%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE021+2 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n022.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 01:50:56 EDT 2022 % Result : Theorem 8.94s 2.77s % Output : Proof 16.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KLE021+2 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n022.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 12:51:47 EDT 2022 % 0.12/0.34 % CPUTime : % 0.50/0.58 ____ _ % 0.50/0.58 ___ / __ \_____(_)___ ________ __________ % 0.50/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.50/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.50/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.50/0.58 % 0.50/0.58 A Theorem Prover for First-Order Logic % 0.50/0.58 (ePrincess v.1.0) % 0.50/0.58 % 0.50/0.58 (c) Philipp Rümmer, 2009-2015 % 0.50/0.58 (c) Peter Backeman, 2014-2015 % 0.50/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.50/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.50/0.58 Bug reports to peter@backeman.se % 0.50/0.58 % 0.50/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.50/0.58 % 0.50/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.50/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.49/0.90 Prover 0: Preprocessing ... % 2.20/1.14 Prover 0: Constructing countermodel ... % 8.94/2.77 Prover 0: proved (2137ms) % 8.94/2.77 % 8.94/2.77 No countermodel exists, formula is valid % 8.94/2.77 % SZS status Theorem for theBenchmark % 8.94/2.77 % 8.94/2.77 Generating proof ... found it (size 143) % 16.04/4.47 % 16.04/4.47 % SZS output start Proof for theBenchmark % 16.04/4.47 Assumed formulas after preprocessing and simplification: % 16.04/4.47 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (c(v1) = v3 & multiplication(v3, v0) = v4 & multiplication(v1, v0) = v2 & addition(v2, v4) = v5 & test(v1) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (multiplication(v7, v8) = v10) | ~ (multiplication(v6, v8) = v9) | ~ (addition(v9, v10) = v11) | ? [v12] : (multiplication(v12, v8) = v11 & addition(v6, v7) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (multiplication(v6, v8) = v10) | ~ (multiplication(v6, v7) = v9) | ~ (addition(v9, v10) = v11) | ? [v12] : (multiplication(v6, v12) = v11 & addition(v7, v8) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v9, v8) = v10) | ~ (multiplication(v6, v7) = v9) | ? [v11] : (multiplication(v7, v8) = v11 & multiplication(v6, v11) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v9, v8) = v10) | ~ (addition(v6, v7) = v9) | ? [v11] : ? [v12] : (multiplication(v7, v8) = v12 & multiplication(v6, v8) = v11 & addition(v11, v12) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v7, v8) = v9) | ~ (multiplication(v6, v9) = v10) | ? [v11] : (multiplication(v11, v8) = v10 & multiplication(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v6, v9) = v10) | ~ (addition(v7, v8) = v9) | ? [v11] : ? [v12] : (multiplication(v6, v8) = v12 & multiplication(v6, v7) = v11 & addition(v11, v12) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (addition(v9, v6) = v10) | ~ (addition(v8, v7) = v9) | ? [v11] : (addition(v8, v11) = v10 & addition(v7, v6) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (addition(v8, v9) = v10) | ~ (addition(v7, v6) = v9) | ? [v11] : (addition(v11, v6) = v10 & addition(v8, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (multiplication(v9, v8) = v7) | ~ (multiplication(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (addition(v9, v8) = v7) | ~ (addition(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (c(v6) = v8) | ~ complement(v6, v7) | ~ test(v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (addition(v6, v7) = v8) | ~ leq(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : (v8 = one | ~ (addition(v6, v7) = v8) | ~ complement(v7, v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = zero | ~ (multiplication(v7, v6) = v8) | ~ complement(v7, v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = zero | ~ (multiplication(v6, v7) = v8) | ~ complement(v7, v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (c(v8) = v7) | ~ (c(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v7, v6) = v8) | ~ complement(v7, v6) | (multiplication(v6, v7) = zero & addition(v6, v7) = one)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v6, v7) = v8) | ~ complement(v7, v6) | (multiplication(v7, v6) = zero & addition(v6, v7) = one)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v7, v6) = v8) | addition(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v6, v7) = v8) | ~ complement(v7, v6) | (multiplication(v7, v6) = zero & multiplication(v6, v7) = zero)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v6, v7) = v8) | addition(v7, v6) = v8) & ! [v6] : ! [v7] : (v7 = v6 | ~ (multiplication(v6, one) = v7)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (multiplication(one, v6) = v7)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (addition(v6, v6) = v7)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (addition(v6, zero) = v7)) & ! [v6] : ! [v7] : (v7 = zero | ~ (c(v6) = v7) | test(v6)) & ! [v6] : ! [v7] : (v7 = zero | ~ (multiplication(v6, zero) = v7)) & ! [v6] : ! [v7] : (v7 = zero | ~ (multiplication(zero, v6) = v7)) & ! [v6] : ! [v7] : ( ~ (c(v6) = v7) | ~ test(v6) | complement(v6, v7)) & ! [v6] : ! [v7] : ( ~ (multiplication(v7, v6) = zero) | complement(v7, v6) | ? [v8] : ? [v9] : (multiplication(v6, v7) = v8 & addition(v6, v7) = v9 & ( ~ (v9 = one) | ~ (v8 = zero)))) & ! [v6] : ! [v7] : ( ~ (multiplication(v6, v7) = zero) | complement(v7, v6) | ? [v8] : ? [v9] : (multiplication(v7, v6) = v8 & addition(v6, v7) = v9 & ( ~ (v9 = one) | ~ (v8 = zero)))) & ! [v6] : ! [v7] : ( ~ (addition(v6, v7) = v7) | leq(v6, v7)) & ! [v6] : ! [v7] : ( ~ (addition(v6, v7) = one) | complement(v7, v6) | ? [v8] : ? [v9] : (multiplication(v7, v6) = v9 & multiplication(v6, v7) = v8 & ( ~ (v9 = zero) | ~ (v8 = zero)))) & ! [v6] : ! [v7] : ( ~ complement(v7, v6) | test(v6)) & ! [v6] : ( ~ test(v6) | ? [v7] : complement(v7, v6)) & ( ~ leq(v5, v0) | ~ leq(v0, v5))) % 16.18/4.51 | 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 yields: % 16.18/4.51 | (1) c(all_0_4_4) = all_0_2_2 & multiplication(all_0_2_2, all_0_5_5) = all_0_1_1 & multiplication(all_0_4_4, all_0_5_5) = all_0_3_3 & addition(all_0_3_3, all_0_1_1) = all_0_0_0 & test(all_0_4_4) & ! [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] : ( ~ (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] : ( ~ (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) | 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)) & ( ~ leq(all_0_0_0, all_0_5_5) | ~ leq(all_0_5_5, all_0_0_0)) % 16.47/4.53 | % 16.47/4.53 | Applying alpha-rule on (1) yields: % 16.47/4.53 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 16.47/4.53 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero)) % 16.47/4.53 | (4) ! [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)) % 16.47/4.54 | (5) ! [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)) % 16.47/4.54 | (6) addition(all_0_3_3, all_0_1_1) = all_0_0_0 % 16.47/4.54 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 16.47/4.54 | (8) ! [v0] : ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) % 16.47/4.54 | (9) ! [v0] : ( ~ test(v0) | ? [v1] : complement(v1, v0)) % 16.47/4.54 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 16.47/4.54 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 16.47/4.54 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 16.47/4.54 | (13) c(all_0_4_4) = all_0_2_2 % 16.47/4.54 | (14) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) % 16.47/4.54 | (15) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 16.47/4.54 | (16) ! [v0] : ! [v1] : (v1 = zero | ~ (c(v0) = v1) | test(v0)) % 16.47/4.54 | (17) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 16.47/4.54 | (18) ! [v0] : ! [v1] : ( ~ (c(v0) = v1) | ~ test(v0) | complement(v0, v1)) % 16.47/4.54 | (19) multiplication(all_0_2_2, all_0_5_5) = all_0_1_1 % 16.47/4.54 | (20) ! [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)) % 16.47/4.54 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0)) % 16.47/4.54 | (22) ! [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)) % 16.47/4.54 | (23) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 16.47/4.54 | (24) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 16.47/4.54 | (25) multiplication(all_0_4_4, all_0_5_5) = all_0_3_3 % 16.47/4.54 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (c(v0) = v2) | ~ complement(v0, v1) | ~ test(v0)) % 16.47/4.54 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) % 16.47/4.54 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 16.47/4.54 | (29) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) | ~ (v2 = zero)))) % 16.47/4.54 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 16.47/4.54 | (31) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 16.47/4.54 | (32) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) % 16.47/4.54 | (33) ~ leq(all_0_0_0, all_0_5_5) | ~ leq(all_0_5_5, all_0_0_0) % 16.47/4.54 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 16.47/4.55 | (35) ! [v0] : ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) % 16.47/4.55 | (36) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 16.47/4.55 | (37) test(all_0_4_4) % 16.47/4.55 | (38) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0)) % 16.47/4.55 | (39) ! [v0] : ! [v1] : ! [v2] : (v2 = one | ~ (addition(v0, v1) = v2) | ~ complement(v1, v0)) % 16.47/4.55 | (40) ! [v0] : ! [v1] : ( ~ complement(v1, v0) | test(v0)) % 16.47/4.55 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one)) % 16.47/4.55 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one)) % 16.47/4.55 | % 16.47/4.55 | Instantiating formula (22) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_5_5, all_0_2_2, all_0_4_4 and discharging atoms multiplication(all_0_2_2, all_0_5_5) = all_0_1_1, multiplication(all_0_4_4, all_0_5_5) = all_0_3_3, addition(all_0_3_3, all_0_1_1) = all_0_0_0, yields: % 16.47/4.55 | (43) ? [v0] : (multiplication(v0, all_0_5_5) = all_0_0_0 & addition(all_0_4_4, all_0_2_2) = v0) % 16.47/4.55 | % 16.47/4.55 | Instantiating