%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE021+4 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n032.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 2.74s % Output : Proof 17.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : KLE021+4 : TPTP v8.1.0. Released v4.0.0. % 0.00/0.10 % Command : ePrincess-casc -timeout=%d %s % 0.10/0.29 % Computer : n032.cluster.edu % 0.10/0.29 % Model : x86_64 x86_64 % 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.29 % Memory : 8042.1875MB % 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.29 % CPULimit : 300 % 0.10/0.29 % WCLimit : 600 % 0.10/0.29 % DateTime : Thu Jun 16 07:55:29 EDT 2022 % 0.10/0.29 % CPUTime : % 0.13/0.47 ____ _ % 0.13/0.47 ___ / __ \_____(_)___ ________ __________ % 0.13/0.47 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.13/0.47 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.13/0.47 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.13/0.47 % 0.13/0.47 A Theorem Prover for First-Order Logic % 0.13/0.47 (ePrincess v.1.0) % 0.13/0.47 % 0.13/0.47 (c) Philipp Rümmer, 2009-2015 % 0.13/0.47 (c) Peter Backeman, 2014-2015 % 0.13/0.47 (contributions by Angelo Brillout, Peter Baumgartner) % 0.13/0.47 Free software under GNU Lesser General Public License (LGPL). % 0.13/0.47 Bug reports to peter@backeman.se % 0.13/0.47 % 0.13/0.47 For more information, visit http://user.uu.se/~petba168/breu/ % 0.13/0.47 % 0.13/0.47 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.13/0.51 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.17/0.77 Prover 0: Preprocessing ... % 2.06/1.03 Prover 0: Constructing countermodel ... % 8.94/2.74 Prover 0: proved (2231ms) % 8.94/2.74 % 8.94/2.74 No countermodel exists, formula is valid % 8.94/2.74 % SZS status Theorem for theBenchmark % 8.94/2.74 % 8.94/2.74 Generating proof ... found it (size 170) % 16.73/4.61 % 16.73/4.61 % SZS output start Proof for theBenchmark % 16.73/4.61 Assumed formulas after preprocessing and simplification: % 16.73/4.61 | (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] : ( ~ (c(v7) = v9) | ~ (c(v6) = v8) | ~ (multiplication(v8, v9) = v10) | ~ test(v7) | ~ test(v6) | ? [v11] : (c(v11) = v10 & addition(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (c(v7) = v9) | ~ (c(v6) = v8) | ~ (addition(v8, v9) = v10) | ~ test(v7) | ~ test(v6) | ? [v11] : (c(v11) = v10 & multiplication(v6, v7) = v11)) & ! [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] : ( ~ (multiplication(v6, v7) = v8) | ~ test(v7) | ~ test(v6) | ? [v9] : ? [v10] : ? [v11] : (c(v8) = v9 & c(v7) = v11 & c(v6) = v10 & addition(v10, v11) = v9)) & ! [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) | ~ test(v7) | ~ test(v6) | ? [v9] : ? [v10] : ? [v11] : (c(v8) = v9 & c(v7) = v11 & c(v6) = v10 & multiplication(v10, v11) = v9)) & ! [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))) % 16.73/4.65 | 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: % 16.73/4.65 | (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] : ( ~ (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)) & ( ~ leq(all_0_0_0, all_0_5_5) | ~ leq(all_0_5_5, all_0_0_0)) % 16.73/4.66 | % 16.73/4.66 | Applying alpha-rule on (1) yields: % 16.73/4.66 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one)) % 16.73/4.66 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one)) % 16.73/4.66 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 16.73/4.66 | (5) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 16.73/4.66 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0)) % 16.73/4.66 | (7) ! [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)) % 16.73/4.66 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 16.73/4.66 | (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)) % 16.73/4.66 | (10) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) | ~ (v2 = zero)))) % 16.73/4.66 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 16.73/4.66 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) % 16.73/4.66 | (13) ! [v0] : ! [v1] : ( ~ (c(v0) = v1) | ~ test(v0) | complement(v0, v1)) % 16.73/4.66 | (14) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 16.73/4.66 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 16.73/4.66 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0)) % 16.73/4.66 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 16.73/4.66 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 16.73/4.66 | (19) c(all_0_4_4) = all_0_2_2 % 16.73/4.66 | (20) ! [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)) % 16.73/4.66 | (21) ! [v0] : ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) % 16.73/4.66 | (22) addition(all_0_3_3, all_0_1_1) = all_0_0_0 % 16.73/4.66 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero)) % 16.73/4.66 | (24) ! [v0] : ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) % 16.73/4.66 | (25) ! [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)) % 16.73/4.66 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (c(v0) = v2) | ~ complement(v0, v1) | ~ test(v0)) % 16.73/4.66 | (27) multiplication(all_0_4_4, all_0_5_5) = all_0_3_3 % 16.73/4.66 | (28) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 16.73/4.66 | (29) ! [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)) % 16.73/4.67 | (30) ! [v0] : ! [v1] : (v1 = zero | ~ (c(v0) = v1) | test(v0)) % 16.73/4.67 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 16.73/4.67 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 16.73/4.67 | (33) ! [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)) % 16.73/4.67 | (34) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 16.73/4.67 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 16.73/4.67 | (36) ! [v0] : ! [v1] : ( ~ complement(v1, v0) | test(v0)) % 16.73/4.67 | (37) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) % 16.73/4.67 | (38) multiplication(all_0_2_2, all_0_5_5) = all_0_1_1 % 16.73/4.67 | (39) ! [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)) % 16.73/4.67 | (40) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) % 16.73/4.67 | (41) test(all_0_4_4) % 16.73/4.67 | (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)) % 16.73/4.67 | (43) ! [v0] : ( ~ test(v0) | ? [v1] : complement(v1, v0)) % 16.73/4.67 | (44) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 16.73/4.67 | (45) ~ leq(all_0_0_0, all_0_5_5) | ~ leq(all_0_5_5, all_0_0_0) % 16.73/4.67 | (46) ! [v0] : ! [v1] : ! [v2] : (v2 = one | ~ (addition(v0, v1) = v2) | ~ complement(v1, v0)) % 16.73/4.67 | % 16.73/4.67 | Instantiating formula (42) 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: % 16.73/4.67 | (47) ? [v0] : (multiplication(v0, all_0_5_5) = all_0_0_0 & addition(all_0_4_4, all_0_2_2) = v0) % 16.73/4.67 | % 16.73/4.67 | Instantiating formula (18) 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: % 16.73/4.67 | (48) addition(all_0_1_1, all_0_3_3) = all_0_0_0 % 16.73/4.67 | % 16.73/4.67 | Instantiating formula (13) 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: % 16.73/4.67 | (49) complement(all_0_4_4, all_0_2_2) % 16.73/4.67 | % 16.73/4.67 | Instantiating (47) with all_9_0_6 yields: % 16.73/4.67 | (50) 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 % 16.73/4.67 | % 16.73/4.67 | Applying alpha-rule on (50) yields: % 16.73/4.67 | (51) multiplication(all_9_0_6, all_0_5_5) = all_0_0_0 % 16.73/4.67 | (52) addition(all_0_4_4, all_0_2_2) = all_9_0_6 % 16.73/4.67 | % 16.73/4.67 | Instantiating formula (42) 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: % 16.73/4.67 | (53) ? [v0] : (multiplication(v0, all_0_5_5) = all_0_0_0 & addition(all_0_2_2, all_0_4_4) = v0) % 16.73/4.67 | % 16.73/4.67 | Instantiating formula (18) 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: % 16.73/4.67 | (54) addition(all_0_2_2, all_0_4_4) = all_9_0_6 % 16.73/4.67 | % 16.73/4.67 | Instantiating formula (36) with all_0_4_4, all_0_2_2 and discharging atoms complement(all_0_4_4, all_0_2_2), yields: % 16.73/4.67 | (55) test(all_0_2_2) % 16.73/4.67 | % 16.73/4.67 | Instantiating (53) with all_19_0_8 yields: % 16.73/4.67 | (56) 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 % 16.73/4.67 | % 16.73/4.67 | Applying alpha-rule on (56) yields: % 16.73/4.67 | (57) multiplication(all_19_0_8, all_0_5_5) = all_0_0_0 % 16.73/4.67 | (58) addition(all_0_2_2, all_0_4_4) = all_19_0_8 % 16.73/4.67 | % 16.73/4.67 | Instantiating formula (46) 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: % 16.73/4.67 | (59) all_19_0_8 = one % 16.73/4.67 | % 16.73/4.67 | Instantiating formula (8) 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: % 16.73/4.67 | (60) all_19_0_8 = all_9_0_6 % 16.73/4.67 | % 16.73/4.67 | Combining equations (59,60) yields a new equation: % 16.73/4.67 | (61) all_9_0_6 = one % 16.73/4.67 | % 16.73/4.67 | From (61) and (51) follows: % 16.73/4.67 | (62) multiplication(one, all_0_5_5) = all_0_0_0 % 16.73/4.67 | % 16.73/4.67 | From (61) and (54) follows: % 16.73/4.67 | (63) addition(all_0_2_2, all_0_4_4) = one % 16.73/4.67 | % 16.73/4.67 | From (61) and (52) follows: % 16.73/4.67 | (64) addition(all_0_4_4, all_0_2_2) = one % 16.73/4.67 | % 16.73/4.67 | Instantiating formula (14) with all_0_0_0, all_0_5_5 and discharging atoms multiplication(one, all_0_5_5) = all_0_0_0, yields: % 16.73/4.67 | (65) all_0_0_0 = all_0_5_5 % 16.73/4.68 | % 16.73/4.68 | From (65) and (62) follows: % 16.73/4.68 | (66) multiplication(one, all_0_5_5) = all_0_5_5 % 16.73/4.68 | % 16.73/4.68 | From (65) and (48) follows: % 16.73/4.68 | (67) addition(all_0_1_1, all_0_3_3) = all_0_5_5 % 16.73/4.68 | % 16.73/4.68 | From (65) and (22) follows: % 16.73/4.68 | (68) addition(all_0_3_3, all_0_1_1) = all_0_5_5 % 16.73/4.68 | % 16.73/4.68 +-Applying beta-rule and splitting (45), into two cases. % 16.73/4.68 |-Branch one: % 16.73/4.68 | (69) ~ leq(all_0_0_0, all_0_5_5) % 16.73/4.68 | % 16.73/4.68 | From (65) and (69) follows: % 16.73/4.68 | (70) ~ leq(all_0_5_5, all_0_5_5) % 16.73/4.68 | % 16.73/4.68 | Instantiating formula (35) 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: % 16.73/4.68 | (71) ? [v0] : (multiplication(v0, all_0_5_5) = all_0_1_1 & multiplication(all_0_2_2, one) = v0) % 16.73/4.68 | % 16.73/4.68 | Instantiating formula (35) 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: % 16.73/4.68 | (72) ? [v0] : (multiplication(v0, all_0_5_5) = all_0_3_3 & multiplication(all_0_4_4, one) = v0) % 16.73/4.68 | % 16.73/4.68 | Instantiating formula (25) 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: % 16.73/4.68 | (73) ? [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) % 16.73/4.68 | % 16.73/4.68 | Instantiating formula (25) 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: % 16.73/4.68 | (74) ? [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) % 16.73/4.68 | % 16.73/4.68 | Instantiating formula (23) 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: % 16.73/4.68 | (75) multiplication(all_0_2_2, all_0_4_4) = zero & multiplication(all_0_4_4, all_0_2_2) = zero % 16.73/4.68 | % 16.73/4.68 | Applying alpha-rule on (75) yields: % 16.73/4.68 | (76) multiplication(all_0_2_2, all_0_4_4) = zero % 16.73/4.68 | (77) multiplication(all_0_4_4, all_0_2_2) = zero % 16.73/4.68 | % 16.73/4.68 | Instantiating formula (25) 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: % 16.73/4.68 | (78) ? [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) % 16.73/4.68 | % 16.73/4.68 | Instantiating formula (25) 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: % 16.73/4.68 | (79) ? [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) % 16.73/4.68 | % 16.73/4.68 | Instantiating formula (10) with all_0_2_2, all_0_4_4 and discharging atoms addition(all_0_4_4, all_0_2_2) = one, yields: % 16.73/4.68 | (80) complement(all_0_2_2, all_0_4_4) | ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_0_4_4) = v1 & multiplication(all_0_4_4, all_0_2_2) = v0 & ( ~ (v1 = zero) | ~ (v0 = zero))) % 16.73/4.68 | % 16.73/4.68 | Instantiating formula (7) with one, all_0_4_4, all_0_2_2 and discharging atoms addition(all_0_2_2, all_0_4_4) = one, test(all_0_2_2), test(all_0_4_4), yields: % 16.73/4.68 | (81) ? [v0] : ? [v1] : ? [v2] : (c(all_0_2_2) = v1 & c(all_0_4_4) = v2 & c(one) = v0 & multiplication(v1, v2) = v0) % 16.73/4.68 | % 16.73/4.68 | Instantiating formula (7) with one, all_0_2_2, all_0_4_4 and discharging atoms addition(all_0_4_4, all_0_2_2) = one, test(all_0_2_2), test(all_0_4_4), yields: % 16.73/4.68 | (82) ? [v0] : ? [v1] : ? [v2] : (c(all_0_2_2) = v2 & c(all_0_4_4) = v1 & c(one) = v0 & multiplication(v1, v2) = v0) % 16.73/4.68 | % 16.73/4.68 | Instantiating (81) with all_41_0_10, all_41_1_11, all_41_2_12 yields: % 16.73/4.68 | (83) c(all_0_2_2) = all_41_1_11 & c(all_0_4_4) = all_41_0_10 & c(one) = all_41_2_12 & multiplication(all_41_1_11, all_41_0_10) = all_41_2_12 % 16.73/4.68 | % 16.73/4.68 | Applying alpha-rule on (83) yields: % 16.73/4.68 | (84) c(all_0_2_2) = all_41_1_11 % 16.73/4.68 | (85) c(all_0_4_4) = all_41_0_10 % 16.73/4.68 | (86) c(one) = all_41_2_12 % 16.73/4.68 | (87) multiplication(all_41_1_11, all_41_0_10) = all_41_2_12 % 16.73/4.68 | % 16.73/4.68 | Instantiating (82) with all_45_0_15, all_45_1_16, all_45_2_17 yields: % 16.73/4.68 | (88) c(all_0_2_2) = all_45_0_15 & c(all_0_4_4) = all_45_1_16 & c(one) = all_45_2_17 & multiplication(all_45_1_16, all_45_0_15) = all_45_2_17 % 16.73/4.68 | % 16.73/4.68 | Applying alpha-rule on (88) yields: % 16.73/4.68 | (89) c(all_0_2_2) = all_45_0_15 % 16.73/4.68 | (90) c(all_0_4_4) = all_45_1_16 % 16.73/4.68 | (91) c(one) = all_45_2_17 % 16.73/4.68 | (92) multiplication(all_45_1_16, all_45_0_15) = all_45_2_17 % 16.73/4.68 | % 16.73/4.68 | Instantiating (74) with all_49_0_20, all_49_1_21 yields: % 16.73/4.68 | (93) multiplication(all_0_4_4, all_0_1_1) = all_49_1_21 & multiplication(all_0_4_4, all_0_3_3) = all_49_0_20 & addition(all_49_1_21, all_49_0_20) = all_0_3_3 % 16.73/4.68 | % 16.73/4.68 | Applying alpha-rule on (93) yields: % 16.73/4.68 | (94) multiplication(all_0_4_4, all_0_1_1) = all_49_1_21 % 16.73/4.68 | (95) multiplication(all_0_4_4, all_0_3_3) = all_49_0_20 % 16.73/4.70 | (96) addition(all_49_1_21, all_49_0_20) = all_0_3_3 % 16.73/4.70 | % 16.73/4.70 | Instantiating (79) with all_51_0_22, all_51_1_23 yields: % 16.73/4.70 | (97) multiplication(all_0_4_4, all_0_1_1) = all_51_0_22 & multiplication(all_0_4_4, all_0_3_3) = all_51_1_23 & addition(all_51_1_23, all_51_0_22) = all_0_3_3 % 16.73/4.70 | % 16.73/4.70 | Applying alpha-rule on (97) yields: % 16.73/4.70 | (98) multiplication(all_0_4_4, all_0_1_1) = all_51_0_22 % 16.73/4.70 | (99) multiplication(all_0_4_4, all_0_3_3) = all_51_1_23 % 16.73/4.70 | (100) addition(all_51_1_23, all_51_0_22) = all_0_3_3 % 16.73/4.70 | % 16.73/4.70 | Instantiating (78) with all_53_0_24, all_53_1_25 yields: % 16.73/4.70 | (101) multiplication(all_0_2_2, all_0_1_1) = all_53_0_24 & multiplication(all_0_2_2, all_0_3_3) = all_53_1_25 & addition(all_53_1_25, all_53_0_24) = all_0_1_1 % 16.73/4.70 | % 16.73/4.70 | Applying alpha-rule on (101) yields: % 16.73/4.70 | (102) multiplication(all_0_2_2, all_0_1_1) = all_53_0_24 % 