%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWV236+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%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 : 600s % DateTime : Wed Jul 20 17:50:28 EDT 2022 % Result : Theorem 32.87s 10.17s % Output : Proof 82.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV236+1 : TPTP v8.1.0. Released v3.2.0. % 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n017.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 : 600 % 0.12/0.34 % DateTime : Tue Jun 14 21:41:09 EDT 2022 % 0.12/0.34 % CPUTime : % 0.54/0.59 ____ _ % 0.54/0.59 ___ / __ \_____(_)___ ________ __________ % 0.54/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.59 % 0.54/0.59 A Theorem Prover for First-Order Logic % 0.61/0.59 (ePrincess v.1.0) % 0.61/0.59 % 0.61/0.59 (c) Philipp Rümmer, 2009-2015 % 0.61/0.59 (c) Peter Backeman, 2014-2015 % 0.61/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.61/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.61/0.59 Bug reports to peter@backeman.se % 0.61/0.59 % 0.61/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.61/0.59 % 0.61/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.56/0.94 Prover 0: Preprocessing ... % 2.20/1.19 Prover 0: Constructing countermodel ... % 17.22/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 17.22/5.98 Prover 1: Preprocessing ... % 18.04/6.10 Prover 1: Constructing countermodel ... % 28.04/8.53 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 28.10/8.56 Prover 2: Preprocessing ... % 28.50/8.64 Prover 2: Warning: ignoring some quantifiers % 28.50/8.65 Prover 2: Constructing countermodel ... % 32.87/10.17 Prover 0: proved (5322ms) % 32.87/10.17 Prover 2: stopped % 32.87/10.17 Prover 1: stopped % 32.87/10.17 % 32.87/10.17 No countermodel exists, formula is valid % 32.87/10.17 % SZS status Theorem for theBenchmark % 32.87/10.17 % 32.87/10.17 Generating proof ... found it (size 1424) % 80.62/47.10 % 80.62/47.10 % SZS output start Proof for theBenchmark % 80.62/47.10 Assumed formulas after preprocessing and simplification: % 80.62/47.10 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (crypt(v3, pp) = v4 & crypt(v2, eurk) = v6 & crypt(v1, eurk) = v5 & xor(km, pin) = v3 & xor(km, data) = v2 & xor(km, exp) = v1 & xor(km, imp) = v0 & p(v6) & p(v5) & p(v4) & p(a) & p(pin) & p(data) & p(kp) & p(exp) & p(imp) & p(id) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (crypt(v14, v16) = v17) | ~ (crypt(v12, v9) = v13) | ~ (decrypt(v15, v13) = v16) | ~ (xor(v11, v10) = v15) | ~ (xor(v7, v8) = v12) | ~ (xor(km, v10) = v14) | ~ p(v13) | ~ p(v10) | p(v17) | ? [v18] : (crypt(v0, v11) = v18 & ~ p(v18))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (crypt(v14, v16) = v17) | ~ (crypt(v7, v8) = v13) | ~ (decrypt(v15, v13) = v16) | ~ (xor(v11, v12) = v14) | ~ (xor(v9, v10) = v15) | ~ p(v13) | ~ p(v9) | p(v17) | ? [v18] : ? [v19] : (crypt(v1, v11) = v19 & crypt(v0, v10) = v18 & ( ~ p(v19) | ~ p(v18)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (crypt(v11, v12) = v13) | ~ (xor(v8, kp) = v10) | ~ (xor(v7, v9) = v12) | ~ (xor(km, v10) = v11) | ~ p(v8) | ~ p(v7) | p(v13) | ? [v14] : ? [v15] : ? [v16] : (crypt(v15, v9) = v16 & xor(kp, v8) = v14 & xor(km, v14) = v15 & ~ p(v16))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (crypt(v10, v11) = v12) | ~ (xor(v9, v7) = v11) | ~ (xor(km, v8) = v10) | ~ p(v8) | ~ p(v7) | p(v12) | ? [v13] : ? [v14] : ? [v15] : (crypt(v14, v9) = v15 & xor(v8, kp) = v13 & xor(km, v13) = v14 & ~ p(v15))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (crypt(v10, v8) = v11) | ~ (crypt(v1, v9) = v12) | ~ (xor(km, v7) = v10) | ~ p(v12) | ~ p(v11) | ~ p(v7) | ? [v13] : ? [v14] : (crypt(v13, v8) = v14 & xor(v9, v7) = v13 & p(v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (crypt(v10, v8) = v11) | ~ (xor(v9, v7) = v10) | ~ p(v7) | p(v11) | ? [v12] : ? [v13] : ? [v14] : (crypt(v12, v8) = v13 & crypt(v1, v9) = v14 & xor(km, v7) = v12 & ( ~ p(v14) | ~ p(v13)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (crypt(v10, v7) = v11) | ~ (xor(kp, v8) = v9) | ~ (xor(km, v9) = v10) | ~ p(v8) | ~ p(v7) | p(v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (xor(v10, v9) = v11) | ~ (xor(v7, v8) = v10) | ? [v12] : (xor(v8, v9) = v12 & xor(v7, v12) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (xor(v8, v9) = v10) | ~ (xor(v7, v10) = v11) | ? [v12] : (xor(v12, v9) = v11 & xor(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (crypt(v7, v8) = v9) | ~ (decrypt(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (crypt(v10, v9) = v8) | ~ (crypt(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (decrypt(v10, v9) = v8) | ~ (decrypt(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (xor(v10, v9) = v8) | ~ (xor(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (crypt(v9, v8) = v10) | ~ (xor(v7, data) = v9) | ~ p(v10) | ? [v11] : (crypt(v7, v8) = v11 & p(v11))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (crypt(v8, v7) = v9) | ~ p(v7) | p(v9) | ? [v10] : (crypt(v2, v8) = v10 & ~ p(v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (crypt(v7, v8) = v9) | ~ p(v9) | ~ p(v7) | p(v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (crypt(v7, v8) = v9) | ~ p(v8) | ~ p(v7) | p(v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (crypt(v7, v8) = v9) | p(v9) | ? [v10] : ? [v11] : (crypt(v10, v8) = v11 & xor(v7, data) = v10 & ~ p(v11))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (decrypt(v8, v7) = v9) | ~ p(v7) | p(v9) | ? [v10] : (crypt(v2, v8) = v10 & ~ p(v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (xor(v8, v7) = v9) | xor(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (xor(v7, v8) = v9) | ~ p(v8) | ~ p(v7) | p(v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (xor(v7, v8) = v9) | xor(v8, v7) = v9) & ! [v7] : ! [v8] : (v8 = v7 | ~ (xor(v7, id) = v8)) & ! [v7] : ! [v8] : (v8 = id | ~ (xor(v7, v7) = v8)) & ! [v7] : ( ~ p(v7) | ? [v8] : (crypt(v1, v7) = v8 & ~ p(v8)))) % 80.73/47.15 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields: % 80.73/47.15 | (1) crypt(all_0_3_3, pp) = all_0_2_2 & crypt(all_0_4_4, eurk) = all_0_0_0 & crypt(all_0_5_5, eurk) = all_0_1_1 & xor(km, pin) = all_0_3_3 & xor(km, data) = all_0_4_4 & xor(km, exp) = all_0_5_5 & xor(km, imp) = all_0_6_6 & p(all_0_0_0) & p(all_0_1_1) & p(all_0_2_2) & p(a) & p(pin) & p(data) & p(kp) & p(exp) & p(imp) & p(id) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (crypt(v7, v9) = v10) | ~ (crypt(v5, v2) = v6) | ~ (decrypt(v8, v6) = v9) | ~ (xor(v4, v3) = v8) | ~ (xor(v0, v1) = v5) | ~ (xor(km, v3) = v7) | ~ p(v6) | ~ p(v3) | p(v10) | ? [v11] : (crypt(all_0_6_6, v4) = v11 & ~ p(v11))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (crypt(v7, v9) = v10) | ~ (crypt(v0, v1) = v6) | ~ (decrypt(v8, v6) = v9) | ~ (xor(v4, v5) = v7) | ~ (xor(v2, v3) = v8) | ~ p(v6) | ~ p(v2) | p(v10) | ? [v11] : ? [v12] : (crypt(all_0_5_5, v4) = v12 & crypt(all_0_6_6, v3) = v11 & ( ~ p(v12) | ~ p(v11)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (crypt(v4, v5) = v6) | ~ (xor(v1, kp) = v3) | ~ (xor(v0, v2) = v5) | ~ (xor(km, v3) = v4) | ~ p(v1) | ~ p(v0) | p(v6) | ? [v7] : ? [v8] : ? [v9] : (crypt(v8, v2) = v9 & xor(kp, v1) = v7 & xor(km, v7) = v8 & ~ p(v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (crypt(v3, v4) = v5) | ~ (xor(v2, v0) = v4) | ~ (xor(km, v1) = v3) | ~ p(v1) | ~ p(v0) | p(v5) | ? [v6] : ? [v7] : ? [v8] : (crypt(v7, v2) = v8 & xor(v1, kp) = v6 & xor(km, v6) = v7 & ~ p(v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (crypt(v3, v1) = v4) | ~ (crypt(all_0_5_5, v2) = v5) | ~ (xor(km, v0) = v3) | ~ p(v5) | ~ p(v4) | ~ p(v0) | ? [v6] : ? [v7] : (crypt(v6, v1) = v7 & xor(v2, v0) = v6 & p(v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (crypt(v3, v1) = v4) | ~ (xor(v2, v0) = v3) | ~ p(v0) | p(v4) | ? [v5] : ? [v6] : ? [v7] : (crypt(v5, v1) = v6 & crypt(all_0_5_5, v2) = v7 & xor(km, v0) = v5 & ( ~ p(v7) | ~ p(v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (crypt(v3, v0) = v4) | ~ (xor(kp, v1) = v2) | ~ (xor(km, v2) = v3) | ~ p(v1) | ~ p(v0) | p(v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (xor(v3, v2) = v4) | ~ (xor(v0, v1) = v3) | ? [v5] : (xor(v1, v2) = v5 & xor(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (xor(v1, v2) = v3) | ~ (xor(v0, v3) = v4) | ? [v5] : (xor(v5, v2) = v4 & xor(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (crypt(v0, v1) = v2) | ~ (decrypt(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (crypt(v3, v2) = v1) | ~ (crypt(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (decrypt(v3, v2) = v1) | ~ (decrypt(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (xor(v3, v2) = v1) | ~ (xor(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (crypt(v2, v1) = v3) | ~ (xor(v0, data) = v2) | ~ p(v3) | ? [v4] : (crypt(v0, v1) = v4 & p(v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (crypt(v1, v0) = v2) | ~ p(v0) | p(v2) | ? [v3] : (crypt(all_0_4_4, v1) = v3 & ~ p(v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (crypt(v0, v1) = v2) | ~ p(v2) | ~ p(v0) | p(v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (crypt(v0, v1) = v2) | ~ p(v1) | ~ p(v0) | p(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (crypt(v0, v1) = v2) | p(v2) | ? [v3] : ? [v4] : (crypt(v3, v1) = v4 & xor(v0, data) = v3 & ~ p(v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (decrypt(v1, v0) = v2) | ~ p(v0) | p(v2) | ? [v3] : (crypt(all_0_4_4, v1) = v3 & ~ p(v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (xor(v1, v0) = v2) | xor(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (xor(v0, v1) = v2) | ~ p(v1) | ~ p(v0) | p(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (xor(v0, v1) = v2) | xor(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (xor(v0, id) = v1)) & ! [v0] : ! [v1] : (v1 = id | ~ (xor(v0, v0) = v1)) & ! [v0] : ( ~ p(v0) | ? [v1] : (crypt(all_0_5_5, v0) = v1 & ~ p(v1))) % 80.73/47.17 | % 80.73/47.17 | Applying alpha-rule on (1) yields: % 80.73/47.17 | (2) p(id) % 80.73/47.17 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (crypt(v0, v1) = v2) | ~ p(v2) | ~ p(v0) | p(v1)) % 80.73/47.17 | (4) ! [v0] : ! [v1] : (v1 = v0 | ~ (xor(v0, id) = v1)) % 80.73/47.17 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (crypt(v0, v1) = v2) | ~ p(v1) | ~ p(v0) | p(v2)) % 80.73/47.17 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (xor(v0, v1) = v2) | ~ p(v1) | ~ p(v0) | p(v2)) % 80.73/47.17 | (7) p(imp) % 80.73/47.17 | (8) p(all_0_2_2) % 80.73/47.17 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (crypt(v0, v1) = v2) | p(v2) | ? [v3] : ? [v4] : (crypt(v3, v1) = v4 & xor(v0, data) = v3 & ~ p(v4))) % 80.73/47.17 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (crypt(v1, v0) = v2) | ~ p(v0) | p(v2) | ? [v3] : (crypt(all_0_4_4, v1) = v3 & ~ p(v3))) % 80.73/47.17 | (11) crypt(all_0_3_3, pp) = all_0_2_2 % 80.73/47.17 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (xor(v1, v2) = v3) | ~ (xor(v0, v3) = v4) | ? [v5] : (xor(v5, v2) = v4 & xor(v0, v1) = v5)) % 80.73/47.17 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (crypt(v3, v1) = v4) | ~ (xor(v2, v0) = v3) | ~ p(v0) | p(v4) | ? [v5] : ? [v6] : ? [v7] : (crypt(v5, v1) = v6 & crypt(all_0_5_5, v2) = v7 & xor(km, v0) = v5 & ( ~ p(v7) | ~ p(v6)))) % 80.73/47.17 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (crypt(v7, v9) = v10) | ~ (crypt(v0, v1) = v6) | ~ (decrypt(v8, v6) = v9) | ~ (xor(v4, v5) = v7) | ~ (xor(v2, v3) = v8) | ~ p(v6) | ~ p(v2) | p(v10) | ? [v11] : ? [v12] : (crypt(all_0_5_5, v4) = v12 & crypt(all_0_6_6, v3) = v11 & ( ~ p(v12) | ~ p(v11)))) % 80.73/47.17 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (xor(v3, v2) = v4) | ~ (xor(v0, v1) = v3) | ? [v5] : (xor(v1, v2) = v5 & xor(v0, v5) = v4)) % 80.73/47.17 | (16) crypt(all_0_5_5, eurk) = all_0_1_1 % 80.73/47.17 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (xor(v3, v2) = v1) | ~ (xor(v3, v2) = v0)) % 80.73/47.17 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (decrypt(v1, v0) = v2) | ~ p(v0) | p(v2) | ? [v3] : (crypt(all_0_4_4, v1) = v3 & ~ p(v3))) % 80.73/47.17 | (19) xor(km, data) = all_0_4_4 % 80.73/47.17 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (decrypt(v3, v2) = v1) | ~ (decrypt(v3, v2) = v0)) % 80.73/47.17 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (crypt(v3, v4) = v5) | ~ (xor(v2, v0) = v4) | ~ (xor(km, v1) = v3) | ~ p(v1) | ~ p(v0) | p(v5) | ? [v6] : ? [v7] : ? [v8] : (crypt(v7, v2) = v8 & xor(v1, kp) = v6 & xor(km, v6) = v7 & ~ p(v8))) % 80.73/47.18 | (22) xor(km, pin) = all_0_3_3 % 80.73/47.18 | (23) xor(km, imp) = all_0_6_6 % 80.73/47.18 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (crypt(v3, v1) = v4) | ~ (crypt(all_0_5_5, v2) = v5) | ~ (xor(km, v0) = v3) | ~ p(v5) | ~ p(v4) | ~ p(v0) | ? [v6] : ? [v7] : (crypt(v6, v1) = v7 & xor(v2, v0) = v6 & p(v7))) % 80.73/47.18 | (25) p(exp) % 80.73/47.18 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (crypt(v2, v1) = v3) | ~ (xor(v0, data) = v2) | ~ p(v3) | ? [v4] : (crypt(v0, v1) = v4 & p(v4))) % 80.73/47.18 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (crypt(v3, v0) = v4) | ~ (xor(kp, v1) = v2) | ~ (xor(km, v2) = v3) | ~ p(v1) | ~ p(v0) | p(v4)) % 80.73/47.18 | (28) p(kp) % 80.73/47.18 | (29) crypt(all_0_4_4, eurk) = all_0_0_0 % 80.73/47.18 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (crypt(v3, v2) = v1) | ~ (crypt(v3, v2) = v0)) % 80.73/47.18 | (31) p(data) % 80.73/47.18 | (32) p(all_0_0_0) % 80.73/47.18 | (33) p(all_0_1_1) % 80.73/47.18 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (xor(v0, v1) = v2) | xor(v1, v0) = v2) % 80.73/47.18 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (xor(v1, v0) = v2) | xor(v0, v1) = v2) % 80.73/47.18 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (crypt(v4, v5) = v6) | ~ (xor(v1, kp) = v3) | ~ (xor(v0, v2) = v5) | ~ (xor(km, v3) = v4) | ~ p(v1) | ~ p(v0) | p(v6) | ? [v7] : ? [v8] : ? [v9] : (crypt(v8, v2) = v9 & xor(kp, v1) = v7 & xor(km, v7) = v8 & ~ p(v9))) % 80.73/47.18 | (37) ! [v0] : ( ~ p(v0) | ? [v1] : (crypt(all_0_5_5, v0) = v1 & ~ p(v1))) % 80.73/47.18 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (crypt(v7, v9) = v10) | ~ (crypt(v5, v2) = v6) | ~ (decrypt(v8, v6) = v9) | ~ (xor(v4, v3) = v8) | ~ (xor(v0, v1) = v5) | ~ (xor(km, v3) = v7) | ~ p(v6) | ~ p(v3) | p(v10) | ? [v11] : (crypt(all_0_6_6, v4) = v11 & ~ p(v11))) % 80.73/47.18 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (crypt(v0, v1) = v2) | ~ (decrypt(v0, v2) = v3)) % 80.73/47.18 | (40) p(pin) % 80.73/47.18 | (41) p(a) % 80.73/47.18 | (42) xor(km, exp) = all_0_5_5 % 80.73/47.18 | (43) ! [v0] : ! [v1] : (v1 = id | ~ (xor(v0, v0) = v1)) % 80.73/47.18 | % 80.73/47.18 | Instantiating formula (35) with all_0_4_4, km, data and discharging atoms xor(km, data) = all_0_4_4, yields: % 80.73/47.18 | (44) xor(data, km) = all_0_4_4 % 80.73/47.18 | % 80.73/47.18 | Instantiating formula (35) with all_0_5_5, km, exp and discharging atoms xor(km, exp) = all_0_5_5, yields: % 80.73/47.18 | (45) xor(exp, km) = all_0_5_5 % 80.73/47.18 | % 80.73/47.18 | Instantiating formula (26) with all_0_0_0, all_0_4_4, eurk, km and discharging atoms crypt(all_0_4_4, eurk) = all_0_0_0, xor(km, data) = all_0_4_4, p(all_0_0_0), yields: % 80.73/47.18 | (46) ? [v0] : (crypt(km, eurk) = v0 & p(v0)) % 80.73/47.18 | % 80.73/47.18 | Instantiating formula (37) with all_0_0_0 and discharging atoms p(all_0_0_0), yields: % 80.73/47.18 | (47) ? [v0] : (crypt(all_0_5_5, all_0_0_0) = v0 & ~ p(v0)) % 80.73/47.18 | % 80.73/47.18 | Instantiating formula (37) with all_0_1_1 and discharging atoms p(all_0_1_1), yields: % 80.73/47.18 | (48) ? [v0] : (crypt(all_0_5_5, all_0_1_1) = v0 & ~ p(v0)) % 80.73/47.18 | % 80.73/47.18 | Instantiating formula (37) with all_0_2_2 and discharging atoms p(all_0_2_2), yields: % 80.73/47.18 | (49) ? [v0] : (crypt(all_0_5_5, all_0_2_2) = v0 & ~ p(v0)) % 80.73/47.18 | % 80.73/47.18 | Instantiating formula (37) with a and discharging atoms p(a), yields: % 80.73/47.18 | (50) ? [v0] : (crypt(all_0_5_5, a) = v0 & ~ p(v0)) % 80.73/47.18 | % 80.73/47.18 | Instantiating formula (24) with all_0_1_1, all_0_2_2, all_0_3_3, eurk, pp, pin and discharging atoms crypt(all_0_3_3, pp) = all_0_2_2, crypt(all_0_5_5, eurk) = all_0_1_1, xor(km, pin) = all_0_3_3, p(all_0_1_1), p(all_0_2_2), p(pin), yields: % 80.73/47.18 | (51) ? [v0] : ? [v1] : (crypt(v0, pp) = v1 & xor(eurk, pin) = v0 & p(v1)) % 80.73/47.19 | % 80.73/47.19 | Instantiating formula (37) with pin and discharging atoms p(pin), yields: % 80.73/47.19 | (52) ? [v0] : (crypt(all_0_5_5, pin) = v0 & ~ p(v0)) % 80.73/47.19 | % 80.73/47.19 | Instantiating formula (24) with all_0_1_1, all_0_0_0, all_0_4_4, eurk, eurk, data and discharging atoms crypt(all_0_4_4, eurk) = all_0_0_0, crypt(all_0_5_5, eurk) = all_0_1_1, xor(km, data) = all_0_4_4, p(all_0_0_0), p(all_0_1_1), p(data), yields: % 80.73/47.19 | (53) ? [v0] : ? [v1] : (crypt(v0, eurk) = v1 & xor(eurk, data) = v0 & p(v1)) % 80.73/47.19 | % 80.73/47.19 | Instantiating formula (37) with data and discharging atoms p(data), yields: % 80.73/47.19 | (54) ? [v0] : (crypt(all_0_5_5, data) = v0 & ~ p(v0)) % 80.73/47.19 | % 80.73/47.19 | Instantiating formula (37) with kp and discharging atoms p(kp), yields: % 80.73/47.19 | (55) ? [v0] : (crypt(all_0_5_5, kp) = v0 & ~ p(v0)) % 80.73/47.19 | % 80.73/47.19 | Instantiating formula (24) with all_0_1_1, all_0_1_1, all_0_5_5, eurk, eurk, exp and discharging atoms crypt(all_0_5_5, eurk) = all_0_1_1, xor(km, exp) = all_0_5_5, p(all_0_1_1), p(exp), yields: % 80.73/47.19 | (56) ? [v0] : ? [v1] : (crypt(v0, eurk) = v1 & xor(eurk, exp) = v0 & p(v1)) % 80.73/47.19 | % 80.73/47.19 | Instantiating formula (37) with exp and discharging atoms p(exp), yields: % 80.73/47.19 | (57) ? [v0] : (crypt(all_0_5_5, exp) = v0 & ~ p(v0)) % 80.73/47.19 | % 80.73/47.19 | Instantiating formula (37) with imp and discharging atoms p(imp), yields: % 80.73/47.19 | (58) ? [v0] : (crypt(all_0_5_5, imp) = v0 & ~ p(v0)) % 80.73/47.19 | % 80.73/47.19 | Instantiating formula (37) with id and discharging atoms p(id), yields: % 80.73/47.19 | (59) ? [v0] : (crypt(all_0_5_5, id) = v0 & ~ p(v0)) % 80.73/47.19 | % 80.73/47.19 | Instantiating (59) with all_9_0_7 yields: % 80.73/47.19 | (60) crypt(all_0_5_5, id) = all_9_0_7 & ~ p(all_9_0_7) % 80.73/47.19 | % 80.73/47.19 | Applying alpha-rule on (60) yields: % 80.73/47.19 | (61) crypt(all_0_5_5, id) = all_9_0_7 % 80.73/47.19 | (62) ~ p(all_9_0_7) % 80.73/47.19 | % 80.73/47.19 | Instantiating (58) with all_11_0_8 yields: % 80.73/47.19 | (63) crypt(all_0_5_5, imp) = all_11_0_8 & ~ p(all_11_0_8) % 80.73/47.19 | % 80.73/47.19 | Applying alpha-rule on (63) yields: % 80.73/47.19 | (64) crypt(all_0_5_5, imp) = all_11_0_8 % 80.73/47.19 | (65) ~ p(all_11_0_8) % 80.73/47.19 | % 80.73/47.19 | Instantiating (57) with all_13_0_9 yields: % 80.73/47.19 | (66) crypt(all_0_5_5, exp) = all_13_0_9 & ~ p(all_13_0_9) % 80.73/47.19 | % 80.73/47.19 | Applying alpha-rule on (66) yields: % 80.73/47.19 | (67) crypt(all_0_5_5, exp) = all_13_0_9 % 80.73/47.19 | (68) ~ p(all_13_0_9) % 80.73/47.19 | % 80.73/47.19 | Instantiating (56) with all_15_0_10, all_15_1_11 yields: % 80.73/47.19 | (69) crypt(all_15_1_11, eurk) = all_15_0_10 & xor(eurk, exp) = all_15_1_11 & p(all_15_0_10) % 80.73/47.19 | % 80.73/47.19 | Applying alpha-rule on (69) yields: % 80.73/47.19 | (70) crypt(all_15_1_11, eurk) = all_15_0_10 % 80.73/47.19 | (71) xor(eurk, exp) = all_15_1_11 % 80.73/47.19 | (72) p(all_15_0_10) % 80.73/47.19 | % 80.73/47.19 | Instantiating (53) with all_17_0_12, all_17_1_13 yields: % 80.73/47.19 | (73) crypt(all_17_1_13, eurk) = all_17_0_12 & xor(eurk, data) = all_17_1_13 & p(all_17_0_12) % 80.73/47.19 | % 80.73/47.19 | Applying alpha-rule on (73) yields: % 80.73/47.19 | (74) crypt(all_17_1_13, eurk) = all_17_0_12 % 80.73/47.19 | (75) xor(eurk, data) = all_17_1_13 % 80.73/47.19 | (76) p(all_17_0_12) % 80.73/47.19 | % 80.73/47.19 | Instantiating (51) with all_19_0_14, all_19_1_15 yields: % 80.73/47.19 | (77) crypt(all_19_1_15, pp) = all_19_0_14 & xor(eurk, pin) = all_19_1_15 & p(all_19_0_14) % 80.73/47.19 | % 80.73/47.19 | Applying alpha-rule on (77) yields: % 80.73/47.19 | (78) crypt(all_19_1_15, pp) = all_19_0_14 % 80.73/47.19 | (79) xor(eurk, pin) = all_19_1_15 % 80.73/47.19 | (80) p(all_19_0_14) % 80.73/47.19 | % 80.73/47.19 | Instantiating (49) with all_21_0_16 yields: % 80.73/47.19 | (81) crypt(all_0_5_5, all_0_2_2) = all_21_0_16 & ~ p(all_21_0_16) % 80.73/47.19 | % 80.73/47.19 | Applying alpha-rule on (81) yields: % 80.73/47.19 | (82) crypt(all_0_5_5, all_0_2_2) = all_21_0_16 % 80.73/47.19 | (83) ~ p(all_21_0_16) % 80.73/47.19 | % 80.73/47.19 | Instantiating (48) with all_23_0_17 yields: % 80.73/47.19 | (84) crypt(all_0_5_5, all_0_1_1) = all_23_0_17 & ~ p(all_23_0_17) % 80.73/47.19 | % 80.73/47.19 | Applying alpha-rule on (84) yields: % 80.73/47.19 | (85) crypt(all_0_5_5, all_0_1_1) = all_23_0_17 % 80.73/47.19 | (86) ~ p(all_23_0_17) % 80.73/47.19 | % 80.73/47.19 | Instantiating (47) with all_25_0_18 yields: % 80.73/47.19 | (87) crypt(all_0_5_5, all_0_0_0) = all_25_0_18 & ~ p(all_25_0_18) % 80.73/47.19 | % 80.73/47.19 | Applying alpha-rule on (87) yields: % 80.73/47.19 | (88) crypt(all_0_5_5, all_0_0_0) = all_25_0_18 % 80.73/47.19 | (89) ~ p(all_25_0_18) % 80.73/47.19 | % 80.73/47.19 | Instantiating (50) with all_27_0_19 yields: % 80.73/47.19 | (90) crypt(all_0_5_5, a) = all_27_0_19 & ~ p(all_27_0_19) % 80.73/47.19 | % 80.73/47.19 | Applying alpha-rule on (90) yields: % 80.73/47.19 | (91) crypt(all_0_5_5, a) = all_27_0_19 % 80.73/47.19 | (92) ~ p(all_27_0_19) % 80.73/47.19 | % 80.73/47.19 | Instantiating (46) with all_29_0_20 yields: % 80.73/47.19 | (93) crypt(km, eurk) = all_29_0_20 & p(all_29_0_20) % 80.73/47.19 | % 80.73/47.20 | Applying alpha-rule on (93) yields: % 80.73/47.20 | (94) crypt(km, eurk) = all_29_0_20 % 80.73/47.20 | (95) p(all_29_0_20) % 80.73/47.20 | % 80.73/47.20 | Instantiating (52) with all_31_0_21 yields: % 80.73/47.20 | (96) crypt(all_0_5_5, pin) = all_31_0_21 & ~ p(all_31_0_21) % 80.73/47.20 | % 80.73/47.20 | Applying alpha-rule on (96) yields: % 80.73/47.20 | (97) crypt(all_0_5_5, pin) = all_31_0_21 % 80.73/47.20 | (98) ~ p(all_31_0_21) % 80.73/47.20 | % 80.73/47.20 | Instantiating (55) with all_33_0_22 yields: % 80.73/47.20 | (99) crypt(all_0_5_5, kp) = all_33_0_22 & ~ p(all_33_0_22) % 80.73/47.20 | % 80.73/47.20 | Applying alpha-rule on (99) yields: % 80.73/47.20 | (100) crypt(all_0_5_5, kp) = all_33_0_22 % 80.73/47.20 | (101) ~ p(all_33_0_22) % 80.73/47.20 | % 80.73/47.20 | Instantiating (54) with all_35_0_23 yields: % 80.73/47.20 | (102) crypt(all_0_5_5, data) = all_35_0_23 & ~ p(all_35_0_23) % 80.73/47.20 | % 80.73/47.20 | Applying alpha-rule on (102) yields: % 80.73/47.20 | (103) crypt(all_0_5_5, data) = all_35_0_23 % 80.73/47.20 | (104) ~ p(all_35_0_23) % 80.73/47.20 | % 80.73/47.20 | Instantiating formula (13) with all_25_0_18, all_0_5_5, km, all_0_0_0, exp and discharging atoms crypt(all_0_5_5, all_0_0_0) = all_25_0_18, xor(km, exp) = all_0_5_5, p(exp), ~ p(all_25_0_18), yields: % 80.73/47.20 | (105) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_0_0_0) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 80.73/47.20 | % 80.73/47.20 | Instantiating formula (9) with all_25_0_18, all_0_0_0, all_0_5_5 and discharging atoms crypt(all_0_5_5, all_0_0_0) = all_25_0_18, ~ p(all_25_0_18), yields: % 80.73/47.20 | (106) ? [v0] : ? [v1] : (crypt(v0, all_0_0_0) = v1 & xor(all_0_5_5, data) = v0 & ~ p(v1)) % 80.73/47.20 | % 80.73/47.20 | Instantiating formula (13) with all_23_0_17, all_0_5_5, km, all_0_1_1, exp and discharging atoms crypt(all_0_5_5, all_0_1_1) = all_23_0_17, xor(km, exp) = all_0_5_5, p(exp), ~ p(all_23_0_17), yields: % 80.73/47.20 | (107) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_0_1_1) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 80.73/47.20 | % 80.73/47.20 | Instantiating formula (9) with all_23_0_17, all_0_1_1, all_0_5_5 and discharging atoms crypt(all_0_5_5, all_0_1_1) = all_23_0_17, ~ p(all_23_0_17), yields: % 80.73/47.20 | (108) ? [v0] : ? [v1] : (crypt(v0, all_0_1_1) = v1 & xor(all_0_5_5, data) = v0 & ~ p(v1)) % 80.73/47.20 | % 80.73/47.20 | Instantiating formula (13) with all_21_0_16, all_0_5_5, km, all_0_2_2, exp and discharging atoms crypt(all_0_5_5, all_0_2_2) = all_21_0_16, xor(km, exp) = all_0_5_5, p(exp), ~ p(all_21_0_16), yields: % 80.73/47.20 | (109) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_0_2_2) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 80.73/47.20 | % 80.73/47.20 | Instantiating formula (9) with all_21_0_16, all_0_2_2, all_0_5_5 and discharging atoms crypt(all_0_5_5, all_0_2_2) = all_21_0_16, ~ p(all_21_0_16), yields: % 80.73/47.20 | (110) ? [v0] : ? [v1] : (crypt(v0, all_0_2_2) = v1 & xor(all_0_5_5, data) = v0 & ~ p(v1)) % 80.73/47.20 | % 80.73/47.20 | Instantiating formula (13) with all_27_0_19, all_0_5_5, km, a, exp and discharging atoms crypt(all_0_5_5, a) = all_27_0_19, xor(km, exp) = all_0_5_5, p(exp), ~ p(all_27_0_19), yields: % 80.73/47.20 | (111) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, a) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 80.73/47.20 | % 80.73/47.20 | Instantiating formula (9) with all_27_0_19, a, all_0_5_5 and discharging atoms crypt(all_0_5_5, a) = all_27_0_19, ~ p(all_27_0_19), yields: % 80.73/47.20 | (112) ? [v0] : ? [v1] : (crypt(v0, a) = v1 & xor(all_0_5_5, data) = v0 & ~ p(v1)) % 80.73/47.20 | % 80.73/47.20 | Instantiating formula (13) with all_31_0_21, all_0_5_5, km, pin, exp and discharging atoms crypt(all_0_5_5, pin) = all_31_0_21, xor(km, exp) = all_0_5_5, p(exp), ~ p(all_31_0_21), yields: % 80.73/47.20 | (113) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, pin) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 80.73/47.20 | % 80.73/47.20 | Instantiating formula (9) with all_31_0_21, pin, all_0_5_5 and discharging atoms crypt(all_0_5_5, pin) = all_31_0_21, ~ p(all_31_0_21), yields: % 80.73/47.20 | (114) ? [v0] : ? [v1] : (crypt(v0, pin) = v1 & xor(all_0_5_5, data) = v0 & ~ p(v1)) % 80.73/47.20 | % 80.73/47.20 | Instantiating formula (13) with all_35_0_23, all_0_5_5, km, data, exp and discharging atoms crypt(all_0_5_5, data) = all_35_0_23, xor(km, exp) = all_0_5_5, p(exp), ~ p(all_35_0_23), yields: % 80.73/47.20 | (115) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, data) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 80.73/47.20 | % 80.73/47.20 | Instantiating formula (9) with all_35_0_23, data, all_0_5_5 and discharging atoms crypt(all_0_5_5, data) = all_35_0_23, ~ p(all_35_0_23), yields: % 80.73/47.20 | (116) ? [v0] : ? [v1] : (crypt(v0, data) = v1 & xor(all_0_5_5, data) = v0 & ~ p(v1)) % 80.73/47.20 | % 80.73/47.20 | Instantiating formula (13) with all_33_0_22, all_0_5_5, km, kp, exp and discharging atoms crypt(all_0_5_5, kp) = all_33_0_22, xor(km, exp) = all_0_5_5, p(exp), ~ p(all_33_0_22), yields: % 80.73/47.21 | (117) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, kp) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 80.73/47.21 | % 80.73/47.21 | Instantiating formula (9) with all_33_0_22, kp, all_0_5_5 and discharging atoms crypt(all_0_5_5, kp) = all_33_0_22, ~ p(all_33_0_22), yields: % 80.73/47.21 | (118) ? [v0] : ? [v1] : (crypt(v0, kp) = v1 & xor(all_0_5_5, data) = v0 & ~ p(v1)) % 80.73/47.21 | % 80.73/47.21 | Instantiating formula (13) with all_13_0_9, all_0_5_5, km, exp, exp and discharging atoms crypt(all_0_5_5, exp) = all_13_0_9, xor(km, exp) = all_0_5_5, p(exp), ~ p(all_13_0_9), yields: % 80.73/47.21 | (119) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, exp) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 80.73/47.21 | % 80.73/47.21 | Instantiating formula (9) with all_13_0_9, exp, all_0_5_5 and discharging atoms crypt(all_0_5_5, exp) = all_13_0_9, ~ p(all_13_0_9), yields: % 80.73/47.21 | (120) ? [v0] : ? [v1] : (crypt(v0, exp) = v1 & xor(all_0_5_5, data) = v0 & ~ p(v1)) % 80.73/47.21 | % 80.73/47.21 | Instantiating formula (13) with all_11_0_8, all_0_5_5, km, imp, exp and discharging atoms crypt(all_0_5_5, imp) = all_11_0_8, xor(km, exp) = all_0_5_5, p(exp), ~ p(all_11_0_8), yields: % 80.73/47.21 | (121) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, imp) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 80.73/47.21 | % 80.73/47.21 | Instantiating formula (9) with all_11_0_8, imp, all_0_5_5 and discharging atoms crypt(all_0_5_5, imp) = all_11_0_8, ~ p(all_11_0_8), yields: % 80.73/47.21 | (122) ? [v0] : ? [v1] : (crypt(v0, imp) = v1 & xor(all_0_5_5, data) = v0 & ~ p(v1)) % 80.73/47.21 | % 80.73/47.21 | Instantiating formula (13) with all_9_0_7, all_0_5_5, km, id, exp and discharging atoms crypt(all_0_5_5, id) = all_9_0_7, xor(km, exp) = all_0_5_5, p(exp), ~ p(all_9_0_7), yields: % 80.73/47.21 | (123) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, id) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 80.73/47.21 | % 80.73/47.21 | Instantiating formula (10) with all_9_0_7, all_0_5_5, id and discharging atoms crypt(all_0_5_5, id) = all_9_0_7, p(id), ~ p(all_9_0_7), yields: % 80.73/47.21 | (124) ? [v0] : (crypt(all_0_4_4, all_0_5_5) = v0 & ~ p(v0)) % 80.73/47.21 | % 80.73/47.21 | Instantiating formula (9) with all_9_0_7, id, all_0_5_5 and discharging atoms crypt(all_0_5_5, id) = all_9_0_7, ~ p(all_9_0_7), yields: % 80.73/47.21 | (125) ? [v0] : ? [v1] : (crypt(v0, id) = v1 & xor(all_0_5_5, data) = v0 & ~ p(v1)) % 80.73/47.21 | % 80.73/47.21 | Instantiating formula (37) with all_29_0_20 and discharging atoms p(all_29_0_20), yields: % 80.73/47.21 | (126) ? [v0] : (crypt(all_0_5_5, all_29_0_20) = v0 & ~ p(v0)) % 80.73/47.21 | % 80.73/47.21 | Instantiating formula (37) with all_19_0_14 and discharging atoms p(all_19_0_14), yields: % 80.73/47.21 | (127) ? [v0] : (crypt(all_0_5_5, all_19_0_14) = v0 & ~ p(v0)) % 80.73/47.21 | % 80.73/47.21 | Instantiating formula (26) with all_17_0_12, all_17_1_13, eurk, eurk and discharging atoms crypt(all_17_1_13, eurk) = all_17_0_12, xor(eurk, data) = all_17_1_13, p(all_17_0_12), yields: % 80.73/47.21 | (128) ? [v0] : (crypt(eurk, eurk) = v0 & p(v0)) % 80.73/47.21 | % 80.73/47.21 | Instantiating formula (37) with all_17_0_12 and discharging atoms p(all_17_0_12), yields: % 80.73/47.21 | (129) ? [v0] : (crypt(all_0_5_5, all_17_0_12) = v0 & ~ p(v0)) % 80.73/47.21 | % 80.73/47.21 | Instantiating formula (37) with all_15_0_10 and discharging atoms p(all_15_0_10), yields: % 80.73/47.21 | (130) ? [v0] : (crypt(all_0_5_5, all_15_0_10) = v0 & ~ p(v0)) % 80.73/47.21 | % 80.73/47.21 | Instantiating (130) with all_43_0_24 yields: % 80.73/47.21 | (131) crypt(all_0_5_5, all_15_0_10) = all_43_0_24 & ~ p(all_43_0_24) % 80.73/47.21 | % 80.73/47.21 | Applying alpha-rule on (131) yields: % 80.73/47.21 | (132) crypt(all_0_5_5, all_15_0_10) = all_43_0_24 % 80.73/47.21 | (133) ~ p(all_43_0_24) % 80.73/47.21 | % 80.73/47.21 | Instantiating (119) with all_45_0_25, all_45_1_26, all_45_2_27 yields: % 80.73/47.21 | (134) crypt(all_45_2_27, exp) = all_45_1_26 & crypt(all_0_5_5, km) = all_45_0_25 & xor(km, exp) = all_45_2_27 & ( ~ p(all_45_0_25) | ~ p(all_45_1_26)) % 80.73/47.21 | % 80.73/47.21 | Applying alpha-rule on (134) yields: % 80.73/47.21 | (135) crypt(all_45_2_27, exp) = all_45_1_26 % 80.73/47.21 | (136) crypt(all_0_5_5, km) = all_45_0_25 % 80.73/47.21 | (137) xor(km, exp) = all_45_2_27 % 80.73/47.21 | (138) ~ p(all_45_0_25) | ~ p(all_45_1_26) % 80.73/47.21 | % 80.73/47.21 | Instantiating (117) with all_47_0_28, all_47_1_29, all_47_2_30 yields: % 80.73/47.21 | (139) crypt(all_47_2_30, kp) = all_47_1_29 & crypt(all_0_5_5, km) = all_47_0_28 & xor(km, exp) = all_47_2_30 & ( ~ p(all_47_0_28) | ~ p(all_47_1_29)) % 80.73/47.21 | % 80.73/47.21 | Applying alpha-rule on (139) yields: % 80.73/47.21 | (140) crypt(all_47_2_30, kp) = all_47_1_29 % 80.73/47.21 | (141) crypt(all_0_5_5, km) = all_47_0_28 % 80.73/47.22 | (142) xor(km, exp) = all_47_2_30 % 80.73/47.22 | (143) ~ p(all_47_0_28) | ~ p(all_47_1_29) % 80.73/47.22 | % 81.16/47.22 | Instantiating (116) with all_49_0_31, all_49_1_32 yields: % 81.16/47.22 | (144) crypt(all_49_1_32, data) = all_49_0_31 & xor(all_0_5_5, data) = all_49_1_32 & ~ p(all_49_0_31) % 81.16/47.22 | % 81.16/47.22 | Applying alpha-rule on (144) yields: % 81.16/47.22 | (145) crypt(all_49_1_32, data) = all_49_0_31 % 81.16/47.22 | (146) xor(all_0_5_5, data) = all_49_1_32 % 81.16/47.22 | (147) ~ p(all_49_0_31) % 81.16/47.22 | % 81.16/47.22 | Instantiating (118) with all_51_0_33, all_51_1_34 yields: % 81.16/47.22 | (148) crypt(all_51_1_34, kp) = all_51_0_33 & xor(all_0_5_5, data) = all_51_1_34 & ~ p(all_51_0_33) % 81.16/47.22 | % 81.16/47.22 | Applying alpha-rule on (148) yields: % 81.16/47.22 | (149) crypt(all_51_1_34, kp) = all_51_0_33 % 81.16/47.22 | (150) xor(all_0_5_5, data) = all_51_1_34 % 81.16/47.22 | (151) ~ p(all_51_0_33) % 81.16/47.22 | % 81.16/47.22 | Instantiating (129) with all_53_0_35 yields: % 81.16/47.22 | (152) crypt(all_0_5_5, all_17_0_12) = all_53_0_35 & ~ p(all_53_0_35) % 81.16/47.22 | % 81.16/47.22 | Applying alpha-rule on (152) yields: % 81.16/47.22 | (153) crypt(all_0_5_5, all_17_0_12) = all_53_0_35 % 81.16/47.22 | (154) ~ p(all_53_0_35) % 81.16/47.22 | % 81.16/47.22 | Instantiating (127) with all_55_0_36 yields: % 81.16/47.22 | (155) crypt(all_0_5_5, all_19_0_14) = all_55_0_36 & ~ p(all_55_0_36) % 81.16/47.22 | % 81.16/47.22 | Applying alpha-rule on (155) yields: % 81.16/47.22 | (156) crypt(all_0_5_5, all_19_0_14) = all_55_0_36 % 81.16/47.22 | (157) ~ p(all_55_0_36) % 81.16/47.22 | % 81.16/47.22 | Instantiating (126) with all_57_0_37 yields: % 81.16/47.22 | (158) crypt(all_0_5_5, all_29_0_20) = all_57_0_37 & ~ p(all_57_0_37) % 81.16/47.22 | % 81.16/47.22 | Applying alpha-rule on (158) yields: % 81.16/47.22 | (159) crypt(all_0_5_5, all_29_0_20) = all_57_0_37 % 81.16/47.22 | (160) ~ p(all_57_0_37) % 81.16/47.22 | % 81.16/47.22 | Instantiating (115) with all_59_0_38, all_59_1_39, all_59_2_40 yields: % 81.16/47.22 | (161) crypt(all_59_2_40, data) = all_59_1_39 & crypt(all_0_5_5, km) = all_59_0_38 & xor(km, exp) = all_59_2_40 & ( ~ p(all_59_0_38) | ~ p(all_59_1_39)) % 81.16/47.22 | % 81.16/47.22 | Applying alpha-rule on (161) yields: % 81.16/47.22 | (162) crypt(all_59_2_40, data) = all_59_1_39 % 81.16/47.22 | (163) crypt(all_0_5_5, km) = all_59_0_38 % 81.16/47.22 | (164) xor(km, exp) = all_59_2_40 % 81.16/47.22 | (165) ~ p(all_59_0_38) | ~ p(all_59_1_39) % 81.16/47.22 | % 81.16/47.22 | Instantiating (113) with all_61_0_41, all_61_1_42, all_61_2_43 yields: % 81.16/47.22 | (166) crypt(all_61_2_43, pin) = all_61_1_42 & crypt(all_0_5_5, km) = all_61_0_41 & xor(km, exp) = all_61_2_43 & ( ~ p(all_61_0_41) | ~ p(all_61_1_42)) % 81.16/47.22 | % 81.16/47.22 | Applying alpha-rule on (166) yields: % 81.16/47.22 | (167) crypt(all_61_2_43, pin) = all_61_1_42 % 81.16/47.22 | (168) crypt(all_0_5_5, km) = all_61_0_41 % 81.16/47.22 | (169) xor(km, exp) = all_61_2_43 % 81.16/47.22 | (170) ~ p(all_61_0_41) | ~ p(all_61_1_42) % 81.16/47.22 | % 81.16/47.22 | Instantiating (112) with all_63_0_44, all_63_1_45 yields: % 81.16/47.22 | (171) crypt(all_63_1_45, a) = all_63_0_44 & xor(all_0_5_5, data) = all_63_1_45 & ~ p(all_63_0_44) % 81.16/47.22 | % 81.16/47.22 | Applying alpha-rule on (171) yields: % 81.16/47.22 | (172) crypt(all_63_1_45, a) = all_63_0_44 % 81.16/47.22 | (173) xor(all_0_5_5, data) = all_63_1_45 % 81.16/47.22 | (174) ~ p(all_63_0_44) % 81.16/47.22 | % 81.16/47.22 | Instantiating (114) with all_65_0_46, all_65_1_47 yields: % 81.16/47.22 | (175) crypt(all_65_1_47, pin) = all_65_0_46 & xor(all_0_5_5, data) = all_65_1_47 & ~ p(all_65_0_46) % 81.16/47.22 | % 81.16/47.22 | Applying alpha-rule on (175) yields: % 81.16/47.22 | (176) crypt(all_65_1_47, pin) = all_65_0_46 % 81.16/47.22 | (177) xor(all_0_5_5, data) = all_65_1_47 % 81.16/47.22 | (178) ~ p(all_65_0_46) % 81.16/47.22 | % 81.16/47.22 | Instantiating (111) with all_67_0_48, all_67_1_49, all_67_2_50 yields: % 81.16/47.22 | (179) crypt(all_67_2_50, a) = all_67_1_49 & crypt(all_0_5_5, km) = all_67_0_48 & xor(km, exp) = all_67_2_50 & ( ~ p(all_67_0_48) | ~ p(all_67_1_49)) % 81.16/47.23 | % 81.16/47.23 | Applying alpha-rule on (179) yields: % 81.16/47.23 | (180) crypt(all_67_2_50, a) = all_67_1_49 % 81.16/47.23 | (181) crypt(all_0_5_5, km) = all_67_0_48 % 81.16/47.23 | (182) xor(km, exp) = all_67_2_50 % 81.16/47.23 | (183) ~ p(all_67_0_48) | ~ p(all_67_1_49) % 81.16/47.23 | % 81.16/47.23 | Instantiating (109) with all_69_0_51, all_69_1_52, all_69_2_53 yields: % 81.16/47.23 | (184) crypt(all_69_2_53, all_0_2_2) = all_69_1_52 & crypt(all_0_5_5, km) = all_69_0_51 & xor(km, exp) = all_69_2_53 & ( ~ p(all_69_0_51) | ~ p(all_69_1_52)) % 81.16/47.23 | % 81.16/47.23 | Applying alpha-rule on (184) yields: % 81.16/47.23 | (185) crypt(all_69_2_53, all_0_2_2) = all_69_1_52 % 81.16/47.23 | (186) crypt(all_0_5_5, km) = all_69_0_51 % 81.16/47.23 | (187) xor(km, exp) = all_69_2_53 % 81.16/47.23 | (188) ~ p(all_69_0_51) | ~ p(all_69_1_52) % 81.16/47.23 | % 81.16/47.23 | Instantiating (108) with all_71_0_54, all_71_1_55 yields: % 81.16/47.23 | (189) crypt(all_71_1_55, all_0_1_1) = all_71_0_54 & xor(all_0_5_5, data) = all_71_1_55 & ~ p(all_71_0_54) % 81.16/47.23 | % 81.16/47.23 | Applying alpha-rule on (189) yields: % 81.16/47.23 | (190) crypt(all_71_1_55, all_0_1_1) = all_71_0_54 % 81.16/47.23 | (191) xor(all_0_5_5, data) = all_71_1_55 % 81.16/47.23 | (192) ~ p(all_71_0_54) % 81.16/47.23 | % 81.16/47.23 | Instantiating (128) with all_73_0_56 yields: % 81.16/47.23 | (193) crypt(eurk, eurk) = all_73_0_56 & p(all_73_0_56) % 81.16/47.23 | % 81.16/47.23 | Applying alpha-rule on (193) yields: % 81.16/47.23 | (194) crypt(eurk, eurk) = all_73_0_56 % 81.16/47.23 | (195) p(all_73_0_56) % 81.16/47.23 | % 81.16/47.23 | Instantiating (123) with all_75_0_57, all_75_1_58, all_75_2_59 yields: % 81.16/47.23 | (196) crypt(all_75_2_59, id) = all_75_1_58 & crypt(all_0_5_5, km) = all_75_0_57 & xor(km, exp) = all_75_2_59 & ( ~ p(all_75_0_57) | ~ p(all_75_1_58)) % 81.16/47.23 | % 81.16/47.23 | Applying alpha-rule on (196) yields: % 81.16/47.23 | (197) crypt(all_75_2_59, id) = all_75_1_58 % 81.16/47.23 | (198) crypt(all_0_5_5, km) = all_75_0_57 % 81.16/47.23 | (199) xor(km, exp) = all_75_2_59 % 81.16/47.23 | (200) ~ p(all_75_0_57) | ~ p(all_75_1_58) % 81.16/47.23 | % 81.16/47.23 | Instantiating (122) with