formula (12) with all_0_0_0, all_0_3_3, all_0_1_1 and discharging atoms addition(all_0_3_3, all_0_1_1) = all_0_0_0, yields: % 16.47/4.55 | (44) addition(all_0_1_1, all_0_3_3) = all_0_0_0 % 16.47/4.55 | % 16.47/4.55 | Instantiating formula (18) with all_0_2_2, all_0_4_4 and discharging atoms c(all_0_4_4) = all_0_2_2, test(all_0_4_4), yields: % 16.47/4.55 | (45) complement(all_0_4_4, all_0_2_2) % 16.47/4.55 | % 16.47/4.55 | Instantiating (43) with all_9_0_6 yields: % 16.47/4.55 | (46) multiplication(all_9_0_6, all_0_5_5) = all_0_0_0 & addition(all_0_4_4, all_0_2_2) = all_9_0_6 % 16.47/4.55 | % 16.47/4.55 | Applying alpha-rule on (46) yields: % 16.47/4.55 | (47) multiplication(all_9_0_6, all_0_5_5) = all_0_0_0 % 16.47/4.55 | (48) addition(all_0_4_4, all_0_2_2) = all_9_0_6 % 16.47/4.55 | % 16.47/4.55 | Instantiating formula (22) with all_0_0_0, all_0_3_3, all_0_1_1, all_0_5_5, all_0_4_4, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_5_5) = all_0_1_1, multiplication(all_0_4_4, all_0_5_5) = all_0_3_3, addition(all_0_1_1, all_0_3_3) = all_0_0_0, yields: % 16.47/4.55 | (49) ? [v0] : (multiplication(v0, all_0_5_5) = all_0_0_0 & addition(all_0_2_2, all_0_4_4) = v0) % 16.47/4.55 | % 16.47/4.55 | Instantiating formula (12) with all_9_0_6, all_0_4_4, all_0_2_2 and discharging atoms addition(all_0_4_4, all_0_2_2) = all_9_0_6, yields: % 16.47/4.55 | (50) addition(all_0_2_2, all_0_4_4) = all_9_0_6 % 16.47/4.55 | % 16.47/4.55 | Instantiating (49) with all_19_0_8 yields: % 16.47/4.55 | (51) multiplication(all_19_0_8, all_0_5_5) = all_0_0_0 & addition(all_0_2_2, all_0_4_4) = all_19_0_8 % 16.47/4.55 | % 16.47/4.55 | Applying alpha-rule on (51) yields: % 16.47/4.55 | (52) multiplication(all_19_0_8, all_0_5_5) = all_0_0_0 % 16.47/4.55 | (53) addition(all_0_2_2, all_0_4_4) = all_19_0_8 % 16.47/4.55 | % 16.47/4.55 | Instantiating formula (39) with all_19_0_8, all_0_4_4, all_0_2_2 and discharging atoms addition(all_0_2_2, all_0_4_4) = all_19_0_8, complement(all_0_4_4, all_0_2_2), yields: % 16.47/4.55 | (54) all_19_0_8 = one % 16.47/4.55 | % 16.47/4.55 | Instantiating formula (28) with all_0_2_2, all_0_4_4, all_9_0_6, all_19_0_8 and discharging atoms addition(all_0_2_2, all_0_4_4) = all_19_0_8, addition(all_0_2_2, all_0_4_4) = all_9_0_6, yields: % 16.47/4.55 | (55) all_19_0_8 = all_9_0_6 % 16.47/4.55 | % 16.47/4.55 | Combining equations (54,55) yields a new equation: % 16.47/4.55 | (56) all_9_0_6 = one % 16.47/4.55 | % 16.47/4.55 | From (56) and (47) follows: % 16.47/4.55 | (57) multiplication(one, all_0_5_5) = all_0_0_0 % 16.47/4.55 | % 16.47/4.55 | From (56) and (50) follows: % 16.47/4.55 | (58) addition(all_0_2_2, all_0_4_4) = one % 16.47/4.55 | % 16.47/4.55 | From (56) and (48) follows: % 16.47/4.55 | (59) addition(all_0_4_4, all_0_2_2) = one % 16.47/4.55 | % 16.47/4.55 | Instantiating formula (31) with all_0_0_0, all_0_5_5 and discharging atoms multiplication(one, all_0_5_5) = all_0_0_0, yields: % 16.47/4.55 | (60) all_0_0_0 = all_0_5_5 % 16.47/4.55 | % 16.47/4.55 | From (60) and (57) follows: % 16.47/4.55 | (61) multiplication(one, all_0_5_5) = all_0_5_5 % 16.47/4.55 | % 16.47/4.55 | From (60) and (44) follows: % 16.47/4.55 | (62) addition(all_0_1_1, all_0_3_3) = all_0_5_5 % 16.47/4.55 | % 16.47/4.55 | From (60) and (6) follows: % 16.47/4.55 | (63) addition(all_0_3_3, all_0_1_1) = all_0_5_5 % 16.47/4.55 | % 16.47/4.55 +-Applying beta-rule and splitting (33), into two cases. % 16.47/4.55 |-Branch one: % 16.47/4.55 | (64) ~ leq(all_0_0_0, all_0_5_5) % 16.47/4.55 | % 16.47/4.55 | From (60) and (64) follows: % 16.47/4.55 | (65) ~ leq(all_0_5_5, all_0_5_5) % 16.47/4.56 | % 16.47/4.56 | Instantiating formula (2) with all_0_1_1, all_0_5_5, all_0_5_5, one, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_5_5) = all_0_1_1, multiplication(one, all_0_5_5) = all_0_5_5, yields: % 16.47/4.56 | (66) ? [v0] : (multiplication(v0, all_0_5_5) = all_0_1_1 & multiplication(all_0_2_2, one) = v0) % 16.47/4.56 | % 16.47/4.56 | Instantiating formula (2) with all_0_3_3, all_0_5_5, all_0_5_5, one, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_5_5) = all_0_3_3, multiplication(one, all_0_5_5) = all_0_5_5, yields: % 16.47/4.56 | (67) ? [v0] : (multiplication(v0, all_0_5_5) = all_0_3_3 & multiplication(all_0_4_4, one) = v0) % 16.47/4.56 | % 16.47/4.56 | Instantiating formula (20) with all_0_1_1, all_0_5_5, all_0_3_3, all_0_1_1, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_5_5) = all_0_1_1, addition(all_0_1_1, all_0_3_3) = all_0_5_5, yields: % 16.47/4.56 | (68) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_0_1_1) = v0 & multiplication(all_0_2_2, all_0_3_3) = v1 & addition(v0, v1) = all_0_1_1) % 16.47/4.56 | % 16.47/4.56 | Instantiating formula (20) with all_0_3_3, all_0_5_5, all_0_3_3, all_0_1_1, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_5_5) = all_0_3_3, addition(all_0_1_1, all_0_3_3) = all_0_5_5, yields: % 16.47/4.56 | (69) ? [v0] : ? [v1] : (multiplication(all_0_4_4, all_0_1_1) = v0 & multiplication(all_0_4_4, all_0_3_3) = v1 & addition(v0, v1) = all_0_3_3) % 16.47/4.56 | % 16.47/4.56 | Instantiating