%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE022+4 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n006.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 01:50:57 EDT 2022 % Result : Theorem 9.86s 3.04s % Output : Proof 18.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : KLE022+4 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n006.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Thu Jun 16 13:02:41 EDT 2022 % 0.13/0.35 % CPUTime : % 0.61/0.60 ____ _ % 0.61/0.60 ___ / __ \_____(_)___ ________ __________ % 0.61/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.61/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.61/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.61/0.60 % 0.61/0.60 A Theorem Prover for First-Order Logic % 0.61/0.61 (ePrincess v.1.0) % 0.61/0.61 % 0.61/0.61 (c) Philipp Rümmer, 2009-2015 % 0.61/0.61 (c) Peter Backeman, 2014-2015 % 0.61/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.61/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.61/0.61 Bug reports to peter@backeman.se % 0.61/0.61 % 0.61/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.61/0.61 % 0.61/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.66/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.54/0.98 Prover 0: Preprocessing ... % 2.48/1.27 Prover 0: Constructing countermodel ... % 9.86/3.04 Prover 0: proved (2364ms) % 9.86/3.04 % 9.86/3.04 No countermodel exists, formula is valid % 9.86/3.04 % SZS status Theorem for theBenchmark % 9.86/3.04 % 9.86/3.04 Generating proof ... found it (size 199) % 17.35/4.86 % 17.35/4.86 % SZS output start Proof for theBenchmark % 17.35/4.86 Assumed formulas after preprocessing and simplification: % 17.35/4.86 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (c(v1) = v3 & multiplication(v0, v3) = v4 & multiplication(v0, v1) = 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))) % 17.81/4.91 | 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: % 17.81/4.91 | (1) c(all_0_4_4) = all_0_2_2 & multiplication(all_0_5_5, all_0_2_2) = all_0_1_1 & multiplication(all_0_5_5, all_0_4_4) = 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)) % 17.98/4.94 | % 17.98/4.94 | Applying alpha-rule on (1) yields: % 17.98/4.94 | (2) ! [v0] : ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) % 17.98/4.94 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 17.98/4.94 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (c(v0) = v2) | ~ complement(v0, v1) | ~ test(v0)) % 17.98/4.94 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 17.98/4.94 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 17.98/4.94 | (7) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 17.98/4.94 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = one | ~ (addition(v0, v1) = v2) | ~ complement(v1, v0)) % 17.98/4.94 | (9) test(all_0_4_4) % 17.98/4.94 | (10) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 17.98/4.94 | (11) ! [v0] : ! [v1] : ( ~ (c(v0) = v1) | ~ test(v0) | complement(v0, v1)) % 17.98/4.94 | (12) ! [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)) % 17.98/4.94 | (13) ! [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)) % 17.98/4.94 | (14) ~ leq(all_0_0_0, all_0_5_5) | ~ leq(all_0_5_5, all_0_0_0) % 17.98/4.94 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 17.98/4.94 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 17.98/4.94 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0)) % 17.98/4.95 | (18) ! [v0] : ! [v1] : (v1 = zero | ~ (c(v0) = v1) | test(v0)) % 17.98/4.95 | (19) ! [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)) % 17.98/4.95 | (20) multiplication(all_0_5_5, all_0_2_2) = all_0_1_1 % 17.98/4.95 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) % 17.98/4.95 | (22) multiplication(all_0_5_5, all_0_4_4) = all_0_3_3 % 17.98/4.95 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0)) % 17.98/4.95 | (24) ! [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)) % 17.98/4.95 | (25) ! [v0] : ( ~ test(v0) | ? [v1] : complement(v1, v0)) % 17.98/4.95 | (26) addition(all_0_3_3, all_0_1_1) = all_0_0_0 % 17.98/4.95 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one)) % 17.98/4.95 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one)) % 17.98/4.95 | (29) ! [v0] : ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) % 17.98/4.95 | (30) c(all_0_4_4) = all_0_2_2 % 17.98/4.95 | (31) ! [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)) % 17.98/4.95 | (32) ! [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)) % 17.98/4.95 | (33) ! [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)) % 17.98/4.95 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 17.98/4.95 | (35) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) % 17.98/4.95 | (36) ! [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)) % 17.98/4.95 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 17.98/4.95 | (38) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) | ~ (v2 = zero)))) % 17.98/4.95 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero)) % 17.98/4.95 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 17.98/4.95 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 17.98/4.95 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 17.98/4.95 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 17.98/4.96 | (44) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) % 17.98/4.96 | (45) ! [v0] : ! [v1] : ( ~ complement(v1, v0) | test(v0)) % 17.98/4.96 | (46) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 17.98/4.96 | % 17.98/4.96 | Instantiating formula (12) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms multiplication(all_0_5_5, all_0_2_2) = all_0_1_1, multiplication(all_0_5_5, all_0_4_4) = all_0_3_3, addition(all_0_3_3, all_0_1_1) = all_0_0_0, yields: % 17.98/4.96 | (47) ? [v0] : (multiplication(all_0_5_5, v0) = all_0_0_0 & addition(all_0_4_4, all_0_2_2) = v0) % 17.98/4.96 | % 17.98/4.96 | Instantiating formula (41) 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: % 17.98/4.96 | (48) addition(all_0_1_1, all_0_3_3) = all_0_0_0 % 17.98/4.96 | % 17.98/4.96 | Instantiating formula (11) 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: % 17.98/4.96 | (49) complement(all_0_4_4, all_0_2_2) % 17.98/4.96 | % 17.98/4.96 | Instantiating (47) with all_9_0_6 yields: % 17.98/4.96 | (50) multiplication(all_0_5_5, all_9_0_6) = all_0_0_0 & addition(all_0_4_4, all_0_2_2) = all_9_0_6 % 17.98/4.96 | % 17.98/4.96 | Applying alpha-rule on (50) yields: % 17.98/4.96 | (51) multiplication(all_0_5_5, all_9_0_6) = all_0_0_0 % 17.98/4.96 | (52) addition(all_0_4_4, all_0_2_2) = all_9_0_6 % 17.98/4.96 | % 17.98/4.96 | Instantiating formula (12) with all_0_0_0, all_0_3_3, all_0_1_1, all_0_4_4, all_0_2_2, all_0_5_5 and discharging atoms multiplication(all_0_5_5, all_0_2_2) = all_0_1_1, multiplication(all_0_5_5, all_0_4_4) = all_0_3_3, addition(all_0_1_1, all_0_3_3) = all_0_0_0, yields: % 17.98/4.96 | (53) ? [v0] : (multiplication(all_0_5_5, v0) = all_0_0_0 & addition(all_0_2_2, all_0_4_4) = v0) % 17.98/4.96 | % 17.98/4.96 | Instantiating formula (41) 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: % 17.98/4.96 | (54) addition(all_0_2_2, all_0_4_4) = all_9_0_6 % 17.98/4.96 | % 17.98/4.96 | Instantiating formula (45) with all_0_4_4, all_0_2_2 and discharging atoms complement(all_0_4_4, all_0_2_2), yields: % 17.98/4.96 | (55) test(all_0_2_2) % 17.98/4.96 | % 17.98/4.96 | Instantiating (53) with all_19_0_8 yields: % 17.98/4.96 | (56) multiplication(all_0_5_5, all_19_0_8) = all_0_0_0 & addition(all_0_2_2, all_0_4_4) = all_19_0_8 % 17.98/4.96 | % 17.98/4.96 | Applying alpha-rule on (56) yields: % 17.98/4.96 | (57) multiplication(all_0_5_5, all_19_0_8) = all_0_0_0 % 17.98/4.96 | (58) addition(all_0_2_2, all_0_4_4) = all_19_0_8 % 17.98/4.96 | % 17.98/4.96 | Instantiating formula (8) 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: % 17.98/4.96 | (59) all_19_0_8 = one % 17.98/4.96 | % 17.98/4.96 | Instantiating formula (42) 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: % 17.98/4.96 | (60) all_19_0_8 = all_9_0_6 % 17.98/4.96 | % 17.98/4.96 | Combining equations (59,60) yields a new equation: % 17.98/4.96 | (61) all_9_0_6 = one % 17.98/4.96 | % 17.98/4.96 | From (61) and (51) follows: % 17.98/4.96 | (62) multiplication(all_0_5_5, one) = all_0_0_0 % 17.98/4.96 | % 17.98/4.96 | From (61) and (54) follows: % 17.98/4.96 | (63) addition(all_0_2_2, all_0_4_4) = one % 17.98/4.96 | % 17.98/4.96 | From (61) and (52) follows: % 17.98/4.96 | (64) addition(all_0_4_4, all_0_2_2) = one % 17.98/4.96 | % 17.98/4.96 | Instantiating formula (46) with all_0_0_0, all_0_5_5 and discharging atoms multiplication(all_0_5_5, one) = all_0_0_0, yields: % 17.98/4.96 | (65) all_0_0_0 = all_0_5_5 % 17.98/4.96 | % 17.98/4.96 | From (65) and (62) follows: % 17.98/4.96 | (66) multiplication(all_0_5_5, one) = all_0_5_5 % 17.98/4.96 | % 17.98/4.96 | From (65) and (48) follows: % 17.98/4.96 | (67) addition(all_0_1_1, all_0_3_3) = all_0_5_5 % 17.98/4.96 | % 17.98/4.96 | From (65) and (26) follows: % 17.98/4.96 | (68) addition(all_0_3_3, all_0_1_1) = all_0_5_5 % 17.98/4.96 | % 17.98/4.96 +-Applying beta-rule and splitting (14), into two cases. % 17.98/4.96 |-Branch one: % 17.98/4.96 | (69) ~ leq(all_0_0_0, all_0_5_5) % 17.98/4.96 | % 17.98/4.96 | From (65) and (69) follows: % 17.98/4.96 | (70) ~ leq(all_0_5_5, all_0_5_5) % 17.98/4.96 | % 17.98/4.96 | Instantiating formula (5) with all_0_1_1, all_0_5_5, all_0_2_2, one, all_0_5_5 and discharging atoms multiplication(all_0_5_5, all_0_2_2) = all_0_1_1, multiplication(all_0_5_5, one) = all_0_5_5, yields: % 17.98/4.96 | (71) ? [v0] : (multiplication(all_0_5_5, v0) = all_0_1_1 & multiplication(one, all_0_2_2) = v0) % 17.98/4.96 | % 17.98/4.96 | Instantiating formula (5) with all_0_3_3, all_0_5_5, all_0_4_4, one, all_0_5_5 and discharging atoms multiplication(all_0_5_5, all_0_4_4) = all_0_3_3, multiplication(all_0_5_5, one) = all_0_5_5, yields: % 17.98/4.96 | (72) ? [v0] : (multiplication(all_0_5_5, v0) = all_0_3_3 & multiplication(one, all_0_4_4) = v0) % 17.98/4.96 | % 17.98/4.96 | Instantiating formula (13) with all_0_1_1, all_0_5_5, all_0_2_2, all_0_3_3, all_0_1_1 and discharging atoms multiplication(all_0_5_5, all_0_2_2) = all_0_1_1, addition(all_0_1_1, all_0_3_3) = all_0_5_5, yields: % 17.98/4.96 | (73) ? [v0] : ? [v1] : (multiplication(all_0_1_1, all_0_2_2) = v0 & multiplication(all_0_3_3, all_0_2_2) = v1 & addition(v0, v1) = all_0_1_1) % 17.98/4.96 | % 17.98/4.96 | Instantiating formula (13) with all_0_3_3, all_0_5_5, all_0_4_4, all_0_3_3, all_0_1_1 and discharging atoms multiplication(all_0_5_5, all_0_4_4) = all_0_3_3, addition(all_0_1_1, all_0_3_3) = all_0_5_5, yields: % 17.98/4.96 | (74) ? [v0] : ? [v1] : (multiplication(all_0_1_1, all_0_4_4) = v0 & multiplication(all_0_3_3, all_0_4_4) = v1 & addition(v0, v1) = all_0_3_3) % 17.98/4.96 | % 17.98/4.96 | Instantiating formula (39) 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: % 17.98/4.96 | (75) multiplication(all_0_2_2, all_0_4_4) = zero & multiplication(all_0_4_4, all_0_2_2) = zero % 17.98/4.97 | % 17.98/4.97 | Applying alpha-rule on (75) yields: % 17.98/4.97 | (76) multiplication(all_0_2_2, all_0_4_4) = zero % 17.98/4.97 | (77) multiplication(all_0_4_4, all_0_2_2) = zero % 17.98/4.97 | % 17.98/4.97 | Instantiating formula (13) with all_0_1_1, all_0_5_5, all_0_2_2, all_0_1_1, all_0_3_3 and discharging atoms multiplication(all_0_5_5, all_0_2_2) = all_0_1_1, addition(all_0_3_3, all_0_1_1) = all_0_5_5, yields: % 17.98/4.97 | (78) ? [v0] : ? [v1] : (multiplication(all_0_1_1, all_0_2_2) = v1 & multiplication(all_0_3_3, all_0_2_2) = v0 & addition(v0, v1) = all_0_1_1) % 17.98/4.97 | % 17.98/4.97 | Instantiating formula (13) with all_0_3_3, all_0_5_5, all_0_4_4, all_0_1_1, all_0_3_3 and discharging atoms multiplication(all_0_5_5, all_0_4_4) = all_0_3_3, addition(all_0_3_3, all_0_1_1) = all_0_5_5, yields: % 17.98/4.97 | (79) ? [v0] : ? [v1] : (multiplication(all_0_1_1, all_0_4_4) = v1 & multiplication(all_0_3_3, all_0_4_4) = v0 & addition(v0, v1) = all_0_3_3) % 17.98/4.97 | % 17.98/4.97 | Instantiating formula (38) with all_0_2_2, all_0_4_4 and discharging atoms addition(all_0_4_4, all_0_2_2) = one, yields: % 17.98/4.97 | (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))) % 17.98/4.97 | % 17.98/4.97 | Instantiating formula (33) 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: % 17.98/4.97 | (81) ? [v0] : ? [v1] : ? [v2] : (c(all_0_2_2) = v1 & c(all_0_4_4) = v2 & c(one) = v0 & multiplication(v1, v2) = v0) % 17.98/4.97 | % 17.98/4.97 | Instantiating formula (33) 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: % 17.98/4.97 | (82) ? [v0] : ? [v1] : ? [v2] : (c(all_0_2_2) = v2 & c(all_0_4_4) = v1 & c(one) = v0 & multiplication(v1, v2) = v0) % 17.98/4.97 | % 17.98/4.97 | Instantiating (81) with all_41_0_10, all_41_1_11, all_41_2_12 yields: % 17.98/4.97 | (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 % 17.98/4.97 | % 17.98/4.97 | Applying alpha-rule on (83) yields: % 17.98/4.97 | (84) c(all_0_2_2) = all_41_1_11 % 17.98/4.97 | (85) c(all_0_4_4) = all_41_0_10 % 17.98/4.97 | (86) c(one) = all_41_2_12 % 17.98/4.97 | (87) multiplication(all_41_1_11, all_41_0_10) = all_41_2_12 % 17.98/4.97 | % 17.98/4.97 | Instantiating (82) with all_45_0_15, all_45_1_16, all_45_2_17 yields: % 17.98/4.97 | (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 % 17.98/4.97 | % 17.98/4.97 | Applying alpha-rule on (88) yields: % 17.98/4.97 | (89) c(all_0_2_2) = all_45_0_15 % 17.98/4.97 | (90) c(all_0_4_4) = all_45_1_16 % 17.98/4.97 | (91) c(one) = all_45_2_17 % 17.98/4.97 | (92) multiplication(all_45_1_16, all_45_0_15) = all_45_2_17 % 17.98/4.97 | % 17.98/4.97 | Instantiating (74) with all_49_0_20, all_49_1_21 yields: % 17.98/4.97 | (93) multiplication(all_0_1_1, all_0_4_4) = all_49_1_21 & multiplication(all_0_3_3, all_0_4_4) = all_49_0_20 & addition(all_49_1_21, all_49_0_20) = all_0_3_3 % 17.98/4.97 | % 17.98/4.97 | Applying alpha-rule on (93) yields: % 17.98/4.97 | (94) multiplication(all_0_1_1, all_0_4_4) = all_49_1_21 % 17.98/4.97 | (95) multiplication(all_0_3_3, all_0_4_4) = all_49_0_20 % 17.98/4.97 | (96) addition(all_49_1_21, all_49_0_20) = all_0_3_3 % 17.98/4.97 | % 17.98/4.97 | Instantiating (79) with all_51_0_22, all_51_1_23 yields: % 17.98/4.97 | (97) multiplication(all_0_1_1, all_0_4_4) = all_51_0_22 & multiplication(all_0_3_3, all_0_4_4) = all_51_1_23 & addition(all_51_1_23, all_51_0_22) = all_0_3_3 % 17.98/4.97 | % 17.98/4.97 | Applying alpha-rule on (97) yields: % 17.98/4.97 | (98) multiplication(all_0_1_1, all_0_4_4) = all_51_0_22 % 17.98/4.97 | (99) multiplication(all_0_3_3, all_0_4_4) = all_51_1_23 % 17.98/4.97 | (100) addition(all_51_1_23, all_51_0_22) = all_0_3_3 % 17.98/4.97 | % 17.98/4.97 | Instantiating (78) with all_53_0_24, all_53_1_25 yields: % 17.98/4.97 | (101) multiplication(all_0_1_1, all_0_2_2) = all_53_0_24 & multiplication(all_0_3_3, all_0_2_2) = all_53_1_25 & addition(all_53_1_25, all_53_0_24) = all_0_1_1 % 17.98/4.97 | % 17.98/4.97 | Applying alpha-rule on (101) yields: % 17.98/4.97 | (102) multiplication(all_0_1_1, all_0_2_2) = all_53_0_24 % 17.98/4.97 | (103) multiplication(all_0_3_3, all_0_2_2) = all_53_1_25 % 17.98/4.97 | (104) addition(all_53_1_25, all_53_0_24) = all_0_1_1 % 17.98/4.97 | % 17.98/4.97 | Instantiating (73) with all_55_0_26, all_55_1_27 yields: % 17.98/4.97 | (105) multiplication(all_0_1_1, all_0_2_2) = all_55_1_27 & multiplication(all_0_3_3, all_0_2_2) = all_55_0_26 & addition(all_55_1_27, all_55_0_26) = all_0_1_1 % 17.98/4.97 | % 17.98/4.97 | Applying alpha-rule on (105) yields: % 17.98/4.97 | (106) multiplication(all_0_1_1, all_0_2_2) = all_55_1_27 % 17.98/4.97 | (107) multiplication(all_0_3_3, all_0_2_2) = all_55_0_26 % 17.98/4.97 | (108) addition(all_55_1_27, all_55_0_26) = all_0_1_1 % 17.98/4.97 | % 17.98/4.97 | Instantiating (72) with all_59_0_29 yields: % 17.98/4.97 | (109) multiplication(all_0_5_5, all_59_0_29) = all_0_3_3 & multiplication(one, all_0_4_4) = all_59_0_29 % 17.98/4.97 | % 17.98/4.97 | Applying alpha-rule on (109) yields: % 17.98/4.97 | (110) multiplication(all_0_5_5, all_59_0_29) = all_0_3_3 % 17.98/4.97 | (111) multiplication(one, all_0_4_4) = all_59_0_29 % 17.98/4.97 | % 17.98/4.97 | Instantiating (71) with all_61_0_30 yields: % 17.98/4.97 | (112) multiplication(all_0_5_5, all_61_0_30) = all_0_1_1 & multiplication(one, all_0_2_2) = all_61_0_30 % 17.98/4.97 | % 17.98/4.97 | Applying alpha-rule on (112) yields: % 17.98/4.97 | (113) multiplication(all_0_5_5, all_61_0_30) = all_0_1_1 % 17.98/4.97 | (114) multiplication(one, all_0_2_2) = all_61_0_30 % 17.98/4.97 | % 17.98/4.97 +-Applying beta-rule and splitting (80), into two cases. % 17.98/4.97 |-Branch one: % 17.98/4.97 | (115) complement(all_0_2_2, all_0_4_4) % 17.98/4.97 | % 17.98/4.97 | Instantiating formula (21) 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: % 17.98/4.97 | (116) all_45_0_15 = all_41_1_11 % 17.98/4.97 | % 17.98/4.97 | Instantiating formula (21) 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: % 17.98/4.97 | (117) all_45_1_16 = all_0_2_2 % 17.98/4.97 | % 17.98/4.97 | Instantiating formula (21) 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: % 17.98/4.97 | (118) all_45_1_16 = all_41_0_10 % 17.98/4.97 | % 17.98/4.97 | Instantiating formula (21) with