all_77_0_60, all_77_1_61 yields: % 81.16/47.23 | (201) crypt(all_77_1_61, imp) = all_77_0_60 & xor(all_0_5_5, data) = all_77_1_61 & ~ p(all_77_0_60) % 81.16/47.23 | % 81.16/47.23 | Applying alpha-rule on (201) yields: % 81.16/47.23 | (202) crypt(all_77_1_61, imp) = all_77_0_60 % 81.16/47.23 | (203) xor(all_0_5_5, data) = all_77_1_61 % 81.16/47.23 | (204) ~ p(all_77_0_60) % 81.16/47.23 | % 81.16/47.23 | Instantiating (125) with all_79_0_62, all_79_1_63 yields: % 81.16/47.23 | (205) crypt(all_79_1_63, id) = all_79_0_62 & xor(all_0_5_5, data) = all_79_1_63 & ~ p(all_79_0_62) % 81.16/47.23 | % 81.16/47.23 | Applying alpha-rule on (205) yields: % 81.16/47.23 | (206) crypt(all_79_1_63, id) = all_79_0_62 % 81.16/47.23 | (207) xor(all_0_5_5, data) = all_79_1_63 % 81.16/47.23 | (208) ~ p(all_79_0_62) % 81.16/47.23 | % 81.16/47.23 | Instantiating (121) with all_81_0_64, all_81_1_65, all_81_2_66 yields: % 81.16/47.23 | (209) crypt(all_81_2_66, imp) = all_81_1_65 & crypt(all_0_5_5, km) = all_81_0_64 & xor(km, exp) = all_81_2_66 & ( ~ p(all_81_0_64) | ~ p(all_81_1_65)) % 81.16/47.23 | % 81.16/47.23 | Applying alpha-rule on (209) yields: % 81.16/47.23 | (210) crypt(all_81_2_66, imp) = all_81_1_65 % 81.16/47.23 | (211) crypt(all_0_5_5, km) = all_81_0_64 % 81.16/47.23 | (212) xor(km, exp) = all_81_2_66 % 81.16/47.23 | (213) ~ p(all_81_0_64) | ~ p(all_81_1_65) % 81.16/47.23 | % 81.16/47.23 | Instantiating (110) with all_83_0_67, all_83_1_68 yields: % 81.16/47.23 | (214) crypt(all_83_1_68, all_0_2_2) = all_83_0_67 & xor(all_0_5_5, data) = all_83_1_68 & ~ p(all_83_0_67) % 81.16/47.24 | % 81.16/47.24 | Applying alpha-rule on (214) yields: % 81.16/47.24 | (215) crypt(all_83_1_68, all_0_2_2) = all_83_0_67 % 81.16/47.24 | (216) xor(all_0_5_5, data) = all_83_1_68 % 81.16/47.24 | (217) ~ p(all_83_0_67) % 81.16/47.24 | % 81.16/47.24 | Instantiating (107) with all_85_0_69, all_85_1_70, all_85_2_71 yields: % 81.16/47.24 | (218) crypt(all_85_2_71, all_0_1_1) = all_85_1_70 & crypt(all_0_5_5, km) = all_85_0_69 & xor(km, exp) = all_85_2_71 & ( ~ p(all_85_0_69) | ~ p(all_85_1_70)) % 81.16/47.24 | % 81.16/47.24 | Applying alpha-rule on (218) yields: % 81.16/47.24 | (219) crypt(all_85_2_71, all_0_1_1) = all_85_1_70 % 81.16/47.24 | (220) crypt(all_0_5_5, km) = all_85_0_69 % 81.16/47.24 | (221) xor(km, exp) = all_85_2_71 % 81.16/47.24 | (222) ~ p(all_85_0_69) | ~ p(all_85_1_70) % 81.16/47.24 | % 81.16/47.24 | Instantiating (124) with all_87_0_72 yields: % 81.16/47.24 | (223) crypt(all_0_4_4, all_0_5_5) = all_87_0_72 & ~ p(all_87_0_72) % 81.16/47.24 | % 81.16/47.24 | Applying alpha-rule on (223) yields: % 81.16/47.24 | (224) crypt(all_0_4_4, all_0_5_5) = all_87_0_72 % 81.16/47.24 | (225) ~ p(all_87_0_72) % 81.16/47.24 | % 81.16/47.24 | Instantiating (105) with all_89_0_73, all_89_1_74, all_89_2_75 yields: % 81.16/47.24 | (226) crypt(all_89_2_75, all_0_0_0) = all_89_1_74 & crypt(all_0_5_5, km) = all_89_0_73 & xor(km, exp) = all_89_2_75 & ( ~ p(all_89_0_73) | ~ p(all_89_1_74)) % 81.16/47.24 | % 81.16/47.24 | Applying alpha-rule on (226) yields: % 81.16/47.24 | (227) crypt(all_89_2_75, all_0_0_0) = all_89_1_74 % 81.16/47.24 | (228) crypt(all_0_5_5, km) = all_89_0_73 % 81.16/47.24 | (229) xor(km, exp) = all_89_2_75 % 81.16/47.24 | (230) ~ p(all_89_0_73) | ~ p(all_89_1_74) % 81.16/47.24 | % 81.16/47.24 | Instantiating (106) with all_91_0_76, all_91_1_77 yields: % 81.16/47.24 | (231) crypt(all_91_1_77, all_0_0_0) = all_91_0_76 & xor(all_0_5_5, data) = all_91_1_77 & ~ p(all_91_0_76) % 81.16/47.24 | % 81.16/47.24 | Applying alpha-rule on (231) yields: % 81.16/47.24 | (232) crypt(all_91_1_77, all_0_0_0) = all_91_0_76 % 81.16/47.24 | (233) xor(all_0_5_5, data) = all_91_1_77 % 81.16/47.24 | (234) ~ p(all_91_0_76) % 81.16/47.24 | % 81.16/47.24 | Instantiating (120) with all_93_0_78, all_93_1_79 yields: % 81.16/47.24 | (235) crypt(all_93_1_79, exp) = all_93_0_78 & xor(all_0_5_5, data) = all_93_1_79 & ~ p(all_93_0_78) % 81.16/47.24 | % 81.16/47.24 | Applying alpha-rule on (235) yields: % 81.16/47.24 | (236) crypt(all_93_1_79, exp) = all_93_0_78 % 81.16/47.24 | (237) xor(all_0_5_5, data) = all_93_1_79 % 81.16/47.24 | (238) ~ p(all_93_0_78) % 81.16/47.24 | % 81.16/47.24 | Instantiating formula (17) with all_0_5_5, data, all_91_1_77, all_93_1_79 and discharging atoms xor(all_0_5_5, data) = all_93_1_79, xor(all_0_5_5, data) = all_91_1_77, yields: % 81.16/47.24 | (239) all_93_1_79 = all_91_1_77 % 81.16/47.24 | % 81.16/47.24 | Instantiating formula (17) with all_0_5_5, data, all_83_1_68, all_93_1_79 and discharging atoms xor(all_0_5_5, data) = all_93_1_79, xor(all_0_5_5, data) = all_83_1_68, yields: % 81.16/47.24 | (240) all_93_1_79 = all_83_1_68 % 81.16/47.24 | % 81.16/47.24 | Instantiating formula (17) with all_0_5_5, data, all_79_1_63, all_83_1_68 and discharging atoms xor(all_0_5_5, data) = all_83_1_68, xor(all_0_5_5, data) = all_79_1_63, yields: % 81.16/47.24 | (241) all_83_1_68 = all_79_1_63 % 81.16/47.24 | % 81.16/47.24 | Instantiating formula (17) with all_0_5_5, data, all_77_1_61, all_79_1_63 and discharging atoms xor(all_0_5_5, data) = all_79_1_63, xor(all_0_5_5, data) = all_77_1_61, yields: % 81.16/47.24 | (242) all_79_1_63 = all_77_1_61 % 81.16/47.24 | % 81.16/47.24 | Instantiating formula (17) with all_0_5_5, data, all_71_1_55, all_77_1_61 and discharging atoms xor(all_0_5_5, data) = all_77_1_61, xor(all_0_5_5, data) = all_71_1_55, yields: % 81.16/47.24 | (243) all_77_1_61 = all_71_1_55 % 81.16/47.24 | % 81.16/47.24 | Instantiating formula (17) with all_0_5_5, data, all_65_1_47, all_71_1_55 and discharging atoms xor(all_0_5_5, data) = all_71_1_55, xor(all_0_5_5, data) = all_65_1_47, yields: % 81.16/47.24 | (244) all_71_1_55 = all_65_1_47 % 81.16/47.24 | % 81.16/47.24 | Instantiating formula (17) with all_0_5_5, data, all_63_1_45, all_65_1_47 and discharging atoms xor(all_0_5_5, data) = all_65_1_47, xor(all_0_5_5, data) = all_63_1_45, yields: % 81.16/47.24 | (245) all_65_1_47 = all_63_1_45 % 81.16/47.24 | % 81.16/47.24 | Instantiating formula (17) with all_0_5_5, data, all_51_1_34, all_93_1_79 and discharging atoms xor(all_0_5_5, data) = all_93_1_79, xor(all_0_5_5, data) = all_51_1_34, yields: % 81.16/47.25 | (246) all_93_1_79 = all_51_1_34 % 81.16/47.25 | % 81.16/47.25 | Instantiating formula (17) with all_0_5_5, data, all_49_1_32, all_63_1_45 and discharging atoms xor(all_0_5_5, data) = all_63_1_45, xor(all_0_5_5, data) = all_49_1_32, yields: % 81.16/47.25 | (247) all_63_1_45 = all_49_1_32 % 81.16/47.25 | % 81.16/47.25 | Instantiating formula (17) with km, exp, all_89_2_75, all_0_5_5 and discharging atoms xor(km, exp) = all_89_2_75, xor(km, exp) = all_0_5_5, yields: % 81.16/47.25 | (248) all_89_2_75 = all_0_5_5 % 81.16/47.25 | % 81.16/47.25 | Instantiating formula (17) with km, exp, all_85_2_71, all_89_2_75 and discharging atoms xor(km, exp) = all_89_2_75, xor(km, exp) = all_85_2_71, yields: % 81.16/47.25 | (249) all_89_2_75 = all_85_2_71 % 81.16/47.25 | % 81.16/47.25 | Instantiating formula (17) with km, exp, all_75_2_59, all_89_2_75 and discharging atoms xor(km, exp) = all_89_2_75, xor(km, exp) = all_75_2_59, yields: % 81.16/47.25 | (250) all_89_2_75 = all_75_2_59 % 81.16/47.25 | % 81.16/47.25 | Instantiating formula (17) with km, exp, all_69_2_53, all_81_2_66 and discharging atoms xor(km, exp) = all_81_2_66, xor(km, exp) = all_69_2_53, yields: % 81.16/47.25 | (251) all_81_2_66 = all_69_2_53 % 81.16/47.25 | % 81.16/47.25 | Instantiating formula (17) with km, exp, all_67_2_50, all_75_2_59 and discharging atoms xor(km, exp) = all_75_2_59, xor(km, exp) = all_67_2_50, yields: % 81.16/47.25 | (252) all_75_2_59 = all_67_2_50 % 81.16/47.25 | % 81.16/47.25 | Instantiating formula (17) with km, exp, all_61_2_43, all_67_2_50 and discharging atoms xor(km, exp) = all_67_2_50, xor(km, exp) = all_61_2_43, yields: % 81.16/47.25 | (253) all_67_2_50 = all_61_2_43 % 81.16/47.25 | % 81.16/47.25 | Instantiating formula (17) with km, exp, all_59_2_40, all_81_2_66 and discharging atoms xor(km, exp) = all_81_2_66, xor(km, exp) = all_59_2_40, yields: % 81.16/47.25 | (254) all_81_2_66 = all_59_2_40 % 81.16/47.25 | % 81.16/47.25 | Instantiating formula (17) with km, exp, all_59_2_40, all_61_2_43 and discharging atoms xor(km, exp) = all_61_2_43, xor(km, exp) = all_59_2_40, yields: % 81.16/47.25 | (255) all_61_2_43 = all_59_2_40 % 81.16/47.25 | % 81.16/47.25 | Instantiating formula (17) with km, exp, all_47_2_30, all_81_2_66 and discharging atoms xor(km, exp) = all_81_2_66, xor(km, exp) = all_47_2_30, yields: % 81.16/47.25 | (256) all_81_2_66 = all_47_2_30 % 81.16/47.25 | % 81.16/47.25 | Instantiating formula (17) with km, exp, all_45_2_27, all_59_2_40 and discharging atoms xor(km, exp) = all_59_2_40, xor(km, exp) = all_45_2_27, yields: % 81.16/47.25 | (257) all_59_2_40 = all_45_2_27 % 81.16/47.25 | % 81.16/47.25 | Combining equations (240,239) yields a new equation: % 81.16/47.25 | (258) all_91_1_77 = all_83_1_68 % 81.16/47.25 | % 81.16/47.25 | Combining equations (246,239) yields a new equation: % 81.16/47.25 | (259) all_91_1_77 = all_51_1_34 % 81.16/47.25 | % 81.16/47.25 | Combining equations (258,259) yields a new equation: % 81.16/47.25 | (260) all_83_1_68 = all_51_1_34 % 81.16/47.25 | % 81.16/47.25 | Simplifying 260 yields: % 81.16/47.25 | (261) all_83_1_68 = all_51_1_34 % 81.16/47.25 | % 81.16/47.25 | Combining equations (250,249) yields a new equation: % 81.16/47.25 | (262) all_85_2_71 = all_75_2_59 % 81.16/47.25 | % 81.16/47.25 | Combining equations (248,249) yields a new equation: % 81.16/47.25 | (263) all_85_2_71 = all_0_5_5 % 81.16/47.25 | % 81.16/47.25 | Combining equations (262,263) yields a new equation: % 81.16/47.25 | (264) all_75_2_59 = all_0_5_5 % 81.16/47.25 | % 81.16/47.25 | Simplifying 264 yields: % 81.16/47.25 | (265) all_75_2_59 = all_0_5_5 % 81.16/47.25 | % 81.16/47.25 | Combining equations (241,261) yields a new equation: % 81.16/47.25 | (266) all_79_1_63 = all_51_1_34 % 81.16/47.25 | % 81.16/47.25 | Simplifying 266 yields: % 81.16/47.25 | (267) all_79_1_63 = all_51_1_34 % 81.16/47.25 | % 81.16/47.25 | Combining equations (254,251) yields a new equation: % 81.16/47.25 | (268) all_69_2_53 = all_59_2_40 % 81.16/47.25 | % 81.16/47.25 | Combining equations (256,251) yields a new equation: % 81.16/47.26 | (269) all_69_2_53 = all_47_2_30 % 81.16/47.26 | % 81.16/47.26 | Combining equations (242,267) yields a new equation: % 81.16/47.26 | (270) all_77_1_61 = all_51_1_34 % 81.16/47.26 | % 81.16/47.26 | Simplifying 270 yields: % 81.16/47.26 | (271) all_77_1_61 = all_51_1_34 % 81.16/47.26 | % 81.16/47.26 | Combining equations (243,271) yields a new equation: % 81.16/47.26 | (272) all_71_1_55 = all_51_1_34 % 81.16/47.26 | % 81.16/47.26 | Simplifying 272 yields: % 81.16/47.26 | (273) all_71_1_55 = all_51_1_34 % 81.16/47.26 | % 81.16/47.26 | Combining equations (252,265) yields a new equation: % 81.16/47.26 | (274) all_67_2_50 = all_0_5_5 % 81.16/47.26 | % 81.16/47.26 | Simplifying 274 yields: % 81.16/47.26 | (275) all_67_2_50 = all_0_5_5 % 81.16/47.26 | % 81.16/47.26 | Combining equations (244,273) yields a new equation: % 81.16/47.26 | (276) all_65_1_47 = all_51_1_34 % 81.16/47.26 | % 81.16/47.26 | Simplifying 276 yields: % 81.16/47.26 | (277) all_65_1_47 = all_51_1_34 % 81.16/47.26 | % 81.16/47.26 | Combining equations (268,269) yields a new equation: % 81.16/47.26 | (278) all_59_2_40 = all_47_2_30 % 81.16/47.26 | % 81.16/47.26 | Simplifying 278 yields: % 81.16/47.26 | (279) all_59_2_40 = all_47_2_30 % 81.16/47.26 | % 81.16/47.26 | Combining equations (253,275) yields a new equation: % 81.16/47.26 | (280) all_61_2_43 = all_0_5_5 % 81.16/47.26 | % 81.16/47.26 | Simplifying 280 yields: % 81.16/47.26 | (281) all_61_2_43 = all_0_5_5 % 81.16/47.26 | % 81.16/47.26 | Combining equations (245,277) yields a new equation: % 81.16/47.26 | (282) all_63_1_45 = all_51_1_34 % 81.16/47.26 | % 81.16/47.26 | Simplifying 282 yields: % 81.16/47.26 | (283) all_63_1_45 = all_51_1_34 % 81.16/47.26 | % 81.16/47.26 | Combining equations (247,283) yields a new equation: % 81.16/47.26 | (284) all_51_1_34 = all_49_1_32 % 81.16/47.26 | % 81.16/47.26 | Combining equations (255,281) yields a new equation: % 81.16/47.26 | (285) all_59_2_40 = all_0_5_5 % 81.16/47.26 | % 81.16/47.26 | Simplifying 285 yields: % 81.16/47.26 | (286) all_59_2_40 = all_0_5_5 % 81.16/47.26 | % 81.16/47.26 | Combining equations (257,279) yields a new equation: % 81.16/47.26 | (287) all_47_2_30 = all_45_2_27 % 81.16/47.26 | % 81.16/47.26 | Combining equations (286,279) yields a new equation: % 81.16/47.26 | (288) all_47_2_30 = all_0_5_5 % 81.16/47.26 | % 81.16/47.26 | Combining equations (288,287) yields a new equation: % 81.16/47.26 | (289) all_45_2_27 = all_0_5_5 % 81.16/47.26 | % 81.16/47.26 | Combining equations (284,283) yields a new equation: % 81.16/47.26 | (247) all_63_1_45 = all_49_1_32 % 81.16/47.26 | % 81.16/47.26 | Combining equations (284,277) yields a new equation: % 81.16/47.26 | (291) all_65_1_47 = all_49_1_32 % 81.16/47.26 | % 81.16/47.26 | Combining equations (284,273) yields a new equation: % 81.16/47.26 | (292) all_71_1_55 = all_49_1_32 % 81.16/47.26 | % 81.16/47.26 | Combining equations (284,271) yields a new equation: % 81.16/47.26 | (293) all_77_1_61 = all_49_1_32 % 81.16/47.26 | % 81.16/47.26 | Combining equations (284,267) yields a new equation: % 81.16/47.26 | (294) all_79_1_63 = all_49_1_32 % 81.16/47.26 | % 81.16/47.26 | Combining equations (284,261) yields a new equation: % 81.16/47.26 | (295) all_83_1_68 = all_49_1_32 % 81.16/47.26 | % 81.16/47.26 | Combining equations (284,259) yields a new equation: % 81.16/47.26 | (296) all_91_1_77 = all_49_1_32 % 81.16/47.26 | % 81.16/47.26 | Combining equations (296,239) yields a new equation: % 81.16/47.26 | (297) all_93_1_79 = all_49_1_32 % 81.16/47.26 | % 81.16/47.26 | From (297) and (236) follows: % 81.16/47.27 | (298) crypt(all_49_1_32, exp) = all_93_0_78 % 81.16/47.27 | % 81.16/47.27 | From (296) and (232) follows: % 81.16/47.27 | (299) crypt(all_49_1_32, all_0_0_0) = all_91_0_76 % 81.16/47.27 | % 81.16/47.27 | From (295) and (215) follows: % 81.16/47.27 | (300) crypt(all_49_1_32, all_0_2_2) = all_83_0_67 % 81.16/47.27 | % 81.16/47.27 | From (294) and (206) follows: % 81.16/47.27 | (301) crypt(all_49_1_32, id) = all_79_0_62 % 81.16/47.27 | % 81.16/47.27 | From (293) and (202) follows: % 81.16/47.27 | (302) crypt(all_49_1_32, imp) = all_77_0_60 % 81.16/47.27 | % 81.16/47.27 | From (265) and (197) follows: % 81.16/47.27 | (303) crypt(all_0_5_5, id) = all_75_1_58 % 81.16/47.27 | % 81.16/47.27 | From (292) and (190) follows: % 81.16/47.27 | (304) crypt(all_49_1_32, all_0_1_1) = all_71_0_54 % 81.16/47.27 | % 81.16/47.27 | From (291) and (176) follows: % 81.16/47.27 | (305) crypt(all_49_1_32, pin) = all_65_0_46 % 81.16/47.27 | % 81.16/47.27 | From (247) and (172) follows: % 81.16/47.27 | (306) crypt(all_49_1_32, a) = all_63_0_44 % 81.16/47.27 | % 81.16/47.27 | From (284) and (149) follows: % 81.16/47.27 | (307) crypt(all_49_1_32, kp) = all_51_0_33 % 81.16/47.27 | % 81.16/47.27 | From (289) and (135) follows: % 81.16/47.27 | (308) crypt(all_0_5_5, exp) = all_45_1_26 % 81.16/47.27 | % 81.16/47.27 | From (284) and (150) follows: % 81.16/47.27 | (146) xor(all_0_5_5, data) = all_49_1_32 % 81.16/47.27 | % 81.16/47.27 | From (289) and (137) follows: % 81.16/47.27 | (42) xor(km, exp) = all_0_5_5 % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (30) with all_0_5_5, exp, all_45_1_26, all_13_0_9 and discharging atoms crypt(all_0_5_5, exp) = all_45_1_26, crypt(all_0_5_5, exp) = all_13_0_9, yields: % 81.16/47.27 | (311) all_45_1_26 = all_13_0_9 % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (30) with all_0_5_5, id, all_75_1_58, all_9_0_7 and discharging atoms crypt(all_0_5_5, id) = all_75_1_58, crypt(all_0_5_5, id) = all_9_0_7, yields: % 81.16/47.27 | (312) all_75_1_58 = all_9_0_7 % 81.16/47.27 | % 81.16/47.27 | From (311) and (308) follows: % 81.16/47.27 | (67) crypt(all_0_5_5, exp) = all_13_0_9 % 81.16/47.27 | % 81.16/47.27 | From (312) and (303) follows: % 81.16/47.27 | (61) crypt(all_0_5_5, id) = all_9_0_7 % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (9) with all_91_0_76, all_0_0_0, all_49_1_32 and discharging atoms crypt(all_49_1_32, all_0_0_0) = all_91_0_76, ~ p(all_91_0_76), yields: % 81.16/47.27 | (315) ? [v0] : ? [v1] : (crypt(v0, all_0_0_0) = v1 & xor(all_49_1_32, data) = v0 & ~ p(v1)) % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (9) with all_71_0_54, all_0_1_1, all_49_1_32 and discharging atoms crypt(all_49_1_32, all_0_1_1) = all_71_0_54, ~ p(all_71_0_54), yields: % 81.16/47.27 | (316) ? [v0] : ? [v1] : (crypt(v0, all_0_1_1) = v1 & xor(all_49_1_32, data) = v0 & ~ p(v1)) % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (9) with all_83_0_67, all_0_2_2, all_49_1_32 and discharging atoms crypt(all_49_1_32, all_0_2_2) = all_83_0_67, ~ p(all_83_0_67), yields: % 81.16/47.27 | (317) ? [v0] : ? [v1] : (crypt(v0, all_0_2_2) = v1 & xor(all_49_1_32, data) = v0 & ~ p(v1)) % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (9) with all_63_0_44, a, all_49_1_32 and discharging atoms crypt(all_49_1_32, a) = all_63_0_44, ~ p(all_63_0_44), yields: % 81.16/47.27 | (318) ? [v0] : ? [v1] : (crypt(v0, a) = v1 & xor(all_49_1_32, data) = v0 & ~ p(v1)) % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (9) with all_65_0_46, pin, all_49_1_32 and discharging atoms crypt(all_49_1_32, pin) = all_65_0_46, ~ p(all_65_0_46), yields: % 81.16/47.27 | (319) ? [v0] : ? [v1] : (crypt(v0, pin) = v1 & xor(all_49_1_32, data) = v0 & ~ p(v1)) % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (9) with all_49_0_31, data, all_49_1_32 and discharging atoms crypt(all_49_1_32, data) = all_49_0_31, ~ p(all_49_0_31), yields: % 81.16/47.27 | (320) ? [v0] : ? [v1] : (crypt(v0, data) = v1 & xor(all_49_1_32, data) = v0 & ~ p(v1)) % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (9) with all_51_0_33, kp, all_49_1_32 and discharging atoms crypt(all_49_1_32, kp) = all_51_0_33, ~ p(all_51_0_33), yields: % 81.16/47.27 | (321) ? [v0] : ? [v1] : (crypt(v0, kp) = v1 & xor(all_49_1_32, data) = v0 & ~ p(v1)) % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (9) with all_93_0_78, exp, all_49_1_32 and discharging atoms crypt(all_49_1_32, exp) = all_93_0_78, ~ p(all_93_0_78), yields: % 81.16/47.27 | (322) ? [v0] : ? [v1] : (crypt(v0, exp) = v1 & xor(all_49_1_32, data) = v0 & ~ p(v1)) % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (9) with all_77_0_60, imp, all_49_1_32 and discharging atoms crypt(all_49_1_32, imp) = all_77_0_60, ~ p(all_77_0_60), yields: % 81.16/47.27 | (323) ? [v0] : ? [v1] : (crypt(v0, imp) = v1 & xor(all_49_1_32, data) = v0 & ~ p(v1)) % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (10) with all_79_0_62, all_49_1_32, id and discharging atoms crypt(all_49_1_32, id) = all_79_0_62, p(id), ~ p(all_79_0_62), yields: % 81.16/47.27 | (324) ? [v0] : (crypt(all_0_4_4, all_49_1_32) = v0 & ~ p(v0)) % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (9) with all_79_0_62, id, all_49_1_32 and discharging atoms crypt(all_49_1_32, id) = all_79_0_62, ~ p(all_79_0_62), yields: % 81.16/47.27 | (325) ? [v0] : ? [v1] : (crypt(v0, id) = v1 & xor(all_49_1_32, data) = v0 & ~ p(v1)) % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (13) with all_87_0_72, all_0_4_4, km, all_0_5_5, data and discharging atoms crypt(all_0_4_4, all_0_5_5) = all_87_0_72, xor(km, data) = all_0_4_4, p(data), ~ p(all_87_0_72), yields: % 81.16/47.27 | (326) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_0_5_5) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (21) with all_87_0_72, all_0_5_5, all_0_4_4, km, data, exp and discharging atoms crypt(all_0_4_4, all_0_5_5) = all_87_0_72, xor(km, data) = all_0_4_4, xor(km, exp) = all_0_5_5, p(data), p(exp), ~ p(all_87_0_72), yields: % 81.16/47.27 | (327) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, km) = v2 & xor(data, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (9) with all_87_0_72, all_0_5_5, all_0_4_4 and discharging atoms crypt(all_0_4_4, all_0_5_5) = all_87_0_72, ~ p(all_87_0_72), yields: % 81.16/47.27 | (328) ? [v0] : ? [v1] : (crypt(v0, all_0_5_5) = v1 & xor(all_0_4_4, data) = v0 & ~ p(v1)) % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (13) with all_57_0_37, all_0_5_5, km, all_29_0_20, exp and discharging atoms crypt(all_0_5_5, all_29_0_20) = all_57_0_37, xor(km, exp) = all_0_5_5, p(exp), ~ p(all_57_0_37), yields: % 81.16/47.27 | (329) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_29_0_20) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (9) with all_57_0_37, all_29_0_20, all_0_5_5 and discharging atoms crypt(all_0_5_5, all_29_0_20) = all_57_0_37, ~ p(all_57_0_37), yields: % 81.16/47.27 | (330) ? [v0] : ? [v1] : (crypt(v0, all_29_0_20) = v1 & xor(all_0_5_5, data) = v0 & ~ p(v1)) % 81.16/47.27 | % 81.16/47.27 | Instantiating formula (13) with all_55_0_36, all_0_5_5, km, all_19_0_14, exp and discharging atoms crypt(all_0_5_5, all_19_0_14) = all_55_0_36, xor(km, exp) = all_0_5_5, p(exp), ~ p(all_55_0_36), yields: % 81.16/47.28 | (331) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_19_0_14) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (9) with all_55_0_36, all_19_0_14, all_0_5_5 and discharging atoms crypt(all_0_5_5, all_19_0_14) = all_55_0_36, ~ p(all_55_0_36), yields: % 81.16/47.28 | (332) ? [v0] : ? [v1] : (crypt(v0, all_19_0_14) = v1 & xor(all_0_5_5, data) = v0 & ~ p(v1)) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (13) with all_53_0_35, all_0_5_5, km, all_17_0_12, exp and discharging atoms crypt(all_0_5_5, all_17_0_12) = all_53_0_35, xor(km, exp) = all_0_5_5, p(exp), ~ p(all_53_0_35), yields: % 81.16/47.28 | (333) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_17_0_12) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (9) with all_53_0_35, all_17_0_12, all_0_5_5 and discharging atoms crypt(all_0_5_5, all_17_0_12) = all_53_0_35, ~ p(all_53_0_35), yields: % 81.16/47.28 | (334) ? [v0] : ? [v1] : (crypt(v0, all_17_0_12) = v1 & xor(all_0_5_5, data) = v0 & ~ p(v1)) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (13) with all_43_0_24, all_0_5_5, km, all_15_0_10, exp and discharging atoms crypt(all_0_5_5, all_15_0_10) = all_43_0_24, xor(km, exp) = all_0_5_5, p(exp), ~ p(all_43_0_24), yields: % 81.16/47.28 | (335) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_15_0_10) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (9) with all_43_0_24, all_15_0_10, all_0_5_5 and discharging atoms crypt(all_0_5_5, all_15_0_10) = all_43_0_24, ~ p(all_43_0_24), yields: % 81.16/47.28 | (336) ? [v0] : ? [v1] : (crypt(v0, all_15_0_10) = v1 & xor(all_0_5_5, data) = v0 & ~ p(v1)) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (13) with all_91_0_76, all_49_1_32, all_0_5_5, all_0_0_0, data and discharging atoms crypt(all_49_1_32, all_0_0_0) = all_91_0_76, xor(all_0_5_5, data) = all_49_1_32, p(data), ~ p(all_91_0_76), yields: % 81.16/47.28 | (337) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_0_0_0) = v1 & crypt(all_0_5_5, all_0_5_5) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (13) with all_71_0_54, all_49_1_32, all_0_5_5, all_0_1_1, data and discharging atoms crypt(all_49_1_32, all_0_1_1) = all_71_0_54, xor(all_0_5_5, data) = all_49_1_32, p(data), ~ p(all_71_0_54), yields: % 81.16/47.28 | (338) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_0_1_1) = v1 & crypt(all_0_5_5, all_0_5_5) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (13) with all_83_0_67, all_49_1_32, all_0_5_5, all_0_2_2, data and discharging atoms crypt(all_49_1_32, all_0_2_2) = all_83_0_67, xor(all_0_5_5, data) = all_49_1_32, p(data), ~ p(all_83_0_67), yields: % 81.16/47.28 | (339) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_0_2_2) = v1 & crypt(all_0_5_5, all_0_5_5) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (13) with all_63_0_44, all_49_1_32, all_0_5_5, a, data and discharging atoms crypt(all_49_1_32, a) = all_63_0_44, xor(all_0_5_5, data) = all_49_1_32, p(data), ~ p(all_63_0_44), yields: % 81.16/47.28 | (340) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, a) = v1 & crypt(all_0_5_5, all_0_5_5) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (13) with all_65_0_46, all_49_1_32, all_0_5_5, pin, data and discharging atoms crypt(all_49_1_32, pin) = all_65_0_46, xor(all_0_5_5, data) = all_49_1_32, p(data), ~ p(all_65_0_46), yields: % 81.16/47.28 | (341) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, pin) = v1 & crypt(all_0_5_5, all_0_5_5) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (13) with all_49_0_31, all_49_1_32, all_0_5_5, data, data and discharging atoms crypt(all_49_1_32, data) = all_49_0_31, xor(all_0_5_5, data) = all_49_1_32, p(data), ~ p(all_49_0_31), yields: % 81.16/47.28 | (342) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, data) = v1 & crypt(all_0_5_5, all_0_5_5) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (13) with all_51_0_33, all_49_1_32, all_0_5_5, kp, data and discharging atoms crypt(all_49_1_32, kp) = all_51_0_33, xor(all_0_5_5, data) = all_49_1_32, p(data), ~ p(all_51_0_33), yields: % 81.16/47.28 | (343) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, kp) = v1 & crypt(all_0_5_5, all_0_5_5) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (13) with all_93_0_78, all_49_1_32, all_0_5_5, exp, data and discharging atoms crypt(all_49_1_32, exp) = all_93_0_78, xor(all_0_5_5, data) = all_49_1_32, p(data), ~ p(all_93_0_78), yields: % 81.16/47.28 | (344) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, exp) = v1 & crypt(all_0_5_5, all_0_5_5) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (13) with all_77_0_60, all_49_1_32, all_0_5_5, imp, data and discharging atoms crypt(all_49_1_32, imp) = all_77_0_60, xor(all_0_5_5, data) = all_49_1_32, p(data), ~ p(all_77_0_60), yields: % 81.16/47.28 | (345) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, imp) = v1 & crypt(all_0_5_5, all_0_5_5) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (13) with all_79_0_62, all_49_1_32, all_0_5_5, id, data and discharging atoms crypt(all_49_1_32, id) = all_79_0_62, xor(all_0_5_5, data) = all_49_1_32, p(data), ~ p(all_79_0_62), yields: % 81.16/47.28 | (346) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, id) = v1 & crypt(all_0_5_5, all_0_5_5) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (15) with all_49_1_32, all_0_5_5, data, km, exp and discharging atoms xor(all_0_5_5, data) = all_49_1_32, xor(exp, km) = all_0_5_5, yields: % 81.16/47.28 | (347) ? [v0] : (xor(exp, v0) = all_49_1_32 & xor(km, data) = v0) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (15) with all_49_1_32, all_0_5_5, data, exp, km and discharging atoms xor(all_0_5_5, data) = all_49_1_32, xor(km, exp) = all_0_5_5, yields: % 81.16/47.28 | (348) ? [v0] : (xor(exp, data) = v0 & xor(km, v0) = all_49_1_32) % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (35) with all_49_1_32, all_0_5_5, data and discharging atoms xor(all_0_5_5, data) = all_49_1_32, yields: % 81.16/47.28 | (349) xor(data, all_0_5_5) = all_49_1_32 % 81.16/47.28 | % 81.16/47.28 | Instantiating formula (37) with all_73_0_56 and discharging atoms p(all_73_0_56), yields: % 81.16/47.28 | (350) ? [v0] : (crypt(all_0_5_5, all_73_0_56) = v0 & ~ p(v0)) % 81.16/47.28 | % 81.16/47.28 | Instantiating (350) with all_109_0_80 yields: % 81.16/47.28 | (351) crypt(all_0_5_5, all_73_0_56) = all_109_0_80 & ~ p(all_109_0_80) % 81.16/47.28 | % 81.16/47.28 | Applying alpha-rule on (351) yields: % 81.16/47.28 | (352) crypt(all_0_5_5, all_73_0_56) = all_109_0_80 % 81.16/47.28 | (353) ~ p(all_109_0_80) % 81.16/47.28 | % 81.16/47.28 | Instantiating (346) with all_111_0_81, all_111_1_82, all_111_2_83 yields: % 81.16/47.28 | (354) crypt(all_111_2_83, id) = all_111_1_82 & crypt(all_0_5_5, all_0_5_5) = all_111_0_81 & xor(km, data) = all_111_2_83 & ( ~ p(all_111_0_81) | ~ p(all_111_1_82)) % 81.16/47.28 | % 81.16/47.28 | Applying alpha-rule on (354) yields: % 81.16/47.28 | (355) crypt(all_111_2_83, id) = all_111_1_82 % 81.16/47.28 | (356) crypt(all_0_5_5, all_0_5_5) = all_111_0_81 % 81.16/47.28 | (357) xor(km, data) = all_111_2_83 % 81.16/47.28 | (358) ~ p(all_111_0_81) | ~ p(all_111_1_82) % 81.16/47.28 | % 81.16/47.28 | Instantiating (345) with all_113_0_84, all_113_1_85, all_113_2_86 yields: % 81.16/47.28 | (359) crypt(all_113_2_86, imp) = all_113_1_85 & crypt(all_0_5_5, all_0_5_5) = all_113_0_84 & xor(km, data) = all_113_2_86 & ( ~ p(all_113_0_84) | ~ p(all_113_1_85)) % 81.16/47.28 | % 81.16/47.28 | Applying alpha-rule on (359) yields: % 81.16/47.28 | (360) crypt(all_113_2_86, imp) = all_113_1_85 % 81.16/47.28 | (361) crypt(all_0_5_5, all_0_5_5) = all_113_0_84 % 81.16/47.28 | (362) xor(km, data) = all_113_2_86 % 81.16/47.28 | (363) ~ p(all_113_0_84) | ~ p(all_113_1_85) % 81.16/47.28 | % 81.16/47.28 | Instantiating (330) with all_115_0_87, all_115_1_88 yields: % 81.16/47.28 | (364) crypt(all_115_1_88, all_29_0_20) = all_115_0_87 & xor(all_0_5_5, data) = all_115_1_88 & ~ p(all_115_0_87) % 81.16/47.29 | % 81.16/47.29 | Applying alpha-rule on (364) yields: % 81.16/47.29 | (365) crypt(all_115_1_88, all_29_0_20) = all_115_0_87 % 81.16/47.29 | (366) xor(all_0_5_5, data) = all_115_1_88 % 81.16/47.29 | (367) ~ p(all_115_0_87) % 81.16/47.29 | % 81.16/47.29 | Instantiating (329) with all_117_0_89, all_117_1_90, all_117_2_91 yields: % 81.16/47.29 | (368) crypt(all_117_2_91, all_29_0_20) = all_117_1_90 & crypt(all_0_5_5, km) = all_117_0_89 & xor(km, exp) = all_117_2_91 & ( ~ p(all_117_0_89) | ~ p(all_117_1_90)) % 81.16/47.29 | % 81.16/47.29 | Applying alpha-rule on (368) yields: % 81.16/47.29 | (369) crypt(all_117_2_91, all_29_0_20) = all_117_1_90 % 81.16/47.29 | (370) crypt(all_0_5_5, km) = all_117_0_89 % 81.16/47.29 | (371) xor(km, exp) = all_117_2_91 % 81.16/47.29 | (372) ~ p(all_117_0_89) | ~ p(all_117_1_90) % 81.16/47.29 | % 81.16/47.29 | Instantiating (328) with all_119_0_92, all_119_1_93 yields: % 81.16/47.29 | (373) crypt(all_119_1_93, all_0_5_5) = all_119_0_92 & xor(all_0_4_4, data) = all_119_1_93 & ~ p(all_119_0_92) % 81.16/47.29 | % 81.16/47.29 | Applying alpha-rule on (373) yields: % 81.16/47.29 | (374) crypt(all_119_1_93, all_0_5_5) = all_119_0_92 % 81.16/47.29 | (375) xor(all_0_4_4, data) = all_119_1_93 % 81.16/47.29 | (376) ~ p(all_119_0_92) % 81.16/47.29 | % 81.16/47.29 | Instantiating (327) with all_121_0_94, all_121_1_95, all_121_2_96 yields: % 81.16/47.29 | (377) crypt(all_121_1_95, km) = all_121_0_94 & xor(data, kp) = all_121_2_96 & xor(km, all_121_2_96) = all_121_1_95 & ~ p(all_121_0_94) % 81.16/47.29 | % 81.16/47.29 | Applying alpha-rule on (377) yields: % 81.16/47.29 | (378) crypt(all_121_1_95, km) = all_121_0_94 % 81.16/47.29 | (379) xor(data, kp) = all_121_2_96 % 81.16/47.29 | (380) xor(km, all_121_2_96) = all_121_1_95 % 81.16/47.29 | (381) ~ p(all_121_0_94) % 81.16/47.29 | % 81.16/47.29 | Instantiating (342) with all_123_0_97, all_123_1_98, all_123_2_99 yields: % 81.16/47.29 | (382) crypt(all_123_2_99, data) = all_123_1_98 & crypt(all_0_5_5, all_0_5_5) = all_123_0_97 & xor(km, data) = all_123_2_99 & ( ~ p(all_123_0_97) | ~ p(all_123_1_98)) % 81.16/47.29 | % 81.16/47.29 | Applying alpha-rule on (382) yields: % 81.16/47.29 | (383) crypt(all_123_2_99, data) = all_123_1_98 % 81.16/47.29 | (384) crypt(all_0_5_5, all_0_5_5) = all_123_0_97 % 81.16/47.29 | (385) xor(km, data) = all_123_2_99 % 81.16/47.29 | (386) ~ p(all_123_0_97) | ~ p(all_123_1_98) % 81.16/47.29 | % 81.16/47.29 | Instantiating (341) with all_125_0_100, all_125_1_101, all_125_2_102 yields: % 81.16/47.29 | (387) crypt(all_125_2_102, pin) = all_125_1_101 & crypt(all_0_5_5, all_0_5_5) = all_125_0_100 & xor(km, data) = all_125_2_102 & ( ~ p(all_125_0_100) | ~ p(all_125_1_101)) % 81.16/47.29 | % 81.16/47.29 | Applying alpha-rule on (387) yields: % 81.16/47.29 | (388) crypt(all_125_2_102, pin) = all_125_1_101 % 81.16/47.29 | (389) crypt(all_0_5_5, all_0_5_5) = all_125_0_100 % 81.16/47.29 | (390) xor(km, data) = all_125_2_102 % 81.16/47.29 | (391) ~ p(all_125_0_100) | ~ p(all_125_1_101) % 81.16/47.29 | % 81.16/47.29 | Instantiating (344) with all_127_0_103, all_127_1_104, all_127_2_105 yields: % 81.16/47.29 | (392) crypt(all_127_2_105, exp) = all_127_1_104 & crypt(all_0_5_5, all_0_5_5) = all_127_0_103 & xor(km, data) = all_127_2_105 & ( ~ p(all_127_0_103) | ~ p(all_127_1_104)) % 81.16/47.29 | % 81.16/47.29 | Applying alpha-rule on (392) yields: % 81.16/47.29 | (393) crypt(all_127_2_105, exp) = all_127_1_104 % 81.16/47.29 | (394) crypt(all_0_5_5, all_0_5_5) = all_127_0_103 % 81.16/47.29 | (395) xor(km, data) = all_127_2_105 % 81.16/47.29 | (396) ~ p(all_127_0_103) | ~ p(all_127_1_104) % 81.16/47.29 | % 81.16/47.29 | Instantiating (338) with all_129_0_106, all_129_1_107, all_129_2_108 yields: % 81.16/47.29 | (397) crypt(all_129_2_108, all_0_1_1) = all_129_1_107 & crypt(all_0_5_5, all_0_5_5) = all_129_0_106 & xor(km, data) = all_129_2_108 & ( ~ p(all_129_0_106) | ~ p(all_129_1_107)) % 81.16/47.29 | % 81.16/47.29 | Applying alpha-rule on (397) yields: % 81.16/47.29 | (398) crypt(all_129_2_108, all_0_1_1) = all_129_1_107 % 81.16/47.29 | (399) crypt(all_0_5_5, all_0_5_5) = all_129_0_106 % 81.16/47.29 | (400) xor(km, data) = all_129_2_108 % 81.16/47.29 | (401) ~ p(all_129_0_106) | ~ p(all_129_1_107) % 81.16/47.29 | % 81.16/47.29 | Instantiating (337) with all_131_0_109, all_131_1_110, all_131_2_111 yields: % 81.16/47.29 | (402) crypt(all_131_2_111, all_0_0_0) = all_131_1_110 & crypt(all_0_5_5, all_0_5_5) = all_131_0_109 & xor(km, data) = all_131_2_111 & ( ~ p(all_131_0_109) | ~ p(all_131_1_110)) % 81.16/47.29 | % 81.16/47.29 | Applying alpha-rule on (402) yields: % 81.16/47.29 | (403) crypt(all_131_2_111, all_0_0_0) = all_131_1_110 % 81.16/47.29 | (404) crypt(all_0_5_5, all_0_5_5) = all_131_0_109 % 81.16/47.29 | (405) xor(km, data) = all_131_2_111 % 81.16/47.29 | (406) ~ p(all_131_0_109) | ~ p(all_131_1_110) % 81.16/47.29 | % 81.16/47.29 | Instantiating (336) with all_133_0_112, all_133_1_113 yields: % 81.16/47.29 | (407) crypt(all_133_1_113, all_15_0_10) = all_133_0_112 & xor(all_0_5_5, data) = all_133_1_113 & ~ p(all_133_0_112) % 81.16/47.29 | % 81.16/47.29 | Applying alpha-rule on (407) yields: % 81.16/47.29 | (408) crypt(all_133_1_113, all_15_0_10) = all_133_0_112 % 81.16/47.29 | (409) xor(all_0_5_5, data) = all_133_1_113 % 81.16/47.29 | (410) ~ p(all_133_0_112) % 81.16/47.29 | % 81.16/47.29 | Instantiating (335) with all_135_0_114, all_135_1_115, all_135_2_116 yields: % 81.16/47.29 | (411) crypt(all_135_2_116, all_15_0_10) = all_135_1_115 & crypt(all_0_5_5, km) = all_135_0_114 & xor(km, exp) = all_135_2_116 & ( ~ p(all_135_0_114) | ~ p(all_135_1_115)) % 81.16/47.29 | % 81.16/47.29 | Applying alpha-rule on (411) yields: % 81.16/47.29 | (412) crypt(all_135_2_116, all_15_0_10) = all_135_1_115 % 81.16/47.29 | (413) crypt(all_0_5_5, km) = all_135_0_114 % 81.16/47.29 | (414) xor(km, exp) = all_135_2_116 % 81.16/47.29 | (415) ~ p(all_135_0_114) | ~ p(all_135_1_115) % 81.16/47.29 | % 81.16/47.29 | Instantiating (334) with all_137_0_117, all_137_1_118 yields: % 81.16/47.29 | (416) crypt(all_137_1_118, all_17_0_12) = all_137_0_117 & xor(all_0_5_5, data) = all_137_1_118 & ~ p(all_137_0_117) % 81.16/47.29 | % 81.16/47.29 | Applying alpha-rule on (416) yields: % 81.16/47.29 | (417) crypt(all_137_1_118, all_17_0_12) = all_137_0_117 % 81.16/47.29 | (418) xor(all_0_5_5, data) = all_137_1_118 % 81.16/47.29 | (419) ~ p(all_137_0_117) % 81.16/47.29 | % 81.16/47.29 | Instantiating (333) with all_139_0_119, all_139_1_120, all_139_2_121 yields: % 81.16/47.29 | (420) crypt(all_139_2_121, all_17_0_12) = all_139_1_120 & crypt(all_0_5_5, km) = all_139_0_119 & xor(km, exp) = all_139_2_121 & ( ~ p(all_139_0_119) | ~ p(all_139_1_120)) % 81.16/47.29 | % 81.16/47.29 | Applying alpha-rule on (420) yields: % 81.49/47.29 | (421) crypt(all_139_2_121, all_17_0_12) = all_139_1_120 % 81.49/47.29 | (422) crypt(all_0_5_5, km) = all_139_0_119 % 81.49/47.29 | (423) xor(km, exp) = all_139_2_121 % 81.49/47.29 | (424) ~ p(all_139_0_119) | ~ p(all_139_1_120) % 81.49/47.29 | % 81.49/47.29 | Instantiating (332) with all_141_0_122, all_141_1_123 yields: % 81.49/47.29 | (425) crypt(all_141_1_123, all_19_0_14) = all_141_0_122 & xor(all_0_5_5, data) = all_141_1_123 & ~ p(all_141_0_122) % 81.49/47.29 | % 81.49/47.29 | Applying alpha-rule on (425) yields: % 81.49/47.29 | (426) crypt(all_141_1_123, all_19_0_14) = all_141_0_122 % 81.49/47.29 | (427) xor(all_0_5_5, data) = all_141_1_123 % 81.49/47.29 | (428) ~ p(all_141_0_122) % 81.49/47.29 | % 81.49/47.29 | Instantiating (331) with all_143_0_124, all_143_1_125, all_143_2_126 yields: % 81.49/47.29 | (429) crypt(all_143_2_126, all_19_0_14) = all_143_1_125 & crypt(all_0_5_5, km) = all_143_0_124 & xor(km, exp) = all_143_2_126 & ( ~ p(all_143_0_124) | ~ p(all_143_1_125)) % 81.49/47.29 | % 81.49/47.29 | Applying alpha-rule on (429) yields: % 81.49/47.29 | (430) crypt(all_143_2_126, all_19_0_14) = all_143_1_125 % 81.49/47.29 | (431) crypt(all_0_5_5, km) = all_143_0_124 % 81.49/47.29 | (432) xor(km, exp) = all_143_2_126 % 81.49/47.29 | (433) ~ p(all_143_0_124) | ~ p(all_143_1_125) % 81.49/47.29 | % 81.49/47.29 | Instantiating (343) with all_145_0_127, all_145_1_128, all_145_2_129 yields: % 81.49/47.29 | (434) crypt(all_145_2_129, kp) = all_145_1_128 & crypt(all_0_5_5, all_0_5_5) = all_145_0_127 & xor(km, data) = all_145_2_129 & ( ~ p(all_145_0_127) | ~ p(all_145_1_128)) % 81.49/47.29 | % 81.49/47.29 | Applying alpha-rule on (434) yields: % 81.49/47.29 | (435) crypt(all_145_2_129, kp) = all_145_1_128 % 81.49/47.29 | (436) crypt(all_0_5_5, all_0_5_5) = all_145_0_127 % 81.49/47.29 | (437) xor(km, data) = all_145_2_129 % 81.49/47.29 | (438) ~ p(all_145_0_127) | ~ p(all_145_1_128) % 81.49/47.29 | % 81.49/47.29 | Instantiating (340) with all_147_0_130, all_147_1_131, all_147_2_132 yields: % 81.49/47.29 | (439) crypt(all_147_2_132, a) = all_147_1_131 & crypt(all_0_5_5, all_0_5_5) = all_147_0_130 & xor(km, data) = all_147_2_132 & ( ~ p(all_147_0_130) | ~ p(all_147_1_131)) % 81.49/47.29 | % 81.49/47.29 | Applying alpha-rule on (439) yields: % 81.49/47.29 | (440) crypt(all_147_2_132, a) = all_147_1_131 % 81.49/47.29 | (441) crypt(all_0_5_5, all_0_5_5) = all_147_0_130 % 81.49/47.29 | (442) xor(km, data) = all_147_2_132 % 81.49/47.29 | (443) ~ p(all_147_0_130) | ~ p(all_147_1_131) % 81.49/47.29 | % 