%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC482_1 : TPTP v8.3.0. Released v8.3.0. % 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 : Tue May 14 09:00:32 EDT 2024 % Result : Theorem 9.66s 2.14s % Output : Proof 11.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SWC482_1 : TPTP v8.3.0. Released v8.3.0. % 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n004.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Mon May 13 15:00:52 EDT 2024 % 0.12/0.34 % CPUTime : % 0.65/0.66 ________ _____ % 0.65/0.66 ___ __ \_________(_)________________________________ % 0.65/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.65/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.65/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.65/0.66 % 0.65/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.65/0.66 (2023-06-19) % 0.65/0.66 % 0.65/0.66 (c) Philipp Rümmer, 2009-2023 % 0.65/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.65/0.66 Amanda Stjerna. % 0.65/0.66 Free software under BSD-3-Clause. % 0.65/0.66 % 0.65/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.65/0.66 % 0.65/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.72/0.68 Running up to 7 provers in parallel. % 0.72/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.72/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.72/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.72/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.72/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.72/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.72/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.35/1.14 Prover 4: Preprocessing ... % 2.35/1.14 Prover 0: Preprocessing ... % 2.35/1.14 Prover 3: Preprocessing ... % 2.35/1.14 Prover 5: Preprocessing ... % 2.35/1.14 Prover 6: Preprocessing ... % 2.35/1.14 Prover 2: Preprocessing ... % 2.83/1.15 Prover 1: Preprocessing ... % 4.78/1.46 Prover 3: Constructing countermodel ... % 4.78/1.46 Prover 4: Constructing countermodel ... % 4.78/1.47 Prover 1: Constructing countermodel ... % 4.78/1.47 Prover 6: Constructing countermodel ... % 5.04/1.49 Prover 0: Proving ... % 5.04/1.53 Prover 5: Proving ... % 5.56/1.57 Prover 2: Proving ... % 9.66/2.14 Prover 5: proved (1450ms) % 9.66/2.14 % 9.66/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.66/2.14 % 9.66/2.14 Prover 0: proved (1457ms) % 9.66/2.14 % 9.66/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.66/2.14 % 9.66/2.14 Prover 3: stopped % 9.84/2.15 Prover 6: stopped % 9.84/2.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.84/2.15 Prover 2: stopped % 9.84/2.16 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.84/2.16 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.84/2.16 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.84/2.16 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.84/2.17 Prover 7: Preprocessing ... % 9.84/2.18 Prover 8: Preprocessing ... % 9.84/2.19 Prover 11: Preprocessing ... % 9.84/2.19 Prover 13: Preprocessing ... % 9.84/2.19 Prover 10: Preprocessing ... % 10.48/2.25 Prover 4: Found proof (size 46) % 10.48/2.25 Prover 11: Constructing countermodel ... % 10.48/2.25 Prover 4: proved (1559ms) % 10.48/2.25 Prover 1: stopped % 10.48/2.26 Prover 8: Warning: ignoring some quantifiers % 10.48/2.26 Prover 7: Constructing countermodel ... % 10.48/2.26 Prover 11: stopped % 10.48/2.26 Prover 8: Constructing countermodel ... % 10.48/2.27 Prover 7: stopped % 10.48/2.27 Prover 8: stopped % 10.48/2.28 Prover 10: Constructing countermodel ... % 10.48/2.28 Prover 13: Warning: ignoring some quantifiers % 10.48/2.28 Prover 10: stopped % 10.48/2.29 Prover 13: Constructing countermodel ... % 10.93/2.29 Prover 13: stopped % 10.93/2.29 % 10.93/2.