16.73/4.70 | (103) multiplication(all_0_2_2, all_0_3_3) = all_53_1_25 % 16.73/4.70 | (104) addition(all_53_1_25, all_53_0_24) = all_0_1_1 % 16.73/4.70 | % 16.73/4.70 | Instantiating (73) with all_55_0_26, all_55_1_27 yields: % 16.73/4.70 | (105) multiplication(all_0_2_2, all_0_1_1) = all_55_1_27 & multiplication(all_0_2_2, all_0_3_3) = all_55_0_26 & addition(all_55_1_27, all_55_0_26) = all_0_1_1 % 16.73/4.70 | % 16.73/4.70 | Applying alpha-rule on (105) yields: % 16.73/4.70 | (106) multiplication(all_0_2_2, all_0_1_1) = all_55_1_27 % 16.73/4.70 | (107) multiplication(all_0_2_2, all_0_3_3) = all_55_0_26 % 16.73/4.70 | (108) addition(all_55_1_27, all_55_0_26) = all_0_1_1 % 16.73/4.70 | % 16.73/4.70 | Instantiating (72) with all_59_0_29 yields: % 16.73/4.70 | (109) multiplication(all_59_0_29, all_0_5_5) = all_0_3_3 & multiplication(all_0_4_4, one) = all_59_0_29 % 16.73/4.70 | % 16.73/4.70 | Applying alpha-rule on (109) yields: % 16.73/4.70 | (110) multiplication(all_59_0_29, all_0_5_5) = all_0_3_3 % 16.73/4.70 | (111) multiplication(all_0_4_4, one) = all_59_0_29 % 16.73/4.70 | % 16.73/4.70 | Instantiating (71) with all_61_0_30 yields: % 16.73/4.70 | (112) multiplication(all_61_0_30, all_0_5_5) = all_0_1_1 & multiplication(all_0_2_2, one) = all_61_0_30 % 16.73/4.70 | % 16.73/4.70 | Applying alpha-rule on (112) yields: % 16.73/4.70 | (113) multiplication(all_61_0_30, all_0_5_5) = all_0_1_1 % 16.73/4.70 | (114) multiplication(all_0_2_2, one) = all_61_0_30 % 16.73/4.70 | % 16.73/4.70 +-Applying beta-rule and splitting (80), into two cases. % 16.73/4.70 |-Branch one: % 16.73/4.70 | (115) complement(all_0_2_2, all_0_4_4) % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (12) with all_0_2_2, all_41_1_11, all_45_0_15 and discharging atoms c(all_0_2_2) = all_45_0_15, c(all_0_2_2) = all_41_1_11, yields: % 16.73/4.70 | (116) all_45_0_15 = all_41_1_11 % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (12) with all_0_4_4, all_45_1_16, all_0_2_2 and discharging atoms c(all_0_4_4) = all_45_1_16, c(all_0_4_4) = all_0_2_2, yields: % 16.73/4.70 | (117) all_45_1_16 = all_0_2_2 % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (12) with all_0_4_4, all_41_0_10, all_45_1_16 and discharging atoms c(all_0_4_4) = all_45_1_16, c(all_0_4_4) = all_41_0_10, yields: % 16.73/4.70 | (118) all_45_1_16 = all_41_0_10 % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (32) with all_0_2_2, all_0_1_1, all_53_0_24, all_55_1_27 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_55_1_27, multiplication(all_0_2_2, all_0_1_1) = all_53_0_24, yields: % 16.73/4.70 | (119) all_55_1_27 = all_53_0_24 % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (32) with all_0_2_2, all_0_3_3, all_53_1_25, all_55_0_26 and discharging atoms multiplication(all_0_2_2, all_0_3_3) = all_55_0_26, multiplication(all_0_2_2, all_0_3_3) = all_53_1_25, yields: % 16.73/4.70 | (120) all_55_0_26 = all_53_1_25 % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (15) with all_61_0_30, all_0_2_2 and discharging atoms multiplication(all_0_2_2, one) = all_61_0_30, yields: % 16.73/4.70 | (121) all_61_0_30 = all_0_2_2 % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (32) with all_0_4_4, all_0_1_1, all_49_1_21, all_51_0_22 and discharging atoms multiplication(all_0_4_4, all_0_1_1) = all_51_0_22, multiplication(all_0_4_4, all_0_1_1) = all_49_1_21, yields: % 16.73/4.70 | (122) all_51_0_22 = all_49_1_21 % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (32) with all_0_4_4, all_0_3_3, all_49_0_20, all_51_1_23 and discharging atoms multiplication(all_0_4_4, all_0_3_3) = all_51_1_23, multiplication(all_0_4_4, all_0_3_3) = all_49_0_20, yields: % 16.73/4.70 | (123) all_51_1_23 = all_49_0_20 % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (15) with all_59_0_29, all_0_4_4 and discharging atoms multiplication(all_0_4_4, one) = all_59_0_29, yields: % 16.73/4.70 | (124) all_59_0_29 = all_0_4_4 % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (26) with all_45_0_15, all_0_4_4, all_0_2_2 and discharging atoms c(all_0_2_2) = all_45_0_15, complement(all_0_2_2, all_0_4_4), test(all_0_2_2), yields: % 16.73/4.70 | (125) all_45_0_15 = all_0_4_4 % 16.73/4.70 | % 16.73/4.70 | Combining equations (125,116) yields a new equation: % 16.73/4.70 | (126) all_41_1_11 = all_0_4_4 % 16.73/4.70 | % 16.73/4.70 | Combining equations (118,117) yields a new equation: % 16.73/4.70 | (127) all_41_0_10 = all_0_2_2 % 16.73/4.70 | % 16.73/4.70 | Simplifying 127 yields: % 16.73/4.70 | (128) all_41_0_10 = all_0_2_2 % 16.73/4.70 | % 16.73/4.70 | From (126) and (84) follows: % 16.73/4.70 | (129) c(all_0_2_2) = all_0_4_4 % 16.73/4.70 | % 16.73/4.70 | From (128) and (85) follows: % 16.73/4.70 | (19) c(all_0_4_4) = all_0_2_2 % 16.73/4.70 | % 16.73/4.70 | From (121) and (113) follows: % 16.73/4.70 | (38) multiplication(all_0_2_2, all_0_5_5) = all_0_1_1 % 16.73/4.70 | % 16.73/4.70 | From (124) and (110) follows: % 16.73/4.70 | (27) multiplication(all_0_4_4, all_0_5_5) = all_0_3_3 % 16.73/4.70 | % 16.73/4.70 | From (126)(128) and (87) follows: % 16.73/4.70 | (133) multiplication(all_0_4_4, all_0_2_2) = all_41_2_12 % 16.73/4.70 | % 16.73/4.70 | From (120) and (107) follows: % 16.73/4.70 | (103) multiplication(all_0_2_2, all_0_3_3) = all_53_1_25 % 16.73/4.70 | % 16.73/4.70 | From (121) and (114) follows: % 16.73/4.70 | (135) multiplication(all_0_2_2, one) = all_0_2_2 % 16.73/4.70 | % 16.73/4.70 | From (122) and (98) follows: % 16.73/4.70 | (94) multiplication(all_0_4_4, all_0_1_1) = all_49_1_21 % 16.73/4.70 | % 16.73/4.70 | From (123) and (99) follows: % 16.73/4.70 | (95) multiplication(all_0_4_4, all_0_3_3) = all_49_0_20 % 16.73/4.70 | % 16.73/4.70 | From (124) and (111) follows: % 16.73/4.70 | (138) multiplication(all_0_4_4, one) = all_0_4_4 % 16.73/4.70 | % 16.73/4.70 | From (119)(120) and (108) follows: % 16.73/4.70 | (139) addition(all_53_0_24, all_53_1_25) = all_0_1_1 % 16.73/4.70 | % 16.73/4.70 | From (123)(122) and (100) follows: % 16.73/4.70 | (140) addition(all_49_0_20, all_49_1_21) = all_0_3_3 % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (6) with all_41_2_12, all_0_4_4, all_0_2_2 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_41_2_12, complement(all_0_4_4, all_0_2_2), yields: % 16.73/4.70 | (141) all_41_2_12 = zero % 16.73/4.70 | % 16.73/4.70 | From (141) and (133) follows: % 16.73/4.70 | (77) multiplication(all_0_4_4, all_0_2_2) = zero % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (20) with one, all_0_4_4, all_0_2_2, all_0_2_2, all_0_4_4 and discharging atoms c(all_0_2_2) = all_0_4_4, c(all_0_4_4) = all_0_2_2, addition(all_0_2_2, all_0_4_4) = one, test(all_0_2_2), test(all_0_4_4), yields: % 16.73/4.70 | (143) ? [v0] : (c(v0) = one & multiplication(all_0_4_4, all_0_2_2) = v0) % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (35) with all_53_1_25, 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_53_1_25, multiplication(all_0_4_4, all_0_5_5) = all_0_3_3, yields: % 16.73/4.70 | (144) ? [v0] : (multiplication(v0, all_0_5_5) = all_53_1_25 & multiplication(all_0_2_2, all_0_4_4) = v0) % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (35) with all_49_1_21, 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_49_1_21, yields: % 16.73/4.70 | (145) ? [v0] : (multiplication(v0, all_0_5_5) = all_49_1_21 & multiplication(all_0_4_4, all_0_2_2) = v0) % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (35) 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: % 16.73/4.70 | (146) ? [v0] : (multiplication(v0, one) = zero & multiplication(all_0_4_4, all_0_2_2) = v0) % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (25) 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: % 16.73/4.70 | (147) ? [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) % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (25) 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: % 16.73/4.70 | (148) ? [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) % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (25) with all_49_1_21, all_0_1_1, all_53_1_25, all_53_0_24, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_1_1) = all_49_1_21, addition(all_53_0_24, all_53_1_25) = all_0_1_1, yields: % 16.73/4.70 | (149) ? [v0] : ? [v1] : (multiplication(all_0_4_4, all_53_0_24) = v0 & multiplication(all_0_4_4, all_53_1_25) = v1 & addition(v0, v1) = all_49_1_21) % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (25) with all_49_1_21, all_0_1_1, all_53_0_24, all_53_1_25, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_1_1) = all_49_1_21, addition(all_53_1_25, all_53_0_24) = all_0_1_1, yields: % 16.73/4.70 | (150) ? [v0] : ? [v1] : (multiplication(all_0_4_4, all_53_0_24) = v1 & multiplication(all_0_4_4, all_53_1_25) = v0 & addition(v0, v1) = all_49_1_21) % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (25) with all_49_0_20, all_0_3_3, all_49_1_21, all_49_0_20, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_3_3) = all_49_0_20, addition(all_49_0_20, all_49_1_21) = all_0_3_3, yields: % 16.73/4.70 | (151) ? [v0] : ? [v1] : (multiplication(all_0_4_4, all_49_0_20) = v0 & multiplication(all_0_4_4, all_49_1_21) = v1 & addition(v0, v1) = all_49_0_20) % 16.73/4.70 | % 16.73/4.70 | Instantiating formula (25) with all_49_0_20, all_0_3_3, all_49_0_20, all_49_1_21, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_3_3) = all_49_0_20, addition(all_49_1_21, all_49_0_20) = all_0_3_3, yields: % 16.73/4.70 | (152) ? [v0] : ? [v1] : (multiplication(all_0_4_4, all_49_0_20) = v1 & multiplication(all_0_4_4, all_49_1_21) = v0 & addition(v0, v1) = all_49_0_20) % 16.73/4.70 | % 16.73/4.70 | Instantiating (150) with all_86_0_36, all_86_1_37 yields: % 16.73/4.70 | (153) multiplication(all_0_4_4, all_53_0_24) = all_86_0_36 & multiplication(all_0_4_4, all_53_1_25) = all_86_1_37 & addition(all_86_1_37, all_86_0_36) = all_49_1_21 % 16.73/4.70 | % 16.73/4.70 | Applying alpha-rule on (153) yields: % 16.73/4.70 | (154) multiplication(all_0_4_4, all_53_0_24) = all_86_0_36 % 16.73/4.70 | (155) multiplication(all_0_4_4, all_53_1_25) = all_86_1_37 % 