%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE139+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n010.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 01:51:31 EDT 2022 % Result : Theorem 3.59s 1.59s % Output : Proof 6.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KLE139+1 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.34 % Computer : n010.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Thu Jun 16 08:54:23 EDT 2022 % 0.14/0.35 % CPUTime : % 0.60/0.61 ____ _ % 0.60/0.61 ___ / __ \_____(_)___ ________ __________ % 0.60/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.60/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.60/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.60/0.61 % 0.60/0.61 A Theorem Prover for First-Order Logic % 0.60/0.61 (ePrincess v.1.0) % 0.60/0.61 % 0.60/0.61 (c) Philipp Rümmer, 2009-2015 % 0.60/0.61 (c) Peter Backeman, 2014-2015 % 0.60/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.60/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.60/0.61 Bug reports to peter@backeman.se % 0.60/0.61 % 0.60/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.60/0.61 % 0.60/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.66/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.56/0.95 Prover 0: Preprocessing ... % 2.23/1.20 Prover 0: Constructing countermodel ... % 3.59/1.59 Prover 0: proved (927ms) % 3.59/1.59 % 3.59/1.59 No countermodel exists, formula is valid % 3.59/1.59 % SZS status Theorem for theBenchmark % 3.59/1.59 % 3.59/1.59 Generating proof ... found it (size 43) % 6.27/2.15 % 6.27/2.15 % SZS output start Proof for theBenchmark % 6.27/2.15 Assumed formulas after preprocessing and simplification: % 6.27/2.15 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v1) & strong_iteration(v0) = v1 & multiplication(v1, v0) = v2 & addition(v2, one) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v5, v6) = v8) | ~ (multiplication(v4, v6) = v7) | ~ (addition(v7, v8) = v9) | ? [v10] : (multiplication(v10, v6) = v9 & addition(v4, v5) = v10)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v4, v6) = v8) | ~ (multiplication(v4, v5) = v7) | ~ (addition(v7, v8) = v9) | ? [v10] : (multiplication(v4, v10) = v9 & addition(v5, v6) = v10)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v5 | ~ (strong_iteration(v4) = v5) | ~ (star(v4) = v6) | ~ (multiplication(v5, zero) = v7) | ~ (addition(v6, v7) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v7, v6) = v8) | ~ (multiplication(v4, v5) = v7) | ? [v9] : (multiplication(v5, v6) = v9 & multiplication(v4, v9) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v7, v6) = v8) | ~ (addition(v4, v5) = v7) | ? [v9] : ? [v10] : (multiplication(v5, v6) = v10 & multiplication(v4, v6) = v9 & addition(v9, v10) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v6, v4) = v7) | ~ (addition(v7, v5) = v8) | ~ leq(v8, v6) | ? [v9] : ? [v10] : (star(v4) = v9 & multiplication(v5, v9) = v10 & leq(v10, v6))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v5, v6) = v7) | ~ (multiplication(v4, v7) = v8) | ? [v9] : (multiplication(v9, v6) = v8 & multiplication(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v4, v7) = v8) | ~ (addition(v5, v6) = v7) | ? [v9] : ? [v10] : (multiplication(v4, v6) = v10 & multiplication(v4, v5) = v9 & addition(v9, v10) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v4, v6) = v7) | ~ (addition(v7, v5) = v8) | ~ leq(v8, v6) | ? [v9] : ? [v10] : (star(v4) = v9 & multiplication(v9, v5) = v10 & leq(v10, v6))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v4, v6) = v7) | ~ (addition(v7, v5) = v8) | ~ leq(v6, v8) | ? [v9] : ? [v10] : (strong_iteration(v4) = v9 & multiplication(v9, v5) = v10 & leq(v6, v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v7, v4) = v8) | ~ (addition(v6, v5) = v7) | ? [v9] : (addition(v6, v9) = v8 & addition(v5, v4) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v6, v7) = v8) | ~ (addition(v5, v4) = v7) | ? [v9] : (addition(v9, v4) = v8 & addition(v6, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (multiplication(v7, v6) = v5) | ~ (multiplication(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (addition(v7, v6) = v5) | ~ (addition(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (addition(v4, v5) = v6) | ~ leq(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (strong_iteration(v6) = v5) | ~ (strong_iteration(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (star(v6) = v5) | ~ (star(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (strong_iteration(v4) = v5) | ~ (multiplication(v4, v5) = v6) | addition(v6, one) = v5) & ! [v4] : ! [v5] : ! [v6] : ( ~ (star(v4) = v5) | ~ (multiplication(v5, v4) = v6) | addition(one, v6) = v5) & ! [v4] : ! [v5] : ! [v6] : ( ~ (star(v4) = v5) | ~ (multiplication(v4, v5) = v6) | addition(one, v6) = v5) & ! [v4] : ! [v5] : ! [v6] : ( ~ (addition(v5, v4) = v6) | addition(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (addition(v4, v5) = v6) | addition(v5, v4) = v6) & ! [v4] : ! [v5] : (v5 = v4 | ~ (multiplication(v4, one) = v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (multiplication(one, v4) = v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (addition(v4, v4) = v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (addition(v4, zero) = v5)) & ! [v4] : ! [v5] : (v5 = zero | ~ (multiplication(zero, v4) = v5)) & ! [v4] : ! [v5] : ( ~ (strong_iteration(v4) = v5) | ? [v6] : ? [v7] : (star(v4) = v6 & multiplication(v5, zero) = v7 & addition(v6, v7) = v5)) & ! [v4] : ! [v5] : ( ~ (strong_iteration(v4) = v5) | ? [v6] : (multiplication(v4, v5) = v6 & addition(v6, one) = v5)) & ! [v4] : ! [v5] : ( ~ (star(v4) = v5) | ? [v6] : (multiplication(v5, v4) = v6 & addition(one, v6) = v5)) & ! [v4] : ! [v5] : ( ~ (star(v4) = v5) | ? [v6] : (multiplication(v4, v5) = v6 & addition(one, v6) = v5)) & ! [v4] : ! [v5] : ( ~ (addition(v4, v5) = v5) | leq(v4, v5))) % 6.27/2.19 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 6.27/2.19 | (1) ~ (all_0_0_0 = all_0_2_2) & strong_iteration(all_0_3_3) = all_0_2_2 & multiplication(all_0_2_2, all_0_3_3) = all_0_1_1 & addition(all_0_1_1, 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)) % 6.27/2.20 | % 6.27/2.20 | Applying alpha-rule on (1) yields: % 6.27/2.20 | (2) multiplication(all_0_2_2, all_0_3_3) = all_0_1_1 % 6.27/2.20 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 6.27/2.20 | (4) ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1)) % 6.27/2.20 | (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))) % 6.27/2.20 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 6.27/2.20 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 6.27/2.20 | (8) ! [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)) % 6.27/2.21 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 6.27/2.21 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (strong_iteration(v0) = v1) | ~ (multiplication(v0, v1) = v2) | addition(v2, one) = v1) % 6.27/2.21 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (star(v0) = v1) | ~ (multiplication(v1, v0) = v2) | addition(one, v2) = v1) % 6.27/2.21 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) % 6.27/2.21 | (13) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 6.27/2.21 | (14) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 6.27/2.21 | (15) ! [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))) % 6.27/2.21 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 6.27/2.21 | (17) ! [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)) % 6.27/2.21 | (18) ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1)) % 6.68/2.21 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 6.68/2.21 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 6.68/2.21 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~ (strong_iteration(v2) = v0)) % 6.68/2.21 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 6.68/2.21 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0)) % 6.68/2.21 | (24) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 6.68/2.21 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 6.68/2.21 | (26) ! [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)) % 6.68/2.21 | (27) ! [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)) % 6.68/2.21 | (28) strong_iteration(all_0_3_3) = all_0_2_2 % 6.68/2.21 | (29) ~ (all_0_0_0 = all_0_2_2) % 6.68/2.21 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (star(v0) = v1) | ~ (multiplication(v0, v1) = v2) | addition(one, v2) = v1) % 6.68/2.21 | (31) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1)) % 6.68/2.21 | (32) addition(all_0_1_1, one) = all_0_0_0 % 6.68/2.21 | (33) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1)) % 6.68/2.21 | (34) ! [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))) % 6.68/2.21 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 6.68/2.21 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 6.68/2.21 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | ~ (strong_iteration(v0) = v1) | ~ (star(v0) = v2) | ~ (multiplication(v1, zero) = v3) | ~ (addition(v2, v3) = v4)) % 6.68/2.21 | % 6.68/2.22 | Instantiating formula (18) with all_0_2_2, all_0_3_3 and discharging atoms strong_iteration(all_0_3_3) = all_0_2_2, yields: % 6.68/2.22 | (38) ? [v0] : ? [v1] : (star(all_0_3_3) = v0 & multiplication(all_0_2_2, zero) = v1 & addition(v0, v1) = all_0_2_2) % 6.68/2.22 | % 6.68/2.22 | Instantiating formula (4) with all_0_2_2, all_0_3_3 and discharging atoms strong_iteration(all_0_3_3) = all_0_2_2, yields: % 6.68/2.22 | (39) ? [v0] : (multiplication(all_0_3_3, all_0_2_2) = v0 & addition(v0, one) = all_0_2_2) % 6.68/2.22 | % 6.68/2.22 | Instantiating formula (36) with all_0_0_0, all_0_1_1, one and discharging atoms addition(all_0_1_1, one) = all_0_0_0, yields: % 6.68/2.22 | (40) addition(one, all_0_1_1) = all_0_0_0 % 6.68/2.22 | % 6.68/2.22 | Instantiating (39) with all_9_0_4 yields: % 6.68/2.22 | (41) multiplication(all_0_3_3, all_0_2_2) = all_9_0_4 & addition(all_9_0_4, one) = all_0_2_2 % 6.68/2.22 | % 6.68/2.22 | Applying alpha-rule on (41) yields: % 6.68/2.22 | (42) multiplication(all_0_3_3, all_0_2_2) = all_9_0_4 % 6.68/2.22 | (43) addition(all_9_0_4, one) = all_0_2_2 % 6.68/2.22 | % 6.68/2.22 | Instantiating (38) with all_11_0_5, all_11_1_6 yields: % 6.68/2.22 | (44) star(all_0_3_3) = all_11_1_6 & multiplication(all_0_2_2, zero) = all_11_0_5 & addition(all_11_1_6, all_11_0_5) = all_0_2_2 % 6.68/2.22 | % 6.68/2.22 | Applying alpha-rule on (44) yields: % 6.68/2.22 | (45) star(all_0_3_3) = all_11_1_6 % 6.68/2.22 | (46) multiplication(all_0_2_2, zero) = all_11_0_5 % 6.68/2.22 | (47) addition(all_11_1_6, all_11_0_5) = all_0_2_2 % 6.68/2.22 | % 6.68/2.22 | Instantiating formula (33) with all_11_1_6, all_0_3_3 and discharging atoms star(all_0_3_3) = all_11_1_6, yields: % 6.68/2.22 | (48) ? [v0] : (multiplication(all_11_1_6, all_0_3_3) = v0 & addition(one, v0) = all_11_1_6) % 