%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC434_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 : n025.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 09:00:29 EDT 2024 % Result : Theorem 180.93s 24.82s % Output : Proof 235.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SWC434_1 : TPTP v8.3.0. Released v8.3.0. % 0.04/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n025.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 14:38:08 EDT 2024 % 0.12/0.34 % CPUTime : % 0.57/0.60 ________ _____ % 0.57/0.60 ___ __ \_________(_)________________________________ % 0.57/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.57/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.57/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.57/0.60 % 0.57/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.57/0.60 (2023-06-19) % 0.57/0.60 % 0.57/0.60 (c) Philipp Rümmer, 2009-2023 % 0.57/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.57/0.60 Amanda Stjerna. % 0.57/0.60 Free software under BSD-3-Clause. % 0.57/0.60 % 0.57/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.57/0.60 % 0.57/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.57/0.62 Running up to 7 provers in parallel. % 0.57/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.57/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.57/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.57/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.57/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.57/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.57/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.80/1.10 Prover 1: Preprocessing ... % 2.80/1.10 Prover 2: Preprocessing ... % 2.80/1.11 Prover 5: Preprocessing ... % 2.80/1.11 Prover 6: Preprocessing ... % 2.80/1.11 Prover 3: Preprocessing ... % 2.80/1.11 Prover 4: Preprocessing ... % 2.80/1.11 Prover 0: Preprocessing ... % 4.74/1.42 Prover 6: Constructing countermodel ... % 4.74/1.43 Prover 3: Constructing countermodel ... % 4.74/1.43 Prover 1: Constructing countermodel ... % 4.74/1.43 Prover 4: Constructing countermodel ... % 5.39/1.46 Prover 0: Proving ... % 5.39/1.48 Prover 5: Proving ... % 5.65/1.51 Prover 2: Proving ... % 6.00/1.54 Prover 6: gave up % 6.00/1.54 Prover 3: gave up % 6.08/1.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.08/1.55 Prover 1: gave up % 6.08/1.55 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 6.08/1.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.08/1.60 Prover 9: Preprocessing ... % 6.08/1.60 Prover 8: Preprocessing ... % 6.08/1.60 Prover 7: Preprocessing ... % 7.01/1.68 Prover 8: Warning: ignoring some quantifiers % 7.01/1.69 Prover 8: Constructing countermodel ... % 7.01/1.70 Prover 7: Constructing countermodel ... % 7.01/1.70 Prover 9: Constructing countermodel ... % 180.93/24.81 Prover 9: proved (23261ms) % 180.93/24.81 % 180.93/24.