%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE150+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n023.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 01:51:37 EDT 2022 % Result : Theorem 2.89s 1.34s % Output : Proof 4.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : KLE150+1 : TPTP v8.1.0. Released v4.0.0. % 0.08/0.15 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.36 % Computer : n023.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Thu Jun 16 07:39:20 EDT 2022 % 0.14/0.37 % CPUTime : % 0.58/0.61 ____ _ % 0.58/0.61 ___ / __ \_____(_)___ ________ __________ % 0.58/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.61 % 0.58/0.61 A Theorem Prover for First-Order Logic % 0.58/0.61 (ePrincess v.1.0) % 0.58/0.61 % 0.58/0.61 (c) Philipp Rümmer, 2009-2015 % 0.58/0.61 (c) Peter Backeman, 2014-2015 % 0.58/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.61 Bug reports to peter@backeman.se % 0.58/0.61 % 0.58/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.61 % 0.58/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.68/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.55/0.94 Prover 0: Preprocessing ... % 1.95/1.17 Prover 0: Constructing countermodel ... % 2.89/1.33 Prover 0: proved (676ms) % 2.89/1.34 % 2.89/1.34 No countermodel exists, formula is valid % 2.89/1.34 % SZS status Theorem for theBenchmark % 2.89/1.34 % 2.89/1.34 Generating proof ... found it (size 16) % 4.13/1.64 % 4.13/1.64 % SZS output start Proof for theBenchmark % 4.13/1.64 Assumed formulas after preprocessing and simplification: % 4.13/1.64 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & strong_iteration(v1) = v2 & multiplication(v0, zero) = v1 & addition(one, v1) = 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))) % 4.13/1.68 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 4.13/1.68 | (1) ~ (all_0_0_0 = all_0_1_1) & strong_iteration(all_0_2_2) = all_0_1_1 & multiplication(all_0_3_3, zero) = all_0_2_2 & addition(one, all_0_2_2) = 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)) % 4.37/1.70 | % 4.37/1.70 | Applying alpha-rule on (1) yields: % 4.37/1.70 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 4.37/1.70 | (3) ! [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))) % 4.37/1.70 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 4.37/1.70 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 4.37/1.70 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 4.37/1.70 | (7) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 4.37/1.70 | (8) ! [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)) % 4.37/1.70 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (star(v0) = v1) | ~ (multiplication(v0, v1) = v2) | addition(one, v2) = v1) % 4.37/1.70 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 4.37/1.70 | (11) ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1)) % 4.37/1.70 | (12) multiplication(all_0_3_3, zero) = all_0_2_2 % 4.37/1.70 | (13) ! [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)) % 4.37/1.70 | (14) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 4.37/1.70 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 4.37/1.70 | (16) ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1)) % 4.37/1.70 | (17) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 4.37/1.70 | (18) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1)) % 4.37/1.70 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0)) % 4.37/1.70 | (20) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 4.37/1.70 | (21) ! [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)) % 4.37/1.71 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 4.37/1.71 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) % 4.37/1.71 | (24) ! [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))) % 4.37/1.71 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (strong_iteration(v0) = v1) | ~ (multiplication(v0, v1) = v2) | addition(v2, one) = v1) % 4.37/1.71 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 4.37/1.71 | (27) ~ (all_0_0_0 = all_0_1_1) % 4.37/1.71 | (28) ! [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)) % 4.37/1.71 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | ~ (strong_iteration(v0) = v1) | ~ (star(v0) = v2) | ~ (multiplication(v1, zero) = v3) | ~ (addition(v2, v3) = v4)) % 4.37/1.71 | (30) ! [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))) % 4.37/1.71 | (31) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1)) % 4.37/1.71 | (32) addition(one, all_0_2_2) = all_0_0_0 % 4.37/1.71 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 4.37/1.71 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 4.37/1.71 | (35) strong_iteration(all_0_2_2) = all_0_1_1 % 4.37/1.71 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~ (strong_iteration(v2) = v0)) % 4.37/1.71 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (star(v0) = v1) | ~ (multiplication(v1, v0) = v2) | addition(one, v2) = v1) % 4.37/1.71 | % 4.37/1.71 | Instantiating formula (11) with all_0_1_1, all_0_2_2 and discharging atoms strong_iteration(all_0_2_2) = all_0_1_1, yields: % 4.37/1.71 | (38) ? [v0] : (multiplication(all_0_2_2, all_0_1_1) = v0 & addition(v0, one) = all_0_1_1) % 4.37/1.71 | % 4.37/1.71 | Instantiating (38) with all_9_0_4 yields: % 4.37/1.71 | (39) multiplication(all_0_2_2, all_0_1_1) = all_9_0_4 & addition(all_9_0_4, one) = all_0_1_1 % 4.37/1.71 | % 4.37/1.71 | Applying alpha-rule on (39) yields: % 4.37/1.71 | (40) multiplication(all_0_2_2, all_0_1_1) = all_9_0_4 % 4.37/1.71 | (41) addition(all_9_0_4, one) = all_0_1_1 % 4.37/1.71 | % 4.37/1.71 | Instantiating formula (26) with all_9_0_4, all_0_2_2, all_0_1_1, zero, all_0_3_3 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_9_0_4, multiplication(all_0_3_3, zero) = all_0_2_2, yields: % 4.37/1.72 | (42) ? [v0] : (multiplication(all_0_3_3, v0) = all_9_0_4 & multiplication(zero, all_0_1_1) = v0) % 4.37/1.72 | % 4.37/1.72 | Instantiating formula (6) with all_0_1_1, all_9_0_4, one and discharging atoms addition(all_9_0_4, one) = all_0_1_1, yields: % 4.37/1.72 | (43) addition(one, all_9_0_4) = all_0_1_1 % 4.37/1.72 | % 4.37/1.72 | Instantiating (42) with all_27_0_15 yields: % 4.37/1.72 | (44) multiplication(all_0_3_3, all_27_0_15) = all_9_0_4 & multiplication(zero, all_0_1_1) = all_27_0_15 % 4.37/1.72 | % 4.37/1.72 | Applying alpha-rule on (44) yields: % 4.37/1.72 | (45) multiplication(all_0_3_3, all_27_0_15) = all_9_0_4 % 4.37/1.72 | (46) multiplication(zero, all_0_1_1) = all_27_0_15 % 4.37/1.72 | % 4.37/1.72 | Instantiating formula (20) with all_27_0_15, all_0_1_1 and discharging atoms multiplication(zero, all_0_1_1) = all_27_0_15, yields: % 4.37/1.72 | (47) all_27_0_15 = zero % 4.37/1.72 | % 4.37/1.72 | From (47) and (45) follows: % 4.37/1.72 | (48) multiplication(all_0_3_3, zero) = all_9_0_4 % 4.37/1.72 | % 4.37/1.72 | Instantiating formula (34) with all_0_3_3, zero, all_9_0_4, all_0_2_2 and discharging atoms multiplication(all_0_3_3, zero) = all_9_0_4, multiplication(all_0_3_3, zero) = all_0_2_2, yields: % 4.37/1.72 | (49) all_9_0_4 = all_0_2_2 % 4.37/1.72 | % 4.37/1.72 | From (49) and (43) follows: % 4.37/1.72 | (50) addition(one, all_0_2_2) = all_0_1_1 % 4.37/1.72 | % 4.37/1.72 | Instantiating formula (4) with one, all_0_2_2, all_0_1_1, all_0_0_0 and discharging atoms addition(one, all_0_2_2) = all_0_0_0, addition(one, all_0_2_2) = all_0_1_1, yields: % 4.37/1.72 | (51) all_0_0_0 = all_0_1_1 % 4.37/1.72 | % 4.37/1.72 | Equations (51) can reduce 27 to: % 4.37/1.72 | (52) $false % 4.37/1.72 | % 4.37/1.72 |-The branch is then unsatisfiable % 4.37/1.72 % SZS output end Proof for theBenchmark % 4.37/1.72 % 4.37/1.72 1102ms %------------------------------------------------------------------------------