formula (3) with one, all_0_4_4, all_0_2_2 and discharging atoms addition(all_0_2_2, all_0_4_4) = one, complement(all_0_4_4, all_0_2_2), yields: % 16.47/4.56 | (70) multiplication(all_0_2_2, all_0_4_4) = zero & multiplication(all_0_4_4, all_0_2_2) = zero % 16.47/4.56 | % 16.47/4.56 | Applying alpha-rule on (70) yields: % 16.47/4.56 | (71) multiplication(all_0_2_2, all_0_4_4) = zero % 16.47/4.56 | (72) multiplication(all_0_4_4, all_0_2_2) = zero % 16.47/4.56 | % 16.47/4.56 | Instantiating formula (20) with all_0_1_1, all_0_5_5, all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_5_5) = all_0_1_1, addition(all_0_3_3, all_0_1_1) = all_0_5_5, yields: % 16.47/4.56 | (73) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_0_1_1) = v1 & multiplication(all_0_2_2, all_0_3_3) = v0 & addition(v0, v1) = all_0_1_1) % 16.47/4.56 | % 16.47/4.56 | Instantiating formula (20) with all_0_3_3, all_0_5_5, all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_5_5) = all_0_3_3, addition(all_0_3_3, all_0_1_1) = all_0_5_5, yields: % 16.47/4.56 | (74) ? [v0] : ? [v1] : (multiplication(all_0_4_4, all_0_1_1) = v1 & multiplication(all_0_4_4, all_0_3_3) = v0 & addition(v0, v1) = all_0_3_3) % 16.47/4.56 | % 16.47/4.56 | Instantiating (73) with all_45_0_14, all_45_1_15 yields: % 16.47/4.56 | (75) multiplication(all_0_2_2, all_0_1_1) = all_45_0_14 & multiplication(all_0_2_2, all_0_3_3) = all_45_1_15 & addition(all_45_1_15, all_45_0_14) = all_0_1_1 % 16.47/4.56 | % 16.47/4.56 | Applying alpha-rule on (75) yields: % 16.47/4.56 | (76) multiplication(all_0_2_2, all_0_1_1) = all_45_0_14 % 16.47/4.56 | (77) multiplication(all_0_2_2, all_0_3_3) = all_45_1_15 % 16.47/4.56 | (78) addition(all_45_1_15, all_45_0_14) = all_0_1_1 % 16.47/4.56 | % 16.47/4.56 | Instantiating (69) with all_47_0_16, all_47_1_17 yields: % 16.47/4.56 | (79) multiplication(all_0_4_4, all_0_1_1) = all_47_1_17 & multiplication(all_0_4_4, all_0_3_3) = all_47_0_16 & addition(all_47_1_17, all_47_0_16) = all_0_3_3 % 16.47/4.56 | % 16.47/4.56 | Applying alpha-rule on (79) yields: % 16.47/4.56 | (80) multiplication(all_0_4_4, all_0_1_1) = all_47_1_17 % 16.47/4.56 | (81) multiplication(all_0_4_4, all_0_3_3) = all_47_0_16 % 16.47/4.56 | (82) addition(all_47_1_17, all_47_0_16) = all_0_3_3 % 16.47/4.56 | % 16.47/4.56 | Instantiating (68) with all_49_0_18, all_49_1_19 yields: % 16.47/4.56 | (83) multiplication(all_0_2_2, all_0_1_1) = all_49_1_19 & multiplication(all_0_2_2, all_0_3_3) = all_49_0_18 & addition(all_49_1_19, all_49_0_18) = all_0_1_1 % 16.47/4.56 | % 16.47/4.56 | Applying alpha-rule on (83) yields: % 16.47/4.56 | (84) multiplication(all_0_2_2, all_0_1_1) = all_49_1_19 % 16.47/4.56 | (85) multiplication(all_0_2_2, all_0_3_3) = all_49_0_18 % 16.47/4.56 | (86) addition(all_49_1_19, all_49_0_18) = all_0_1_1 % 16.47/4.56 | % 16.47/4.56 | Instantiating (67) with all_51_0_20 yields: % 16.47/4.56 | (87) multiplication(all_51_0_20, all_0_5_5) = all_0_3_3 & multiplication(all_0_4_4, one) = all_51_0_20 % 16.47/4.56 | % 16.47/4.56 | Applying alpha-rule on (87) yields: % 16.47/4.56 | (88) multiplication(all_51_0_20, all_0_5_5) = all_0_3_3 % 16.47/4.56 | (89) multiplication(all_0_4_4, one) = all_51_0_20 % 16.47/4.56 | % 16.47/4.56 | Instantiating (66) with all_53_0_21 yields: % 16.47/4.56 | (90) multiplication(all_53_0_21, all_0_5_5) = all_0_1_1 & multiplication(all_0_2_2, one) = all_53_0_21 % 16.47/4.56 | % 16.47/4.56 | Applying alpha-rule on (90) yields: % 16.47/4.56 | (91) multiplication(all_53_0_21, all_0_5_5) = all_0_1_1 % 16.47/4.56 | (92) multiplication(all_0_2_2, one) = all_53_0_21 % 16.47/4.56 | % 16.47/4.56 | Instantiating (74) with all_55_0_22, all_55_1_23 yields: % 16.47/4.56 | (93) multiplication(all_0_4_4, all_0_1_1) = all_55_0_22 & multiplication(all_0_4_4, all_0_3_3) = all_55_1_23 & addition(all_55_1_23, all_55_0_22) = all_0_3_3 % 16.47/4.56 | % 16.47/4.56 | Applying alpha-rule on (93) yields: % 16.47/4.56 | (94) multiplication(all_0_4_4, all_0_1_1) = all_55_0_22 % 16.47/4.56 | (95) multiplication(all_0_4_4, all_0_3_3) = all_55_1_23 % 16.47/4.56 | (96) addition(all_55_1_23, all_55_0_22) = all_0_3_3 % 16.47/4.56 | % 16.47/4.56 | Instantiating formula (34) with all_0_2_2, all_0_1_1, all_45_0_14, all_49_1_19 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_49_1_19, multiplication(all_0_2_2, all_0_1_1) = all_45_0_14, yields: % 16.47/4.56 | (97) all_49_1_19 = all_45_0_14 % 16.47/4.56 | % 16.47/4.56 | Instantiating formula (34) with all_0_2_2, all_0_3_3, all_45_1_15, all_49_0_18 and discharging atoms multiplication(all_0_2_2, all_0_3_3) = all_49_0_18, multiplication(all_0_2_2, all_0_3_3) = all_45_1_15, yields: % 16.47/4.56 | (98) all_49_0_18 = all_45_1_15 % 16.47/4.56 | % 16.47/4.56 | Instantiating formula (23) with all_53_0_21, all_0_2_2 and discharging atoms multiplication(all_0_2_2, one) = all_53_0_21, yields: % 16.47/4.56 | (99) all_53_0_21 = all_0_2_2 % 16.47/4.56 | % 16.47/4.56 | Instantiating formula (34) with all_0_4_4, all_0_1_1, all_47_1_17, all_55_0_22 and discharging atoms multiplication(all_0_4_4, all_0_1_1) = all_55_0_22, multiplication(all_0_4_4, all_0_1_1) = all_47_1_17, yields: % 16.47/4.56 | (100) all_55_0_22 = all_47_1_17 % 16.47/4.56 | % 16.47/4.56 | Instantiating formula (34) with all_0_4_4, all_0_3_3, all_47_0_16, all_55_1_23 and discharging atoms multiplication(all_0_4_4, all_0_3_3) = all_55_1_23, multiplication(all_0_4_4, all_0_3_3) = all_47_0_16, yields: % 16.47/4.56 | (101) all_55_1_23 = all_47_0_16 % 16.47/4.56 | % 16.47/4.56 | Instantiating formula (23) with all_51_0_20, all_0_4_4 and discharging atoms multiplication(all_0_4_4, one) = all_51_0_20, yields: % 16.47/4.56 | (102) all_51_0_20 = all_0_4_4 % 16.47/4.56 | % 16.47/4.56 | From (99) and (91) follows: % 16.47/4.56 | (19) multiplication(all_0_2_2, all_0_5_5) = all_0_1_1 % 16.47/4.56 | % 16.47/4.56 | From (102) and (88) follows: % 16.47/4.56 | (25) multiplication(all_0_4_4, all_0_5_5) = all_0_3_3 % 16.47/4.56 | % 16.47/4.56 | From (98) and (85) follows: % 16.47/4.56 | (77) multiplication(all_0_2_2, all_0_3_3) = all_45_1_15 % 16.47/4.56 | % 16.47/4.56 | From (99) and (92) follows: % 16.47/4.56 | (106) multiplication(all_0_2_2, one) = all_0_2_2 % 16.47/4.56 | % 16.47/4.56 | From (100) and (94) follows: % 16.47/4.56 | (80) multiplication(all_0_4_4, all_0_1_1) = all_47_1_17 % 16.47/4.56 | % 16.47/4.56 | From (101) and (95) follows: % 16.47/4.56 | (81) multiplication(all_0_4_4, all_0_3_3) = all_47_0_16 % 16.47/4.56 | % 16.47/4.56 | From (102) and (89) follows: % 16.47/4.56 | (109) multiplication(all_0_4_4, one) = all_0_4_4 % 16.47/4.56 | % 16.47/4.56 | From (101)(100) and (96) follows: % 16.47/4.57 | (110) addition(all_47_0_16, all_47_1_17) = all_0_3_3 % 16.47/4.57 | % 16.47/4.57 | From (97)(98) and (86) follows: % 16.47/4.57 | (111) addition(all_45_0_14, all_45_1_15) = all_0_1_1 % 16.47/4.57 | % 16.47/4.57 | Instantiating formula (2) with all_45_1_15, all_0_3_3, all_0_5_5, all_0_4_4, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_3_3) = all_45_1_15, multiplication(all_0_4_4, all_0_5_5) = all_0_3_3, yields: % 16.47/4.57 | (112) ? [v0] : (multiplication(v0, all_0_5_5) = all_45_1_15 & multiplication(all_0_2_2, all_0_4_4) = v0) % 16.47/4.57 | % 16.47/4.57 | Instantiating formula (20) with all_0_2_2, one, all_0_2_2, all_0_4_4, all_0_2_2 and discharging atoms multiplication(all_0_2_2, one) = all_0_2_2, addition(all_0_4_4, all_0_2_2) = one, yields: % 16.47/4.57 | (113) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_0_2_2) = v1 & multiplication(all_0_2_2, all_0_4_4) = v0 & addition(v0, v1) = all_0_2_2) % 16.47/4.57 | % 16.47/4.57 | Instantiating formula (2) with all_47_1_17, all_0_1_1, all_0_5_5, all_0_2_2, all_0_4_4 and discharging atoms multiplication(all_0_2_2, all_0_5_5) = all_0_1_1, multiplication(all_0_4_4, all_0_1_1) = all_47_1_17, yields: % 16.47/4.57 | (114) ? [v0] : (multiplication(v0, all_0_5_5) = all_47_1_17 & multiplication(all_0_4_4, all_0_2_2) = v0) % 16.47/4.57 | % 16.47/4.57 | Instantiating formula (2) with zero, all_0_2_2, one, all_0_2_2, all_0_4_4 and discharging atoms multiplication(all_0_2_2, one) = all_0_2_2, multiplication(all_0_4_4, all_0_2_2) = zero, yields: % 16.47/4.57 | (115) ? [v0] : (multiplication(v0, one) = zero & multiplication(all_0_4_4, all_0_2_2) = v0) % 16.47/4.57 | % 16.47/4.57 | Instantiating formula (2) with zero, all_0_4_4, one, all_0_4_4, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_4_4) = zero, multiplication(all_0_4_4, one) = all_0_4_4, yields: % 16.47/4.57 | (116) ? [v0] : (multiplication(v0, one) = zero & multiplication(all_0_2_2, all_0_4_4) = v0) % 16.47/4.57 | % 16.47/4.57 | Instantiating formula (20) with all_0_4_4, one, all_0_4_4, all_0_2_2, all_0_4_4 and discharging atoms multiplication(all_0_4_4, one) = all_0_4_4, addition(all_0_2_2, all_0_4_4) = one, yields: % 16.47/4.57 | (117) ? [v0] : ? [v1] : (multiplication(all_0_4_4, all_0_2_2) = v0 & multiplication(all_0_4_4, all_0_4_4) = v1 & addition(v0, v1) = all_0_4_4) % 16.47/4.57 | % 16.47/4.57 | Instantiating formula (20) with all_0_4_4, one, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms multiplication(all_0_4_4, one) = all_0_4_4, addition(all_0_4_4, all_0_2_2) = one, yields: % 16.47/4.57 | (118) ? [v0] : ? [v1] : (multiplication(all_0_4_4, all_0_2_2) = v1 & multiplication(all_0_4_4, all_0_4_4) = v0 & addition(v0, v1) = all_0_4_4) % 16.47/4.57 | % 16.47/4.57 | Instantiating formula (20) with all_47_0_16, all_0_3_3, all_47_1_17, all_47_0_16, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_3_3) = all_47_0_16, addition(all_47_0_16, all_47_1_17) = all_0_3_3, yields: % 16.47/4.57 | (119) ? [v0] : ? [v1] : (multiplication(all_0_4_4, all_47_0_16) = v0 & multiplication(all_0_4_4, all_47_1_17) = v1 & addition(v0, v1) = all_47_0_16) % 16.47/4.57 | % 16.47/4.57 | Instantiating formula (20) with all_47_0_16, all_0_3_3, all_47_0_16, all_47_1_17, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_3_3) = all_47_0_16, addition(all_47_1_17, all_47_0_16) = all_0_3_3, yields: % 16.47/4.57 | (120) ? [v0] : ? [v1] : (multiplication(all_0_4_4, all_47_0_16) = v1 & multiplication(all_0_4_4, all_47_1_17) = v0 & addition(v0, v1) = all_47_0_16) % 16.47/4.57 | % 16.47/4.57 | Instantiating