%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE146+1 : 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 01:51:35 EDT 2022 % Result : Theorem 12.68s 3.74s % Output : Proof 25.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : KLE146+1 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.35 % Computer : n006.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Thu Jun 16 16:30:11 EDT 2022 % 0.13/0.35 % CPUTime : % 0.52/0.60 ____ _ % 0.52/0.60 ___ / __ \_____(_)___ ________ __________ % 0.52/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.60 % 0.52/0.60 A Theorem Prover for First-Order Logic % 0.52/0.60 (ePrincess v.1.0) % 0.52/0.60 % 0.52/0.60 (c) Philipp Rümmer, 2009-2015 % 0.52/0.60 (c) Peter Backeman, 2014-2015 % 0.52/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.60 Bug reports to peter@backeman.se % 0.52/0.60 % 0.52/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.60 % 0.52/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.69/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.58/0.95 Prover 0: Preprocessing ... % 2.24/1.21 Prover 0: Constructing countermodel ... % 12.68/3.74 Prover 0: proved (3094ms) % 12.68/3.74 % 12.68/3.74 No countermodel exists, formula is valid % 12.68/3.74 % SZS status Theorem for theBenchmark % 12.68/3.74 % 12.68/3.74 Generating proof ... found it (size 131) % 25.44/7.06 % 25.44/7.06 % SZS output start Proof for theBenchmark % 25.44/7.06 Assumed formulas after preprocessing and simplification: % 25.44/7.06 | (0) ? [v0] : ? [v1] : (strong_iteration(v0) = v1 & ~ leq(one, v1) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (multiplication(v3, v4) = v6) | ~ (multiplication(v2, v4) = v5) | ~ (addition(v5, v6) = v7) | ? [v8] : (multiplication(v8, v4) = v7 & addition(v2, v3) = v8)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (multiplication(v2, v4) = v6) | ~ (multiplication(v2, v3) = v5) | ~ (addition(v5, v6) = v7) | ? [v8] : (multiplication(v2, v8) = v7 & addition(v3, v4) = v8)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v3 | ~ (strong_iteration(v2) = v3) | ~ (star(v2) = v4) | ~ (multiplication(v3, zero) = v5) | ~ (addition(v4, v5) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (multiplication(v5, v4) = v6) | ~ (multiplication(v2, v3) = v5) | ? [v7] : (multiplication(v3, v4) = v7 & multiplication(v2, v7) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (multiplication(v5, v4) = v6) | ~ (addition(v2, v3) = v5) | ? [v7] : ? [v8] : (multiplication(v3, v4) = v8 & multiplication(v2, v4) = v7 & addition(v7, v8) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (multiplication(v4, v2) = v5) | ~ (addition(v5, v3) = v6) | ~ leq(v6, v4) | ? [v7] : ? [v8] : (star(v2) = v7 & multiplication(v3, v7) = v8 & leq(v8, v4))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (multiplication(v3, v4) = v5) | ~ (multiplication(v2, v5) = v6) | ? [v7] : (multiplication(v7, v4) = v6 & multiplication(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (multiplication(v2, v5) = v6) | ~ (addition(v3, v4) = v5) | ? [v7] : ? [v8] : (multiplication(v2, v4) = v8 & multiplication(v2, v3) = v7 & addition(v7, v8) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (multiplication(v2, v4) = v5) | ~ (addition(v5, v3) = v6) | ~ leq(v6, v4) | ? [v7] : ? [v8] : (star(v2) = v7 & multiplication(v7, v3) = v8 & leq(v8, v4))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (multiplication(v2, v4) = v5) | ~ (addition(v5, v3) = v6) | ~ leq(v4, v6) | ? [v7] : ? [v8] : (strong_iteration(v2) = v7 & multiplication(v7, v3) = v8 & leq(v4, v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (addition(v5, v2) = v6) | ~ (addition(v4, v3) = v5) | ? [v7] : (addition(v4, v7) = v6 & addition(v3, v2) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (addition(v4, v5) = v6) | ~ (addition(v3, v2) = v5) | ? [v7] : (addition(v7, v2) = v6 & addition(v4, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (multiplication(v5, v4) = v3) | ~ (multiplication(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (addition(v5, v4) = v3) | ~ (addition(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (addition(v2, v3) = v4) | ~ leq(v2, v3)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (strong_iteration(v4) = v3) | ~ (strong_iteration(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (star(v4) = v3) | ~ (star(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (strong_iteration(v2) = v3) | ~ (multiplication(v2, v3) = v4) | addition(v4, one) = v3) & ! [v2] : ! [v3] : ! [v4] : ( ~ (star(v2) = v3) | ~ (multiplication(v3, v2) = v4) | addition(one, v4) = v3) & ! [v2] : ! [v3] : ! [v4] : ( ~ (star(v2) = v3) | ~ (multiplication(v2, v3) = v4) | addition(one, v4) = v3) & ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v2) = v4) | addition(v2, v3) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | addition(v3, v2) = v4) & ! [v2] : ! [v3] : (v3 = v2 | ~ (multiplication(v2, one) = v3)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (multiplication(one, v2) = v3)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (addition(v2, v2) = v3)) & ! [v2] : ! [v3] : (v3 = v2 | ~ (addition(v2, zero) = v3)) & ! [v2] : ! [v3] : (v3 = zero | ~ (multiplication(zero, v2) = v3)) & ! [v2] : ! [v3] : ( ~ (strong_iteration(v2) = v3) | ? [v4] : ? [v5] : (star(v2) = v4 & multiplication(v3, zero) = v5 & addition(v4, v5) = v3)) & ! [v2] : ! [v3] : ( ~ (strong_iteration(v2) = v3) | ? [v4] : (multiplication(v2, v3) = v4 & addition(v4, one) = v3)) & ! [v2] : ! [v3] : ( ~ (star(v2) = v3) | ? [v4] : (multiplication(v3, v2) = v4 & addition(one, v4) = v3)) & ! [v2] : ! [v3] : ( ~ (star(v2) = v3) | ? [v4] : (multiplication(v2, v3) = v4 & addition(one, v4) = v3)) & ! [v2] : ! [v3] : ( ~ (addition(v2, v3) = v3) | leq(v2, v3))) % 25.67/7.11 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 25.67/7.11 | (1) strong_iteration(all_0_1_1) = all_0_0_0 & ~ leq(one, all_0_0_0) & ! [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] : (v4 = v1 | ~ (strong_iteration(v0) = v1) | ~ (star(v0) = v2) | ~ (multiplication(v1, zero) = v3) | ~ (addition(v2, v3) = v4)) & ! [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(v2, v0) = v3) | ~ (addition(v3, v1) = v4) | ~ leq(v4, v2) | ? [v5] : ? [v6] : (star(v0) = v5 & multiplication(v1, v5) = v6 & leq(v6, v2))) & ! [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] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ~ leq(v4, v2) | ? [v5] : ? [v6] : (star(v0) = v5 & multiplication(v5, v1) = v6 & leq(v6, v2))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ~ leq(v2, v4) | ? [v5] : ? [v6] : (strong_iteration(v0) = v5 & multiplication(v5, v1) = v6 & leq(v2, v6))) & ! [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 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~ (strong_iteration(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (strong_iteration(v0) = v1) | ~ (multiplication(v0, v1) = v2) | addition(v2, one) = v1) & ! [v0] : ! [v1] : ! [v2] : ( ~ (star(v0) = v1) | ~ (multiplication(v1, v0) = v2) | addition(one, v2) = v1) & ! [v0] : ! [v1] : ! [v2] : ( ~ (star(v0) = v1) | ~ (multiplication(v0, v1) = v2) | addition(one, v2) = v1) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) & ! [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 | ~ (multiplication(zero, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1)) & ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1)) & ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 25.67/7.12 | % 25.67/7.12 | Applying alpha-rule on (1) yields: % 25.67/7.12 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v2, v0) = v3) | ~ (addition(v3, v1) = v4) | ~ leq(v4, v2) | ? [v5] : ? [v6] : (star(v0) = v5 & multiplication(v1, v5) = v6 & leq(v6, v2))) % 25.67/7.12 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 25.67/7.13 | (4) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 25.67/7.13 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ~ leq(v2, v4) | ? [v5] : ? [v6] : (strong_iteration(v0) = v5 & multiplication(v5, v1) = v6 & leq(v2, v6))) % 25.67/7.13 | (6) ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1)) % 25.67/7.13 | (7) ! [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)) % 25.67/7.13 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (star(v0) = v1) | ~ (multiplication(v1, v0) = v2) | addition(one, v2) = v1) % 25.67/7.13 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 25.67/7.13 | (10) strong_iteration(all_0_1_1) = all_0_0_0 % 25.67/7.13 | (11) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 25.67/7.13 | (12) ! [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)) % 25.67/7.13 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (strong_iteration(v0) = v1) | ~ (multiplication(v0, v1) = v2) | addition(v2, one) = v1) % 25.67/7.13 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 25.67/7.13 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 25.67/7.13 | (16) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1)) % 25.67/7.13 | (17) ~ leq(one, all_0_0_0) % 25.67/7.13 | (18) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 25.67/7.13 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ~ leq(v4, v2) | ? [v5] : ? [v6] : (star(v0) = v5 & multiplication(v5, v1) = v6 & leq(v6, v2))) % 25.67/7.13 | (20) ! [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)) % 25.67/7.13 | (21) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1)) % 25.67/7.13 | (22) ! [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)) % 25.67/7.13 | (23) ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1)) % 25.67/7.13 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0)) % 25.67/7.13 