%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE148+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n021.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 01:51:36 EDT 2022 % Result : Theorem 3.97s 1.69s % Output : Proof 7.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : KLE148+1 : TPTP v8.1.0. Released v4.0.0. % 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.35 % Computer : n021.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 16:20:00 EDT 2022 % 0.13/0.35 % CPUTime : % 0.59/0.60 ____ _ % 0.59/0.60 ___ / __ \_____(_)___ ________ __________ % 0.59/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.59/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.59/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.59/0.60 % 0.59/0.60 A Theorem Prover for First-Order Logic % 0.59/0.60 (ePrincess v.1.0) % 0.59/0.60 % 0.59/0.60 (c) Philipp Rümmer, 2009-2015 % 0.59/0.60 (c) Peter Backeman, 2014-2015 % 0.59/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.59/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.59/0.60 Bug reports to peter@backeman.se % 0.59/0.60 % 0.59/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.59/0.60 % 0.59/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.73/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.62/0.98 Prover 0: Preprocessing ... % 2.33/1.26 Prover 0: Constructing countermodel ... % 3.97/1.68 Prover 0: proved (1031ms) % 3.97/1.69 % 3.97/1.69 No countermodel exists, formula is valid % 3.97/1.69 % SZS status Theorem for theBenchmark % 3.97/1.69 % 3.97/1.69 Generating proof ... found it (size 57) % 6.66/2.26 % 6.66/2.26 % SZS output start Proof for theBenchmark % 6.66/2.26 Assumed formulas after preprocessing and simplification: % 6.66/2.27 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v0) & strong_iteration(v1) = v2 & multiplication(v0, v2) = v3 & multiplication(v0, v1) = zero & ! [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))) % 7.04/2.31 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 7.04/2.31 | (1) ~ (all_0_0_0 = all_0_3_3) & strong_iteration(all_0_2_2) = all_0_1_1 & multiplication(all_0_3_3, all_0_1_1) = all_0_0_0 & multiplication(all_0_3_3, all_0_2_2) = zero & ! [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)) % 7.04/2.32 | % 7.04/2.32 | Applying alpha-rule on (1) yields: % 7.04/2.32 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) % 7.04/2.32 | (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))) % 7.04/2.32 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~ (strong_iteration(v2) = v0)) % 7.04/2.32 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 7.04/2.32 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (star(v0) = v1) | ~ (multiplication(v0, v1) = v2) | addition(one, v2) = v1) % 7.04/2.32 | (7) ! [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)) % 7.04/2.32 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 7.04/2.32 | (9) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 7.04/2.32 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (strong_iteration(v0) = v1) | ~ (multiplication(v0, v1) = v2) | addition(v2, one) = v1) % 7.04/2.32 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v1 | ~ (strong_iteration(v0) = v1) | ~ (star(v0) = v2) | ~ (multiplication(v1, zero) = v3) | ~ (addition(v2, v3) = v4)) % 7.04/2.32 | (12) ! [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)) % 7.04/2.32 | (13) ! [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)) % 7.04/2.32 | (14) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 7.04/2.32 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 