formula (20) with all_47_1_17, all_0_1_1, all_45_1_15, all_45_0_14, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_1_1) = all_47_1_17, addition(all_45_0_14, all_45_1_15) = all_0_1_1, yields: % 16.47/4.57 | (121) ? [v0] : ? [v1] : (multiplication(all_0_4_4, all_45_0_14) = v0 & multiplication(all_0_4_4, all_45_1_15) = v1 & addition(v0, v1) = all_47_1_17) % 16.47/4.57 | % 16.47/4.57 | Instantiating formula (20) with all_47_1_17, all_0_1_1, all_45_0_14, all_45_1_15, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_1_1) = all_47_1_17, addition(all_45_1_15, all_45_0_14) = all_0_1_1, yields: % 16.47/4.57 | (122) ? [v0] : ? [v1] : (multiplication(all_0_4_4, all_45_0_14) = v1 & multiplication(all_0_4_4, all_45_1_15) = v0 & addition(v0, v1) = all_47_1_17) % 16.47/4.57 | % 16.47/4.57 | Instantiating (121) with all_76_0_28, all_76_1_29 yields: % 16.47/4.57 | (123) multiplication(all_0_4_4, all_45_0_14) = all_76_1_29 & multiplication(all_0_4_4, all_45_1_15) = all_76_0_28 & addition(all_76_1_29, all_76_0_28) = all_47_1_17 % 16.47/4.57 | % 16.47/4.57 | Applying alpha-rule on (123) yields: % 16.47/4.57 | (124) multiplication(all_0_4_4, all_45_0_14) = all_76_1_29 % 16.47/4.57 | (125) multiplication(all_0_4_4, all_45_1_15) = all_76_0_28 % 16.47/4.57 | (126) addition(all_76_1_29, all_76_0_28) = all_47_1_17 % 16.47/4.57 | % 16.47/4.57 | Instantiating (120) with all_90_0_40, all_90_1_41 yields: % 16.47/4.57 | (127) multiplication(all_0_4_4, all_47_0_16) = all_90_0_40 & multiplication(all_0_4_4, all_47_1_17) = all_90_1_41 & addition(all_90_1_41, all_90_0_40) = all_47_0_16 % 16.47/4.57 | % 16.47/4.57 | Applying alpha-rule on (127) yields: % 16.47/4.57 | (128) multiplication(all_0_4_4, all_47_0_16) = all_90_0_40 % 16.47/4.57 | (129) multiplication(all_0_4_4, all_47_1_17) = all_90_1_41 % 16.47/4.57 | (130) addition(all_90_1_41, all_90_0_40) = all_47_0_16 % 16.66/4.57 | % 16.66/4.57 | Instantiating (122) with all_96_0_44, all_96_1_45 yields: % 16.66/4.57 | (131) multiplication(all_0_4_4, all_45_0_14) = all_96_0_44 & multiplication(all_0_4_4, all_45_1_15) = all_96_1_45 & addition(all_96_1_45, all_96_0_44) = all_47_1_17 % 16.66/4.57 | % 16.66/4.57 | Applying alpha-rule on (131) yields: % 16.66/4.57 | (132) multiplication(all_0_4_4, all_45_0_14) = all_96_0_44 % 16.66/4.57 | (133) multiplication(all_0_4_4, all_45_1_15) = all_96_1_45 % 16.66/4.57 | (134) addition(all_96_1_45, all_96_0_44) = all_47_1_17 % 16.66/4.57 | % 16.66/4.57 | Instantiating (115) with all_116_0_59 yields: % 16.66/4.57 | (135) multiplication(all_116_0_59, one) = zero & multiplication(all_0_4_4, all_0_2_2) = all_116_0_59 % 16.66/4.57 | % 16.66/4.57 | Applying alpha-rule on (135) yields: % 16.66/4.57 | (136) multiplication(all_116_0_59, one) = zero % 16.66/4.57 | (137) multiplication(all_0_4_4, all_0_2_2) = all_116_0_59 % 16.66/4.57 | % 16.66/4.57 | Instantiating (112) with all_120_0_62 yields: % 16.66/4.57 | (138) multiplication(all_120_0_62, all_0_5_5) = all_45_1_15 & multiplication(all_0_2_2, all_0_4_4) = all_120_0_62 % 16.66/4.57 | % 16.66/4.57 | Applying alpha-rule on (138) yields: % 16.66/4.57 | (139) multiplication(all_120_0_62, all_0_5_5) = all_45_1_15 % 16.66/4.57 | (140) multiplication(all_0_2_2, all_0_4_4) = all_120_0_62 % 16.66/4.57 | % 16.66/4.57 | Instantiating (114) with all_128_0_66 yields: % 16.66/4.57 | (141) multiplication(all_128_0_66, all_0_5_5) = all_47_1_17 & multiplication(all_0_4_4, all_0_2_2) = all_128_0_66 % 16.66/4.57 | % 16.66/4.57 | Applying alpha-rule on (141) yields: % 16.66/4.57 | (142) multiplication(all_128_0_66, all_0_5_5) = all_47_1_17 % 16.66/4.57 | (143) multiplication(all_0_4_4, all_0_2_2) = all_128_0_66 % 16.66/4.57 | % 16.66/4.57 | Instantiating (113) with all_130_0_67, all_130_1_68 yields: % 16.66/4.57 | (144) multiplication(all_0_2_2, all_0_2_2) = all_130_0_67 & multiplication(all_0_2_2, all_0_4_4) = all_130_1_68 & addition(all_130_1_68, all_130_0_67) = all_0_2_2 % 16.66/4.57 | % 16.66/4.57 | Applying alpha-rule on (144) yields: % 16.66/4.57 | (145) multiplication(all_0_2_2, all_0_2_2) = all_130_0_67 % 16.66/4.57 | (146) multiplication(all_0_2_2, all_0_4_4) = all_130_1_68 % 16.66/4.58 | (147) addition(all_130_1_68, all_130_0_67) = all_0_2_2 % 16.66/4.58 | % 16.66/4.58 | Instantiating (119) with all_136_0_73, all_136_1_74 yields: % 16.66/4.58 | (148) multiplication(all_0_4_4, all_47_0_16) = all_136_1_74 & multiplication(all_0_4_4, all_47_1_17) = all_136_0_73 & addition(all_136_1_74, all_136_0_73) = all_47_0_16 % 16.66/4.58 | % 16.66/4.58 | Applying alpha-rule on (148) yields: % 16.66/4.58 | (149) multiplication(all_0_4_4, all_47_0_16) = all_136_1_74 % 16.66/4.58 | (150) multiplication(all_0_4_4, all_47_1_17) = all_136_0_73 % 16.66/4.58 | (151) addition(all_136_1_74, all_136_0_73) = all_47_0_16 % 16.66/4.58 | % 16.66/4.58 | Instantiating (118) with all_138_0_75, all_138_1_76 yields: % 16.66/4.58 | (152) multiplication(all_0_4_4, all_0_2_2) = all_138_0_75 & multiplication(all_0_4_4, all_0_4_4) = all_138_1_76 & addition(all_138_1_76, all_138_0_75) = all_0_4_4 % 16.66/4.58 | % 16.66/4.58 | Applying alpha-rule