81.49/47.29 | Instantiating (321) with all_149_0_133, all_149_1_134 yields: % 81.49/47.29 | (444) crypt(all_149_1_134, kp) = all_149_0_133 & xor(all_49_1_32, data) = all_149_1_134 & ~ p(all_149_0_133) % 81.49/47.29 | % 81.49/47.29 | Applying alpha-rule on (444) yields: % 81.49/47.29 | (445) crypt(all_149_1_134, kp) = all_149_0_133 % 81.49/47.29 | (446) xor(all_49_1_32, data) = all_149_1_134 % 81.49/47.29 | (447) ~ p(all_149_0_133) % 81.49/47.29 | % 81.49/47.29 | Instantiating (320) with all_151_0_135, all_151_1_136 yields: % 81.49/47.29 | (448) crypt(all_151_1_136, data) = all_151_0_135 & xor(all_49_1_32, data) = all_151_1_136 & ~ p(all_151_0_135) % 81.49/47.29 | % 81.49/47.29 | Applying alpha-rule on (448) yields: % 81.49/47.29 | (449) crypt(all_151_1_136, data) = all_151_0_135 % 81.49/47.29 | (450) xor(all_49_1_32, data) = all_151_1_136 % 81.49/47.29 | (451) ~ p(all_151_0_135) % 81.49/47.30 | % 81.49/47.30 | Instantiating (319) with all_153_0_137, all_153_1_138 yields: % 81.49/47.30 | (452) crypt(all_153_1_138, pin) = all_153_0_137 & xor(all_49_1_32, data) = all_153_1_138 & ~ p(all_153_0_137) % 81.49/47.30 | % 81.49/47.30 | Applying alpha-rule on (452) yields: % 81.49/47.30 | (453) crypt(all_153_1_138, pin) = all_153_0_137 % 81.49/47.30 | (454) xor(all_49_1_32, data) = all_153_1_138 % 81.49/47.30 | (455) ~ p(all_153_0_137) % 81.49/47.30 | % 81.49/47.30 | Instantiating (326) with all_155_0_139, all_155_1_140, all_155_2_141 yields: % 81.49/47.30 | (456) crypt(all_155_2_141, all_0_5_5) = all_155_1_140 & crypt(all_0_5_5, km) = all_155_0_139 & xor(km, data) = all_155_2_141 & ( ~ p(all_155_0_139) | ~ p(all_155_1_140)) % 81.49/47.30 | % 81.49/47.30 | Applying alpha-rule on (456) yields: % 81.49/47.30 | (457) crypt(all_155_2_141, all_0_5_5) = all_155_1_140 % 81.49/47.30 | (458) crypt(all_0_5_5, km) = all_155_0_139 % 81.49/47.30 | (459) xor(km, data) = all_155_2_141 % 81.49/47.30 | (460) ~ p(all_155_0_139) | ~ p(all_155_1_140) % 81.49/47.30 | % 81.49/47.30 | Instantiating (323) with all_157_0_142, all_157_1_143 yields: % 81.49/47.30 | (461) crypt(all_157_1_143, imp) = all_157_0_142 & xor(all_49_1_32, data) = all_157_1_143 & ~ p(all_157_0_142) % 81.49/47.30 | % 81.49/47.30 | Applying alpha-rule on (461) yields: % 81.49/47.30 | (462) crypt(all_157_1_143, imp) = all_157_0_142 % 81.49/47.30 | (463) xor(all_49_1_32, data) = all_157_1_143 % 81.49/47.30 | (464) ~ p(all_157_0_142) % 81.49/47.30 | % 81.49/47.30 | Instantiating (322) with all_159_0_144, all_159_1_145 yields: % 81.49/47.30 | (465) crypt(all_159_1_145, exp) = all_159_0_144 & xor(all_49_1_32, data) = all_159_1_145 & ~ p(all_159_0_144) % 81.49/47.30 | % 81.49/47.30 | Applying alpha-rule on (465) yields: % 81.49/47.30 | (466) crypt(all_159_1_145, exp) = all_159_0_144 % 81.49/47.30 | (467) xor(all_49_1_32, data) = all_159_1_145 % 81.49/47.30 | (468) ~ p(all_159_0_144) % 81.49/47.30 | % 81.49/47.30 | Instantiating (325) with all_161_0_146, all_161_1_147 yields: % 81.49/47.30 | (469) crypt(all_161_1_147, id) = all_161_0_146 & xor(all_49_1_32, data) = all_161_1_147 & ~ p(all_161_0_146) % 81.49/47.30 | % 81.49/47.30 | Applying alpha-rule on (469) yields: % 81.49/47.30 | (470) crypt(all_161_1_147, id) = all_161_0_146 % 81.49/47.30 | (471) xor(all_49_1_32, data) = all_161_1_147 % 81.49/47.30 | (472) ~ p(all_161_0_146) % 81.49/47.30 | % 81.49/47.30 | Instantiating (317) with all_163_0_148, all_163_1_149 yields: % 81.49/47.30 | (473) crypt(all_163_1_149, all_0_2_2) = all_163_0_148 & xor(all_49_1_32, data) = all_163_1_149 & ~ p(all_163_0_148) % 81.49/47.30 | % 81.49/47.30 | Applying alpha-rule on (473) yields: % 81.49/47.30 | (474) crypt(all_163_1_149, all_0_2_2) = all_163_0_148 % 81.49/47.30 | (475) xor(all_49_1_32, data) = all_163_1_149 % 81.49/47.30 | (476) ~ p(all_163_0_148) % 81.49/47.30 | % 81.49/47.30 | Instantiating (315) with all_165_0_150, all_165_1_151 yields: % 81.49/47.30 | (477) crypt(all_165_1_151, all_0_0_0) = all_165_0_150 & xor(all_49_1_32, data) = all_165_1_151 & ~ p(all_165_0_150) % 81.49/47.30 | % 81.49/47.30 | Applying alpha-rule on (477) yields: % 81.49/47.30 | (478) crypt(all_165_1_151, all_0_0_0) = all_165_0_150 % 81.49/47.30 | (479) xor(all_49_1_32, data) = all_165_1_151 % 81.49/47.30 | (480) ~ p(all_165_0_150) % 81.49/47.30 | % 81.49/47.30 | Instantiating (318) with all_167_0_152, all_167_1_153 yields: % 81.49/47.30 | (481) crypt(all_167_1_153, a) = all_167_0_152 & xor(all_49_1_32, data) = all_167_1_153 & ~ p(all_167_0_152) % 81.49/47.30 | % 81.49/47.30 | Applying alpha-rule on (481) yields: % 81.49/47.30 | (482) crypt(all_167_1_153, a) = all_167_0_152 % 81.49/47.30 | (483) xor(all_49_1_32, data) = all_167_1_153 % 81.49/47.30 | (484) ~ p(all_167_0_152) % 81.49/47.30 | % 81.49/47.30 | Instantiating (324) with all_169_0_154 yields: % 81.49/47.30 | (485) crypt(all_0_4_4, all_49_1_32) = all_169_0_154 & ~ p(all_169_0_154) % 81.49/47.30 | % 81.49/47.30 | Applying alpha-rule on (485) yields: % 81.49/47.30 | (486) crypt(all_0_4_4, all_49_1_32) = all_169_0_154 % 81.49/47.30 | (487) ~ p(all_169_0_154) % 81.49/47.30 | % 81.49/47.30 | Instantiating (316) with all_171_0_155, all_171_1_156 yields: % 81.49/47.30 | (488) crypt(all_171_1_156, all_0_1_1) = all_171_0_155 & xor(all_49_1_32, data) = all_171_1_156 & ~ p(all_171_0_155) % 81.49/47.30 | % 81.49/47.30 | Applying alpha-rule on (488) yields: % 81.49/47.30 | (489) crypt(all_171_1_156, all_0_1_1) = all_171_0_155 % 81.49/47.30 | (490) xor(all_49_1_32, data) = all_171_1_156 % 81.49/47.30 | (491) ~ p(all_171_0_155) % 81.49/47.30 | % 81.49/47.30 | Instantiating (339) with all_173_0_157, all_173_1_158, all_173_2_159 yields: % 81.49/47.30 | (492) crypt(all_173_2_159, all_0_2_2) = all_173_1_158 & crypt(all_0_5_5, all_0_5_5) = all_173_0_157 & xor(km, data) = all_173_2_159 & ( ~ p(all_173_0_157) | ~ p(all_173_1_158)) % 81.49/47.30 | % 81.49/47.30 | Applying alpha-rule on (492) yields: % 81.49/47.30 | (493) crypt(all_173_2_159, all_0_2_2) = all_173_1_158 % 81.49/47.30 | (494) crypt(all_0_5_5, all_0_5_5) = all_173_0_157 % 81.49/47.30 | (495) xor(km, data) = all_173_2_159 % 81.49/47.30 | (496) ~ p(all_173_0_157) | ~ p(all_173_1_158) % 81.49/47.30 | % 81.49/47.30 | Instantiating (348) with all_175_0_160 yields: % 81.49/47.30 | (497) xor(exp, data) = all_175_0_160 & xor(km, all_175_0_160) = all_49_1_32 % 81.49/47.30 | % 81.49/47.30 | Applying alpha-rule on (497) yields: % 81.49/47.30 | (498) xor(exp, data) = all_175_0_160 % 81.49/47.30 | (499) xor(km, all_175_0_160) = all_49_1_32 % 81.49/47.30 | % 81.49/47.30 | Instantiating (347) with all_177_0_161 yields: % 81.49/47.30 | (500) xor(exp, all_177_0_161) = all_49_1_32 & xor(km, data) = all_177_0_161 % 81.49/47.30 | % 81.49/47.30 | Applying alpha-rule on (500) yields: % 81.49/47.30 | (501) xor(exp, all_177_0_161) = all_49_1_32 % 81.49/47.30 | (502) xor(km, data) = all_177_0_161 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (30) with all_0_5_5, all_0_5_5, all_147_0_130, all_173_0_157 and discharging atoms crypt(all_0_5_5, all_0_5_5) = all_173_0_157, crypt(all_0_5_5, all_0_5_5) = all_147_0_130, yields: % 81.49/47.30 | (503) all_173_0_157 = all_147_0_130 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (30) with all_0_5_5, all_0_5_5, all_145_0_127, all_147_0_130 and discharging atoms crypt(all_0_5_5, all_0_5_5) = all_147_0_130, crypt(all_0_5_5, all_0_5_5) = all_145_0_127, yields: % 81.49/47.30 | (504) all_147_0_130 = all_145_0_127 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (30) with all_0_5_5, all_0_5_5, all_131_0_109, all_145_0_127 and discharging atoms crypt(all_0_5_5, all_0_5_5) = all_145_0_127, crypt(all_0_5_5, all_0_5_5) = all_131_0_109, yields: % 81.49/47.30 | (505) all_145_0_127 = all_131_0_109 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (30) with all_0_5_5, all_0_5_5, all_129_0_106, all_145_0_127 and discharging atoms crypt(all_0_5_5, all_0_5_5) = all_145_0_127, crypt(all_0_5_5, all_0_5_5) = all_129_0_106, yields: % 81.49/47.30 | (506) all_145_0_127 = all_129_0_106 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (30) with all_0_5_5, all_0_5_5, all_127_0_103, all_173_0_157 and discharging atoms crypt(all_0_5_5, all_0_5_5) = all_173_0_157, crypt(all_0_5_5, all_0_5_5) = all_127_0_103, yields: % 81.49/47.30 | (507) all_173_0_157 = all_127_0_103 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (30) with all_0_5_5, all_0_5_5, all_125_0_100, all_129_0_106 and discharging atoms crypt(all_0_5_5, all_0_5_5) = all_129_0_106, crypt(all_0_5_5, all_0_5_5) = all_125_0_100, yields: % 81.49/47.30 | (508) all_129_0_106 = all_125_0_100 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (30) with all_0_5_5, all_0_5_5, all_123_0_97, all_129_0_106 and discharging atoms crypt(all_0_5_5, all_0_5_5) = all_129_0_106, crypt(all_0_5_5, all_0_5_5) = all_123_0_97, yields: % 81.49/47.30 | (509) all_129_0_106 = all_123_0_97 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (30) with all_0_5_5, all_0_5_5, all_113_0_84, all_129_0_106 and discharging atoms crypt(all_0_5_5, all_0_5_5) = all_129_0_106, crypt(all_0_5_5, all_0_5_5) = all_113_0_84, yields: % 81.49/47.30 | (510) all_129_0_106 = all_113_0_84 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (30) with all_0_5_5, all_0_5_5, all_111_0_81, all_129_0_106 and discharging atoms crypt(all_0_5_5, all_0_5_5) = all_129_0_106, crypt(all_0_5_5, all_0_5_5) = all_111_0_81, yields: % 81.49/47.30 | (511) all_129_0_106 = all_111_0_81 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with all_49_1_32, data, all_165_1_151, all_171_1_156 and discharging atoms xor(all_49_1_32, data) = all_171_1_156, xor(all_49_1_32, data) = all_165_1_151, yields: % 81.49/47.30 | (512) all_171_1_156 = all_165_1_151 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with all_49_1_32, data, all_165_1_151, all_167_1_153 and discharging atoms xor(all_49_1_32, data) = all_167_1_153, xor(all_49_1_32, data) = all_165_1_151, yields: % 81.49/47.30 | (513) all_167_1_153 = all_165_1_151 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with all_49_1_32, data, all_163_1_149, all_167_1_153 and discharging atoms xor(all_49_1_32, data) = all_167_1_153, xor(all_49_1_32, data) = all_163_1_149, yields: % 81.49/47.30 | (514) all_167_1_153 = all_163_1_149 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with all_49_1_32, data, all_161_1_147, all_165_1_151 and discharging atoms xor(all_49_1_32, data) = all_165_1_151, xor(all_49_1_32, data) = all_161_1_147, yields: % 81.49/47.30 | (515) all_165_1_151 = all_161_1_147 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with all_49_1_32, data, all_159_1_145, all_161_1_147 and discharging atoms xor(all_49_1_32, data) = all_161_1_147, xor(all_49_1_32, data) = all_159_1_145, yields: % 81.49/47.30 | (516) all_161_1_147 = all_159_1_145 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with all_49_1_32, data, all_157_1_143, all_161_1_147 and discharging atoms xor(all_49_1_32, data) = all_161_1_147, xor(all_49_1_32, data) = all_157_1_143, yields: % 81.49/47.30 | (517) all_161_1_147 = all_157_1_143 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with all_49_1_32, data, all_153_1_138, all_171_1_156 and discharging atoms xor(all_49_1_32, data) = all_171_1_156, xor(all_49_1_32, data) = all_153_1_138, yields: % 81.49/47.30 | (518) all_171_1_156 = all_153_1_138 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with all_49_1_32, data, all_151_1_136, all_157_1_143 and discharging atoms xor(all_49_1_32, data) = all_157_1_143, xor(all_49_1_32, data) = all_151_1_136, yields: % 81.49/47.30 | (519) all_157_1_143 = all_151_1_136 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with all_49_1_32, data, all_149_1_134, all_157_1_143 and discharging atoms xor(all_49_1_32, data) = all_157_1_143, xor(all_49_1_32, data) = all_149_1_134, yields: % 81.49/47.30 | (520) all_157_1_143 = all_149_1_134 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with all_0_5_5, data, all_137_1_118, all_141_1_123 and discharging atoms xor(all_0_5_5, data) = all_141_1_123, xor(all_0_5_5, data) = all_137_1_118, yields: % 81.49/47.30 | (521) all_141_1_123 = all_137_1_118 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with all_0_5_5, data, all_133_1_113, all_49_1_32 and discharging atoms xor(all_0_5_5, data) = all_133_1_113, xor(all_0_5_5, data) = all_49_1_32, yields: % 81.49/47.30 | (522) all_133_1_113 = all_49_1_32 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with all_0_5_5, data, all_133_1_113, all_137_1_118 and discharging atoms xor(all_0_5_5, data) = all_137_1_118, xor(all_0_5_5, data) = all_133_1_113, yields: % 81.49/47.30 | (523) all_137_1_118 = all_133_1_113 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with all_0_5_5, data, all_115_1_88, all_141_1_123 and discharging atoms xor(all_0_5_5, data) = all_141_1_123, xor(all_0_5_5, data) = all_115_1_88, yields: % 81.49/47.30 | (524) all_141_1_123 = all_115_1_88 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with km, data, all_177_0_161, all_0_4_4 and discharging atoms xor(km, data) = all_177_0_161, xor(km, data) = all_0_4_4, yields: % 81.49/47.30 | (525) all_177_0_161 = all_0_4_4 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with km, data, all_155_2_141, all_173_2_159 and discharging atoms xor(km, data) = all_173_2_159, xor(km, data) = all_155_2_141, yields: % 81.49/47.30 | (526) all_173_2_159 = all_155_2_141 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with km, data, all_145_2_129, all_177_0_161 and discharging atoms xor(km, data) = all_177_0_161, xor(km, data) = all_145_2_129, yields: % 81.49/47.30 | (527) all_177_0_161 = all_145_2_129 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with km, data, all_145_2_129, all_173_2_159 and discharging atoms xor(km, data) = all_173_2_159, xor(km, data) = all_145_2_129, yields: % 81.49/47.30 | (528) all_173_2_159 = all_145_2_129 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with km, data, all_131_2_111, all_173_2_159 and discharging atoms xor(km, data) = all_173_2_159, xor(km, data) = all_131_2_111, yields: % 81.49/47.30 | (529) all_173_2_159 = all_131_2_111 % 81.49/47.30 | % 81.49/47.30 | Instantiating formula (17) with km, data, all_129_2_108, all_173_2_159 and discharging atoms xor(km, data) = all_173_2_159, xor(km, data) = all_129_2_108, yields: % 81.49/47.31 | (530) all_173_2_159 = all_129_2_108 % 81.49/47.31 | % 81.49/47.31 | Instantiating formula (17) with km, data, all_129_2_108, all_147_2_132 and discharging atoms xor(km, data) = all_147_2_132, xor(km, data) = all_129_2_108, yields: % 81.49/47.31 | (531) all_147_2_132 = all_129_2_108 % 81.49/47.31 | % 81.49/47.31 | Instantiating formula (17) with km, data, all_127_2_105, all_145_2_129 and discharging atoms xor(km, data) = all_145_2_129, xor(km, data) = all_127_2_105, yields: % 81.49/47.31 | (532) all_145_2_129 = all_127_2_105 % 81.49/47.31 | % 81.49/47.31 | Instantiating formula (17) with km, data, all_125_2_102, all_145_2_129 and discharging atoms xor(km, data) = all_145_2_129, xor(km, data) = all_125_2_102, yields: % 81.49/47.31 | (533) all_145_2_129 = all_125_2_102 % 81.49/47.31 | % 81.49/47.31 | Instantiating formula (17) with km, data, all_123_2_99, all_155_2_141 and discharging atoms xor(km, data) = all_155_2_141, xor(km, data) = all_123_2_99, yields: % 81.49/47.31 | (534) all_155_2_141 = all_123_2_99 % 81.49/47.31 | % 81.49/47.31 | Instantiating formula (17) with km, data, all_113_2_86, all_147_2_132 and discharging atoms xor(km, data) = all_147_2_132, xor(km, data) = all_113_2_86, yields: % 81.49/47.31 | (535) all_147_2_132 = all_113_2_86 % 81.49/47.31 | % 81.49/47.31 | Instantiating formula (17) with km, data, all_111_2_83, all_129_2_108 and discharging atoms xor(km, data) = all_129_2_108, xor(km, data) = all_111_2_83, yields: % 81.49/47.31 | (536) all_129_2_108 = all_111_2_83 % 81.49/47.31 | % 81.49/47.31 | Instantiating formula (17) with km, exp, all_139_2_121, all_0_5_5 and discharging atoms xor(km, exp) = all_139_2_121, xor(km, exp) = all_0_5_5, yields: % 81.49/47.31 | (537) all_139_2_121 = all_0_5_5 % 81.49/47.31 | % 81.49/47.31 | Instantiating formula (17) with km, exp, all_139_2_121, all_143_2_126 and discharging atoms xor(km, exp) = all_143_2_126, xor(km, exp) = all_139_2_121, yields: % 81.49/47.31 | (538) all_143_2_126 = all_139_2_121 % 81.49/47.31 | % 81.49/47.31 | Instantiating formula (17) with km, exp, all_135_2_116, all_143_2_126 and discharging atoms xor(km, exp) = all_143_2_126, xor(km, exp) = all_135_2_116, yields: % 81.49/47.31 | (539) all_143_2_126 = all_135_2_116 % 81.49/47.31 | % 81.49/47.31 | Instantiating formula (17) with km, exp, all_117_2_91, all_139_2_121 and discharging atoms xor(km, exp) = all_139_2_121, xor(km, exp) = all_117_2_91, yields: % 81.49/47.31 | (540) all_139_2_121 = all_117_2_91 % 81.49/47.31 | % 81.49/47.31 | Combining equations (527,525) yields a new equation: % 81.49/47.31 | (541) all_145_2_129 = all_0_4_4 % 81.49/47.31 | % 81.49/47.31 | Simplifying 541 yields: % 81.49/47.31 | (542) all_145_2_129 = all_0_4_4 % 81.49/47.31 | % 81.49/47.31 | Combining equations (503,507) yields a new equation: % 81.49/47.31 | (543) all_147_0_130 = all_127_0_103 % 81.49/47.31 | % 81.49/47.31 | Simplifying 543 yields: % 81.49/47.31 | (544) all_147_0_130 = all_127_0_103 % 81.49/47.31 | % 81.49/47.31 | Combining equations (530,529) yields a new equation: % 81.49/47.31 | (545) all_131_2_111 = all_129_2_108 % 81.49/47.31 | % 81.49/47.31 | Combining equations (528,529) yields a new equation: % 81.49/47.31 | (546) all_145_2_129 = all_131_2_111 % 81.49/47.31 | % 81.49/47.31 | Simplifying 546 yields: % 81.49/47.31 | (547) all_145_2_129 = all_131_2_111 % 81.49/47.31 | % 81.49/47.31 | Combining equations (526,529) yields a new equation: % 81.49/47.31 | (548) all_155_2_141 = all_131_2_111 % 81.49/47.31 | % 81.49/47.31 | Simplifying 548 yields: % 81.49/47.31 | (549) all_155_2_141 = all_131_2_111 % 81.49/47.31 | % 81.49/47.31 | Combining equations (512,518) yields a new equation: % 81.49/47.31 | (550) all_165_1_151 = all_153_1_138 % 81.49/47.31 | % 81.49/47.31 | Simplifying 550 yields: % 81.49/47.31 | (551) all_165_1_151 = all_153_1_138 % 81.49/47.31 | % 81.49/47.31 | Combining equations (513,514) yields a new equation: % 81.49/47.31 | (552) all_165_1_151 = all_163_1_149 % 81.49/47.31 | % 81.49/47.31 | Simplifying 552 yields: % 81.49/47.31 | (553) all_165_1_151 = all_163_1_149 % 81.49/47.31 | % 81.49/47.31 | Combining equations (515,553) yields a new equation: % 81.49/47.31 | (554) all_163_1_149 = all_161_1_147 % 81.49/47.31 | % 81.49/47.31 | Combining equations (551,553) yields a new equation: % 81.49/47.31 | (555) all_163_1_149 = all_153_1_138 % 81.49/47.31 | % 81.49/47.31 | Combining equations (554,555) yields a new equation: % 81.49/47.31 | (556) all_161_1_147 = all_153_1_138 % 81.49/47.31 | % 81.49/47.31 | Simplifying 556 yields: % 81.49/47.31 | (557) all_161_1_147 = all_153_1_138 % 81.49/47.31 | % 81.49/47.31 | Combining equations (517,516) yields a new equation: % 81.49/47.31 | (558) all_159_1_145 = all_157_1_143 % 81.49/47.31 | % 81.49/47.31 | Combining equations (557,516) yields a new equation: % 81.49/47.31 | (559) all_159_1_145 = all_153_1_138 % 81.49/47.31 | % 81.49/47.31 | Combining equations (558,559) yields a new equation: % 81.49/47.31 | (560) all_157_1_143 = all_153_1_138 % 81.49/47.31 | % 81.49/47.31 | Simplifying 560 yields: % 81.49/47.31 | (561) all_157_1_143 = all_153_1_138 % 81.49/47.31 | % 81.49/47.31 | Combining equations (520,561) yields a new equation: % 81.49/47.31 | (562) all_153_1_138 = all_149_1_134 % 81.49/47.31 | % 81.49/47.31 | Combining equations (519,561) yields a new equation: % 81.49/47.31 | (563) all_153_1_138 = all_151_1_136 % 81.49/47.31 | % 81.49/47.31 | Combining equations (549,534) yields a new equation: % 81.49/47.31 | (564) all_131_2_111 = all_123_2_99 % 81.49/47.31 | % 81.49/47.31 | Simplifying 564 yields: % 81.49/47.31 | (565) all_131_2_111 = all_123_2_99 % 81.49/47.31 | % 81.49/47.31 | Combining equations (562,563) yields a new equation: % 81.49/47.31 | (566) all_151_1_136 = all_149_1_134 % 81.49/47.31 | % 81.49/47.31 | Combining equations (504,544) yields a new equation: % 81.49/47.31 | (567) all_145_0_127 = all_127_0_103 % 81.49/47.31 | % 81.49/47.31 | Simplifying 567 yields: % 81.49/47.31 | (568) all_145_0_127 = all_127_0_103 % 81.49/47.31 | % 81.49/47.31 | Combining equations (531,535) yields a new equation: % 81.49/47.31 | (569) all_129_2_108 = all_113_2_86 % 81.49/47.31 | % 81.49/47.31 | Simplifying 569 yields: % 81.49/47.31 | (570) all_129_2_108 = all_113_2_86 % 81.49/47.31 | % 81.49/47.31 | Combining equations (506,505) yields a new equation: % 81.49/47.31 | (571) all_131_0_109 = all_129_0_106 % 81.49/47.31 | % 81.49/47.31 | Combining equations (568,505) yields a new equation: % 81.49/47.31 | (572) all_131_0_109 = all_127_0_103 % 81.49/47.31 | % 81.49/47.31 | Combining equations (533,532) yields a new equation: % 81.49/47.31 | (573) all_127_2_105 = all_125_2_102 % 81.49/47.31 | % 81.49/47.31 | Combining equations (542,532) yields a new equation: % 81.49/47.31 | (574) all_127_2_105 = all_0_4_4 % 81.49/47.31 | % 81.49/47.31 | Combining equations (547,532) yields a new equation: % 81.49/47.31 | (575) all_131_2_111 = all_127_2_105 % 81.49/47.31 | % 81.49/47.31 | Simplifying 575 yields: % 81.49/47.31 | (576) all_131_2_111 = all_127_2_105 % 81.49/47.31 | % 81.49/47.31 | Combining equations (538,539) yields a new equation: % 81.49/47.31 | (577) all_139_2_121 = all_135_2_116 % 81.49/47.31 | % 81.49/47.31 | Simplifying 577 yields: % 81.49/47.31 | (578) all_139_2_121 = all_135_2_116 % 81.49/47.31 | % 81.49/47.31 | Combining equations (521,524) yields a new equation: % 81.49/47.31 | (579) all_137_1_118 = all_115_1_88 % 81.49/47.31 | % 81.49/47.31 | Simplifying 579 yields: % 81.49/47.31 | (580) all_137_1_118 = all_115_1_88 % 81.49/47.31 | % 81.49/47.31 | Combining equations (540,578) yields a new equation: % 81.49/47.31 | (581) all_135_2_116 = all_117_2_91 % 81.49/47.31 | % 81.49/47.31 | Combining equations (537,578) yields a new equation: % 81.49/47.31 | (582) all_135_2_116 = all_0_5_5 % 81.49/47.31 | % 81.49/47.31 | Combining equations (523,580) yields a new equation: % 81.49/47.31 | (583) all_133_1_113 = all_115_1_88 % 81.49/47.31 | % 81.49/47.31 | Simplifying 583 yields: % 81.49/47.31 | (584) all_133_1_113 = all_115_1_88 % 81.49/47.31 | % 81.49/47.31 | Combining equations (582,581) yields a new equation: % 81.49/47.31 | (585) all_117_2_91 = all_0_5_5 % 81.49/47.31 | % 81.49/47.31 | Combining equations (522,584) yields a new equation: % 81.49/47.31 | (586) all_115_1_88 = all_49_1_32 % 81.49/47.31 | % 81.49/47.31 | Combining equations (571,572) yields a new equation: % 81.49/47.31 | (587) all_129_0_106 = all_127_0_103 % 81.49/47.31 | % 81.49/47.31 | Simplifying 587 yields: % 81.49/47.31 | (588) all_129_0_106 = all_127_0_103 % 81.49/47.31 | % 81.49/47.31 | Combining equations (576,565) yields a new equation: % 81.49/47.31 | (589) all_127_2_105 = all_123_2_99 % 81.49/47.31 | % 81.49/47.31 | Simplifying 589 yields: % 81.49/47.31 | (590) all_127_2_105 = all_123_2_99 % 81.49/47.31 | % 81.49/47.31 | Combining equations (545,565) yields a new equation: % 81.49/47.31 | (591) all_129_2_108 = all_123_2_99 % 81.49/47.31 | % 81.49/47.31 | Simplifying 591 yields: % 81.49/47.31 | (592) all_129_2_108 = all_123_2_99 % 81.49/47.31 | % 81.49/47.31 | Combining equations (509,588) yields a new equation: % 81.49/47.31 | (593) all_127_0_103 = all_123_0_97 % 81.49/47.31 | % 81.49/47.31 | Combining equations (511,588) yields a new equation: % 81.49/47.31 | (594) all_127_0_103 = all_111_0_81 % 81.49/47.31 | % 81.49/47.31 | Combining equations (510,588) yields a new equation: % 81.49/47.31 | (595) all_127_0_103 = all_113_0_84 % 81.49/47.31 | % 81.49/47.31 | Combining equations (508,588) yields a new equation: % 81.49/47.31 | (596) all_127_0_103 = all_125_0_100 % 81.49/47.31 | % 81.49/47.31 | Combining equations (536,570) yields a new equation: % 81.49/47.31 | (597) all_113_2_86 = all_111_2_83 % 81.49/47.31 | % 81.49/47.31 | Combining equations (592,570) yields a new equation: % 81.49/47.31 | (598) all_123_2_99 = all_113_2_86 % 81.49/47.31 | % 81.49/47.31 | Simplifying 598 yields: % 81.49/47.31 | (599) all_123_2_99 = all_113_2_86 % 81.49/47.31 | % 81.49/47.31 | Combining equations (594,596) yields a new equation: % 81.49/47.31 | (600) all_125_0_100 = all_111_0_81 % 81.49/47.31 | % 81.49/47.31 | Combining equations (593,596) yields a new equation: % 81.49/47.31 | (601) all_125_0_100 = all_123_0_97 % 81.49/47.31 | % 81.49/47.31 | Combining equations (595,596) yields a new equation: % 81.49/47.31 | (602) all_125_0_100 = all_113_0_84 % 81.49/47.31 | % 81.49/47.31 | Combining equations (574,573) yields a new equation: % 81.49/47.31 | (603) all_125_2_102 = all_0_4_4 % 81.49/47.31 | % 81.49/47.31 | Combining equations (590,573) yields a new equation: % 81.49/47.31 | (604) all_125_2_102 = all_123_2_99 % 81.49/47.31 | % 81.49/47.31 | Combining equations (600,601) yields a new equation: % 81.49/47.31 | (605) all_123_0_97 = all_111_0_81 % 81.49/47.31 | % 81.49/47.31 | Combining equations (602,601) yields a new equation: % 81.49/47.31 | (606) all_123_0_97 = all_113_0_84 % 81.49/47.31 | % 81.49/47.31 | Combining equations (604,603) yields a new equation: % 81.49/47.31 | (607) all_123_2_99 = all_0_4_4 % 81.49/47.31 | % 81.49/47.31 | Simplifying 607 yields: % 81.49/47.31 | (608) all_123_2_99 = all_0_4_4 % 81.49/47.31 | % 81.49/47.31 | Combining equations (605,606) yields a new equation: % 81.49/47.31 | (609) all_113_0_84 = all_111_0_81 % 81.49/47.31 | % 81.49/47.31 | Combining equations (599,608) yields a new equation: % 81.49/47.31 | (610) all_113_2_86 = all_0_4_4 % 81.49/47.31 | % 81.49/47.31 | Simplifying 610 yields: % 81.49/47.31 | (611) all_113_2_86 = all_0_4_4 % 81.49/47.31 | % 81.49/47.31 | Combining equations (597,611) yields a new equation: % 81.49/47.31 | (612) all_111_2_83 = all_0_4_4 % 81.49/47.31 | % 81.49/47.31 | Simplifying 612 yields: % 81.49/47.31 | (613) all_111_2_83 = all_0_4_4 % 81.49/47.31 | % 81.49/47.31 | Combining equations (586,584) yields a new equation: % 81.49/47.31 | (522) all_133_1_113 = all_49_1_32 % 81.49/47.31 | % 81.49/47.31 | Combining equations (586,580) yields a new equation: % 81.49/47.31 | (615) all_137_1_118 = all_49_1_32 % 81.49/47.31 | % 81.49/47.31 | Combining equations (586,524) yields a new equation: % 81.49/47.31 | (616) all_141_1_123 = all_49_1_32 % 81.49/47.31 | % 81.49/47.31 | Combining equations (566,563) yields a new equation: % 81.49/47.31 | (562) all_153_1_138 = all_149_1_134 % 81.49/47.31 | % 81.49/47.31 | Combining equations (608,534) yields a new equation: % 81.49/47.31 | (618) all_155_2_141 = all_0_4_4 % 81.49/47.31 | % 81.49/47.31 | Combining equations (562,561) yields a new equation: % 81.49/47.31 | (520) all_157_1_143 = all_149_1_134 % 81.49/47.31 | % 81.49/47.31 | Combining equations (562,559) yields a new equation: % 81.49/47.31 | (620) all_159_1_145 = all_149_1_134 % 81.49/47.31 | % 81.49/47.31 | Combining equations (620,516) yields a new equation: % 81.49/47.31 | (621) all_161_1_147 = all_149_1_134 % 81.49/47.31 | % 81.49/47.31 | Combining equations (562,555) yields a new equation: % 81.49/47.31 | (622) all_163_1_149 = all_149_1_134 % 81.49/47.31 | % 81.49/47.31 | Combining equations (622,553) yields a new equation: % 81.49/47.31 | (623) all_165_1_151 = all_149_1_134 % 81.49/47.31 | % 81.49/47.31 | Combining equations (622,514) yields a new equation: % 81.49/47.31 | (624) all_167_1_153 = all_149_1_134 % 81.49/47.31 | % 81.49/47.31 | Combining equations (562,518) yields a new equation: % 81.49/47.31 | (625) all_171_1_156 = all_149_1_134 % 81.49/47.31 | % 81.49/47.31 | From (625) and (489) follows: % 81.49/47.31 | (626) crypt(all_149_1_134, all_0_1_1) = all_171_0_155 % 81.49/47.31 | % 81.49/47.31 | From (624) and (482) follows: % 81.49/47.31 | (627) crypt(all_149_1_134, a) = all_167_0_152 % 81.49/47.31 | % 81.49/47.31 | From (623) and (478) follows: % 81.49/47.31 | (628) crypt(all_149_1_134, all_0_0_0) = all_165_0_150 % 81.49/47.31 | % 81.49/47.31 | From (622) and (474) follows: % 81.49/47.31 | (629) crypt(all_149_1_134, all_0_2_2) = all_163_0_148 % 81.49/47.31 | % 81.49/47.31 | From (621) and (470) follows: % 81.49/47.31 | (630) crypt(all_149_1_134, id) = all_161_0_146 % 81.49/47.31 | % 81.49/47.31 | From (620) and (466) follows: % 81.49/47.31 | (631) crypt(all_149_1_134, exp) = all_159_0_144 % 81.49/47.31 | % 81.49/47.31 | From (520) and (462) follows: % 81.49/47.31 | (632) crypt(all_149_1_134, imp) = all_157_0_142 % 81.49/47.31 | % 81.49/47.31 | From (618) and (457) follows: % 81.49/47.31 | (633) crypt(all_0_4_4, all_0_5_5) = all_155_1_140 % 81.49/47.31 | % 81.49/47.31 | From (562) and (453) follows: % 81.49/47.31 | (634) crypt(all_149_1_134, pin) = all_153_0_137 % 81.49/47.31 | % 81.49/47.31 | From (566) and (449) follows: % 81.49/47.31 | (635) crypt(all_149_1_134, data) = all_151_0_135 % 81.49/47.31 | % 81.49/47.31 | From (616) and (426) follows: % 81.49/47.31 | (636) crypt(all_49_1_32, all_19_0_14) = all_141_0_122 % 81.49/47.31 | % 81.49/47.31 | From (615) and (417) follows: % 81.49/47.31 | (637) crypt(all_49_1_32, all_17_0_12) = all_137_0_117 % 81.49/47.31 | % 81.49/47.31 | From (522) and (408) follows: % 81.49/47.31 | (638) crypt(all_49_1_32, all_15_0_10) = all_133_0_112 % 81.49/47.31 | % 81.49/47.31 | From (586) and (365) follows: % 81.49/47.31 | (639) crypt(all_49_1_32, all_29_0_20) = all_115_0_87 % 81.49/47.31 | % 81.49/47.31 | From (613) and (355) follows: % 81.49/47.31 | (640) crypt(all_0_4_4, id) = all_111_1_82 % 81.49/47.31 | % 81.49/47.31 | From (609) and (361) follows: % 81.49/47.31 | (356) crypt(all_0_5_5, all_0_5_5) = all_111_0_81 % 81.49/47.31 | % 81.49/47.31 | From (566) and (450) follows: % 81.49/47.31 | (446) xor(all_49_1_32, data) = all_149_1_134 % 81.49/47.31 | % 81.49/47.31 | From (586) and (366) follows: % 81.49/47.31 | (146) xor(all_0_5_5, data) = all_49_1_32 % 81.49/47.32 | % 81.49/47.32 | From (525) and (501) follows: % 81.49/47.32 | (644) xor(exp, all_0_4_4) = all_49_1_32 % 81.49/47.32 | % 81.49/47.32 | From (613) and (357) follows: % 81.49/47.32 | (19) xor(km, data) = all_0_4_4 % 81.49/47.32 | % 81.49/47.32 | From (585) and (371) follows: % 81.49/47.32 | (42) xor(km, exp) = all_0_5_5 % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (30) with all_0_4_4, all_0_5_5, all_155_1_140, all_87_0_72 and discharging atoms crypt(all_0_4_4, all_0_5_5) = all_155_1_140, crypt(all_0_4_4, all_0_5_5) = all_87_0_72, yields: % 81.49/47.32 | (647) all_155_1_140 = all_87_0_72 % 81.49/47.32 | % 81.49/47.32 | From (647) and (633) follows: % 81.49/47.32 | (224) crypt(all_0_4_4, all_0_5_5) = all_87_0_72 % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_165_0_150, all_0_0_0, all_149_1_134 and discharging atoms crypt(all_149_1_134, all_0_0_0) = all_165_0_150, ~ p(all_165_0_150), yields: % 81.49/47.32 | (649) ? [v0] : ? [v1] : (crypt(v0, all_0_0_0) = v1 & xor(all_149_1_134, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_171_0_155, all_0_1_1, all_149_1_134 and discharging atoms crypt(all_149_1_134, all_0_1_1) = all_171_0_155, ~ p(all_171_0_155), yields: % 81.49/47.32 | (650) ? [v0] : ? [v1] : (crypt(v0, all_0_1_1) = v1 & xor(all_149_1_134, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_163_0_148, all_0_2_2, all_149_1_134 and discharging atoms crypt(all_149_1_134, all_0_2_2) = all_163_0_148, ~ p(all_163_0_148), yields: % 81.49/47.32 | (651) ? [v0] : ? [v1] : (crypt(v0, all_0_2_2) = v1 & xor(all_149_1_134, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_167_0_152, a, all_149_1_134 and discharging atoms crypt(all_149_1_134, a) = all_167_0_152, ~ p(all_167_0_152), yields: % 81.49/47.32 | (652) ? [v0] : ? [v1] : (crypt(v0, a) = v1 & xor(all_149_1_134, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_153_0_137, pin, all_149_1_134 and discharging atoms crypt(all_149_1_134, pin) = all_153_0_137, ~ p(all_153_0_137), yields: % 81.49/47.32 | (653) ? [v0] : ? [v1] : (crypt(v0, pin) = v1 & xor(all_149_1_134, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_151_0_135, data, all_149_1_134 and discharging atoms crypt(all_149_1_134, data) = all_151_0_135, ~ p(all_151_0_135), yields: % 81.49/47.32 | (654) ? [v0] : ? [v1] : (crypt(v0, data) = v1 & xor(all_149_1_134, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_149_0_133, kp, all_149_1_134 and discharging atoms crypt(all_149_1_134, kp) = all_149_0_133, ~ p(all_149_0_133), yields: % 81.49/47.32 | (655) ? [v0] : ? [v1] : (crypt(v0, kp) = v1 & xor(all_149_1_134, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_159_0_144, exp, all_149_1_134 and discharging atoms crypt(all_149_1_134, exp) = all_159_0_144, ~ p(all_159_0_144), yields: % 81.49/47.32 | (656) ? [v0] : ? [v1] : (crypt(v0, exp) = v1 & xor(all_149_1_134, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_157_0_142, imp, all_149_1_134 and discharging atoms crypt(all_149_1_134, imp) = all_157_0_142, ~ p(all_157_0_142), yields: % 81.49/47.32 | (657) ? [v0] : ? [v1] : (crypt(v0, imp) = v1 & xor(all_149_1_134, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (10) with all_161_0_146, all_149_1_134, id and discharging atoms crypt(all_149_1_134, id) = all_161_0_146, p(id), ~ p(all_161_0_146), yields: % 81.49/47.32 | (658) ? [v0] : (crypt(all_0_4_4, all_149_1_134) = v0 & ~ p(v0)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_161_0_146, id, all_149_1_134 and discharging atoms crypt(all_149_1_134, id) = all_161_0_146, ~ p(all_161_0_146), yields: % 81.49/47.32 | (659) ? [v0] : ? [v1] : (crypt(v0, id) = v1 & xor(all_149_1_134, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_121_0_94, km, all_121_1_95 and discharging atoms crypt(all_121_1_95, km) = all_121_0_94, ~ p(all_121_0_94), yields: % 81.49/47.32 | (660) ? [v0] : ? [v1] : (crypt(v0, km) = v1 & xor(all_121_1_95, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_119_0_92, all_0_5_5, all_119_1_93 and discharging atoms crypt(all_119_1_93, all_0_5_5) = all_119_0_92, ~ p(all_119_0_92), yields: % 81.49/47.32 | (661) ? [v0] : ? [v1] : (crypt(v0, all_0_5_5) = v1 & xor(all_119_1_93, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (13) with all_115_0_87, all_49_1_32, all_0_5_5, all_29_0_20, data and discharging atoms crypt(all_49_1_32, all_29_0_20) = all_115_0_87, xor(all_0_5_5, data) = all_49_1_32, p(data), ~ p(all_115_0_87), yields: % 81.49/47.32 | (662) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_29_0_20) = v1 & crypt(all_0_5_5, all_0_5_5) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_115_0_87, all_29_0_20, all_49_1_32 and discharging atoms crypt(all_49_1_32, all_29_0_20) = all_115_0_87, ~ p(all_115_0_87), yields: % 81.49/47.32 | (663) ? [v0] : ? [v1] : (crypt(v0, all_29_0_20) = v1 & xor(all_49_1_32, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (13) with all_141_0_122, all_49_1_32, all_0_5_5, all_19_0_14, data and discharging atoms crypt(all_49_1_32, all_19_0_14) = all_141_0_122, xor(all_0_5_5, data) = all_49_1_32, p(data), ~ p(all_141_0_122), yields: % 81.49/47.32 | (664) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_19_0_14) = v1 & crypt(all_0_5_5, all_0_5_5) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_141_0_122, all_19_0_14, all_49_1_32 and discharging atoms crypt(all_49_1_32, all_19_0_14) = all_141_0_122, ~ p(all_141_0_122), yields: % 81.49/47.32 | (665) ? [v0] : ? [v1] : (crypt(v0, all_19_0_14) = v1 & xor(all_49_1_32, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (13) with all_137_0_117, all_49_1_32, all_0_5_5, all_17_0_12, data and discharging atoms crypt(all_49_1_32, all_17_0_12) = all_137_0_117, xor(all_0_5_5, data) = all_49_1_32, p(data), ~ p(all_137_0_117), yields: % 81.49/47.32 | (666) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_17_0_12) = v1 & crypt(all_0_5_5, all_0_5_5) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_137_0_117, all_17_0_12, all_49_1_32 and discharging atoms crypt(all_49_1_32, all_17_0_12) = all_137_0_117, ~ p(all_137_0_117), yields: % 81.49/47.32 | (667) ? [v0] : ? [v1] : (crypt(v0, all_17_0_12) = v1 & xor(all_49_1_32, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (13) with all_133_0_112, all_49_1_32, all_0_5_5, all_15_0_10, data and discharging atoms crypt(all_49_1_32, all_15_0_10) = all_133_0_112, xor(all_0_5_5, data) = all_49_1_32, p(data), ~ p(all_133_0_112), yields: % 81.49/47.32 | (668) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_15_0_10) = v1 & crypt(all_0_5_5, all_0_5_5) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_133_0_112, all_15_0_10, all_49_1_32 and discharging atoms crypt(all_49_1_32, all_15_0_10) = all_133_0_112, ~ p(all_133_0_112), yields: % 81.49/47.32 | (669) ? [v0] : ? [v1] : (crypt(v0, all_15_0_10) = v1 & xor(all_49_1_32, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (21) with all_169_0_154, all_49_1_32, all_0_4_4, all_0_5_5, data, data and discharging atoms crypt(all_0_4_4, all_49_1_32) = all_169_0_154, xor(all_0_5_5, data) = all_49_1_32, xor(km, data) = all_0_4_4, p(data), ~ p(all_169_0_154), yields: % 81.49/47.32 | (670) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, all_0_5_5) = v2 & xor(data, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (13) with all_169_0_154, all_0_4_4, km, all_49_1_32, data and discharging atoms crypt(all_0_4_4, all_49_1_32) = all_169_0_154, xor(km, data) = all_0_4_4, p(data), ~ p(all_169_0_154), yields: % 81.49/47.32 | (671) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_49_1_32) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_169_0_154, all_49_1_32, all_0_4_4 and discharging atoms crypt(all_0_4_4, all_49_1_32) = all_169_0_154, ~ p(all_169_0_154), yields: % 81.49/47.32 | (672) ? [v0] : ? [v1] : (crypt(v0, all_49_1_32) = v1 & xor(all_0_4_4, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_111_1_82, id, all_0_4_4 and discharging atoms crypt(all_0_4_4, id) = all_111_1_82, yields: % 81.49/47.32 | (673) p(all_111_1_82) | ? [v0] : ? [v1] : (crypt(v0, id) = v1 & xor(all_0_4_4, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (13) with all_109_0_80, all_0_5_5, km, all_73_0_56, exp and discharging atoms crypt(all_0_5_5, all_73_0_56) = all_109_0_80, xor(km, exp) = all_0_5_5, p(exp), ~ p(all_109_0_80), yields: % 81.49/47.32 | (674) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_73_0_56) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_109_0_80, all_73_0_56, all_0_5_5 