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 25.67/7.13 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 25.67/7.13 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~ (strong_iteration(v2) = v0)) % 25.67/7.13 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) % 25.67/7.13 | (29) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 25.67/7.13 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (star(v0) = v1) | ~ (multiplication(v0, v1) = v2) | addition(one, v2) = v1) % 25.67/7.13 | (31) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 25.67/7.13 | (32) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 25.67/7.13 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 25.67/7.14 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | ~ (strong_iteration(v0) = v1) | ~ (star(v0) = v2) | ~ (multiplication(v1, zero) = v3) | ~ (addition(v2, v3) = v4)) % 25.67/7.14 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 25.67/7.14 | % 25.67/7.14 | Instantiating formula (6) with all_0_0_0, all_0_1_1 and discharging atoms strong_iteration(all_0_1_1) = all_0_0_0, yields: % 25.67/7.14 | (36) ? [v0] : ? [v1] : (star(all_0_1_1) = v0 & multiplication(all_0_0_0, zero) = v1 & addition(v0, v1) = all_0_0_0) % 25.67/7.14 | % 25.67/7.14 | Instantiating formula (23) with all_0_0_0, all_0_1_1 and discharging atoms strong_iteration(all_0_1_1) = all_0_0_0, yields: % 25.67/7.14 | (37) ? [v0] : (multiplication(all_0_1_1, all_0_0_0) = v0 & addition(v0, one) = all_0_0_0) % 25.67/7.14 | % 25.67/7.14 | Instantiating (37) with all_8_0_2 yields: % 25.67/7.14 | (38) multiplication(all_0_1_1, all_0_0_0) = all_8_0_2 & addition(all_8_0_2, one) = all_0_0_0 % 25.67/7.14 | % 25.67/7.14 | Applying alpha-rule on (38) yields: % 25.67/7.14 | (39) multiplication(all_0_1_1, all_0_0_0) = all_8_0_2 % 25.67/7.14 | (40) addition(all_8_0_2, one) = all_0_0_0 % 25.67/7.14 | % 25.67/7.14 | Instantiating (36) with all_10_0_3, all_10_1_4 yields: % 25.67/7.14 | (41) star(all_0_1_1) = all_10_1_4 & multiplication(all_0_0_0, zero) = all_10_0_3 & addition(all_10_1_4, all_10_0_3) = all_0_0_0 % 25.67/7.14 | % 25.67/7.14 | Applying alpha-rule on (41) yields: % 25.67/7.14 | (42) star(all_0_1_1) = all_10_1_4 % 25.67/7.14 | (43) multiplication(all_0_0_0, zero) = all_10_0_3 % 25.67/7.14 | (44) addition(all_10_1_4, all_10_0_3) = all_0_0_0 % 25.67/7.14 | % 25.67/7.14 | Instantiating formula (16) with all_10_1_4, all_0_1_1 and discharging atoms star(all_0_1_1) = all_10_1_4, yields: % 25.67/7.14 | (45) ? [v0] : (multiplication(all_10_1_4, all_0_1_1) = v0 & addition(one, v0) = all_10_1_4) % 25.67/7.14 | % 25.67/7.14 | Instantiating formula (21) with all_10_1_4, all_0_1_1 and discharging atoms star(all_0_1_1) = all_10_1_4, yields: % 25.67/7.14 | (46) ? [v0] : (multiplication(all_0_1_1, all_10_1_4) = v0 & addition(one, v0) = all_10_1_4) % 25.67/7.14 | % 25.67/7.14 | Instantiating formula (20) with all_10_0_3, all_0_0_0, zero, all_10_0_3, all_10_1_4 and discharging atoms multiplication(all_0_0_0, zero) = all_10_0_3, addition(all_10_1_4, all_10_0_3) = all_0_0_0, yields: % 25.67/7.14 | (47) ? [v0] : ? [v1] : (multiplication(all_10_0_3, zero) = v1 & multiplication(all_10_1_4, zero) = v0 & addition(v0, v1) = all_10_0_3) % 25.67/7.14 | % 25.67/7.14 | Instantiating formula (7) with all_8_0_2, all_0_0_0, all_10_0_3, all_10_1_4, all_0_1_1 and discharging atoms multiplication(all_0_1_1, all_0_0_0) = all_8_0_2, addition(all_10_1_4, all_10_0_3) = all_0_0_0, yields: % 25.67/7.14 | (48) ? [v0] : ? [v1] : (multiplication(all_0_1_1, all_10_0_3) = v1 & multiplication(all_0_1_1, all_10_1_4) = v0 & addition(v0, v1) = all_8_0_2) % 25.67/7.14 | % 25.67/7.14 | Instantiating formula (20) with all_10_0_3, all_0_0_0, zero, one, all_8_0_2 and discharging atoms multiplication(all_0_0_0, zero) = all_10_0_3, addition(all_8_0_2, one) = all_0_0_0, yields: % 25.67/7.14 | (49) ? [v0] : ? [v1] : (multiplication(all_8_0_2, zero) = v0 & multiplication(one, zero) = v1 & addition(v0, v1) = all_10_0_3) % 25.67/7.14 | % 25.67/7.14 | Instantiating formula (26) with all_0_0_0, all_8_0_2, one and discharging atoms addition(all_8_0_2, one) = all_0_0_0, yields: % 25.67/7.14 | (50) addition(one, all_8_0_2) = all_0_0_0 % 25.67/7.14 | % 25.67/7.14 | Instantiating (48) with all_20_0_7, all_20_1_8 yields: % 25.67/7.14 | (51) multiplication(all_0_1_1, all_10_0_3) = all_20_0_7 & multiplication(all_0_1_1, all_10_1_4) = all_20_1_8 & addition(all_20_1_8, all_20_0_7) = all_8_0_2 % 25.67/7.14 | % 25.67/7.14 | Applying alpha-rule on (51) yields: % 25.67/7.14 | (52) multiplication(all_0_1_1, all_10_0_3) = all_20_0_7 % 25.67/7.14 | (53) multiplication(all_0_1_1, all_10_1_4) = all_20_1_8 % 25.67/7.14 | (54) addition(all_20_1_8, all_20_0_7) = all_8_0_2 % 25.67/7.14 | % 25.67/7.14 | Instantiating (47) with all_22_0_9, all_22_1_10 