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 180.93/24.82 % 180.93/24.82 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 181.34/24.86 Prover 10: Preprocessing ... % 181.34/24.86 Prover 2: stopped % 181.34/24.87 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 181.34/24.89 Prover 11: Preprocessing ... % 181.83/24.91 Prover 10: Constructing countermodel ... % 181.83/24.93 Prover 10: gave up % 181.83/24.95 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 181.83/24.96 Prover 11: Constructing countermodel ... % 182.16/24.97 Prover 13: Preprocessing ... % 182.81/25.06 Prover 13: Warning: ignoring some quantifiers % 182.81/25.06 Prover 13: Constructing countermodel ... % 183.62/25.15 Prover 5: stopped % 183.62/25.17 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 183.62/25.20 Prover 16: Preprocessing ... % 184.45/25.27 Prover 16: Warning: ignoring some quantifiers % 184.45/25.28 Prover 16: Constructing countermodel ... % 186.27/25.51 Prover 16: gave up % 186.27/25.53 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 186.64/25.55 Prover 19: Preprocessing ... % 186.64/25.61 Prover 19: Warning: ignoring some quantifiers % 186.64/25.61 Prover 19: Constructing countermodel ... % 186.64/25.64 Prover 0: stopped % 209.70/28.53 Prover 19: stopped % 210.29/28.64 Prover 13: stopped % 217.14/29.89 Prover 7: Found proof (size 78) % 217.14/29.89 Prover 7: proved (28339ms) % 217.43/29.90 Prover 8: stopped % 234.72/38.33 Prover 11: stopped % 235.05/38.54 Prover 4: stopped % 235.05/38.54 % 235.05/38.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 235.05/38.54 % 235.05/38.55 % SZS output start Proof for theBenchmark % 235.05/38.56 Assumptions after simplification: % 235.05/38.56 --------------------------------- % 235.05/38.56 % 235.05/38.56 (conjecture_1) % 235.19/38.57 ? [v0: int] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) & $lesseq(0, v0) & % 235.19/38.57 fast(v0) = v2 & small(v0) = v1) % 235.19/38.57 % 235.19/38.57 (formula_1) % 235.19/38.57 ! [v0: int] : ! [v1: int] : ( ~ (f0(v0) = v1) | $product(v0, v0) = v1) % 235.19/38.57 % 235.19/38.57 (formula_10) % 235.19/38.57 ! [v0: int] : ! [v1: int] : ( ~ (v0(v0) = v1) | ? [v2: int] : (u0(g0, v2) = % 235.19/38.57 v1 & h0(v0) = v2)) & ! [v0: int] : ! [v1: int] : ( ~ (h0(v0) = v1) | ? % 235.19/38.57 [v2: int] : (v0(v0) = v2 & u0(g0, v1) = v2)) % 235.19/38.57 % 235.19/38.57 (formula_11) % 235.19/38.57 ! [v0: int] : ! [v1: int] : ( ~ (small(v0) = v1) | v0(v0) = v1) & ! [v0: % 235.19/38.57 int] : ! [v1: int] : ( ~ (v0(v0) = v1) | small(v0) = v1) % 235.19/38.57 % 235.19/38.57 (formula_12) % 235.19/38.57 ! [v0: int] : ! [v1: int] : ( ~ (f2(v0) = v1) | $product(v0, v0) = v1) % 235.19/38.57 % 235.19/38.57 (formula_13) % 235.19/38.57 g2 = 3 % 235.19/38.57 % 235.19/38.57 (formula_14) % 235.19/38.57 ! [v0: int] : ! [v1: int] : ($difference(v1, $product(8, v0)) = 3 | ~ % 235.19/38.57 (h2(v0) = v1)) % 235.19/38.57 % 235.19/38.57 (formula_15) % 235.19/38.58 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, 0) | % 235.19/38.58 ~ (u2(v0, v1) = v2)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ % 235.19/38.58 ($lesseq(1, v0)) | ~ (u2($sum(v0, -1), v1) = v2) | ? [v3: int] : (u2(v0, % 235.19/38.58 v1) = v3 & f2(v2) = v3)) & ! [v0: int] : ! [v1: int] : ! [v2: int] % 235.19/38.58 : ( ~ ($lesseq(1, v0)) | ~ (u2(v0, v1) = v2) | ? [v3: int] : (u2($sum(v0, % 235.19/38.58 -1), v1) = v3 & f2(v3) = v2)) % 235.19/38.58 % 235.19/38.58 (formula_16) % 235.19/38.58 ! [v0: int] : ! [v1: int] : ( ~ (v2(v0) = v1) | ? [v2: int] : (u2(g2, v2) = % 235.19/38.58 v1 & h2(v0) = v2)) & ! [v0: int] : ! [v1: int] : ( ~ (h2(v0) = v1) | ? % 235.19/38.58 [v2: int] : (v2(v0) = v2 & u2(g2, v1) = v2)) % 235.19/38.58 % 235.19/38.58 (formula_17) % 235.19/38.58 ! [v0: int] : ! [v1: int] : ( ~ (fast(v0) = v1) | v2(v0) = v1) & ! [v0: % 235.19/38.58 int] : ! [v1: int] : ( ~ (v2(v0) = v1) | fast(v0) = v1) % 235.19/38.58 % 235.19/38.58 (formula_2) % 235.19/38.58 g0 = 3 % 235.19/38.58 % 235.19/38.58 (formula_3) % 235.19/38.58 ! [v0: int] : ! [v1: int] : ($difference(v1, $product(2, v0)) = 1 | ~ % 235.19/38.58 (f1(v0) = v1)) % 235.19/38.58 % 235.19/38.58 (formula_4) % 235.19/38.58 g1 = 2 % 235.19/38.58 % 235.19/38.58 (formula_5) % 235.19/38.58 ! [v0: int] : ! [v1: int] : (v1 = $product(2, v0) | ~ (h1(v0) = v1)) % 235.19/38.58 % 235.19/38.58 (formula_6) % 235.19/38.58 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, 0) | % 235.19/38.58 ~ (u1(v0, v1) = v2)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ % 235.19/38.58 ($lesseq(1, v0)) | ~ (u1($sum(v0, -1), v1) = v2) | ? [v3: int] : (u1(v0, % 235.19/38.58 v1) = v3 & f1(v2) = v3)) & ! [v0: int] : ! [v1: int] : ! [v2: int] % 235.19/38.58 : ( ~ ($lesseq(1, v0)) | ~ (u1(v0, v1) = v2) | ? [v3: int] : (u1($sum(v0, % 235.19/38.58 -1), v1) = v3 & f1(v3) = v2)) % 235.19/38.58 % 235.19/38.58 (formula_7) % 235.19/38.59 ! [v0: int] : ! [v1: int] : ( ~ (v1(v0) = v1) | ? [v2: int] : (u1(g1, v2) = % 235.19/38.59 v1 & h1(v0) = v2)) & ! [v0: int] : ! [v1: int] : ( ~ (h1(v0) = v1) | ? % 235.19/38.59 [v2: int] : (v1(v0) = v2 & u1(g1, v1) = v2)) % 235.19/38.59 % 235.19/38.59 (formula_8) % 235.19/38.59 ! [v0: int] : ! [v1: int] : ( ~ (h0(v0) = v1) | v1(v0) = v1) & ! [v0: int] % 235.19/38.59 : ! [v1: int] : ( ~ (v1(v0) = v1) | h0(v0) = v1) % 235.19/38.59 % 235.19/38.59 (formula_9) % 235.19/38.59 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, 0) | % 235.19/38.59 ~ (u0(v0, v1) = v2)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ % 235.19/38.59 ($lesseq(1, v0)) | ~ (u0($sum(v0, -1), v1) = v2) | ? [v3: int] : (u0(v0, % 235.19/38.59 v1) = v3 & f0(v2) = v3)) & ! [v0: int] : ! [v1: int] : ! [v2: int] % 235.19/38.59 : ( ~ ($lesseq(1, v0)) | ~ (u0(v0, v1) = v2) | ? [v3: int] : (u0($sum(v0, % 235.19/38.59 -1), v1) = v3 & f0(v3) = v2)) % 235.19/38.59 % 235.19/38.59 Those formulas are unsatisfiable: % 235.19/38.59 --------------------------------- % 235.19/38.59 % 235.19/38.59 Begin of proof % 235.19/38.59 | % 235.19/38.59 | ALPHA: (formula_6) implies: % 235.19/38.59 | (1) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v0)) | ~ % 235.19/38.59 | (u1(v0, v1) = v2) | ? [v3: int] : (u1($sum(v0, -1), v1) = v3 & % 235.19/38.59 | f1(v3) = v2)) % 235.19/38.59 | (2) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, % 