one, all_41_2_12, all_45_2_17 and discharging atoms c(one) = all_45_2_17, c(one) = all_41_2_12, yields: % 17.98/4.97 | (119) all_45_2_17 = all_41_2_12 % 17.98/4.97 | % 17.98/4.97 | Instantiating formula (34) with all_0_1_1, all_0_2_2, all_53_0_24, all_55_1_27 and discharging atoms multiplication(all_0_1_1, all_0_2_2) = all_55_1_27, multiplication(all_0_1_1, all_0_2_2) = all_53_0_24, yields: % 17.98/4.98 | (120) all_55_1_27 = all_53_0_24 % 17.98/4.98 | % 17.98/4.98 | Instantiating formula (34) with all_0_1_1, all_0_4_4, all_49_1_21, all_51_0_22 and discharging atoms multiplication(all_0_1_1, all_0_4_4) = all_51_0_22, multiplication(all_0_1_1, all_0_4_4) = all_49_1_21, yields: % 17.98/4.98 | (121) all_51_0_22 = all_49_1_21 % 17.98/4.98 | % 17.98/4.98 | Instantiating formula (34) with all_0_3_3, all_0_2_2, all_53_1_25, all_55_0_26 and discharging atoms multiplication(all_0_3_3, all_0_2_2) = all_55_0_26, multiplication(all_0_3_3, all_0_2_2) = all_53_1_25, yields: % 17.98/4.98 | (122) all_55_0_26 = all_53_1_25 % 17.98/4.98 | % 17.98/4.98 | Instantiating formula (34) with all_0_3_3, all_0_4_4, all_49_0_20, all_51_1_23 and discharging atoms multiplication(all_0_3_3, all_0_4_4) = all_51_1_23, multiplication(all_0_3_3, all_0_4_4) = all_49_0_20, yields: % 17.98/4.98 | (123) all_51_1_23 = all_49_0_20 % 17.98/4.98 | % 17.98/4.98 | Instantiating formula (16) with all_61_0_30, all_0_2_2 and discharging atoms multiplication(one, all_0_2_2) = all_61_0_30, yields: % 17.98/4.98 | (124) all_61_0_30 = all_0_2_2 % 17.98/4.98 | % 17.98/4.98 | Instantiating formula (16) with all_59_0_29, all_0_4_4 and discharging atoms multiplication(one, all_0_4_4) = all_59_0_29, yields: % 17.98/4.98 | (125) all_59_0_29 = all_0_4_4 % 17.98/4.98 | % 17.98/4.98 | Instantiating formula (4) 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: % 17.98/4.98 | (126) all_45_0_15 = all_0_4_4 % 17.98/4.98 | % 17.98/4.98 | Combining equations (126,116) yields a new equation: % 17.98/4.98 | (127) all_41_1_11 = all_0_4_4 % 17.98/4.98 | % 17.98/4.98 | Combining equations (117,118) yields a new equation: % 17.98/4.98 | (128) all_41_0_10 = all_0_2_2 % 17.98/4.98 | % 17.98/4.98 | Combining equations (128,118) yields a new equation: % 17.98/4.98 | (117) all_45_1_16 = all_0_2_2 % 17.98/4.98 | % 17.98/4.98 | Combining equations (127,116) yields a new equation: % 17.98/4.98 | (126) all_45_0_15 = all_0_4_4 % 17.98/4.98 | % 17.98/4.98 | From (127) and (84) follows: % 17.98/4.98 | (131) c(all_0_2_2) = all_0_4_4 % 17.98/4.98 | % 17.98/4.98 | From (128) and (85) follows: % 17.98/4.98 | (30) c(all_0_4_4) = all_0_2_2 % 17.98/4.98 | % 17.98/4.98 | From (117)(126)(119) and (92) follows: % 17.98/4.98 | (133) multiplication(all_0_2_2, all_0_4_4) = all_41_2_12 % 17.98/4.98 | % 17.98/4.98 | From (127)(128) and (87) follows: % 17.98/4.98 | (134) multiplication(all_0_4_4, all_0_2_2) = all_41_2_12 % 17.98/4.98 | % 17.98/4.98 | From (121) and (98) follows: % 17.98/4.98 | (94) multiplication(all_0_1_1, all_0_4_4) = all_49_1_21 % 17.98/4.98 | % 17.98/4.98 | From (122) and (107) follows: % 17.98/4.98 | (103) multiplication(all_0_3_3, all_0_2_2) = all_53_1_25 % 17.98/4.98 | % 17.98/4.98 | From (123) and (99) follows: % 17.98/4.98 | (95) multiplication(all_0_3_3, all_0_4_4) = all_49_0_20 % 17.98/4.98 | % 17.98/4.98 | From (124) and (113) follows: % 17.98/4.98 | (20) multiplication(all_0_5_5, all_0_2_2) = all_0_1_1 % 17.98/4.98 | % 17.98/4.98 | From (125) and (110) follows: % 17.98/4.98 | (22) multiplication(all_0_5_5, all_0_4_4) = all_0_3_3 % 17.98/4.98 | % 17.98/4.98 | From (124) and (114) follows: % 17.98/4.98 | (140) multiplication(one, all_0_2_2) = all_0_2_2 % 17.98/4.98 | % 17.98/4.98 | From (125) and (111) follows: % 17.98/4.98 | (141) multiplication(one, all_0_4_4) = all_0_4_4 % 17.98/4.98 | % 17.98/4.98 | From (120)(122) and (108) follows: % 17.98/4.98 | (142) addition(all_53_0_24, all_53_1_25) = all_0_1_1 % 17.98/4.98 | % 17.98/4.98 | From (123)(121) and (100) follows: % 17.98/4.98 | (143) addition(all_49_0_20, all_49_1_21) = all_0_3_3 % 17.98/4.98 | % 17.98/4.98 | Instantiating formula (17) 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: % 17.98/4.98 | (144) all_41_2_12 = zero % 17.98/4.98 | % 17.98/4.98 | From (144) and (133) follows: % 17.98/4.98 | (76) multiplication(all_0_2_2, all_0_4_4) = zero % 17.98/4.98 | % 17.98/4.98 | From (144) and (134) follows: % 17.98/4.98 | (77) multiplication(all_0_4_4, all_0_2_2) = zero % 17.98/4.98 | % 17.98/4.98 | Instantiating formula (32) 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: % 17.98/4.98 | (147) ? [v0] : (c(v0) = one & multiplication(all_0_4_4, all_0_2_2) = v0) % 17.98/4.98 | % 17.98/4.98 | Instantiating formula (32) with one, all_0_2_2, all_0_4_4, all_0_4_4, all_0_2_2 and discharging atoms c(all_0_2_2) = all_0_4_4, c(all_0_4_4) = all_0_2_2, addition(all_0_4_4, all_0_2_2) = one, test(all_0_2_2), test(all_0_4_4), yields: % 17.98/4.98 | (148) ? [v0] : (c(v0) = one & multiplication(all_0_2_2, all_0_4_4) = v0) % 17.98/4.98 | % 17.98/4.98 | Instantiating formula (5) with all_49_1_21, all_0_1_1, all_0_4_4, all_0_2_2, all_0_5_5 and discharging atoms multiplication(all_0_1_1, all_0_4_4) = all_49_1_21, multiplication(all_0_5_5, all_0_2_2) = all_0_1_1, yields: % 17.98/4.98 | (149) ? [v0] : (multiplication(all_0_2_2, all_0_4_4) = v0 & multiplication(all_0_5_5, v0) = all_49_1_21) % 17.98/4.98 | % 17.98/4.98 | Instantiating formula (5) with all_53_1_25, all_0_3_3, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms multiplication(all_0_3_3, all_0_2_2) = all_53_1_25, multiplication(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 17.98/4.98 | (150) ? [v0] : (multiplication(all_0_4_4, all_0_2_2) = v0 & multiplication(all_0_5_5, v0) = all_53_1_25) % 17.98/4.98 | % 17.98/4.98 | Instantiating formula (5) with zero, all_0_2_2, all_0_4_4, all_0_2_2, one and discharging atoms multiplication(all_0_2_2, all_0_4_4) = zero, multiplication(one, all_0_2_2) = all_0_2_2, yields: % 17.98/4.98 | (151) ? [v0] : (multiplication(all_0_2_2, all_0_4_4) = v0 & multiplication(one, v0) = zero) % 17.98/4.98 | % 17.98/4.98 | Instantiating formula (13) with all_0_2_2, one, all_0_2_2, all_0_4_4, all_0_2_2 and discharging atoms multiplication(one, all_0_2_2) = all_0_2_2, addition(all_0_2_2, all_0_4_4) = one, yields: % 17.98/4.98 | (152) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_0_2_2) = v0 & multiplication(all_0_4_4, all_0_2_2) = v1 & addition(v0, v1) = all_0_2_2) % 17.98/4.98 | % 17.98/4.98 | Instantiating formula (13) with all_0_2_2, one, all_0_2_2, all_0_2_2, all_0_4_4 and discharging atoms multiplication(one, all_0_2_2) = all_0_2_2, addition(all_0_4_4, all_0_2_2) = one, yields: % 17.98/4.98 | (153) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_0_2_2) = v1 & multiplication(all_0_4_4, all_0_2_2) = v0 & addition(v0, v1) = all_0_2_2) % 17.98/4.98 | % 17.98/4.98 | Instantiating formula (5) with zero, all_0_4_4, all_0_2_2, all_0_4_4, one and discharging atoms multiplication(all_0_4_4, all_0_2_2) = zero, multiplication(one, all_0_4_4) = all_0_4_4, yields: % 17.98/4.99 | (154) ? [v0] : (multiplication(all_0_4_4, all_0_2_2) = v0 & multiplication(one, v0) = zero) % 17.98/4.99 | % 17.98/4.99 | Instantiating formula (13) with all_0_4_4, one, all_0_4_4, all_0_4_4, all_0_2_2 and discharging atoms multiplication(one, all_0_4_4) = all_0_4_4, addition(all_0_2_2, all_0_4_4) = one, yields: % 17.98/4.99 | (155) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_0_4_4) = v0 & multiplication(all_0_4_4, all_0_4_4) = v1 & addition(v0, v1) = all_0_4_4) % 17.98/4.99 | % 17.98/4.99 | Instantiating formula (13) with all_0_4_4, one, all_0_4_4, all_0_2_2, all_0_4_4 and discharging atoms multiplication(one, all_0_4_4) = all_0_4_4, addition(all_0_4_4, all_0_2_2) = one, yields: % 17.98/4.99 | (156) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_0_4_4) = v1 & multiplication(all_0_4_4, all_0_4_4) = v0 & addition(v0, v1) = all_0_4_4) % 17.98/4.99 | % 17.98/4.99 | Instantiating formula (13) with all_49_1_21, all_0_1_1, all_0_4_4, all_53_1_25, all_53_0_24 and discharging atoms multiplication(all_0_1_1, all_0_4_4) = all_49_1_21, addition(all_53_0_24, all_53_1_25) = all_0_1_1, yields: % 17.98/4.99 | (157) ? [v0] : ? [v1] : (multiplication(all_53_0_24, all_0_4_4) = v0 & multiplication(all_53_1_25, all_0_4_4) = v1 & addition(v0, v1) = all_49_1_21) % 17.98/4.99 | % 17.98/4.99 | Instantiating formula (13) with all_49_1_21, all_0_1_1, all_0_4_4, all_53_0_24, all_53_1_25 and discharging atoms multiplication(all_0_1_1, all_0_4_4) = all_49_1_21, addition(all_53_1_25, all_53_0_24) = all_0_1_1, yields: % 17.98/4.99 | (158) ? [v0] : ? [v1] : (multiplication(all_53_0_24, all_0_4_4) = v1 & multiplication(all_53_1_25, all_0_4_4) = v0 & addition(v0, v1) = all_49_1_21) % 17.98/4.99 | % 17.98/4.99 | Instantiating formula (13) with all_49_0_20, all_0_3_3, all_0_4_4, all_49_1_21, all_49_0_20 and discharging atoms multiplication(all_0_3_3, all_0_4_4) = all_49_0_20, addition(all_49_0_20, all_49_1_21) = all_0_3_3, yields: % 17.98/4.99 | (159) ? [v0] : ? [v1] : (multiplication(all_49_0_20, all_0_4_4) = v0 & multiplication(all_49_1_21, all_0_4_4) = v1 & addition(v0, v1) = all_49_0_20) % 17.98/4.99 | % 17.98/4.99 | Instantiating formula (13) with all_49_0_20, all_0_3_3, all_0_4_4, all_49_0_20, all_49_1_21 and discharging atoms multiplication(all_0_3_3, all_0_4_4) = all_49_0_20, addition(all_49_1_21, all_49_0_20) = all_0_3_3, yields: % 17.98/4.99 | (160) ? [v0] : ? [v1] : (multiplication(all_49_0_20, all_0_4_4) = v1 & multiplication(all_49_1_21, all_0_4_4) = v0 & addition(v0, v1) = all_49_0_20) % 17.98/4.99 | % 17.98/4.99 | Instantiating (158) with all_86_0_36, all_86_1_37 yields: % 17.98/4.99 | (161) multiplication(all_53_0_24, all_0_4_4) = all_86_0_36 & multiplication(all_53_1_25, all_0_4_4) = all_86_1_37 & addition(all_86_1_37, all_86_0_36) = all_49_1_21 % 17.98/4.99 | % 17.98/4.99 | Applying alpha-rule on (161) yields: % 17.98/4.99 | (162) multiplication(all_53_0_24, all_0_4_4) = all_86_0_36 % 17.98/4.99 | (163) multiplication(all_53_1_25, all_0_4_4) = all_86_1_37 % 17.98/4.99 | (164) addition(all_86_1_37, all_86_0_36) = all_49_1_21 % 17.98/4.99 | % 17.98/4.99 | Instantiating (157) with all_90_0_39, all_90_1_40 yields: % 17.98/4.99 | (165) multiplication(all_53_0_24, all_0_4_4) = all_90_1_40 & multiplication(all_53_1_25, all_0_4_4) = all_90_0_39 & addition(all_90_1_40, all_90_0_39) = all_49_1_21 % 17.98/4.99 | % 17.98/4.99 | Applying alpha-rule on (165) yields: % 17.98/4.99 | (166) multiplication(all_53_0_24, all_0_4_4) = all_90_1_40 % 17.98/4.99 | (167) multiplication(all_53_1_25, all_0_4_4) = all_90_0_39 % 17.98/4.99 | (168) addition(all_90_1_40, all_90_0_39) = all_49_1_21 % 17.98/4.99 | % 17.98/4.99 | Instantiating (151) with all_94_0_42 yields: % 17.98/4.99 | (169) multiplication(all_0_2_2, all_0_4_4) = all_94_0_42 & multiplication(one, all_94_0_42) = zero % 17.98/4.99 | % 17.98/4.99 | Applying alpha-rule on (169) yields: % 17.98/4.99 | (170) multiplication(all_0_2_2, all_0_4_4) = all_94_0_42 % 17.98/4.99 | (171) multiplication(one, all_94_0_42) = zero % 17.98/4.99 | % 17.98/4.99 | Instantiating (160) with all_104_0_50, all_104_1_51 yields: % 17.98/4.99 | (172) multiplication(all_49_0_20, all_0_4_4) = all_104_0_50 & multiplication(all_49_1_21, all_0_4_4) = all_104_1_51 & addition(all_104_1_51, all_104_0_50) = all_49_0_20 % 17.98/4.99 | % 17.98/4.99 | Applying alpha-rule on (172) yields: % 17.98/4.99 | (173) multiplication(all_49_0_20, all_0_4_4) = all_104_0_50 % 17.98/4.99 | (174) multiplication(all_49_1_21, all_0_4_4) = all_104_1_51 % 17.98/4.99 | (175) addition(all_104_1_51, all_104_0_50) = all_49_0_20 % 17.98/4.99 | % 17.98/4.99 | Instantiating (159) with all_112_0_56, all_112_1_57 yields: % 17.98/4.99 | (176) multiplication(all_49_0_20, all_0_4_4) = all_112_1_57 & multiplication(all_49_1_21, all_0_4_4) = all_112_0_56 & addition(all_112_1_57, all_112_0_56) = all_49_0_20 % 17.98/4.99 | % 17.98/4.99 | Applying alpha-rule on (176) yields: % 17.98/4.99 | (177) multiplication(all_49_0_20, all_0_4_4) = all_112_1_57 % 17.98/4.99 | (178) multiplication(all_49_1_21, all_0_4_4) = all_112_0_56 % 17.98/4.99 | (179) addition(all_112_1_57, all_112_0_56) = all_49_0_20 % 17.98/4.99 | % 17.98/4.99 | Instantiating (156) with all_128_0_69, all_128_1_70 yields: % 17.98/4.99 | (180) multiplication(all_0_2_2, all_0_4_4) = all_128_0_69 & multiplication(all_0_4_4, all_0_4_4) = all_128_1_70 & addition(all_128_1_70, all_128_0_69) = all_0_4_4 % 17.98/4.99 | % 17.98/4.99 | Applying alpha-rule on (180) yields: % 17.98/4.99 | (181) multiplication(all_0_2_2, all_0_4_4) = all_128_0_69 % 17.98/4.99 | (182) multiplication(all_0_4_4, all_0_4_4) = all_128_1_70 % 17.98/4.99 | (183) addition(all_128_1_70, all_128_0_69) = all_0_4_4 % 17.98/4.99 | % 17.98/4.99 | Instantiating (155) with all_130_0_71, all_130_1_72 yields: % 17.98/4.99 | (184) multiplication(all_0_2_2, all_0_4_4) = all_130_1_72 & multiplication(all_0_4_4, all_0_4_4) = all_130_0_71 & addition(all_130_1_72, all_130_0_71) = all_0_4_4 % 17.98/4.99 | % 17.98/4.99 | Applying alpha-rule on (184) yields: % 17.98/4.99 | (185) multiplication(all_0_2_2, all_0_4_4) = all_130_1_72 % 17.98/4.99 | (186) multiplication(all_0_4_4, all_0_4_4) = all_130_0_71 % 17.98/4.99 | (187) addition(all_130_1_72, all_130_0_71) = all_0_4_4 % 17.98/4.99 | % 17.98/4.99 | Instantiating (149) with all_138_0_81 yields: % 17.98/4.99 | (188) multiplication(all_0_2_2, all_0_4_4) = all_138_0_81 & multiplication(all_0_5_5, all_138_0_81) = all_49_1_21 % 17.98/4.99 | % 17.98/4.99 | Applying alpha-rule on (188) yields: % 17.98/4.99 | (189) multiplication(all_0_2_2, all_0_4_4) = all_138_0_81 % 17.98/4.99 | (190) multiplication(all_0_5_5, all_138_0_81) = all_49_1_21 % 17.98/4.99 | % 17.98/4.99 | Instantiating (148) with all_140_0_82 yields: % 17.98/4.99 | (191) c(all_140_0_82) = one & multiplication(all_0_2_2, all_0_4_4) = all_140_0_82 % 17.98/4.99 | % 17.98/4.99 | Applying alpha-rule on (191) yields: % 17.98/4.99 | (192) c(all_140_0_82) = one % 17.98/4.99 | (193) multiplication(all_0_2_2, all_0_4_4) = all_140_0_82 % 17.98/5.00 | % 17.98/5.00 | Instantiating (147) with all_144_0_85 yields: % 17.98/5.00 | (194) c(all_144_0_85) = one & multiplication(all_0_4_4, all_0_2_2) = all_144_0_85 % 17.98/5.00 | % 17.98/5.00 | Applying alpha-rule on (194) yields: % 17.98/5.00 | (195) c(all_144_0_85) = one % 17.98/5.00 | (196) multiplication(all_0_4_4, all_0_2_2) = all_144_0_85 % 17.98/5.00 | % 17.98/5.00 | Instantiating (154) with all_152_0_90 yields: % 17.98/5.00 | (197) multiplication(all_0_4_4, all_0_2_2) = all_152_0_90 & multiplication(one, all_152_0_90) = zero % 17.98/5.00 | % 17.98/5.00 | Applying alpha-rule on (197) yields: % 17.98/5.00 | (198) multiplication(all_0_4_4, all_0_2_2) = all_152_0_90 % 17.98/5.00 | (199) multiplication(one, all_152_0_90) = zero % 17.98/5.00 | % 17.98/5.00 | Instantiating (153) with all_154_0_91, all_154_1_92 yields: % 17.98/5.00 | (200) multiplication(all_0_2_2, all_0_2_2) = all_154_0_91 & multiplication(all_0_4_4, all_0_2_2) = all_154_1_92 & addition(all_154_1_92, all_154_0_91) = all_0_2_2 % 17.98/5.00 | % 17.98/5.00 | Applying alpha-rule on (200) yields: % 17.98/5.00 | (201) multiplication(all_0_2_2, all_0_2_2) = all_154_0_91 % 17.98/5.00 | (202) multiplication(all_0_4_4, all_0_2_2) = all_154_1_92 % 17.98/5.00 | (203) addition(all_154_1_92, all_154_0_91) = all_0_2_2 % 17.98/5.00 | % 17.98/5.00 | Instantiating (152) with all_162_0_97, all_162_1_98 yields: % 17.98/5.00 | (204) multiplication(all_0_2_2, all_0_2_2) = all_162_1_98 & multiplication(all_0_4_4, all_0_2_2) = all_162_0_97 & addition(all_162_1_98, all_162_0_97) = all_0_2_2 % 17.98/5.00 | % 17.98/5.00 | Applying alpha-rule on (204) yields: % 17.98/5.00 | (205) multiplication(all_0_2_2, all_0_2_2) = all_162_1_98 % 17.98/5.00 | (206) multiplication(all_0_4_4, all_0_2_2) = all_162_0_97 % 17.98/5.00 | (207) addition(all_162_1_98, all_162_0_97) = all_0_2_2 % 17.98/5.00 | % 17.98/5.00 | Instantiating (150) with all_164_0_99 yields: % 17.98/5.00 | (208) multiplication(all_0_4_4, all_0_2_2) = all_164_0_99 & multiplication(all_0_5_5, all_164_0_99) = all_53_1_25 % 17.98/5.00 | % 17.98/5.00 | Applying alpha-rule on (208) yields: % 17.98/5.00 | (209) multiplication(all_0_4_4, all_0_2_2) = all_164_0_99 % 17.98/5.00 | (210) multiplication(all_0_5_5, all_164_0_99) = all_53_1_25 % 17.98/5.00 | % 17.98/5.00 | Instantiating formula (34) with all_53_0_24, all_0_4_4, all_86_0_36, all_90_1_40 and discharging atoms multiplication(all_53_0_24, all_0_4_4) = all_90_1_40, multiplication(all_53_0_24, all_0_4_4) = all_86_0_36, yields: % 17.98/5.00 | (211) all_90_1_40 = all_86_0_36 % 17.98/5.00 | % 17.98/5.00 | Instantiating formula (34) with all_53_1_25, all_0_4_4, all_86_1_37, all_90_0_39 and discharging atoms multiplication(all_53_1_25, all_0_4_4) = all_90_0_39, multiplication(all_53_1_25, all_0_4_4) = all_86_1_37, yields: % 17.98/5.00 | (212) all_90_0_39 = all_86_1_37 % 17.98/5.00 | % 17.98/5.00 | Instantiating formula (34) with all_49_1_21, all_0_4_4, all_104_1_51, all_112_0_56 and discharging atoms multiplication(all_49_1_21, all_0_4_4) = all_112_0_56, multiplication(all_49_1_21, all_0_4_4) = all_104_1_51, yields: % 17.98/5.00 | (213) all_112_0_56 = all_104_1_51 % 17.98/5.00 | % 17.98/5.00 | Instantiating formula (34) with all_0_2_2, all_0_4_4, all_130_1_72, all_140_0_82 