%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE027+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n005.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 : Sun Jul 17 01:50:59 EDT 2022 % Result : Theorem 6.41s 2.41s % Output : Proof 12.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : KLE027+3 : TPTP v8.1.0. Released v4.0.0. % 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n005.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 : Thu Jun 16 09:28:39 EDT 2022 % 0.12/0.34 % CPUTime : % 0.61/0.67 ____ _ % 0.61/0.67 ___ / __ \_____(_)___ ________ __________ % 0.61/0.67 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.61/0.67 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.61/0.67 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.61/0.67 % 0.61/0.67 A Theorem Prover for First-Order Logic % 0.61/0.67 (ePrincess v.1.0) % 0.61/0.67 % 0.61/0.67 (c) Philipp Rümmer, 2009-2015 % 0.61/0.67 (c) Peter Backeman, 2014-2015 % 0.61/0.67 (contributions by Angelo Brillout, Peter Baumgartner) % 0.61/0.67 Free software under GNU Lesser General Public License (LGPL). % 0.61/0.67 Bug reports to peter@backeman.se % 0.61/0.67 % 0.61/0.67 For more information, visit http://user.uu.se/~petba168/breu/ % 0.61/0.67 % 0.61/0.67 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.77/0.74 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.83/1.14 Prover 0: Preprocessing ... % 3.19/1.61 Prover 0: Constructing countermodel ... % 6.41/2.41 Prover 0: proved (1668ms) % 6.41/2.41 % 6.41/2.41 No countermodel exists, formula is valid % 6.41/2.41 % SZS status Theorem for theBenchmark % 6.41/2.41 % 6.41/2.41 Generating proof ... found it (size 141) % 11.87/3.69 % 11.87/3.69 % SZS output start Proof for theBenchmark % 11.87/3.69 Assumed formulas after preprocessing and simplification: % 11.87/3.69 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = v11) & c(v3) = v6 & multiplication(v6, v2) = v10 & multiplication(v6, v1) = v7 & multiplication(v3, v8) = v9 & multiplication(v3, v0) = v5 & addition(v9, v10) = v11 & addition(v5, v10) = v12 & addition(v5, v7) = v8 & test(v4) & test(v3) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (multiplication(v14, v15) = v17) | ~ (multiplication(v13, v15) = v16) | ~ (addition(v16, v17) = v18) | ? [v19] : (multiplication(v19, v15) = v18 & addition(v13, v14) = v19)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (multiplication(v13, v15) = v17) | ~ (multiplication(v13, v14) = v16) | ~ (addition(v16, v17) = v18) | ? [v19] : (multiplication(v13, v19) = v18 & addition(v14, v15) = v19)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (c(v14) = v16) | ~ (c(v13) = v15) | ~ (multiplication(v15, v16) = v17) | ~ test(v14) | ~ test(v13) | ? [v18] : (c(v18) = v17 & addition(v13, v14) = v18)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (c(v14) = v16) | ~ (c(v13) = v15) | ~ (addition(v15, v16) = v17) | ~ test(v14) | ~ test(v13) | ? [v18] : (c(v18) = v17 & multiplication(v13, v14) = v18)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (multiplication(v16, v15) = v17) | ~ (multiplication(v13, v14) = v16) | ? [v18] : (multiplication(v14, v15) = v18 & multiplication(v13, v18) = v17)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (multiplication(v16, v15) = v17) | ~ (addition(v13, v14) = v16) | ? [v18] : ? [v19] : (multiplication(v14, v15) = v19 & multiplication(v13, v15) = v18 & addition(v18, v19) = v17)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (multiplication(v14, v15) = v16) | ~ (multiplication(v13, v16) = v17) | ? [v18] : (multiplication(v18, v15) = v17 & multiplication(v13, v14) = v18)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (multiplication(v13, v16) = v17) | ~ (addition(v14, v15) = v16) | ? [v18] : ? [v19] : (multiplication(v13, v15) = v19 & multiplication(v13, v14) = v18 & addition(v18, v19) = v17)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (addition(v16, v13) = v17) | ~ (addition(v15, v14) = v16) | ? [v18] : (addition(v15, v18) = v17 & addition(v14, v13) = v18)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (addition(v15, v16) = v17) | ~ (addition(v14, v13) = v16) | ? [v18] : (addition(v18, v13) = v17 & addition(v15, v14) = v18)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (multiplication(v16, v15) = v14) | ~ (multiplication(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (addition(v16, v15) = v14) | ~ (addition(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (c(v13) = v15) | ~ complement(v13, v14) | ~ test(v13)) & ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (addition(v13, v14) = v15) | ~ leq(v13, v14)) & ! [v13] : ! [v14] : ! [v15] : (v15 = one | ~ (addition(v13, v14) = v15) | ~ complement(v14, v13)) & ! [v13] : ! [v14] : ! [v15] : (v15 = zero | ~ (multiplication(v14, v13) = v15) | ~ complement(v14, v13)) & ! [v13] : ! [v14] : ! [v15] : (v15 = zero | ~ (multiplication(v13, v14) = v15) | ~ complement(v14, v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (c(v15) = v14) | ~ (c(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (multiplication(v14, v13) = v15) | ~ complement(v14, v13) | (multiplication(v13, v14) = zero & addition(v13, v14) = one)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (multiplication(v13, v14) = v15) | ~ complement(v14, v13) | (multiplication(v14, v13) = zero & addition(v13, v14) = one)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (multiplication(v13, v14) = v15) | ~ test(v14) | ~ test(v13) | ? [v16] : ? [v17] : ? [v18] : (c(v15) = v16 & c(v14) = v18 & c(v13) = v17 & addition(v17, v18) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (addition(v14, v13) = v15) | addition(v13, v14) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (addition(v13, v14) = v15) | ~ complement(v14, v13) | (multiplication(v14, v13) = zero & multiplication(v13, v14) = zero)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (addition(v13, v14) = v15) | ~ test(v14) | ~ test(v13) | ? [v16] : ? [v17] : ? [v18] : (c(v15) = v16 & c(v14) = v18 & c(v13) = v17 & multiplication(v17, v18) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (addition(v13, v14) = v15) | addition(v14, v13) = v15) & ! [v13] : ! [v14] : (v14 = v13 | ~ (multiplication(v13, one) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (multiplication(one, v13) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (addition(v13, v13) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (addition(v13, zero) = v14)) & ! [v13] : ! [v14] : (v14 = zero | ~ (c(v13) = v14) | test(v13)) & ! [v13] : ! [v14] : (v14 = zero | ~ (multiplication(v13, zero) = v14)) & ! [v13] : ! [v14] : (v14 = zero | ~ (multiplication(zero, v13) = v14)) & ! [v13] : ! [v14] : ( ~ (c(v13) = v14) | ~ test(v13) | complement(v13, v14)) & ! [v13] : ! [v14] : ( ~ (multiplication(v14, v13) = zero) | complement(v14, v13) | ? [v15] : ? [v16] : (multiplication(v13, v14) = v15 & addition(v13, v14) = v16 & ( ~ (v16 = one) | ~ (v15 = zero)))) & ! [v13] : ! [v14] : ( ~ (multiplication(v13, v14) = zero) | complement(v14, v13) | ? [v15] : ? [v16] : (multiplication(v14, v13) = v15 & addition(v13, v14) = v16 & ( ~ (v16 = one) | ~ (v15 = zero)))) & ! [v13] : ! [v14] : ( ~ (addition(v13, v14) = v14) | leq(v13, v14)) & ! [v13] : ! [v14] : ( ~ (addition(v13, v14) = one) | complement(v14, v13) | ? [v15] : ? [v16] : (multiplication(v14, v13) = v16 & multiplication(v13, v14) = v15 & ( ~ (v16 = zero) | ~ (v15 = zero)))) & ! [v13] : ! [v14] : ( ~ complement(v14, v13) | test(v13)) & ! [v13] : ( ~ test(v13) | ? [v14] : complement(v14, v13))) % 12.05/3.77 | 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, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12 yields: % 12.05/3.77 | (1) ~ (all_0_0_0 = all_0_1_1) & c(all_0_9_9) = all_0_6_6 & multiplication(all_0_6_6, all_0_10_10) = all_0_2_2 & multiplication(all_0_6_6, all_0_11_11) = all_0_5_5 & multiplication(all_0_9_9, all_0_4_4) = all_0_3_3 & multiplication(all_0_9_9, all_0_12_12) = all_0_7_7 & addition(all_0_3_3, all_0_2_2) = all_0_1_1 & addition(all_0_7_7, all_0_2_2) = all_0_0_0 & addition(all_0_7_7, all_0_5_5) = all_0_4_4 & test(all_0_8_8) & test(all_0_9_9) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (c(v1) = v3) | ~ (c(v0) = v2) | ~ (multiplication(v2, v3) = v4) | ~ test(v1) | ~ test(v0) | ? [v5] : (c(v5) = v4 & addition(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (c(v1) = v3) | ~ (c(v0) = v2) | ~ (addition(v2, v3) = v4) | ~ test(v1) | ~ test(v0) | ? [v5] : (c(v5) = v4 & multiplication(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ? [v5] : ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ? [v5] : ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (c(v0) = v2) | ~ complement(v0, v1) | ~ test(v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = one | ~ (addition(v0, v1) = v2) | ~ complement(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ~ test(v1) | ~ test(v0) | ? [v3] : ? [v4] : ? [v5] : (c(v2) = v3 & c(v1) = v5 & c(v0) = v4 & addition(v4, v5) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ~ test(v1) | ~ test(v0) | ? [v3] : ? [v4] : ? [v5] : (c(v2) = v3 & c(v1) = v5 & c(v0) = v4 & multiplication(v4, v5) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (c(v0) = v1) | test(v0)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (c(v0) = v1) | ~ test(v0) | complement(v0, v1)) & ! [v0] : ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) & ! [v0] : ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) | ~ (v2 = zero)))) & ! [v0] : ! [v1] : ( ~ complement(v1, v0) | test(v0)) & ! [v0] : ( ~ test(v0) | ? [v1] : complement(v1, v0)) % 12.05/3.80 | % 12.05/3.80 | Applying alpha-rule on (1) yields: % 12.05/3.80 | (2) ! [v0] : ! [v1] : ( ~ complement(v1, v0) | test(v0)) % 12.05/3.80 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 12.05/3.80 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = one | ~ (addition(v0, v1) = v2) | ~ complement(v1, v0)) % 12.05/3.80 | (5) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 12.05/3.80 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 12.05/3.80 | (7) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 12.05/3.81 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0)) % 12.05/3.81 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (c(v1) = v3) | ~ (c(v0) = v2) | ~ (multiplication(v2, v3) = v4) | ~ test(v1) | ~ test(v0) | ? [v5] : (c(v5) = v4 & addition(v0, v1) = v5)) % 12.05/3.81 | (10) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) % 12.05/3.81 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 12.05/3.81 | (12) addition(all_0_7_7, all_0_5_5) = all_0_4_4 % 12.05/3.81 | (13) ! [v0] : ! [v1] : (v1 = zero | ~ (c(v0) = v1) | test(v0)) % 12.05/3.81 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ~ test(v1) | ~ test(v0) | ? [v3] : ? [v4] : ? [v5] : (c(v2) = v3 & c(v1) = v5 & c(v0) = v4 & addition(v4, v5) = v3)) % 12.45/3.81 | (15) multiplication(all_0_6_6, all_0_11_11) = all_0_5_5 % 12.45/3.81 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 12.45/3.82 | (17) ! [v0] : ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) % 12.45/3.82 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 12.45/3.82 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 12.45/3.82 | (20) test(all_0_9_9) % 12.45/3.82 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 12.45/3.83 | (22) addition(all_0_7_7, all_0_2_2) = all_0_0_0 % 12.45/3.83 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (c(v1) = v3) | ~ (c(v0) = v2) | ~ (addition(v2, v3) = v4) | ~ test(v1) | ~ test(v0) | ? [v5] : (c(v5) = v4 & multiplication(v0, v1) = v5)) % 12.45/3.83 | (24) ! [v0] : ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) % 12.45/3.83 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero)) % 12.45/3.83 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0)) % 12.45/3.83 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ? [v5] : ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4)) % 12.45/3.84 | (28) test(all_0_8_8) % 12.45/3.84 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ? [v5] : ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4)) % 12.45/3.84 | (30) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 12.45/3.84 | (31) addition(all_0_3_3, all_0_2_2) = all_0_1_1 % 12.45/3.84 | (32) ! [v0] : ! [v1] : ( ~ (c(v0) = v1) | ~ test(v0) | complement(v0, v1)) % 12.45/3.84 | (33) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (c(v0) = v2) | ~ complement(v0, v1) | ~ test(v0)) % 12.45/3.84 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) % 12.45/3.84 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ~ test(v1) | ~ test(v0) | ? [v3] : ? [v4] : ? [v5] : (c(v2) = v3 & c(v1) = v5 & c(v0) = v4 & multiplication(v4, v5) = v3)) % 12.45/3.84 | (36) multiplication(all_0_9_9, all_0_12_12) = all_0_7_7 % 12.45/3.84 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one)) % 12.45/3.85 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one)) % 12.45/3.85 | (39) multiplication(all_0_6_6, all_0_10_10) = all_0_2_2 % 12.45/3.85 | (40) ~ (all_0_0_0 = all_0_1_1) % 12.45/3.85 | (41) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) % 12.45/3.85 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) % 12.45/3.85 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 12.45/3.85 | (44) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) | ~ (v2 = zero)))) % 12.45/3.85 | (45) c(all_0_9_9) = all_0_6_6 % 12.45/3.86 | (46) ! [v0] : ( ~ test(v0) | ? [v1] : complement(v1, v0)) % 12.45/3.86 | (47) multiplication(all_0_9_9, all_0_4_4) = all_0_3_3 % 12.45/3.86 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 12.45/3.86 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 12.45/3.86 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 12.45/3.86 | (51) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) % 12.45/3.86 | % 12.45/3.86 | Instantiating formula (50) with all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms addition(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 12.45/3.86 | (52) addition(all_0_2_2, all_0_3_3) = all_0_1_1 % 12.45/3.86 | % 12.45/3.86 | Instantiating formula (27) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_7_7, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_4_4) = all_0_3_3, addition(all_0_7_7, all_0_5_5) = all_0_4_4, yields: % 12.45/3.86 | (53) ? [v0] : ? [v1] : (multiplication(all_0_9_9, all_0_5_5) = v1 & multiplication(all_0_9_9, all_0_7_7) = v0 & addition(v0, v1) = all_0_3_3) % 12.45/3.86 | % 12.45/3.86 | Instantiating formula (50) with all_0_4_4, all_0_7_7, all_0_5_5 and discharging atoms addition(all_0_7_7, all_0_5_5) = all_0_4_4, yields: % 12.45/3.86 | (54) addition(all_0_5_5, all_0_7_7) = all_0_4_4 % 12.45/3.86 | % 12.45/3.86 | Instantiating formula (32) with all_0_6_6, all_0_9_9 and discharging atoms c(all_0_9_9) = all_0_6_6, test(all_0_9_9), yields: % 12.45/3.87 | (55) complement(all_0_9_9, all_0_6_6) % 12.45/3.87 | % 12.45/3.87 | Instantiating (53) with all_13_0_15, all_13_1_16 yields: % 12.45/3.87 | (56) multiplication(all_0_9_9, all_0_5_5) = all_13_0_15 & multiplication(all_0_9_9, all_0_7_7) = all_13_1_16 & addition(all_13_1_16, all_13_0_15) = all_0_3_3 % 12.45/3.87 | % 12.45/3.87 | Applying alpha-rule on (56) yields: % 12.45/3.87 | (57) multiplication(all_0_9_9, all_0_5_5) = all_13_0_15 % 12.45/3.87 | (58) multiplication(all_0_9_9, all_0_7_7) = all_13_1_16 % 12.45/3.87 | (59) addition(all_13_1_16, all_13_0_15) = all_0_3_3 % 12.45/3.87 | % 12.45/3.87 | Instantiating formula (18) with all_13_0_15, all_0_5_5, all_0_11_11, all_0_6_6, all_0_9_9 and discharging atoms multiplication(all_0_6_6, all_0_11_11) = all_0_5_5, multiplication(all_0_9_9, all_0_5_5) = all_13_0_15, yields: % 12.45/3.87 | (60) ? [v0] : (multiplication(v0, all_0_11_11) = all_13_0_15 & multiplication(all_0_9_9, all_0_6_6) = v0) % 12.45/3.87 | % 12.45/3.87 | Instantiating formula (18) with all_13_1_16, all_0_7_7, all_0_12_12, all_0_9_9, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_7_7) = all_13_1_16, multiplication(all_0_9_9, all_0_12_12) = all_0_7_7, yields: % 12.45/3.87 | (61) ? [v0] : (multiplication(v0, all_0_12_12) = all_13_1_16 & multiplication(all_0_9_9, all_0_9_9) = v0) % 12.45/3.87 | % 12.45/3.87 | Instantiating formula (19) with