7.04/2.32 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0)) % 7.04/2.32 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 7.04/2.32 | (18) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1)) % 7.04/2.32 | (19) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1)) % 7.04/2.32 | (20) ! [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))) % 7.04/2.32 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (star(v0) = v1) | ~ (multiplication(v1, v0) = v2) | addition(one, v2) = v1) % 7.04/2.32 | (22) ~ (all_0_0_0 = all_0_3_3) % 7.04/2.32 | (23) multiplication(all_0_3_3, all_0_2_2) = zero % 7.04/2.32 | (24) ! [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)) % 7.04/2.32 | (25) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 7.04/2.32 | (26) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 7.04/2.32 | (27) strong_iteration(all_0_2_2) = all_0_1_1 % 7.04/2.32 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 7.04/2.32 | (29) ! [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))) % 7.04/2.32 | (30) multiplication(all_0_3_3, all_0_1_1) = all_0_0_0 % 7.04/2.32 | (31) ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1)) % 7.04/2.33 | (32) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 7.04/2.33 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 7.04/2.33 | (34) ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1)) % 7.04/2.33 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 7.04/2.33 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 7.04/2.33 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 7.04/2.33 | % 7.04/2.33 | Instantiating formula (31) with all_0_1_1, all_0_2_2 and discharging atoms strong_iteration(all_0_2_2) = all_0_1_1, yields: % 7.04/2.33 | (38) ? [v0] : ? [v1] : (star(all_0_2_2) = v0 & multiplication(all_0_1_1, zero) = v1 & addition(v0, v1) = all_0_1_1) % 7.04/2.33 | % 7.04/2.33 | Instantiating formula (34) with all_0_1_1, all_0_2_2 and discharging atoms strong_iteration(all_0_2_2) = all_0_1_1, yields: % 7.04/2.33 | (39) ? [v0] : (multiplication(all_0_2_2, all_0_1_1) = v0 & addition(v0, one) = all_0_1_1) % 7.04/2.33 | % 7.04/2.33 | Instantiating (39) with all_8_0_4 yields: % 7.04/2.33 | (40) multiplication(all_0_2_2, all_0_1_1) = all_8_0_4 & addition(all_8_0_4, one) = all_0_1_1 % 7.04/2.33 | % 7.04/2.33 | Applying alpha-rule on (40) yields: % 7.04/2.33 | (41) multiplication(all_0_2_2, all_0_1_1) = all_8_0_4 % 7.04/2.33 | (42) addition(all_8_0_4, one) = all_0_1_1 % 7.04/2.33 | % 7.04/2.33 | Instantiating (38) with all_10_0_5, all_10_1_6 yields: % 7.04/2.33 | (43) star(all_0_2_2) = all_10_1_6 & multiplication(all_0_1_1, zero) = all_10_0_5 & addition(all_10_1_6, all_10_0_5) = all_0_1_1 % 7.04/2.33 | % 7.04/2.33 | Applying alpha-rule on (43) yields: % 7.04/2.33 | (44) star(all_0_2_2) = all_10_1_6 % 7.04/2.33 | (45) multiplication(all_0_1_1, zero) = all_10_0_5 % 7.04/2.33 | (46) addition(all_10_1_6, all_10_0_5) = all_0_1_1 % 7.04/2.33 | % 7.04/2.33 | Instantiating formula (19) with all_10_1_6, all_0_2_2 and discharging atoms star(all_0_2_2) = all_10_1_6, yields: % 7.04/2.33 | (47) ? [v0] : (multiplication(all_0_2_2, all_10_1_6) = v0 & addition(one, v0) = all_10_1_6) % 7.04/2.33 | % 7.04/2.33 | Instantiating formula (24) with all_0_0_0, all_0_1_1, all_10_0_5, all_10_1_6, all_0_3_3 and discharging atoms multiplication(all_0_3_3, all_0_1_1) = all_0_0_0, addition(all_10_1_6, all_10_0_5) = all_0_1_1, yields: % 7.04/2.33 | (48) ? [v0] : ? [v1] : (multiplication(all_0_3_3, all_10_0_5) = v1 & multiplication(all_0_3_3, all_10_1_6) = v0 & addition(v0, v1) = all_0_0_0) % 7.04/2.33 | % 