and discharging atoms multiplication(all_0_2_2, all_0_4_4) = all_140_0_82, multiplication(all_0_2_2, all_0_4_4) = all_130_1_72, yields: % 17.98/5.00 | (214) all_140_0_82 = all_130_1_72 % 17.98/5.00 | % 17.98/5.00 | Instantiating formula (34) with all_0_2_2, all_0_4_4, all_130_1_72, all_138_0_81 and discharging atoms multiplication(all_0_2_2, all_0_4_4) = all_138_0_81, multiplication(all_0_2_2, all_0_4_4) = all_130_1_72, yields: % 17.98/5.00 | (215) all_138_0_81 = all_130_1_72 % 17.98/5.00 | % 17.98/5.00 | Instantiating formula (23) with all_130_1_72, all_0_4_4, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_4_4) = all_130_1_72, complement(all_0_4_4, all_0_2_2), yields: % 17.98/5.00 | (216) all_130_1_72 = zero % 17.98/5.00 | % 17.98/5.00 | Instantiating formula (34) with all_0_2_2, all_0_4_4, all_128_0_69, all_138_0_81 and discharging atoms multiplication(all_0_2_2, all_0_4_4) = all_138_0_81, multiplication(all_0_2_2, all_0_4_4) = all_128_0_69, yields: % 17.98/5.00 | (217) all_138_0_81 = all_128_0_69 % 17.98/5.00 | % 17.98/5.00 | Instantiating formula (34) with all_0_2_2, all_0_4_4, all_94_0_42, all_140_0_82 and discharging atoms multiplication(all_0_2_2, all_0_4_4) = all_140_0_82, multiplication(all_0_2_2, all_0_4_4) = all_94_0_42, yields: % 17.98/5.00 | (218) all_140_0_82 = all_94_0_42 % 17.98/5.00 | % 17.98/5.00 | Instantiating formula (34) with all_0_4_4, all_0_2_2, all_162_0_97, all_164_0_99 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_164_0_99, multiplication(all_0_4_4, all_0_2_2) = all_162_0_97, yields: % 17.98/5.00 | (219) all_164_0_99 = all_162_0_97 % 17.98/5.00 | % 17.98/5.00 | Instantiating formula (34) with all_0_4_4, all_0_2_2, all_154_1_92, all_164_0_99 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_164_0_99, multiplication(all_0_4_4, all_0_2_2) = all_154_1_92, yields: % 18.36/5.00 | (220) all_164_0_99 = all_154_1_92 % 18.36/5.00 | % 18.36/5.00 | Instantiating formula (34) with all_0_4_4, all_0_2_2, all_152_0_90, all_154_1_92 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_154_1_92, multiplication(all_0_4_4, all_0_2_2) = all_152_0_90, yields: % 18.36/5.00 | (221) all_154_1_92 = all_152_0_90 % 18.36/5.00 | % 18.36/5.00 | Instantiating formula (34) with all_0_4_4, all_0_2_2, all_144_0_85, all_164_0_99 and discharging atoms multiplication(all_0_4_4, all_0_2_2) = all_164_0_99, multiplication(all_0_4_4, all_0_2_2) = all_144_0_85, yields: % 18.36/5.00 | (222) all_164_0_99 = all_144_0_85 % 18.36/5.00 | % 18.36/5.00 | Instantiating formula (16) with zero, all_152_0_90 and discharging atoms multiplication(one, all_152_0_90) = zero, yields: % 18.36/5.00 | (223) all_152_0_90 = zero % 18.36/5.00 | % 18.36/5.00 | Combining equations (220,219) yields a new equation: % 18.36/5.00 | (224) all_162_0_97 = all_154_1_92 % 18.36/5.00 | % 18.36/5.00 | Combining equations (222,219) yields a new equation: % 18.36/5.00 | (225) all_162_0_97 = all_144_0_85 % 18.36/5.00 | % 18.36/5.00 | Combining equations (224,225) yields a new equation: % 18.36/5.00 | (226) all_154_1_92 = all_144_0_85 % 18.36/5.00 | % 18.36/5.00 | Simplifying 226 yields: % 18.36/5.00 | (227) all_154_1_92 = all_144_0_85 % 18.36/5.00 | % 18.36/5.00 | Combining equations (221,227) yields a new equation: % 18.36/5.00 | (228) all_152_0_90 = all_144_0_85 % 18.36/5.00 | % 18.36/5.00 | Simplifying 228 yields: % 18.36/5.00 | (229) all_152_0_90 = all_144_0_85 % 18.36/5.00 | % 18.36/5.00 | Combining equations (229,223) yields a new equation: % 18.36/5.00 | (230) all_144_0_85 = zero % 18.36/5.00 | % 18.36/5.00 | Simplifying 230 yields: % 18.36/5.00 | (231) all_144_0_85 = zero % 18.36/5.00 | % 18.36/5.01 | Combining equations (214,218) yields a new equation: % 18.36/5.01 | (232) all_130_1_72 = all_94_0_42 % 18.36/5.01 | % 18.36/5.01 | Simplifying 232 yields: % 18.36/5.01 | (233) all_130_1_72 = all_94_0_42 % 18.36/5.01 | % 18.36/5.01 | Combining equations (215,217) yields a new equation: % 18.36/5.01 | (234) all_130_1_72 = all_128_0_69 % 18.36/5.01 | % 18.36/5.01 | Simplifying 234 yields: % 18.36/5.01 | (235) all_130_1_72 = all_128_0_69 % 18.36/5.01 | % 18.36/5.01 | Combining equations (216,235) yields a new equation: % 18.36/5.01 | (236) all_128_0_69 = zero % 18.36/5.01 | % 18.36/5.01 | Combining equations (233,235) yields a new equation: % 18.36/5.01 | (237) all_128_0_69 = all_94_0_42 % 18.36/5.01 | % 18.36/5.01 | Combining equations (236,237) yields a new equation: % 18.36/5.01 | (238) all_94_0_42 = zero % 18.36/5.01 | % 18.36/5.01 | Combining equations (238,237) yields a new equation: % 18.36/5.01 | (236) all_128_0_69 = zero % 18.36/5.01 | % 18.36/5.01 | Combining equations (236,217) yields a new equation: % 18.36/5.01 | (240) all_138_0_81 = zero % 18.36/5.01 | % 18.36/5.01 | Combining equations (231,225) yields a new equation: % 18.36/5.01 | (241) all_162_0_97 = zero % 18.36/5.01 | % 18.36/5.01 | Combining equations (241,219) yields a new equation: % 18.36/5.01 | (242) all_164_0_99 = zero % 18.36/5.01 | % 18.36/5.01 | From (212) and (167) follows: % 18.36/5.01 | (163) multiplication(all_53_1_25, all_0_4_4) = all_86_1_37 % 18.36/5.01 | % 18.36/5.01 | From (213) and (178) follows: % 18.36/5.01 | (174) multiplication(all_49_1_21, all_0_4_4) = all_104_1_51 % 18.36/5.01 | % 18.36/5.01 | From (242) and (210) follows: % 18.36/5.01 | (245) multiplication(all_0_5_5, zero) = all_53_1_25 % 18.36/5.01 | % 18.36/5.01 | From (240) and (190) follows: % 18.36/5.01 | (246) multiplication(all_0_5_5, zero) = all_49_1_21 % 18.36/5.01 | % 18.36/5.01 | From (211)(212) and (168) follows: % 18.36/5.01 | (247) addition(all_86_0_36, all_86_1_37) = all_49_1_21 % 18.36/5.01 | % 18.36/5.01 | Instantiating formula (44) with all_53_1_25, all_0_5_5 and discharging atoms multiplication(all_0_5_5, zero) = all_53_1_25, yields: % 18.36/5.01 | (248) all_53_1_25 = zero % 18.36/5.01 | % 18.36/5.01 | Instantiating formula (34) with all_0_5_5, zero, all_49_1_21, all_53_1_25 and discharging atoms multiplication(all_0_5_5, zero) = all_53_1_25, multiplication(all_0_5_5, zero) = all_49_1_21, yields: % 18.36/5.01 | (249) all_53_1_25 = all_49_1_21 % 18.36/5.01 | % 18.36/5.01 | Combining equations (249,248) yields a new equation: % 18.36/5.01 | (250) all_49_1_21 = zero % 18.36/5.01 | % 18.36/5.01 | Simplifying 250 yields: % 18.36/5.01 | (251) all_49_1_21 = zero % 18.36/5.01 | % 18.36/5.01 | From (248) and (163) follows: % 18.36/5.01 | (252) multiplication(zero, all_0_4_4) = all_86_1_37 % 18.36/5.01 | % 18.36/5.01 | From (251) and (174) follows: % 18.36/5.01 | (253) multiplication(zero, all_0_4_4) = all_104_1_51 % 18.36/5.01 | % 18.36/5.01 | From (251) and (246) follows: % 18.36/5.01 | (254) multiplication(all_0_5_5, zero) = zero % 18.36/5.01 | % 18.36/5.01 | From (251) and (247) follows: % 18.36/5.01 | (255) addition(all_86_0_36, all_86_1_37) = zero % 18.36/5.01 | % 18.36/5.01 | From (251) and (164) follows: % 18.36/5.01 | (256) addition(all_86_1_37, all_86_0_36) = zero % 18.36/5.01 | % 18.36/5.01 | Instantiating formula (10) with all_104_1_51, all_0_4_4 and discharging atoms multiplication(zero, all_0_4_4) = all_104_1_51, yields: % 18.36/5.01 | (257) all_104_1_51 = zero % 18.36/5.01 | % 18.36/5.01 | Instantiating formula (34) with zero, all_0_4_4, all_86_1_37, all_104_1_51 and discharging atoms multiplication(zero, all_0_4_4) = all_104_1_51, multiplication(zero, all_0_4_4) = all_86_1_37, yields: % 18.36/5.01 | (258) all_104_1_51 = all_86_1_37 % 18.36/5.01 | % 18.36/5.01 | Combining equations (258,257) yields a new equation: % 18.36/5.01 | (259) all_86_1_37 = zero % 18.36/5.01 | % 18.36/5.01 | Simplifying 259 yields: % 18.36/5.01 | (260) all_86_1_37 = zero % 18.36/5.01 | % 18.36/5.01 | From (260) and (255) follows: % 18.36/5.01 | (261) addition(all_86_0_36, zero) = zero % 18.36/5.01 | % 18.36/5.01 | From (260) and (256) follows: % 18.36/5.01 | (262) addition(zero, all_86_0_36) = zero % 18.36/5.01 | % 18.36/5.01 | Instantiating formula (15) with zero, all_86_0_36 and discharging atoms addition(all_86_0_36, zero) = zero, yields: % 18.36/5.01 | (263) all_86_0_36 = zero % 18.36/5.01 | % 18.36/5.01 | From (263) and (262) follows: % 18.36/5.01 | (264) addition(zero, zero) = zero % 18.36/5.01 | % 18.36/5.01 | Instantiating formula (24) with zero, zero, zero, zero, all_0_5_5, all_0_5_5 and discharging atoms multiplication(all_0_5_5, zero) = zero, addition(zero, zero) = zero, yields: % 18.36/5.01 | (265) ? [v0] : (multiplication(v0, zero) = zero & addition(all_0_5_5, all_0_5_5) = v0) % 18.36/5.01 | % 18.36/5.01 | Instantiating (265) with all_236_0_128 yields: % 18.36/5.01 | (266) multiplication(all_236_0_128, zero) = zero & addition(all_0_5_5, all_0_5_5) = all_236_0_128 % 18.36/5.01 | % 18.36/5.02 | Applying alpha-rule on (266) yields: % 18.36/5.02 | (267) multiplication(all_236_0_128, zero) = zero % 18.36/5.02 | (268) addition(all_0_5_5, all_0_5_5) = all_236_0_128 % 18.36/5.02 | % 18.36/5.02 | Instantiating formula (6) with all_236_0_128, all_0_5_5 and discharging atoms addition(all_0_5_5, all_0_5_5) = all_236_0_128, yields: % 18.36/5.02 | (269) all_236_0_128 = all_0_5_5 % 18.36/5.02 | % 18.36/5.02 | From (269) and (268) follows: % 18.36/5.02 | (270) addition(all_0_5_5, all_0_5_5) = all_0_5_5 % 18.36/5.02 | % 18.36/5.02 | Instantiating formula (7) 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: % 18.36/5.02 | (271) $false % 18.36/5.02 | % 18.36/5.02 |-The branch is then unsatisfiable % 18.36/5.02 |-Branch two: % 18.36/5.02 | (272) ~ complement(all_0_2_2, all_0_4_4) % 18.36/5.02 | (273) ? [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))) % 18.36/5.02 | % 18.36/5.02 | Instantiating (273) with all_67_0_242, all_67_1_243 yields: % 18.36/5.02 | (274) 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)) % 18.36/5.02 | % 18.36/5.02 | Applying alpha-rule on (274) yields: % 18.36/5.02 | (275) multiplication(all_0_2_2, all_0_4_4) = all_67_0_242 % 18.36/5.02 | (276) multiplication(all_0_4_4, all_0_2_2) = all_67_1_243 % 18.36/5.02 | (277) ~ (all_67_0_242 = zero) | ~ (all_67_1_243 = zero) % 18.36/5.02 | % 18.36/5.02 | Instantiating formula (34) 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: % 18.36/5.02 | (278) all_67_0_242 = zero % 18.36/5.02 | % 18.36/5.02 | Instantiating formula (34) 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: % 18.36/5.02 | (279) all_67_1_243 = zero % 18.36/5.02 | % 18.36/5.02 +-Applying beta-rule and splitting (277), into two cases. % 18.36/5.02 |-Branch one: % 18.36/5.02 | (280) ~ (all_67_0_242 = zero) % 18.36/5.02 | % 18.36/5.02 | Equations (278) can reduce 280 to: % 18.36/5.02 | (281) $false % 18.36/5.02 | % 18.36/5.02 |-The branch is then unsatisfiable % 18.36/5.02 |-Branch two: % 18.36/5.02 | (278) all_67_0_242 = zero % 18.36/5.02 | (283) ~ (all_67_1_243 = zero) % 18.36/5.02 | % 18.36/5.02 | Equations (279) can reduce 283 to: % 18.36/5.02 | (281) $false % 18.36/5.02 | % 18.36/5.02 |-The branch is then unsatisfiable % 18.36/5.02 |-Branch two: % 18.36/5.02 | (285) leq(all_0_0_0, all_0_5_5) % 18.36/5.02 | (286) ~ leq(all_0_5_5, all_0_0_0) % 18.36/5.02 | % 18.36/5.02 | From (65) and (285) follows: % 18.36/5.02 | (287) leq(all_0_5_5, all_0_5_5) % 18.36/5.02 | % 18.36/5.02 | From (65) and (286) follows: % 18.36/5.02 | (70) ~ leq(all_0_5_5, all_0_5_5) % 18.36/5.02 | % 18.36/5.02 | Using (287) and (70) yields: % 18.36/5.02 | (271) $false % 18.36/5.02 | % 18.36/5.02 |-The branch is then unsatisfiable % 18.36/5.02 % SZS output end Proof for theBenchmark % 18.36/5.02 % 18.36/5.02 4400ms %------------------------------------------------------------------------------