on (152) yields: % 16.66/4.58 | (153) multiplication(all_0_4_4, all_0_2_2) = all_138_0_75 % 16.66/4.58 | (154) multiplication(all_0_4_4, all_0_4_4) = all_138_1_76 % 16.66/4.58 | (155) addition(all_138_1_76, all_138_0_75) = all_0_4_4 % 16.66/4.58 | % 16.66/4.58 | Instantiating (117) with all_140_0_77, all_140_1_78 yields: % 16.66/4.58 | (156) multiplication(all_0_4_4, all_0_2_2) = all_140_1_78 & multiplication(all_0_4_4, all_0_4_4) = all_140_0_77 & addition(all_140_1_78, all_140_0_77) = all_0_4_4 % 16.66/4.58 | % 16.66/4.58 | Applying alpha-rule on (156) yields: % 16.66/4.58 | (157) multiplication(all_0_4_4, all_0_2_2) = all_140_1_78 % 16.66/4.58 | (158) multiplication(all_0_4_4, all_0_4_4) = all_140_0_77 % 16.66/4.58 | (159) addition(all_140_1_78, all_140_0_77) = all_0_4_4 % 16.66/4.58 | % 16.66/4.58 | Instantiating (116) with all_146_0_82 yields: % 16.66/4.58 | (160) multiplication(all_146_0_82, one) = zero & multiplication(all_0_2_2, all_0_4_4) = all_146_0_82 % 16.66/4.58 | % 16.66/4.58 | Applying alpha-rule on (160) yields: % 16.66/4.58 | (161) multiplication(all_146_0_82, one) = zero % 16.66/4.58 | (162) multiplication(all_0_2_2, all_0_4_4) = all_146_0_82 % 16.66/4.58 | % 16.66/4.58 | Instantiating formula (38) with all_146_0_82, all_0_4_4, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_4_4) = all_146_0_82, complement(all_0_4_4, all_0_2_2), yields: % 16.66/4.58 | (163) all_146_0_82 = zero % 16.66/4.58 | % 16.66/4.58 | Instantiating formula (34) with all_0_2_2, all_0_4_4, all_130_1_68, all_146_0_82 and discharging atoms multiplication(all_0_2_2, all_0_4_4) = all_146_0_82, multiplication(all_0_2_2, all_0_4_4) = all_130_1_68, yields: % 16.66/4.58 | (164) all_146_0_82 = all_130_1_68 % 16.66/4.58 | % 16.66/4.58 | Instantiating formula (34) with all_0_2_2, all_0_4_4, all_120_0_62, all_130_1_68 and discharging atoms multiplication(all_0_2_2, all_0_4_4) = all_130_1_68, multiplication(all_0_2_2, all_0_4_4) = all_120_0_62, yields: % 16.66/4.58 | (165) all_130_1_68 = all_120_0_62 % 16.66/4.58 | % 16.66/4.58 | Instantiating formula (34) with all_0_4_4, all_47_1_17, all_90_1_41, all_136_0_73 and discharging atoms multiplication(all_0_4_4, all_47_1_17) = all_136_0_73, multiplication(all_0_4_4, all_47_1_17) = all_90_1_41, yields: % 16.66/4.58 | (166) all_136_0_73 = all_90_1_41 % 16.66/4.58 | % 16.66/4.58 | Instantiating formula (34) with all_0_4_4, all_45_0_14, all_76_1_29, all_96_0_44 and discharging atoms multiplication(all_0_4_4, all_45_0_14) = all_96_0_44, multiplication(all_0_4_4, all_45_0_14) = all_76_1_29, yields: % 16.66/4.58 | (167) all_96_0_44 = all_76_1_29 % 16.66/4.58 | % 16.66/4.58 | Instantiating formula (34) with all_0_4_4, all_45_1_15, all_76_0_28, all_96_1_45 and discharging atoms multiplication(all_0_4_4, all_45_1_15) = all_96_1_45, multiplication(all_0_4_4, all_45_1_15) = all_76_0_28, yields: % 16.66/4.58 | (168) all_96_1_45 = all_76_0_28 % 16.66/4.58 | % 16.66/4.58 | Instantiating formula (21) with all_140_1_78, all_0_4_4, all_0_2_2 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_140_1_78, complement(all_0_4_4, all_0_2_2), yields: % 16.66/4.58 | (169) all_140_1_78 = zero % 16.66/4.58 | % 16.66/4.58 | Instantiating formula (34) with all_0_4_4, all_0_2_2, all_128_0_66, all_140_1_78 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_140_1_78, multiplication(all_0_4_4, all_0_2_2) = all_128_0_66, yields: % 16.66/4.58 | (170) all_140_1_78 = all_128_0_66 % 16.66/4.58 | % 16.66/4.58 | Instantiating formula (34) with all_0_4_4, all_0_2_2, all_128_0_66, all_138_0_75 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_138_0_75, multiplication(all_0_4_4, all_0_2_2) = all_128_0_66, yields: % 16.66/4.58 | (171) all_138_0_75 = all_128_0_66 % 16.66/4.58 | % 16.66/4.58 | Instantiating formula (34) with all_0_4_4, all_0_2_2, all_116_0_59, all_138_0_75 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_138_0_75, multiplication(all_0_4_4, all_0_2_2) = all_116_0_59, yields: % 16.66/4.58 | (172) all_138_0_75 = all_116_0_59 % 16.66/4.58 | % 16.66/4.58 | Combining equations (164,163) yields a new equation: % 16.66/4.58 | (173) all_130_1_68 = zero % 16.66/4.58 | % 16.66/4.58 | Simplifying 173 yields: % 16.66/4.58 | (174) all_130_1_68 = zero % 16.66/4.58 | % 16.66/4.58 | Combining equations (170,169) yields a new equation: % 16.66/4.58 | (175) all_128_0_66 = zero % 16.66/4.58 | % 16.66/4.58 | Simplifying 175 yields: % 16.66/4.58 | (176) all_128_0_66 = zero % 16.66/4.58 | % 16.66/4.58 | Combining equations (171,172) yields a new equation: % 16.66/4.58 | (177) all_128_0_66 = all_116_0_59 % 16.66/4.58 | % 16.66/4.58 | Simplifying 177 yields: % 16.66/4.58 | (178) all_128_0_66 = all_116_0_59 % 16.66/4.58 | % 16.66/4.58 | Combining equations (165,174) yields a new equation: % 16.66/4.58 | (179) all_120_0_62 = zero % 16.66/4.58 | % 16.66/4.58 | Simplifying 179 yields: % 16.66/4.58 | (180) all_120_0_62 = zero % 16.66/4.58 | % 16.66/4.58 | Combining equations (176,178) yields a new equation: % 16.66/4.58 | (181) all_116_0_59 = zero % 16.66/4.58 | % 16.66/4.58 | Combining equations (181,178) yields a new