and discharging atoms crypt(all_0_5_5, all_73_0_56) = all_109_0_80, ~ p(all_109_0_80), yields: % 81.49/47.32 | (675) ? [v0] : ? [v1] : (crypt(v0, all_73_0_56) = v1 & xor(all_0_5_5, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (21) with all_111_0_81, all_0_5_5, all_0_5_5, km, exp, exp and discharging atoms crypt(all_0_5_5, all_0_5_5) = all_111_0_81, xor(km, exp) = all_0_5_5, p(exp), yields: % 81.49/47.32 | (676) p(all_111_0_81) | ? [v0] : ? [v1] : ? [v2] : (crypt(v1, km) = v2 & xor(exp, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (9) with all_111_0_81, all_0_5_5, all_0_5_5 and discharging atoms crypt(all_0_5_5, all_0_5_5) = all_111_0_81, yields: % 81.49/47.32 | (677) p(all_111_0_81) | ? [v0] : ? [v1] : (crypt(v0, all_0_5_5) = v1 & xor(all_0_5_5, data) = v0 & ~ p(v1)) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (13) with all_165_0_150, all_149_1_134, all_49_1_32, all_0_0_0, data and discharging atoms crypt(all_149_1_134, all_0_0_0) = all_165_0_150, xor(all_49_1_32, data) = all_149_1_134, p(data), ~ p(all_165_0_150), yields: % 81.49/47.32 | (678) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_0_0_0) = v1 & crypt(all_0_5_5, all_49_1_32) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (13) with all_171_0_155, all_149_1_134, all_49_1_32, all_0_1_1, data and discharging atoms crypt(all_149_1_134, all_0_1_1) = all_171_0_155, xor(all_49_1_32, data) = all_149_1_134, p(data), ~ p(all_171_0_155), yields: % 81.49/47.32 | (679) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_0_1_1) = v1 & crypt(all_0_5_5, all_49_1_32) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (13) with all_163_0_148, all_149_1_134, all_49_1_32, all_0_2_2, data and discharging atoms crypt(all_149_1_134, all_0_2_2) = all_163_0_148, xor(all_49_1_32, data) = all_149_1_134, p(data), ~ p(all_163_0_148), yields: % 81.49/47.32 | (680) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_0_2_2) = v1 & crypt(all_0_5_5, all_49_1_32) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (13) with all_167_0_152, all_149_1_134, all_49_1_32, a, data and discharging atoms crypt(all_149_1_134, a) = all_167_0_152, xor(all_49_1_32, data) = all_149_1_134, p(data), ~ p(all_167_0_152), yields: % 81.49/47.32 | (681) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, a) = v1 & crypt(all_0_5_5, all_49_1_32) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.49/47.32 | % 81.49/47.32 | Instantiating formula (13) with all_153_0_137, all_149_1_134, all_49_1_32, pin, data and discharging atoms crypt(all_149_1_134, pin) = all_153_0_137, xor(all_49_1_32, data) = all_149_1_134, p(data), ~ p(all_153_0_137), yields: % 81.49/47.33 | (682) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, pin) = v1 & crypt(all_0_5_5, all_49_1_32) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (13) with all_151_0_135, all_149_1_134, all_49_1_32, data, data and discharging atoms crypt(all_149_1_134, data) = all_151_0_135, xor(all_49_1_32, data) = all_149_1_134, p(data), ~ p(all_151_0_135), yields: % 81.49/47.33 | (683) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, data) = v1 & crypt(all_0_5_5, all_49_1_32) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (13) with all_149_0_133, all_149_1_134, all_49_1_32, kp, data and discharging atoms crypt(all_149_1_134, kp) = all_149_0_133, xor(all_49_1_32, data) = all_149_1_134, p(data), ~ p(all_149_0_133), yields: % 81.49/47.33 | (684) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, kp) = v1 & crypt(all_0_5_5, all_49_1_32) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (13) with all_159_0_144, all_149_1_134, all_49_1_32, exp, data and discharging atoms crypt(all_149_1_134, exp) = all_159_0_144, xor(all_49_1_32, data) = all_149_1_134, p(data), ~ p(all_159_0_144), yields: % 81.49/47.33 | (685) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, exp) = v1 & crypt(all_0_5_5, all_49_1_32) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (13) with all_157_0_142, all_149_1_134, all_49_1_32, imp, data and discharging atoms crypt(all_149_1_134, imp) = all_157_0_142, xor(all_49_1_32, data) = all_149_1_134, p(data), ~ p(all_157_0_142), yields: % 81.49/47.33 | (686) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, imp) = v1 & crypt(all_0_5_5, all_49_1_32) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (13) with all_161_0_146, all_149_1_134, all_49_1_32, id, data and discharging atoms crypt(all_149_1_134, id) = all_161_0_146, xor(all_49_1_32, data) = all_149_1_134, p(data), ~ p(all_161_0_146), yields: % 81.49/47.33 | (687) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, id) = v1 & crypt(all_0_5_5, all_49_1_32) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (15) with all_149_1_134, all_49_1_32, data, data, all_0_5_5 and discharging atoms xor(all_49_1_32, data) = all_149_1_134, xor(all_0_5_5, data) = all_49_1_32, yields: % 81.49/47.33 | (688) ? [v0] : (xor(all_0_5_5, v0) = all_149_1_134 & xor(data, data) = v0) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (13) with all_119_0_92, all_119_1_93, all_0_4_4, all_0_5_5, data and discharging atoms crypt(all_119_1_93, all_0_5_5) = all_119_0_92, xor(all_0_4_4, data) = all_119_1_93, p(data), ~ p(all_119_0_92), yields: % 81.49/47.33 | (689) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_0_5_5) = v1 & crypt(all_0_5_5, all_0_4_4) = v2 & xor(km, data) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (15) with all_119_1_93, all_0_4_4, data, km, data and discharging atoms xor(all_0_4_4, data) = all_119_1_93, xor(data, km) = all_0_4_4, yields: % 81.49/47.33 | (690) ? [v0] : (xor(data, v0) = all_119_1_93 & xor(km, data) = v0) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (15) with all_119_1_93, all_0_4_4, data, data, km and discharging atoms xor(all_0_4_4, data) = all_119_1_93, xor(km, data) = all_0_4_4, yields: % 81.49/47.33 | (691) ? [v0] : (xor(data, data) = v0 & xor(km, v0) = all_119_1_93) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (12) with all_49_1_32, all_0_5_5, km, exp, data and discharging atoms xor(data, all_0_5_5) = all_49_1_32, xor(exp, km) = all_0_5_5, yields: % 81.49/47.33 | (692) ? [v0] : (xor(v0, km) = all_49_1_32 & xor(data, exp) = v0) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (12) with all_49_1_32, all_0_5_5, exp, km, data and discharging atoms xor(data, all_0_5_5) = all_49_1_32, xor(km, exp) = all_0_5_5, yields: % 81.49/47.33 | (693) ? [v0] : (xor(v0, exp) = all_49_1_32 & xor(data, km) = v0) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (15) with all_149_1_134, all_49_1_32, data, all_0_5_5, data and discharging atoms xor(all_49_1_32, data) = all_149_1_134, xor(data, all_0_5_5) = all_49_1_32, yields: % 81.49/47.33 | (694) ? [v0] : (xor(all_0_5_5, data) = v0 & xor(data, v0) = all_149_1_134) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (6) with all_121_2_96, kp, data and discharging atoms xor(data, kp) = all_121_2_96, p(data), p(kp), yields: % 81.49/47.33 | (695) p(all_121_2_96) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (35) with all_121_2_96, data, kp and discharging atoms xor(data, kp) = all_121_2_96, yields: % 81.49/47.33 | (696) xor(kp, data) = all_121_2_96 % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (12) with all_49_1_32, all_0_4_4, km, data, exp and discharging atoms xor(data, km) = all_0_4_4, xor(exp, all_0_4_4) = all_49_1_32, yields: % 81.49/47.33 | (697) ? [v0] : (xor(v0, km) = all_49_1_32 & xor(exp, data) = v0) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (15) with all_149_1_134, all_49_1_32, data, all_0_4_4, exp and discharging atoms xor(all_49_1_32, data) = all_149_1_134, xor(exp, all_0_4_4) = all_49_1_32, yields: % 81.49/47.33 | (698) ? [v0] : (xor(all_0_4_4, data) = v0 & xor(exp, v0) = all_149_1_134) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (6) with all_175_0_160, data, exp and discharging atoms xor(exp, data) = all_175_0_160, p(data), p(exp), yields: % 81.49/47.33 | (699) p(all_175_0_160) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (35) with all_175_0_160, exp, data and discharging atoms xor(exp, data) = all_175_0_160, yields: % 81.49/47.33 | (700) xor(data, exp) = all_175_0_160 % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (15) with all_149_1_134, all_49_1_32, data, all_175_0_160, km and discharging atoms xor(all_49_1_32, data) = all_149_1_134, xor(km, all_175_0_160) = all_49_1_32, yields: % 81.49/47.33 | (701) ? [v0] : (xor(all_175_0_160, data) = v0 & xor(km, v0) = all_149_1_134) % 81.49/47.33 | % 81.49/47.33 | Instantiating formula (12) with all_121_1_95, all_121_2_96, kp, data, km and discharging atoms xor(data, kp) = all_121_2_96, xor(km, all_121_2_96) = all_121_1_95, yields: % 81.49/47.33 | (702) ? [v0] : (xor(v0, kp) = all_121_1_95 & xor(km, data) = v0) % 81.49/47.33 | % 81.49/47.33 | Instantiating (701) with all_193_0_162 yields: % 81.49/47.33 | (703) xor(all_175_0_160, data) = all_193_0_162 & xor(km, all_193_0_162) = all_149_1_134 % 81.49/47.33 | % 81.49/47.33 | Applying alpha-rule on (703) yields: % 81.49/47.33 | (704) xor(all_175_0_160, data) = all_193_0_162 % 81.49/47.33 | (705) xor(km, all_193_0_162) = all_149_1_134 % 81.49/47.33 | % 81.49/47.33 | Instantiating (692) with all_195_0_163 yields: % 81.49/47.33 | (706) xor(all_195_0_163, km) = all_49_1_32 & xor(data, exp) = all_195_0_163 % 81.49/47.33 | % 81.49/47.33 | Applying alpha-rule on (706) yields: % 81.49/47.33 | (707) xor(all_195_0_163, km) = all_49_1_32 % 81.49/47.33 | (708) xor(data, exp) = all_195_0_163 % 81.49/47.33 | % 81.49/47.33 | Instantiating (682) with all_197_0_164, all_197_1_165, all_197_2_166 yields: % 81.49/47.33 | (709) crypt(all_197_2_166, pin) = all_197_1_165 & crypt(all_0_5_5, all_49_1_32) = all_197_0_164 & xor(km, data) = all_197_2_166 & ( ~ p(all_197_0_164) | ~ p(all_197_1_165)) % 81.49/47.33 | % 81.49/47.33 | Applying alpha-rule on (709) yields: % 81.49/47.33 | (710) crypt(all_197_2_166, pin) = all_197_1_165 % 81.49/47.33 | (711) crypt(all_0_5_5, all_49_1_32) = all_197_0_164 % 81.49/47.33 | (712) xor(km, data) = all_197_2_166 % 81.49/47.33 | (713) ~ p(all_197_0_164) | ~ p(all_197_1_165) % 81.49/47.33 | % 81.49/47.33 | Instantiating (681) with all_199_0_167, all_199_1_168, all_199_2_169 yields: % 81.49/47.33 | (714) crypt(all_199_2_169, a) = all_199_1_168 & crypt(all_0_5_5, all_49_1_32) = all_199_0_167 & xor(km, data) = all_199_2_169 & ( ~ p(all_199_0_167) | ~ p(all_199_1_168)) % 81.49/47.33 | % 81.49/47.33 | Applying alpha-rule on (714) yields: % 81.49/47.33 | (715) crypt(all_199_2_169, a) = all_199_1_168 % 81.49/47.33 | (716) crypt(all_0_5_5, all_49_1_32) = all_199_0_167 % 81.49/47.33 | (717) xor(km, data) = all_199_2_169 % 81.49/47.33 | (718) ~ p(all_199_0_167) | ~ p(all_199_1_168) % 81.49/47.33 | % 81.49/47.33 | Instantiating (694) with all_201_0_170 yields: % 81.49/47.33 | (719) xor(all_0_5_5, data) = all_201_0_170 & xor(data, all_201_0_170) = all_149_1_134 % 81.49/47.33 | % 81.49/47.33 | Applying alpha-rule on (719) yields: % 81.49/47.33 | (720) xor(all_0_5_5, data) = all_201_0_170 % 81.49/47.33 | (721) xor(data, all_201_0_170) = all_149_1_134 % 81.49/47.33 | % 81.49/47.33 | Instantiating (693) with all_203_0_171 yields: % 81.49/47.33 | (722) xor(all_203_0_171, exp) = all_49_1_32 & xor(data, km) = all_203_0_171 % 81.49/47.33 | % 81.49/47.33 | Applying alpha-rule on (722) yields: % 81.49/47.33 | (723) xor(all_203_0_171, exp) = all_49_1_32 % 81.49/47.33 | (724) xor(data, km) = all_203_0_171 % 81.49/47.33 | % 81.49/47.33 | Instantiating (688) with all_205_0_172 yields: % 81.49/47.33 | (725) xor(all_0_5_5, all_205_0_172) = all_149_1_134 & xor(data, data) = all_205_0_172 % 81.49/47.33 | % 81.49/47.33 | Applying alpha-rule on (725) yields: % 81.49/47.33 | (726) xor(all_0_5_5, all_205_0_172) = all_149_1_134 % 81.49/47.33 | (727) xor(data, data) = all_205_0_172 % 81.49/47.33 | % 81.49/47.33 | Instantiating (687) with all_207_0_173, all_207_1_174, all_207_2_175 yields: % 81.49/47.33 | (728) crypt(all_207_2_175, id) = all_207_1_174 & crypt(all_0_5_5, all_49_1_32) = all_207_0_173 & xor(km, data) = all_207_2_175 & ( ~ p(all_207_0_173) | ~ p(all_207_1_174)) % 81.49/47.33 | % 81.49/47.33 | Applying alpha-rule on (728) yields: % 81.49/47.33 | (729) crypt(all_207_2_175, id) = all_207_1_174 % 81.49/47.33 | (730) crypt(all_0_5_5, all_49_1_32) = all_207_0_173 % 81.49/47.33 | (731) xor(km, data) = all_207_2_175 % 81.49/47.33 | (732) ~ p(all_207_0_173) | ~ p(all_207_1_174) % 81.49/47.33 | % 81.49/47.33 | Instantiating (678) with all_209_0_176, all_209_1_177, all_209_2_178 yields: % 81.49/47.33 | (733) crypt(all_209_2_178, all_0_0_0) = all_209_1_177 & crypt(all_0_5_5, all_49_1_32) = all_209_0_176 & xor(km, data) = all_209_2_178 & ( ~ p(all_209_0_176) | ~ p(all_209_1_177)) % 81.49/47.33 | % 81.49/47.33 | Applying alpha-rule on (733) yields: % 81.49/47.33 | (734) crypt(all_209_2_178, all_0_0_0) = all_209_1_177 % 81.49/47.33 | (735) crypt(all_0_5_5, all_49_1_32) = all_209_0_176 % 81.49/47.33 | (736) xor(km, data) = all_209_2_178 % 81.49/47.33 | (737) ~ p(all_209_0_176) | ~ p(all_209_1_177) % 81.49/47.33 | % 81.49/47.33 | Instantiating (680) with all_211_0_179, all_211_1_180, all_211_2_181 yields: % 81.49/47.33 | (738) crypt(all_211_2_181, all_0_2_2) = all_211_1_180 & crypt(all_0_5_5, all_49_1_32) = all_211_0_179 & xor(km, data) = all_211_2_181 & ( ~ p(all_211_0_179) | ~ p(all_211_1_180)) % 81.49/47.33 | % 81.49/47.33 | Applying alpha-rule on (738) yields: % 81.49/47.33 | (739) crypt(all_211_2_181, all_0_2_2) = all_211_1_180 % 81.49/47.33 | (740) crypt(all_0_5_5, all_49_1_32) = all_211_0_179 % 81.49/47.33 | (741) xor(km, data) = all_211_2_181 % 81.49/47.33 | (742) ~ p(all_211_0_179) | ~ p(all_211_1_180) % 81.49/47.33 | % 81.49/47.33 | Instantiating (679) with all_213_0_182, all_213_1_183, all_213_2_184 yields: % 81.49/47.33 | (743) crypt(all_213_2_184, all_0_1_1) = all_213_1_183 & crypt(all_0_5_5, all_49_1_32) = all_213_0_182 & xor(km, data) = all_213_2_184 & ( ~ p(all_213_0_182) | ~ p(all_213_1_183)) % 81.49/47.33 | % 81.49/47.33 | Applying alpha-rule on (743) yields: % 81.49/47.33 | (744) crypt(all_213_2_184, all_0_1_1) = all_213_1_183 % 81.49/47.33 | (745) crypt(all_0_5_5, all_49_1_32) = all_213_0_182 % 81.49/47.33 | (746) xor(km, data) = all_213_2_184 % 81.49/47.33 | (747) ~ p(all_213_0_182) | ~ p(all_213_1_183) % 81.49/47.33 | % 81.49/47.33 | Instantiating (675) with all_215_0_185, all_215_1_186 yields: % 81.49/47.33 | (748) crypt(all_215_1_186, all_73_0_56) = all_215_0_185 & xor(all_0_5_5, data) = all_215_1_186 & ~ p(all_215_0_185) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (748) yields: % 81.49/47.34 | (749) crypt(all_215_1_186, all_73_0_56) = all_215_0_185 % 81.49/47.34 | (750) xor(all_0_5_5, data) = all_215_1_186 % 81.49/47.34 | (751) ~ p(all_215_0_185) % 81.49/47.34 | % 81.49/47.34 | Instantiating (674) with all_217_0_187, all_217_1_188, all_217_2_189 yields: % 81.49/47.34 | (752) crypt(all_217_2_189, all_73_0_56) = all_217_1_188 & crypt(all_0_5_5, km) = all_217_0_187 & xor(km, exp) = all_217_2_189 & ( ~ p(all_217_0_187) | ~ p(all_217_1_188)) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (752) yields: % 81.49/47.34 | (753) crypt(all_217_2_189, all_73_0_56) = all_217_1_188 % 81.49/47.34 | (754) crypt(all_0_5_5, km) = all_217_0_187 % 81.49/47.34 | (755) xor(km, exp) = all_217_2_189 % 81.49/47.34 | (756) ~ p(all_217_0_187) | ~ p(all_217_1_188) % 81.49/47.34 | % 81.49/47.34 | Instantiating (702) with all_219_0_190 yields: % 81.49/47.34 | (757) xor(all_219_0_190, kp) = all_121_1_95 & xor(km, data) = all_219_0_190 % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (757) yields: % 81.49/47.34 | (758) xor(all_219_0_190, kp) = all_121_1_95 % 81.49/47.34 | (759) xor(km, data) = all_219_0_190 % 81.49/47.34 | % 81.49/47.34 | Instantiating (698) with all_221_0_191 yields: % 81.49/47.34 | (760) xor(all_0_4_4, data) = all_221_0_191 & xor(exp, all_221_0_191) = all_149_1_134 % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (760) yields: % 81.49/47.34 | (761) xor(all_0_4_4, data) = all_221_0_191 % 81.49/47.34 | (762) xor(exp, all_221_0_191) = all_149_1_134 % 81.49/47.34 | % 81.49/47.34 | Instantiating (689) with all_223_0_192, all_223_1_193, all_223_2_194 yields: % 81.49/47.34 | (763) crypt(all_223_2_194, all_0_5_5) = all_223_1_193 & crypt(all_0_5_5, all_0_4_4) = all_223_0_192 & xor(km, data) = all_223_2_194 & ( ~ p(all_223_0_192) | ~ p(all_223_1_193)) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (763) yields: % 81.49/47.34 | (764) crypt(all_223_2_194, all_0_5_5) = all_223_1_193 % 81.49/47.34 | (765) crypt(all_0_5_5, all_0_4_4) = all_223_0_192 % 81.49/47.34 | (766) xor(km, data) = all_223_2_194 % 81.49/47.34 | (767) ~ p(all_223_0_192) | ~ p(all_223_1_193) % 81.49/47.34 | % 81.49/47.34 | Instantiating (672) with all_225_0_195, all_225_1_196 yields: % 81.49/47.34 | (768) crypt(all_225_1_196, all_49_1_32) = all_225_0_195 & xor(all_0_4_4, data) = all_225_1_196 & ~ p(all_225_0_195) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (768) yields: % 81.49/47.34 | (769) crypt(all_225_1_196, all_49_1_32) = all_225_0_195 % 81.49/47.34 | (770) xor(all_0_4_4, data) = all_225_1_196 % 81.49/47.34 | (771) ~ p(all_225_0_195) % 81.49/47.34 | % 81.49/47.34 | Instantiating (671) with all_227_0_197, all_227_1_198, all_227_2_199 yields: % 81.49/47.34 | (772) crypt(all_227_2_199, all_49_1_32) = all_227_1_198 & crypt(all_0_5_5, km) = all_227_0_197 & xor(km, data) = all_227_2_199 & ( ~ p(all_227_0_197) | ~ p(all_227_1_198)) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (772) yields: % 81.49/47.34 | (773) crypt(all_227_2_199, all_49_1_32) = all_227_1_198 % 81.49/47.34 | (774) crypt(all_0_5_5, km) = all_227_0_197 % 81.49/47.34 | (775) xor(km, data) = all_227_2_199 % 81.49/47.34 | (776) ~ p(all_227_0_197) | ~ p(all_227_1_198) % 81.49/47.34 | % 81.49/47.34 | Instantiating (670) with all_229_0_200, all_229_1_201, all_229_2_202 yields: % 81.49/47.34 | (777) crypt(all_229_1_201, all_0_5_5) = all_229_0_200 & xor(data, kp) = all_229_2_202 & xor(km, all_229_2_202) = all_229_1_201 & ~ p(all_229_0_200) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (777) yields: % 81.49/47.34 | (778) crypt(all_229_1_201, all_0_5_5) = all_229_0_200 % 81.49/47.34 | (779) xor(data, kp) = all_229_2_202 % 81.49/47.34 | (780) xor(km, all_229_2_202) = all_229_1_201 % 81.49/47.34 | (781) ~ p(all_229_0_200) % 81.49/47.34 | % 81.49/47.34 | Instantiating (669) with all_231_0_203, all_231_1_204 yields: % 81.49/47.34 | (782) crypt(all_231_1_204, all_15_0_10) = all_231_0_203 & xor(all_49_1_32, data) = all_231_1_204 & ~ p(all_231_0_203) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (782) yields: % 81.49/47.34 | (783) crypt(all_231_1_204, all_15_0_10) = all_231_0_203 % 81.49/47.34 | (784) xor(all_49_1_32, data) = all_231_1_204 % 81.49/47.34 | (785) ~ p(all_231_0_203) % 81.49/47.34 | % 81.49/47.34 | Instantiating (664) with all_233_0_205, all_233_1_206, all_233_2_207 yields: % 81.49/47.34 | (786) crypt(all_233_2_207, all_19_0_14) = all_233_1_206 & crypt(all_0_5_5, all_0_5_5) = all_233_0_205 & xor(km, data) = all_233_2_207 & ( ~ p(all_233_0_205) | ~ p(all_233_1_206)) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (786) yields: % 81.49/47.34 | (787) crypt(all_233_2_207, all_19_0_14) = all_233_1_206 % 81.49/47.34 | (788) crypt(all_0_5_5, all_0_5_5) = all_233_0_205 % 81.49/47.34 | (789) xor(km, data) = all_233_2_207 % 81.49/47.34 | (790) ~ p(all_233_0_205) | ~ p(all_233_1_206) % 81.49/47.34 | % 81.49/47.34 | Instantiating (662) with all_235_0_208, all_235_1_209, all_235_2_210 yields: % 81.49/47.34 | (791) crypt(all_235_2_210, all_29_0_20) = all_235_1_209 & crypt(all_0_5_5, all_0_5_5) = all_235_0_208 & xor(km, data) = all_235_2_210 & ( ~ p(all_235_0_208) | ~ p(all_235_1_209)) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (791) yields: % 81.49/47.34 | (792) crypt(all_235_2_210, all_29_0_20) = all_235_1_209 % 81.49/47.34 | (793) crypt(all_0_5_5, all_0_5_5) = all_235_0_208 % 81.49/47.34 | (794) xor(km, data) = all_235_2_210 % 81.49/47.34 | (795) ~ p(all_235_0_208) | ~ p(all_235_1_209) % 81.49/47.34 | % 81.49/47.34 | Instantiating (661) with all_237_0_211, all_237_1_212 yields: % 81.49/47.34 | (796) crypt(all_237_1_212, all_0_5_5) = all_237_0_211 & xor(all_119_1_93, data) = all_237_1_212 & ~ p(all_237_0_211) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (796) yields: % 81.49/47.34 | (797) crypt(all_237_1_212, all_0_5_5) = all_237_0_211 % 81.49/47.34 | (798) xor(all_119_1_93, data) = all_237_1_212 % 81.49/47.34 | (799) ~ p(all_237_0_211) % 81.49/47.34 | % 81.49/47.34 | Instantiating (686) with all_239_0_213, all_239_1_214, all_239_2_215 yields: % 81.49/47.34 | (800) crypt(all_239_2_215, imp) = all_239_1_214 & crypt(all_0_5_5, all_49_1_32) = all_239_0_213 & xor(km, data) = all_239_2_215 & ( ~ p(all_239_0_213) | ~ p(all_239_1_214)) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (800) yields: % 81.49/47.34 | (801) crypt(all_239_2_215, imp) = all_239_1_214 % 81.49/47.34 | (802) crypt(all_0_5_5, all_49_1_32) = all_239_0_213 % 81.49/47.34 | (803) xor(km, data) = all_239_2_215 % 81.49/47.34 | (804) ~ p(all_239_0_213) | ~ p(all_239_1_214) % 81.49/47.34 | % 81.49/47.34 | Instantiating (684) with all_241_0_216, all_241_1_217, all_241_2_218 yields: % 81.49/47.34 | (805) crypt(all_241_2_218, kp) = all_241_1_217 & crypt(all_0_5_5, all_49_1_32) = all_241_0_216 & xor(km, data) = all_241_2_218 & ( ~ p(all_241_0_216) | ~ p(all_241_1_217)) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (805) yields: % 81.49/47.34 | (806) crypt(all_241_2_218, kp) = all_241_1_217 % 81.49/47.34 | (807) crypt(all_0_5_5, all_49_1_32) = all_241_0_216 % 81.49/47.34 | (808) xor(km, data) = all_241_2_218 % 81.49/47.34 | (809) ~ p(all_241_0_216) | ~ p(all_241_1_217) % 81.49/47.34 | % 81.49/47.34 | Instantiating (683) with all_243_0_219, all_243_1_220, all_243_2_221 yields: % 81.49/47.34 | (810) crypt(all_243_2_221, data) = all_243_1_220 & crypt(all_0_5_5, all_49_1_32) = all_243_0_219 & xor(km, data) = all_243_2_221 & ( ~ p(all_243_0_219) | ~ p(all_243_1_220)) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (810) yields: % 81.49/47.34 | (811) crypt(all_243_2_221, data) = all_243_1_220 % 81.49/47.34 | (812) crypt(all_0_5_5, all_49_1_32) = all_243_0_219 % 81.49/47.34 | (813) xor(km, data) = all_243_2_221 % 81.49/47.34 | (814) ~ p(all_243_0_219) | ~ p(all_243_1_220) % 81.49/47.34 | % 81.49/47.34 | Instantiating (685) with all_245_0_222, all_245_1_223, all_245_2_224 yields: % 81.49/47.34 | (815) crypt(all_245_2_224, exp) = all_245_1_223 & crypt(all_0_5_5, all_49_1_32) = all_245_0_222 & xor(km, data) = all_245_2_224 & ( ~ p(all_245_0_222) | ~ p(all_245_1_223)) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (815) yields: % 81.49/47.34 | (816) crypt(all_245_2_224, exp) = all_245_1_223 % 81.49/47.34 | (817) crypt(all_0_5_5, all_49_1_32) = all_245_0_222 % 81.49/47.34 | (818) xor(km, data) = all_245_2_224 % 81.49/47.34 | (819) ~ p(all_245_0_222) | ~ p(all_245_1_223) % 81.49/47.34 | % 81.49/47.34 | Instantiating (655) with all_247_0_225, all_247_1_226 yields: % 81.49/47.34 | (820) crypt(all_247_1_226, kp) = all_247_0_225 & xor(all_149_1_134, data) = all_247_1_226 & ~ p(all_247_0_225) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (820) yields: % 81.49/47.34 | (821) crypt(all_247_1_226, kp) = all_247_0_225 % 81.49/47.34 | (822) xor(all_149_1_134, data) = all_247_1_226 % 81.49/47.34 | (823) ~ p(all_247_0_225) % 81.49/47.34 | % 81.49/47.34 | Instantiating (653) with all_249_0_227, all_249_1_228 yields: % 81.49/47.34 | (824) crypt(all_249_1_228, pin) = all_249_0_227 & xor(all_149_1_134, data) = all_249_1_228 & ~ p(all_249_0_227) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (824) yields: % 81.49/47.34 | (825) crypt(all_249_1_228, pin) = all_249_0_227 % 81.49/47.34 | (826) xor(all_149_1_134, data) = all_249_1_228 % 81.49/47.34 | (827) ~ p(all_249_0_227) % 81.49/47.34 | % 81.49/47.34 | Instantiating (652) with all_251_0_229, all_251_1_230 yields: % 81.49/47.34 | (828) crypt(all_251_1_230, a) = all_251_0_229 & xor(all_149_1_134, data) = all_251_1_230 & ~ p(all_251_0_229) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (828) yields: % 81.49/47.34 | (829) crypt(all_251_1_230, a) = all_251_0_229 % 81.49/47.34 | (830) xor(all_149_1_134, data) = all_251_1_230 % 81.49/47.34 | (831) ~ p(all_251_0_229) % 81.49/47.34 | % 81.49/47.34 | Instantiating (663) with all_253_0_231, all_253_1_232 yields: % 81.49/47.34 | (832) crypt(all_253_1_232, all_29_0_20) = all_253_0_231 & xor(all_49_1_32, data) = all_253_1_232 & ~ p(all_253_0_231) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (832) yields: % 81.49/47.34 | (833) crypt(all_253_1_232, all_29_0_20) = all_253_0_231 % 81.49/47.34 | (834) xor(all_49_1_32, data) = all_253_1_232 % 81.49/47.34 | (835) ~ p(all_253_0_231) % 81.49/47.34 | % 81.49/47.34 | Instantiating (660) with all_255_0_233, all_255_1_234 yields: % 81.49/47.34 | (836) crypt(all_255_1_234, km) = all_255_0_233 & xor(all_121_1_95, data) = all_255_1_234 & ~ p(all_255_0_233) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (836) yields: % 81.49/47.34 | (837) crypt(all_255_1_234, km) = all_255_0_233 % 81.49/47.34 | (838) xor(all_121_1_95, data) = all_255_1_234 % 81.49/47.34 | (839) ~ p(all_255_0_233) % 81.49/47.34 | % 81.49/47.34 | Instantiating (659) with all_257_0_235, all_257_1_236 yields: % 81.49/47.34 | (840) crypt(all_257_1_236, id) = all_257_0_235 & xor(all_149_1_134, data) = all_257_1_236 & ~ p(all_257_0_235) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (840) yields: % 81.49/47.34 | (841) crypt(all_257_1_236, id) = all_257_0_235 % 81.49/47.34 | (842) xor(all_149_1_134, data) = all_257_1_236 % 81.49/47.34 | (843) ~ p(all_257_0_235) % 81.49/47.34 | % 81.49/47.34 | Instantiating (654) with all_259_0_237, all_259_1_238 yields: % 81.49/47.34 | (844) crypt(all_259_1_238, data) = all_259_0_237 & xor(all_149_1_134, data) = all_259_1_238 & ~ p(all_259_0_237) % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (844) yields: % 81.49/47.34 | (845) crypt(all_259_1_238, data) = all_259_0_237 % 81.49/47.34 | (846) xor(all_149_1_134, data) = all_259_1_238 % 81.49/47.34 | (847) ~ p(all_259_0_237) % 81.49/47.34 | % 81.49/47.34 | Instantiating (697) with all_261_0_239 yields: % 81.49/47.34 | (848) xor(all_261_0_239, km) = all_49_1_32 & xor(exp, data) = all_261_0_239 % 81.49/47.34 | % 81.49/47.34 | Applying alpha-rule on (848) yields: % 81.49/47.34 | (849) xor(all_261_0_239, km) = all_49_1_32 % 81.49/47.34 | (850) xor(exp, data) = all_261_0_239 % 81.49/47.35 | % 81.49/47.35 | Instantiating (691) with all_263_0_240 yields: % 81.49/47.35 | (851) xor(data, data) = all_263_0_240 & xor(km, all_263_0_240) = all_119_1_93 % 81.49/47.35 | % 81.49/47.35 | Applying alpha-rule on (851) yields: % 81.49/47.35 | (852) xor(data, data) = all_263_0_240 % 81.49/47.35 | (853) xor(km, all_263_0_240) = all_119_1_93 % 81.49/47.35 | % 81.49/47.35 | Instantiating (651) with all_265_0_241, all_265_1_242 yields: % 81.49/47.35 | (854) crypt(all_265_1_242, all_0_2_2) = all_265_0_241 & xor(all_149_1_134, data) = all_265_1_242 & ~ p(all_265_0_241) % 81.49/47.35 | % 81.49/47.35 | Applying alpha-rule on (854) yields: % 81.49/47.35 | (855) crypt(all_265_1_242, all_0_2_2) = all_265_0_241 % 81.49/47.35 | (856) xor(all_149_1_134, data) = all_265_1_242 % 81.49/47.35 | (857) ~ p(all_265_0_241) % 81.49/47.35 | % 81.49/47.35 | Instantiating (650) with all_267_0_243, all_267_1_244 yields: % 81.49/47.35 | (858) crypt(all_267_1_244, all_0_1_1) = all_267_0_243 & xor(all_149_1_134, data) = all_267_1_244 & ~ p(all_267_0_243) % 81.49/47.35 | % 81.49/47.35 | Applying alpha-rule on (858) yields: % 81.49/47.35 | (859) crypt(all_267_1_244, all_0_1_1) = all_267_0_243 % 81.49/47.35 | (860) xor(all_149_1_134, data) = all_267_1_244 % 81.49/47.35 | (861) ~ p(all_267_0_243) % 81.49/47.35 | % 81.49/47.35 | Instantiating (668) with all_269_0_245, all_269_1_246, all_269_2_247 yields: % 81.49/47.35 | (862) crypt(all_269_2_247, all_15_0_10) = all_269_1_246 & crypt(all_0_5_5, all_0_5_5) = all_269_0_245 & xor(km, data) = all_269_2_247 & ( ~ p(all_269_0_245) | ~ p(all_269_1_246)) % 81.49/47.35 | % 81.49/47.35 | Applying alpha-rule on (862) yields: % 81.49/47.35 | (863) crypt(all_269_2_247, all_15_0_10) = all_269_1_246 % 81.49/47.35 | (864) crypt(all_0_5_5, all_0_5_5) = all_269_0_245 % 81.49/47.35 | (865) xor(km, data) = all_269_2_247 % 81.49/47.35 | (866) ~ p(all_269_0_245) | ~ p(all_269_1_246) % 81.49/47.35 | % 81.49/47.35 | Instantiating (667) with all_271_0_248, all_271_1_249 yields: % 81.49/47.35 | (867) crypt(all_271_1_249, all_17_0_12) = all_271_0_248 & xor(all_49_1_32, data) = all_271_1_249 & ~ p(all_271_0_248) % 81.49/47.35 | % 81.49/47.35 | Applying alpha-rule on (867) yields: % 81.49/47.35 | (868) crypt(all_271_1_249, all_17_0_12) = all_271_0_248 % 81.49/47.35 | (869) xor(all_49_1_32, data) = all_271_1_249 % 81.49/47.35 | (870) ~ p(all_271_0_248) % 81.49/47.35 | % 81.49/47.35 | Instantiating (657) with all_273_0_250, all_273_1_251 yields: % 81.49/47.35 | (871) crypt(all_273_1_251, imp) = all_273_0_250 & xor(all_149_1_134, data) = all_273_1_251 & ~ p(all_273_0_250) % 81.49/47.35 | % 81.49/47.35 | Applying alpha-rule on (871) yields: % 81.49/47.35 | (872) crypt(all_273_1_251, imp) = all_273_0_250 % 81.49/47.35 | (873) xor(all_149_1_134, data) = all_273_1_251 % 81.49/47.35 | (874) ~ p(all_273_0_250) % 81.49/47.35 | % 81.49/47.35 | Instantiating (656) with all_275_0_252, all_275_1_253 yields: % 81.49/47.35 | (875) crypt(all_275_1_253, exp) = all_275_0_252 & xor(all_149_1_134, data) = all_275_1_253 & ~ p(all_275_0_252) % 81.49/47.35 | % 81.49/47.35 | Applying alpha-rule on (875) yields: % 81.49/47.35 | (876) crypt(all_275_1_253, exp) = all_275_0_252 % 81.49/47.35 | (877) xor(all_149_1_134, data) = all_275_1_253 % 81.49/47.35 | (878) ~ p(all_275_0_252) % 81.49/47.35 | % 81.49/47.35 | Instantiating (649) with all_277_0_254, all_277_1_255 yields: % 81.49/47.35 | (879) crypt(all_277_1_255, all_0_0_0) = all_277_0_254 & xor(all_149_1_134, data) = all_277_1_255 & ~ p(all_277_0_254) % 81.49/47.35 | % 81.49/47.35 | Applying alpha-rule on (879) yields: % 81.49/47.35 | (880) crypt(all_277_1_255, all_0_0_0) = all_277_0_254 % 81.49/47.35 | (881) xor(all_149_1_134, data) = all_277_1_255 % 81.49/47.35 | (882) ~ p(all_277_0_254) % 81.49/47.35 | % 81.49/47.35 | Instantiating (690) with all_279_0_256 yields: % 81.49/47.35 | (883) xor(data, all_279_0_256) = all_119_1_93 & xor(km, data) = all_279_0_256 % 81.49/47.35 | % 81.49/47.35 | Applying alpha-rule on (883) yields: % 81.49/47.35 | (884) xor(data, all_279_0_256) = all_119_1_93 % 81.49/47.35 | (885) xor(km, data) = all_279_0_256 % 81.49/47.35 | % 81.49/47.35 | Instantiating (658) with all_281_0_257 yields: % 81.49/47.35 | (886) crypt(all_0_4_4, all_149_1_134) = all_281_0_257 & ~ p(all_281_0_257) % 81.49/47.35 | % 81.49/47.35 | Applying alpha-rule on (886) yields: % 81.49/47.35 | (887) crypt(all_0_4_4, all_149_1_134) = all_281_0_257 % 81.49/47.35 | (888) ~ p(all_281_0_257) % 81.49/47.35 | % 81.49/47.35 | Instantiating (666) with all_283_0_258, all_283_1_259, all_283_2_260 yields: % 81.49/47.35 | (889) crypt(all_283_2_260, all_17_0_12) = all_283_1_259 & crypt(all_0_5_5, all_0_5_5) = all_283_0_258 & xor(km, data) = all_283_2_260 & ( ~ p(all_283_0_258) | ~ p(all_283_1_259)) % 81.49/47.35 | % 81.49/47.35 | Applying alpha-rule on (889) yields: % 81.49/47.35 | (890) crypt(all_283_2_260, all_17_0_12) = all_283_1_259 % 81.49/47.35 | (891) crypt(all_0_5_5, all_0_5_5) = all_283_0_258 % 81.49/47.35 | (892) xor(km, data) = all_283_2_260 % 81.49/47.35 | (893) ~ p(all_283_0_258) | ~ p(all_283_1_259) % 81.49/47.35 | % 81.49/47.35 | Instantiating (665) with all_285_0_261, all_285_1_262 yields: % 81.49/47.35 | (894) crypt(all_285_1_262, all_19_0_14) = all_285_0_261 & xor(all_49_1_32, data) = all_285_1_262 & ~ p(all_285_0_261) % 81.49/47.35 | % 81.49/47.35 | Applying alpha-rule on (894) yields: % 81.49/47.35 | (895) crypt(all_285_1_262, all_19_0_14) = all_285_0_261 % 81.49/47.35 | (896) xor(all_49_1_32, data) = all_285_1_262 % 81.49/47.35 | (897) ~ p(all_285_0_261) % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (30) with all_0_5_5, all_49_1_32, all_241_0_216, all_245_0_222 and discharging atoms crypt(all_0_5_5, all_49_1_32) = all_245_0_222, crypt(all_0_5_5, all_49_1_32) = all_241_0_216, yields: % 81.49/47.35 | (898) all_245_0_222 = all_241_0_216 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (30) with all_0_5_5, all_49_1_32, all_239_0_213, all_241_0_216 and discharging atoms crypt(all_0_5_5, all_49_1_32) = all_241_0_216, crypt(all_0_5_5, all_49_1_32) = all_239_0_213, yields: % 81.49/47.35 | (899) all_241_0_216 = all_239_0_213 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (30) with all_0_5_5, all_49_1_32, all_213_0_182, all_243_0_219 and discharging atoms crypt(all_0_5_5, all_49_1_32) = all_243_0_219, crypt(all_0_5_5, all_49_1_32) = all_213_0_182, yields: % 81.49/47.35 | (900) all_243_0_219 = all_213_0_182 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (30) with all_0_5_5, all_49_1_32, all_213_0_182, all_239_0_213 and discharging atoms crypt(all_0_5_5, all_49_1_32) = all_239_0_213, crypt(all_0_5_5, all_49_1_32) = all_213_0_182, yields: % 81.49/47.35 | (901) all_239_0_213 = all_213_0_182 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (30) with all_0_5_5, all_49_1_32, all_211_0_179, all_213_0_182 and discharging atoms crypt(all_0_5_5, all_49_1_32) = all_213_0_182, crypt(all_0_5_5, all_49_1_32) = all_211_0_179, yields: % 81.49/47.35 | (902) all_213_0_182 = all_211_0_179 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (30) with all_0_5_5, all_49_1_32, all_209_0_176, all_243_0_219 and discharging atoms crypt(all_0_5_5, all_49_1_32) = all_243_0_219, crypt(all_0_5_5, all_49_1_32) = all_209_0_176, yields: % 81.49/47.35 | (903) all_243_0_219 = all_209_0_176 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (30) with all_0_5_5, all_49_1_32, all_207_0_173, all_243_0_219 and discharging atoms crypt(all_0_5_5, all_49_1_32) = all_243_0_219, crypt(all_0_5_5, all_49_1_32) = all_207_0_173, yields: % 81.49/47.35 | (904) all_243_0_219 = all_207_0_173 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (30) with all_0_5_5, all_49_1_32, all_199_0_167, all_207_0_173 and discharging atoms crypt(all_0_5_5, all_49_1_32) = all_207_0_173, crypt(all_0_5_5, all_49_1_32) = all_199_0_167, yields: % 81.49/47.35 | (905) all_207_0_173 = all_199_0_167 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (30) with all_0_5_5, all_49_1_32, all_197_0_164, all_245_0_222 and discharging atoms crypt(all_0_5_5, all_49_1_32) = all_245_0_222, crypt(all_0_5_5, all_49_1_32) = all_197_0_164, yields: % 81.49/47.35 | (906) all_245_0_222 = all_197_0_164 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (30) with all_0_5_5, all_0_5_5, all_269_0_245, all_283_0_258 and discharging atoms crypt(all_0_5_5, all_0_5_5) = all_283_0_258, crypt(all_0_5_5, all_0_5_5) = all_269_0_245, yields: % 81.49/47.35 | (907) all_283_0_258 = all_269_0_245 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (30) with all_0_5_5, all_0_5_5, all_235_0_208, all_111_0_81 and discharging atoms crypt(all_0_5_5, all_0_5_5) = all_235_0_208, crypt(all_0_5_5, all_0_5_5) = all_111_0_81, yields: % 81.49/47.35 | (908) all_235_0_208 = all_111_0_81 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (30) with all_0_5_5, all_0_5_5, all_235_0_208, all_283_0_258 and discharging atoms crypt(all_0_5_5, all_0_5_5) = all_283_0_258, crypt(all_0_5_5, all_0_5_5) = all_235_0_208, yields: % 81.49/47.35 | (909) all_283_0_258 = all_235_0_208 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (30) with all_0_5_5, all_0_5_5, all_233_0_205, all_283_0_258 and discharging atoms crypt(all_0_5_5, all_0_5_5) = all_283_0_258, crypt(all_0_5_5, all_0_5_5) = all_233_0_205, yields: % 81.49/47.35 | (910) all_283_0_258 = all_233_0_205 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with all_149_1_134, data, all_273_1_251, all_277_1_255 and discharging atoms xor(all_149_1_134, data) = all_277_1_255, xor(all_149_1_134, data) = all_273_1_251, yields: % 81.49/47.35 | (911) all_277_1_255 = all_273_1_251 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with all_149_1_134, data, all_265_1_242, all_267_1_244 and discharging atoms xor(all_149_1_134, data) = all_267_1_244, xor(all_149_1_134, data) = all_265_1_242, yields: % 81.49/47.35 | (912) all_267_1_244 = all_265_1_242 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with all_149_1_134, data, all_259_1_238, all_277_1_255 and discharging atoms xor(all_149_1_134, data) = all_277_1_255, xor(all_149_1_134, data) = all_259_1_238, yields: % 81.49/47.35 | (913) all_277_1_255 = all_259_1_238 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with all_149_1_134, data, all_257_1_236, all_275_1_253 and discharging atoms xor(all_149_1_134, data) = all_275_1_253, xor(all_149_1_134, data) = all_257_1_236, yields: % 81.49/47.35 | (914) all_275_1_253 = all_257_1_236 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with all_149_1_134, data, all_257_1_236, all_265_1_242 and discharging atoms xor(all_149_1_134, data) = all_265_1_242, xor(all_149_1_134, data) = all_257_1_236, yields: % 81.49/47.35 | (915) all_265_1_242 = all_257_1_236 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with all_149_1_134, data, all_257_1_236, all_259_1_238 and discharging atoms xor(all_149_1_134, data) = all_259_1_238, xor(all_149_1_134, data) = all_257_1_236, yields: % 81.49/47.35 | (916) all_259_1_238 = all_257_1_236 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with all_149_1_134, data, all_251_1_230, all_267_1_244 and discharging atoms xor(all_149_1_134, data) = all_267_1_244, xor(all_149_1_134, data) = all_251_1_230, yields: % 81.49/47.35 | (917) all_267_1_244 = all_251_1_230 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with all_149_1_134, data, all_249_1_228, all_275_1_253 and discharging atoms xor(all_149_1_134, data) = all_275_1_253, xor(all_149_1_134, data) = all_249_1_228, yields: % 81.49/47.35 | (918) all_275_1_253 = all_249_1_228 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with all_149_1_134, data, all_247_1_226, all_277_1_255 and discharging atoms xor(all_149_1_134, data) = all_277_1_255, xor(all_149_1_134, data) = all_247_1_226, yields: % 81.49/47.35 | (919) all_277_1_255 = all_247_1_226 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with all_49_1_32, data, all_271_1_249, all_149_1_134 and discharging atoms xor(all_49_1_32, data) = all_271_1_249, xor(all_49_1_32, data) = all_149_1_134, yields: % 81.49/47.35 | (920) all_271_1_249 = all_149_1_134 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with all_49_1_32, data, all_271_1_249, all_285_1_262 and discharging atoms xor(all_49_1_32, data) = all_285_1_262, xor(all_49_1_32, data) = all_271_1_249, yields: % 81.49/47.35 | (921) all_285_1_262 = all_271_1_249 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with all_49_1_32, data, all_253_1_232, all_285_1_262 and discharging atoms xor(all_49_1_32, data) = all_285_1_262, xor(all_49_1_32, data) = all_253_1_232, yields: % 81.49/47.35 | (922) all_285_1_262 = all_253_1_232 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with all_49_1_32, data, all_231_1_204, all_285_1_262 and discharging atoms xor(all_49_1_32, data) = all_285_1_262, xor(all_49_1_32, data) = all_231_1_204, yields: % 81.49/47.35 | (923) all_285_1_262 = all_231_1_204 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with all_0_4_4, data, all_225_1_196, all_119_1_93 and discharging atoms xor(all_0_4_4, data) = all_225_1_196, xor(all_0_4_4, data) = all_119_1_93, yields: % 81.49/47.35 | (924) all_225_1_196 = all_119_1_93 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with all_0_4_4, data, all_221_0_191, all_225_1_196 and discharging atoms xor(all_0_4_4, data) = all_225_1_196, xor(all_0_4_4, data) = all_221_0_191, yields: % 81.49/47.35 | (925) all_225_1_196 = all_221_0_191 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with all_0_5_5, data, all_215_1_186, all_49_1_32 and discharging atoms xor(all_0_5_5, data) = all_215_1_186, xor(all_0_5_5, data) = all_49_1_32, yields: % 81.49/47.35 | (926) all_215_1_186 = all_49_1_32 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with all_0_5_5, data, all_201_0_170, all_215_1_186 and discharging atoms xor(all_0_5_5, data) = all_215_1_186, xor(all_0_5_5, data) = all_201_0_170, yields: % 81.49/47.35 | (927) all_215_1_186 = all_201_0_170 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (43) with all_263_0_240, data and discharging atoms xor(data, data) = all_263_0_240, yields: % 81.49/47.35 | (928) all_263_0_240 = id % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with data, data, all_205_0_172, all_263_0_240 and discharging atoms xor(data, data) = all_263_0_240, xor(data, data) = all_205_0_172, yields: % 81.49/47.35 | (929) all_263_0_240 = all_205_0_172 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with data, kp, all_229_2_202, all_121_2_96 and discharging atoms xor(data, kp) = all_229_2_202, xor(data, kp) = all_121_2_96, yields: % 81.49/47.35 | (930) all_229_2_202 = all_121_2_96 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with data, exp, all_175_0_160, all_195_0_163 and discharging atoms xor(data, exp) = all_195_0_163, xor(data, exp) = all_175_0_160, yields: % 81.49/47.35 | (931) all_195_0_163 = all_175_0_160 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with data, km, all_203_0_171, all_0_4_4 and discharging atoms xor(data, km) = all_203_0_171, xor(data, km) = all_0_4_4, yields: % 81.49/47.35 | (932) all_203_0_171 = all_0_4_4 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with exp, data, all_261_0_239, all_175_0_160 and discharging atoms xor(exp, data) = all_261_0_239, xor(exp, data) = all_175_0_160, yields: % 81.49/47.35 | (933) all_261_0_239 = all_175_0_160 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with km, data, all_245_2_224, all_269_2_247 and discharging atoms xor(km, data) = all_269_2_247, xor(km, data) = all_245_2_224, yields: % 81.49/47.35 | (934) all_269_2_247 = all_245_2_224 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with km, data, all_241_2_218, all_283_2_260 and discharging atoms xor(km, data) = all_283_2_260, xor(km, data) = all_241_2_218, yields: % 81.49/47.35 | (935) all_283_2_260 = all_241_2_218 % 81.49/47.35 | % 81.49/47.35 | Instantiating formula (17) with km, data, all_241_2_218, all_279_0_256 and discharging atoms xor(km, data) = all_279_0_256, xor(km, data) = all_241_2_218, yields: % 81.49/47.35 | (936) all_279_0_256 = all_241_2_218 % 81.49/47.36 | % 81.49/47.36 | Instantiating formula (17) with km, data, all_239_2_215, all_245_2_224 and discharging atoms xor(km, data) = all_245_2_224, xor(km, data) = all_239_2_215, yields: % 81.49/47.36 | (937) all_245_2_224 = all_239_2_215 % 81.49/47.36 | % 81.49/47.36 | Instantiating formula (17) with km, data, all_235_2_210, all_243_2_221 and discharging atoms xor(km, data) = all_243_2_221, xor(km, data) = all_235_2_210, yields: % 81.49/47.36 | (938) all_243_2_221 = all_235_2_210 % 81.49/47.36 | % 81.49/47.36 | Instantiating formula (17) with km, data, all_235_2_210, all_239_2_215 and discharging atoms xor(km, data) = all_239_2_215, xor(km, data) = all_235_2_210, yields: % 81.49/47.36 | (939) all_239_2_215 = all_235_2_210 % 81.49/47.36 | % 81.49/47.36 | Instantiating formula (17) with km, data, all_233_2_207, all_279_0_256 and discharging atoms xor(km, data) = all_279_0_256, xor(km, data) = all_233_2_207, yields: % 81.49/47.36 | (940) all_279_0_256 = all_233_2_207 % 81.49/47.36 | % 81.49/47.36 | Instantiating formula (17) with km, data, all_227_2_199, all_269_2_247 and discharging atoms xor(km, data) = all_269_2_247, xor(km, data) = all_227_2_199, yields: % 81.49/47.36 | (941) all_269_2_247 = all_227_2_199 % 81.49/47.36 | % 81.49/47.36 | Instantiating formula (17) with km, data, all_223_2_194, all_243_2_221 and discharging atoms xor(km, data) = all_243_2_221, xor(km, data) = all_223_2_194, yields: % 81.49/47.36 | (942) all_243_2_221 = all_223_2_194 % 81.49/47.36 | % 81.49/47.36 | Instantiating formula (17) with km, data, all_223_2_194, all_241_2_218 and discharging atoms xor(km, data) = all_241_2_218, xor(km, data) = all_223_2_194, yields: % 81.49/47.36 | (943) all_241_2_218 = all_223_2_194 % 81.49/47.36 | % 81.49/47.36 | Instantiating formula (17) with km, data, all_219_0_190, all_235_2_210 and discharging atoms xor(km, data) = all_235_2_210, xor(km, data) = all_219_0_190, yields: % 81.49/47.36 | (944) all_235_2_210 = all_219_0_190 % 81.49/47.36 | % 81.49/47.36 | Instantiating formula (17) with km, data, all_213_2_184, all_243_2_221 and discharging atoms xor(km, data) = all_243_2_221, xor(km, data) = all_213_2_184, yields: % 81.49/47.36 | (945) all_243_2_221 = all_213_2_184 % 81.49/47.36 | % 81.49/47.36 | Instantiating formula (17) with km, data, all_211_2_181, all_235_2_210 and discharging atoms xor(km, data) = all_235_2_210, xor(km, data) = all_211_2_181, yields: % 81.49/47.36 | (946) all_235_2_210 = all_211_2_181 % 81.49/47.36 | % 81.49/47.36 | Instantiating formula (17) with km, data, all_209_2_178, all_235_2_210 and discharging atoms xor(km, data) = all_235_2_210, xor(km, data) = all_209_2_178, yields: % 81.49/47.36 | (947) all_235_2_210 = all_209_2_178 % 81.49/47.36 | % 81.49/47.36 | Instantiating formula (17) with km, data, all_207_2_175, all_209_2_178 and discharging atoms xor(km, data) = all_209_2_178, xor(km, data) = all_207_2_175, yields: % 81.49/47.36 | (948) all_209_2_178 = all_207_2_175 % 81.49/47.36 | % 81.49/47.36 | Instantiating formula (17) with km, data, all_199_2_169, all_0_4_4 and discharging atoms xor(km, data) = all_199_2_169, xor(km, data) = all_0_4_4, yields: % 81.49/47.36 | (949) all_199_2_169 = all_0_4_4 % 81.49/47.36 | % 81.49/47.36 | Instantiating formula (17) with km, data, all_199_2_169, all_207_2_175 and discharging atoms xor(km, data) = all_207_2_175, xor(km, data) = all_199_2_169, yields: % 81.49/47.36 | (950) all_207_2_175 = all_199_2_169 % 81.49/47.36 | % 81.49/47.36 | Instantiating formula (17) with km, data, all_197_2_166, all_283_2_260 and discharging atoms xor(km, data) = all_283_2_260, xor(km, data) = all_197_2_166, yields: % 81.49/47.36 | (951) all_283_2_260 = all_197_2_166 % 81.49/47.36 | % 81.49/47.36 | Instantiating formula (17) with km, exp, all_217_2_189, all_0_5_5 and discharging atoms xor(km, exp) = all_217_2_189, xor(km, exp) = all_0_5_5, yields: % 81.49/47.36 | (952) all_217_2_189 = all_0_5_5 % 81.49/47.36 | % 81.49/47.36 | Combining equations (921,922) yields a new equation: % 81.49/47.36 | (953) all_271_1_249 = all_253_1_232 % 81.49/47.36 | % 81.49/47.36 | Simplifying 953 yields: % 81.49/47.36 | (954) all_271_1_249 = all_253_1_232 % 81.49/47.36 | % 81.49/47.36 | Combining equations (923,922) yields a new equation: % 81.49/47.36 | (955) all_253_1_232 = all_231_1_204 % 81.49/47.36 | % 81.49/47.36 | Combining equations (909,907) yields a new equation: % 81.49/47.36 | (956) all_269_0_245 = all_235_0_208 % 81.49/47.36 | % 81.49/47.36 | Combining equations (910,907) yields a new equation: % 81.49/47.36 | (957) all_269_0_245 = all_233_0_205 % 81.49/47.36 | % 81.49/47.36 | Combining equations (935,951) yields a new equation: % 81.49/47.36 | (958) all_241_2_218 = all_197_2_166 % 81.49/47.36 | % 81.49/47.36 | Simplifying 958 yields: % 81.49/47.36 | (959) all_241_2_218 = all_197_2_166 % 81.49/47.36 | % 81.49/47.36 | Combining equations (936,940) yields a new equation: % 81.49/47.36 | (960) all_241_2_218 = all_233_2_207 % 81.49/47.36 | % 81.49/47.36 | Simplifying 960 yields: % 81.49/47.36 | (961) all_241_2_218 = all_233_2_207 % 81.49/47.36 | % 81.49/47.36 | Combining equations (913,911) yields a new equation: % 81.49/47.36 | (962) all_273_1_251 = all_259_1_238 % 81.49/47.36 | % 81.49/47.36 | Combining equations (919,911) yields a new equation: % 81.49/47.36 | (963) all_273_1_251 = all_247_1_226 % 81.49/47.36 | % 81.49/47.36 | Combining equations (914,918) yields a new equation: % 81.49/47.36 | (964) all_257_1_236 = all_249_1_228 % 81.49/47.36 | % 81.49/47.36 | Simplifying 964 yields: % 81.49/47.36 | (965) all_257_1_236 = all_249_1_228 % 81.49/47.36 | % 81.49/47.36 | Combining equations (962,963) yields a new equation: % 81.49/47.36 | (966) all_259_1_238 = all_247_1_226 % 81.49/47.36 | % 81.49/47.36 | Simplifying 966 yields: % 81.49/47.36 | (967) all_259_1_238 = all_247_1_226 % 81.49/47.36 | % 81.49/47.36 | Combining equations (954,920) yields a new equation: % 81.49/47.36 | (968) all_253_1_232 = all_149_1_134 % 81.49/47.36 | % 81.49/47.36 | Simplifying 968 yields: % 81.49/47.36 | (969) all_253_1_232 = all_149_1_134 % 81.49/47.36 | % 81.49/47.36 | Combining equations (956,957) yields a new equation: % 81.49/47.36 | (970) all_235_0_208 = all_233_0_205 % 81.49/47.36 | % 81.49/47.36 | Simplifying 970 yields: % 81.49/47.36 | (971) all_235_0_208 = all_233_0_205 % 81.49/47.36 | % 81.49/47.36 | Combining equations (934,941) yields a new equation: % 81.49/47.36 | (972) all_245_2_224 = all_227_2_199 % 81.49/47.36 | % 81.49/47.36 | Simplifying 972 yields: % 81.49/47.36 | (973) all_245_2_224 = all_227_2_199 % 81.49/47.36 | % 81.49/47.36 | Combining equations (912,917) yields a new equation: % 81.49/47.36 | (974) all_265_1_242 = all_251_1_230 % 81.49/47.36 | % 81.49/47.36 | Simplifying 974 yields: % 81.49/47.36 | (975) all_265_1_242 = all_251_1_230 % 81.49/47.36 | % 81.49/47.36 | Combining equations (915,975) yields a new equation: % 81.49/47.36 | (976) all_257_1_236 = all_251_1_230 % 81.49/47.36 | % 81.49/47.36 | Simplifying 976 yields: % 81.49/47.36 | (977) all_257_1_236 = all_251_1_230 % 81.49/47.36 | % 81.49/47.36 | Combining equations (928,929) yields a new equation: % 81.49/47.36 | (978) all_205_0_172 = id % 81.49/47.36 | % 81.49/47.36 | Combining equations (916,967) yields a new equation: % 81.49/47.36 | (979) all_257_1_236 = all_247_1_226 % 81.49/47.36 | % 81.49/47.36 | Simplifying 979 yields: % 81.49/47.36 | (980) all_257_1_236 = all_247_1_226 % 81.49/47.36 | % 81.49/47.36 | Combining equations (980,977) yields a new equation: % 81.49/47.36 | (981) all_251_1_230 = all_247_1_226 % 81.49/47.36 | % 81.49/47.36 | Combining equations (965,977) yields a new equation: % 81.49/47.36 | (982) all_251_1_230 = all_249_1_228 % 81.49/47.36 | % 81.49/47.36 | Combining equations (955,969) yields a new equation: % 81.49/47.36 | (983) all_231_1_204 = all_149_1_134 % 81.49/47.36 | % 81.49/47.36 | Simplifying 983 yields: % 81.49/47.36 | (984) all_231_1_204 = all_149_1_134 % 81.49/47.36 | % 81.49/47.36 | Combining equations (981,982) yields a new equation: % 81.49/47.36 | (985) all_249_1_228 = all_247_1_226 % 81.49/47.36 | % 81.49/47.36 | Combining equations (898,906) yields a new equation: % 81.49/47.36 | (986) all_241_0_216 = all_197_0_164 % 81.49/47.36 | % 81.49/47.36 | Simplifying 986 yields: % 81.49/47.36 | (987) all_241_0_216 = all_197_0_164 % 81.49/47.36 | % 81.49/47.36 | Combining equations (937,973) yields a new equation: % 81.49/47.36 | (988) all_239_2_215 = all_227_2_199 % 81.49/47.36 | % 81.49/47.36 | Simplifying 988 yields: % 81.49/47.36 | (989) all_239_2_215 = all_227_2_199 % 81.49/47.36 | % 81.49/47.36 | Combining equations (904,903) yields a new equation: % 81.49/47.36 | (990) all_209_0_176 = all_207_0_173 % 81.49/47.36 | % 81.49/47.36 | Combining equations (900,903) yields a new equation: % 81.49/47.36 | (991) all_213_0_182 = all_209_0_176 % 81.49/47.36 | % 81.49/47.36 | Simplifying 991 yields: % 81.49/47.36 | (992) all_213_0_182 = all_209_0_176 % 81.49/47.36 | % 81.49/47.36 | Combining equations (938,945) yields a new equation: % 81.49/47.36 | (993) all_235_2_210 = all_213_2_184 % 81.49/47.36 | % 81.49/47.36 | Simplifying 993 yields: % 81.49/47.36 | (994) all_235_2_210 = all_213_2_184 % 81.49/47.36 | % 81.49/47.36 | Combining equations (942,945) yields a new equation: % 81.49/47.36 | (995) all_223_2_194 = all_213_2_184 % 81.49/47.36 | % 81.49/47.36 | Simplifying 995 yields: % 81.49/47.36 | (996) all_223_2_194 = all_213_2_184 % 81.49/47.36 | % 81.49/47.36 | Combining equations (899,987) yields a new equation: % 81.49/47.36 | (997) all_239_0_213 = all_197_0_164 % 81.49/47.36 | % 81.49/47.36 | Simplifying 997 yields: % 81.49/47.36 | (998) all_239_0_213 = all_197_0_164 % 81.49/47.36 | % 81.49/47.36 | Combining equations (943,961) yields a new equation: % 81.49/47.36 | (999) all_233_2_207 = all_223_2_194 % 81.49/47.36 | % 81.49/47.36 | Combining equations (959,961) yields a new equation: % 81.49/47.36 | (1000) all_233_2_207 = all_197_2_166 % 81.49/47.36 | % 81.49/47.36 | Combining equations (901,998) yields a new equation: % 81.49/47.36 | (1001) all_213_0_182 = all_197_0_164 % 81.49/47.36 | % 81.49/47.36 | Simplifying 1001 yields: % 81.49/47.36 | (1002) all_213_0_182 = all_197_0_164 % 81.49/47.36 | % 81.49/47.36 | Combining equations (939,989) yields a new equation: % 81.49/47.36 | (1003) all_235_2_210 = all_227_2_199 % 81.49/47.36 | % 81.49/47.36 | Simplifying 1003 yields: % 81.49/47.36 | (1004) all_235_2_210 = all_227_2_199 % 81.49/47.36 | % 81.49/47.36 | Combining equations (908,971) yields a new equation: % 81.49/47.36 | (1005) all_233_0_205 = all_111_0_81 % 81.49/47.36 | % 81.49/47.36 | Combining equations (947,1004) yields a new equation: % 81.49/47.36 | (1006) all_227_2_199 = all_209_2_178 % 81.49/47.36 | % 81.49/47.36 | Combining equations (946,1004) yields a new equation: % 81.49/47.36 | (1007) all_227_2_199 = all_211_2_181 % 81.49/47.36 | % 81.49/47.36 | Combining equations (944,1004) yields a new equation: % 81.49/47.36 | (1008) all_227_2_199 = all_219_0_190 % 81.49/47.36 | % 81.49/47.36 | Combining equations (994,1004) yields a new equation: % 81.49/47.36 | (1009) all_227_2_199 = all_213_2_184 % 81.49/47.36 | % 81.49/47.36 | Combining equations (999,1000) yields a new equation: % 81.49/47.36 | (1010) all_223_2_194 = all_197_2_166 % 81.49/47.36 | % 81.49/47.36 | Simplifying 1010 yields: % 81.49/47.36 | (1011) all_223_2_194 = all_197_2_166 % 81.49/47.36 | % 81.49/47.36 | Combining equations (1006,1008) yields a new equation: % 81.49/47.36 | (1012) all_219_0_190 = all_209_2_178 % 81.49/47.36 | % 81.49/47.36 | Combining equations (1009,1008) yields a new equation: % 81.49/47.36 | (1013) all_219_0_190 = all_213_2_184 % 81.49/47.36 | % 81.49/47.36 | Combining equations (1007,1008) yields a new equation: % 81.49/47.36 | (1014) all_219_0_190 = all_211_2_181 % 81.49/47.36 | % 81.49/47.36 | Combining equations (924,925) yields a new equation: % 81.49/47.36 | (1015) all_221_0_191 = all_119_1_93 % 81.49/47.36 | % 81.49/47.36 | Combining equations (996,1011) yields a new equation: % 81.49/47.36 | (1016) all_213_2_184 = all_197_2_166 % 81.49/47.36 | % 81.49/47.36 | Simplifying 1016 yields: % 81.49/47.36 | (1017) all_213_2_184 = all_197_2_166 % 81.49/47.36 | % 81.49/47.36 | Combining equations (1012,1014) yields a new equation: % 81.49/47.36 | (1018) all_211_2_181 = all_209_2_178 % 81.49/47.36 | % 81.49/47.36 | Combining equations (1013,1014) yields a new equation: % 81.49/47.36 | (1019) all_213_2_184 = all_211_2_181 % 81.49/47.36 | % 81.49/47.36 | Simplifying 1019 yields: % 81.49/47.36 | (1020) all_213_2_184 = all_211_2_181 % 81.49/47.36 | % 81.49/47.36 | Combining equations (927,926) yields a new equation: % 81.49/47.36 | (1021) all_201_0_170 = all_49_1_32 % 81.49/47.36 | % 81.49/47.36 | Simplifying 1021 yields: % 81.49/47.36 | (1022) all_201_0_170 = all_49_1_32 % 81.49/47.36 | % 81.49/47.36 | Combining equations (992,902) yields a new equation: % 81.49/47.36 | (1023) all_211_0_179 = all_209_0_176 % 81.49/47.36 | % 81.49/47.36 | Combining equations (1002,902) yields a new equation: % 81.49/47.36 | (1024) all_211_0_179 = all_197_0_164 % 81.49/47.36 | % 81.49/47.36 | Combining equations (1020,1017) yields a new equation: % 81.49/47.36 | (1025) all_211_2_181 = all_197_2_166 % 81.49/47.36 | % 81.49/47.36 | Simplifying 1025 yields: % 81.49/47.36 | (1026) all_211_2_181 = all_197_2_166 % 81.49/47.36 | % 81.49/47.36 | Combining equations (1023,1024) yields a new equation: % 81.49/47.36 | (1027) all_209_0_176 = all_197_0_164 % 81.49/47.36 | % 81.49/47.36 | Simplifying 1027 yields: % 81.49/47.36 | (1028) all_209_0_176 = all_197_0_164 % 81.49/47.36 | % 81.49/47.36 | Combining equations (1018,1026) yields a new equation: % 81.49/47.36 | (1029) all_209_2_178 = all_197_2_166 % 81.49/47.36 | % 81.49/47.36 | Simplifying 1029 yields: % 81.49/47.36 | (1030) all_209_2_178 = all_197_2_166 % 81.49/47.36 | % 81.49/47.36 | Combining equations (990,1028) yields a new equation: % 81.49/47.36 | (1031) all_207_0_173 = all_197_0_164 % 81.49/47.36 | % 81.49/47.36 | Simplifying 1031 yields: % 81.49/47.36 | (1032) all_207_0_173 = all_197_0_164 % 81.49/47.36 | % 81.49/47.36 | Combining equations (948,1030) yields a new equation: % 81.49/47.36 | (1033) all_207_2_175 = all_197_2_166 % 81.49/47.36 | % 81.49/47.36 | Simplifying 1033 yields: % 81.49/47.36 | (1034) all_207_2_175 = all_197_2_166 % 81.49/47.36 | % 81.49/47.36 | Combining equations (905,1032) yields a new equation: % 81.49/47.36 | (1035) all_199_0_167 = all_197_0_164 % 81.49/47.36 | % 81.49/47.36 | Simplifying 1035 yields: % 81.49/47.36 | (1036) all_199_0_167 = all_197_0_164 % 81.49/47.36 | % 81.49/47.36 | Combining equations (950,1034) yields a new equation: % 81.49/47.36 | (1037) all_199_2_169 = all_197_2_166 % 81.49/47.36 | % 81.49/47.36 | Simplifying 1037 yields: % 81.49/47.36 | (1038) all_199_2_169 = all_197_2_166 % 81.49/47.36 | % 81.49/47.36 | Combining equations (949,1038) yields a new equation: % 81.49/47.36 | (1039) all_197_2_166 = all_0_4_4 % 81.49/47.36 | % 81.49/47.36 | Combining equations (1039,1034) yields a new equation: % 81.49/47.36 | (1040) all_207_2_175 = all_0_4_4 % 81.49/47.36 | % 81.49/47.36 | Combining equations (1039,1026) yields a new equation: % 81.49/47.36 | (1041) all_211_2_181 = all_0_4_4 % 81.49/47.36 | % 81.49/47.36 | Combining equations (1041,1014) yields a new equation: % 81.49/47.36 | (1042) all_219_0_190 = all_0_4_4 % 81.49/47.36 | % 81.49/47.36 | Combining equations (1039,1011) yields a new equation: % 81.49/47.36 | (1043) all_223_2_194 = all_0_4_4 % 81.49/47.36 | % 81.49/47.36 | Combining equations (1042,1008) yields a new equation: % 81.49/47.36 | (1044) all_227_2_199 = all_0_4_4 % 81.49/47.36 | % 81.49/47.36 | Combining equations (1039,1000) yields a new equation: % 81.49/47.36 | (1045) all_233_2_207 = all_0_4_4 % 81.49/47.36 | % 81.49/47.36 | Combining equations (985,982) yields a new equation: % 81.49/47.36 | (981) all_251_1_230 = all_247_1_226 % 81.49/47.36 | % 81.49/47.36 | Combining equations (981,977) yields a new equation: % 81.49/47.36 | (980) all_257_1_236 = all_247_1_226 % 81.49/47.36 | % 81.49/47.36 | Combining equations (978,929) yields a new equation: % 81.49/47.36 | (928) all_263_0_240 = id % 81.49/47.36 | % 81.49/47.36 | Combining equations (981,975) yields a new equation: % 81.49/47.36 | (1049) all_265_1_242 = all_247_1_226 % 81.49/47.36 | % 81.49/47.36 | Combining equations (981,917) yields a new equation: % 81.49/47.36 | (1050) all_267_1_244 = all_247_1_226 % 81.49/47.37 | % 81.49/47.37 | Combining equations (985,918) yields a new equation: % 81.49/47.37 | (1051) all_275_1_253 = all_247_1_226 % 81.49/47.37 | % 81.49/47.37 | Combining equations (963,911) yields a new equation: % 81.49/47.37 | (919) all_277_1_255 = all_247_1_226 % 81.49/47.37 | % 81.49/47.37 | Combining equations (1045,940) yields a new equation: % 81.49/47.37 | (1053) all_279_0_256 = all_0_4_4 % 81.49/47.37 | % 81.49/47.37 | From (919) and (880) follows: % 81.49/47.37 | (1054) crypt(all_247_1_226, all_0_0_0) = all_277_0_254 % 81.49/47.37 | % 81.49/47.37 | From (1051) and (876) follows: % 81.49/47.37 | (1055) crypt(all_247_1_226, exp) = all_275_0_252 % 81.49/47.37 | % 81.49/47.37 | From (963) and (872) follows: % 81.49/47.37 | (1056) crypt(all_247_1_226, imp) = all_273_0_250 % 81.49/47.37 | % 81.49/47.37 | From (1050) and (859) follows: % 81.49/47.37 | (1057) crypt(all_247_1_226, all_0_1_1) = all_267_0_243 % 81.49/47.37 | % 81.49/47.37 | From (1049) and (855) follows: % 81.49/47.37 | (1058) crypt(all_247_1_226, all_0_2_2) = all_265_0_241 % 81.49/47.37 | % 81.49/47.37 | From (967) and (845) follows: % 81.49/47.37 | (1059) crypt(all_247_1_226, data) = all_259_0_237 % 81.49/47.37 | % 81.49/47.37 | From (980) and (841) follows: % 81.49/47.37 | (1060) crypt(all_247_1_226, id) = all_257_0_235 % 81.49/47.37 | % 81.49/47.37 | From (981) and (829) follows: % 81.49/47.37 | (1061) crypt(all_247_1_226, a) = all_251_0_229 % 81.49/47.37 | % 81.49/47.37 | From (985) and (825) follows: % 81.49/47.37 | (1062) crypt(all_247_1_226, pin) = all_249_0_227 % 81.49/47.37 | % 81.49/47.37 | From (1044) and (773) follows: % 81.49/47.37 | (1063) crypt(all_0_4_4, all_49_1_32) = all_227_1_198 % 81.49/47.37 | % 81.49/47.37 | From (1043) and (764) follows: % 81.49/47.37 | (1064) crypt(all_0_4_4, all_0_5_5) = all_223_1_193 % 81.49/47.37 | % 81.49/47.37 | From (1040) and (729) follows: % 81.49/47.37 | (1065) crypt(all_0_4_4, id) = all_207_1_174 % 81.49/47.37 | % 81.49/47.37 | From (1036) and (716) follows: % 81.49/47.37 | (711) crypt(all_0_5_5, all_49_1_32) = all_197_0_164 % 81.49/47.37 | % 81.49/47.37 | From (1005) and (788) follows: % 81.49/47.37 | (356) crypt(all_0_5_5, all_0_5_5) = all_111_0_81 % 81.49/47.37 | % 81.49/47.37 | From (1042) and (758) follows: % 81.49/47.37 | (1068) xor(all_0_4_4, kp) = all_121_1_95 % 81.49/47.37 | % 81.49/47.37 | From (932) and (723) follows: % 81.49/47.37 | (1069) xor(all_0_4_4, exp) = all_49_1_32 % 81.49/47.37 | % 81.49/47.37 | From (931) and (707) follows: % 81.49/47.37 | (1070) xor(all_175_0_160, km) = all_49_1_32 % 81.49/47.37 | % 81.49/47.37 | From (985) and (826) follows: % 81.49/47.37 | (822) xor(all_149_1_134, data) = all_247_1_226 % 81.49/47.37 | % 81.49/47.37 | From (984) and (784) follows: % 81.49/47.37 | (446) xor(all_49_1_32, data) = all_149_1_134 % 81.49/47.37 | % 81.49/47.37 | From (1015) and (761) follows: % 81.49/47.37 | (375) xor(all_0_4_4, data) = all_119_1_93 % 81.49/47.37 | % 81.49/47.37 | From (978) and (726) follows: % 81.49/47.37 | (1074) xor(all_0_5_5, id) = all_149_1_134 % 81.49/47.37 | % 81.49/47.37 | From (1022) and (720) follows: % 81.49/47.37 | (146) xor(all_0_5_5, data) = all_49_1_32 % 81.49/47.37 | % 81.49/47.37 | From (1053) and (884) follows: % 81.49/47.37 | (1076) xor(data, all_0_4_4) = all_119_1_93 % 81.49/47.37 | % 81.49/47.37 | From (1022) and (721) follows: % 81.49/47.37 | (1077) xor(data, all_49_1_32) = all_149_1_134 % 81.49/47.37 | % 81.49/47.37 | From (978) and (727) follows: % 81.49/47.37 | (1078) xor(data, data) = id % 81.49/47.37 | % 81.49/47.37 | From (930) and (779) follows: % 81.49/47.37 | (379) xor(data, kp) = all_121_2_96 % 81.49/47.37 | % 81.49/47.37 | From (931) and (708) follows: % 81.49/47.37 | (700) xor(data, exp) = all_175_0_160 % 81.49/47.37 | % 81.49/47.37 | From (932) and (724) follows: % 81.49/47.37 | (44) xor(data, km) = all_0_4_4 % 81.49/47.37 | % 81.49/47.37 | From (1015) and (762) follows: % 81.49/47.37 | (1082) xor(exp, all_119_1_93) = all_149_1_134 % 81.49/47.37 | % 81.49/47.37 | From (933) and (850) follows: % 81.49/47.37 | (498) xor(exp, data) = all_175_0_160 % 81.49/47.37 | % 81.49/47.37 | From (928) and (853) follows: % 81.49/47.37 | (1084) xor(km, id) = all_119_1_93 % 81.49/47.37 | % 81.49/47.37 | From (930) and (780) follows: % 81.49/47.37 | (1085) xor(km, all_121_2_96) = all_229_1_201 % 81.49/47.37 | % 81.49/47.37 | From (1039) and (712) follows: % 81.49/47.37 | (19) xor(km, data) = all_0_4_4 % 81.49/47.37 | % 81.49/47.37 | From (952) and (755) follows: % 81.49/47.37 | (42) xor(km, exp) = all_0_5_5 % 81.49/47.37 | % 81.49/47.37 | Instantiating formula (30) with all_0_4_4, all_49_1_32, all_227_1_198, all_169_0_154 and discharging atoms crypt(all_0_4_4, all_49_1_32) = all_227_1_198, crypt(all_0_4_4, all_49_1_32) = all_169_0_154, yields: % 81.49/47.37 | (1088) all_227_1_198 = all_169_0_154 % 81.49/47.37 | % 81.49/47.37 | Instantiating formula (30) with all_0_4_4, all_0_5_5, all_223_1_193, all_87_0_72 and discharging atoms crypt(all_0_4_4, all_0_5_5) = all_223_1_193, crypt(all_0_4_4, all_0_5_5) = all_87_0_72, yields: % 81.49/47.37 | (1089) all_223_1_193 = all_87_0_72 % 81.49/47.37 | % 81.49/47.37 | Instantiating formula (30) with all_0_4_4, id, all_207_1_174, all_111_1_82 and discharging atoms crypt(all_0_4_4, id) = all_207_1_174, crypt(all_0_4_4, id) = all_111_1_82, yields: % 81.49/47.37 | (1090) all_207_1_174 = all_111_1_82 % 81.49/47.37 | % 81.49/47.37 | Instantiating formula (4) with all_149_1_134, all_0_5_5 and discharging atoms xor(all_0_5_5, id) = all_149_1_134, yields: % 81.49/47.37 | (1091) all_149_1_134 = all_0_5_5 % 81.49/47.37 | % 81.49/47.37 | Instantiating formula (17) with km, all_121_2_96, all_229_1_201, all_121_1_95 and discharging atoms xor(km, all_121_2_96) = all_229_1_201, xor(km, all_121_2_96) = all_121_1_95, yields: % 81.49/47.37 | (1092) all_229_1_201 = all_121_1_95 % 81.49/47.37 | % 81.49/47.37 | Instantiating formula (4) with all_119_1_93, km and discharging atoms xor(km, id) = all_119_1_93, yields: % 81.49/47.37 | (1093) all_119_1_93 = km % 81.49/47.37 | % 81.49/47.37 | From (1092) and (778) follows: % 81.49/47.37 | (1094) crypt(all_121_1_95, all_0_5_5) = all_229_0_200 % 81.49/47.37 | % 81.49/47.37 | From (1091) and (631) follows: % 81.49/47.37 | (1095) crypt(all_0_5_5, exp) = all_159_0_144 % 81.49/47.37 | % 81.49/47.37 | From (1091) and (630) follows: % 81.49/47.37 | (1096) crypt(all_0_5_5, id) = all_161_0_146 % 81.49/47.37 | % 81.49/47.37 | From (1091) and (887) follows: % 81.49/47.37 | (1097) crypt(all_0_4_4, all_0_5_5) = all_281_0_257 % 81.49/47.37 | % 81.49/47.37 | From (1088) and (1063) follows: % 81.49/47.37 | (486) crypt(all_0_4_4, all_49_1_32) = all_169_0_154 % 81.49/47.37 | % 81.49/47.37 | From (1089) and (1064) follows: % 81.49/47.37 | (224) crypt(all_0_4_4, all_0_5_5) = all_87_0_72 % 81.49/47.37 | % 81.49/47.37 | From (1090) and (1065) follows: % 81.49/47.37 | (640) crypt(all_0_4_4, id) = all_111_1_82 % 81.49/47.37 | % 81.49/47.37 | From (1091) and (822) follows: % 81.49/47.37 | (1101) xor(all_0_5_5, data) = all_247_1_226 % 81.49/47.37 | % 81.49/47.37 | From (1093) and (798) follows: % 81.49/47.37 | (1102) xor(km, data) = all_237_1_212 % 81.49/47.37 | % 81.49/47.37 | From (1091) and (446) follows: % 81.49/47.37 | (1103) xor(all_49_1_32, data) = all_0_5_5 % 81.49/47.37 | % 81.49/47.37 | From (1093) and (375) follows: % 81.49/47.37 | (1104) xor(all_0_4_4, data) = km % 81.49/47.37 | % 81.49/47.37 | From (1091) and (1074) follows: % 81.49/47.37 | (1105) xor(all_0_5_5, id) = all_0_5_5 % 81.49/47.37 | % 81.49/47.37 | From (1091) and (1077) follows: % 81.49/47.37 | (1106) xor(data, all_49_1_32) = all_0_5_5 % 81.49/47.37 | % 81.49/47.37 | From (1093) and (1076) follows: % 81.82/47.37 | (1107) xor(data, all_0_4_4) = km % 81.82/47.37 | % 81.82/47.37 | From (1093)(1091) and (1082) follows: % 81.82/47.37 | (45) xor(exp, km) = all_0_5_5 % 81.82/47.37 | % 81.82/47.37 | From (1091) and (705) follows: % 81.82/47.37 | (1109) xor(km, all_193_0_162) = all_0_5_5 % 81.82/47.37 | % 81.82/47.37 | From (1092) and (1085) follows: % 81.82/47.37 | (380) xor(km, all_121_2_96) = all_121_1_95 % 81.82/47.37 | % 81.82/47.37 | From (1093) and (1084) follows: % 81.82/47.37 | (1111) xor(km, id) = km % 81.82/47.37 | % 81.82/47.37 | Instantiating formula (30) with all_0_4_4, all_0_5_5, all_281_0_257, all_87_0_72 and discharging atoms crypt(all_0_4_4, all_0_5_5) = all_281_0_257, crypt(all_0_4_4, all_0_5_5) = all_87_0_72, yields: % 81.82/47.37 | (1112) all_281_0_257 = all_87_0_72 % 81.82/47.37 | % 81.82/47.37 | Instantiating formula (30) with all_0_5_5, exp, all_159_0_144, all_13_0_9 and discharging atoms crypt(all_0_5_5, exp) = all_159_0_144, crypt(all_0_5_5, exp) = all_13_0_9, yields: % 81.82/47.37 | (1113) all_159_0_144 = all_13_0_9 % 81.82/47.37 | % 81.82/47.37 | Instantiating formula (30) with all_0_5_5, id, all_161_0_146, all_9_0_7 and discharging atoms crypt(all_0_5_5, id) = all_161_0_146, crypt(all_0_5_5, id) = all_9_0_7, yields: % 81.82/47.37 | (1114) all_161_0_146 = all_9_0_7 % 81.82/47.37 | % 81.82/47.37 | Instantiating formula (17) with all_0_5_5, data, all_247_1_226, all_49_1_32 and discharging atoms xor(all_0_5_5, data) = all_247_1_226, xor(all_0_5_5, data) = all_49_1_32, yields: % 81.82/47.37 | (1115) all_247_1_226 = all_49_1_32 % 81.82/47.37 | % 81.82/47.37 | Instantiating formula (17) with km, data, all_237_1_212, all_0_4_4 and discharging atoms xor(km, data) = all_237_1_212, xor(km, data) = all_0_4_4, yields: % 81.82/47.37 | (1116) all_237_1_212 = all_0_4_4 % 81.82/47.37 | % 81.82/47.37 | From (1115) and (1054) follows: % 81.82/47.37 | (1117) crypt(all_49_1_32, all_0_0_0) = all_277_0_254 % 81.82/47.37 | % 81.82/47.37 | From (1115) and (1057) follows: % 81.82/47.37 | (1118) crypt(all_49_1_32, all_0_1_1) = all_267_0_243 % 81.82/47.37 | % 81.82/47.37 | From (1115) and (1058) follows: % 81.82/47.37 | (1119) crypt(all_49_1_32, all_0_2_2) = all_265_0_241 % 81.82/47.38 | % 81.82/47.38 | From (1115) and (1061) follows: % 81.82/47.38 | (1120) crypt(all_49_1_32, a) = all_251_0_229 % 81.82/47.38 | % 81.82/47.38 | From (1115) and (1062) follows: % 81.82/47.38 | (1121) crypt(all_49_1_32, pin) = all_249_0_227 % 81.82/47.38 | % 81.82/47.38 | From (1115) and (1059) follows: % 81.82/47.38 | (1122) crypt(all_49_1_32, data) = all_259_0_237 % 81.82/47.38 | % 81.82/47.38 | From (1115) and (1055) follows: % 81.82/47.38 | (1123) crypt(all_49_1_32, exp) = all_275_0_252 % 81.82/47.38 | % 81.82/47.38 | From (1115) and (1056) follows: % 81.82/47.38 | (1124) crypt(all_49_1_32, imp) = all_273_0_250 % 81.82/47.38 | % 81.82/47.38 | From (1115) and (1060) follows: % 81.82/47.38 | (1125) crypt(all_49_1_32, id) = all_257_0_235 % 81.82/47.38 | % 81.82/47.38 | From (1116) and (797) follows: % 81.82/47.38 | (1126) crypt(all_0_4_4, all_0_5_5) = all_237_0_211 % 81.82/47.38 | % 81.82/47.38 | From (1112) and (1097) follows: % 81.82/47.38 | (224) crypt(all_0_4_4, all_0_5_5) = all_87_0_72 % 81.82/47.38 | % 81.82/47.38 | From (1113) and (1095) follows: % 81.82/47.38 | (67) crypt(all_0_5_5, exp) = all_13_0_9 % 81.82/47.38 | % 81.82/47.38 | From (1114) and (1096) follows: % 81.82/47.38 | (61) crypt(all_0_5_5, id) = all_9_0_7 % 81.82/47.38 | % 81.82/47.38 | From (1115) and (1101) follows: % 81.82/47.38 | (146) xor(all_0_5_5, data) = all_49_1_32 % 81.82/47.38 | % 81.82/47.38 | From (1116) and (1102) follows: % 81.82/47.38 | (19) xor(km, data) = all_0_4_4 % 81.82/47.38 | % 81.82/47.38 | From (1114) and (472) follows: % 81.82/47.38 | (62) ~ p(all_9_0_7) % 81.82/47.38 | % 81.82/47.38 | From (1113) and (468) follows: % 81.82/47.38 | (68) ~ p(all_13_0_9) % 81.82/47.38 | % 81.82/47.38 | Instantiating formula (30) with all_49_1_32, all_0_0_0, all_277_0_254, all_91_0_76 and discharging atoms crypt(all_49_1_32, all_0_0_0) = all_277_0_254, crypt(all_49_1_32, all_0_0_0) = all_91_0_76, yields: % 81.82/47.38 | (1134) all_277_0_254 = all_91_0_76 % 81.82/47.38 | % 81.82/47.38 | Instantiating formula (30) with all_49_1_32, all_0_1_1, all_267_0_243, all_71_0_54 and discharging atoms crypt(all_49_1_32, all_0_1_1) = all_267_0_243, crypt(all_49_1_32, all_0_1_1) = all_71_0_54, yields: % 81.82/47.38 | (1135) all_267_0_243 = all_71_0_54 % 81.82/47.38 | % 81.82/47.38 | Instantiating formula (30) with all_49_1_32, all_0_2_2, all_265_0_241, all_83_0_67 and discharging atoms crypt(all_49_1_32, all_0_2_2) = all_265_0_241, crypt(all_49_1_32, all_0_2_2) = all_83_0_67, yields: % 81.82/47.38 | (1136) all_265_0_241 = all_83_0_67 % 81.82/47.38 | % 81.82/47.38 | Instantiating formula (30) with all_49_1_32, a, all_251_0_229, all_63_0_44 and discharging atoms crypt(all_49_1_32, a) = all_251_0_229, crypt(all_49_1_32, a) = all_63_0_44, yields: % 81.82/47.38 | (1137) all_251_0_229 = all_63_0_44 % 81.82/47.38 | % 81.82/47.38 | Instantiating formula (30) with all_49_1_32, pin, all_249_0_227, all_65_0_46 and discharging atoms crypt(all_49_1_32, pin) = all_249_0_227, crypt(all_49_1_32, pin) = all_65_0_46, yields: % 81.82/47.38 | (1138) all_249_0_227 = all_65_0_46 % 81.82/47.38 | % 81.82/47.38 | Instantiating formula (30) with all_49_1_32, data, all_259_0_237, all_49_0_31 and discharging atoms crypt(all_49_1_32, data) = all_259_0_237, crypt(all_49_1_32, data) = all_49_0_31, yields: % 81.82/47.38 | (1139) all_259_0_237 = all_49_0_31 % 81.82/47.38 | % 81.82/47.38 | Instantiating formula (30) with all_49_1_32, exp, all_275_0_252, all_93_0_78 and discharging atoms crypt(all_49_1_32, exp) = all_275_0_252, crypt(all_49_1_32, exp) = all_93_0_78, yields: % 81.85/47.38 | (1140) all_275_0_252 = all_93_0_78 % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (30) with all_49_1_32, imp, all_273_0_250, all_77_0_60 and discharging atoms crypt(all_49_1_32, imp) = all_273_0_250, crypt(all_49_1_32, imp) = all_77_0_60, yields: % 81.85/47.38 | (1141) all_273_0_250 = all_77_0_60 % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (30) with all_49_1_32, id, all_257_0_235, all_79_0_62 and discharging atoms crypt(all_49_1_32, id) = all_257_0_235, crypt(all_49_1_32, id) = all_79_0_62, yields: % 81.85/47.38 | (1142) all_257_0_235 = all_79_0_62 % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (30) with all_0_4_4, all_0_5_5, all_237_0_211, all_87_0_72 and discharging atoms crypt(all_0_4_4, all_0_5_5) = all_237_0_211, crypt(all_0_4_4, all_0_5_5) = all_87_0_72, yields: % 81.85/47.38 | (1143) all_237_0_211 = all_87_0_72 % 81.85/47.38 | % 81.85/47.38 | From (1134) and (1117) follows: % 81.85/47.38 | (299) crypt(all_49_1_32, all_0_0_0) = all_91_0_76 % 81.85/47.38 | % 81.85/47.38 | From (1135) and (1118) follows: % 81.85/47.38 | (304) crypt(all_49_1_32, all_0_1_1) = all_71_0_54 % 81.85/47.38 | % 81.85/47.38 | From (1136) and (1119) follows: % 81.85/47.38 | (300) crypt(all_49_1_32, all_0_2_2) = all_83_0_67 % 81.85/47.38 | % 81.85/47.38 | From (1137) and (1120) follows: % 81.85/47.38 | (306) crypt(all_49_1_32, a) = all_63_0_44 % 81.85/47.38 | % 81.85/47.38 | From (1138) and (1121) follows: % 81.85/47.38 | (305) crypt(all_49_1_32, pin) = all_65_0_46 % 81.85/47.38 | % 81.85/47.38 | From (1139) and (1122) follows: % 81.85/47.38 | (145) crypt(all_49_1_32, data) = all_49_0_31 % 81.85/47.38 | % 81.85/47.38 | From (1140) and (1123) follows: % 81.85/47.38 | (298) crypt(all_49_1_32, exp) = all_93_0_78 % 81.85/47.38 | % 81.85/47.38 | From (1141) and (1124) follows: % 81.85/47.38 | (302) crypt(all_49_1_32, imp) = all_77_0_60 % 81.85/47.38 | % 81.85/47.38 | From (1142) and (1125) follows: % 81.85/47.38 | (301) crypt(all_49_1_32, id) = all_79_0_62 % 81.85/47.38 | % 81.85/47.38 | From (1143) and (1126) follows: % 81.85/47.38 | (224) crypt(all_0_4_4, all_0_5_5) = all_87_0_72 % 81.85/47.38 | % 81.85/47.38 | From (1134) and (882) follows: % 81.85/47.38 | (234) ~ p(all_91_0_76) % 81.85/47.38 | % 81.85/47.38 | From (1140) and (878) follows: % 81.85/47.38 | (238) ~ p(all_93_0_78) % 81.85/47.38 | % 81.85/47.38 | From (1141) and (874) follows: % 81.85/47.38 | (204) ~ p(all_77_0_60) % 81.85/47.38 | % 81.85/47.38 | From (1135) and (861) follows: % 81.85/47.38 | (192) ~ p(all_71_0_54) % 81.85/47.38 | % 81.85/47.38 | From (1136) and (857) follows: % 81.85/47.38 | (217) ~ p(all_83_0_67) % 81.85/47.38 | % 81.85/47.38 | From (1139) and (847) follows: % 81.85/47.38 | (147) ~ p(all_49_0_31) % 81.85/47.38 | % 81.85/47.38 | From (1142) and (843) follows: % 81.85/47.38 | (208) ~ p(all_79_0_62) % 81.85/47.38 | % 81.85/47.38 | From (1137) and (831) follows: % 81.85/47.38 | (174) ~ p(all_63_0_44) % 81.85/47.38 | % 81.85/47.38 | From (1138) and (827) follows: % 81.85/47.38 | (178) ~ p(all_65_0_46) % 81.85/47.38 | % 81.85/47.38 | From (1143) and (799) follows: % 81.85/47.38 | (225) ~ p(all_87_0_72) % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (15) with all_193_0_162, all_175_0_160, data, data, exp and discharging atoms xor(all_175_0_160, data) = all_193_0_162, xor(exp, data) = all_175_0_160, yields: % 81.85/47.38 | (1164) ? [v0] : (xor(data, data) = v0 & xor(exp, v0) = all_193_0_162) % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (35) with all_193_0_162, all_175_0_160, data and discharging atoms xor(all_175_0_160, data) = all_193_0_162, yields: % 81.85/47.38 | (1165) xor(data, all_175_0_160) = all_193_0_162 % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (21) with all_87_0_72, all_0_5_5, all_0_4_4, all_49_1_32, data, data and discharging atoms crypt(all_0_4_4, all_0_5_5) = all_87_0_72, xor(all_49_1_32, data) = all_0_5_5, xor(km, data) = all_0_4_4, p(data), ~ p(all_87_0_72), yields: % 