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.93/2.29 % 10.93/2.30 % SZS output start Proof for theBenchmark % 10.93/2.30 Assumptions after simplification: % 10.93/2.30 --------------------------------- % 10.93/2.30 % 10.93/2.30 (conjecture_1) % 10.93/2.32 ? [v0: int] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) & $lesseq(0, v0) & % 10.93/2.32 fast(v0) = v2 & small(v0) = v1) % 10.93/2.32 % 10.93/2.32 (formula_1) % 10.93/2.32 ! [v0: int] : ! [v1: int] : ( ~ (f0(v0) = v1) | $product(v0, v0) = v1) % 10.93/2.32 % 10.93/2.32 (formula_10) % 10.93/2.32 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, 0) | % 10.93/2.32 ~ (u1(v0, v1) = v2)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ % 10.93/2.32 ($lesseq(1, v0)) | ~ (u1($sum(v0, -1), v1) = v2) | ? [v3: int] : (u1(v0, % 10.93/2.32 v1) = v3 & f1(v2) = v3)) & ! [v0: int] : ! [v1: int] : ! [v2: int] % 10.93/2.32 : ( ~ ($lesseq(1, v0)) | ~ (u1(v0, v1) = v2) | ? [v3: int] : (u1($sum(v0, % 10.93/2.32 -1), v1) = v3 & f1(v3) = v2)) % 10.93/2.32 % 10.93/2.32 (formula_11) % 10.93/2.33 ! [v0: int] : ! [v1: int] : ( ~ (v1(v0) = v1) | ? [v2: int] : (u1(g1, v2) = % 10.93/2.33 v1 & h1(v0) = v2)) & ! [v0: int] : ! [v1: int] : ( ~ (h1(v0) = v1) | ? % 10.93/2.33 [v2: int] : (v1(v0) = v2 & u1(g1, v1) = v2)) % 10.93/2.33 % 10.93/2.33 (formula_12) % 10.93/2.33 ! [v0: int] : ! [v1: int] : ( ~ (fast(v0) = v1) | ? [v2: int] : ? [v3: % 10.93/2.33 int] : (v1(v0) = v2 & $product($sum($difference(v2, v3), v0), v0) = v1 & % 10.93/2.33 $product(v0, v0) = v3)) & ! [v0: int] : ! [v1: int] : ( ~ (v1(v0) = v1) % 10.93/2.33 | ? [v2: int] : ? [v3: int] : (fast(v0) = v2 & % 10.93/2.33 $product($sum($difference(v1, v3), v0), v0) = v2 & $product(v0, v0) = v3)) % 10.93/2.33 % 10.93/2.33 (formula_2) % 10.93/2.33 g0 = 2 % 10.93/2.33 % 10.93/2.33 (formula_3) % 10.93/2.33 h0 = 2 % 10.93/2.33 % 10.93/2.33 (formula_4) % 10.93/2.33 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, 0) | % 10.93/2.33 ~ (u0(v0, v1) = v2)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ % 10.93/2.33 ($lesseq(1, v0)) | ~ (u0($sum(v0, -1), v1) = v2) | ? [v3: int] : (u0(v0, % 10.93/2.33 v1) = v3 & f0(v2) = v3)) & ! [v0: int] : ! [v1: int] : ! [v2: int] % 10.93/2.33 : ( ~ ($lesseq(1, v0)) | ~ (u0(v0, v1) = v2) | ? [v3: int] : (u0($sum(v0, % 10.93/2.33 -1), v1) = v3 & f0(v3) = v2)) % 10.93/2.33 % 10.93/2.33 (formula_5) % 10.93/2.33 u0(g0, h0) = v0 % 10.93/2.33 % 10.93/2.33 (formula_6) % 10.93/2.34 ! [v0: int] : ! [v1: int] : ( ~ (small(v0) = v1) | ? [v2: int] : ? [v3: % 10.93/2.34 int] : ($product($sum(v3, 4), v0) = v1 & $product(v0, v0) = v2 & % 10.93/2.34 $product($sum(v0, -1), $difference(v2, v0)) = v3)) % 10.93/2.34 % 10.93/2.34 (formula_7) % 10.93/2.34 ! [v0: int] : ! [v1: int] : ( ~ (f1(v0) = v1) | $product(v0, v0) = v1) % 10.93/2.34 % 10.93/2.34 (formula_8) % 10.93/2.34 g1 = 1 % 10.93/2.34 % 10.93/2.34 (formula_9) % 10.93/2.34 ! [v0: int] : ! [v1: int] : ($sum(v1, $product(4, v0)) = 2 | ~ (h1(v0) = % 