instantiating (41) with all_27_7, all_27_6, all_66_1, % 12.76/2.45 | | | all_66_0, simplifying with (30), (38), (39) gives: % 12.76/2.45 | | | (42) $difference($difference(all_66_0, all_66_1), $product(2, % 12.76/2.45 | | | all_27_7)) = 3 % 12.76/2.45 | | | % 12.76/2.45 | | | THEORY_AXIOM GroebnerMultiplication: % 12.76/2.45 | | | (43) ! [v0: int] : ! [v1: int] : ! [v2: int] : % 12.76/2.45 | | | ($difference($difference(v2, v1), $product(2, v0)) = 4 | ~ % 12.76/2.45 | | | ($product($sum(v0, 2), $sum(v0, 2)) = v2) | ~ % 12.76/2.45 | | | ($product($sum(v0, 1), $sum(v0, 1)) = $sum(v1, 1))) % 12.76/2.45 | | | % 12.76/2.45 | | | GROUND_INST: instantiating (43) with all_27_7, all_27_6, all_66_0, % 12.76/2.45 | | | simplifying with (30), (39) gives: % 12.76/2.45 | | | (44) $difference($difference(all_66_0, all_27_6), $product(2, % 12.76/2.45 | | | all_27_7)) = 4 % 12.76/2.45 | | | % 12.76/2.45 | | | COMBINE_EQS: (42), (44) imply: % 12.76/2.45 | | | (45) $difference(all_66_1, all_27_6) = 1 % 12.76/2.45 | | | % 12.76/2.45 | | | BETA: splitting (40) gives: % 12.76/2.45 | | | % 12.76/2.45 | | | Case 1: % 12.76/2.45 | | | | % 12.76/2.45 | | | | (46) $lesseq(-1, $difference(all_27_6, all_66_0)) % 12.76/2.45 | | | | % 12.76/2.46 | | | | REDUCE: (44), (46) imply: % 12.76/2.46 | | | | (47) $lesseq(all_27_7, -2) % 12.76/2.46 | | | | % 12.76/2.46 | | | | SIMP: (47) implies: % 12.76/2.46 | | | | (48) $lesseq(all_27_7, -2) % 12.76/2.46 | | | | % 12.76/2.46 | | | | COMBINE_INEQS: (29), (48) imply: % 12.76/2.46 | | | | (49) $false % 12.76/2.46 | | | | % 12.76/2.46 | | | | CLOSE: (49) is inconsistent. % 12.76/2.46 | | | | % 12.76/2.46 | | | Case 2: % 12.76/2.46 | | | | % 12.76/2.46 | | | | (50) $lesseq(2, $difference(all_66_1, all_27_6)) % 12.76/2.46 | | | | % 12.76/2.46 | | | | REDUCE: (45), (50) imply: % 12.76/2.46 | | | | (51) $false % 12.76/2.46 | | | | % 12.76/2.46 | | | | CLOSE: (51) is inconsistent. % 12.76/2.46 | | | | % 12.76/2.46 | | | End of split % 12.76/2.46 | | | % 12.76/2.46 | | End of split % 12.76/2.46 | | % 12.76/2.46 | End of split % 12.76/2.46 | % 12.76/2.46 End of proof % 12.76/2.46 % SZS output end Proof for theBenchmark % 12.76/2.46 % 12.76/2.46 1852ms %------------------------------------------------------------------------------