81.85/47.38 | (1166) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, all_49_1_32) = v2 & xor(data, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (21) with all_111_0_81, all_0_5_5, all_0_5_5, all_49_1_32, exp, data and discharging atoms crypt(all_0_5_5, all_0_5_5) = all_111_0_81, xor(all_49_1_32, data) = all_0_5_5, xor(km, exp) = all_0_5_5, p(data), p(exp), yields: % 81.85/47.38 | (1167) p(all_111_0_81) | ? [v0] : ? [v1] : ? [v2] : (crypt(v1, all_49_1_32) = v2 & xor(exp, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (15) with all_49_1_32, all_0_5_5, data, data, all_49_1_32 and discharging atoms xor(all_49_1_32, data) = all_0_5_5, xor(all_0_5_5, data) = all_49_1_32, yields: % 81.85/47.38 | (1168) ? [v0] : (xor(all_49_1_32, v0) = all_49_1_32 & xor(data, data) = v0) % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (15) with all_49_1_32, km, all_175_0_160, data, all_0_4_4 and discharging atoms xor(all_0_4_4, data) = km, xor(km, all_175_0_160) = all_49_1_32, yields: % 81.85/47.38 | (1169) ? [v0] : (xor(all_0_4_4, v0) = all_49_1_32 & xor(data, all_175_0_160) = v0) % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (15) with all_0_4_4, km, data, data, all_0_4_4 and discharging atoms xor(all_0_4_4, data) = km, xor(km, data) = all_0_4_4, yields: % 81.85/47.38 | (1170) ? [v0] : (xor(all_0_4_4, v0) = all_0_4_4 & xor(data, data) = v0) % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (15) with all_0_5_5, km, exp, data, all_0_4_4 and discharging atoms xor(all_0_4_4, data) = km, xor(km, exp) = all_0_5_5, yields: % 81.85/47.38 | (1171) ? [v0] : (xor(all_0_4_4, v0) = all_0_5_5 & xor(data, exp) = v0) % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (15) with all_255_1_234, all_121_1_95, data, kp, all_0_4_4 and discharging atoms xor(all_121_1_95, data) = all_255_1_234, xor(all_0_4_4, kp) = all_121_1_95, yields: % 81.85/47.38 | (1172) ? [v0] : (xor(all_0_4_4, v0) = all_255_1_234 & xor(kp, data) = v0) % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (13) with all_137_0_117, all_49_1_32, all_0_4_4, all_17_0_12, exp and discharging atoms crypt(all_49_1_32, all_17_0_12) = all_137_0_117, xor(all_0_4_4, exp) = all_49_1_32, p(exp), ~ p(all_137_0_117), yields: % 81.85/47.38 | (1173) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_17_0_12) = v1 & crypt(all_0_5_5, all_0_4_4) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (13) with all_133_0_112, all_49_1_32, all_0_4_4, all_15_0_10, exp and discharging atoms crypt(all_49_1_32, all_15_0_10) = all_133_0_112, xor(all_0_4_4, exp) = all_49_1_32, p(exp), ~ p(all_133_0_112), yields: % 81.85/47.38 | (1174) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_15_0_10) = v1 & crypt(all_0_5_5, all_0_4_4) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (13) with all_91_0_76, all_49_1_32, all_0_4_4, all_0_0_0, exp and discharging atoms crypt(all_49_1_32, all_0_0_0) = all_91_0_76, xor(all_0_4_4, exp) = all_49_1_32, p(exp), ~ p(all_91_0_76), yields: % 81.85/47.38 | (1175) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_0_0_0) = v1 & crypt(all_0_5_5, all_0_4_4) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (13) with all_71_0_54, all_49_1_32, all_0_4_4, all_0_1_1, exp and discharging atoms crypt(all_49_1_32, all_0_1_1) = all_71_0_54, xor(all_0_4_4, exp) = all_49_1_32, p(exp), ~ p(all_71_0_54), yields: % 81.85/47.38 | (1176) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_0_1_1) = v1 & crypt(all_0_5_5, all_0_4_4) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (13) with all_83_0_67, all_49_1_32, all_0_4_4, all_0_2_2, exp and discharging atoms crypt(all_49_1_32, all_0_2_2) = all_83_0_67, xor(all_0_4_4, exp) = all_49_1_32, p(exp), ~ p(all_83_0_67), yields: % 81.85/47.38 | (1177) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_0_2_2) = v1 & crypt(all_0_5_5, all_0_4_4) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.85/47.38 | % 81.85/47.38 | Instantiating formula (13) with all_63_0_44, all_49_1_32, all_0_4_4, a, exp and discharging atoms crypt(all_49_1_32, a) = all_63_0_44, xor(all_0_4_4, exp) = all_49_1_32, p(exp), ~ p(all_63_0_44), yields: % 81.85/47.39 | (1178) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, a) = v1 & crypt(all_0_5_5, all_0_4_4) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (13) with all_65_0_46, all_49_1_32, all_0_4_4, pin, exp and discharging atoms crypt(all_49_1_32, pin) = all_65_0_46, xor(all_0_4_4, exp) = all_49_1_32, p(exp), ~ p(all_65_0_46), yields: % 81.85/47.39 | (1179) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, pin) = v1 & crypt(all_0_5_5, all_0_4_4) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (13) with all_49_0_31, all_49_1_32, all_0_4_4, data, exp and discharging atoms crypt(all_49_1_32, data) = all_49_0_31, xor(all_0_4_4, exp) = all_49_1_32, p(exp), ~ p(all_49_0_31), yields: % 81.85/47.39 | (1180) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, data) = v1 & crypt(all_0_5_5, all_0_4_4) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (13) with all_93_0_78, all_49_1_32, all_0_4_4, exp, exp and discharging atoms crypt(all_49_1_32, exp) = all_93_0_78, xor(all_0_4_4, exp) = all_49_1_32, p(exp), ~ p(all_93_0_78), yields: % 81.85/47.39 | (1181) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, exp) = v1 & crypt(all_0_5_5, all_0_4_4) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (13) with all_77_0_60, all_49_1_32, all_0_4_4, imp, exp and discharging atoms crypt(all_49_1_32, imp) = all_77_0_60, xor(all_0_4_4, exp) = all_49_1_32, p(exp), ~ p(all_77_0_60), yields: % 81.85/47.39 | (1182) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, imp) = v1 & crypt(all_0_5_5, all_0_4_4) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (13) with all_79_0_62, all_49_1_32, all_0_4_4, id, exp and discharging atoms crypt(all_49_1_32, id) = all_79_0_62, xor(all_0_4_4, exp) = all_49_1_32, p(exp), ~ p(all_79_0_62), yields: % 81.85/47.39 | (1183) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, id) = v1 & crypt(all_0_5_5, all_0_4_4) = v2 & xor(km, exp) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (21) with all_169_0_154, all_49_1_32, all_0_4_4, all_0_4_4, data, exp and discharging atoms crypt(all_0_4_4, all_49_1_32) = all_169_0_154, xor(all_0_4_4, exp) = all_49_1_32, xor(km, data) = all_0_4_4, p(data), p(exp), ~ p(all_169_0_154), yields: % 81.85/47.39 | (1184) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, all_0_4_4) = v2 & xor(data, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (21) with all_197_0_164, all_49_1_32, all_0_5_5, all_0_4_4, exp, exp and discharging atoms crypt(all_0_5_5, all_49_1_32) = all_197_0_164, xor(all_0_4_4, exp) = all_49_1_32, xor(km, exp) = all_0_5_5, p(exp), yields: % 81.85/47.39 | (1185) p(all_197_0_164) | ? [v0] : ? [v1] : ? [v2] : (crypt(v1, all_0_4_4) = v2 & xor(exp, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (15) with all_0_5_5, all_49_1_32, data, exp, all_0_4_4 and discharging atoms xor(all_49_1_32, data) = all_0_5_5, xor(all_0_4_4, exp) = all_49_1_32, yields: % 81.85/47.39 | (1186) ? [v0] : (xor(all_0_4_4, v0) = all_0_5_5 & xor(exp, data) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (21) with all_111_0_81, all_0_5_5, all_0_5_5, all_0_5_5, exp, id and discharging atoms crypt(all_0_5_5, all_0_5_5) = all_111_0_81, xor(all_0_5_5, id) = all_0_5_5, xor(km, exp) = all_0_5_5, p(exp), p(id), yields: % 81.85/47.39 | (1187) p(all_111_0_81) | ? [v0] : ? [v1] : ? [v2] : (crypt(v1, all_0_5_5) = v2 & xor(exp, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (15) with all_0_5_5, all_0_5_5, id, exp, km and discharging atoms xor(all_0_5_5, id) = all_0_5_5, xor(km, exp) = all_0_5_5, yields: % 81.85/47.39 | (1188) ? [v0] : (xor(exp, id) = v0 & xor(km, v0) = all_0_5_5) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (15) with all_0_5_5, all_0_5_5, id, data, all_49_1_32 and discharging atoms xor(all_49_1_32, data) = all_0_5_5, xor(all_0_5_5, id) = all_0_5_5, yields: % 81.85/47.39 | (1189) ? [v0] : (xor(all_49_1_32, v0) = all_0_5_5 & xor(data, id) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (15) with all_0_5_5, all_0_5_5, id, id, all_0_5_5 and discharging atoms xor(all_0_5_5, id) = all_0_5_5, yields: % 81.85/47.39 | (1190) ? [v0] : (xor(all_0_5_5, v0) = all_0_5_5 & xor(id, id) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (36) with all_229_0_200, all_0_5_5, all_121_1_95, all_121_2_96, all_49_1_32, data, data and discharging atoms crypt(all_121_1_95, all_0_5_5) = all_229_0_200, xor(data, all_49_1_32) = all_0_5_5, xor(data, kp) = all_121_2_96, xor(km, all_121_2_96) = all_121_1_95, p(data), ~ p(all_229_0_200), yields: % 81.85/47.39 | (1191) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, all_49_1_32) = v2 & xor(kp, data) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (12) with all_49_1_32, all_0_5_5, all_49_1_32, data, data and discharging atoms xor(data, all_49_1_32) = all_0_5_5, xor(data, all_0_5_5) = all_49_1_32, yields: % 81.85/47.39 | (1192) ? [v0] : (xor(v0, all_49_1_32) = all_49_1_32 & xor(data, data) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (12) with all_0_5_5, all_49_1_32, all_0_5_5, data, data and discharging atoms xor(data, all_49_1_32) = all_0_5_5, xor(data, all_0_5_5) = all_49_1_32, yields: % 81.85/47.39 | (1193) ? [v0] : (xor(v0, all_0_5_5) = all_0_5_5 & xor(data, data) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (12) with all_0_5_5, all_49_1_32, all_0_4_4, exp, data and discharging atoms xor(data, all_49_1_32) = all_0_5_5, xor(exp, all_0_4_4) = all_49_1_32, yields: % 81.85/47.39 | (1194) ? [v0] : (xor(v0, all_0_4_4) = all_0_5_5 & xor(data, exp) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (12) with all_0_5_5, all_49_1_32, km, all_175_0_160, data and discharging atoms xor(all_175_0_160, km) = all_49_1_32, xor(data, all_49_1_32) = all_0_5_5, yields: % 81.85/47.39 | (1195) ? [v0] : (xor(v0, km) = all_0_5_5 & xor(data, all_175_0_160) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (36) with all_121_0_94, km, all_121_1_95, all_121_2_96, all_0_4_4, data, data and discharging atoms crypt(all_121_1_95, km) = all_121_0_94, xor(data, all_0_4_4) = km, xor(data, kp) = all_121_2_96, xor(km, all_121_2_96) = all_121_1_95, p(data), ~ p(all_121_0_94), yields: % 81.85/47.39 | (1196) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, all_0_4_4) = v2 & xor(kp, data) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (12) with all_0_4_4, km, all_0_4_4, data, data and discharging atoms xor(data, all_0_4_4) = km, xor(data, km) = all_0_4_4, yields: % 81.85/47.39 | (1197) ? [v0] : (xor(v0, all_0_4_4) = all_0_4_4 & xor(data, data) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (12) with km, all_0_4_4, km, data, data and discharging atoms xor(data, all_0_4_4) = km, xor(data, km) = all_0_4_4, yields: % 81.85/47.39 | (1198) ? [v0] : (xor(v0, km) = km & xor(data, data) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (12) with all_0_5_5, km, all_0_4_4, data, exp and discharging atoms xor(data, all_0_4_4) = km, xor(exp, km) = all_0_5_5, yields: % 81.85/47.39 | (1199) ? [v0] : (xor(v0, all_0_4_4) = all_0_5_5 & xor(exp, data) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (12) with all_49_1_32, km, all_0_4_4, data, all_175_0_160 and discharging atoms xor(all_175_0_160, km) = all_49_1_32, xor(data, all_0_4_4) = km, yields: % 81.85/47.39 | (1200) ? [v0] : (xor(v0, all_0_4_4) = all_49_1_32 & xor(all_175_0_160, data) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (21) with all_111_1_82, id, all_0_4_4, data, data, data and discharging atoms crypt(all_0_4_4, id) = all_111_1_82, xor(data, data) = id, xor(km, data) = all_0_4_4, p(data), yields: % 81.85/47.39 | (1201) p(all_111_1_82) | ? [v0] : ? [v1] : ? [v2] : (crypt(v1, data) = v2 & xor(data, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (21) with all_9_0_7, id, all_0_5_5, data, exp, data and discharging atoms crypt(all_0_5_5, id) = all_9_0_7, xor(data, data) = id, xor(km, exp) = all_0_5_5, p(data), p(exp), ~ p(all_9_0_7), yields: % 81.85/47.39 | (1202) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, data) = v2 & xor(exp, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (15) with all_193_0_162, all_175_0_160, data, exp, data and discharging atoms xor(all_175_0_160, data) = all_193_0_162, xor(data, exp) = all_175_0_160, yields: % 81.85/47.39 | (1203) ? [v0] : (xor(data, v0) = all_193_0_162 & xor(exp, data) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (15) with all_49_1_32, all_0_5_5, data, all_193_0_162, km and discharging atoms xor(all_0_5_5, data) = all_49_1_32, xor(km, all_193_0_162) = all_0_5_5, yields: % 81.85/47.39 | (1204) ? [v0] : (xor(all_193_0_162, data) = v0 & xor(km, v0) = all_49_1_32) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (15) with all_0_5_5, km, all_193_0_162, data, all_0_4_4 and discharging atoms xor(all_0_4_4, data) = km, xor(km, all_193_0_162) = all_0_5_5, yields: % 81.85/47.39 | (1205) ? [v0] : (xor(all_0_4_4, v0) = all_0_5_5 & xor(data, all_193_0_162) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (15) with all_0_5_5, all_0_5_5, id, all_193_0_162, km and discharging atoms xor(all_0_5_5, id) = all_0_5_5, xor(km, all_193_0_162) = all_0_5_5, yields: % 81.85/47.39 | (1206) ? [v0] : (xor(all_193_0_162, id) = v0 & xor(km, v0) = all_0_5_5) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (15) with all_49_1_32, km, all_175_0_160, id, km and discharging atoms xor(km, all_175_0_160) = all_49_1_32, xor(km, id) = km, yields: % 81.85/47.39 | (1207) ? [v0] : (xor(km, v0) = all_49_1_32 & xor(id, all_175_0_160) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (15) with all_0_5_5, km, exp, id, km and discharging atoms xor(km, exp) = all_0_5_5, xor(km, id) = km, yields: % 81.85/47.39 | (1208) ? [v0] : (xor(km, v0) = all_0_5_5 & xor(id, exp) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (15) with km, km, id, data, all_0_4_4 and discharging atoms xor(all_0_4_4, data) = km, xor(km, id) = km, yields: % 81.85/47.39 | (1209) ? [v0] : (xor(all_0_4_4, v0) = km & xor(data, id) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (15) with km, km, id, all_0_4_4, data and discharging atoms xor(data, all_0_4_4) = km, xor(km, id) = km, yields: % 81.85/47.39 | (1210) ? [v0] : (xor(all_0_4_4, id) = v0 & xor(data, v0) = km) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (15) with all_0_5_5, km, all_193_0_162, id, km and discharging atoms xor(km, all_193_0_162) = all_0_5_5, xor(km, id) = km, yields: % 81.85/47.39 | (1211) ? [v0] : (xor(km, v0) = all_0_5_5 & xor(id, all_193_0_162) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (15) with km, km, id, id, km and discharging atoms xor(km, id) = km, yields: % 81.85/47.39 | (1212) ? [v0] : (xor(km, v0) = km & xor(id, id) = v0) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (24) with all_0_1_1, all_29_0_20, km, eurk, eurk, id and discharging atoms crypt(all_0_5_5, eurk) = all_0_1_1, crypt(km, eurk) = all_29_0_20, xor(km, id) = km, p(all_29_0_20), p(all_0_1_1), p(id), yields: % 81.85/47.39 | (1213) ? [v0] : ? [v1] : (crypt(v0, eurk) = v1 & xor(eurk, id) = v0 & p(v1)) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (21) with all_79_0_62, id, all_49_1_32, data, all_175_0_160, data and discharging atoms crypt(all_49_1_32, id) = all_79_0_62, xor(data, data) = id, xor(km, all_175_0_160) = all_49_1_32, p(all_175_0_160), p(data), ~ p(all_79_0_62), yields: % 81.85/47.39 | (1214) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, data) = v2 & xor(all_175_0_160, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (6) with all_193_0_162, data, all_175_0_160 and discharging atoms xor(all_175_0_160, data) = all_193_0_162, p(all_175_0_160), p(data), yields: % 81.85/47.39 | (1215) p(all_193_0_162) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (13) with all_121_0_94, all_121_1_95, km, km, all_121_2_96 and discharging atoms crypt(all_121_1_95, km) = all_121_0_94, xor(km, all_121_2_96) = all_121_1_95, p(all_121_2_96), ~ p(all_121_0_94), yields: % 81.85/47.39 | (1216) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, km) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, all_121_2_96) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (13) with all_229_0_200, all_121_1_95, km, all_0_5_5, all_121_2_96 and discharging atoms crypt(all_121_1_95, all_0_5_5) = all_229_0_200, xor(km, all_121_2_96) = all_121_1_95, p(all_121_2_96), ~ p(all_229_0_200), yields: % 81.85/47.39 | (1217) ? [v0] : ? [v1] : ? [v2] : (crypt(v0, all_0_5_5) = v1 & crypt(all_0_5_5, km) = v2 & xor(km, all_121_2_96) = v0 & ( ~ p(v2) | ~ p(v1))) % 81.85/47.39 | % 81.85/47.39 | Instantiating formula (37) with all_121_2_96 and discharging atoms p(all_121_2_96), yields: % 81.85/47.39 | (1218) ? [v0] : (crypt(all_0_5_5, all_121_2_96) = v0 & ~ p(v0)) % 81.85/47.40 | % 81.85/47.40 | Instantiating (1172) with all_315_0_272 yields: % 81.85/47.40 | (1219) xor(all_0_4_4, all_315_0_272) = all_255_1_234 & xor(kp, data) = all_315_0_272 % 81.85/47.40 | % 81.85/47.40 | Applying alpha-rule on (1219) yields: % 81.85/47.40 | (1220) xor(all_0_4_4, all_315_0_272) = all_255_1_234 % 81.85/47.40 | (1221) xor(kp, data) = all_315_0_272 % 81.85/47.40 | % 81.85/47.40 | Instantiating (1218) with all_321_0_277 yields: % 81.85/47.40 | (1222) crypt(all_0_5_5, all_121_2_96) = all_321_0_277 & ~ p(all_321_0_277) % 81.85/47.40 | % 81.85/47.40 | Applying alpha-rule on (1222) yields: % 81.85/47.40 | (1223) crypt(all_0_5_5, all_121_2_96) = all_321_0_277 % 81.85/47.40 | (1224) ~ p(all_321_0_277) % 81.85/47.40 | % 81.85/47.40 | Instantiating (1217) with all_325_0_281, all_325_1_282, all_325_2_283 yields: % 81.85/47.40 | (1225) crypt(all_325_2_283, all_0_5_5) = all_325_1_282 & crypt(all_0_5_5, km) = all_325_0_281 & xor(km, all_121_2_96) = all_325_2_283 & ( ~ p(all_325_0_281) | ~ p(all_325_1_282)) % 81.85/47.40 | % 81.85/47.40 | Applying alpha-rule on (1225) yields: % 81.85/47.40 | (1226) crypt(all_325_2_283, all_0_5_5) = all_325_1_282 % 81.85/47.40 | (1227) crypt(all_0_5_5, km) = all_325_0_281 % 81.85/47.40 | (1228) xor(km, all_121_2_96) = all_325_2_283 % 81.85/47.40 | (1229) ~ p(all_325_0_281) | ~ p(all_325_1_282) % 81.85/47.40 | % 81.85/47.40 | Instantiating (1216) with all_349_0_311, all_349_1_312, all_349_2_313 yields: % 81.85/47.40 | (1230) crypt(all_349_2_313, km) = all_349_1_312 & crypt(all_0_5_5, km) = all_349_0_311 & xor(km, all_121_2_96) = all_349_2_313 & ( ~ p(all_349_0_311) | ~ p(all_349_1_312)) % 81.85/47.40 | % 81.85/47.40 | Applying alpha-rule on (1230) yields: % 81.85/47.40 | (1231) crypt(all_349_2_313, km) = all_349_1_312 % 81.85/47.40 | (1232) crypt(all_0_5_5, km) = all_349_0_311 % 81.85/47.40 | (1233) xor(km, all_121_2_96) = all_349_2_313 % 81.85/47.40 | (1234) ~ p(all_349_0_311) | ~ p(all_349_1_312) % 81.85/47.40 | % 81.85/47.40 | Instantiating (1213) with all_357_0_323, all_357_1_324 yields: % 81.85/47.40 | (1235) crypt(all_357_1_324, eurk) = all_357_0_323 & xor(eurk, id) = all_357_1_324 & p(all_357_0_323) % 81.85/47.40 | % 81.85/47.40 | Applying alpha-rule on (1235) yields: % 81.85/47.40 | (1236) crypt(all_357_1_324, eurk) = all_357_0_323 % 81.85/47.40 | (1237) xor(eurk, id) = all_357_1_324 % 81.85/47.40 | (1238) p(all_357_0_323) % 81.85/47.40 | % 81.85/47.40 | Instantiating (1212) with all_359_0_325 yields: % 81.85/47.40 | (1239) xor(km, all_359_0_325) = km & xor(id, id) = all_359_0_325 % 81.85/47.40 | % 81.85/47.40 | Applying alpha-rule on (1239) yields: % 81.85/47.40 | (1240) xor(km, all_359_0_325) = km % 81.85/47.40 | (1241) xor(id, id) = all_359_0_325 % 81.85/47.40 | % 81.85/47.40 | Instantiating (1164) with all_365_0_330 yields: % 81.85/47.40 | (1242) xor(data, data) = all_365_0_330 & xor(exp, all_365_0_330) = all_193_0_162 % 81.85/47.40 | % 81.85/47.40 | Applying alpha-rule on (1242) yields: % 81.85/47.40 | (1243) xor(data, data) = all_365_0_330 % 81.85/47.40 | (1244) xor(exp, all_365_0_330) = all_193_0_162 % 81.85/47.40 | % 81.85/47.40 | Instantiating (1211) with all_367_0_331 yields: % 81.85/47.40 | (1245) xor(km, all_367_0_331) = all_0_5_5 & xor(id, all_193_0_162) = all_367_0_331 % 81.85/47.40 | % 81.85/47.40 | Applying alpha-rule on (1245) yields: % 81.85/47.40 | (1246) xor(km, all_367_0_331) = all_0_5_5 % 81.85/47.40 | (1247) xor(id, all_193_0_162) = all_367_0_331 % 81.85/47.40 | % 81.85/47.40 | Instantiating (1210) with all_369_0_332 yields: % 81.85/47.40 | (1248) xor(all_0_4_4, id) = all_369_0_332 & xor(data, all_369_0_332) = km % 81.85/47.40 | % 81.85/47.40 | Applying alpha-rule on (1248) yields: % 81.85/47.40 | (1249) xor(all_0_4_4, id) = all_369_0_332 % 81.85/47.40 | (1250) xor(data, all_369_0_332) = km % 81.85/47.40 | % 81.85/47.40 | Instantiating (1204) with all_387_0_351 yields: % 81.85/47.40 | (1251) xor(all_193_0_162, data) = all_387_0_351 & xor(km, all_387_0_351) = all_49_1_32 % 81.85/47.40 | % 81.85/47.40 | Applying alpha-rule on (1251) yields: % 81.85/47.40 | (1252) xor(all_193_0_162, data) = all_387_0_351 % 81.85/47.40 | (1253) xor(km, all_387_0_351) = all_49_1_32 % 81.85/47.40 | % 81.85/47.40 | Instantiating (1190) with all_389_0_352 yields: % 81.85/47.40 | (1254) xor(all_0_5_5, all_389_0_352) = all_0_5_5 & xor(id, id) = all_389_0_352 % 81.85/47.40 | % 81.85/47.40 | Applying alpha-rule on (1254) yields: % 81.85/47.40 | (1255) xor(all_0_5_5, all_389_0_352) = all_0_5_5 % 81.85/47.40 | (1256) xor(id, id) = all_389_0_352 % 81.85/47.40 | % 81.85/47.40 | Instantiating (1214) with all_393_0_356, all_393_1_357, all_393_2_358 yields: % 81.85/47.40 | (1257) crypt(all_393_1_357, data) = all_393_0_356 & xor(all_175_0_160, kp) = all_393_2_358 & xor(km, all_393_2_358) = all_393_1_357 & ~ p(all_393_0_356) % 81.85/47.40 | % 81.85/47.40 | Applying alpha-rule on (1257) yields: % 81.85/47.40 | (1258) crypt(all_393_1_357, data) = all_393_0_356 % 81.85/47.40 | (1259) xor(all_175_0_160, kp) = all_393_2_358 % 81.85/47.40 | (1260) xor(km, all_393_2_358) = all_393_1_357 % 81.85/47.40 | (1261) ~ p(all_393_0_356) % 81.85/47.40 | % 81.85/47.40 | Instantiating (1169) with all_401_0_362 yields: % 81.85/47.40 | (1262) xor(all_0_4_4, all_401_0_362) = all_49_1_32 & xor(data, all_175_0_160) = all_401_0_362 % 81.85/47.40 | % 81.85/47.40 | Applying alpha-rule on (1262) yields: % 81.85/47.40 | (1263) xor(all_0_4_4, all_401_0_362) = all_49_1_32 % 81.85/47.40 | (1264) xor(data, all_175_0_160) = all_401_0_362 % 81.85/47.40 | % 81.85/47.40 | Instantiating (1209) with all_403_0_363 yields: % 81.85/47.40 | (1265) xor(all_0_4_4, all_403_0_363) = km & xor(data, id) = all_403_0_363 % 81.85/47.40 | % 81.85/47.40 | Applying alpha-rule on (1265) yields: % 81.85/47.40 | (1266) xor(all_0_4_4, all_403_0_363) = km % 81.85/47.40 | (1267) xor(data, id) = all_403_0_363 % 81.85/47.40 | % 81.85/47.40 | Instantiating (1171) with all_411_0_367 yields: % 81.85/47.40 | (1268) xor(all_0_4_4, all_411_0_367) = all_0_5_5 & xor(data, exp) = all_411_0_367 % 81.85/47.40 | % 81.85/47.40 | Applying alpha-rule on (1268) yields: % 81.85/47.40 | (1269) xor(all_0_4_4, all_411_0_367) = all_0_5_5 % 81.85/47.40 | (1270) xor(data, exp) = all_411_0_367 % 81.85/47.40 | % 81.85/47.40 | Instantiating (1170) with all_415_0_371 yields: % 81.85/47.40 | (1271) xor(all_0_4_4, all_415_0_371) = all_0_4_4 & xor(data, data) = all_415_0_371 % 81.85/47.40 | % 81.85/47.40 | Applying alpha-rule on (1271) yields: % 81.85/47.40 | (1272) xor(all_0_4_4, all_415_0_371) = all_0_4_4 % 81.85/47.40 | (1273) xor(data, data) = all_415_0_371 % 81.85/47.40 | % 81.85/47.40 | Instantiating (1189) with all_425_0_384 yields: % 81.85/47.40 | (1274) xor(all_49_1_32, all_425_0_384) = all_0_5_5 & xor(data, id) = all_425_0_384 % 81.85/47.40 | % 81.85/47.40 | Applying alpha-rule on (1274) yields: % 81.85/47.40 | (1275) xor(all_49_1_32, all_425_0_384) = all_0_5_5 % 81.85/47.40 | (1276) xor(data, id) = all_425_0_384 % 81.85/47.40 | % 81.85/47.40 | Instantiating (1168) with all_449_0_412 yields: % 81.85/47.40 | (1277) xor(all_49_1_32, all_449_0_412) = all_49_1_32 & xor(data, data) = all_449_0_412 % 81.94/47.40 | % 81.94/47.40 | Applying alpha-rule on (1277) yields: % 81.94/47.40 | (1278) xor(all_49_1_32, all_449_0_412) = all_49_1_32 % 81.94/47.40 | (1279) xor(data, data) = all_449_0_412 % 81.94/47.40 | % 81.94/47.40 | Instantiating (1188) with all_471_0_437 yields: % 81.94/47.40 | (1280) xor(exp, id) = all_471_0_437 & xor(km, all_471_0_437) = all_0_5_5 % 81.94/47.40 | % 81.94/47.40 | Applying alpha-rule on (1280) yields: % 81.94/47.40 | (1281) xor(exp, id) = all_471_0_437 % 81.94/47.40 | (1282) xor(km, all_471_0_437) = all_0_5_5 % 81.94/47.40 | % 81.94/47.40 | Instantiating (1203) with all_473_0_438 yields: % 81.94/47.40 | (1283) xor(data, all_473_0_438) = all_193_0_162 & xor(exp, data) = all_473_0_438 % 81.94/47.40 | % 81.94/47.40 | Applying alpha-rule on (1283) yields: % 81.94/47.40 | (1284) xor(data, all_473_0_438) = all_193_0_162 % 81.94/47.40 | (1285) xor(exp, data) = all_473_0_438 % 81.94/47.40 | % 81.94/47.40 | Instantiating (1202) with all_475_0_439, all_475_1_440, all_475_2_441 yields: % 81.94/47.40 | (1286) crypt(all_475_1_440, data) = all_475_0_439 & xor(exp, kp) = all_475_2_441 & xor(km, all_475_2_441) = all_475_1_440 & ~ p(all_475_0_439) % 81.94/47.40 | % 81.94/47.40 | Applying alpha-rule on (1286) yields: % 81.94/47.40 | (1287) crypt(all_475_1_440, data) = all_475_0_439 % 81.94/47.40 | (1288) xor(exp, kp) = all_475_2_441 % 81.94/47.40 | (1289) xor(km, all_475_2_441) = all_475_1_440 % 81.94/47.40 | (1290) ~ p(all_475_0_439) % 81.94/47.40 | % 81.94/47.40 | Instantiating (1200) with all_485_0_448 yields: % 81.94/47.40 | (1291) xor(all_485_0_448, all_0_4_4) = all_49_1_32 & xor(all_175_0_160, data) = all_485_0_448 % 81.94/47.40 | % 81.94/47.40 | Applying alpha-rule on (1291) yields: % 81.94/47.40 | (1292) xor(all_485_0_448, all_0_4_4) = all_49_1_32 % 81.94/47.40 | (1293) xor(all_175_0_160, data) = all_485_0_448 % 81.94/47.40 | % 81.94/47.40 | Instantiating (1166) with all_495_0_459, all_495_1_460, all_495_2_461 yields: % 81.94/47.40 | (1294) crypt(all_495_1_460, all_49_1_32) = all_495_0_459 & xor(data, kp) = all_495_2_461 & xor(km, all_495_2_461) = all_495_1_460 & ~ p(all_495_0_459) % 81.94/47.40 | % 81.94/47.40 | Applying alpha-rule on (1294) yields: % 81.94/47.40 | (1295) crypt(all_495_1_460, all_49_1_32) = all_495_0_459 % 81.94/47.40 | (1296) xor(data, kp) = all_495_2_461 % 81.94/47.40 | (1297) xor(km, all_495_2_461) = all_495_1_460 % 81.94/47.40 | (1298) ~ p(all_495_0_459) % 81.94/47.40 | % 81.94/47.40 | Instantiating (1199) with all_507_0_467 yields: % 81.94/47.40 | (1299) xor(all_507_0_467, all_0_4_4) = all_0_5_5 & xor(exp, data) = all_507_0_467 % 81.94/47.40 | % 81.94/47.40 | Applying alpha-rule on (1299) yields: % 81.94/47.40 | (1300) xor(all_507_0_467, all_0_4_4) = all_0_5_5 % 81.94/47.40 | (1301) xor(exp, data) = all_507_0_467 % 81.94/47.40 | % 81.94/47.40 | Instantiating (1197) with all_513_0_470 yields: % 81.94/47.40 | (1302) xor(all_513_0_470, all_0_4_4) = all_0_4_4 & xor(data, data) = all_513_0_470 % 81.94/47.40 | % 81.94/47.41 | Applying alpha-rule on (1302) yields: % 81.94/47.41 | (1303) xor(all_513_0_470, all_0_4_4) = all_0_4_4 % 81.94/47.41 | (1304) xor(data, data) = all_513_0_470 % 81.94/47.41 | % 81.94/47.41 | Instantiating (1186) with all_521_0_478 yields: % 81.94/47.41 | (1305) xor(all_0_4_4, all_521_0_478) = all_0_5_5 & xor(exp, data) = all_521_0_478 % 81.94/47.41 | % 81.94/47.41 | Applying alpha-rule on (1305) yields: % 81.94/47.41 | (1306) xor(all_0_4_4, all_521_0_478) = all_0_5_5 % 81.94/47.41 | (1307) xor(exp, data) = all_521_0_478 % 81.94/47.41 | % 81.94/47.41 | Instantiating (1184) with all_525_0_482, all_525_1_483, all_525_2_484 yields: % 81.94/47.41 | (1308) crypt(all_525_1_483, all_0_4_4) = all_525_0_482 & xor(data, kp) = all_525_2_484 & xor(km, all_525_2_484) = all_525_1_483 & ~ p(all_525_0_482) % 81.94/47.41 | % 81.94/47.41 | Applying alpha-rule on (1308) yields: % 81.94/47.41 | (1309) crypt(all_525_1_483, all_0_4_4) = all_525_0_482 % 81.94/47.41 | (1310) xor(data, kp) = all_525_2_484 % 81.94/47.41 | (1311) xor(km, all_525_2_484) = all_525_1_483 % 81.94/47.41 | (1312) ~ p(all_525_0_482) % 81.94/47.41 | % 81.94/47.41 | Instantiating (1183) with all_527_0_485, all_527_1_486, all_527_2_487 yields: % 81.94/47.41 | (1313) crypt(all_527_2_487, id) = all_527_1_486 & crypt(all_0_5_5, all_0_4_4) = all_527_0_485 & xor(km, exp) = all_527_2_487 & ( ~ p(all_527_0_485) | ~ p(all_527_1_486)) % 81.94/47.41 | % 81.94/47.41 | Applying alpha-rule on (1313) yields: % 81.94/47.41 | (1314) crypt(all_527_2_487, id) = all_527_1_486 % 81.94/47.41 | (1315) crypt(all_0_5_5, all_0_4_4) = all_527_0_485 % 81.94/47.41 | (1316) xor(km, exp) = all_527_2_487 % 81.94/47.41 | (1317) ~ p(all_527_0_485) | ~ p(all_527_1_486) % 81.94/47.41 | % 81.94/47.41 | Instantiating (1181) with all_529_0_488, all_529_1_489, all_529_2_490 yields: % 81.94/47.41 | (1318) crypt(all_529_2_490, exp) = all_529_1_489 & crypt(all_0_5_5, all_0_4_4) = all_529_0_488 & xor(km, exp) = all_529_2_490 & ( ~ p(all_529_0_488) | ~ p(all_529_1_489)) % 81.94/47.41 | % 81.94/47.41 | Applying alpha-rule on (1318) yields: % 81.94/47.41 | (1319) crypt(all_529_2_490, exp) = all_529_1_489 % 81.94/47.41 | (1320) crypt(all_0_5_5, all_0_4_4) = all_529_0_488 % 81.94/47.41 | (1321) xor(km, exp) = all_529_2_490 % 81.94/47.41 | (1322) ~ p(all_529_0_488) | ~ p(all_529_1_489) % 81.94/47.41 | % 81.94/47.41 | Instantiating (1180) with all_557_0_530, all_557_1_531, all_557_2_532 yields: % 81.94/47.41 | (1323) crypt(all_557_2_532, data) = all_557_1_531 & crypt(all_0_5_5, all_0_4_4) = all_557_0_530 & xor(km, exp) = all_557_2_532 & ( ~ p(all_557_0_530) | ~ p(all_557_1_531)) % 81.94/47.41 | % 81.94/47.41 | Applying alpha-rule on (1323) yields: % 81.94/47.41 | (1324) crypt(all_557_2_532, data) = all_557_1_531 % 81.94/47.41 | (1325) crypt(all_0_5_5, all_0_4_4) = all_557_0_530 % 81.94/47.41 | (1326) xor(km, exp) = all_557_2_532 % 81.94/47.41 | (1327) ~ p(all_557_0_530) | ~ p(all_557_1_531) % 81.94/47.41 | % 81.94/47.41 | Instantiating (1179) with all_559_0_533, all_559_1_534, all_559_2_535 yields: % 81.94/47.41 | (1328) crypt(all_559_2_535, pin) = all_559_1_534 & crypt(all_0_5_5, all_0_4_4) = all_559_0_533 & xor(km, exp) = all_559_2_535 & ( ~ p(all_559_0_533) | ~ p(all_559_1_534)) % 81.94/47.41 | % 81.94/47.41 | Applying alpha-rule on (1328) yields: % 81.94/47.41 | (1329) crypt(all_559_2_535, pin) = all_559_1_534 % 81.94/47.41 | (1330) crypt(all_0_5_5, all_0_4_4) = all_559_0_533 % 81.94/47.41 | (1331) xor(km, exp) = all_559_2_535 % 81.94/47.41 | (1332) ~ p(all_559_0_533) | ~ p(all_559_1_534) % 81.94/47.41 | % 81.94/47.41 | Instantiating (1182) with all_561_0_536, all_561_1_537, all_561_2_538 yields: % 81.94/47.41 | (1333) crypt(all_561_2_538, imp) = all_561_1_537 & crypt(all_0_5_5, all_0_4_4) = all_561_0_536 & xor(km, exp) = all_561_2_538 & ( ~ p(all_561_0_536) | ~ p(all_561_1_537)) % 81.94/47.41 | % 81.94/47.41 | Applying alpha-rule on (1333) yields: % 81.94/47.41 | (1334) crypt(all_561_2_538, imp) = all_561_1_537 % 81.94/47.41 | (1335) crypt(all_0_5_5, all_0_4_4) = all_561_0_536 % 81.94/47.41 | (1336) xor(km, exp) = all_561_2_538 % 81.94/47.41 | (1337) ~ p(all_561_0_536) | ~ p(all_561_1_537) % 81.94/47.41 | % 81.94/47.41 | Instantiating (1176) with all_565_0_542, all_565_1_543, all_565_2_544 yields: % 81.94/47.41 | (1338) crypt(all_565_2_544, all_0_1_1) = all_565_1_543 & crypt(all_0_5_5, all_0_4_4) = all_565_0_542 & xor(km, exp) = all_565_2_544 & ( ~ p(all_565_0_542) | ~ p(all_565_1_543)) % 81.94/47.41 | % 81.94/47.41 | Applying alpha-rule on (1338) yields: % 81.94/47.41 | (1339) crypt(all_565_2_544, all_0_1_1) = all_565_1_543 % 81.94/47.41 | (1340) crypt(all_0_5_5, all_0_4_4) = all_565_0_542 % 81.94/47.41 | (1341) xor(km, exp) = all_565_2_544 % 81.94/47.41 | (1342) ~ p(all_565_0_542) | ~ p(all_565_1_543) % 81.94/47.41 | % 81.94/47.41 | Instantiating (1175) with all_567_0_545, all_567_1_546, all_567_2_547 yields: % 81.94/47.41 | (1343) crypt(all_567_2_547, all_0_0_0) = all_567_1_546 & crypt(all_0_5_5, all_0_4_4) = all_567_0_545 & xor(km, exp) = all_567_2_547 & ( ~ p(all_567_0_545) | ~ p(all_567_1_546)) % 81.94/47.41 | % 81.94/47.41 | Applying alpha-rule on (1343) yields: % 81.94/47.41 | (1344) crypt(all_567_2_547, all_0_0_0) = all_567_1_546 % 81.94/47.41 | (1345) crypt(all_0_5_5, all_0_4_4) = all_567_0_545 % 81.94/47.41 | (1346) xor(km, exp) = all_567_2_547 % 81.94/47.41 | (1347) ~ p(all_567_0_545) | ~ p(all_567_1_546) % 81.94/47.41 | % 81.94/47.41 | Instantiating (1178) with all_569_0_548, all_569_1_549, all_569_2_550 yields: % 81.94/47.41 | (1348) crypt(all_569_2_550, a) = all_569_1_549 & crypt(all_0_5_5, all_0_4_4) = all_569_0_548 & xor(km, exp) = all_569_2_550 & ( ~ p(all_569_0_548) | ~ p(all_569_1_549)) % 81.94/47.41 | % 81.94/47.41 | Applying alpha-rule on (1348) yields: % 81.94/47.41 | (1349) crypt(all_569_2_550, a) = all_569_1_549 % 81.94/47.41 | (1350) crypt(all_0_5_5, all_0_4_4) = all_569_0_548 % 81.94/47.41 | (1351) xor(km, exp) = all_569_2_550 % 81.94/47.41 | (1352) ~ p(all_569_0_548) | ~ p(all_569_1_549) % 81.94/47.41 | % 81.94/47.41 | Instantiating (1177) with all_571_0_551, all_571_1_552, all_571_2_553 yields: % 81.94/47.41 | (1353) crypt(all_571_2_553, all_0_2_2) = all_571_1_552 & crypt(all_0_5_5, all_0_4_4) = all_571_0_551 & xor(km, exp) = all_571_2_553 & ( ~ p(all_571_0_551) | ~ p(all_571_1_552)) % 81.94/47.41 | % 81.94/47.41 | Applying alpha-rule on (1353) yields: % 81.94/47.41 | (1354) crypt(all_571_2_553, all_0_2_2) = all_571_1_552 % 81.94/47.41 | (1355) crypt(all_0_5_5, all_0_4_4) = all_571_0_551 % 81.94/47.41 | (1356) xor(km, exp) = all_571_2_553 % 81.94/47.41 | (1357) ~ p(all_571_0_551) | ~ p(all_571_1_552) % 81.94/47.41 | % 81.94/47.41 | Instantiating (1174) with all_573_0_554, all_573_1_555, all_573_2_556 yields: % 81.94/47.41 | (1358) crypt(all_573_2_556, all_15_0_10) = all_573_1_555 & crypt(all_0_5_5, all_0_4_4) = all_573_0_554 & xor(km, exp) = all_573_2_556 & ( ~ p(all_573_0_554) | ~ p(all_573_1_555)) % 81.94/47.41 | % 81.94/47.41 | Applying alpha-rule on (1358) yields: % 81.94/47.41 | (1359) crypt(all_573_2_556, all_15_0_10) = all_573_1_555 % 81.94/47.41 | (1360) crypt(all_0_5_5, all_0_4_4) = all_573_0_554 % 81.94/47.41 | (1361) xor(km, exp) = all_573_2_556 % 81.94/47.41 | (1362) ~ p(all_573_0_554) | ~ p(all_573_1_555) % 81.94/47.41 | % 81.94/47.41 | Instantiating (1173) with all_575_0_557, all_575_1_558, all_575_2_559 yields: % 81.94/47.41 | (1363) crypt(all_575_2_559, all_17_0_12) = all_575_1_558 & crypt(all_0_5_5, all_0_4_4) = all_575_0_557 & xor(km, exp) = all_575_2_559 & ( ~ p(all_575_0_557) | ~ p(all_575_1_558)) % 81.94/47.41 | % 81.94/47.41 | Applying alpha-rule on (1363) yields: % 81.94/47.41 | (1364) crypt(all_575_2_559, all_17_0_12) = all_575_1_558 % 81.94/47.41 | (1365) crypt(all_0_5_5, all_0_4_4) = all_575_0_557 % 81.94/47.41 | (1366) xor(km, exp) = all_575_2_559 % 81.94/47.41 | (1367) ~ p(all_575_0_557) | ~ p(all_575_1_558) % 81.94/47.41 | % 81.94/47.41 | Instantiating (1195) with all_577_0_560 yields: % 81.94/47.41 | (1368) xor(all_577_0_560, km) = all_0_5_5 & xor(data, all_175_0_160) = all_577_0_560 % 81.94/47.41 | % 81.94/47.41 | Applying alpha-rule on (1368) yields: % 81.94/47.41 | (1369) xor(all_577_0_560, km) = all_0_5_5 % 81.94/47.41 | (1370) xor(data, all_175_0_160) = all_577_0_560 % 81.94/47.41 | % 81.94/47.41 | Instantiating (1196) with all_581_0_562, all_581_1_563, all_581_2_564 yields: % 81.94/47.41 | (1371) crypt(all_581_1_563, all_0_4_4) = all_581_0_562 & xor(kp, data) = all_581_2_564 & xor(km, all_581_2_564) = all_581_1_563 & ~ p(all_581_0_562) % 81.94/47.41 | % 81.94/47.41 | Applying alpha-rule on (1371) yields: % 81.94/47.41 | (1372) crypt(all_581_1_563, all_0_4_4) = all_581_0_562 % 81.94/47.41 | (1373) xor(kp, data) = all_581_2_564 % 81.94/47.41 | (1374) xor(km, all_581_2_564) = all_581_1_563 % 81.94/47.41 | (1375) ~ p(all_581_0_562) % 81.94/47.41 | % 81.94/47.41 | Instantiating (1198) with all_589_0_568 yields: % 81.94/47.41 | (1376) xor(all_589_0_568, km) = km & xor(data, data) = all_589_0_568 % 81.94/47.41 | % 81.94/47.41 | Applying alpha-rule on (1376) yields: % 81.94/47.41 | (1377) xor(all_589_0_568, km) = km % 81.94/47.41 | (1378) xor(data, data) = all_589_0_568 % 81.94/47.41 | % 81.94/47.41 | Instantiating (1192) with all_591_0_569 yields: % 81.94/47.41 | (1379) xor(all_591_0_569, all_49_1_32) = all_49_1_32 & xor(data, data) = all_591_0_569 % 81.94/47.41 | % 81.94/47.41 | Applying alpha-rule on (1379) yields: % 81.94/47.41 | (1380) xor(all_591_0_569, all_49_1_32) = all_49_1_32 % 81.94/47.42 | (1381) xor(data, data) = all_591_0_569 % 81.94/47.42 | % 81.94/47.42 | Instantiating (1207) with all_593_0_570 yields: % 81.94/47.42 | (1382) xor(km, all_593_0_570) = all_49_1_32 & xor(id, all_175_0_160) = all_593_0_570 % 81.94/47.42 | % 81.94/47.42 | Applying alpha-rule on (1382) yields: % 81.94/47.42 | (1383) xor(km, all_593_0_570) = all_49_1_32 % 81.94/47.42 | (1384) xor(id, all_175_0_160) = all_593_0_570 % 81.94/47.42 | % 81.94/47.42 | Instantiating (1194) with all_597_0_572 yields: % 81.94/47.42 | (1385) xor(all_597_0_572, all_0_4_4) = all_0_5_5 & xor(data, exp) = all_597_0_572 % 81.94/47.42 | % 81.94/47.42 | Applying alpha-rule on (1385) yields: % 81.94/47.42 | (1386) xor(all_597_0_572, all_0_4_4) = all_0_5_5 % 81.94/47.42 | (1387) xor(data, exp) = all_597_0_572 % 81.94/47.42 | % 81.94/47.42 | Instantiating (1193) with all_599_0_573 yields: % 81.94/47.42 | (1388) xor(all_599_0_573, all_0_5_5) = all_0_5_5 & xor(data, data) = all_599_0_573 % 81.94/47.42 | % 81.94/47.42 | Applying alpha-rule on (1388) yields: % 81.94/47.42 | (1389) xor(all_599_0_573, all_0_5_5) = all_0_5_5 % 81.94/47.42 | (1390) xor(data, data) = all_599_0_573 % 81.94/47.42 | % 81.94/47.42 | Instantiating (1208) with all_601_0_574 yields: % 81.94/47.42 | (1391) xor(km, all_601_0_574) = all_0_5_5 & xor(id, exp) = all_601_0_574 % 81.94/47.42 | % 81.94/47.42 | Applying alpha-rule on (1391) yields: % 81.94/47.42 | (1392) xor(km, all_601_0_574) = all_0_5_5 % 81.94/47.42 | (1393) xor(id, exp) = all_601_0_574 % 81.94/47.42 | % 81.94/47.42 | Instantiating (1206) with all_611_0_583 yields: % 81.94/47.42 | (1394) xor(all_193_0_162, id) = all_611_0_583 & xor(km, all_611_0_583) = all_0_5_5 % 81.94/47.42 | % 81.94/47.42 | Applying alpha-rule on (1394) yields: % 81.94/47.42 | (1395) xor(all_193_0_162, id) = all_611_0_583 % 81.94/47.42 | (1396) xor(km, all_611_0_583) = all_0_5_5 % 81.94/47.42 | % 81.94/47.42 | Instantiating (1205) with all_613_0_584 yields: % 81.94/47.42 | (1397) xor(all_0_4_4, all_613_0_584) = all_0_5_5 & xor(data, all_193_0_162) = all_613_0_584 % 81.94/47.42 | % 81.94/47.42 | Applying alpha-rule on (1397) yields: % 81.94/47.42 | (1398) xor(all_0_4_4, all_613_0_584) = all_0_5_5 % 81.94/47.42 | (1399) xor(data, all_193_0_162) = all_613_0_584 % 81.94/47.42 | % 81.94/47.42 | Instantiating (1191) with all_615_0_585, all_615_1_586, all_615_2_587 yields: % 81.94/47.42 | (1400) crypt(all_615_1_586, all_49_1_32) = all_615_0_585 & xor(kp, data) = all_615_2_587 & xor(km, all_615_2_587) = all_615_1_586 & ~ p(all_615_0_585) % 81.94/47.42 | % 81.94/47.42 | Applying alpha-rule on (1400) yields: % 81.94/47.42 | (1401) crypt(all_615_1_586, all_49_1_32) = all_615_0_585 % 81.94/47.42 | (1402) xor(kp, data) = all_615_2_587 % 81.94/47.42 | (1403) xor(km, all_615_2_587) = all_615_1_586 % 81.94/47.42 | (1404) ~ p(all_615_0_585) % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (4) with all_611_0_583, all_193_0_162 and discharging atoms xor(all_193_0_162, id) = all_611_0_583, yields: % 81.94/47.42 | (1405) all_611_0_583 = all_193_0_162 % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (17) with all_175_0_160, data, all_485_0_448, all_193_0_162 and discharging atoms xor(all_175_0_160, data) = all_485_0_448, xor(all_175_0_160, data) = all_193_0_162, yields: % 81.94/47.42 | (1406) all_485_0_448 = all_193_0_162 % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (4) with all_369_0_332, all_0_4_4 and discharging atoms xor(all_0_4_4, id) = all_369_0_332, yields: % 81.94/47.42 | (1407) all_369_0_332 = all_0_4_4 % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (4) with all_357_1_324, eurk and discharging atoms xor(eurk, id) = all_357_1_324, yields: % 81.94/47.42 | (1408) all_357_1_324 = eurk % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (17) with data, all_175_0_160, all_401_0_362, all_577_0_560 and discharging atoms xor(data, all_175_0_160) = all_577_0_560, xor(data, all_175_0_160) = all_401_0_362, yields: % 81.94/47.42 | (1409) all_577_0_560 = all_401_0_362 % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (17) with data, all_175_0_160, all_193_0_162, all_577_0_560 and discharging atoms xor(data, all_175_0_160) = all_577_0_560, xor(data, all_175_0_160) = all_193_0_162, yields: % 81.94/47.42 | (1410) all_577_0_560 = all_193_0_162 % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (17) with data, data, all_591_0_569, all_599_0_573 and discharging atoms xor(data, data) = all_599_0_573, xor(data, data) = all_591_0_569, yields: % 81.94/47.42 | (1411) all_599_0_573 = all_591_0_569 % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (43) with all_589_0_568, data and discharging atoms xor(data, data) = all_589_0_568, yields: % 81.94/47.42 | (1412) all_589_0_568 = id % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (17) with data, data, all_513_0_470, all_589_0_568 and discharging atoms xor(data, data) = all_589_0_568, xor(data, data) = all_513_0_470, yields: % 81.94/47.42 | (1413) all_589_0_568 = all_513_0_470 % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (17) with data, data, all_449_0_412, all_599_0_573 and discharging atoms xor(data, data) = all_599_0_573, xor(data, data) = all_449_0_412, yields: % 81.94/47.42 | (1414) all_599_0_573 = all_449_0_412 % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (17) with data, data, all_449_0_412, all_513_0_470 and discharging atoms xor(data, data) = all_513_0_470, xor(data, data) = all_449_0_412, yields: % 81.94/47.42 | (1415) all_513_0_470 = all_449_0_412 % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (17) with data, data, all_415_0_371, all_599_0_573 and discharging atoms xor(data, data) = all_599_0_573, xor(data, data) = all_415_0_371, yields: % 81.94/47.42 | (1416) all_599_0_573 = all_415_0_371 % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (17) with data, data, all_365_0_330, all_599_0_573 and discharging atoms xor(data, data) = all_599_0_573, xor(data, data) = all_365_0_330, yields: % 81.94/47.42 | (1417) all_599_0_573 = all_365_0_330 % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (17) with data, kp, all_525_2_484, all_121_2_96 and discharging atoms xor(data, kp) = all_525_2_484, xor(data, kp) = all_121_2_96, yields: % 81.94/47.42 | (1418) all_525_2_484 = all_121_2_96 % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (17) with data, kp, all_495_2_461, all_525_2_484 and discharging atoms xor(data, kp) = all_525_2_484, xor(data, kp) = all_495_2_461, yields: % 81.94/47.42 | (1419) all_525_2_484 = all_495_2_461 % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (17) with data, exp, all_597_0_572, all_175_0_160 and discharging atoms xor(data, exp) = all_597_0_572, xor(data, exp) = all_175_0_160, yields: % 81.94/47.42 | (1420) all_597_0_572 = all_175_0_160 % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (17) with data, exp, all_411_0_367, all_597_0_572 and discharging atoms xor(data, exp) = all_597_0_572, xor(data, exp) = all_411_0_367, yields: % 81.94/47.42 | (1421) all_597_0_572 = all_411_0_367 % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (4) with all_425_0_384, data and discharging atoms xor(data, id) = all_425_0_384, yields: % 81.94/47.42 | (1422) all_425_0_384 = data % 81.94/47.42 | % 81.94/47.42 | Instantiating formula (17) with data, id, all_403_0_363, all_425_0_384 and discharging atoms xor(data, id) = all_425_0_384, xor(data, id) = all_403_0_363, yields: % 81.94/47.42 | (1423) all_425_0_384 = all_403_0_363 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with kp, data, all_581_2_564, all_121_2_96 and discharging atoms xor(kp, data) = all_581_2_564, xor(kp, data) = all_121_2_96, yields: % 82.00/47.42 | (1424) all_581_2_564 = all_121_2_96 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with kp, data, all_581_2_564, all_615_2_587 and discharging atoms xor(kp, data) = all_615_2_587, xor(kp, data) = all_581_2_564, yields: % 82.00/47.42 | (1425) all_615_2_587 = all_581_2_564 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with kp, data, all_315_0_272, all_615_2_587 and discharging atoms xor(kp, data) = all_615_2_587, xor(kp, data) = all_315_0_272, yields: % 82.00/47.42 | (1426) all_615_2_587 = all_315_0_272 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with exp, data, all_521_0_478, all_175_0_160 and discharging atoms xor(exp, data) = all_521_0_478, xor(exp, data) = all_175_0_160, yields: % 82.00/47.42 | (1427) all_521_0_478 = all_175_0_160 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with exp, data, all_507_0_467, all_521_0_478 and discharging atoms xor(exp, data) = all_521_0_478, xor(exp, data) = all_507_0_467, yields: % 82.00/47.42 | (1428) all_521_0_478 = all_507_0_467 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with exp, data, all_473_0_438, all_507_0_467 and discharging atoms xor(exp, data) = all_507_0_467, xor(exp, data) = all_473_0_438, yields: % 82.00/47.42 | (1429) all_507_0_467 = all_473_0_438 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (4) with all_471_0_437, exp and discharging atoms xor(exp, id) = all_471_0_437, yields: % 82.00/47.42 | (1430) all_471_0_437 = exp % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with km, all_121_2_96, all_349_2_313, all_121_1_95 and discharging atoms xor(km, all_121_2_96) = all_349_2_313, xor(km, all_121_2_96) = all_121_1_95, yields: % 82.00/47.42 | (1431) all_349_2_313 = all_121_1_95 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with km, all_121_2_96, all_325_2_283, all_349_2_313 and discharging atoms xor(km, all_121_2_96) = all_349_2_313, xor(km, all_121_2_96) = all_325_2_283, yields: % 82.00/47.42 | (1432) all_349_2_313 = all_325_2_283 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with km, exp, all_573_2_556, all_575_2_559 and discharging atoms xor(km, exp) = all_575_2_559, xor(km, exp) = all_573_2_556, yields: % 82.00/47.42 | (1433) all_575_2_559 = all_573_2_556 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with km, exp, all_569_2_550, all_571_2_553 and discharging atoms xor(km, exp) = all_571_2_553, xor(km, exp) = all_569_2_550, yields: % 82.00/47.42 | (1434) all_571_2_553 = all_569_2_550 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with km, exp, all_567_2_547, all_0_5_5 and discharging atoms xor(km, exp) = all_567_2_547, xor(km, exp) = all_0_5_5, yields: % 82.00/47.42 | (1435) all_567_2_547 = all_0_5_5 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with km, exp, all_567_2_547, all_569_2_550 and discharging atoms xor(km, exp) = all_569_2_550, xor(km, exp) = all_567_2_547, yields: % 82.00/47.42 | (1436) all_569_2_550 = all_567_2_547 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with km, exp, all_565_2_544, all_567_2_547 and discharging atoms xor(km, exp) = all_567_2_547, xor(km, exp) = all_565_2_544, yields: % 82.00/47.42 | (1437) all_567_2_547 = all_565_2_544 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with km, exp, all_561_2_538, all_567_2_547 and discharging atoms xor(km, exp) = all_567_2_547, xor(km, exp) = all_561_2_538, yields: % 82.00/47.42 | (1438) all_567_2_547 = all_561_2_538 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with km, exp, all_559_2_535, all_571_2_553 and discharging atoms xor(km, exp) = all_571_2_553, xor(km, exp) = all_559_2_535, yields: % 82.00/47.42 | (1439) all_571_2_553 = all_559_2_535 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with km, exp, all_557_2_532, all_575_2_559 and discharging atoms xor(km, exp) = all_575_2_559, xor(km, exp) = all_557_2_532, yields: % 82.00/47.42 | (1440) all_575_2_559 = all_557_2_532 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with km, exp, all_529_2_490, all_573_2_556 and discharging atoms xor(km, exp) = all_573_2_556, xor(km, exp) = all_529_2_490, yields: % 82.00/47.42 | (1441) all_573_2_556 = all_529_2_490 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with km, exp, all_529_2_490, all_567_2_547 and discharging atoms xor(km, exp) = all_567_2_547, xor(km, exp) = all_529_2_490, yields: % 82.00/47.42 | (1442) all_567_2_547 = all_529_2_490 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with km, exp, all_527_2_487, all_573_2_556 and discharging atoms xor(km, exp) = all_573_2_556, xor(km, exp) = all_527_2_487, yields: % 82.00/47.42 | (1443) all_573_2_556 = all_527_2_487 % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (4) with all_389_0_352, id and discharging atoms xor(id, id) = all_389_0_352, yields: % 82.00/47.42 | (1444) all_389_0_352 = id % 82.00/47.42 | % 82.00/47.42 | Instantiating formula (17) with id, id, all_359_0_325, all_389_0_352 and discharging atoms xor(id, id) = all_389_0_352, xor(id, id) = all_359_0_325, yields: % 82.00/47.42 | (1445) all_389_0_352 = all_359_0_325 % 82.00/47.42 | % 82.00/47.42 | Combining equations (1425,1426) yields a new equation: % 82.00/47.42 | (1446) all_581_2_564 = all_315_0_272 % 82.00/47.42 | % 82.00/47.42 | Simplifying 1446 yields: % 82.00/47.42 | (1447) all_581_2_564 = all_315_0_272 % 82.00/47.42 | % 82.00/47.42 | Combining equations (1416,1411) yields a new equation: % 82.00/47.42 | (1448) all_591_0_569 = all_415_0_371 % 82.00/47.42 | % 82.00/47.42 | Combining equations (1414,1411) yields a new equation: % 82.00/47.42 | (1449) all_591_0_569 = all_449_0_412 % 82.00/47.42 | % 82.00/47.42 | Combining equations (1417,1411) yields a new equation: % 82.00/47.42 | (1450) all_591_0_569 = all_365_0_330 % 82.00/47.42 | % 82.00/47.42 | Combining equations (1421,1420) yields a new equation: % 82.00/47.42 | (1451) all_411_0_367 = all_175_0_160 % 82.00/47.42 | % 82.00/47.42 | Simplifying 1451 yields: % 82.00/47.42 | (1452) all_411_0_367 = all_175_0_160 % 82.00/47.42 | % 82.00/47.42 | Combining equations (1450,1448) yields a new equation: % 82.00/47.42 | (1453) all_415_0_371 = all_365_0_330 % 82.00/47.42 | % 82.00/47.42 | Combining equations (1449,1448) yields a new equation: % 82.00/47.42 | (1454) all_449_0_412 = all_415_0_371 % 82.00/47.42 | % 82.00/47.42 | Simplifying 1454 yields: % 82.00/47.42 | (1455) all_449_0_412 = all_415_0_371 % 82.00/47.42 | % 82.00/47.42 | Combining equations (1413,1412) yields a new equation: % 82.00/47.42 | (1456) all_513_0_470 = id % 82.00/47.42 | % 82.00/47.43 | Simplifying 1456 yields: % 82.00/47.43 | (1457) all_513_0_470 = id % 82.00/47.43 | % 82.00/47.43 | Combining equations (1424,1447) yields a new equation: % 82.00/47.43 | (1458) all_315_0_272 = all_121_2_96 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1409,1410) yields a new equation: % 82.00/47.43 | (1459) all_401_0_362 = all_193_0_162 % 82.00/47.43 | % 82.00/47.43 | Simplifying 1459 yields: % 82.00/47.43 | (1460) all_401_0_362 = all_193_0_162 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1433,1440) yields a new equation: % 82.00/47.43 | (1461) all_573_2_556 = all_557_2_532 % 82.00/47.43 | % 82.00/47.43 | Simplifying 1461 yields: % 82.00/47.43 | (1462) all_573_2_556 = all_557_2_532 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1441,1462) yields a new equation: % 82.00/47.43 | (1463) all_557_2_532 = all_529_2_490 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1443,1462) yields a new equation: % 82.00/47.43 | (1464) all_557_2_532 = all_527_2_487 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1434,1439) yields a new equation: % 82.00/47.43 | (1465) all_569_2_550 = all_559_2_535 % 82.00/47.43 | % 82.00/47.43 | Simplifying 1465 yields: % 82.00/47.43 | (1466) all_569_2_550 = all_559_2_535 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1436,1466) yields a new equation: % 82.00/47.43 | (1467) all_567_2_547 = all_559_2_535 % 82.00/47.43 | % 82.00/47.43 | Simplifying 1467 yields: % 82.00/47.43 | (1468) all_567_2_547 = all_559_2_535 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1438,1437) yields a new equation: % 82.00/47.43 | (1469) all_565_2_544 = all_561_2_538 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1442,1437) yields a new equation: % 82.00/47.43 | (1470) all_565_2_544 = all_529_2_490 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1435,1437) yields a new equation: % 82.00/47.43 | (1471) all_565_2_544 = all_0_5_5 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1468,1437) yields a new equation: % 82.00/47.43 | (1472) all_565_2_544 = all_559_2_535 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1470,1469) yields a new equation: % 82.00/47.43 | (1473) all_561_2_538 = all_529_2_490 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1471,1469) yields a new equation: % 82.00/47.43 | (1474) all_561_2_538 = all_0_5_5 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1472,1469) yields a new equation: % 82.00/47.43 | (1475) all_561_2_538 = all_559_2_535 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1473,1475) yields a new equation: % 82.00/47.43 | (1476) all_559_2_535 = all_529_2_490 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1474,1475) yields a new equation: % 82.00/47.43 | (1477) all_559_2_535 = all_0_5_5 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1476,1477) yields a new equation: % 82.00/47.43 | (1478) all_529_2_490 = all_0_5_5 % 82.00/47.43 | % 82.00/47.43 | Simplifying 1478 yields: % 82.00/47.43 | (1479) all_529_2_490 = all_0_5_5 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1463,1464) yields a new equation: % 82.00/47.43 | (1480) all_529_2_490 = all_527_2_487 % 82.00/47.43 | % 82.00/47.43 | Simplifying 1480 yields: % 82.00/47.43 | (1481) all_529_2_490 = all_527_2_487 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1481,1479) yields a new equation: % 82.00/47.43 | (1482) all_527_2_487 = all_0_5_5 % 82.00/47.43 | % 82.00/47.43 | Simplifying 1482 yields: % 82.00/47.43 | (1483) all_527_2_487 = all_0_5_5 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1418,1419) yields a new equation: % 82.00/47.43 | (1484) all_495_2_461 = all_121_2_96 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1428,1427) yields a new equation: % 82.00/47.43 | (1485) all_507_0_467 = all_175_0_160 % 82.00/47.43 | % 82.00/47.43 | Simplifying 1485 yields: % 82.00/47.43 | (1486) all_507_0_467 = all_175_0_160 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1415,1457) yields a new equation: % 82.00/47.43 | (1487) all_449_0_412 = id % 82.00/47.43 | % 82.00/47.43 | Simplifying 1487 yields: % 82.00/47.43 | (1488) all_449_0_412 = id % 82.00/47.43 | % 82.00/47.43 | Combining equations (1429,1486) yields a new equation: % 82.00/47.43 | (1489) all_473_0_438 = all_175_0_160 % 82.00/47.43 | % 82.00/47.43 | Simplifying 1489 yields: % 82.00/47.43 | (1490) all_473_0_438 = all_175_0_160 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1455,1488) yields a new equation: % 82.00/47.43 | (1491) all_415_0_371 = id % 82.00/47.43 | % 82.00/47.43 | Simplifying 1491 yields: % 82.00/47.43 | (1492) all_415_0_371 = id % 82.00/47.43 | % 82.00/47.43 | Combining equations (1423,1422) yields a new equation: % 82.00/47.43 | (1493) all_403_0_363 = data % 82.00/47.43 | % 82.00/47.43 | Simplifying 1493 yields: % 82.00/47.43 | (1494) all_403_0_363 = data % 82.00/47.43 | % 82.00/47.43 | Combining equations (1453,1492) yields a new equation: % 82.00/47.43 | (1495) all_365_0_330 = id % 82.00/47.43 | % 82.00/47.43 | Simplifying 1495 yields: % 82.00/47.43 | (1496) all_365_0_330 = id % 82.00/47.43 | % 82.00/47.43 | Combining equations (1444,1445) yields a new equation: % 82.00/47.43 | (1497) all_359_0_325 = id % 82.00/47.43 | % 82.00/47.43 | Combining equations (1431,1432) yields a new equation: % 82.00/47.43 | (1498) all_325_2_283 = all_121_1_95 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1484,1419) yields a new equation: % 82.00/47.43 | (1418) all_525_2_484 = all_121_2_96 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1458,1447) yields a new equation: % 82.00/47.43 | (1424) all_581_2_564 = all_121_2_96 % 82.00/47.43 | % 82.00/47.43 | Combining equations (1492,1448) yields a new equation: % 82.00/47.43 | (1501) all_591_0_569 = id % 82.00/47.43 | % 82.00/47.43 | Combining equations (1501,1411) yields a new equation: % 82.00/47.43 | (1502) all_599_0_573 = id % 82.00/47.43 | % 82.00/47.43 | Combining equations (1458,1426) yields a new equation: % 82.00/47.43 | (1503) all_615_2_587 = all_121_2_96 % 82.00/47.43 | % 82.00/47.43 | From (1479) and (1319) follows: % 82.00/47.43 | (1504) crypt(all_0_5_5, exp) = all_529_1_489 % 82.00/47.43 | % 82.00/47.43 | From (1483) and (1314) follows: % 82.00/47.43 | (1505) crypt(all_0_5_5, id) = all_527_1_486 % 82.00/47.43 | % 82.00/47.43 | From (1502) and (1389) follows: % 82.00/47.43 | (1506) xor(id, all_0_5_5) = all_0_5_5 % 82.00/47.43 | % 82.00/47.43 | From (1501) and (1380) follows: % 82.00/47.43 | (1507) xor(id, all_49_1_32) = all_49_1_32 % 82.00/47.43 | % 82.00/47.43 | From (1412) and (1377) follows: % 82.00/47.43 | (1508) xor(id, km) = km % 82.00/47.43 | % 82.00/47.43 | From (1410) and (1369) follows: % 82.00/47.43 | (1509) xor(all_193_0_162, km) = all_0_5_5 % 82.00/47.43 | % 82.00/47.43 | From (1457) and (1303) follows: % 82.00/47.43 | (1510) xor(id, all_0_4_4) = all_0_4_4 % 82.00/47.43 | % 82.00/47.43 | From (1406) and (1292) follows: % 82.00/47.43 | (1511) xor(all_193_0_162, all_0_4_4) = all_49_1_32 % 82.00/47.43 | % 82.00/47.43 | From (1406) and (1293) follows: % 82.00/47.43 | (704) xor(all_175_0_160, data) = all_193_0_162 % 82.00/47.43 | % 82.00/47.43 | From (1460) and (1263) follows: % 82.00/47.43 | (1513) xor(all_0_4_4, all_193_0_162) = all_49_1_32 % 82.00/47.43 | % 82.00/47.43 | From (1407) and (1249) follows: % 82.00/47.43 | (1514) xor(all_0_4_4, id) = all_0_4_4 % 82.00/47.43 | % 82.00/47.43 | From (1408) and (1237) follows: % 82.00/47.43 | (1515) xor(eurk, id) = eurk % 82.00/47.43 | % 82.00/47.43 | From (1484) and (1296) follows: % 82.00/47.43 | (379) xor(data, kp) = all_121_2_96 % 82.00/47.43 | % 82.00/47.43 | From (1452) and (1270) follows: % 82.00/47.43 | (700) xor(data, exp) = all_175_0_160 % 82.00/47.43 | % 82.00/47.43 | From (1494) and (1267) follows: % 82.00/47.43 | (1518) xor(data, id) = data % 82.00/47.43 | % 82.00/47.43 | From (1458) and (1221) follows: % 82.00/47.43 | (696) xor(kp, data) = all_121_2_96 % 82.00/47.43 | % 82.00/47.43 | From (1496) and (1244) follows: % 82.00/47.43 | (1520) xor(exp, id) = all_193_0_162 % 82.00/47.43 | % 82.00/47.43 | From (1490) and (1285) follows: % 82.00/47.43 | (498) xor(exp, data) = all_175_0_160 % 82.00/47.43 | % 82.00/47.43 | From (1430) and (1281) follows: % 82.00/47.43 | (1522) xor(exp, id) = exp % 82.00/47.43 | % 82.00/47.43 | From (1503) and (1403) follows: % 82.00/47.43 | (1523) xor(km, all_121_2_96) = all_615_1_586 % 82.00/47.43 | % 82.00/47.43 | From (1405) and (1396) follows: % 82.00/47.43 | (1109) xor(km, all_193_0_162) = all_0_5_5 % 82.00/47.43 | % 82.00/47.43 | From (1424) and (1374) follows: % 82.00/47.43 | (1525) xor(km, all_121_2_96) = all_581_1_563 % 82.00/47.43 | % 82.00/47.43 | From (1418) and (1311) follows: % 82.00/47.43 | (1526) xor(km, all_121_2_96) = all_525_1_483 % 82.00/47.43 | % 82.00/47.43 | From (1484) and (1297) follows: % 82.00/47.43 | (1527) xor(km, all_121_2_96) = all_495_1_460 % 82.00/47.43 | % 82.00/47.43 | From (1498) and (1228) follows: % 82.00/47.43 | (380) xor(km, all_121_2_96) = all_121_1_95 % 82.00/47.43 | % 82.00/47.43 | From (1497) and (1241) follows: % 82.00/47.44 | (1529) xor(id, id) = id % 82.00/47.44 | % 82.00/47.44 | Instantiating formula (30) with all_0_5_5, exp, all_529_1_489, all_13_0_9 and discharging atoms crypt(all_0_5_5, exp) = all_529_1_489, crypt(all_0_5_5, exp) = all_13_0_9, yields: % 82.00/47.44 | (1530) all_529_1_489 = all_13_0_9 % 82.00/47.44 | % 82.00/47.44 | Instantiating formula (30) with all_0_5_5, id, all_527_1_486, all_9_0_7 and discharging atoms crypt(all_0_5_5, id) = all_527_1_486, crypt(all_0_5_5, id) = all_9_0_7, yields: % 82.00/47.44 | (1531) all_527_1_486 = all_9_0_7 % 82.00/47.44 | % 82.00/47.44 | Instantiating formula (17) with exp, id, exp, all_193_0_162 and discharging atoms xor(exp, id) = all_193_0_162, xor(exp, id) = exp, yields: % 82.00/47.44 | (1532) all_193_0_162 = exp % 82.00/47.44 | % 82.00/47.44 | Instantiating formula (17) with km, all_121_2_96, all_581_1_563, all_121_1_95 and discharging atoms xor(km, all_121_2_96) = all_581_1_563, xor(km, all_121_2_96) = all_121_1_95, yields: % 82.00/47.44 | (1533) all_581_1_563 = all_121_1_95 % 82.00/47.44 | % 82.00/47.44 | Instantiating formula (17) with km, all_121_2_96, all_581_1_563, all_615_1_586 and discharging atoms xor(km, all_121_2_96) = all_615_1_586, xor(km, all_121_2_96) = all_581_1_563, yields: % 82.00/47.44 | (1534) all_615_1_586 = all_581_1_563 % 82.00/47.44 | % 82.00/47.44 | Instantiating formula (17) with km, all_121_2_96, all_525_1_483, all_615_1_586 and discharging atoms xor(km, all_121_2_96) = all_615_1_586, xor(km, all_121_2_96) = all_525_1_483, yields: % 82.00/47.44 | (1535) all_615_1_586 = all_525_1_483 % 82.00/47.44 | % 82.00/47.44 | Instantiating formula (17) with km, all_121_2_96, all_495_1_460, all_581_1_563 and discharging atoms xor(km, all_121_2_96) = all_581_1_563, xor(km, all_121_2_96) = all_495_1_460, yields: % 82.00/47.44 | (1536) all_581_1_563 = all_495_1_460 % 82.00/47.44 | % 82.00/47.44 | Combining equations (1534,1535) yields a new equation: % 82.00/47.44 | (1537) all_581_1_563 = all_525_1_483 % 82.00/47.44 | % 82.00/47.44 | Simplifying 1537 yields: % 82.00/47.44 | (1538) all_581_1_563 = all_525_1_483 % 82.00/47.44 | % 82.00/47.44 | Combining equations (1536,1538) yields a new equation: % 82.00/47.44 | (1539) all_525_1_483 = all_495_1_460 % 82.00/47.44 | % 82.00/47.44 | Combining equations (1533,1538) yields a new equation: % 82.00/47.44 | (1540) all_525_1_483 = all_121_1_95 % 82.00/47.44 | % 82.00/47.44 | Combining equations (1540,1539) yields a new equation: % 82.00/47.44 | (1541) all_495_1_460 = all_121_1_95 % 82.00/47.44 | % 82.00/47.44 | From (1530) and (1504) follows: % 82.00/47.44 | (67) crypt(all_0_5_5, exp) = all_13_0_9 % 82.00/47.44 | % 82.00/47.44 | From (1531) and (1505) follows: % 82.00/47.44 | (61) crypt(all_0_5_5, id) = all_9_0_7 % 82.00/47.44 | % 82.00/47.44 | From (1532) and (1511) follows: % 82.00/47.44 | (644) xor(exp, all_0_4_4) = all_49_1_32 % 82.00/47.44 | % 82.00/47.44 | From (1532) and (1252) follows: % 82.00/47.44 | (1545) xor(exp, data) = all_387_0_351 % 82.00/47.44 | % 82.00/47.44 | From (1532) and (1509) follows: % 82.00/47.44 | (45) xor(exp, km) = all_0_5_5 % 82.00/47.44 | % 82.00/47.44 | From (1532) and (704) follows: % 82.00/47.44 | (1547) xor(all_175_0_160, data) = exp % 82.00/47.44 | % 82.00/47.44 | From (1532) and (1513) follows: % 82.00/47.44 | (1069) xor(all_0_4_4, exp) = all_49_1_32 % 82.00/47.44 | % 82.00/47.44 | From (1532) and (1399) follows: % 82.00/47.44 | (1549) xor(data, exp) = all_613_0_584 % 82.00/47.44 | % 82.00/47.44 | From (1532) and (1520) follows: % 82.00/47.44 | (1522) xor(exp, id) = exp % 82.00/47.44 | % 82.00/47.44 | From (1532) and (1109) follows: % 82.00/47.44 | (42) xor(km, exp) = all_0_5_5 % 82.00/47.44 | % 82.00/47.44 | From (1541) and (1527) follows: % 82.00/47.44 | (380) xor(km, all_121_2_96) = all_121_1_95 % 82.00/47.44 | % 82.00/47.44 | From (1532) and (1247) follows: % 82.00/47.44 | (1553) xor(id, exp) = all_367_0_331 % 82.00/47.44 | % 82.00/47.44 | From (1532) and (1215) follows: % 82.00/47.44 | (25) p(exp) % 82.00/47.44 | % 82.00/47.44 | Instantiating formula (17) with data, exp, all_613_0_584, all_175_0_160 and discharging atoms xor(data, exp) = all_613_0_584, xor(data, exp) = all_175_0_160, yields: % 82.00/47.44 | (1555) all_613_0_584 = all_175_0_160 % 82.00/47.44 | % 82.00/47.44 | Instantiating formula (17) with exp, data, all_387_0_351, all_175_0_160 and discharging atoms xor(exp, data) = all_387_0_351, xor(exp, data) = all_175_0_160, yields: % 82.00/47.44 | (1556) all_387_0_351 = all_175_0_160 % 82.00/47.44 | % 82.00/47.44 | Instantiating formula (17) with id, exp, all_367_0_331, all_601_0_574 and discharging atoms xor(id, exp) = all_601_0_574, xor(id, exp) = all_367_0_331, yields: % 82.00/47.44 | (1557) all_601_0_574 = all_367_0_331 % 82.00/47.44 | % 82.00/47.44 | From (1555) and (1549) follows: % 82.00/47.44 | (700) xor(data, exp) = all_175_0_160 % 82.00/47.44 | % 82.00/47.44 | From (1556) and (1545) follows: % 82.00/47.44 | (498) xor(exp, data) = all_175_0_160 % 82.00/47.44 | % 82.00/47.44 | From (1557) and (1393) follows: % 82.00/47.44 | (1553) xor(id, exp) = all_367_0_331 % 82.00/47.44 | % 82.00/47.44 +-Applying beta-rule and splitting (358), into two cases. % 82.00/47.44 |-Branch one: % 82.00/47.44 | (1561) ~ p(all_111_0_81) % 82.00/47.44 | % 82.00/47.44 +-Applying beta-rule and splitting (676), into two cases. % 82.00/47.44 |-Branch one: % 82.00/47.44 | (1562) p(all_111_0_81) % 82.00/47.44 | % 82.00/47.44 | Using (1562) and (1561) yields: % 82.00/47.44 | (1563) $false % 82.00/47.44 | % 82.00/47.44 |-The branch is then unsatisfiable % 82.00/47.44 |-Branch two: % 82.00/47.44 | (1561) ~ p(all_111_0_81) % 82.00/47.44 | (1565) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, km) = v2 & xor(exp, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 82.00/47.44 | % 82.00/47.44 | Instantiating (1565) with all_643_0_588, all_643_1_589, all_643_2_590 yields: % 82.00/47.44 | (1566) crypt(all_643_1_589, km) = all_643_0_588 & xor(exp, kp) = all_643_2_590 & xor(km, all_643_2_590) = all_643_1_589 & ~ p(all_643_0_588) % 82.00/47.44 | % 82.00/47.44 | Applying alpha-rule on (1566) yields: % 82.00/47.44 | (1567) crypt(all_643_1_589, km) = all_643_0_588 % 82.00/47.44 | (1568) xor(exp, kp) = all_643_2_590 % 82.00/47.44 | (1569) xor(km, all_643_2_590) = all_643_1_589 % 82.00/47.44 | (1570) ~ p(all_643_0_588) % 82.00/47.44 | % 82.00/47.44 +-Applying beta-rule and splitting (677), into two cases. % 82.00/47.44 |-Branch one: % 82.00/47.44 | (1562) p(all_111_0_81) % 82.00/47.44 | % 82.00/47.44 | Using (1562) and (1561) yields: % 82.00/47.44 | (1563) $false % 82.00/47.44 | % 82.00/47.44 |-The branch is then unsatisfiable % 82.00/47.44 |-Branch two: % 82.00/47.44 | (1561) ~ p(all_111_0_81) % 82.00/47.44 | (1574) ? [v0] : ? [v1] : (crypt(v0, all_0_5_5) = v1 & xor(all_0_5_5, data) = v0 & ~ p(v1)) % 82.00/47.44 | % 82.00/47.44 +-Applying beta-rule and splitting (1187), into two cases. % 82.00/47.44 |-Branch one: % 82.00/47.44 | (1562) p(all_111_0_81) % 82.00/47.44 | % 82.00/47.44 | Using (1562) and (1561) yields: % 82.00/47.44 | (1563) $false % 82.00/47.44 | % 82.00/47.44 |-The branch is then unsatisfiable % 82.00/47.44 |-Branch two: % 82.00/47.44 | (1561) ~ p(all_111_0_81) % 82.00/47.44 | (1578) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, all_0_5_5) = v2 & xor(exp, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 82.00/47.44 | % 82.00/47.44 | Instantiating (1578) with all_653_0_593, all_653_1_594, all_653_2_595 yields: % 82.00/47.44 | (1579) crypt(all_653_1_594, all_0_5_5) = all_653_0_593 & xor(exp, kp) = all_653_2_595 & xor(km, all_653_2_595) = all_653_1_594 & ~ p(all_653_0_593) % 82.00/47.44 | % 82.00/47.44 | Applying alpha-rule on (1579) yields: % 82.00/47.44 | (1580) crypt(all_653_1_594, all_0_5_5) = all_653_0_593 % 82.00/47.44 | (1581) xor(exp, kp) = all_653_2_595 % 82.00/47.44 | (1582) xor(km, all_653_2_595) = all_653_1_594 % 82.00/47.44 | (1583) ~ p(all_653_0_593) % 82.00/47.44 | % 82.00/47.44 +-Applying beta-rule and splitting (1167), into two cases. % 82.00/47.44 |-Branch one: % 82.00/47.44 | (1562) p(all_111_0_81) % 82.00/47.44 | % 82.00/47.44 | Using (1562) and (1561) yields: % 82.00/47.44 | (1563) $false % 82.00/47.44 | % 82.00/47.44 |-The branch is then unsatisfiable % 82.00/47.44 |-Branch two: % 82.00/47.44 | (1561) ~ p(all_111_0_81) % 82.00/47.44 | (1587) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, all_49_1_32) = v2 & xor(exp, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 82.00/47.44 | % 82.00/47.44 | Instantiating (1587) with all_658_0_596, all_658_1_597, all_658_2_598 yields: % 82.00/47.44 | (1588) crypt(all_658_1_597, all_49_1_32) = all_658_0_596 & xor(exp, kp) = all_658_2_598 & xor(km, all_658_2_598) = all_658_1_597 & ~ p(all_658_0_596) % 82.00/47.44 | % 82.00/47.44 | Applying alpha-rule on (1588) yields: % 82.00/47.44 | (1589) crypt(all_658_1_597, all_49_1_32) = all_658_0_596 % 82.00/47.45 | (1590) xor(exp, kp) = all_658_2_598 % 82.00/47.45 | (1591) xor(km, all_658_2_598) = all_658_1_597 % 82.00/47.45 | (1592) ~ p(all_658_0_596) % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (17) with exp, kp, all_653_2_595, all_475_2_441 and discharging atoms xor(exp, kp) = all_653_2_595, xor(exp, kp) = all_475_2_441, yields: % 82.00/47.45 | (1593) all_653_2_595 = all_475_2_441 % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (17) with exp, kp, all_653_2_595, all_658_2_598 and discharging atoms xor(exp, kp) = all_658_2_598, xor(exp, kp) = all_653_2_595, yields: % 82.00/47.45 | (1594) all_658_2_598 = all_653_2_595 % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (17) with exp, kp, all_643_2_590, all_658_2_598 and discharging atoms xor(exp, kp) = all_658_2_598, xor(exp, kp) = all_643_2_590, yields: % 82.00/47.45 | (1595) all_658_2_598 = all_643_2_590 % 82.00/47.45 | % 82.00/47.45 | Combining equations (1594,1595) yields a new equation: % 82.00/47.45 | (1596) all_653_2_595 = all_643_2_590 % 82.00/47.45 | % 82.00/47.45 | Simplifying 1596 yields: % 82.00/47.45 | (1597) all_653_2_595 = all_643_2_590 % 82.00/47.45 | % 82.00/47.45 | Combining equations (1593,1597) yields a new equation: % 82.00/47.45 | (1598) all_643_2_590 = all_475_2_441 % 82.00/47.45 | % 82.00/47.45 | Combining equations (1598,1597) yields a new equation: % 82.00/47.45 | (1593) all_653_2_595 = all_475_2_441 % 82.00/47.45 | % 82.00/47.45 | Combining equations (1598,1595) yields a new equation: % 82.00/47.45 | (1600) all_658_2_598 = all_475_2_441 % 82.00/47.45 | % 82.00/47.45 | From (1598) and (1568) follows: % 82.00/47.45 | (1288) xor(exp, kp) = all_475_2_441 % 82.00/47.45 | % 82.00/47.45 | From (1600) and (1591) follows: % 82.00/47.45 | (1602) xor(km, all_475_2_441) = all_658_1_597 % 82.00/47.45 | % 82.00/47.45 | From (1593) and (1582) follows: % 82.00/47.45 | (1603) xor(km, all_475_2_441) = all_653_1_594 % 82.00/47.45 | % 82.00/47.45 | From (1598) and (1569) follows: % 82.00/47.45 | (1604) xor(km, all_475_2_441) = all_643_1_589 % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (17) with km, all_475_2_441, all_658_1_597, all_475_1_440 and discharging atoms xor(km, all_475_2_441) = all_658_1_597, xor(km, all_475_2_441) = all_475_1_440, yields: % 82.00/47.45 | (1605) all_658_1_597 = all_475_1_440 % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (17) with km, all_475_2_441, all_653_1_594, all_658_1_597 and discharging atoms xor(km, all_475_2_441) = all_658_1_597, xor(km, all_475_2_441) = all_653_1_594, yields: % 82.00/47.45 | (1606) all_658_1_597 = all_653_1_594 % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (17) with km, all_475_2_441, all_643_1_589, all_658_1_597 and discharging atoms xor(km, all_475_2_441) = all_658_1_597, xor(km, all_475_2_441) = all_643_1_589, yields: % 82.00/47.45 | (1607) all_658_1_597 = all_643_1_589 % 82.00/47.45 | % 82.00/47.45 | Combining equations (1607,1606) yields a new equation: % 82.00/47.45 | (1608) all_653_1_594 = all_643_1_589 % 82.00/47.45 | % 82.00/47.45 | Combining equations (1605,1606) yields a new equation: % 82.00/47.45 | (1609) all_653_1_594 = all_475_1_440 % 82.00/47.45 | % 82.00/47.45 | Combining equations (1608,1609) yields a new equation: % 82.00/47.45 | (1610) all_643_1_589 = all_475_1_440 % 82.00/47.45 | % 82.00/47.45 | Simplifying 1610 yields: % 82.00/47.45 | (1611) all_643_1_589 = all_475_1_440 % 82.00/47.45 | % 82.00/47.45 | Combining equations (1609,1606) yields a new equation: % 82.00/47.45 | (1605) all_658_1_597 = all_475_1_440 % 82.00/47.45 | % 82.00/47.45 | From (1605) and (1589) follows: % 82.00/47.45 | (1613) crypt(all_475_1_440, all_49_1_32) = all_658_0_596 % 82.00/47.45 | % 82.00/47.45 | From (1609) and (1580) follows: % 82.00/47.45 | (1614) crypt(all_475_1_440, all_0_5_5) = all_653_0_593 % 82.00/47.45 | % 82.00/47.45 | From (1611) and (1567) follows: % 82.00/47.45 | (1615) crypt(all_475_1_440, km) = all_643_0_588 % 82.00/47.45 | % 82.00/47.45 | From (1611) and (1604) follows: % 82.00/47.45 | (1289) xor(km, all_475_2_441) = all_475_1_440 % 82.00/47.45 | % 82.00/47.45 +-Applying beta-rule and splitting (673), into two cases. % 82.00/47.45 |-Branch one: % 82.00/47.45 | (1617) p(all_111_1_82) % 82.00/47.45 | % 82.00/47.45 +-Applying beta-rule and splitting (732), into two cases. % 82.00/47.45 |-Branch one: % 82.00/47.45 | (1618) ~ p(all_207_0_173) % 82.00/47.45 | % 82.00/47.45 | From (1032) and (1618) follows: % 82.00/47.45 | (1619) ~ p(all_197_0_164) % 82.00/47.45 | % 82.00/47.45 +-Applying beta-rule and splitting (1185), into two cases. % 82.00/47.45 |-Branch one: % 82.00/47.45 | (1620) p(all_197_0_164) % 82.00/47.45 | % 82.00/47.45 | Using (1620) and (1619) yields: % 82.00/47.45 | (1563) $false % 82.00/47.45 | % 82.00/47.45 |-The branch is then unsatisfiable % 82.00/47.45 |-Branch two: % 82.00/47.45 | (1619) ~ p(all_197_0_164) % 82.00/47.45 | (1623) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, all_0_4_4) = v2 & xor(exp, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 82.00/47.45 | % 82.00/47.45 | Instantiating (1623) with all_712_0_1729, all_712_1_1730, all_712_2_1731 yields: % 82.00/47.45 | (1624) crypt(all_712_1_1730, all_0_4_4) = all_712_0_1729 & xor(exp, kp) = all_712_2_1731 & xor(km, all_712_2_1731) = all_712_1_1730 & ~ p(all_712_0_1729) % 82.00/47.45 | % 82.00/47.45 | Applying alpha-rule on (1624) yields: % 82.00/47.45 | (1625) crypt(all_712_1_1730, all_0_4_4) = all_712_0_1729 % 82.00/47.45 | (1626) xor(exp, kp) = all_712_2_1731 % 82.00/47.45 | (1627) xor(km, all_712_2_1731) = all_712_1_1730 % 82.00/47.45 | (1628) ~ p(all_712_0_1729) % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (17) with exp, kp, all_712_2_1731, all_475_2_441 and discharging atoms xor(exp, kp) = all_712_2_1731, xor(exp, kp) = all_475_2_441, yields: % 82.00/47.45 | (1629) all_712_2_1731 = all_475_2_441 % 82.00/47.45 | % 82.00/47.45 | From (1629) and (1626) follows: % 82.00/47.45 | (1288) xor(exp, kp) = all_475_2_441 % 82.00/47.45 | % 82.00/47.45 | From (1629) and (1627) follows: % 82.00/47.45 | (1631) xor(km, all_475_2_441) = all_712_1_1730 % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (17) with km, all_475_2_441, all_712_1_1730, all_475_1_440 and discharging atoms xor(km, all_475_2_441) = all_712_1_1730, xor(km, all_475_2_441) = all_475_1_440, yields: % 82.00/47.45 | (1632) all_712_1_1730 = all_475_1_440 % 82.00/47.45 | % 82.00/47.45 | From (1632) and (1625) follows: % 82.00/47.45 | (1633) crypt(all_475_1_440, all_0_4_4) = all_712_0_1729 % 82.00/47.45 | % 82.00/47.45 | From (1632) and (1631) follows: % 82.00/47.45 | (1289) xor(km, all_475_2_441) = all_475_1_440 % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (21) with all_321_0_277, all_121_2_96, all_0_5_5, kp, exp, data and discharging atoms crypt(all_0_5_5, all_121_2_96) = all_321_0_277, xor(kp, data) = all_121_2_96, xor(km, exp) = all_0_5_5, p(data), p(exp), ~ p(all_321_0_277), yields: % 82.00/47.45 | (1635) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, kp) = v2 & xor(exp, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (21) with all_13_0_9, exp, all_0_5_5, all_175_0_160, exp, data and discharging atoms crypt(all_0_5_5, exp) = all_13_0_9, xor(all_175_0_160, data) = exp, xor(km, exp) = all_0_5_5, p(data), p(exp), ~ p(all_13_0_9), yields: % 82.00/47.45 | (1636) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, all_175_0_160) = v2 & xor(exp, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (15) with all_393_2_358, all_175_0_160, kp, exp, data and discharging atoms xor(all_175_0_160, kp) = all_393_2_358, xor(data, exp) = all_175_0_160, yields: % 82.00/47.45 | (1637) ? [v0] : (xor(data, v0) = all_393_2_358 & xor(exp, kp) = v0) % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (15) with all_49_1_32, all_0_4_4, exp, id, all_0_4_4 and discharging atoms xor(all_0_4_4, exp) = all_49_1_32, xor(all_0_4_4, id) = all_0_4_4, yields: % 82.00/47.45 | (1638) ? [v0] : (xor(all_0_4_4, v0) = all_49_1_32 & xor(id, exp) = v0) % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (15) with all_15_1_11, eurk, exp, id, eurk