all_0_1_1, all_0_3_3, all_13_1_16, all_13_0_15, all_0_2_2 and discharging atoms addition(all_13_1_16, all_13_0_15) = all_0_3_3, addition(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 12.45/3.87 | (62) ? [v0] : (addition(all_13_0_15, all_0_2_2) = v0 & addition(all_13_1_16, v0) = all_0_1_1) % 12.45/3.87 | % 12.45/3.87 | Instantiating formula (48) with all_0_1_1, all_0_3_3, all_0_2_2, all_13_1_16, all_13_0_15 and discharging atoms addition(all_13_1_16, all_13_0_15) = all_0_3_3, addition(all_0_2_2, all_0_3_3) = all_0_1_1, yields: % 12.45/3.87 | (63) ? [v0] : (addition(v0, all_13_0_15) = all_0_1_1 & addition(all_0_2_2, all_13_1_16) = v0) % 12.45/3.87 | % 12.45/3.87 | Instantiating formula (27) with all_0_3_3, all_0_4_4, all_0_7_7, all_0_5_5, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_4_4) = all_0_3_3, addition(all_0_5_5, all_0_7_7) = all_0_4_4, yields: % 12.45/3.87 | (64) ? [v0] : ? [v1] : (multiplication(all_0_9_9, all_0_5_5) = v0 & multiplication(all_0_9_9, all_0_7_7) = v1 & addition(v0, v1) = all_0_3_3) % 12.45/3.88 | % 12.45/3.88 | Instantiating formula (2) with all_0_9_9, all_0_6_6 and discharging atoms complement(all_0_9_9, all_0_6_6), yields: % 12.45/3.88 | (65) test(all_0_6_6) % 12.45/3.88 | % 12.45/3.88 | Instantiating (62) with all_21_0_17 yields: % 12.45/3.88 | (66) addition(all_13_0_15, all_0_2_2) = all_21_0_17 & addition(all_13_1_16, all_21_0_17) = all_0_1_1 % 12.45/3.88 | % 12.45/3.88 | Applying alpha-rule on (66) yields: % 12.45/3.88 | (67) addition(all_13_0_15, all_0_2_2) = all_21_0_17 % 12.45/3.88 | (68) addition(all_13_1_16, all_21_0_17) = all_0_1_1 % 12.45/3.88 | % 12.45/3.88 | Instantiating (64) with all_23_0_18, all_23_1_19 yields: % 12.45/3.88 | (69) multiplication(all_0_9_9, all_0_5_5) = all_23_1_19 & multiplication(all_0_9_9, all_0_7_7) = all_23_0_18 & addition(all_23_1_19, all_23_0_18) = all_0_3_3 % 12.45/3.88 | % 12.45/3.88 | Applying alpha-rule on (69) yields: % 12.45/3.88 | (70) multiplication(all_0_9_9, all_0_5_5) = all_23_1_19 % 12.45/3.88 | (71) multiplication(all_0_9_9, all_0_7_7) = all_23_0_18 % 12.45/3.88 | (72) addition(all_23_1_19, all_23_0_18) = all_0_3_3 % 12.45/3.88 | % 12.45/3.88 | Instantiating (63) with all_25_0_20 yields: % 12.45/3.88 | (73) addition(all_25_0_20, all_13_0_15) = all_0_1_1 & addition(all_0_2_2, all_13_1_16) = all_25_0_20 % 12.45/3.88 | % 12.45/3.88 | Applying alpha-rule on (73) yields: % 12.45/3.88 | (74) addition(all_25_0_20, all_13_0_15) = all_0_1_1 % 12.45/3.88 | (75) addition(all_0_2_2, all_13_1_16) = all_25_0_20 % 12.45/3.88 | % 12.45/3.88 | Instantiating (61) with all_27_0_21 yields: % 12.45/3.88 | (76) multiplication(all_27_0_21, all_0_12_12) = all_13_1_16 & multiplication(all_0_9_9, all_0_9_9) = all_27_0_21 % 12.45/3.88 | % 12.45/3.88 | Applying alpha-rule on (76) yields: % 12.45/3.88 | (77) multiplication(all_27_0_21, all_0_12_12) = all_13_1_16 % 12.45/3.88 | (78) multiplication(all_0_9_9, all_0_9_9) = all_27_0_21 % 12.45/3.88 | % 12.45/3.88 | Instantiating (60) with all_29_0_22 yields: % 12.45/3.88 | (79) multiplication(all_29_0_22, all_0_11_11) = all_13_0_15 & multiplication(all_0_9_9, all_0_6_6) = all_29_0_22 % 12.45/3.88 | % 12.45/3.88 | Applying alpha-rule on (79) yields: % 12.45/3.88 | (80) multiplication(all_29_0_22, all_0_11_11) = all_13_0_15 % 12.45/3.88 | (81) multiplication(all_0_9_9, all_0_6_6) = all_29_0_22 % 12.45/3.88 | % 12.45/3.88 | Instantiating formula (11) with all_0_9_9, all_0_5_5, all_23_1_19, all_13_0_15 and discharging atoms multiplication(all_0_9_9, all_0_5_5) = all_23_1_19, multiplication(all_0_9_9, all_0_5_5) = all_13_0_15, yields: % 12.45/3.88 | (82) all_23_1_19 = all_13_0_15 % 12.45/3.88 | % 12.45/3.88 | Instantiating formula (8) with all_29_0_22, all_0_9_9, all_0_6_6 and discharging atoms multiplication(all_0_9_9, all_0_6_6) = all_29_0_22, complement(all_0_9_9, all_0_6_6), yields: % 12.45/3.88 | (83) all_29_0_22 = zero % 12.45/3.88 | % 12.45/3.88 | Instantiating formula (11) with all_0_9_9, all_0_7_7, all_23_0_18, all_13_1_16 and discharging atoms multiplication(all_0_9_9, all_0_7_7) = all_23_0_18, multiplication(all_0_9_9, all_0_7_7) = all_13_1_16, yields: % 12.45/3.89 | (84) all_23_0_18 = all_13_1_16 % 12.45/3.89 | % 12.45/3.89 | From (83) and (80) follows: % 12.45/3.89 | (85) multiplication(zero, all_0_11_11) = all_13_0_15 % 12.79/3.89 | % 12.79/3.89 | From (83) and (81) follows: % 12.79/3.89 | (86) multiplication(all_0_9_9, all_0_6_6) = zero % 12.79/3.89 | % 12.79/3.89 | From (82)(84) and (72) follows: % 12.79/3.89 | (87) addition(all_13_0_15, all_13_1_16) = all_0_3_3 % 12.79/3.89 | % 12.79/3.89 | Instantiating formula (7) with all_13_0_15, all_0_11_11 and discharging atoms multiplication(zero, all_0_11_11) = all_13_0_15, yields: % 12.79/3.89 | (88) all_13_0_15 = zero % 12.79/3.89 | % 12.79/3.89 | From (88) and (74) follows: % 12.79/3.89 | (89) addition(all_25_0_20, zero) = all_0_1_1 % 12.79/3.89 | % 12.79/3.89 | From (88) and (87) follows: % 12.79/3.89 | (90) addition(zero, all_13_1_16) = all_0_3_3 % 12.79/3.89 | % 12.79/3.89 | From (88) and (67) follows: % 12.79/3.89 | (91) addition(zero, all_0_2_2) = all_21_0_17 % 12.79/3.89 | % 12.79/3.89 | From (88) and (59) follows: % 12.79/3.89 | (92) addition(all_13_1_16, zero) = all_0_3_3 % 12.79/3.89 | % 12.79/3.89 | Instantiating formula (6) with all_0_1_1, all_25_0_20 and discharging atoms addition(all_25_0_20, zero) = all_0_1_1, yields: % 12.79/3.89 | (93) all_25_0_20 = all_0_1_1 % 12.79/3.89 | % 12.79/3.89 | Instantiating formula (6) with all_0_3_3, all_13_1_16 and discharging atoms addition(all_13_1_16, zero) = all_0_3_3, yields: % 12.79/3.89 | (94) all_13_1_16 = all_0_3_3 % 12.79/3.89 | % 12.79/3.89 | From (94) and (77) follows: % 12.79/3.89 | (95) multiplication(all_27_0_21, all_0_12_12) = all_0_3_3 % 12.79/3.89 | % 12.79/3.89 | From (93) and (89) follows: % 12.79/3.89 | (96) addition(all_0_1_1, zero) = all_0_1_1 % 12.79/3.89 | % 12.79/3.89 | From (94) and (68) follows: % 12.79/3.89 | (97) addition(all_0_3_3, all_21_0_17) = all_0_1_1 % 12.79/3.89 | % 12.79/3.89 | From (94) and (92) follows: % 12.79/3.89 | (98) addition(all_0_3_3, zero) = all_0_3_3 % 12.79/3.89 | % 12.79/3.89 | From (94)(93) and (75) follows: % 12.79/3.89 | (52) addition(all_0_2_2, all_0_3_3) = all_0_1_1 % 12.79/3.89 | % 12.79/3.89 | From (94) and (90) follows: % 12.79/3.89 | (100) addition(zero, all_0_3_3) = all_0_3_3 % 12.79/3.89 | % 12.79/3.89 | Instantiating formula (38) with zero, all_0_9_9, all_0_6_6 and discharging atoms multiplication(all_0_9_9, all_0_6_6) = zero, complement(all_0_9_9, all_0_6_6), yields: % 12.79/3.89 | (101) multiplication(all_0_6_6, all_0_9_9) = zero & addition(all_0_6_6, all_0_9_9) = one % 12.79/3.89 | % 12.79/3.89 | Applying alpha-rule on (101) yields: % 12.79/3.89 | (102) multiplication(all_0_6_6, all_0_9_9) = zero % 12.79/3.89 | (103) addition(all_0_6_6, all_0_9_9) = one % 12.79/3.89 | % 12.79/3.89 | Instantiating formula (17) with all_0_6_6, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_6_6) = zero, yields: % 12.79/3.89 | (104) complement(all_0_6_6, all_0_9_9) | ? [v0] : ? [v1] : (multiplication(all_0_6_6, all_0_9_9) = v0 & addition(all_0_9_9, all_0_6_6) = v1 & ( ~ (v1 = one) | ~ (v0 = zero))) % 12.79/3.90 | % 12.79/3.90 | Instantiating formula (14) with all_27_0_21, all_0_9_9, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_9_9) = all_27_0_21, test(all_0_9_9), yields: % 12.79/3.90 | (105) ? [v0] : ? [v1] : ? [v2] : (c(all_27_0_21) = v0 & c(all_0_9_9) = v2 & c(all_0_9_9) = v1 & addition(v1, v2) = v0) % 12.79/3.90 | % 12.79/3.90 | Instantiating formula (19) with all_0_1_1, all_0_1_1, all_0_3_3, all_0_2_2, zero and discharging atoms addition(all_0_1_1, zero) = all_0_1_1, addition(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 12.79/3.90 | (106) ? [v0] : (addition(all_0_2_2, zero) = v0 & addition(all_0_3_3, v0) = all_0_1_1) % 12.79/3.90 | % 12.79/3.90 | Instantiating formula (19) with all_0_1_1, all_0_3_3, all_0_3_3, zero, all_21_0_17 and discharging atoms addition(all_0_3_3, all_21_0_17) = all_0_1_1, addition(all_0_3_3, zero) = all_0_3_3, yields: % 12.79/3.90 | (107) ? [v0] : (addition(all_0_3_3, v0) = all_0_1_1 & addition(zero, all_21_0_17) = v0) % 12.79/3.90 | % 12.79/3.90 | Instantiating formula (50) with all_21_0_17, zero, all_0_2_2 and discharging atoms addition(zero, all_0_2_2) = all_21_0_17, yields: % 12.79/3.90 | (108) addition(all_0_2_2, zero) = all_21_0_17 % 12.79/3.90 | % 12.79/3.90 | Instantiating formula (48) with all_0_1_1, all_0_3_3, all_0_2_2, zero, all_0_3_3 and discharging atoms addition(all_0_2_2, all_0_3_3) = all_0_1_1, addition(zero, all_0_3_3) = all_0_3_3, yields: % 12.79/3.90 | (109) ? [v0] : (addition(v0, all_0_3_3) = all_0_1_1 & addition(all_0_2_2, zero) = v0) % 12.79/3.90 | % 12.79/3.90 | Instantiating formula (14) with zero, all_0_6_6, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_6_6) = zero, test(all_0_6_6), test(all_0_9_9), yields: % 12.79/3.90 | (110) ? [v0] : ? [v1] : ? [v2] : (c(all_0_6_6) = v2 & c(all_0_9_9) = v1 & c(zero) = v0 & addition(v1, v2) = v0) % 12.79/3.90 | % 12.79/3.90 | Instantiating (107) with all_65_0_31 yields: % 12.79/3.90 | (111) addition(all_0_3_3, all_65_0_31) = all_0_1_1 & addition(zero, all_21_0_17) = all_65_0_31 % 12.79/3.90 | % 12.79/3.90 | Applying alpha-rule on (111) yields: % 12.79/3.90 | (112) addition(all_0_3_3, all_65_0_31) = all_0_1_1 % 12.79/3.90 | (113) addition(zero, all_21_0_17) = all_65_0_31 % 12.79/3.90 | % 12.79/3.90 | Instantiating (110) with all_69_0_33, all_69_1_34, all_69_2_35 yields: % 12.79/3.90 | (114) c(all_0_6_6) = all_69_0_33 & c(all_0_9_9) = all_69_1_34 & c(zero) = all_69_2_35 & addition(all_69_1_34, all_69_0_33) = all_69_2_35 % 12.79/3.90 | % 12.79/3.90 | Applying alpha-rule on (114) yields: % 12.79/3.90 | (115) c(all_0_6_6) = all_69_0_33 % 12.79/3.90 | (116) c(all_0_9_9) = all_69_1_34 % 12.79/3.90 | (117) c(zero) = all_69_2_35 % 12.79/3.90 | (118) addition(all_69_1_34, all_69_0_33) = all_69_2_35 % 12.79/3.90 | % 12.79/3.90 | Instantiating (106) with all_71_0_36 yields: % 12.79/3.90 | (119) addition(all_0_2_2, zero) = all_71_0_36 & addition(all_0_3_3, all_71_0_36) = all_0_1_1 % 12.79/3.91 | % 12.79/3.91 | Applying alpha-rule on (119) yields: % 12.79/3.91 | (120) addition(all_0_2_2, zero) = all_71_0_36 % 12.79/3.91 | (121) addition(all_0_3_3, all_71_0_36) = all_0_1_1 % 12.79/3.91 | % 12.79/3.91 | Instantiating (109) with all_73_0_37 yields: % 12.79/3.91 | (122) addition(all_73_0_37, all_0_3_3) = all_0_1_1 & addition(all_0_2_2, zero) = all_73_0_37 % 12.79/3.91 | % 12.79/3.91 | Applying alpha-rule on (122) yields: % 12.79/3.91 | (123) addition(all_73_0_37, all_0_3_3) = all_0_1_1 % 12.79/3.91 | (124) addition(all_0_2_2, zero) = all_73_0_37 % 12.79/3.91 | % 12.79/3.91 | Instantiating (105) with