16.73/4.70 | (156) addition(all_86_1_37, all_86_0_36) = all_49_1_21 % 16.73/4.70 | % 16.73/4.70 | Instantiating (149) with all_90_0_39, all_90_1_40 yields: % 16.73/4.70 | (157) multiplication(all_0_4_4, all_53_0_24) = all_90_1_40 & multiplication(all_0_4_4, all_53_1_25) = all_90_0_39 & addition(all_90_1_40, all_90_0_39) = all_49_1_21 % 16.73/4.70 | % 16.73/4.70 | Applying alpha-rule on (157) yields: % 16.73/4.70 | (158) multiplication(all_0_4_4, all_53_0_24) = all_90_1_40 % 17.28/4.70 | (159) multiplication(all_0_4_4, all_53_1_25) = all_90_0_39 % 17.28/4.70 | (160) addition(all_90_1_40, all_90_0_39) = all_49_1_21 % 17.28/4.70 | % 17.28/4.70 | Instantiating (148) with all_92_0_41, all_92_1_42 yields: % 17.28/4.70 | (161) multiplication(all_0_4_4, all_0_2_2) = all_92_0_41 & multiplication(all_0_4_4, all_0_4_4) = all_92_1_42 & addition(all_92_1_42, all_92_0_41) = all_0_4_4 % 17.28/4.70 | % 17.28/4.70 | Applying alpha-rule on (161) yields: % 17.28/4.70 | (162) multiplication(all_0_4_4, all_0_2_2) = all_92_0_41 % 17.28/4.70 | (163) multiplication(all_0_4_4, all_0_4_4) = all_92_1_42 % 17.28/4.70 | (164) addition(all_92_1_42, all_92_0_41) = all_0_4_4 % 17.28/4.70 | % 17.28/4.70 | Instantiating (147) with all_94_0_43, all_94_1_44 yields: % 17.28/4.70 | (165) multiplication(all_0_4_4, all_0_2_2) = all_94_1_44 & multiplication(all_0_4_4, all_0_4_4) = all_94_0_43 & addition(all_94_1_44, all_94_0_43) = all_0_4_4 % 17.28/4.70 | % 17.28/4.70 | Applying alpha-rule on (165) yields: % 17.28/4.70 | (166) multiplication(all_0_4_4, all_0_2_2) = all_94_1_44 % 17.28/4.70 | (167) multiplication(all_0_4_4, all_0_4_4) = all_94_0_43 % 17.28/4.70 | (168) addition(all_94_1_44, all_94_0_43) = all_0_4_4 % 17.28/4.70 | % 17.28/4.70 | Instantiating (152) with all_104_0_52, all_104_1_53 yields: % 17.28/4.70 | (169) multiplication(all_0_4_4, all_49_0_20) = all_104_0_52 & multiplication(all_0_4_4, all_49_1_21) = all_104_1_53 & addition(all_104_1_53, all_104_0_52) = all_49_0_20 % 17.28/4.70 | % 17.28/4.70 | Applying alpha-rule on (169) yields: % 17.28/4.70 | (170) multiplication(all_0_4_4, all_49_0_20) = all_104_0_52 % 17.28/4.70 | (171) multiplication(all_0_4_4, all_49_1_21) = all_104_1_53 % 17.28/4.70 | (172) addition(all_104_1_53, all_104_0_52) = all_49_0_20 % 17.28/4.70 | % 17.28/4.70 | Instantiating (151) with all_112_0_58, all_112_1_59 yields: % 17.28/4.70 | (173) multiplication(all_0_4_4, all_49_0_20) = all_112_1_59 & multiplication(all_0_4_4, all_49_1_21) = all_112_0_58 & addition(all_112_1_59, all_112_0_58) = all_49_0_20 % 17.28/4.70 | % 17.28/4.70 | Applying alpha-rule on (173) yields: % 17.28/4.70 | (174) multiplication(all_0_4_4, all_49_0_20) = all_112_1_59 % 17.28/4.70 | (175) multiplication(all_0_4_4, all_49_1_21) = all_112_0_58 % 17.28/4.70 | (176) addition(all_112_1_59, all_112_0_58) = all_49_0_20 % 17.28/4.70 | % 17.28/4.70 | Instantiating (144) with all_138_0_80 yields: % 17.28/4.70 | (177) multiplication(all_138_0_80, all_0_5_5) = all_53_1_25 & multiplication(all_0_2_2, all_0_4_4) = all_138_0_80 % 17.28/4.70 | % 17.28/4.70 | Applying alpha-rule on (177) yields: % 17.28/4.70 | (178) multiplication(all_138_0_80, all_0_5_5) = all_53_1_25 % 17.28/4.70 | (179) multiplication(all_0_2_2, all_0_4_4) = all_138_0_80 % 17.28/4.70 | % 17.28/4.70 | Instantiating (143) with all_144_0_83 yields: % 17.28/4.70 | (180) c(all_144_0_83) = one & multiplication(all_0_4_4, all_0_2_2) = all_144_0_83 % 17.28/4.70 | % 17.28/4.70 | Applying alpha-rule on (180) yields: % 17.28/4.70 | (181) c(all_144_0_83) = one % 17.28/4.71 | (182) multiplication(all_0_4_4, all_0_2_2) = all_144_0_83 % 17.28/4.71 | % 17.28/4.71 | Instantiating (146) with all_160_0_96 yields: % 17.28/4.71 | (183) multiplication(all_160_0_96, one) = zero & multiplication(all_0_4_4, all_0_2_2) = all_160_0_96 % 17.28/4.71 | % 17.28/4.71 | Applying alpha-rule on (183) yields: % 17.28/4.71 | (184) multiplication(all_160_0_96, one) = zero % 17.28/4.71 | (185) multiplication(all_0_4_4, all_0_2_2) = all_160_0_96 % 17.28/4.71 | % 17.28/4.71 | Instantiating (145) with all_164_0_98 yields: % 17.28/4.71 | (186) multiplication(all_164_0_98, all_0_5_5) = all_49_1_21 & multiplication(all_0_4_4, all_0_2_2) = all_164_0_98 % 17.28/4.71 | % 17.28/4.71 | Applying alpha-rule on (186) yields: % 17.28/4.71 | (187) multiplication(all_164_0_98, all_0_5_5) = all_49_1_21 % 17.28/4.71 | (188) multiplication(all_0_4_4, all_0_2_2) = all_164_0_98 % 17.28/4.71 | % 17.28/4.71 | Instantiating formula (16) with all_138_0_80, all_0_4_4, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_4_4) = all_138_0_80, complement(all_0_4_4, all_0_2_2), yields: % 17.28/4.71 | (189) all_138_0_80 = zero % 17.28/4.71 | % 17.28/4.71 | Instantiating formula (32) with all_0_4_4, all_53_0_24, all_86_0_36, all_90_1_40 and discharging atoms multiplication(all_0_4_4, all_53_0_24) = all_90_1_40, multiplication(all_0_4_4, all_53_0_24) = all_86_0_36, yields: % 17.28/4.71 | (190) all_90_1_40 = all_86_0_36 % 17.28/4.71 | % 17.28/4.71 | Instantiating formula (32) with