10.93/2.34 v1)) % 10.93/2.34 % 10.93/2.34 Those formulas are unsatisfiable: % 10.93/2.34 --------------------------------- % 10.93/2.34 % 10.93/2.34 Begin of proof % 10.93/2.34 | % 10.93/2.34 | ALPHA: (formula_4) implies: % 10.93/2.34 | (1) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v0)) | ~ % 10.93/2.34 | (u0(v0, v1) = v2) | ? [v3: int] : (u0($sum(v0, -1), v1) = v3 & % 10.93/2.34 | f0(v3) = v2)) % 10.93/2.34 | (2) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, % 10.93/2.34 | 0) | ~ (u0(v0, v1) = v2)) % 10.93/2.34 | % 10.93/2.34 | ALPHA: (formula_10) implies: % 10.93/2.34 | (3) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v0)) | ~ % 10.93/2.34 | (u1(v0, v1) = v2) | ? [v3: int] : (u1($sum(v0, -1), v1) = v3 & % 10.93/2.34 | f1(v3) = v2)) % 10.93/2.34 | (4) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, % 10.93/2.34 | 0) | ~ (u1(v0, v1) = v2)) % 10.93/2.34 | % 10.93/2.34 | ALPHA: (formula_11) implies: % 10.93/2.35 | (5) ! [v0: int] : ! [v1: int] : ( ~ (v1(v0) = v1) | ? [v2: int] : % 10.93/2.35 | (u1(g1, v2) = v1 & h1(v0) = v2)) % 10.93/2.35 | % 10.93/2.35 | ALPHA: (formula_12) implies: % 10.93/2.35 | (6) ! [v0: int] : ! [v1: int] : ( ~ (fast(v0) = v1) | ? [v2: int] : ? % 10.93/2.35 | [v3: int] : (v1(v0) = v2 & $product($sum($difference(v2, v3), v0), % 10.93/2.35 | v0) = v1 & $product(v0, v0) = v3)) % 10.93/2.35 | % 10.93/2.35 | DELTA: instantiating (conjecture_1) with fresh symbols all_12_0, all_12_1, % 10.93/2.35 | all_12_2 gives: % 10.93/2.35 | (7) ~ (all_12_0 = all_12_1) & $lesseq(0, all_12_2) & fast(all_12_2) = % 10.93/2.35 | all_12_0 & small(all_12_2) = all_12_1 % 10.93/2.35 | % 10.93/2.35 | ALPHA: (7) implies: % 10.93/2.35 | (8) ~ (all_12_0 = all_12_1) % 10.93/2.35 | (9) small(all_12_2) = all_12_1 % 10.93/2.35 | (10) fast(all_12_2) = all_12_0 % 10.93/2.35 | % 10.93/2.35 | REDUCE: (formula_2), (formula_3), (formula_5) imply: % 10.93/2.35 | (11) u0(2, 2) = v0 % 10.93/2.35 | % 10.93/2.35 | GROUND_INST: instantiating (1) with 2, 2, v0, simplifying with (11) gives: % 10.93/2.35 | (12) ? [v0: int] : (u0(1, 2) = v0 & f0(v0) = v0) % 10.93/2.35 | % 10.93/2.35 | GROUND_INST: instantiating (formula_6) with all_12_2, all_12_1, simplifying % 10.93/2.35 | with (9) gives: % 10.93/2.35 | (13) ? [v0: int] : ? [v1: int] : ($product($sum(v1, 4), all_12_2) = % 10.93/2.35 | all_12_1 & $product(all_12_2, all_12_2) = v0 & $product($sum(v0, % 10.93/2.35 | -1), $difference(v0, all_12_2)) = v1) % 10.93/2.35 | % 10.93/2.36 | GROUND_INST: instantiating (6) with all_12_2, all_12_0, simplifying with (10) % 10.93/2.36 | gives: % 10.93/2.36 | (14) ? [v0: int] : ? [v1: int] : (v1(all_12_2) = v0 & % 10.93/2.36 | $product($sum($difference(v0, v1), all_12_2), all_12_2) = all_12_0 & % 10.93/2.36 | $product(all_12_2, all_12_2) = v1) % 10.93/2.36 | % 10.93/2.36 | DELTA: instantiating (12) with fresh symbol all_22_0 gives: % 10.93/2.36 | (15) u0(1, 2) = all_22_0 & f0(all_22_0) = v0 % 10.93/2.36 | % 10.93/2.36 | ALPHA: (15) implies: % 10.93/2.36 | (16) f0(all_22_0) = v0 % 10.93/2.36 | (17) u0(1, 2) = all_22_0 % 10.93/2.36 | % 10.93/2.36 | DELTA: instantiating (14) with fresh symbols all_26_0, all_26_1 gives: % 10.93/2.36 | (18) v1(all_12_2) = all_26_1 & $product($sum($difference(all_26_1, % 10.93/2.36 | all_26_0), all_12_2), all_12_2) = all_12_0 & $product(all_12_2, % 10.93/2.36 | all_12_2) = all_26_0 % 10.93/2.36 | % 10.93/2.36 | ALPHA: (18) implies: % 10.93/2.36 | (19) $product(all_12_2, all_12_2) = all_26_0 % 10.93/2.36 | (20) $product($sum($difference(all_26_1, all_26_0), all_12_2), all_12_2) = % 10.93/2.36 | all_12_0 % 10.93/2.36 | (21) v1(all_12_2) = all_26_1 % 10.93/2.36 | % 10.93/2.36 | DELTA: instantiating (13) with fresh symbols all_28_0, all_28_1 gives: % 11.28/2.36 | (22) $product($sum(all_28_0, 4), all_12_2) = all_12_1 & $product(all_12_2, % 11.28/2.36 | all_12_2) = all_28_1 & $product($sum(v0, -1), $difference(all_28_1, % 11.28/2.36 | all_12_2)) = all_28_0 % 11.28/2.36 | % 11.28/2.36 | ALPHA: (22) implies: % 11.28/2.36 | (23) $product($sum(v0, -1), $difference(all_28_1, all_12_2)) = all_28_0 % 11.28/2.36 | (24) $product(all_12_2, all_12_2) = all_28_1 % 11.28/2.36 | (25) $product($sum(all_28_0, 4), all_12_2) = all_12_1 % 11.28/2.36 | % 11.28/2.36 | THEORY_AXIOM GroebnerMultiplication: % 11.28/2.36 | (26) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ % 11.28/2.36 | ($product(v0, v0) = v2) | ~ ($product(v0, v0) = v1)) % 11.28/2.36 | % 11.28/2.36 | GROUND_INST: instantiating (26) with all_12_2, all_26_0, all_28_1, simplifying % 11.28/2.36 | with (19), (24) gives: % 11.28/2.36 | (27) all_28_1 = all_26_0 % 11.28/2.36 | % 11.28/2.36 | REDUCE: (23), (27) imply: % 11.28/2.36 | (28) $product($sum(v0, -1), $difference(all_26_0, all_12_2)) = all_28_0 % 11.28/2.36 | % 11.28/2.36 | GROUND_INST: instantiating (formula_1) with all_22_0, v0, simplifying with % 11.28/2.36 | (16) gives: % 11.28/2.36 | (29) $product(all_22_0, all_22_0) = v0 % 11.28/2.36 | % 11.28/2.36 | GROUND_INST: instantiating (1) with 1, 2, all_22_0, simplifying with (17) % 11.28/2.36 | gives: % 11.28/2.36 | (30) ? [v0: int] : (u0(0, 2) = v0 & f0(v0) = all_22_0) % 11.28/2.36 | % 11.28/2.36 | GROUND_INST: instantiating (5) with all_12_2, all_26_1, simplifying with (21) % 11.28/2.36 | gives: % 11.28/2.36 | (31) ? [v0: int] : (u1(g1, v0) = all_26_1 & h1(all_12_2) = v0) % 11.28/2.36 | % 11.28/2.36 | DELTA: instantiating (31) with fresh symbol all_45_0 gives: % 11.28/2.36 | (32) u1(g1, all_45_0) = all_26_1 & h1(all_12_2) = all_45_0 % 11.28/2.36 | % 11.28/2.36 | ALPHA: (32) implies: % 11.28/2.36 | (33) h1(all_12_2) = all_45_0 % 11.28/2.37 | (34) u1(g1, all_45_0) = all_26_1 % 11.28/2.37 | % 11.28/2.37 | DELTA: instantiating (30) with fresh symbol all_49_0 gives: % 11.28/2.37 | (35) u0(0, 2) = all_49_0 & f0(all_49_0) = all_22_0 % 11.28/2.37 | % 11.28/2.37 | ALPHA: (35) implies: % 11.28/2.37 | (36) f0(all_49_0) = all_22_0 % 11.28/2.37 | (37) u0(0, 2) = all_49_0 % 11.28/2.37 | % 11.28/2.37 | REDUCE: (34), (formula_8) imply: % 11.28/2.37 | (38) u1(1, all_45_0) = all_26_1 % 11.28/2.37 | % 11.28/2.37 | GROUND_INST: instantiating (2) with 0, 2, all_49_0, simplifying with (37) % 11.28/2.37 | gives: % 11.28/2.37 | (39) all_49_0 = 2 % 11.28/2.37 | % 11.32/2.37 | GROUND_INST: instantiating (formula_9) with all_12_2, all_45_0, simplifying % 11.32/2.37 | with (33) gives: % 11.32/2.37 | (40) $sum(all_45_0, $product(4, all_12_2)) = 2 % 11.32/2.37 | % 11.32/2.37 | REDUCE: (38), (40) imply: % 11.32/2.37 | (41) u1(1, $difference(2, $product(4, all_12_2))) = all_26_1 % 11.32/2.37 | % 11.32/2.37 | REDUCE: (36), (39) imply: % 11.32/2.37 | (42) f0(2) = all_22_0 % 11.32/2.37 | % 11.32/2.37 | GROUND_INST: instantiating (formula_1) with 