6.68/2.22 | % 6.68/2.22 | Instantiating formula (8) with all_0_1_1, all_0_2_2, all_0_3_3, all_11_0_5, all_11_1_6 and discharging atoms multiplication(all_0_2_2, all_0_3_3) = all_0_1_1, addition(all_11_1_6, all_11_0_5) = all_0_2_2, yields: % 6.68/2.22 | (49) ? [v0] : ? [v1] : (multiplication(all_11_0_5, all_0_3_3) = v1 & multiplication(all_11_1_6, all_0_3_3) = v0 & addition(v0, v1) = all_0_1_1) % 6.68/2.22 | % 6.68/2.22 | Instantiating formula (8) with all_11_0_5, all_0_2_2, zero, one, all_9_0_4 and discharging atoms multiplication(all_0_2_2, zero) = all_11_0_5, addition(all_9_0_4, one) = all_0_2_2, yields: % 6.68/2.22 | (50) ? [v0] : ? [v1] : (multiplication(all_9_0_4, zero) = v0 & multiplication(one, zero) = v1 & addition(v0, v1) = all_11_0_5) % 6.68/2.22 | % 6.68/2.22 | Instantiating (50) with all_19_0_7, all_19_1_8 yields: % 6.68/2.22 | (51) multiplication(all_9_0_4, zero) = all_19_1_8 & multiplication(one, zero) = all_19_0_7 & addition(all_19_1_8, all_19_0_7) = all_11_0_5 % 6.68/2.22 | % 6.68/2.22 | Applying alpha-rule on (51) yields: % 6.68/2.22 | (52) multiplication(all_9_0_4, zero) = all_19_1_8 % 6.68/2.22 | (53) multiplication(one, zero) = all_19_0_7 % 6.68/2.22 | (54) addition(all_19_1_8, all_19_0_7) = all_11_0_5 % 6.68/2.22 | % 6.68/2.22 | Instantiating (49) with all_29_0_17, all_29_1_18 yields: % 6.68/2.22 | (55) multiplication(all_11_0_5, all_0_3_3) = all_29_0_17 & multiplication(all_11_1_6, all_0_3_3) = all_29_1_18 & addition(all_29_1_18, all_29_0_17) = all_0_1_1 % 6.68/2.22 | % 6.68/2.22 | Applying alpha-rule on (55) yields: % 6.68/2.22 | (56) multiplication(all_11_0_5, all_0_3_3) = all_29_0_17 % 6.68/2.22 | (57) multiplication(all_11_1_6, all_0_3_3) = all_29_1_18 % 6.68/2.22 | (58) addition(all_29_1_18, all_29_0_17) = all_0_1_1 % 6.68/2.22 | % 6.68/2.22 | Instantiating (48) with all_33_0_20 yields: % 6.68/2.22 | (59) multiplication(all_11_1_6, all_0_3_3) = all_33_0_20 & addition(one, all_33_0_20) = all_11_1_6 % 6.68/2.22 | % 6.68/2.22 | Applying alpha-rule on (59) yields: % 6.68/2.22 | (60) multiplication(all_11_1_6, all_0_3_3) = all_33_0_20 % 6.68/2.22 | (61) addition(one, all_33_0_20) = all_11_1_6 % 6.68/2.22 | % 6.68/2.22 | Instantiating formula (3) with all_11_1_6, all_0_3_3, all_29_1_18, all_33_0_20 and discharging atoms multiplication(all_11_1_6, all_0_3_3) = all_33_0_20, multiplication(all_11_1_6, all_0_3_3) = all_29_1_18, yields: % 6.68/2.22 | (62) all_33_0_20 = all_29_1_18 % 6.68/2.22 | % 6.68/2.22 | Instantiating formula (19) with all_19_0_7, zero and discharging atoms multiplication(one, zero) = all_19_0_7, yields: % 6.68/2.22 | (63) all_19_0_7 = zero % 6.68/2.22 | % 6.68/2.22 | From (63) and (54) follows: % 6.68/2.22 | (64) addition(all_19_1_8, zero) = all_11_0_5 % 6.68/2.22 | % 6.68/2.22 | From (62) and (61) follows: % 6.68/2.22 | (65) addition(one, all_29_1_18) = all_11_1_6 % 6.68/2.22 | % 6.68/2.22 | Instantiating formula (20) with all_11_0_5, all_19_1_8 and discharging atoms addition(all_19_1_8, zero) = all_11_0_5, yields: % 6.68/2.22 | (66) all_19_1_8 = all_11_0_5 % 6.68/2.22 | % 6.68/2.22 | From (66) and (52) follows: % 6.68/2.22 | (67) multiplication(all_9_0_4, zero) = all_11_0_5 % 6.68/2.22 | % 6.68/2.22 | Instantiating formula (22) with all_29_0_17, all_11_0_5, all_0_3_3, zero, all_0_2_2 and discharging atoms multiplication(all_11_0_5, all_0_3_3) = all_29_0_17, multiplication(all_0_2_2, zero) = all_11_0_5, yields: % 6.68/2.22 | (68) ? [v0] : (multiplication(all_0_2_2, v0) = all_29_0_17 & multiplication(zero, all_0_3_3) = v0) % 6.68/2.22 | % 6.68/2.22 | Instantiating formula (22) with all_29_0_17, all_11_0_5, all_0_3_3, zero, all_9_0_4 