7.04/2.33 | Instantiating formula (24) with all_8_0_4, all_0_1_1, all_10_0_5, all_10_1_6, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_8_0_4, addition(all_10_1_6, all_10_0_5) = all_0_1_1, yields: % 7.04/2.33 | (49) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_10_0_5) = v1 & multiplication(all_0_2_2, all_10_1_6) = v0 & addition(v0, v1) = all_8_0_4) % 7.04/2.33 | % 7.04/2.33 | Instantiating formula (24) with all_0_0_0, all_0_1_1, one, all_8_0_4, all_0_3_3 and discharging atoms multiplication(all_0_3_3, all_0_1_1) = all_0_0_0, addition(all_8_0_4, one) = all_0_1_1, yields: % 7.04/2.33 | (50) ? [v0] : ? [v1] : (multiplication(all_0_3_3, all_8_0_4) = v0 & multiplication(all_0_3_3, one) = v1 & addition(v0, v1) = all_0_0_0) % 7.04/2.33 | % 7.04/2.33 | Instantiating formula (12) with all_10_0_5, all_0_1_1, zero, one, all_8_0_4 and discharging atoms multiplication(all_0_1_1, zero) = all_10_0_5, addition(all_8_0_4, one) = all_0_1_1, yields: % 7.04/2.33 | (51) ? [v0] : ? [v1] : (multiplication(all_8_0_4, zero) = v0 & multiplication(one, zero) = v1 & addition(v0, v1) = all_10_0_5) % 7.04/2.33 | % 7.04/2.33 | Instantiating formula (37) with all_0_1_1, all_8_0_4, one and discharging atoms addition(all_8_0_4, one) = all_0_1_1, yields: % 7.04/2.33 | (52) addition(one, all_8_0_4) = all_0_1_1 % 7.04/2.33 | % 7.04/2.33 | Instantiating (49) with all_18_0_7, all_18_1_8 yields: % 7.04/2.33 | (53) multiplication(all_0_2_2, all_10_0_5) = all_18_0_7 & multiplication(all_0_2_2, all_10_1_6) = all_18_1_8 & addition(all_18_1_8, all_18_0_7) = all_8_0_4 % 7.04/2.33 | % 7.04/2.33 | Applying alpha-rule on (53) yields: % 7.04/2.33 | (54) multiplication(all_0_2_2, all_10_0_5) = all_18_0_7 % 7.04/2.33 | (55) multiplication(all_0_2_2, all_10_1_6) = all_18_1_8 % 7.04/2.33 | (56) addition(all_18_1_8, all_18_0_7) = all_8_0_4 % 7.04/2.33 | % 7.04/2.33 | Instantiating (51) with all_22_0_11, all_22_1_12 yields: % 7.04/2.33 | (57) multiplication(all_8_0_4, zero) = all_22_1_12 & multiplication(one, zero) = all_22_0_11 & addition(all_22_1_12, all_22_0_11) = all_10_0_5 % 7.04/2.33 | % 7.04/2.33 | Applying alpha-rule on (57) yields: % 7.04/2.33 | (58) multiplication(all_8_0_4, zero) = all_22_1_12 % 7.04/2.33 | (59) multiplication(one, zero) = all_22_0_11 % 7.04/2.33 | (60) addition(all_22_1_12, all_22_0_11) = all_10_0_5 % 7.04/2.33 | % 7.04/2.33 | Instantiating (50) with all_26_0_15, all_26_1_16 yields: % 7.04/2.33 | (61) multiplication(all_0_3_3, all_8_0_4) = all_26_1_16 & multiplication(all_0_3_3, one) = all_26_0_15 & addition(all_26_1_16, all_26_0_15) = all_0_0_0 % 7.04/2.33 | % 7.04/2.33 | Applying alpha-rule on (61) yields: % 7.04/2.33 | (62) multiplication(all_0_3_3, all_8_0_4) = all_26_1_16 % 7.04/2.33 | (63) multiplication(all_0_3_3, one) = all_26_0_15 % 7.04/2.33 | (64) addition(all_26_1_16, all_26_0_15) = all_0_0_0 % 7.04/2.33 | % 7.04/2.33 | Instantiating (48) with all_28_0_17, all_28_1_18 yields: % 7.04/2.33 | (65) multiplication(all_0_3_3, all_10_0_5) = all_28_0_17 & multiplication(all_0_3_3, all_10_1_6) = all_28_1_18 & addition(all_28_1_18, all_28_0_17) = all_0_0_0 % 7.04/2.33 | % 7.04/2.33 | Applying alpha-rule on (65) yields: % 7.04/2.33 | (66) multiplication(all_0_3_3, all_10_0_5) = all_28_0_17 % 7.04/2.33 | (67) multiplication(all_0_3_3, all_10_1_6) = all_28_1_18 % 7.04/2.33 | (68) addition(all_28_1_18, all_28_0_17) = all_0_0_0 % 7.04/2.34 | % 7.04/2.34 | Instantiating (47) with all_32_0_20 yields: % 7.04/2.34 | (69) multiplication(all_0_2_2, all_10_1_6) = all_32_0_20 & addition(one, all_32_0_20) = all_10_1_6 % 7.04/2.34 | % 7.04/2.34 | Applying alpha-rule on (69) yields: % 7.04/2.34 | (70) multiplication(all_0_2_2, all_10_1_6) = all_32_0_20 % 7.04/2.34 | (71) addition(one, all_32_0_20) = all_10_1_6 % 7.04/2.34 | % 7.04/2.34 | Instantiating formula (28) with all_0_2_2, all_10_1_6, all_18_1_8, all_32_0_20 and discharging atoms multiplication(all_0_2_2, all_10_1_6) = all_32_0_20, multiplication(all_0_2_2, all_10_1_6) = all_18_1_8, yields: % 7.04/2.34 | (72) all_32_0_20 = all_18_1_8 % 7.04/2.34 | % 7.04/2.34 | Instantiating formula (14) with all_22_0_11, zero and discharging atoms multiplication(one, zero) = all_22_0_11, yields: % 7.04/2.34 | (73) all_22_0_11 = zero % 7.04/2.34 | % 7.04/2.34 | From (73) and (60) follows: % 7.04/2.34 | (74) addition(all_22_1_12, zero) = all_10_0_5 % 7.04/2.34 | % 7.04/2.34 | From (72) and (71) follows: % 7.04/2.34 | (75) addition(one, all_18_1_8) = all_10_1_6 % 7.04/2.34 | % 7.04/2.34 | Instantiating formula (25) with all_10_0_5, all_22_1_12 and discharging atoms addition(all_22_1_12, zero) = all_10_0_5, yields: % 7.04/2.34 | (76) all_22_1_12 = all_10_0_5 % 7.04/2.34 | % 7.04/2.34 | From (76) and (58) follows: % 7.04/2.34 | (77) multiplication(all_8_0_4, zero) = all_10_0_5 % 7.04/2.34 | % 7.04/2.34 | Instantiating formula (5) with all_28_0_17, all_10_0_5, zero, all_8_0_4, all_0_3_3 and discharging atoms multiplication(all_8_0_4, zero) = all_10_0_5, multiplication(all_0_3_3, all_10_0_5) = all_28_0_17, yields: % 7.04/2.34 | (78) ? [v0] : (multiplication(v0, zero) = all_28_0_17 & multiplication(all_0_3_3, all_8_0_4) = v0) % 7.04/2.34 | % 7.04/2.34 | Instantiating formula (5) with all_26_1_16, all_8_0_4, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_8_0_4, multiplication(all_0_3_3, all_8_0_4) = all_26_1_16, yields: % 7.04/2.34 | (79) ? [v0] : (multiplication(v0, all_0_1_1) = all_26_1_16 & multiplication(all_0_3_3, all_0_2_2) = v0) % 7.04/2.34 | % 7.04/2.34 | Instantiating formula (24) with all_28_1_18, all_10_1_6, all_18_1_8, one, all_0_3_3 and discharging atoms multiplication(all_0_3_3, all_10_1_6) = all_28_1_18, addition(one, all_18_1_8) = all_10_1_6, yields: % 7.04/2.34 | (80) ? [v0] : ? [v1] : (multiplication(all_0_3_3, all_18_1_8) = v1 & multiplication(all_0_3_3, one) = v0 & addition(v0, v1) = all_28_1_18) % 7.04/2.34 | % 7.04/2.34 | Instantiating formula (24) with all_0_0_0, all_0_1_1, all_8_0_4, one, all_0_3_3 and discharging atoms multiplication(all_0_3_3, all_0_1_1) = all_0_0_0, addition(one, all_8_0_4) = all_0_1_1, yields: % 7.04/2.34 | (81) ? [v0] : ? [v1] : (multiplication(all_0_3_3, all_8_0_4) = v1 & multiplication(all_0_3_3, one) = v0 & addition(v0, v1) = all_0_0_0) % 7.04/2.34 | % 7.04/2.34 | Instantiating (79) with all_72_0_37 yields: % 7.04/2.34 | (82) multiplication(all_72_0_37, all_0_1_1) = all_26_1_16 & multiplication(all_0_3_3, all_0_2_2) = all_72_0_37 % 7.04/2.34 | % 7.04/2.34 | Applying alpha-rule on (82) yields: % 7.04/2.34 | (83) multiplication(all_72_0_37, all_0_1_1) = all_26_1_16 % 7.04/2.34 | (84) multiplication(all_0_3_3, all_0_2_2) = all_72_0_37 % 7.04/2.34 | % 7.04/2.34 | Instantiating (78) with all_88_0_47 yields: % 7.04/2.34 | (85) multiplication(all_88_0_47, zero) = all_28_0_17 & multiplication(all_0_3_3, all_8_0_4) = all_88_0_47 % 7.04/2.34 | % 7.04/2.34 | Applying alpha-rule on (85) yields: % 7.04/2.34 | (86) multiplication(all_88_0_47, zero) = all_28_0_17 % 7.04/2.34 | (87) multiplication(all_0_3_3, all_8_0_4) = all_88_0_47 % 7.04/2.34 | % 7.04/2.34 | Instantiating (81) with all_152_0_91, all_152_1_92 yields: % 7.04/2.34 | (88) multiplication(all_0_3_3, all_8_0_4) = all_152_0_91 & multiplication(all_0_3_3, one) = all_152_1_92 & addition(all_152_1_92, all_152_0_91) = all_0_0_0 % 7.04/2.34 | % 7.04/2.34 | Applying alpha-rule on (88) yields: % 7.04/2.34 | (89) multiplication(all_0_3_3, all_8_0_4) = all_152_0_91 % 7.04/2.34 | (90) multiplication(all_0_3_3, one) = all_152_1_92 % 7.04/2.34 | (91) addition(all_152_1_92, all_152_0_91) = all_0_0_0 % 7.04/2.34 | % 7.04/2.34 | Instantiating (80) with all_158_0_95, all_158_1_96 yields: % 7.04/2.34 | (92) multiplication(all_0_3_3, all_18_1_8) = all_158_0_95 & multiplication(all_0_3_3, one) = all_158_1_96 & addition(all_158_1_96, all_158_0_95) = all_28_1_18 % 7.04/2.34 | % 7.04/2.34 | Applying alpha-rule on (92) yields: % 7.04/2.34 | (93) multiplication(all_0_3_3, all_18_1_8) = all_158_0_95 % 7.04/2.34 | (94) multiplication(all_0_3_3, one) = all_158_1_96 % 7.04/2.34 | (95) addition(all_158_1_96, all_158_0_95) = all_28_1_18 % 7.04/2.34 | % 7.04/2.34 | Instantiating formula (28) with all_0_3_3, all_8_0_4, all_152_0_91, all_26_1_16 and discharging atoms multiplication(all_0_3_3, all_8_0_4) = all_152_0_91, multiplication(all_0_3_3, all_8_0_4) = all_26_1_16, yields: % 7.04/2.34 | (96) all_152_0_91 = all_26_1_16 % 7.04/2.34 | % 7.04/2.34 | Instantiating formula (28) with all_0_3_3, all_8_0_4, all_88_0_47, all_152_0_91 and discharging atoms multiplication(all_0_3_3, all_8_0_4) = all_152_0_91, multiplication(all_0_3_3, all_8_0_4) = all_88_0_47, yields: % 7.04/2.34 | (97) all_152_0_91 = all_88_0_47 % 7.04/2.34 | % 7.04/2.34 | Instantiating formula (28) with all_0_3_3, all_0_2_2, all_72_0_37, zero and discharging atoms multiplication(all_0_3_3, all_0_2_2) = all_72_0_37, multiplication(all_0_3_3, all_0_2_2) = zero, yields: % 7.04/2.34 | (98) all_72_0_37 = zero % 7.04/2.34 | % 7.04/2.34 | Instantiating formula (32) with all_158_1_96, all_0_3_3 and discharging atoms multiplication(all_0_3_3, one) = all_158_1_96, yields: % 7.04/2.34 | (99) all_158_1_96 = all_0_3_3 % 7.04/2.34 | % 7.04/2.34 | Instantiating formula (28) with all_0_3_3, one, all_152_1_92, all_158_1_96 and discharging atoms multiplication(all_0_3_3, one) = all_158_1_96, multiplication(all_0_3_3, one) = all_152_1_92, yields: % 7.04/2.35 | (100) all_158_1_96 = all_152_1_92 % 7.04/2.35 | % 7.04/2.35 | Combining equations (99,100) yields a new equation: % 7.04/2.35 | (101) all_152_1_92 = all_0_3_3 % 7.04/2.35 | % 7.04/2.35 | Combining equations (96,97) yields a new equation: % 7.04/2.35 | (102) all_88_0_47 = all_26_1_16 % 7.04/2.35 | % 7.04/2.35 | Combining equations (102,97) yields a new equation: % 7.04/2.35 | (96) all_152_0_91 = all_26_1_16 % 7.04/2.35 | % 7.04/2.35 | From (98) and (83) follows: % 7.04/2.35 | (104) multiplication(zero, all_0_1_1) = all_26_1_16 % 7.04/2.35 | % 7.04/2.35 | From (101)(96) and (91) follows: % 7.04/2.35 | (105) addition(all_0_3_3, all_26_1_16) = all_0_0_0 % 7.04/2.35 | % 7.04/2.35 | Instantiating formula (9) with all_26_1_16, all_0_1_1 and discharging atoms multiplication(zero, all_0_1_1) = all_26_1_16, yields: % 7.04/2.35 | (106) all_26_1_16 = zero % 7.04/2.35 | % 7.04/2.35 | From (106) and (105) follows: % 7.04/2.35 | (107) addition(all_0_3_3, zero) = all_0_0_0 % 7.04/2.35 | % 7.04/2.35 | Instantiating formula (25) with all_0_0_0, all_0_3_3 and discharging atoms addition(all_0_3_3, zero) = all_0_0_0, yields: % 7.04/2.35 | (108) all_0_0_0 = all_0_3_3 % 7.04/2.35 | % 7.04/2.35 | Equations (108) can reduce 22 to: % 7.04/2.35 | (109) $false % 7.04/2.35 | % 7.04/2.35 |-The branch is then unsatisfiable % 7.04/2.35 % SZS output end Proof for theBenchmark % 7.04/2.35 % 7.04/2.35 1737ms %------------------------------------------------------------------------------