235.19/38.59 | 0) | ~ (u1(v0, v1) = v2)) % 235.19/38.59 | % 235.19/38.59 | ALPHA: (formula_7) implies: % 235.19/38.59 | (3) ! [v0: int] : ! [v1: int] : ( ~ (v1(v0) = v1) | ? [v2: int] : % 235.19/38.59 | (u1(g1, v2) = v1 & h1(v0) = v2)) % 235.19/38.59 | % 235.19/38.59 | ALPHA: (formula_8) implies: % 235.19/38.60 | (4) ! [v0: int] : ! [v1: int] : ( ~ (h0(v0) = v1) | v1(v0) = v1) % 235.19/38.60 | % 235.19/38.60 | ALPHA: (formula_9) implies: % 235.19/38.60 | (5) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v0)) | ~ % 235.19/38.60 | (u0(v0, v1) = v2) | ? [v3: int] : (u0($sum(v0, -1), v1) = v3 & % 235.19/38.60 | f0(v3) = v2)) % 235.19/38.60 | (6) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, % 235.19/38.60 | 0) | ~ (u0(v0, v1) = v2)) % 235.19/38.60 | % 235.19/38.60 | ALPHA: (formula_10) implies: % 235.19/38.60 | (7) ! [v0: int] : ! [v1: int] : ( ~ (v0(v0) = v1) | ? [v2: int] : % 235.19/38.60 | (u0(g0, v2) = v1 & h0(v0) = v2)) % 235.19/38.60 | % 235.19/38.60 | ALPHA: (formula_11) implies: % 235.19/38.60 | (8) ! [v0: int] : ! [v1: int] : ( ~ (small(v0) = v1) | v0(v0) = v1) % 235.19/38.60 | % 235.19/38.60 | ALPHA: (formula_15) implies: % 235.19/38.60 | (9) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v0)) | ~ % 235.19/38.60 | (u2(v0, v1) = v2) | ? [v3: int] : (u2($sum(v0, -1), v1) = v3 & % 235.19/38.60 | f2(v3) = v2)) % 235.19/38.60 | (10) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ % 235.19/38.60 | ($lesseq(v0, 0) | ~ (u2(v0, v1) = v2)) % 235.19/38.60 | % 235.19/38.60 | ALPHA: (formula_16) implies: % 235.19/38.60 | (11) ! [v0: int] : ! [v1: int] : ( ~ (v2(v0) = v1) | ? [v2: int] : % 235.19/38.60 | (u2(g2, v2) = v1 & h2(v0) = v2)) % 235.19/38.60 | % 235.19/38.60 | ALPHA: (formula_17) implies: % 235.19/38.60 | (12) ! [v0: int] : ! [v1: int] : ( ~ (fast(v0) = v1) | v2(v0) = v1) % 235.19/38.60 | % 235.19/38.60 | DELTA: instantiating (conjecture_1) with fresh symbols all_18_0, all_18_1, % 235.19/38.60 | all_18_2 gives: % 235.19/38.60 | (13) ~ (all_18_0 = all_18_1) & $lesseq(0, all_18_2) & fast(all_18_2) = % 235.19/38.60 | all_18_0 & small(all_18_2) = all_18_1 % 235.19/38.60 | % 235.19/38.60 | ALPHA: (13) implies: % 235.19/38.60 | (14) ~ (all_18_0 = all_18_1) % 235.19/38.60 | (15) small(all_18_2) = all_18_1 % 235.19/38.60 | (16) fast(all_18_2) = all_18_0 % 235.19/38.60 | % 235.61/38.65 | GROUND_INST: instantiating (8) with all_18_2, all_18_1, simplifying with (15) % 235.61/38.65 | gives: % 235.61/38.65 | (17) v0(all_18_2) = all_18_1 % 235.61/38.65 | % 235.61/38.65 | GROUND_INST: instantiating (12) with all_18_2, all_18_0, simplifying with (16) % 235.61/38.65 | gives: % 235.61/38.65 | (18) v2(all_18_2) = all_18_0 % 235.61/38.65 | % 235.61/38.65 | GROUND_INST: instantiating (7) with all_18_2, all_18_1, simplifying with (17) % 235.61/38.65 | gives: % 235.61/38.65 | (19) ? [v0: int] : (u0(g0, v0) = all_18_1 & h0(all_18_2) = v0) % 235.61/38.65 | % 235.61/38.65 | GROUND_INST: instantiating (11) with all_18_2, all_18_0, simplifying with (18) % 235.61/38.65 | gives: % 235.61/38.65 | (20) ? [v0: int] : (u2(g2, v0) = all_18_0 & h2(all_18_2) = v0) % 235.61/38.65 | % 235.61/38.65 | DELTA: instantiating (20) with fresh symbol all_36_0 gives: % 235.61/38.65 | (21) u2(g2, all_36_0) = all_18_0 & h2(all_18_2) = all_36_0 % 235.61/38.65 | % 235.61/38.65 | ALPHA: (21) implies: % 235.61/38.65 | (22) h2(all_18_2) = all_36_0 % 235.61/38.65 | (23) u2(g2, all_36_0) = all_18_0 % 235.61/38.65 | % 235.61/38.65 | DELTA: instantiating (19) with fresh symbol all_38_0 gives: % 235.61/38.65 | (24) u0(g0, all_38_0) = all_18_1 & h0(all_18_2) = all_38_0 % 235.61/38.65 | % 235.61/38.65 | ALPHA: (24) implies: % 235.61/38.65 | (25) h0(all_18_2) = all_38_0 % 235.61/38.65 | (26) u0(g0, all_38_0) = all_18_1 % 235.61/38.65 | % 235.61/38.65 | REDUCE: (23), (formula_13) imply: % 235.61/38.65 | (27) u2(3, all_36_0) = all_18_0 % 235.61/38.65 | % 235.61/38.65 | REDUCE: (26), (formula_2) imply: % 235.61/38.66 | (28) u0(3, all_38_0) = all_18_1 % 235.61/38.66 | % 235.61/38.66 | GROUND_INST: instantiating (formula_14) with all_18_2, all_36_0, simplifying % 235.61/38.66 | with (22) gives: % 235.61/38.66 | (29) $difference(all_36_0, $product(8, all_18_2)) = 3 % 235.61/38.66 | % 235.61/38.66 | REDUCE: (27), (29) imply: % 235.61/38.66 | (30) u2(3, $sum($product(8, all_18_2), 3)) = all_18_0 % 235.61/38.66 | % 235.61/38.66 | GROUND_INST: instantiating (4) with all_18_2, all_38_0, simplifying with (25) % 235.61/38.66 | gives: % 235.61/38.66 | (31) v1(all_18_2) = all_38_0 % 235.61/38.66 | % 235.61/38.66 | GROUND_INST: instantiating (5) with 3, all_38_0, all_18_1, simplifying with % 235.61/38.66 | (28) gives: % 235.61/38.66 | (32) ? [v0: int] : (u0(2, all_38_0) = v0 & f0(v0) = all_18_1) % 235.61/38.66 | % 235.61/38.66 | GROUND_INST: instantiating (9) with 3, $sum($product(8, all_18_2), 3), % 235.61/38.66 | all_18_0, simplifying with (30) gives: % 235.61/38.66 | (33) ? [v0: int] : (u2(2, $sum($product(8, all_18_2), 3)) = v0 & f2(v0) = % 235.61/38.66 | all_18_0) % 235.61/38.66 | % 235.61/38.66 | DELTA: instantiating (33) with fresh symbol all_53_0 gives: % 235.61/38.66 | (34) u2(2, $sum($product(8, all_18_2), 3)) = all_53_0 & f2(all_53_0) = % 235.61/38.66 | all_18_0 % 235.61/38.66 | % 235.61/38.66 | ALPHA: (34) implies: % 235.61/38.66 | (35) f2(all_53_0) = all_18_0 % 235.61/38.66 | (36) u2(2, $sum($product(8, all_18_2), 3)) = all_53_0 % 235.61/38.66 | % 235.61/38.66 | DELTA: instantiating (32) with fresh symbol all_59_0 gives: % 235.61/38.66 | (37) u0(2, all_38_0) = all_59_0 & f0(all_59_0) = all_18_1 % 235.61/38.66 | % 235.61/38.66 | ALPHA: (37) implies: % 235.61/38.66 | (38) f0(all_59_0) = all_18_1 % 235.61/38.66 | (39) u0(2, all_38_0) = all_59_0 % 235.61/38.66 | % 235.61/38.66 | GROUND_INST: instantiating (formula_1) with all_59_0, all_18_1, simplifying % 235.61/38.66 | with (38) gives: % 235.61/38.67 | (40) $product(all_59_0, all_59_0) = all_18_1 % 235.61/38.67 | % 235.61/38.67 | GROUND_INST: instantiating (3) with all_18_2, all_38_0, simplifying with (31) % 235.61/38.67 | gives: % 235.61/38.67 | (41) ? [v0: int] : (u1(g1, v0) = all_38_0 & h1(all_18_2) = v0) % 