all_81_0_41, all_81_1_42, all_81_2_43 yields: % 12.79/3.91 | (125) c(all_27_0_21) = all_81_2_43 & c(all_0_9_9) = all_81_0_41 & c(all_0_9_9) = all_81_1_42 & addition(all_81_1_42, all_81_0_41) = all_81_2_43 % 12.79/3.91 | % 12.79/3.91 | Applying alpha-rule on (125) yields: % 12.79/3.91 | (126) c(all_27_0_21) = all_81_2_43 % 12.79/3.91 | (127) c(all_0_9_9) = all_81_0_41 % 12.79/3.91 | (128) c(all_0_9_9) = all_81_1_42 % 12.79/3.91 | (129) addition(all_81_1_42, all_81_0_41) = all_81_2_43 % 12.79/3.91 | % 12.79/3.91 | Instantiating formula (51) with all_0_9_9, all_81_0_41, all_0_6_6 and discharging atoms c(all_0_9_9) = all_81_0_41, c(all_0_9_9) = all_0_6_6, yields: % 12.79/3.91 | (130) all_81_0_41 = all_0_6_6 % 12.79/3.91 | % 12.79/3.91 | Instantiating formula (51) with all_0_9_9, all_81_1_42, all_81_0_41 and discharging atoms c(all_0_9_9) = all_81_0_41, c(all_0_9_9) = all_81_1_42, yields: % 12.79/3.91 | (131) all_81_0_41 = all_81_1_42 % 12.79/3.91 | % 12.79/3.91 | Instantiating formula (6) with all_73_0_37, all_0_2_2 and discharging atoms addition(all_0_2_2, zero) = all_73_0_37, yields: % 12.79/3.91 | (132) all_73_0_37 = all_0_2_2 % 12.79/3.91 | % 12.79/3.91 | Instantiating formula (21) with all_0_2_2, zero, all_71_0_36, all_73_0_37 and discharging atoms addition(all_0_2_2, zero) = all_73_0_37, addition(all_0_2_2, zero) = all_71_0_36, yields: % 12.79/3.91 | (133) all_73_0_37 = all_71_0_36 % 12.79/3.91 | % 12.79/3.91 | Instantiating formula (21) with all_0_2_2, zero, all_21_0_17, all_73_0_37 and discharging atoms addition(all_0_2_2, zero) = all_73_0_37, addition(all_0_2_2, zero) = all_21_0_17, yields: % 12.79/3.91 | (134) all_73_0_37 = all_21_0_17 % 12.79/3.91 | % 12.79/3.91 | Combining equations (130,131) yields a new equation: % 12.79/3.91 | (135) all_81_1_42 = all_0_6_6 % 12.79/3.91 | % 12.79/3.91 | Combining equations (134,133) yields a new equation: % 12.79/3.91 | (136) all_71_0_36 = all_21_0_17 % 12.79/3.91 | % 12.79/3.91 | Combining equations (132,133) yields a new equation: % 12.79/3.91 | (137) all_71_0_36 = all_0_2_2 % 12.79/3.91 | % 12.79/3.91 | Combining equations (137,136) yields a new equation: % 12.79/3.91 | (138) all_21_0_17 = all_0_2_2 % 12.79/3.91 | % 12.79/3.91 | Combining equations (135,131) yields a new equation: % 12.79/3.91 | (130) all_81_0_41 = all_0_6_6 % 12.79/3.91 | % 12.79/3.91 | From (135)(130) and (129) follows: % 12.79/3.91 | (140) addition(all_0_6_6, all_0_6_6) = all_81_2_43 % 12.79/3.91 | % 12.79/3.91 | From (138) and (108) follows: % 12.79/3.91 | (141) addition(all_0_2_2, zero) = all_0_2_2 % 12.79/3.91 | % 12.79/3.91 | From (138) and (113) follows: % 12.79/3.91 | (142) addition(zero, all_0_2_2) = all_65_0_31 % 12.79/3.92 | % 12.79/3.92 | From (138) and (91) follows: % 12.79/3.92 | (143) addition(zero, all_0_2_2) = all_0_2_2 % 12.79/3.92 | % 12.79/3.92 | Instantiating formula (3) with all_81_2_43, all_0_6_6 and discharging atoms addition(all_0_6_6, all_0_6_6) = all_81_2_43, yields: % 12.79/3.92 | (144) all_81_2_43 = all_0_6_6 % 12.79/3.92 | % 12.79/3.92 | Instantiating formula (21) with zero, all_0_2_2, all_0_2_2, all_65_0_31 and discharging atoms addition(zero, all_0_2_2) = all_65_0_31, addition(zero, all_0_2_2) = all_0_2_2, yields: % 12.79/3.92 | (145) all_65_0_31 = all_0_2_2 % 12.79/3.92 | % 12.79/3.92 | From (145) and (112) follows: % 12.79/3.92 | (31) addition(all_0_3_3, all_0_2_2) = all_0_1_1 % 12.79/3.92 | % 12.79/3.92 | From (144) and (140) follows: % 12.79/3.92 | (147) addition(all_0_6_6, all_0_6_6) = all_0_6_6 % 12.79/3.92 | % 12.79/3.92 | Instantiating formula (32) with all_69_0_33, all_0_6_6 and discharging atoms c(all_0_6_6) = all_69_0_33, test(all_0_6_6), yields: % 12.79/3.92 | (148) complement(all_0_6_6, all_69_0_33) % 12.79/3.92 | % 12.79/3.92 | Instantiating formula (14) with zero, all_0_9_9, all_0_6_6 and discharging atoms multiplication(all_0_6_6, all_0_9_9) = zero, test(all_0_6_6), test(all_0_9_9), yields: % 12.79/3.92 | (149) ? [v0] : ? [v1] : ? [v2] : (c(all_0_6_6) = v1 & c(all_0_9_9) = v2 & c(zero) = v0 & addition(v1, v2) = v0) % 12.79/3.92 | % 12.79/3.92 | Instantiating formula (24) with all_0_6_6, all_0_9_9 and discharging atoms multiplication(all_0_6_6, all_0_9_9) = zero, yields: % 12.79/3.92 | (150) complement(all_0_6_6, all_0_9_9) | ? [v0] : ? [v1] : (multiplication(all_0_9_9, all_0_6_6) = v0 & addition(all_0_9_9, all_0_6_6) = v1 & ( ~ (v1 = one) | ~ (v0 = zero))) % 12.79/3.92 | % 12.79/3.92 | Instantiating formula (48) with all_0_0_0, all_0_2_2, all_0_7_7, all_0_2_2, zero and discharging atoms addition(all_0_2_2, zero) = all_0_2_2, addition(all_0_7_7, all_0_2_2) = all_0_0_0, yields: % 12.79/3.92 | (151) ? [v0] : (addition(v0, zero) = all_0_0_0 & addition(all_0_7_7, all_0_2_2) = v0) % 12.79/3.92 | % 12.79/3.92 | Instantiating formula (35) with all_0_6_6, all_0_6_6, all_0_6_6 and discharging atoms addition(all_0_6_6, all_0_6_6) = all_0_6_6, test(all_0_6_6), yields: % 12.79/3.92 | (152) ? [v0] : ? [v1] : ? [v2] : (c(all_0_6_6) = v2 & c(all_0_6_6) = v1 & c(all_0_6_6) = v0 & multiplication(v1, v2) = v0) % 12.79/3.92 | % 12.79/3.92 | Instantiating formula (35) with one, all_0_9_9, all_0_6_6 and discharging atoms addition(all_0_6_6, all_0_9_9) = one, test(all_0_6_6), test(all_0_9_9), yields: % 12.79/3.92 | (153) ? [v0] : ? [v1] : ? [v2] : (c(all_0_6_6) = v1 & c(all_0_9_9) = v2 & c(one) = v0 & multiplication(v1, v2) = v0) % 12.79/3.92 | % 12.79/3.92 | Instantiating