yields: % 25.67/7.14 | (55) multiplication(all_10_0_3, zero) = all_22_0_9 & multiplication(all_10_1_4, zero) = all_22_1_10 & addition(all_22_1_10, all_22_0_9) = all_10_0_3 % 25.67/7.14 | % 25.67/7.14 | Applying alpha-rule on (55) yields: % 25.67/7.14 | (56) multiplication(all_10_0_3, zero) = all_22_0_9 % 25.67/7.14 | (57) multiplication(all_10_1_4, zero) = all_22_1_10 % 25.67/7.14 | (58) addition(all_22_1_10, all_22_0_9) = all_10_0_3 % 25.67/7.14 | % 25.67/7.14 | Instantiating (46) with all_24_0_11 yields: % 25.67/7.14 | (59) multiplication(all_0_1_1, all_10_1_4) = all_24_0_11 & addition(one, all_24_0_11) = all_10_1_4 % 25.67/7.14 | % 25.67/7.14 | Applying alpha-rule on (59) yields: % 25.67/7.14 | (60) multiplication(all_0_1_1, all_10_1_4) = all_24_0_11 % 25.67/7.14 | (61) addition(one, all_24_0_11) = all_10_1_4 % 25.67/7.14 | % 25.67/7.14 | Instantiating (49) with all_26_0_12, all_26_1_13 yields: % 25.67/7.14 | (62) multiplication(all_8_0_2, zero) = all_26_1_13 & multiplication(one, zero) = all_26_0_12 & addition(all_26_1_13, all_26_0_12) = all_10_0_3 % 25.67/7.14 | % 25.67/7.14 | Applying alpha-rule on (62) yields: % 25.67/7.14 | (63) multiplication(all_8_0_2, zero) = all_26_1_13 % 25.67/7.14 | (64) multiplication(one, zero) = all_26_0_12 % 25.67/7.14 | (65) addition(all_26_1_13, all_26_0_12) = all_10_0_3 % 25.67/7.14 | % 25.67/7.14 | Instantiating (45) with all_28_0_14 yields: % 25.67/7.14 | (66) multiplication(all_10_1_4, all_0_1_1) = all_28_0_14 & addition(one, all_28_0_14) = all_10_1_4 % 25.67/7.14 | % 25.67/7.14 | Applying alpha-rule on (66) yields: % 25.67/7.14 | (67) multiplication(all_10_1_4, all_0_1_1) = all_28_0_14 % 25.67/7.14 | (68) addition(one, all_28_0_14) = all_10_1_4 % 25.67/7.14 | % 25.67/7.14 | Instantiating formula (15) with all_0_1_1, all_10_1_4, all_20_1_8, all_24_0_11 and discharging atoms multiplication(all_0_1_1, all_10_1_4) = all_24_0_11, multiplication(all_0_1_1, all_10_1_4) = all_20_1_8, yields: % 25.67/7.14 | (69) all_24_0_11 = all_20_1_8 % 25.67/7.15 | % 25.67/7.15 | Instantiating formula (11) with all_26_0_12, zero and discharging atoms multiplication(one, zero) = all_26_0_12, yields: % 25.67/7.15 | (70) all_26_0_12 = zero % 25.67/7.15 | % 25.67/7.15 | From (70) and (64) follows: % 25.67/7.15 | (71) multiplication(one, zero) = zero % 25.67/7.15 | % 25.67/7.15 | From (70) and (65) follows: % 25.67/7.15 | (72) addition(all_26_1_13, zero) = all_10_0_3 % 25.67/7.15 | % 25.67/7.15 | From (69) and (61) follows: % 25.67/7.15 | (73) addition(one, all_20_1_8) = all_10_1_4 % 25.67/7.15 | % 25.67/7.15 | Instantiating formula (31) with all_10_0_3, all_26_1_13 and discharging atoms addition(all_26_1_13, zero) = all_10_0_3, yields: % 25.67/7.15 | (74) all_26_1_13 = all_10_0_3 % 25.67/7.15 | % 25.67/7.15 | From (74) and (63) follows: % 25.67/7.15 | (75) multiplication(all_8_0_2, zero) = all_10_0_3 % 25.67/7.15 | % 25.67/7.15 | From (74) and (72) follows: % 25.67/7.15 | (76) addition(all_10_0_3, zero) = all_10_0_3 % 25.67/7.15 | % 25.67/7.15 | Instantiating formula (35) with all_22_0_9, all_10_0_3, zero, zero, all_0_0_0 and discharging atoms multiplication(all_10_0_3, zero) = all_22_0_9, multiplication(all_0_0_0, zero) = all_10_0_3, yields: % 25.67/7.15 | (77) ? [v0] : (multiplication(all_0_0_0, v0) = all_22_0_9 & multiplication(zero, zero) = v0) % 25.67/7.15 | % 25.67/7.15 | Instantiating formula (35) with all_10_0_3, all_8_0_2, zero, all_0_0_0, all_0_1_1 and discharging atoms multiplication(all_8_0_2, zero) = all_10_0_3, multiplication(all_0_1_1, all_0_0_0) = all_8_0_2, yields: % 25.67/7.15 | (78) ? [v0] : (multiplication(all_0_0_0, zero) = v0 & multiplication(all_0_1_1, v0) = all_10_0_3) % 25.67/7.15 | % 25.67/7.15 | Instantiating formula (35) with all_22_0_9, all_10_0_3, zero, zero, all_8_0_2 and discharging atoms multiplication(all_10_0_3, zero) = all_22_0_9, multiplication(all_8_0_2, zero) = all_10_0_3, yields: % 25.67/7.15 | (79) ? [v0] : (multiplication(all_8_0_2, v0) = all_22_0_9 & multiplication(zero, zero) = v0) % 25.67/7.15 | % 25.67/7.15 | Instantiating formula (14) with all_20_0_7, all_10_0_3, zero, all_0_0_0, all_0_1_1 and discharging atoms multiplication(all_0_0_0, zero) = all_10_0_3, multiplication(all_0_1_1, all_10_0_3) = all_20_0_7, yields: % 25.67/7.15 | (80) ? [v0] : (multiplication(v0, zero) = all_20_0_7 & multiplication(all_0_1_1, all_0_0_0) = v0) % 25.67/7.15 | % 25.67/7.15 | Instantiating formula (20) with all_22_0_9, all_10_0_3, zero, zero, all_10_0_3 and discharging atoms multiplication(all_10_0_3, zero) = all_22_0_9, addition(all_10_0_3, zero) = all_10_0_3, yields: % 25.67/7.15 | (81) ? [v0] : ? [v1] : (multiplication(all_10_0_3, zero) = v0 & multiplication(zero, zero) = v1 & addition(v0, v1) = all_22_0_9) % 25.67/7.15 | % 25.67/7.15 | Instantiating formula (12) with