235.61/38.67 | % 235.61/38.67 | GROUND_INST: instantiating (5) with 2, all_38_0, all_59_0, simplifying with % 235.61/38.67 | (39) gives: % 235.61/38.67 | (42) ? [v0: int] : (u0(1, all_38_0) = v0 & f0(v0) = all_59_0) % 235.61/38.67 | % 235.61/38.67 | GROUND_INST: instantiating (formula_12) with all_53_0, all_18_0, simplifying % 235.61/38.67 | with (35) gives: % 235.61/38.67 | (43) $product(all_53_0, all_53_0) = all_18_0 % 235.61/38.67 | % 235.61/38.67 | GROUND_INST: instantiating (9) with 2, $sum($product(8, all_18_2), 3), % 235.61/38.67 | all_53_0, simplifying with (36) gives: % 235.61/38.67 | (44) ? [v0: int] : (u2(1, $sum($product(8, all_18_2), 3)) = v0 & f2(v0) = % 235.61/38.67 | all_53_0) % 235.61/38.67 | % 235.61/38.67 | DELTA: instantiating (44) with fresh symbol all_69_0 gives: % 235.61/38.67 | (45) u2(1, $sum($product(8, all_18_2), 3)) = all_69_0 & f2(all_69_0) = % 235.61/38.67 | all_53_0 % 235.61/38.67 | % 235.61/38.67 | ALPHA: (45) implies: % 235.61/38.67 | (46) f2(all_69_0) = all_53_0 % 235.61/38.67 | (47) u2(1, $sum($product(8, all_18_2), 3)) = all_69_0 % 235.61/38.67 | % 235.61/38.67 | DELTA: instantiating (42) with fresh symbol all_75_0 gives: % 235.61/38.67 | (48) u0(1, all_38_0) = all_75_0 & f0(all_75_0) = all_59_0 % 235.61/38.67 | % 235.61/38.67 | ALPHA: (48) implies: % 235.61/38.67 | (49) f0(all_75_0) = all_59_0 % 235.61/38.67 | (50) u0(1, all_38_0) = all_75_0 % 235.61/38.67 | % 235.61/38.67 | DELTA: instantiating (41) with fresh symbol all_77_0 gives: % 235.61/38.67 | (51) u1(g1, all_77_0) = all_38_0 & h1(all_18_2) = all_77_0 % 235.61/38.67 | % 235.61/38.67 | ALPHA: (51) implies: % 235.61/38.67 | (52) h1(all_18_2) = all_77_0 % 235.61/38.67 | (53) u1(g1, all_77_0) = all_38_0 % 235.61/38.67 | % 235.61/38.67 | REDUCE: (53), (formula_4) imply: % 235.61/38.68 | (54) u1(2, all_77_0) = all_38_0 % 235.61/38.68 | % 235.61/38.68 | GROUND_INST: instantiating (formula_5) with all_18_2, all_77_0, simplifying % 235.61/38.68 | with (52) gives: % 235.61/38.68 | (55) all_77_0 = $product(2, all_18_2) % 235.61/38.68 | % 235.61/38.68 | REDUCE: (54), (55) imply: % 235.61/38.68 | (56) u1(2, $product(2, all_18_2)) = all_38_0 % 235.61/38.68 | % 235.61/38.68 | GROUND_INST: instantiating (formula_1) with all_75_0, all_59_0, simplifying % 235.61/38.68 | with (49) gives: % 235.61/38.68 | (57) $product(all_75_0, all_75_0) = all_59_0 % 235.61/38.68 | % 235.61/38.68 | GROUND_INST: instantiating (1) with 2, $product(2, all_18_2), all_38_0, % 235.61/38.68 | simplifying with (56) gives: % 235.61/38.68 | (58) ? [v0: int] : (u1(1, $product(2, all_18_2)) = v0 & f1(v0) = all_38_0) % 235.61/38.68 | % 235.61/38.68 | GROUND_INST: instantiating (5) with 1, all_38_0, all_75_0, simplifying with % 235.61/38.68 | (50) gives: % 235.61/38.68 | (59) ? [v0: int] : (u0(0, all_38_0) = v0 & f0(v0) = all_75_0) % 235.61/38.68 | % 235.61/38.68 | GROUND_INST: instantiating (formula_12) with all_69_0, all_53_0, simplifying % 235.61/38.68 | with (46) gives: % 235.61/38.68 | (60) $product(all_69_0, all_69_0) = all_53_0 % 235.61/38.68 | % 235.79/38.68 | GROUND_INST: instantiating (9) with 1, $sum($product(8, all_18_2), 3), % 235.79/38.68 | all_69_0, simplifying with (47) gives: % 235.79/38.68 | (61) ? [v0: int] : (u2(0, $sum($product(8, all_18_2), 3)) = v0 & f2(v0) = % 235.79/38.68 | all_69_0) % 235.79/38.68 | % 235.79/38.68 | DELTA: instantiating (58) with fresh symbol all_96_0 gives: % 235.79/38.68 | (62) u1(1, $product(2, all_18_2)) = all_96_0 & f1(all_96_0) = all_38_0 % 235.79/38.68 | % 235.79/38.68 | ALPHA: (62) implies: % 235.79/38.68 | (63) f1(all_96_0) = all_38_0 % 235.79/38.68 | (64) u1(1, $product(2, all_18_2)) = all_96_0 % 235.79/38.68 | % 235.79/38.68 | DELTA: instantiating (61) with fresh symbol all_102_0 gives: % 235.79/38.68 | (65) u2(0, $sum($product(8, all_18_2), 3)) = all_102_0 & f2(all_102_0) = % 235.79/38.68 | all_69_0 % 235.79/38.68 | % 235.79/38.68 | ALPHA: (65) implies: % 235.79/38.68 | (66) f2(all_102_0) = all_69_0 % 235.79/38.69 | (67) u2(0, $sum($product(8, all_18_2), 3)) = all_102_0 % 235.79/38.69 | % 235.79/38.69 | DELTA: instantiating (59) with fresh symbol all_106_0 gives: % 235.79/38.69 | (68) u0(0, all_38_0) = all_106_0 & f0(all_106_0) = all_75_0 % 235.79/38.69 | % 235.79/38.69 | ALPHA: (68) implies: % 235.79/38.69 | (69) f0(all_106_0) = all_75_0 % 235.79/38.69 | (70) u0(0, all_38_0) = all_106_0 % 235.79/38.69 | % 235.79/38.69 | GROUND_INST: instantiating (formula_3) with all_96_0, all_38_0, simplifying % 235.79/38.69 | with (63) gives: % 235.79/38.69 | (71) $difference($product(2, all_96_0), all_38_0) = -1 % 235.79/38.69 | % 235.79/38.69 | GROUND_INST: instantiating (6) with 0, all_38_0, all_106_0, simplifying with % 235.79/38.69 | (70) gives: % 235.79/38.69 | (72) all_106_0 = all_38_0 % 235.79/38.69 | % 235.79/38.69 | GROUND_INST: instantiating (10) with 0, $sum($product(8, all_18_2), 3), % 235.79/38.69 | all_102_0, simplifying with (67) gives: % 235.79/38.69 | (73) $difference(all_102_0, $product(8, all_18_2)) = 3 % 235.79/38.69 | % 235.79/38.69 | COL_REDUCE: introducing fresh symbol sc_117_0_0 defined by: % 235.79/38.69 | (74) $difference(all_96_0, all_38_0) = sc_117_0_0 % 235.79/38.69 | % 235.79/38.69 | COMBINE_EQS: (71), (74) imply: % 235.79/38.69 | (75) $sum(all_38_0, $product(2, sc_117_0_0)) = -1 % 235.79/38.69 | % 235.79/38.69 | COMBINE_EQS: (74), (75) imply: % 235.79/38.69 | (76) $sum(all_96_0, sc_117_0_0) = -1 % 235.79/38.69 | % 235.79/38.69 | COMBINE_EQS: (72), (75) imply: % 235.79/38.69 | (77) $sum(all_106_0, $product(2, sc_117_0_0)) = -1 % 235.79/38.69 | % 235.79/38.69 | REDUCE: (66), (73) imply: % 235.79/38.69 | (78) f2($sum($product(8, all_18_2), 3)) = all_69_0 % 235.79/38.69 | % 235.79/38.69 | REDUCE: (64), (76) imply: % 235.79/38.69 | (79) u1(1, $product(2, all_18_2)) = $difference(-1, sc_117_0_0) % 235.79/38.69 | % 235.79/38.69 | REDUCE: (69), (77) imply: % 235.79/38.69 | (80) f0($difference(-1, $product(2, sc_117_0_0))) = all_75_0 % 235.79/38.69 | % 235.79/38.69 | GROUND_INST: instantiating (formula_1) with $difference(-1, $product(2, % 235.79/38.69 | sc_117_0_0)), all_75_0, simplifying with (80) gives: % 