formula (50) with one, all_0_6_6, all_0_9_9 and discharging atoms addition(all_0_6_6, all_0_9_9) = one, yields: % 12.79/3.92 | (154) addition(all_0_9_9, all_0_6_6) = one % 12.79/3.92 | % 12.79/3.92 | Instantiating (153) with all_151_0_71, all_151_1_72, all_151_2_73 yields: % 12.79/3.92 | (155) c(all_0_6_6) = all_151_1_72 & c(all_0_9_9) = all_151_0_71 & c(one) = all_151_2_73 & multiplication(all_151_1_72, all_151_0_71) = all_151_2_73 % 12.79/3.93 | % 12.79/3.93 | Applying alpha-rule on (155) yields: % 12.79/3.93 | (156) c(all_0_6_6) = all_151_1_72 % 12.79/3.93 | (157) c(all_0_9_9) = all_151_0_71 % 12.79/3.93 | (158) c(one) = all_151_2_73 % 12.79/3.93 | (159) multiplication(all_151_1_72, all_151_0_71) = all_151_2_73 % 12.79/3.93 | % 12.79/3.93 | Instantiating (152) with all_155_0_75, all_155_1_76, all_155_2_77 yields: % 12.79/3.93 | (160) c(all_0_6_6) = all_155_0_75 & c(all_0_6_6) = all_155_1_76 & c(all_0_6_6) = all_155_2_77 & multiplication(all_155_1_76, all_155_0_75) = all_155_2_77 % 12.79/3.93 | % 12.79/3.93 | Applying alpha-rule on (160) yields: % 12.79/3.93 | (161) c(all_0_6_6) = all_155_0_75 % 12.79/3.93 | (162) c(all_0_6_6) = all_155_1_76 % 12.79/3.93 | (163) c(all_0_6_6) = all_155_2_77 % 12.79/3.93 | (164) multiplication(all_155_1_76, all_155_0_75) = all_155_2_77 % 12.79/3.93 | % 12.79/3.93 | Instantiating (149) with all_189_0_94, all_189_1_95, all_189_2_96 yields: % 12.79/3.93 | (165) c(all_0_6_6) = all_189_1_95 & c(all_0_9_9) = all_189_0_94 & c(zero) = all_189_2_96 & addition(all_189_1_95, all_189_0_94) = all_189_2_96 % 12.79/3.93 | % 12.79/3.93 | Applying alpha-rule on (165) yields: % 12.79/3.93 | (166) c(all_0_6_6) = all_189_1_95 % 12.79/3.93 | (167) c(all_0_9_9) = all_189_0_94 % 12.79/3.93 | (168) c(zero) = all_189_2_96 % 12.79/3.93 | (169) addition(all_189_1_95, all_189_0_94) = all_189_2_96 % 12.79/3.93 | % 12.79/3.93 | Instantiating (151) with all_275_0_141 yields: % 12.79/3.93 | (170) addition(all_275_0_141, zero) = all_0_0_0 & addition(all_0_7_7, all_0_2_2) = all_275_0_141 % 12.79/3.93 | % 12.79/3.93 | Applying alpha-rule on (170) yields: % 12.79/3.93 | (171) addition(all_275_0_141, zero) = all_0_0_0 % 12.79/3.93 | (172) addition(all_0_7_7, all_0_2_2) = all_275_0_141 % 12.79/3.93 | % 12.79/3.93 +-Applying beta-rule and splitting (150), into two cases. % 12.79/3.93 |-Branch one: % 12.79/3.93 | (173) complement(all_0_6_6, all_0_9_9) % 12.79/3.93 | % 12.79/3.93 | Instantiating formula (51) with all_0_6_6, all_155_1_76, all_189_1_95 and discharging atoms c(all_0_6_6) = all_189_1_95, c(all_0_6_6) = all_155_1_76, yields: % 12.79/3.93 | (174) all_189_1_95 = all_155_1_76 % 12.79/3.93 | % 12.79/3.93 | Instantiating formula (51) with all_0_6_6, all_155_2_77, all_189_1_95 and discharging atoms c(all_0_6_6) = all_189_1_95, c(all_0_6_6) = all_155_2_77, yields: % 12.79/3.93 | (175) all_189_1_95 = all_155_2_77 % 12.79/3.93 | % 12.79/3.93 | Instantiating formula (51) with all_0_6_6, all_155_2_77, all_155_0_75 and discharging atoms c(all_0_6_6) = all_155_0_75, c(all_0_6_6) = all_155_2_77, yields: % 12.79/3.93 | (176) all_155_0_75 = all_155_2_77 % 12.79/3.93 | % 12.79/3.93 | Instantiating formula (51) with all_0_6_6, all_151_1_72, all_155_2_77 and discharging atoms c(all_0_6_6) = all_155_2_77, c(all_0_6_6) = all_151_1_72, yields: % 12.79/3.93 | (177) all_155_2_77 = all_151_1_72 % 12.79/3.93 | % 12.79/3.93 | Instantiating formula (21) with all_0_7_7, all_0_2_2, all_275_0_141, all_0_0_0 and discharging atoms addition(all_0_7_7, all_0_2_2) = all_275_0_141, addition(all_0_7_7, all_0_2_2) = all_0_0_0, yields: % 12.79/3.93 | (178) all_275_0_141 = all_0_0_0 % 12.79/3.93 | % 12.79/3.93 | Instantiating formula (33) with all_189_1_95, all_69_0_33, all_0_6_6 and discharging atoms c(all_0_6_6) = all_189_1_95, complement(all_0_6_6, all_69_0_33), test(all_0_6_6), yields: % 12.79/3.94 | (179) all_189_1_95 = all_69_0_33 % 12.79/3.94 | % 12.79/3.94 | Instantiating formula (33) with all_155_0_75, all_0_9_9, all_0_6_6 and discharging atoms c(all_0_6_6) = all_155_0_75, complement(all_0_6_6, all_0_9_9), test(all_0_6_6), yields: % 12.79/3.94 | (180) all_155_0_75 = all_0_9_9 % 12.79/3.94 | % 12.79/3.94 | Combining equations (175,174) yields a new equation: % 12.79/3.94 | (181) all_155_1_76 = all_155_2_77 % 12.79/3.94 | % 12.79/3.94 | Combining equations (179,174) yields a new equation: % 12.79/3.94 | (182) all_155_1_76 = all_69_0_33 % 12.79/3.94 | % 12.79/3.94 | Combining equations (176,180) yields a new equation: % 12.79/3.94 | (183) all_155_2_77 = all_0_9_9 % 12.79/3.94 | % 12.79/3.94 | Simplifying 183 yields: % 12.79/3.94 | (184) all_155_2_77 = all_0_9_9 % 12.79/3.94 | % 12.79/3.94 | Combining equations (181,182) yields a new equation: % 12.79/3.94 | (185) all_155_2_77 = all_69_0_33 % 12.79/3.94 | % 12.79/3.94 | Simplifying 185 yields: % 12.79/3.94 | (186) all_155_2_77 = all_69_0_33 % 12.79/3.94 | % 12.79/3.94 | Combining equations (184,177) yields a new equation: % 12.79/3.94 | (187) all_151_1_72 = all_0_9_9 % 12.79/3.94 | % 12.79/3.94 | Combining equations (186,177) yields a new equation: % 12.79/3.94 | (188) all_151_1_72 = all_69_0_33 % 12.79/3.94 | % 12.79/3.94 | Combining equations (188,187) yields a new equation: % 12.79/3.94 | (189) all_69_0_33 = all_0_9_9 % 12.79/3.94 | % 12.79/3.94 | Simplifying 189 yields: % 12.79/3.94 | (190) all_69_0_33 = all_0_9_9 % 12.79/3.94 | % 12.79/3.94 | Combining equations (187,177) yields a new equation: % 12.79/3.94 | (184) all_155_2_77 = all_0_9_9 % 12.79/3.94 | % 12.79/3.94 | Combining equations (190,182) yields a new equation: % 12.79/3.94 | (192) all_155_1_76 = all_0_9_9 % 12.79/3.94 | % 12.79/3.94 | From (192)(180)(184) and (164) follows: % 12.79/3.94 | (193) multiplication(all_0_9_9, all_0_9_9) = all_0_9_9 % 12.79/3.94 | % 12.79/3.94 | From (178) and (172) follows: % 12.79/3.94 | (22) addition(all_0_7_7, all_0_2_2) = all_0_0_0 % 12.79/3.94 | % 12.79/3.94 | Instantiating formula (11) with all_0_9_9, all_0_9_9, all_0_9_9, all_27_0_21 and discharging atoms multiplication(all_0_9_9, all_0_9_9) = all_27_0_21, multiplication(all_0_9_9, all_0_9_9) = all_0_9_9, yields: % 12.79/3.94 | (195) all_27_0_21 = all_0_9_9 % 12.79/3.94 | % 12.79/3.94 | From (195) and (95) follows: % 12.79/3.94 | (196) multiplication(all_0_9_9, all_0_12_12) = all_0_3_3 % 12.79/3.94 | % 12.79/3.94 | Instantiating formula (11) with all_0_9_9, all_0_12_12, all_0_3_3, all_0_7_7 and discharging atoms multiplication(all_0_9_9, all_0_12_12) = all_0_3_3, multiplication(all_0_9_9, all_0_12_12) = all_0_7_7, yields: % 12.79/3.94 | (197) all_0_3_3 = all_0_7_7 % 12.79/3.94 | % 12.79/3.94 | From (197) and (31) follows: % 12.79/3.94 | (198) addition(all_0_7_7, all_0_2_2) = all_0_1_1 % 12.79/3.94 | % 12.79/3.94 | Instantiating formula (21) with all_0_7_7, all_0_2_2, all_0_1_1, all_0_0_0 and discharging atoms addition(all_0_7_7, all_0_2_2) = all_0_0_0, addition(all_0_7_7, all_0_2_2) = all_0_1_1, yields: % 12.79/3.94 | (199) all_0_0_0 = all_0_1_1 % 12.79/3.94 | % 12.79/3.94 | Equations (199) can reduce 40 to: % 12.79/3.94 | (200) $false % 12.79/3.94 | % 12.79/3.94 |-The branch is then unsatisfiable % 12.79/3.94 |-Branch two: % 12.79/3.94 | (201) ~ complement(all_0_6_6, all_0_9_9) % 12.79/3.94 | (202) ? [v0] : ? [v1] : (multiplication(all_0_9_9, all_0_6_6) = v0 & addition(all_0_9_9, all_0_6_6) = v1 & ( ~ (v1 = one) | ~ (v0 = zero))) % 12.79/3.94 | % 12.79/3.94 | Instantiating (202) with all_289_0_146, all_289_1_147 yields: % 12.79/3.95 | (203) multiplication(all_0_9_9, all_0_6_6) = all_289_1_147 & addition(all_0_9_9, all_0_6_6) = all_289_0_146 & ( ~ (all_289_0_146 = one) | ~ (all_289_1_147 = zero)) % 12.79/3.95 | % 12.79/3.95 | Applying alpha-rule on (203) yields: % 12.79/3.95 | (204) multiplication(all_0_9_9, all_0_6_6) = all_289_1_147 % 12.79/3.95 | (205) addition(all_0_9_9, all_0_6_6) = all_289_0_146 % 12.79/3.95 | (206) ~ (all_289_0_146 = one) | ~ (all_289_1_147 = zero) % 12.79/3.95 | % 12.79/3.95 +-Applying beta-rule and splitting (104), into two cases. % 12.79/3.95 |-Branch one: % 12.79/3.95 | (173) complement(all_0_6_6, all_0_9_9) % 12.79/3.95 | % 12.79/3.95 | Using (173) and (201) yields: % 12.79/3.95 | (208) $false % 12.79/3.95 | % 12.79/3.95 |-The branch is then unsatisfiable % 12.79/3.95 |-Branch two: % 12.79/3.95 | (201) ~ complement(all_0_6_6, all_0_9_9) % 12.79/3.95 | (210) ? [v0] : ? [v1] : (multiplication(all_0_6_6, all_0_9_9) = v0 & addition(all_0_9_9, all_0_6_6) = v1 & ( ~ (v1 = one) | ~ (v0 = zero))) % 12.79/3.95 | % 12.79/3.95 | Instantiating (210) with all_295_0_148, all_295_1_149 yields: % 12.79/3.95 | (211) multiplication(all_0_6_6, all_0_9_9) = all_295_1_149 & addition(all_0_9_9, all_0_6_6) = all_295_0_148 & ( ~ (all_295_0_148 = one) | ~ (all_295_1_149 = zero)) % 12.79/3.95 | % 12.79/3.95 | Applying alpha-rule on (211) yields: % 12.79/3.95 | (212) multiplication(all_0_6_6, all_0_9_9) = all_295_1_149 % 12.79/3.95 | (213) addition(all_0_9_9, all_0_6_6) = all_295_0_148 % 12.79/3.95 | (214) ~ (all_295_0_148 = one) | ~ (all_295_1_149 = zero) % 12.79/3.95 | % 12.79/3.95 | Instantiating formula (8) with all_289_1_147, all_0_9_9, all_0_6_6 and discharging atoms multiplication(all_0_9_9, all_0_6_6) = all_289_1_147, complement(all_0_9_9, all_0_6_6), yields: % 12.79/3.95 | (215) all_289_1_147 = zero % 12.79/3.95 | % 12.79/3.95 | Instantiating formula (21) with all_0_9_9, all_0_6_6, all_289_0_146, all_295_0_148 and discharging atoms addition(all_0_9_9, all_0_6_6) = all_295_0_148, addition(all_0_9_9, all_0_6_6) = all_289_0_146, yields: % 12.79/3.95 | (216) all_295_0_148 = all_289_0_146 % 12.79/3.95 | % 12.79/3.95 | Instantiating formula (21) with all_0_9_9, all_0_6_6, one, all_295_0_148 and discharging atoms addition(all_0_9_9, all_0_6_6) = all_295_0_148, addition(all_0_9_9, all_0_6_6) = one, yields: % 12.79/3.95 | (217) all_295_0_148 = one % 12.79/3.95 | % 12.79/3.95 | Combining equations (216,217) yields a new equation: % 12.79/3.95 | (218) all_289_0_146 = one % 12.79/3.95 | % 12.79/3.95 | Simplifying 218 yields: % 12.79/3.95 | (219) all_289_0_146 = one % 12.79/3.95 | % 12.79/3.95 +-Applying beta-rule and splitting (206), into two cases. % 12.79/3.95 |-Branch one: % 12.79/3.95 | (220) ~ (all_289_1_147 = zero) % 12.79/3.95 | % 12.79/3.95 | Equations (215) can reduce 220 to: % 12.79/3.95 | (200) $false % 12.79/3.95 | % 12.79/3.95 |-The branch is then unsatisfiable % 12.79/3.95 |-Branch two: % 12.79/3.95 | (215) all_289_1_147 = zero % 12.79/3.95 | (223) ~ (all_289_0_146 = one) % 12.79/3.95 | % 12.79/3.95 | Equations (219) can reduce 223 to: % 12.79/3.95 | (200) $false % 12.79/3.95 | % 12.79/3.95 |-The branch is then unsatisfiable % 12.79/3.95 % SZS output end Proof for theBenchmark % 12.79/3.95 % 12.79/3.95 3271ms %------------------------------------------------------------------------------