2, all_22_0, simplifying with (42) % 11.32/2.37 | gives: % 11.32/2.37 | (43) $product(2, 2) = all_22_0 % 11.32/2.37 | % 11.32/2.37 | GROUND_INST: instantiating (3) with 1, $difference(2, $product(4, all_12_2)), % 11.32/2.37 | all_26_1, simplifying with (41) gives: % 11.32/2.37 | (44) ? [v0: int] : (u1(0, $difference(2, $product(4, all_12_2))) = v0 & % 11.32/2.37 | f1(v0) = all_26_1) % 11.32/2.37 | % 11.32/2.37 | DELTA: instantiating (44) with fresh symbol all_73_0 gives: % 11.32/2.37 | (45) u1(0, $difference(2, $product(4, all_12_2))) = all_73_0 & f1(all_73_0) % 11.32/2.37 | = all_26_1 % 11.32/2.37 | % 11.32/2.37 | ALPHA: (45) implies: % 11.32/2.37 | (46) f1(all_73_0) = all_26_1 % 11.32/2.37 | (47) u1(0, $difference(2, $product(4, all_12_2))) = all_73_0 % 11.32/2.37 | % 11.32/2.37 | THEORY_AXIOM GroebnerMultiplication: % 11.32/2.37 | (48) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: % 11.32/2.37 | int] : ($sum($difference(v4, $product(15, v3)), $product(15, v1)) = % 11.32/2.37 | 0 | ~ ($product(v2, v2) = v0) | ~ ($product(v1, v1) = v3) | ~ % 11.32/2.37 | ($product($sum(v0, -1), $difference(v3, v1)) = v4) | ~ ($product(2, % 11.32/2.37 | 2) = v2)) % 11.32/2.37 | % 11.32/2.37 | GROUND_INST: instantiating (48) with v0, all_12_2, all_22_0, all_26_0, % 11.32/2.37 | all_28_0, simplifying with (19), (28), (29), (43) gives: % 11.32/2.37 | (49) $sum($difference(all_28_0, $product(15, all_26_0)), $product(15, % 11.32/2.37 | all_12_2)) = 0 % 11.32/2.37 | % 11.32/2.37 | REDUCE: (25), (49) imply: % 11.32/2.37 | (50) $product($sum($difference($product(15, all_26_0), $product(15, % 11.32/2.37 | all_12_2)), 4), all_12_2) = all_12_1 % 11.32/2.37 | % 11.32/2.37 | GROUND_INST: instantiating (4) with 0, $difference(2, $product(4, all_12_2)), % 11.32/2.37 | all_73_0, simplifying with (47) gives: % 11.32/2.37 | (51) $sum(all_73_0, $product(4, all_12_2)) = 2 % 11.32/2.37 | % 11.32/2.37 | REDUCE: (46), (51) imply: % 11.32/2.37 | (52) f1($difference(2, $product(4, all_12_2))) = all_26_1 % 11.32/2.37 | % 11.32/2.37 | GROUND_INST: instantiating (formula_7) with $difference(2, $product(4, % 11.32/2.37 | all_12_2)), all_26_1, simplifying with (52) gives: % 11.32/2.37 | (53) $product($difference(2, $product(4, all_12_2)), $difference(2, % 11.32/2.37 | $product(4, all_12_2))) = all_26_1 % 11.32/2.37 | % 11.32/2.37 | THEORY_AXIOM GroebnerMultiplication: % 11.32/2.38 | (54) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: % 11.32/2.38 | int] : (v2 = v1 | ~ ($product($sum($difference($product(15, v4), % 11.32/2.38 | $product(15, v0)), 4), v0) = v1) | ~ % 11.32/2.38 | ($product($sum($difference(v3, v4), v0), v0) = v2) | ~ % 11.32/2.38 | ($product($difference(2, $product(4, v0)), $difference(2, % 11.32/2.38 | $product(4, v0))) = v3) | ~ ($product(v0, v0) = v4)) % 11.32/2.38 | % 11.32/2.38 | GROUND_INST: instantiating (54) with all_12_2, all_12_1, all_12_0, all_26_1, % 11.32/2.38 | all_26_0, simplifying with (19), (20), (50), (53) gives: % 11.32/2.38 | (55) all_12_0 = all_12_1 % 11.32/2.38 | % 11.32/2.38 | REDUCE: (8), (55) imply: % 11.32/2.38 | (56) $false % 11.32/2.38 | % 11.32/2.38 | CLOSE: (56) is inconsistent. % 11.32/2.38 | % 11.32/2.38 End of proof % 11.32/2.38 % SZS output end Proof for theBenchmark % 11.32/2.38 % 11.32/2.38 1714ms %------------------------------------------------------------------------------