235.79/38.69 | (81) $product($difference(-1, $product(2, sc_117_0_0)), $difference(-1, % 235.79/38.69 | $product(2, sc_117_0_0))) = all_75_0 % 235.79/38.69 | % 235.79/38.69 | GROUND_INST: instantiating (1) with 1, $product(2, all_18_2), $difference(-1, % 235.79/38.69 | sc_117_0_0), simplifying with (79) gives: % 235.79/38.69 | (82) ? [v0: int] : (u1(0, $product(2, all_18_2)) = v0 & f1(v0) = % 235.79/38.69 | $difference(-1, sc_117_0_0)) % 235.79/38.69 | % 235.79/38.69 | GROUND_INST: instantiating (formula_12) with $sum($product(8, all_18_2), 3), % 235.79/38.69 | all_69_0, simplifying with (78) gives: % 235.79/38.70 | (83) $product($sum($product(8, all_18_2), 3), $sum($product(8, all_18_2), % 235.79/38.70 | 3)) = all_69_0 % 235.79/38.70 | % 235.79/38.70 | DELTA: instantiating (82) with fresh symbol all_131_0 gives: % 235.79/38.70 | (84) u1(0, $product(2, all_18_2)) = all_131_0 & f1(all_131_0) = % 235.79/38.70 | $difference(-1, sc_117_0_0) % 235.79/38.70 | % 235.79/38.70 | ALPHA: (84) implies: % 235.79/38.70 | (85) f1(all_131_0) = $difference(-1, sc_117_0_0) % 235.79/38.70 | (86) u1(0, $product(2, all_18_2)) = all_131_0 % 235.79/38.70 | % 235.79/38.70 | GROUND_INST: instantiating (formula_3) with all_131_0, $difference(-1, % 235.79/38.70 | sc_117_0_0), simplifying with (85) gives: % 235.79/38.70 | (87) $sum($product(2, all_131_0), sc_117_0_0) = -2 % 235.79/38.70 | % 235.79/38.70 | GROUND_INST: instantiating (2) with 0, $product(2, all_18_2), all_131_0, % 235.79/38.70 | simplifying with (86) gives: % 235.79/38.70 | (88) all_131_0 = $product(2, all_18_2) % 235.79/38.70 | % 235.79/38.70 | COMBINE_EQS: (87), (88) imply: % 235.79/38.70 | (89) $sum(sc_117_0_0, $product(4, all_18_2)) = -2 % 235.79/38.70 | % 235.79/38.70 | REDUCE: (81), (89) imply: % 235.79/38.70 | (90) $product($sum($product(8, all_18_2), 3), $sum($product(8, all_18_2), % 235.79/38.70 | 3)) = all_75_0 % 235.79/38.70 | % 235.79/38.70 | THEORY_AXIOM GroebnerMultiplication: % 235.79/38.70 | (91) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: % 235.79/38.70 | int] : ! [v5: int] : ! [v6: int] : (v2 = v1 | ~ ($product(v6, v6) % 235.79/38.70 | = v4) | ~ ($product(v5, v5) = v3) | ~ ($product(v4, v4) = v1) | % 235.79/38.70 | ~ ($product(v3, v3) = v2) | ~ ($product($sum($product(8, v0), 3), % 235.79/38.70 | $sum($product(8, v0), 3)) = v6) | ~ ($product($sum($product(8, % 235.79/38.70 | v0), 3), $sum($product(8, v0), 3)) = v5)) % 235.79/38.70 | % 235.79/38.70 | GROUND_INST: instantiating (91) with all_18_2, all_18_1, all_18_0, all_53_0, % 235.79/38.70 | all_59_0, all_69_0, all_75_0, simplifying with (40), (43), (57), % 235.79/38.70 | (60), (83), (90) gives: % 235.79/38.70 | (92) all_18_0 = all_18_1 % 235.79/38.70 | % 235.79/38.70 | REDUCE: (14), (92) imply: % 235.79/38.70 | (93) $false % 235.79/38.71 | % 235.79/38.71 | CLOSE: (93) is inconsistent. % 235.79/38.71 | % 235.79/38.71 End of proof % 235.79/38.71 % SZS output end Proof for theBenchmark % 235.79/38.71 % 235.79/38.71 38101ms %------------------------------------------------------------------------------