all_0_4_4, all_53_1_25, all_86_1_37, all_90_0_39 and discharging atoms multiplication(all_0_4_4, all_53_1_25) = all_90_0_39, multiplication(all_0_4_4, all_53_1_25) = all_86_1_37, yields: % 17.28/4.71 | (191) all_90_0_39 = all_86_1_37 % 17.28/4.71 | % 17.28/4.71 | Instantiating formula (32) with all_0_4_4, all_49_1_21, all_104_1_53, all_112_0_58 and discharging atoms multiplication(all_0_4_4, all_49_1_21) = all_112_0_58, multiplication(all_0_4_4, all_49_1_21) = all_104_1_53, yields: % 17.28/4.71 | (192) all_112_0_58 = all_104_1_53 % 17.28/4.71 | % 17.28/4.71 | Instantiating formula (32) with all_0_4_4, all_0_2_2, all_160_0_96, all_164_0_98 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_164_0_98, multiplication(all_0_4_4, all_0_2_2) = all_160_0_96, yields: % 17.28/4.71 | (193) all_164_0_98 = all_160_0_96 % 17.28/4.71 | % 17.28/4.71 | Instantiating formula (6) with all_160_0_96, all_0_4_4, all_0_2_2 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_160_0_96, complement(all_0_4_4, all_0_2_2), yields: % 17.28/4.71 | (194) all_160_0_96 = zero % 17.28/4.71 | % 17.28/4.71 | Instantiating formula (32) with all_0_4_4, all_0_2_2, all_144_0_83, all_160_0_96 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_160_0_96, multiplication(all_0_4_4, all_0_2_2) = all_144_0_83, yields: % 17.28/4.71 | (195) all_160_0_96 = all_144_0_83 % 17.28/4.71 | % 17.28/4.71 | Instantiating formula (32) with all_0_4_4, all_0_2_2, all_94_1_44, all_164_0_98 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_164_0_98, multiplication(all_0_4_4, all_0_2_2) = all_94_1_44, yields: % 17.28/4.71 | (196) all_164_0_98 = all_94_1_44 % 17.28/4.71 | % 17.28/4.71 | Instantiating formula (32) with all_0_4_4, all_0_2_2, all_92_0_41, all_164_0_98 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_164_0_98, multiplication(all_0_4_4, all_0_2_2) = all_92_0_41, yields: % 17.28/4.71 | (197) all_164_0_98 = all_92_0_41 % 17.28/4.71 | % 17.28/4.71 | Combining equations (197,196) yields a new equation: % 17.28/4.71 | (198) all_94_1_44 = all_92_0_41 % 17.28/4.71 | % 17.28/4.71 | Combining equations (193,196) yields a new equation: % 17.28/4.71 | (199) all_160_0_96 = all_94_1_44 % 17.28/4.71 | % 17.28/4.71 | Simplifying 199 yields: % 17.28/4.71 | (200) all_160_0_96 = all_94_1_44 % 17.28/4.71 | % 17.28/4.71 | Combining equations (194,195) yields a new equation: % 17.28/4.71 | (201) all_144_0_83 = zero % 17.28/4.71 | % 17.28/4.71 | Combining equations (200,195) yields a new equation: % 17.28/4.71 | (202) all_144_0_83 = all_94_1_44 % 17.28/4.71 | % 17.28/4.71 | Combining equations (202,201) yields a new equation: % 17.28/4.71 | (203) all_94_1_44 = zero % 17.28/4.71 | % 17.28/4.71 | Simplifying 203 yields: % 17.28/4.71 | (204) all_94_1_44 = zero % 17.28/4.71 | % 17.28/4.71 | Combining equations (204,198) yields a new equation: % 17.28/4.71 | (205) all_92_0_41 = zero % 17.28/4.71 | % 17.28/4.71 | Combining equations (205,198) yields a new equation: % 17.28/4.71 | (204) all_94_1_44 = zero % 17.28/4.71 | % 17.28/4.71 | Combining equations (204,196) yields a new equation: % 17.28/4.71 | (207) all_164_0_98 = zero % 17.28/4.71 | % 17.28/4.71 | From (207) and (187) follows: % 17.28/4.71 | (208) multiplication(zero, all_0_5_5) = all_49_1_21 % 17.28/4.71 | % 17.28/4.71 | From (189) and (178) follows: % 17.28/4.71 | (209) multiplication(zero, all_0_5_5) = all_53_1_25 % 17.28/4.71 | % 17.28/4.71 | From (191) and (159) follows: % 17.28/4.71 | (155) multiplication(all_0_4_4, all_53_1_25) = all_86_1_37 % 17.28/4.71 | % 17.28/4.71 | From (192) and (175) follows: % 17.28/4.71 | (171) multiplication(all_0_4_4, all_49_1_21) = all_104_1_53 % 17.28/4.71 | % 17.28/4.71 | From (190)(191) and (160) follows: % 17.28/4.71 | (212) addition(all_86_0_36, all_86_1_37) = all_49_1_21 % 17.28/4.71 | % 17.28/4.71 | Instantiating formula (5) with all_53_1_25, all_0_5_5 and discharging atoms multiplication(zero, all_0_5_5) = all_53_1_25, yields: % 17.28/4.71 | (213) all_53_1_25 = zero % 17.28/4.71 | % 17.28/4.71 | Instantiating formula (32) with zero, all_0_5_5, all_49_1_21, all_53_1_25 and discharging atoms multiplication(zero, all_0_5_5) = all_53_1_25, multiplication(zero, all_0_5_5) = all_49_1_21, yields: % 17.28/4.71 | (214) all_53_1_25 = all_49_1_21 % 17.28/4.71 | % 17.28/4.71 | Combining equations (213,214) yields a new equation: % 17.28/4.71 | (215) all_49_1_21 = zero % 17.28/4.71 | % 17.28/4.71 | Combining equations (215,214) yields a new equation: % 17.28/4.71 | (213) all_53_1_25 = zero % 17.28/4.71 | % 17.28/4.71 | From (213) and (155) follows: % 17.28/4.71 | (217) multiplication(all_0_4_4, zero) = all_86_1_37 % 17.28/4.71 | % 17.28/4.71 | From (215) and (171) follows: % 17.28/4.71 | (218) multiplication(all_0_4_4, zero) = all_104_1_53 % 17.28/4.71 | % 17.28/4.71 | From (215) and (208) follows: % 17.28/4.71 | (219) multiplication(zero, all_0_5_5) = zero % 17.28/4.71 | % 17.28/4.71 | From (215) and (212) follows: % 17.28/4.71 | (220) addition(all_86_0_36, all_86_1_37) = zero % 17.28/4.71 | % 17.28/4.71 | From (215) and (156) follows: % 17.28/4.71 | (221) addition(all_86_1_37, all_86_0_36) = zero % 17.28/4.71 | % 17.28/4.71 | Instantiating formula (40) with all_104_1_53, all_0_4_4 and discharging atoms multiplication(all_0_4_4, zero) = all_104_1_53, yields: % 17.28/4.71 | (222) all_104_1_53 = zero % 17.28/4.71 | % 17.28/4.71 | Instantiating formula (32) with all_0_4_4, zero, all_86_1_37, all_104_1_53 and discharging atoms multiplication(all_0_4_4, zero) = all_104_1_53, multiplication(all_0_4_4, zero) = all_86_1_37, yields: % 17.28/4.71 | (223) all_104_1_53 = all_86_1_37 % 17.28/4.71 | % 17.28/4.71 | Combining equations (223,222) yields a new equation: % 17.28/4.71 | (224) all_86_1_37 = zero % 17.28/4.71 | % 17.28/4.71 | Simplifying 224 yields: % 17.28/4.71 | (225) all_86_1_37 = zero % 17.28/4.71 | % 17.28/4.71 | From (225) and (220) follows: % 17.28/4.71 | (226) addition(all_86_0_36, zero) = zero % 17.35/4.71 | % 17.35/4.71 | From (225) and (221) follows: % 17.35/4.71 | (227) addition(zero, all_86_0_36) = zero % 17.35/4.71 | % 17.35/4.71 | Instantiating formula (44) with zero, all_86_0_36 and discharging atoms addition(all_86_0_36, zero) = zero, yields: % 17.35/4.71 | (228) all_86_0_36 = zero % 17.35/4.71 | % 17.35/4.71 | From (228) and (227) follows: % 17.35/4.71 | (229) addition(zero, zero) = zero % 17.35/4.71 | % 17.35/4.71 | Instantiating formula (33) 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: % 17.35/4.71 | (230) ? [v0] : (multiplication(zero, v0) = zero & addition(all_0_5_5, all_0_5_5) = v0) % 17.35/4.71 | % 17.35/4.71 | Instantiating (230) with all_224_0_121 yields: % 17.35/4.71 | (231) multiplication(zero, all_224_0_121) = zero & addition(all_0_5_5, all_0_5_5) = all_224_0_121 % 17.35/4.71 | % 17.35/4.71 | Applying alpha-rule on (231) yields: % 17.35/4.71 | (232) multiplication(zero, all_224_0_121) = zero % 17.35/4.71 | (233) addition(all_0_5_5, all_0_5_5) = all_224_0_121 % 17.35/4.71 | % 17.35/4.71 | Instantiating formula (28) with all_224_0_121, all_0_5_5 and discharging atoms addition(all_0_5_5, all_0_5_5) = all_224_0_121, yields: % 17.35/4.71 | (234) all_224_0_121 = all_0_5_5 % 17.35/4.71 | % 17.35/4.71 | From (234) and (233) follows: % 17.35/4.71 | (235) addition(all_0_5_5, all_0_5_5) = all_0_5_5 % 17.35/4.71 | % 17.35/4.71 | Instantiating formula (34) 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: % 17.35/4.71 | (236) $false % 17.35/4.72 | % 17.35/4.72 |-The branch is then unsatisfiable % 17.35/4.72 |-Branch two: % 17.35/4.72 | (237) ~ complement(all_0_2_2, all_0_4_4) % 17.35/4.72 | (238) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_0_4_4) = v1 & multiplication(all_0_4_4, all_0_2_2) = v0 & ( ~ (v1 = zero) | ~ (v0 = zero))) % 17.35/4.72 | % 17.35/4.72 | Instantiating (238) with all_67_0_242, all_67_1_243 yields: % 17.35/4.72 | (239) multiplication(all_0_2_2, all_0_4_4) = all_67_0_242 & multiplication(all_0_4_4, all_0_2_2) = all_67_1_243 & ( ~ (all_67_0_242 = zero) | ~ (all_67_1_243 = zero)) % 17.35/4.72 | % 17.35/4.72 | Applying alpha-rule on (239) yields: % 17.35/4.72 | (240) multiplication(all_0_2_2, all_0_4_4) = all_67_0_242 % 17.35/4.72 | (241) multiplication(all_0_4_4, all_0_2_2) = all_67_1_243 % 17.35/4.72 | (242) ~ (all_67_0_242 = zero) | ~ (all_67_1_243 = zero) % 17.35/4.72 | % 17.35/4.72 | Instantiating formula (32) with all_0_2_2, all_0_4_4, zero, all_67_0_242 and discharging atoms multiplication(all_0_2_2, all_0_4_4) = all_67_0_242, multiplication(all_0_2_2, all_0_4_4) = zero, yields: % 17.35/4.72 | (243) all_67_0_242 = zero % 17.35/4.72 | % 17.35/4.72 | Instantiating formula (32) with all_0_4_4, all_0_2_2, zero, all_67_1_243 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_67_1_243, multiplication(all_0_4_4, all_0_2_2) = zero, yields: % 17.35/4.72 | (244) all_67_1_243 = zero % 17.35/4.72 | % 17.35/4.72 +-Applying beta-rule and splitting (242), into two cases. % 17.35/4.72 |-Branch one: % 17.35/4.72 | (245) ~ (all_67_0_242 = zero) % 17.35/4.72 | % 17.35/4.72 | Equations (243) can reduce 245 to: % 17.35/4.72 | (246) $false % 17.35/4.72 | % 17.35/4.72 |-The branch is then unsatisfiable % 17.35/4.72 |-Branch two: % 17.35/4.72 | (243) all_67_0_242 = zero % 17.35/4.72 | (248) ~ (all_67_1_243 = zero) % 17.35/4.72 | % 17.35/4.72 | Equations (244) can reduce 248 to: % 17.35/4.72 | (246) $false % 17.35/4.72 | % 17.35/4.72 |-The branch is then unsatisfiable % 17.35/4.72 |-Branch two: % 17.35/4.72 | (250) leq(all_0_0_0, all_0_5_5) % 17.35/4.72 | (251) ~ leq(all_0_5_5, all_0_0_0) % 17.35/4.72 | % 17.35/4.72 | From (65) and (250) follows: % 17.35/4.72 | (252) leq(all_0_5_5, all_0_5_5) % 17.35/4.72 | % 17.35/4.72 | From (65) and (251) follows: % 17.35/4.72 | (70) ~ leq(all_0_5_5, all_0_5_5) % 17.35/4.72 | % 17.35/4.72 | Using (252) and (70) yields: % 17.35/4.72 | (236) $false % 17.35/4.72 | % 17.35/4.72 |-The branch is then unsatisfiable % 17.35/4.72 % SZS output end Proof for theBenchmark % 17.35/4.72 % 17.35/4.72 4244ms %------------------------------------------------------------------------------