equation: % 16.66/4.58 | (176) all_128_0_66 = zero % 16.66/4.58 | % 16.66/4.58 | From (176) and (142) follows: % 16.66/4.58 | (183) multiplication(zero, all_0_5_5) = all_47_1_17 % 16.66/4.58 | % 16.66/4.58 | From (180) and (139) follows: % 16.66/4.58 | (184) multiplication(zero, all_0_5_5) = all_45_1_15 % 16.66/4.58 | % 16.66/4.58 | From (166) and (150) follows: % 16.66/4.58 | (129) multiplication(all_0_4_4, all_47_1_17) = all_90_1_41 % 16.66/4.58 | % 16.66/4.58 | From (168) and (133) follows: % 16.66/4.58 | (125) multiplication(all_0_4_4, all_45_1_15) = all_76_0_28 % 16.66/4.58 | % 16.66/4.58 | From (168)(167) and (134) follows: % 16.66/4.58 | (187) addition(all_76_0_28, all_76_1_29) = all_47_1_17 % 16.66/4.58 | % 16.66/4.58 | Instantiating formula (36) with all_47_1_17, all_0_5_5 and discharging atoms multiplication(zero, all_0_5_5) = all_47_1_17, yields: % 16.66/4.58 | (188) all_47_1_17 = zero % 16.66/4.58 | % 16.66/4.58 | Instantiating formula (34) with zero, all_0_5_5, all_45_1_15, all_47_1_17 and discharging atoms multiplication(zero, all_0_5_5) = all_47_1_17, multiplication(zero, all_0_5_5) = all_45_1_15, yields: % 16.66/4.59 | (189) all_47_1_17 = all_45_1_15 % 16.66/4.59 | % 16.66/4.59 | Combining equations (189,188) yields a new equation: % 16.66/4.59 | (190) all_45_1_15 = zero % 16.66/4.59 | % 16.66/4.59 | Simplifying 190 yields: % 16.66/4.59 | (191) all_45_1_15 = zero % 16.66/4.59 | % 16.66/4.59 | From (188) and (129) follows: % 16.66/4.59 | (192) multiplication(all_0_4_4, zero) = all_90_1_41 % 16.66/4.59 | % 16.66/4.59 | From (191) and (125) follows: % 16.66/4.59 | (193) multiplication(all_0_4_4, zero) = all_76_0_28 % 16.66/4.59 | % 16.66/4.59 | From (191) and (184) follows: % 16.66/4.59 | (194) multiplication(zero, all_0_5_5) = zero % 16.66/4.59 | % 16.66/4.59 | From (188) and (187) follows: % 16.66/4.59 | (195) addition(all_76_0_28, all_76_1_29) = zero % 16.66/4.59 | % 16.66/4.59 | From (188) and (126) follows: % 16.66/4.59 | (196) addition(all_76_1_29, all_76_0_28) = zero % 16.66/4.59 | % 16.66/4.59 | Instantiating formula (14) with all_90_1_41, all_0_4_4 and discharging atoms multiplication(all_0_4_4, zero) = all_90_1_41, yields: % 16.66/4.59 | (197) all_90_1_41 = zero % 16.66/4.59 | % 16.66/4.59 | Instantiating formula (34) with all_0_4_4, zero, all_76_0_28, all_90_1_41 and discharging atoms multiplication(all_0_4_4, zero) = all_90_1_41, multiplication(all_0_4_4, zero) = all_76_0_28, yields: % 16.66/4.59 | (198) all_90_1_41 = all_76_0_28 % 16.66/4.59 | % 16.66/4.59 | Combining equations (197,198) yields a new equation: % 16.66/4.59 | (199) all_76_0_28 = zero % 16.66/4.59 | % 16.66/4.59 | From (199) and (195) follows: % 16.66/4.59 | (200) addition(zero, all_76_1_29) = zero % 16.66/4.59 | % 16.66/4.59 | From (199) and (196) follows: % 16.66/4.59 | (201) addition(all_76_1_29, zero) = zero % 16.66/4.59 | % 16.66/4.59 | Instantiating formula (24) with zero, all_76_1_29 and discharging atoms addition(all_76_1_29, zero) = zero, yields: % 16.66/4.59 | (202) all_76_1_29 = zero % 16.66/4.59 | % 16.66/4.59 | From (202) and (200) follows: % 16.66/4.59 | (203) addition(zero, zero) = zero % 16.66/4.59 | % 16.66/4.59 | Instantiating formula (4) with zero, zero, zero, all_0_5_5, all_0_5_5, zero and discharging atoms multiplication(zero, all_0_5_5) = zero, addition(zero, zero) = zero, yields: % 16.66/4.59 | (204) ? [v0] : (multiplication(zero, v0) = zero & addition(all_0_5_5, all_0_5_5) = v0) % 16.66/4.59 | % 16.66/4.59 | Instantiating (204) with all_194_0_97 yields: % 16.66/4.59 | (205) multiplication(zero, all_194_0_97) = zero & addition(all_0_5_5, all_0_5_5) = all_194_0_97 % 16.66/4.59 | % 16.66/4.59 | Applying alpha-rule on (205) yields: % 16.66/4.59 | (206) multiplication(zero, all_194_0_97) = zero % 16.66/4.59 | (207) addition(all_0_5_5, all_0_5_5) = all_194_0_97 % 16.66/4.59 | % 16.66/4.59 | Instantiating formula (17) with all_194_0_97, all_0_5_5 and discharging atoms addition(all_0_5_5, all_0_5_5) = all_194_0_97, yields: % 16.66/4.59 | (208) all_194_0_97 = all_0_5_5 % 16.66/4.59 | % 16.66/4.59 | From (208) and (207) follows: % 16.66/4.59 | (209) addition(all_0_5_5, all_0_5_5) = all_0_5_5 % 16.66/4.59 | % 16.66/4.59 | Instantiating formula (15) with all_0_5_5, all_0_5_5 and discharging atoms addition(all_0_5_5, all_0_5_5) = all_0_5_5, ~ leq(all_0_5_5, all_0_5_5), yields: % 16.66/4.59 | (210) $false % 16.66/4.59 | % 16.66/4.59 |-The branch is then unsatisfiable % 16.66/4.59 |-Branch two: % 16.66/4.59 | (211) leq(all_0_0_0, all_0_5_5) % 16.66/4.59 | (212) ~ leq(all_0_5_5, all_0_0_0) % 16.66/4.59 | % 16.66/4.59 | From (60) and (211) follows: % 16.66/4.59 | (213) leq(all_0_5_5, all_0_5_5) % 16.66/4.59 | % 16.66/4.59 | From (60) and (212) follows: % 16.66/4.59 | (65) ~ leq(all_0_5_5, all_0_5_5) % 16.66/4.59 | % 16.66/4.59 | Using (213) and (65) yields: % 16.66/4.59 | (210) $false % 16.66/4.59 | % 16.66/4.59 |-The branch is then unsatisfiable % 16.66/4.59 % SZS output end Proof for theBenchmark % 16.66/4.59 % 16.66/4.59 3999ms %------------------------------------------------------------------------------