and discharging atoms multiplication(all_11_0_5, all_0_3_3) = all_29_0_17, multiplication(all_9_0_4, zero) = all_11_0_5, yields: % 6.68/2.22 | (69) ? [v0] : (multiplication(all_9_0_4, v0) = all_29_0_17 & multiplication(zero, all_0_3_3) = v0) % 6.68/2.23 | % 6.68/2.23 | Instantiating formula (6) with all_0_0_0, all_0_1_1, one, all_29_1_18, all_29_0_17 and discharging atoms addition(all_29_1_18, all_29_0_17) = all_0_1_1, addition(one, all_0_1_1) = all_0_0_0, yields: % 6.68/2.23 | (70) ? [v0] : (addition(v0, all_29_0_17) = all_0_0_0 & addition(one, all_29_1_18) = v0) % 6.68/2.23 | % 6.68/2.23 | Instantiating (70) with all_153_0_96 yields: % 6.68/2.23 | (71) addition(all_153_0_96, all_29_0_17) = all_0_0_0 & addition(one, all_29_1_18) = all_153_0_96 % 6.68/2.23 | % 6.68/2.23 | Applying alpha-rule on (71) yields: % 6.68/2.23 | (72) addition(all_153_0_96, all_29_0_17) = all_0_0_0 % 6.68/2.23 | (73) addition(one, all_29_1_18) = all_153_0_96 % 6.68/2.23 | % 6.68/2.23 | Instantiating (68) with all_179_0_110 yields: % 6.68/2.23 | (74) multiplication(all_0_2_2, all_179_0_110) = all_29_0_17 & multiplication(zero, all_0_3_3) = all_179_0_110 % 6.68/2.23 | % 6.68/2.23 | Applying alpha-rule on (74) yields: % 6.68/2.23 | (75) multiplication(all_0_2_2, all_179_0_110) = all_29_0_17 % 6.68/2.23 | (76) multiplication(zero, all_0_3_3) = all_179_0_110 % 6.68/2.23 | % 6.68/2.23 | Instantiating (69) with all_195_0_118 yields: % 6.68/2.23 | (77) multiplication(all_9_0_4, all_195_0_118) = all_29_0_17 & multiplication(zero, all_0_3_3) = all_195_0_118 % 6.68/2.23 | % 6.68/2.23 | Applying alpha-rule on (77) yields: % 6.68/2.23 | (78) multiplication(all_9_0_4, all_195_0_118) = all_29_0_17 % 6.68/2.23 | (79) multiplication(zero, all_0_3_3) = all_195_0_118 % 6.68/2.23 | % 6.68/2.23 | Instantiating formula (14) with all_195_0_118, all_0_3_3 and discharging atoms multiplication(zero, all_0_3_3) = all_195_0_118, yields: % 6.68/2.23 | (80) all_195_0_118 = zero % 6.68/2.23 | % 6.68/2.23 | Instantiating formula (3) with zero, all_0_3_3, all_179_0_110, all_195_0_118 and discharging atoms multiplication(zero, all_0_3_3) = all_195_0_118, multiplication(zero, all_0_3_3) = all_179_0_110, yields: % 6.68/2.23 | (81) all_195_0_118 = all_179_0_110 % 6.68/2.23 | % 6.68/2.23 | Instantiating formula (25) with one, all_29_1_18, all_153_0_96, all_11_1_6 and discharging atoms addition(one, all_29_1_18) = all_153_0_96, addition(one, all_29_1_18) = all_11_1_6, yields: % 6.68/2.23 | (82) all_153_0_96 = all_11_1_6 % 6.68/2.23 | % 6.68/2.23 | Combining equations (81,80) yields a new equation: % 6.68/2.23 | (83) all_179_0_110 = zero % 6.68/2.23 | % 6.68/2.23 | Simplifying 83 yields: % 6.68/2.23 | (84) all_179_0_110 = zero % 6.68/2.23 | % 6.68/2.23 | From (84) and (75) follows: % 6.68/2.23 | (85) multiplication(all_0_2_2, zero) = all_29_0_17 % 6.68/2.23 | % 6.68/2.23 | From (82) and (72) follows: % 6.68/2.23 | (86) addition(all_11_1_6, all_29_0_17) = all_0_0_0 % 6.68/2.23 | % 6.68/2.23 | Instantiating formula (37) with all_0_0_0, all_29_0_17, all_11_1_6, all_0_2_2, all_0_3_3 and discharging atoms strong_iteration(all_0_3_3) = all_0_2_2, star(all_0_3_3) = all_11_1_6, multiplication(all_0_2_2, zero) = all_29_0_17, addition(all_11_1_6, all_29_0_17) = all_0_0_0, yields: % 6.68/2.23 | (87) all_0_0_0 = all_0_2_2 % 6.68/2.23 | % 6.68/2.23 | Equations (87) can reduce 29 to: % 6.68/2.23 | (88) $false % 6.68/2.23 | % 6.68/2.23 |-The branch is then unsatisfiable % 6.68/2.23 % SZS output end Proof for theBenchmark % 6.68/2.23 % 6.68/2.23 1613ms %------------------------------------------------------------------------------