all_10_0_3, zero, all_10_0_3, zero, one, all_0_0_0 and discharging atoms multiplication(all_0_0_0, zero) = all_10_0_3, multiplication(one, zero) = zero, addition(all_10_0_3, zero) = all_10_0_3, yields: % 25.67/7.15 | (82) ? [v0] : (multiplication(v0, zero) = all_10_0_3 & addition(all_0_0_0, one) = v0) % 25.67/7.15 | % 25.67/7.15 | Instantiating formula (33) with all_10_0_3, all_10_0_3, all_10_0_3, zero, zero and discharging atoms addition(all_10_0_3, zero) = all_10_0_3, yields: % 25.67/7.15 | (83) ? [v0] : (addition(all_10_0_3, v0) = all_10_0_3 & addition(zero, zero) = v0) % 25.67/7.15 | % 25.67/7.15 | Instantiating formula (20) with all_22_1_10, all_10_1_4, zero, all_28_0_14, one and discharging atoms multiplication(all_10_1_4, zero) = all_22_1_10, addition(one, all_28_0_14) = all_10_1_4, yields: % 25.67/7.15 | (84) ? [v0] : ? [v1] : (multiplication(all_28_0_14, zero) = v1 & multiplication(one, zero) = v0 & addition(v0, v1) = all_22_1_10) % 25.67/7.15 | % 25.67/7.15 | Instantiating formula (20) with all_22_1_10, all_10_1_4, zero, all_20_1_8, one and discharging atoms multiplication(all_10_1_4, zero) = all_22_1_10, addition(one, all_20_1_8) = all_10_1_4, yields: % 25.67/7.15 | (85) ? [v0] : ? [v1] : (multiplication(all_20_1_8, zero) = v1 & multiplication(one, zero) = v0 & addition(v0, v1) = all_22_1_10) % 25.67/7.15 | % 25.67/7.15 | Instantiating formula (33) with all_0_0_0, all_10_1_4, one, all_20_1_8, all_10_0_3 and discharging atoms addition(all_10_1_4, all_10_0_3) = all_0_0_0, addition(one, all_20_1_8) = all_10_1_4, yields: % 25.67/7.15 | (86) ? [v0] : (addition(all_20_1_8, all_10_0_3) = v0 & addition(one, v0) = all_0_0_0) % 25.67/7.15 | % 25.67/7.15 | Instantiating formula (20) with all_10_0_3, all_0_0_0, zero, all_8_0_2, one and discharging atoms multiplication(all_0_0_0, zero) = all_10_0_3, addition(one, all_8_0_2) = all_0_0_0, yields: % 25.67/7.15 | (87) ? [v0] : ? [v1] : (multiplication(all_8_0_2, zero) = v1 & multiplication(one, zero) = v0 & addition(v0, v1) = all_10_0_3) % 25.67/7.15 | % 25.67/7.15 | Instantiating (83) with all_46_0_17 yields: % 25.67/7.15 | (88) addition(all_10_0_3, all_46_0_17) = all_10_0_3 & addition(zero, zero) = all_46_0_17 % 25.67/7.15 | % 25.67/7.15 | Applying alpha-rule on (88) yields: % 25.67/7.15 | (89) addition(all_10_0_3, all_46_0_17) = all_10_0_3 % 25.67/7.15 | (90) addition(zero, zero) = all_46_0_17 % 25.67/7.15 | % 25.67/7.15 | Instantiating (85) with all_52_0_21, all_52_1_22 yields: % 25.67/7.15 | (91) multiplication(all_20_1_8, zero) = all_52_0_21 & multiplication(one, zero) = all_52_1_22 & addition(all_52_1_22, all_52_0_21) = all_22_1_10 % 25.67/7.15 | % 25.67/7.15 | Applying alpha-rule on (91) yields: % 25.67/7.15 | (92) multiplication(all_20_1_8, zero) = all_52_0_21 % 25.67/7.15 | (93) multiplication(one, zero) = all_52_1_22 % 25.67/7.15 | (94) addition(all_52_1_22, all_52_0_21) = all_22_1_10 % 25.67/7.15 | % 25.91/7.15 | Instantiating (81) with all_58_0_25, all_58_1_26 yields: % 25.91/7.15 | (95) multiplication(all_10_0_3, zero) = all_58_1_26 & multiplication(zero, zero) = all_58_0_25 & addition(all_58_1_26, all_58_0_25) = all_22_0_9 % 25.91/7.15 | % 25.91/7.15 | Applying alpha-rule on (95) yields: % 25.91/7.16 | (96) multiplication(all_10_0_3, zero) = all_58_1_26 % 25.91/7.16 | (97) multiplication(zero, zero) = all_58_0_25 % 25.91/7.16 | (98) addition(all_58_1_26, all_58_0_25) = all_22_0_9 % 25.91/7.16 | % 25.91/7.16 | Instantiating (82) with all_66_0_32 yields: % 25.91/7.16 | (99) multiplication(all_66_0_32, zero) = all_10_0_3 & addition(all_0_0_0, one) = all_66_0_32 % 25.91/7.16 | % 25.91/7.16 | Applying alpha-rule on (99) yields: % 25.91/7.16 | (100) multiplication(all_66_0_32, zero) = all_10_0_3 % 25.91/7.16 | (101) addition(all_0_0_0, one) = all_66_0_32 % 25.91/7.16 | % 25.91/7.16 | Instantiating (86) with all_82_0_44 yields: % 25.91/7.16 | (102) addition(all_20_1_8, all_10_0_3) = all_82_0_44 & addition(one, all_82_0_44) = all_0_0_0 % 25.91/7.16 | % 25.91/7.16 | Applying alpha-rule on (102) yields: % 25.91/7.16 | (103) addition(all_20_1_8, all_10_0_3) = all_82_0_44 % 25.91/7.16 | (104) addition(one, all_82_0_44) = all_0_0_0 % 25.91/7.16 | % 25.91/7.16 | Instantiating (84) with all_92_0_51, all_92_1_52 yields: % 25.91/7.16 | (105) multiplication(all_28_0_14, zero) = all_92_0_51 & multiplication(one, zero) = all_92_1_52 & addition(all_92_1_52, all_92_0_51) = all_22_1_10 % 25.91/7.16 | % 25.91/7.16 | Applying alpha-rule on (105) yields: % 25.91/7.16 | (106) multiplication(all_28_0_14, zero) = all_92_0_51 % 25.91/7.16 | (107) multiplication(one, zero) = all_92_1_52 % 25.91/7.16 | (108) addition(all_92_1_52, all_92_0_51) = all_22_1_10 % 25.91/7.16 | % 25.91/7.16 | Instantiating (87) with all_102_0_59, all_102_1_60 yields: % 25.91/7.16 | (109) multiplication(all_8_0_2, zero) = all_102_0_59 & multiplication(one, zero) = all_102_1_60 & addition(all_102_1_60, all_102_0_59) = all_10_0_3 % 25.91/7.16 | % 25.91/7.16 | Applying alpha-rule on (109) yields: % 25.91/7.16 | (110) multiplication(all_8_0_2, zero) = all_102_0_59 % 25.91/7.16 | (111) multiplication(one, zero) = all_102_1_60 % 25.91/7.16 | (112) addition(all_102_1_60, all_102_0_59) = all_10_0_3 % 25.91/7.16 | % 25.91/7.16 | Instantiating (80) with all_124_0_73 yields: % 25.91/7.16 | (113) multiplication(all_124_0_73, zero) = all_20_0_7 & multiplication(all_0_1_1, all_0_0_0) = all_124_0_73 % 25.91/7.16 | % 25.91/7.16 | Applying alpha-rule on (113) yields: % 25.91/7.16 | (114) multiplication(all_124_0_73, zero) = all_20_0_7 % 25.91/7.16 | (115) multiplication(all_0_1_1, all_0_0_0) = all_124_0_73 % 25.91/7.16 | % 25.91/7.16 | Instantiating (78) with all_126_0_74 yields: % 25.91/7.16 | (116) multiplication(all_0_0_0, zero) = all_126_0_74 & multiplication(all_0_1_1, all_126_0_74) = all_10_0_3 % 25.91/7.16 | % 25.91/7.16 | Applying alpha-rule on (116) yields: % 25.91/7.16 | (117) multiplication(all_0_0_0, zero) = all_126_0_74 % 25.91/7.16 | (118) multiplication(all_0_1_1, all_126_0_74) = all_10_0_3 % 25.91/7.16 | % 25.91/7.16 | Instantiating (77) with all_134_0_78 yields: % 25.91/7.16 | (119) multiplication(all_0_0_0, all_134_0_78) = all_22_0_9 & multiplication(zero, zero) = all_134_0_78 % 25.91/7.16 | % 25.91/7.16 | Applying alpha-rule on (119) yields: % 25.91/7.16 | (120) multiplication(all_0_0_0, all_134_0_78) = all_22_0_9 % 25.91/7.16 | (121) multiplication(zero, zero) = all_134_0_78 % 25.91/7.16 | % 25.91/7.16 | Instantiating (79) with all_138_0_80 yields: % 25.91/7.16 | (122) multiplication(all_8_0_2, all_138_0_80) = all_22_0_9 & multiplication(zero, zero) = all_138_0_80 % 25.91/7.16 | % 25.91/7.16 | Applying alpha-rule on (122) yields: % 25.91/7.16 | (123) multiplication(all_8_0_2, all_138_0_80) = all_22_0_9 % 25.91/7.16 | (124) multiplication(zero, zero) = all_138_0_80 % 25.91/7.16 | % 25.91/7.16 | Instantiating formula (15) with all_8_0_2, zero, all_102_0_59, all_10_0_3 and discharging atoms multiplication(all_8_0_2, zero) = all_102_0_59, multiplication(all_8_0_2, zero) = all_10_0_3, yields: % 25.91/7.16 | (125) all_102_0_59 = all_10_0_3 % 25.91/7.16 | % 25.91/7.16 | Instantiating formula (15) with all_0_0_0, zero, all_126_0_74, all_10_0_3 and discharging atoms multiplication(all_0_0_0, zero) = all_126_0_74, multiplication(all_0_0_0, zero) = all_10_0_3, yields: % 25.91/7.16 | (126) all_126_0_74 = all_10_0_3 % 25.91/7.16 | % 25.91/7.16 | Instantiating formula (15) with all_0_1_1, all_0_0_0, all_124_0_73, all_8_0_2 and discharging atoms multiplication(all_0_1_1, all_0_0_0) = all_124_0_73, multiplication(all_0_1_1, all_0_0_0) = all_8_0_2, yields: % 25.91/7.16 | (127) all_124_0_73 = all_8_0_2 % 25.91/7.16 | % 25.91/7.16 | Instantiating formula (15) with one, zero, all_92_1_52, all_102_1_60 and discharging atoms multiplication(one, zero) = all_102_1_60, multiplication(one, zero) = all_92_1_52, yields: % 25.91/7.16 | (128) all_102_1_60 = all_92_1_52 % 25.91/7.16 | % 25.91/7.16 | Instantiating formula (11) with all_92_1_52, zero and discharging atoms multiplication(one, zero) = all_92_1_52, yields: % 25.91/7.16 | (129) all_92_1_52 = zero % 25.91/7.16 | % 25.91/7.16 | Instantiating formula (15) with one, zero, all_52_1_22, all_102_1_60 and discharging atoms multiplication(one, zero) = all_102_1_60, multiplication(one, zero) = all_52_1_22, yields: % 25.91/7.16 | (130) all_102_1_60 = all_52_1_22 % 25.91/7.16 | % 25.91/7.16 | Instantiating formula (15) with zero, zero, all_134_0_78, all_138_0_80 and discharging atoms multiplication(zero, zero) = all_138_0_80, multiplication(zero, zero) = all_134_0_78, yields: % 25.91/7.16 | (131) all_138_0_80 = all_134_0_78 % 25.91/7.16 | % 25.91/7.16 | Instantiating formula (18) with all_134_0_78, zero and discharging atoms multiplication(zero, zero) = all_134_0_78, yields: % 25.91/7.16 | (132) all_134_0_78 = zero % 25.91/7.16 | % 25.91/7.16 | Instantiating formula (15) with zero, zero, all_58_0_25, all_138_0_80 and discharging atoms multiplication(zero, zero) = all_138_0_80, multiplication(zero, zero) = all_58_0_25, yields: % 25.91/7.16 | (133) all_138_0_80 = all_58_0_25 % 25.91/7.16 | % 25.91/7.16 | Instantiating formula (4) with all_46_0_17, zero and discharging atoms addition(zero, zero) = all_46_0_17, yields: % 25.91/7.16 | (134) all_46_0_17 = zero % 25.91/7.16 | % 25.91/7.17 | Combining equations (131,133) yields a new equation: % 25.91/7.17 | (135) all_134_0_78 = all_58_0_25 % 25.91/7.17 | % 25.91/7.17 | Simplifying 135 yields: % 25.91/7.17 | (136) all_134_0_78 = all_58_0_25 % 25.91/7.17 | % 25.91/7.17 | Combining equations (132,136) yields a new equation: % 25.91/7.17 | (137) all_58_0_25 = zero % 25.91/7.17 | % 