and discharging atoms xor(eurk, exp) = all_15_1_11, xor(eurk, id) = eurk, yields: % 82.00/47.45 | (1639) ? [v0] : (xor(eurk, v0) = all_15_1_11 & xor(id, exp) = v0) % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (15) with all_175_0_160, data, exp, id, data and discharging atoms xor(data, exp) = all_175_0_160, xor(data, id) = data, yields: % 82.00/47.45 | (1640) ? [v0] : (xor(data, v0) = all_175_0_160 & xor(id, exp) = v0) % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (35) with all_475_2_441, exp, kp and discharging atoms xor(exp, kp) = all_475_2_441, yields: % 82.00/47.45 | (1641) xor(kp, exp) = all_475_2_441 % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (21) with all_13_0_9, exp, all_0_5_5, exp, exp, id and discharging atoms crypt(all_0_5_5, exp) = all_13_0_9, xor(exp, id) = exp, xor(km, exp) = all_0_5_5, p(exp), p(id), ~ p(all_13_0_9), yields: % 82.00/47.45 | (1642) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, exp) = v2 & xor(exp, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (35) with exp, exp, id and discharging atoms xor(exp, id) = exp, yields: % 82.00/47.45 | (1643) xor(id, exp) = exp % 82.00/47.45 | % 82.00/47.45 | Instantiating formula (36) with all_475_0_439, data, all_475_1_440, all_475_2_441, id, exp, data and discharging atoms crypt(all_475_1_440, data) = all_475_0_439, xor(data, id) = data, xor(exp, kp) = all_475_2_441, xor(km, all_475_2_441) = all_475_1_440, p(data), p(exp), ~ p(all_475_0_439), yields: % 82.00/47.45 | (1644) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, id) = v2 & xor(kp, exp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 82.00/47.46 | % 82.00/47.46 | Instantiating formula (12) with all_593_0_570, all_175_0_160, data, exp, id and discharging atoms xor(exp, data) = all_175_0_160, xor(id, all_175_0_160) = all_593_0_570, yields: % 82.00/47.46 | (1645) ? [v0] : (xor(v0, data) = all_593_0_570 & xor(id, exp) = v0) % 82.00/47.46 | % 82.00/47.46 | Instantiating formula (36) with all_658_0_596, all_49_1_32, all_475_1_440, all_475_2_441, all_49_1_32, exp, id and discharging atoms crypt(all_475_1_440, all_49_1_32) = all_658_0_596, xor(exp, kp) = all_475_2_441, xor(km, all_475_2_441) = all_475_1_440, xor(id, all_49_1_32) = all_49_1_32, p(exp), p(id), ~ p(all_658_0_596), yields: % 82.00/47.46 | (1646) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, all_49_1_32) = v2 & xor(kp, exp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 82.00/47.46 | % 82.00/47.46 | Instantiating formula (12) with all_49_1_32, all_49_1_32, all_0_4_4, exp, id and discharging atoms xor(exp, all_0_4_4) = all_49_1_32, xor(id, all_49_1_32) = all_49_1_32, yields: % 82.00/47.46 | (1647) ? [v0] : (xor(v0, all_0_4_4) = all_49_1_32 & xor(id, exp) = v0) % 82.00/47.46 | % 82.00/47.46 | Instantiating formula (36) with all_712_0_1729, all_0_4_4, all_475_1_440, all_475_2_441, all_0_4_4, exp, id and discharging atoms crypt(all_475_1_440, all_0_4_4) = all_712_0_1729, xor(exp, kp) = all_475_2_441, xor(km, all_475_2_441) = all_475_1_440, xor(id, all_0_4_4) = all_0_4_4, p(exp), p(id), ~ p(all_712_0_1729), yields: % 82.00/47.46 | (1648) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, all_0_4_4) = v2 & xor(kp, exp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 82.00/47.46 | % 82.00/47.46 | Instantiating formula (36) with all_653_0_593, all_0_5_5, all_475_1_440, all_475_2_441, all_0_5_5, exp, id and discharging atoms crypt(all_475_1_440, all_0_5_5) = all_653_0_593, xor(exp, kp) = all_475_2_441, xor(km, all_475_2_441) = all_475_1_440, xor(id, all_0_5_5) = all_0_5_5, p(exp), p(id), ~ p(all_653_0_593), yields: % 82.00/47.46 | (1649) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, all_0_5_5) = v2 & xor(kp, exp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 82.00/47.46 | % 82.00/47.46 | Instantiating formula (12) with all_0_5_5, all_0_5_5, km, exp, id and discharging atoms xor(exp, km) = all_0_5_5, xor(id, all_0_5_5) = all_0_5_5, yields: % 82.00/47.46 | (1650) ? [v0] : (xor(v0, km) = all_0_5_5 & xor(id, exp) = v0) % 82.00/47.46 | % 82.00/47.46 | Instantiating formula (12) with all_367_0_331, exp, id, exp, id and discharging atoms xor(exp, id) = exp, xor(id, exp) = all_367_0_331, yields: % 82.00/47.46 | (1651) ? [v0] : (xor(v0, id) = all_367_0_331 & xor(id, exp) = v0) % 82.00/47.46 | % 82.00/47.46 | Instantiating formula (6) with all_367_0_331, exp, id and discharging atoms xor(id, exp) = all_367_0_331, p(exp), p(id), yields: % 82.00/47.46 | (1652) p(all_367_0_331) % 82.00/47.46 | % 82.00/47.46 | Instantiating formula (36) with all_643_0_588, km, all_475_1_440, all_475_2_441, km, exp, id and discharging atoms crypt(all_475_1_440, km) = all_643_0_588, xor(exp, kp) = all_475_2_441, xor(km, all_475_2_441) = all_475_1_440, xor(id, km) = km, p(exp), p(id), ~ p(all_643_0_588), yields: % 82.00/47.46 | (1653) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, km) = v2 & xor(kp, exp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 82.00/47.46 | % 82.00/47.46 | Instantiating formula (15) with all_475_1_440, km, all_475_2_441, km, id and discharging atoms xor(km, all_475_2_441) = all_475_1_440, xor(id, km) = km, yields: % 82.00/47.46 | (1654) ? [v0] : (xor(km, all_475_2_441) = v0 & xor(id, v0) = all_475_1_440) % 82.00/47.46 | % 82.00/47.46 | Instantiating formula (21) with all_9_0_7, id, all_0_5_5, id, exp, id and discharging atoms crypt(all_0_5_5, id) = all_9_0_7, xor(km, exp) = all_0_5_5, xor(id, id) = id, p(exp), p(id), ~ p(all_9_0_7), yields: % 82.00/47.46 | (1655) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, id) = v2 & xor(exp, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 82.00/47.46 | % 82.00/47.46 | Instantiating formula (15) with all_367_0_331, id, exp, id, id and discharging atoms xor(id, exp) = all_367_0_331, xor(id, id) = id, yields: % 82.00/47.46 | (1656) ? [v0] : (xor(id, v0) = all_367_0_331 & xor(id, exp) = v0) % 82.00/47.46 | % 82.00/47.46 | Instantiating (1640) with all_813_0_1761 yields: % 82.00/47.46 | (1657) xor(data, all_813_0_1761) = all_175_0_160 & xor(id, exp) = all_813_0_1761 % 82.00/47.46 | % 82.00/47.46 | Applying alpha-rule on (1657) yields: % 82.00/47.46 | (1658) xor(data, all_813_0_1761) = all_175_0_160 % 82.00/47.46 | (1659) xor(id, exp) = all_813_0_1761 % 82.00/47.46 | % 82.00/47.46 | Instantiating (1642) with all_857_0_1791, all_857_1_1792, all_857_2_1793 yields: % 82.00/47.46 | (1660) crypt(all_857_1_1792, exp) = all_857_0_1791 & xor(exp, kp) = all_857_2_1793 & xor(km, all_857_2_1793) = all_857_1_1792 & ~ p(all_857_0_1791) % 82.00/47.46 | % 82.00/47.46 | Applying alpha-rule on (1660) yields: % 82.00/47.46 | (1661) crypt(all_857_1_1792, exp) = all_857_0_1791 % 82.00/47.46 | (1662) xor(exp, kp) = all_857_2_1793 % 82.00/47.46 | (1663) xor(km, all_857_2_1793) = all_857_1_1792 % 82.00/47.46 | (1664) ~ p(all_857_0_1791) % 82.00/47.46 | % 82.00/47.46 | Instantiating (1637) with all_907_0_1830 yields: % 82.00/47.46 | (1665) xor(data, all_907_0_1830) = all_393_2_358 & xor(exp, kp) = all_907_0_1830 % 82.00/47.46 | % 82.00/47.46 | Applying alpha-rule on (1665) yields: % 82.00/47.46 | (1666) xor(data, all_907_0_1830) = all_393_2_358 % 82.00/47.46 | (1667) xor(exp, kp) = all_907_0_1830 % 82.00/47.46 | % 82.00/47.46 | Instantiating (1639) with all_951_0_1852 yields: % 82.00/47.46 | (1668) xor(eurk, all_951_0_1852) = all_15_1_11 & xor(id, exp) = all_951_0_1852 % 82.00/47.46 | % 82.00/47.46 | Applying alpha-rule on (1668) yields: % 82.00/47.46 | (1669) xor(eurk, all_951_0_1852) = all_15_1_11 % 82.00/47.46 | (1670) xor(id, exp) = all_951_0_1852 % 82.00/47.46 | % 82.00/47.46 | Instantiating (1638) with all_1059_0_1908 yields: % 82.00/47.46 | (1671) xor(all_0_4_4, all_1059_0_1908) = all_49_1_32 & xor(id, exp) = all_1059_0_1908 % 82.00/47.46 | % 82.00/47.46 | Applying alpha-rule on (1671) yields: % 82.00/47.46 | (1672) xor(all_0_4_4, all_1059_0_1908) = all_49_1_32 % 82.00/47.46 | (1673) xor(id, exp) = all_1059_0_1908 % 82.00/47.46 | % 82.00/47.46 | Instantiating (1645) with all_1067_0_1912 yields: % 82.00/47.46 | (1674) xor(all_1067_0_1912, data) = all_593_0_570 & xor(id, exp) = all_1067_0_1912 % 82.00/47.46 | % 82.00/47.46 | Applying alpha-rule on (1674) yields: % 82.00/47.46 | (1675) xor(all_1067_0_1912, data) = all_593_0_570 % 82.00/47.46 | (1676) xor(id, exp) = all_1067_0_1912 % 82.00/47.46 | % 82.00/47.46 | Instantiating (1651) with all_1129_0_1943 yields: % 82.00/47.46 | (1677) xor(all_1129_0_1943, id) = all_367_0_331 & xor(id, exp) = all_1129_0_1943 % 82.00/47.46 | % 82.00/47.46 | Applying alpha-rule on (1677) yields: % 82.00/47.46 | (1678) xor(all_1129_0_1943, id) = all_367_0_331 % 82.00/47.46 | (1679) xor(id, exp) = all_1129_0_1943 % 82.00/47.46 | % 82.00/47.46 | Instantiating (1647) with all_1173_0_1969 yields: % 82.00/47.46 | (1680) xor(all_1173_0_1969, all_0_4_4) = all_49_1_32 & xor(id, exp) = all_1173_0_1969 % 82.00/47.46 | % 82.00/47.46 | Applying alpha-rule on (1680) yields: % 82.00/47.46 | (1681) xor(all_1173_0_1969, all_0_4_4) = all_49_1_32 % 82.00/47.46 | (1682) xor(id, exp) = all_1173_0_1969 % 82.00/47.46 | % 82.00/47.46 | Instantiating (1650) with all_1289_0_2063 yields: % 82.00/47.46 | (1683) xor(all_1289_0_2063, km) = all_0_5_5 & xor(id, exp) = all_1289_0_2063 % 82.00/47.46 | % 82.00/47.46 | Applying alpha-rule on (1683) yields: % 82.00/47.46 | (1684) xor(all_1289_0_2063, km) = all_0_5_5 % 82.00/47.46 | (1685) xor(id, exp) = all_1289_0_2063 % 82.00/47.46 | % 82.00/47.46 | Instantiating (1656) with all_1317_0_2077 yields: % 82.00/47.46 | (1686) xor(id, all_1317_0_2077) = all_367_0_331 & xor(id, exp) = all_1317_0_2077 % 82.00/47.46 | % 82.00/47.46 | Applying alpha-rule on (1686) yields: % 82.00/47.46 | (1687) xor(id, all_1317_0_2077) = all_367_0_331 % 82.00/47.46 | (1688) xor(id, exp) = all_1317_0_2077 % 82.00/47.46 | % 82.00/47.46 | Instantiating (1655) with all_1325_0_2081, all_1325_1_2082, all_1325_2_2083 yields: % 82.00/47.46 | (1689) crypt(all_1325_1_2082, id) = all_1325_0_2081 & xor(exp, kp) = all_1325_2_2083 & xor(km, all_1325_2_2083) = all_1325_1_2082 & ~ p(all_1325_0_2081) % 82.00/47.46 | % 82.00/47.46 | Applying alpha-rule on (1689) yields: % 82.00/47.46 | (1690) crypt(all_1325_1_2082, id) = all_1325_0_2081 % 82.00/47.46 | (1691) xor(exp, kp) = all_1325_2_2083 % 82.00/47.46 | (1692) xor(km, all_1325_2_2083) = all_1325_1_2082 % 82.00/47.46 | (1693) ~ p(all_1325_0_2081) % 82.00/47.46 | % 82.00/47.46 | Instantiating (1635) with all_1353_0_2105, all_1353_1_2106, all_1353_2_2107 yields: % 82.00/47.46 | (1694) crypt(all_1353_1_2106, kp) = all_1353_0_2105 & xor(exp, kp) = all_1353_2_2107 & xor(km, all_1353_2_2107) = all_1353_1_2106 & ~ p(all_1353_0_2105) % 82.00/47.46 | % 82.00/47.46 | Applying alpha-rule on (1694) yields: % 82.00/47.46 | (1695) crypt(all_1353_1_2106, kp) = all_1353_0_2105 % 82.00/47.46 | (1696) xor(exp, kp) = all_1353_2_2107 % 82.00/47.46 | (1697) xor(km, all_1353_2_2107) = all_1353_1_2106 % 82.00/47.46 | (1698) ~ p(all_1353_0_2105) % 82.00/47.46 | % 82.00/47.46 | Instantiating (1644) with all_1431_0_2190, all_1431_1_2191, all_1431_2_2192 yields: % 82.00/47.46 | (1699) crypt(all_1431_1_2191, id) = all_1431_0_2190 & xor(kp, exp) = all_1431_2_2192 & xor(km, all_1431_2_2192) = all_1431_1_2191 & ~ p(all_1431_0_2190) % 82.00/47.46 | % 82.00/47.46 | Applying alpha-rule on (1699) yields: % 82.00/47.46 | (1700) crypt(all_1431_1_2191, id) = all_1431_0_2190 % 82.00/47.46 | (1701) xor(kp, exp) = all_1431_2_2192 % 82.00/47.46 | (1702) xor(km, all_1431_2_2192) = all_1431_1_2191 % 82.00/47.46 | (1703) ~ p(all_1431_0_2190) % 82.00/47.46 | % 82.00/47.46 | Instantiating (1654) with all_1449_0_2201 yields: % 82.00/47.46 | (1704) xor(km, all_475_2_441) = all_1449_0_2201 & xor(id, all_1449_0_2201) = all_475_1_440 % 82.00/47.47 | % 82.00/47.47 | Applying alpha-rule on (1704) yields: % 82.00/47.47 | (1705) xor(km, all_475_2_441) = all_1449_0_2201 % 82.00/47.47 | (1706) xor(id, all_1449_0_2201) = all_475_1_440 % 82.00/47.47 | % 82.00/47.47 | Instantiating (1649) with all_1467_0_2210, all_1467_1_2211, all_1467_2_2212 yields: % 82.00/47.47 | (1707) crypt(all_1467_1_2211, all_0_5_5) = all_1467_0_2210 & xor(kp, exp) = all_1467_2_2212 & xor(km, all_1467_2_2212) = all_1467_1_2211 & ~ p(all_1467_0_2210) % 82.00/47.47 | % 82.00/47.47 | Applying alpha-rule on (1707) yields: % 82.00/47.47 | (1708) crypt(all_1467_1_2211, all_0_5_5) = all_1467_0_2210 % 82.00/47.47 | (1709) xor(kp, exp) = all_1467_2_2212 % 82.00/47.47 | (1710) xor(km, all_1467_2_2212) = all_1467_1_2211 % 82.00/47.47 | (1711) ~ p(all_1467_0_2210) % 82.00/47.47 | % 82.00/47.47 | Instantiating (1653) with all_1469_0_2213, all_1469_1_2214, all_1469_2_2215 yields: % 82.00/47.47 | (1712) crypt(all_1469_1_2214, km) = all_1469_0_2213 & xor(kp, exp) = all_1469_2_2215 & xor(km, all_1469_2_2215) = all_1469_1_2214 & ~ p(all_1469_0_2213) % 82.00/47.47 | % 82.00/47.47 | Applying alpha-rule on (1712) yields: % 82.00/47.47 | (1713) crypt(all_1469_1_2214, km) = all_1469_0_2213 % 82.00/47.47 | (1714) xor(kp, exp) = all_1469_2_2215 % 82.00/47.47 | (1715) xor(km, all_1469_2_2215) = all_1469_1_2214 % 82.00/47.47 | (1716) ~ p(all_1469_0_2213) % 82.00/47.47 | % 82.00/47.47 | Instantiating (1646) with all_1505_0_2241, all_1505_1_2242, all_1505_2_2243 yields: % 82.00/47.47 | (1717) crypt(all_1505_1_2242, all_49_1_32) = all_1505_0_2241 & xor(kp, exp) = all_1505_2_2243 & xor(km, all_1505_2_2243) = all_1505_1_2242 & ~ p(all_1505_0_2241) % 82.00/47.47 | % 82.00/47.47 | Applying alpha-rule on (1717) yields: % 82.00/47.47 | (1718) crypt(all_1505_1_2242, all_49_1_32) = all_1505_0_2241 % 82.00/47.47 | (1719) xor(kp, exp) = all_1505_2_2243 % 82.00/47.47 | (1720) xor(km, all_1505_2_2243) = all_1505_1_2242 % 82.00/47.47 | (1721) ~ p(all_1505_0_2241) % 82.00/47.47 | % 82.00/47.47 | Instantiating (1648) with all_1509_0_2245, all_1509_1_2246, all_1509_2_2247 yields: % 82.00/47.47 | (1722) crypt(all_1509_1_2246, all_0_4_4) = all_1509_0_2245 & xor(kp, exp) = all_1509_2_2247 & xor(km, all_1509_2_2247) = all_1509_1_2246 & ~ p(all_1509_0_2245) % 82.00/47.47 | % 82.00/47.47 | Applying alpha-rule on (1722) yields: % 82.00/47.47 | (1723) crypt(all_1509_1_2246, all_0_4_4) = all_1509_0_2245 % 82.00/47.47 | (1724) xor(kp, exp) = all_1509_2_2247 % 82.00/47.47 | (1725) xor(km, all_1509_2_2247) = all_1509_1_2246 % 82.00/47.47 | (1726) ~ p(all_1509_0_2245) % 82.00/47.47 | % 82.00/47.47 | Instantiating (1636) with all_1531_0_2260, all_1531_1_2261, all_1531_2_2262 yields: % 82.00/47.47 | (1727) crypt(all_1531_1_2261, all_175_0_160) = all_1531_0_2260 & xor(exp, kp) = all_1531_2_2262 & xor(km, all_1531_2_2262) = all_1531_1_2261 & ~ p(all_1531_0_2260) % 82.00/47.47 | % 82.00/47.47 | Applying alpha-rule on (1727) yields: % 82.00/47.47 | (1728) crypt(all_1531_1_2261, all_175_0_160) = all_1531_0_2260 % 82.00/47.47 | (1729) xor(exp, kp) = all_1531_2_2262 % 82.00/47.47 | (1730) xor(km, all_1531_2_2262) = all_1531_1_2261 % 82.00/47.47 | (1731) ~ p(all_1531_0_2260) % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with kp, exp, all_1505_2_2243, all_1509_2_2247 and discharging atoms xor(kp, exp) = all_1509_2_2247, xor(kp, exp) = all_1505_2_2243, yields: % 82.00/47.47 | (1732) all_1509_2_2247 = all_1505_2_2243 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with kp, exp, all_1469_2_2215, all_1509_2_2247 and discharging atoms xor(kp, exp) = all_1509_2_2247, xor(kp, exp) = all_1469_2_2215, yields: % 82.00/47.47 | (1733) all_1509_2_2247 = all_1469_2_2215 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with kp, exp, all_1467_2_2212, all_1469_2_2215 and discharging atoms xor(kp, exp) = all_1469_2_2215, xor(kp, exp) = all_1467_2_2212, yields: % 82.00/47.47 | (1734) all_1469_2_2215 = all_1467_2_2212 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with kp, exp, all_1431_2_2192, all_1509_2_2247 and discharging atoms xor(kp, exp) = all_1509_2_2247, xor(kp, exp) = all_1431_2_2192, yields: % 82.00/47.47 | (1735) all_1509_2_2247 = all_1431_2_2192 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with kp, exp, all_475_2_441, all_1467_2_2212 and discharging atoms xor(kp, exp) = all_1467_2_2212, xor(kp, exp) = all_475_2_441, yields: % 82.00/47.47 | (1736) all_1467_2_2212 = all_475_2_441 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with exp, kp, all_1353_2_2107, all_475_2_441 and discharging atoms xor(exp, kp) = all_1353_2_2107, xor(exp, kp) = all_475_2_441, yields: % 82.00/47.47 | (1737) all_1353_2_2107 = all_475_2_441 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with exp, kp, all_1325_2_2083, all_1531_2_2262 and discharging atoms xor(exp, kp) = all_1531_2_2262, xor(exp, kp) = all_1325_2_2083, yields: % 82.00/47.47 | (1738) all_1531_2_2262 = all_1325_2_2083 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with exp, kp, all_907_0_1830, all_1531_2_2262 and discharging atoms xor(exp, kp) = all_1531_2_2262, xor(exp, kp) = all_907_0_1830, yields: % 82.00/47.47 | (1739) all_1531_2_2262 = all_907_0_1830 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with exp, kp, all_907_0_1830, all_1353_2_2107 and discharging atoms xor(exp, kp) = all_1353_2_2107, xor(exp, kp) = all_907_0_1830, yields: % 82.00/47.47 | (1740) all_1353_2_2107 = all_907_0_1830 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with exp, kp, all_857_2_1793, all_1531_2_2262 and discharging atoms xor(exp, kp) = all_1531_2_2262, xor(exp, kp) = all_857_2_1793, yields: % 82.00/47.47 | (1741) all_1531_2_2262 = all_857_2_1793 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with km, all_475_2_441, all_1449_0_2201, all_475_1_440 and discharging atoms xor(km, all_475_2_441) = all_1449_0_2201, xor(km, all_475_2_441) = all_475_1_440, yields: % 82.00/47.47 | (1742) all_1449_0_2201 = all_475_1_440 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with id, exp, all_1289_0_2063, all_1317_0_2077 and discharging atoms xor(id, exp) = all_1317_0_2077, xor(id, exp) = all_1289_0_2063, yields: % 82.00/47.47 | (1743) all_1317_0_2077 = all_1289_0_2063 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with id, exp, all_1173_0_1969, all_1289_0_2063 and discharging atoms xor(id, exp) = all_1289_0_2063, xor(id, exp) = all_1173_0_1969, yields: % 82.00/47.47 | (1744) all_1289_0_2063 = all_1173_0_1969 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with id, exp, all_1129_0_1943, all_1317_0_2077 and discharging atoms xor(id, exp) = all_1317_0_2077, xor(id, exp) = all_1129_0_1943, yields: % 82.00/47.47 | (1745) all_1317_0_2077 = all_1129_0_1943 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with id, exp, all_1067_0_1912, all_1173_0_1969 and discharging atoms xor(id, exp) = all_1173_0_1969, xor(id, exp) = all_1067_0_1912, yields: % 82.00/47.47 | (1746) all_1173_0_1969 = all_1067_0_1912 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with id, exp, all_1059_0_1908, all_367_0_331 and discharging atoms xor(id, exp) = all_1059_0_1908, xor(id, exp) = all_367_0_331, yields: % 82.00/47.47 | (1747) all_1059_0_1908 = all_367_0_331 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with id, exp, all_951_0_1852, all_1067_0_1912 and discharging atoms xor(id, exp) = all_1067_0_1912, xor(id, exp) = all_951_0_1852, yields: % 82.00/47.47 | (1748) all_1067_0_1912 = all_951_0_1852 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with id, exp, all_813_0_1761, all_1059_0_1908 and discharging atoms xor(id, exp) = all_1059_0_1908, xor(id, exp) = all_813_0_1761, yields: % 82.00/47.47 | (1749) all_1059_0_1908 = all_813_0_1761 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with id, exp, all_813_0_1761, all_951_0_1852 and discharging atoms xor(id, exp) = all_951_0_1852, xor(id, exp) = all_813_0_1761, yields: % 82.00/47.47 | (1750) all_951_0_1852 = all_813_0_1761 % 82.00/47.47 | % 82.00/47.47 | Instantiating formula (17) with id, exp, exp, all_1173_0_1969 and discharging atoms xor(id, exp) = all_1173_0_1969, xor(id, exp) = exp, yields: % 82.00/47.47 | (1751) all_1173_0_1969 = exp % 82.00/47.47 | % 82.00/47.47 | Combining equations (1741,1738) yields a new equation: % 82.00/47.47 | (1752) all_1325_2_2083 = all_857_2_1793 % 82.00/47.47 | % 82.00/47.47 | Combining equations (1739,1738) yields a new equation: % 82.00/47.47 | (1753) all_1325_2_2083 = all_907_0_1830 % 82.00/47.47 | % 82.00/47.47 | Combining equations (1735,1732) yields a new equation: % 82.00/47.47 | (1754) all_1505_2_2243 = all_1431_2_2192 % 82.00/47.47 | % 82.00/47.47 | Combining equations (1733,1732) yields a new equation: % 82.00/47.47 | (1755) all_1505_2_2243 = all_1469_2_2215 % 82.00/47.47 | % 82.00/47.47 | Combining equations (1755,1754) yields a new equation: % 82.00/47.47 | (1756) all_1469_2_2215 = all_1431_2_2192 % 82.00/47.47 | % 82.00/47.47 | Simplifying 1756 yields: % 82.00/47.47 | (1757) all_1469_2_2215 = all_1431_2_2192 % 82.00/47.47 | % 82.00/47.47 | Combining equations (1734,1757) yields a new equation: % 82.00/47.47 | (1758) all_1467_2_2212 = all_1431_2_2192 % 82.00/47.47 | % 82.00/47.47 | Simplifying 1758 yields: % 82.00/47.47 | (1759) all_1467_2_2212 = all_1431_2_2192 % 82.00/47.47 | % 82.00/47.47 | Combining equations (1736,1759) yields a new equation: % 82.00/47.47 | (1760) all_1431_2_2192 = all_475_2_441 % 82.00/47.47 | % 82.00/47.47 | Combining equations (1740,1737) yields a new equation: % 82.00/47.47 | (1761) all_907_0_1830 = all_475_2_441 % 82.00/47.47 | % 82.00/47.47 | Simplifying 1761 yields: % 82.00/47.47 | (1762) all_907_0_1830 = all_475_2_441 % 82.00/47.47 | % 82.00/47.47 | Combining equations (1753,1752) yields a new equation: % 82.00/47.47 | (1763) all_907_0_1830 = all_857_2_1793 % 82.00/47.47 | % 82.00/47.47 | Simplifying 1763 yields: % 82.00/47.47 | (1764) all_907_0_1830 = all_857_2_1793 % 82.00/47.47 | % 82.00/47.47 | Combining equations (1743,1745) yields a new equation: % 82.00/47.47 | (1765) all_1289_0_2063 = all_1129_0_1943 % 82.00/47.47 | % 82.00/47.47 | Simplifying 1765 yields: % 82.00/47.47 | (1766) all_1289_0_2063 = all_1129_0_1943 % 82.00/47.47 | % 82.00/47.47 | Combining equations (1744,1766) yields a new equation: % 82.00/47.47 | (1767) all_1173_0_1969 = all_1129_0_1943 % 82.00/47.47 | % 82.00/47.47 | Simplifying 1767 yields: % 82.00/47.47 | (1768) all_1173_0_1969 = all_1129_0_1943 % 82.00/47.47 | % 82.00/47.47 | Combining equations (1751,1768) yields a new equation: % 82.00/47.47 | (1769) all_1129_0_1943 = exp % 82.00/47.47 | % 82.00/47.47 | Combining equations (1746,1768) yields a new equation: % 82.00/47.47 | (1770) all_1129_0_1943 = all_1067_0_1912 % 82.00/47.47 | % 82.00/47.47 | Combining equations (1770,1769) yields a new equation: % 82.00/47.47 | (1771) all_1067_0_1912 = exp % 82.00/47.47 | % 82.00/47.47 | Simplifying 1771 yields: % 82.00/47.47 | (1772) all_1067_0_1912 = exp % 82.00/47.47 | % 82.00/47.47 | Combining equations (1748,1772) yields a new equation: % 82.00/47.47 | (1773) all_951_0_1852 = exp % 82.00/47.47 | % 82.00/47.47 | Simplifying 1773 yields: % 82.00/47.47 | (1774) all_951_0_1852 = exp % 82.00/47.47 | % 82.00/47.47 | Combining equations (1749,1747) yields a new equation: % 82.00/47.47 | (1775) all_813_0_1761 = all_367_0_331 % 82.00/47.47 | % 82.00/47.47 | Simplifying 1775 yields: % 82.00/47.47 | (1776) all_813_0_1761 = all_367_0_331 % 82.00/47.47 | % 82.00/47.47 | Combining equations (1750,1774) yields a new equation: % 82.00/47.47 | (1777) all_813_0_1761 = exp % 82.00/47.47 | % 82.00/47.47 | Simplifying 1777 yields: % 82.00/47.47 | (1778) all_813_0_1761 = exp % 82.00/47.47 | % 82.00/47.47 | Combining equations (1762,1764) yields a new equation: % 82.00/47.47 | (1779) all_857_2_1793 = all_475_2_441 % 82.00/47.47 | % 82.00/47.48 | Combining equations (1776,1778) yields a new equation: % 82.00/47.48 | (1780) all_367_0_331 = exp % 82.00/47.48 | % 82.00/47.48 | Simplifying 1780 yields: % 82.00/47.48 | (1781) all_367_0_331 = exp % 82.00/47.48 | % 82.00/47.48 | Combining equations (1779,1752) yields a new equation: % 82.00/47.48 | (1782) all_1325_2_2083 = all_475_2_441 % 82.00/47.48 | % 82.00/47.48 | Combining equations (1760,1759) yields a new equation: % 82.00/47.48 | (1736) all_1467_2_2212 = all_475_2_441 % 82.00/47.48 | % 82.00/47.48 | Combining equations (1760,1757) yields a new equation: % 82.00/47.48 | (1784) all_1469_2_2215 = all_475_2_441 % 82.00/47.48 | % 82.00/47.48 | Combining equations (1760,1754) yields a new equation: % 82.00/47.48 | (1785) all_1505_2_2243 = all_475_2_441 % 82.00/47.48 | % 82.00/47.48 | Combining equations (1785,1732) yields a new equation: % 82.00/47.48 | (1786) all_1509_2_2247 = all_475_2_441 % 82.00/47.48 | % 82.00/47.48 | Combining equations (1782,1738) yields a new equation: % 82.00/47.48 | (1787) all_1531_2_2262 = all_475_2_441 % 82.00/47.48 | % 82.00/47.48 | From (1760) and (1701) follows: % 82.00/47.48 | (1641) xor(kp, exp) = all_475_2_441 % 82.00/47.48 | % 82.00/47.48 | From (1787) and (1730) follows: % 82.00/47.48 | (1789) xor(km, all_475_2_441) = all_1531_1_2261 % 82.00/47.48 | % 82.00/47.48 | From (1786) and (1725) follows: % 82.00/47.48 | (1790) xor(km, all_475_2_441) = all_1509_1_2246 % 82.00/47.48 | % 82.00/47.48 | From (1785) and (1720) follows: % 82.00/47.48 | (1791) xor(km, all_475_2_441) = all_1505_1_2242 % 82.00/47.48 | % 82.00/47.48 | From (1784) and (1715) follows: % 82.00/47.48 | (1792) xor(km, all_475_2_441) = all_1469_1_2214 % 82.00/47.48 | % 82.00/47.48 | From (1736) and (1710) follows: % 82.00/47.48 | (1793) xor(km, all_475_2_441) = all_1467_1_2211 % 82.00/47.48 | % 82.00/47.48 | From (1760) and (1702) follows: % 82.00/47.48 | (1794) xor(km, all_475_2_441) = all_1431_1_2191 % 82.00/47.48 | % 82.00/47.48 | From (1737) and (1697) follows: % 82.00/47.48 | (1795) xor(km, all_475_2_441) = all_1353_1_2106 % 82.00/47.48 | % 82.00/47.48 | From (1782) and (1692) follows: % 82.00/47.48 | (1796) xor(km, all_475_2_441) = all_1325_1_2082 % 82.00/47.48 | % 82.00/47.48 | From (1779) and (1663) follows: % 82.00/47.48 | (1797) xor(km, all_475_2_441) = all_857_1_1792 % 82.00/47.48 | % 82.00/47.48 | From (1742) and (1705) follows: % 82.00/47.48 | (1289) xor(km, all_475_2_441) = all_475_1_440 % 82.00/47.48 | % 82.00/47.48 | From (1781) and (1652) follows: % 82.00/47.48 | (25) p(exp) % 82.00/47.48 | % 82.00/47.48 | Instantiating formula (17) with km, all_475_2_441, all_1509_1_2246, all_1531_1_2261 and discharging atoms xor(km, all_475_2_441) = all_1531_1_2261, xor(km, all_475_2_441) = all_1509_1_2246, yields: % 82.00/47.48 | (1800) all_1531_1_2261 = all_1509_1_2246 % 82.00/47.48 | % 82.00/47.48 | Instantiating formula (17) with km, all_475_2_441, all_1505_1_2242, all_1531_1_2261 and discharging atoms xor(km, all_475_2_441) = all_1531_1_2261, xor(km, all_475_2_441) = all_1505_1_2242, yields: % 82.00/47.48 | (1801) all_1531_1_2261 = all_1505_1_2242 % 82.00/47.48 | % 82.00/47.48 | Instantiating formula (17) with km, all_475_2_441, all_1469_1_2214, all_1509_1_2246 and discharging atoms xor(km, all_475_2_441) = all_1509_1_2246, xor(km, all_475_2_441) = all_1469_1_2214, yields: % 82.00/47.48 | (1802) all_1509_1_2246 = all_1469_1_2214 % 82.00/47.48 | % 82.00/47.48 | Instantiating formula (17) with km, all_475_2_441, all_1467_1_2211, all_475_1_440 and discharging atoms xor(km, all_475_2_441) = all_1467_1_2211, xor(km, all_475_2_441) = all_475_1_440, yields: % 82.00/47.48 | (1803) all_1467_1_2211 = all_475_1_440 % 82.00/47.48 | % 82.00/47.48 | Instantiating formula (17) with km, all_475_2_441, all_1467_1_2211, all_1469_1_2214 and discharging atoms xor(km, all_475_2_441) = all_1469_1_2214, xor(km, all_475_2_441) = all_1467_1_2211, yields: % 82.00/47.48 | (1804) all_1469_1_2214 = all_1467_1_2211 % 82.00/47.48 | % 82.00/47.48 | Instantiating formula (17) with km, all_475_2_441, all_1431_1_2191, all_1509_1_2246 and discharging atoms xor(km, all_475_2_441) = all_1509_1_2246, xor(km, all_475_2_441) = all_1431_1_2191, yields: % 82.00/47.48 | (1805) all_1509_1_2246 = all_1431_1_2191 % 82.00/47.48 | % 82.00/47.48 | Instantiating formula (17) with km, all_475_2_441, all_1325_1_2082, all_1469_1_2214 and discharging atoms xor(km, all_475_2_441) = all_1469_1_2214, xor(km, all_475_2_441) = all_1325_1_2082, yields: % 82.00/47.48 | (1806) all_1469_1_2214 = all_1325_1_2082 % 82.00/47.48 | % 82.00/47.48 | Instantiating formula (17) with km, all_475_2_441, all_1325_1_2082, all_1353_1_2106 and discharging atoms xor(km, all_475_2_441) = all_1353_1_2106, xor(km, all_475_2_441) = all_1325_1_2082, yields: % 82.00/47.48 | (1807) all_1353_1_2106 = all_1325_1_2082 % 82.00/47.48 | % 82.00/47.48 | Instantiating formula (17) with km, all_475_2_441, all_857_1_1792, all_1353_1_2106 and discharging atoms xor(km, all_475_2_441) = all_1353_1_2106, xor(km, all_475_2_441) = all_857_1_1792, yields: % 82.00/47.48 | (1808) all_1353_1_2106 = all_857_1_1792 % 82.00/47.48 | % 82.00/47.48 | Combining equations (1800,1801) yields a new equation: % 82.00/47.48 | (1809) all_1509_1_2246 = all_1505_1_2242 % 82.00/47.48 | % 82.00/47.48 | Simplifying 1809 yields: % 82.00/47.48 | (1810) all_1509_1_2246 = all_1505_1_2242 % 82.00/47.48 | % 82.00/47.48 | Combining equations (1802,1810) yields a new equation: % 82.00/47.48 | (1811) all_1505_1_2242 = all_1469_1_2214 % 82.00/47.48 | % 82.00/47.48 | Combining equations (1805,1810) yields a new equation: % 82.00/47.48 | (1812) all_1505_1_2242 = all_1431_1_2191 % 82.00/47.48 | % 82.00/47.48 | Combining equations (1811,1812) yields a new equation: % 82.00/47.48 | (1813) all_1469_1_2214 = all_1431_1_2191 % 82.00/47.48 | % 82.00/47.48 | Simplifying 1813 yields: % 82.00/47.48 | (1814) all_1469_1_2214 = all_1431_1_2191 % 82.00/47.48 | % 82.00/47.48 | Combining equations (1806,1814) yields a new equation: % 82.00/47.48 | (1815) all_1431_1_2191 = all_1325_1_2082 % 82.00/47.48 | % 82.00/47.48 | Combining equations (1804,1814) yields a new equation: % 82.00/47.48 | (1816) all_1467_1_2211 = all_1431_1_2191 % 82.00/47.48 | % 82.00/47.48 | Simplifying 1816 yields: % 82.00/47.48 | (1817) all_1467_1_2211 = all_1431_1_2191 % 82.00/47.48 | % 82.00/47.48 | Combining equations (1817,1803) yields a new equation: % 82.00/47.48 | (1818) all_1431_1_2191 = all_475_1_440 % 82.00/47.48 | % 82.00/47.48 | Simplifying 1818 yields: % 82.00/47.48 | (1819) all_1431_1_2191 = all_475_1_440 % 82.00/47.48 | % 82.00/47.48 | Combining equations (1815,1819) yields a new equation: % 82.00/47.48 | (1820) all_1325_1_2082 = all_475_1_440 % 82.00/47.48 | % 82.00/47.48 | Simplifying 1820 yields: % 82.00/47.48 | (1821) all_1325_1_2082 = all_475_1_440 % 82.00/47.48 | % 82.00/47.48 | Combining equations (1807,1808) yields a new equation: % 82.00/47.48 | (1822) all_1325_1_2082 = all_857_1_1792 % 82.00/47.48 | % 82.00/47.48 | Simplifying 1822 yields: % 82.00/47.48 | (1823) all_1325_1_2082 = all_857_1_1792 % 82.00/47.48 | % 82.00/47.48 | Combining equations (1823,1821) yields a new equation: % 82.00/47.48 | (1824) all_857_1_1792 = all_475_1_440 % 82.00/47.48 | % 82.00/47.48 | Simplifying 1824 yields: % 82.00/47.48 | (1825) all_857_1_1792 = all_475_1_440 % 82.00/47.48 | % 82.00/47.48 | From (1819) and (1700) follows: % 82.00/47.48 | (1826) crypt(all_475_1_440, id) = all_1431_0_2190 % 82.00/47.48 | % 82.00/47.48 | From (1821) and (1690) follows: % 82.00/47.48 | (1827) crypt(all_475_1_440, id) = all_1325_0_2081 % 82.00/47.48 | % 82.00/47.48 | From (1825) and (1797) follows: % 82.00/47.48 | (1289) xor(km, all_475_2_441) = all_475_1_440 % 82.00/47.48 | % 82.00/47.48 | Instantiating formula (30) with all_475_1_440, id, all_1325_0_2081, all_1431_0_2190 and discharging atoms crypt(all_475_1_440, id) = all_1431_0_2190, crypt(all_475_1_440, id) = all_1325_0_2081, yields: % 82.00/47.48 | (1829) all_1431_0_2190 = all_1325_0_2081 % 82.00/47.48 | % 82.00/47.48 | From (1829) and (1826) follows: % 82.00/47.48 | (1827) crypt(all_475_1_440, id) = all_1325_0_2081 % 82.00/47.48 | % 82.00/47.48 | From (1829) and (1703) follows: % 82.00/47.48 | (1693) ~ p(all_1325_0_2081) % 82.00/47.48 | % 82.00/47.48 | Instantiating formula (27) with all_1325_0_2081, all_475_1_440, all_475_2_441, exp, id and discharging atoms crypt(all_475_1_440, id) = all_1325_0_2081, xor(kp, exp) = all_475_2_441, xor(km, all_475_2_441) = all_475_1_440, p(exp), p(id), ~ p(all_1325_0_2081), yields: % 82.00/47.48 | (1563) $false % 82.00/47.48 | % 82.00/47.48 |-The branch is then unsatisfiable % 82.00/47.48 |-Branch two: % 82.00/47.48 | (1833) p(all_207_0_173) % 82.00/47.48 | (1834) ~ p(all_207_1_174) % 82.00/47.48 | % 82.00/47.48 | From (1090) and (1834) follows: % 82.00/47.48 | (1835) ~ p(all_111_1_82) % 82.00/47.48 | % 82.00/47.48 | Using (1617) and (1835) yields: % 82.00/47.48 | (1563) $false % 82.00/47.48 | % 82.00/47.48 |-The branch is then unsatisfiable % 82.00/47.48 |-Branch two: % 82.00/47.48 | (1835) ~ p(all_111_1_82) % 82.00/47.48 | (1838) ? [v0] : ? [v1] : (crypt(v0, id) = v1 & xor(all_0_4_4, data) = v0 & ~ p(v1)) % 82.00/47.48 | % 82.00/47.48 +-Applying beta-rule and splitting (1201), into two cases. % 82.00/47.48 |-Branch one: % 82.00/47.48 | (1617) p(all_111_1_82) % 82.00/47.48 | % 82.00/47.48 | Using (1617) and (1835) yields: % 82.00/47.49 | (1563) $false % 82.00/47.49 | % 82.00/47.49 |-The branch is then unsatisfiable % 82.00/47.49 |-Branch two: % 82.00/47.49 | (1835) ~ p(all_111_1_82) % 82.00/47.49 | (1842) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, data) = v2 & xor(data, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 82.00/47.49 | % 82.00/47.49 | Instantiating (1842) with all_710_0_2287, all_710_1_2288, all_710_2_2289 yields: % 82.00/47.49 | (1843) crypt(all_710_1_2288, data) = all_710_0_2287 & xor(data, kp) = all_710_2_2289 & xor(km, all_710_2_2289) = all_710_1_2288 & ~ p(all_710_0_2287) % 82.00/47.49 | % 82.00/47.49 | Applying alpha-rule on (1843) yields: % 82.00/47.49 | (1844) crypt(all_710_1_2288, data) = all_710_0_2287 % 82.00/47.49 | (1845) xor(data, kp) = all_710_2_2289 % 82.00/47.49 | (1846) xor(km, all_710_2_2289) = all_710_1_2288 % 82.00/47.49 | (1847) ~ p(all_710_0_2287) % 82.00/47.49 | % 82.00/47.49 | Instantiating formula (17) with data, kp, all_710_2_2289, all_121_2_96 and discharging atoms xor(data, kp) = all_710_2_2289, xor(data, kp) = all_121_2_96, yields: % 82.00/47.49 | (1848) all_710_2_2289 = all_121_2_96 % 82.00/47.49 | % 82.00/47.49 | From (1848) and (1846) follows: % 82.00/47.49 | (1849) xor(km, all_121_2_96) = all_710_1_2288 % 82.00/47.49 | % 82.00/47.49 | Instantiating formula (17) with km, all_121_2_96, all_710_1_2288, all_121_1_95 and discharging atoms xor(km, all_121_2_96) = all_710_1_2288, xor(km, all_121_2_96) = all_121_1_95, yields: % 82.00/47.49 | (1850) all_710_1_2288 = all_121_1_95 % 82.00/47.49 | % 82.00/47.49 | From (1850) and (1844) follows: % 82.00/47.49 | (1851) crypt(all_121_1_95, data) = all_710_0_2287 % 82.00/47.49 | % 82.00/47.49 | From (1850) and (1849) follows: % 82.00/47.49 | (380) xor(km, all_121_2_96) = all_121_1_95 % 82.00/47.49 | % 82.00/47.49 | Instantiating formula (27) with all_710_0_2287, all_121_1_95, all_121_2_96, data, data and discharging atoms crypt(all_121_1_95, data) = all_710_0_2287, xor(kp, data) = all_121_2_96, xor(km, all_121_2_96) = all_121_1_95, p(data), ~ p(all_710_0_2287), yields: % 82.00/47.49 | (1563) $false % 82.00/47.49 | % 82.00/47.49 |-The branch is then unsatisfiable % 82.00/47.49 |-Branch two: % 82.00/47.49 | (1562) p(all_111_0_81) % 82.00/47.49 | (1835) ~ p(all_111_1_82) % 82.00/47.49 | % 82.00/47.49 +-Applying beta-rule and splitting (673), into two cases. % 82.00/47.49 |-Branch one: % 82.00/47.49 | (1617) p(all_111_1_82) % 82.00/47.49 | % 82.00/47.49 | Using (1617) and (1835) yields: % 82.00/47.49 | (1563) $false % 82.00/47.49 | % 82.00/47.49 |-The branch is then unsatisfiable % 82.00/47.49 |-Branch two: % 82.00/47.49 | (1835) ~ p(all_111_1_82) % 82.00/47.49 | (1838) ? [v0] : ? [v1] : (crypt(v0, id) = v1 & xor(all_0_4_4, data) = v0 & ~ p(v1)) % 82.00/47.49 | % 82.00/47.49 +-Applying beta-rule and splitting (1201), into two cases. % 82.00/47.49 |-Branch one: % 82.00/47.49 | (1617) p(all_111_1_82) % 82.00/47.49 | % 82.00/47.49 | Using (1617) and (1835) yields: % 82.00/47.49 | (1563) $false % 82.00/47.49 | % 82.00/47.49 |-The branch is then unsatisfiable % 82.00/47.49 |-Branch two: % 82.00/47.49 | (1835) ~ p(all_111_1_82) % 82.00/47.49 | (1842) ? [v0] : ? [v1] : ? [v2] : (crypt(v1, data) = v2 & xor(data, kp) = v0 & xor(km, v0) = v1 & ~ p(v2)) % 82.00/47.49 | % 82.00/47.49 | Instantiating (1842) with all_796_0_2319, all_796_1_2320, all_796_2_2321 yields: % 82.00/47.49 | (1864) crypt(all_796_1_2320, data) = all_796_0_2319 & xor(data, kp) = all_796_2_2321 & xor(km, all_796_2_2321) = all_796_1_2320 & ~ p(all_796_0_2319) % 82.00/47.49 | % 82.00/47.49 | Applying alpha-rule on (1864) yields: % 82.00/47.49 | (1865) crypt(all_796_1_2320, data) = all_796_0_2319 % 82.00/47.49 | (1866) xor(data, kp) = all_796_2_2321 % 82.00/47.49 | (1867) xor(km, all_796_2_2321) = all_796_1_2320 % 82.00/47.49 | (1868) ~ p(all_796_0_2319) % 82.00/47.49 | % 82.00/47.49 | Instantiating formula (17) with data, kp, all_796_2_2321, all_121_2_96 and discharging atoms xor(data, kp) = all_796_2_2321, xor(data, kp) = all_121_2_96, yields: % 82.00/47.49 | (1869) all_796_2_2321 = all_121_2_96 % 82.00/47.49 | % 82.00/47.49 | From (1869) and (1867) follows: % 82.00/47.49 | (1870) xor(km, all_121_2_96) = all_796_1_2320 % 82.00/47.49 | % 82.00/47.49 | Instantiating formula (17) with km, all_121_2_96, all_796_1_2320, all_121_1_95 and discharging atoms xor(km, all_121_2_96) = all_796_1_2320, xor(km, all_121_2_96) = all_121_1_95, yields: % 82.00/47.49 | (1871) all_796_1_2320 = all_121_1_95 % 82.00/47.49 | % 82.00/47.49 | From (1871) and (1865) follows: % 82.00/47.49 | (1872) crypt(all_121_1_95, data) = all_796_0_2319 % 82.00/47.49 | % 82.00/47.49 | From (1871) and (1870) follows: % 82.00/47.49 | (380) xor(km, all_121_2_96) = all_121_1_95 % 82.00/47.49 | % 82.00/47.49 | Instantiating formula (27) with all_796_0_2319, all_121_1_95, all_121_2_96, data, data and discharging atoms crypt(all_121_1_95, data) = all_796_0_2319, xor(kp, data) = all_121_2_96, xor(km, all_121_2_96) = all_121_1_95, p(data), ~ p(all_796_0_2319), yields: % 82.00/47.49 | (1563) $false % 82.00/47.49 | % 82.00/47.49 |-The branch is then unsatisfiable % 82.00/47.49 % SZS output end Proof for theBenchmark % 82.00/47.49 % 82.00/47.49 46891ms %------------------------------------------------------------------------------