25.91/7.17 | Combining equations (128,130) yields a new equation: % 25.91/7.17 | (138) all_92_1_52 = all_52_1_22 % 25.91/7.17 | % 25.91/7.17 | Simplifying 138 yields: % 25.91/7.17 | (139) all_92_1_52 = all_52_1_22 % 25.91/7.17 | % 25.91/7.17 | Combining equations (129,139) yields a new equation: % 25.91/7.17 | (140) all_52_1_22 = zero % 25.91/7.17 | % 25.91/7.17 | Combining equations (140,130) yields a new equation: % 25.91/7.17 | (141) all_102_1_60 = zero % 25.91/7.17 | % 25.91/7.17 | Combining equations (137,136) yields a new equation: % 25.91/7.17 | (132) all_134_0_78 = zero % 25.91/7.17 | % 25.91/7.17 | Combining equations (137,133) yields a new equation: % 25.91/7.17 | (143) all_138_0_80 = zero % 25.91/7.17 | % 25.91/7.17 | From (127) and (114) follows: % 25.91/7.17 | (144) multiplication(all_8_0_2, zero) = all_20_0_7 % 25.91/7.17 | % 25.91/7.17 | From (143) and (123) follows: % 25.91/7.17 | (145) multiplication(all_8_0_2, zero) = all_22_0_9 % 25.91/7.17 | % 25.91/7.17 | From (132) and (120) follows: % 25.91/7.17 | (146) multiplication(all_0_0_0, zero) = all_22_0_9 % 25.91/7.17 | % 25.91/7.17 | From (126) and (117) follows: % 25.91/7.17 | (43) multiplication(all_0_0_0, zero) = all_10_0_3 % 25.91/7.17 | % 25.91/7.17 | From (140) and (93) follows: % 25.91/7.17 | (71) multiplication(one, zero) = zero % 25.91/7.17 | % 25.91/7.17 | From (141)(125) and (112) follows: % 25.91/7.17 | (149) addition(zero, all_10_0_3) = all_10_0_3 % 25.91/7.17 | % 25.91/7.17 | From (134) and (90) follows: % 25.91/7.17 | (150) addition(zero, zero) = zero % 25.91/7.17 | % 25.91/7.17 | Instantiating formula (15) with all_8_0_2, zero, all_20_0_7, all_22_0_9 and discharging atoms multiplication(all_8_0_2, zero) = all_22_0_9, multiplication(all_8_0_2, zero) = all_20_0_7, yields: % 25.91/7.17 | (151) all_22_0_9 = all_20_0_7 % 25.91/7.17 | % 25.91/7.17 | Instantiating formula (15) with all_0_0_0, zero, all_22_0_9, all_10_0_3 and discharging atoms multiplication(all_0_0_0, zero) = all_22_0_9, multiplication(all_0_0_0, zero) = all_10_0_3, yields: % 25.91/7.17 | (152) all_22_0_9 = all_10_0_3 % 25.91/7.17 | % 25.91/7.17 | Combining equations (152,151) yields a new equation: % 25.91/7.17 | (153) all_20_0_7 = all_10_0_3 % 25.91/7.17 | % 25.91/7.17 | Combining equations (153,151) yields a new equation: % 25.91/7.17 | (152) all_22_0_9 = all_10_0_3 % 25.91/7.17 | % 25.91/7.17 | From (152) and (146) follows: % 25.91/7.17 | (43) multiplication(all_0_0_0, zero) = all_10_0_3 % 25.91/7.17 | % 25.91/7.17 | From (153) and (54) follows: % 25.91/7.17 | (156) addition(all_20_1_8, all_10_0_3) = all_8_0_2 % 25.91/7.17 | % 25.91/7.17 | Instantiating formula (3) with all_20_1_8, all_10_0_3, all_8_0_2, all_82_0_44 and discharging atoms addition(all_20_1_8, all_10_0_3) = all_82_0_44, addition(all_20_1_8, all_10_0_3) = all_8_0_2, yields: % 25.91/7.17 | (157) all_82_0_44 = all_8_0_2 % 25.91/7.17 | % 25.91/7.17 | From (157) and (104) follows: % 25.91/7.17 | (50) addition(one, all_8_0_2) = all_0_0_0 % 25.91/7.17 | % 25.91/7.17 | Instantiating formula (33) with all_66_0_32, all_0_0_0, all_8_0_2, one, one and discharging atoms addition(all_8_0_2, one) = all_0_0_0, addition(all_0_0_0, one) = all_66_0_32, yields: % 25.91/7.17 | (159) ? [v0] : (addition(all_8_0_2, v0) = all_66_0_32 & addition(one, one) = v0) % 25.91/7.17 | % 25.91/7.17 | Instantiating formula (33) with all_66_0_32, all_0_0_0, one, all_8_0_2, one and discharging atoms addition(all_0_0_0, one) = all_66_0_32, addition(one, all_8_0_2) = all_0_0_0, yields: % 25.91/7.17 | (160) ? [v0] : (addition(all_8_0_2, one) = v0 & addition(one, v0) = all_66_0_32) % 25.91/7.17 | % 25.91/7.17 | Instantiating formula (26) with all_66_0_32, all_0_0_0, one and discharging atoms addition(all_0_0_0, one) = all_66_0_32, yields: % 25.91/7.17 | (161) addition(one, all_0_0_0) = all_66_0_32 % 25.91/7.17 | % 25.91/7.17 | Instantiating formula (12) with all_10_0_3, all_10_0_3, zero, zero, all_0_0_0, one and discharging atoms multiplication(all_0_0_0, zero) = all_10_0_3, multiplication(one, zero) = zero, addition(zero, all_10_0_3) = all_10_0_3, yields: % 25.91/7.17 | (162) ? [v0] : (multiplication(v0, zero) = all_10_0_3 & addition(one, all_0_0_0) = v0) % 25.91/7.17 | % 25.91/7.17 | Instantiating formula (12) with all_10_0_3, all_10_0_3, zero, zero, all_66_0_32, one and discharging atoms multiplication(all_66_0_32, zero) = all_10_0_3, multiplication(one, zero) = zero, addition(zero, all_10_0_3) = all_10_0_3, yields: % 25.91/7.17 | (163) ? [v0] : (multiplication(v0, zero) = all_10_0_3 & addition(one, all_66_0_32) = v0) % 25.91/7.17 | % 25.91/7.17 | Instantiating formula (12) with zero, zero, zero, zero, one, one and discharging atoms multiplication(one, zero) = zero, addition(zero, zero) = zero, yields: % 25.91/7.17 | (164) ? [v0] : (multiplication(v0, zero) = zero & addition(one, one) = v0) % 25.91/7.18 | % 25.91/7.18 | Instantiating (164) with all_692_0_443 yields: % 25.91/7.18 | (165) multiplication(all_692_0_443, zero) = zero & addition(one, one) = all_692_0_443 % 25.91/7.18 | % 25.91/7.18 | Applying alpha-rule on (165) yields: % 25.91/7.18 | (166) multiplication(all_692_0_443, zero) = zero % 25.91/7.18 | (167) addition(one, one) = all_692_0_443 % 25.91/7.18 | % 25.91/7.18 | Instantiating (160) with all_734_0_471 yields: % 25.91/7.18 | (168) addition(all_8_0_2, one) = all_734_0_471 & addition(one, all_734_0_471) = all_66_0_32 % 25.91/7.18 | % 25.91/7.18 | Applying alpha-rule on (168) yields: % 25.91/7.18 | (169) addition(all_8_0_2, one) = all_734_0_471 % 25.91/7.18 | (170) addition(one, all_734_0_471) = all_66_0_32 % 25.91/7.18 | % 25.91/7.18 | Instantiating (159) with all_742_0_475 yields: % 25.91/7.18 | (171) addition(all_8_0_2, all_742_0_475) = all_66_0_32 & addition(one, one) = all_742_0_475 % 25.91/7.18 | % 25.91/7.18 | Applying alpha-rule on (171) yields: % 25.91/7.18 | (172) addition(all_8_0_2, all_742_0_475) = all_66_0_32 % 25.91/7.18 | (173) addition(one, one) = all_742_0_475 % 25.91/7.18 | % 25.91/7.18 | Instantiating (162) with all_840_0_536 yields: % 25.91/7.18 | (174) multiplication(all_840_0_536, zero) = all_10_0_3 & addition(one, all_0_0_0) = all_840_0_536 % 25.91/7.18 | % 25.91/7.18 | Applying alpha-rule on (174) yields: % 25.91/7.18 | (175) multiplication(all_840_0_536, zero) = all_10_0_3 % 25.91/7.18 | (176) addition(one, all_0_0_0) = all_840_0_536 % 25.91/7.18 | % 25.91/7.18 | Instantiating (163) with all_842_0_537 yields: % 25.91/7.18 | (177) multiplication(all_842_0_537, zero) = all_10_0_3 & addition(one, all_66_0_32) = all_842_0_537 % 25.91/7.18 | % 25.91/7.18 | Applying alpha-rule on (177) yields: % 25.91/7.18 | (178) multiplication(all_842_0_537, zero) = all_10_0_3 % 25.91/7.18 | (179) addition(one, all_66_0_32) = all_842_0_537 % 25.91/7.18 | % 25.91/7.18 | Instantiating formula (3) with all_8_0_2, one, all_734_0_471, all_0_0_0 and discharging atoms addition(all_8_0_2, one) = all_734_0_471, addition(all_8_0_2, one) = all_0_0_0, yields: % 25.91/7.18 | (180) all_734_0_471 = all_0_0_0 % 25.91/7.18 | % 25.91/7.18 | Instantiating formula (3) with one, all_0_0_0, all_66_0_32, all_840_0_536 and discharging atoms addition(one, all_0_0_0) = all_840_0_536, addition(one, all_0_0_0) = all_66_0_32, yields: % 25.91/7.18 | (181) all_840_0_536 = all_66_0_32 % 25.91/7.18 | % 25.91/7.18 | Instantiating formula (4) with all_742_0_475, one and discharging atoms addition(one, one) = all_742_0_475, yields: % 25.91/7.18 | (182) all_742_0_475 = one % 25.91/7.18 | % 25.91/7.18 | Instantiating formula (3) with one, one, all_692_0_443, all_742_0_475 and discharging atoms addition(one, one) = all_742_0_475, addition(one, one) = all_692_0_443, yields: % 25.91/7.18 | (183) all_742_0_475 = all_692_0_443 % 25.91/7.18 | % 25.91/7.18 | Combining equations (182,183) yields a new equation: % 25.91/7.18 | (184) all_692_0_443 = one % 25.91/7.18 | % 25.91/7.18 | Combining equations (184,183) yields a new equation: % 25.91/7.18 | (182) all_742_0_475 = one % 25.91/7.18 | % 25.91/7.18 | From (182) and (172) follows: % 25.91/7.18 | (186) addition(all_8_0_2, one) = all_66_0_32 % 25.91/7.18 | % 25.91/7.18 | From (180) and (169) follows: % 25.91/7.18 | (40) addition(all_8_0_2, one) = all_0_0_0 % 25.91/7.18 | % 25.91/7.18 | From (181) and (176) follows: % 25.91/7.18 | (161) addition(one, all_0_0_0) = all_66_0_32 % 25.91/7.18 | % 25.91/7.18 | Instantiating formula (3) with all_8_0_2, one, all_66_0_32, all_0_0_0 and discharging atoms addition(all_8_0_2, one) = all_66_0_32, addition(all_8_0_2, one) = all_0_0_0, yields: % 25.91/7.18 | (189) all_66_0_32 = all_0_0_0 % 25.91/7.18 | % 25.91/7.18 | From (189) and (179) follows: % 25.91/7.18 | (190) addition(one, all_0_0_0) = all_842_0_537 % 25.91/7.18 | % 25.91/7.18 | From (189) and (161) follows: % 25.91/7.18 | (191) addition(one, all_0_0_0) = all_0_0_0 % 25.91/7.18 | % 25.91/7.18 | Instantiating formula (3) with one, all_0_0_0, all_0_0_0, all_842_0_537 and discharging atoms addition(one, all_0_0_0) = all_842_0_537, addition(one, all_0_0_0) = all_0_0_0, yields: % 25.91/7.18 | (192) all_842_0_537 = all_0_0_0 % 25.91/7.18 | % 25.91/7.18 | From (192) and (190) follows: % 25.91/7.18 | (191) addition(one, all_0_0_0) = all_0_0_0 % 25.91/7.18 | % 25.91/7.18 | Instantiating formula (29) with all_0_0_0, one and discharging atoms addition(one, all_0_0_0) = all_0_0_0, ~ leq(one, all_0_0_0), yields: % 25.91/7.18 | (194) $false % 25.91/7.18 | % 25.91/7.19 |-The branch is then unsatisfiable % 25.91/7.19 % SZS output end Proof for theBenchmark % 25.91/7.19 % 25.91/7.19 6578ms %------------------------------------------------------------------------------