%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE059+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n015.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 01:51:11 EDT 2022 % Result : Theorem 2.58s 1.31s % Output : Proof 3.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KLE059+1 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n015.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Thu Jun 16 08:30:41 EDT 2022 % 0.12/0.34 % CPUTime : % 0.19/0.58 ____ _ % 0.19/0.58 ___ / __ \_____(_)___ ________ __________ % 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.58 % 0.19/0.58 A Theorem Prover for First-Order Logic % 0.19/0.58 (ePrincess v.1.0) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2015 % 0.19/0.58 (c) Peter Backeman, 2014-2015 % 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.58 Bug reports to peter@backeman.se % 0.19/0.58 % 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.75/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.65/0.93 Prover 0: Preprocessing ... % 2.32/1.21 Prover 0: Constructing countermodel ... % 2.58/1.31 Prover 0: proved (675ms) % 2.58/1.31 % 2.58/1.31 No countermodel exists, formula is valid % 2.58/1.31 % SZS status Theorem for theBenchmark % 2.58/1.31 % 2.58/1.31 Generating proof ... found it (size 14) % 3.79/1.52 % 3.79/1.52 % SZS output start Proof for theBenchmark % 3.79/1.52 Assumed formulas after preprocessing and simplification: % 3.79/1.52 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = v3) & domain(v1) = v3 & domain(v0) = v2 & domain(zero) = zero & addition(v2, v3) = v4 & addition(v0, v1) = v1 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v6, v7) = v9) | ~ (multiplication(v5, v7) = v8) | ~ (addition(v8, v9) = v10) | ? [v11] : (multiplication(v11, v7) = v10 & addition(v5, v6) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v5, v7) = v9) | ~ (multiplication(v5, v6) = v8) | ~ (addition(v8, v9) = v10) | ? [v11] : (multiplication(v5, v11) = v10 & addition(v6, v7) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (domain(v6) = v8) | ~ (domain(v5) = v7) | ~ (addition(v7, v8) = v9) | ? [v10] : (domain(v10) = v9 & addition(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v8, v7) = v9) | ~ (multiplication(v5, v6) = v8) | ? [v10] : (multiplication(v6, v7) = v10 & multiplication(v5, v10) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v8, v7) = v9) | ~ (addition(v5, v6) = v8) | ? [v10] : ? [v11] : (multiplication(v6, v7) = v11 & multiplication(v5, v7) = v10 & addition(v10, v11) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v6, v7) = v8) | ~ (multiplication(v5, v8) = v9) | ? [v10] : (multiplication(v10, v7) = v9 & multiplication(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v5, v8) = v9) | ~ (addition(v6, v7) = v8) | ? [v10] : ? [v11] : (multiplication(v5, v7) = v11 & multiplication(v5, v6) = v10 & addition(v10, v11) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (addition(v8, v5) = v9) | ~ (addition(v7, v6) = v8) | ? [v10] : (addition(v7, v10) = v9 & addition(v6, v5) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (addition(v7, v8) = v9) | ~ (addition(v6, v5) = v8) | ? [v10] : (addition(v10, v5) = v9 & addition(v7, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (domain(v5) = v6) | ~ (multiplication(v6, v5) = v7) | ~ (addition(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (multiplication(v8, v7) = v6) | ~ (multiplication(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (addition(v8, v7) = v6) | ~ (addition(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (domain(v6) = v7) | ~ (multiplication(v5, v7) = v8) | ? [v9] : ? [v10] : (domain(v9) = v10 & domain(v8) = v10 & multiplication(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (addition(v5, v6) = v7) | ~ leq(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (domain(v7) = v6) | ~ (domain(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (domain(v5) = v6) | ~ (multiplication(v6, v5) = v7) | addition(v5, v7) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (multiplication(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : (domain(v10) = v8 & domain(v7) = v8 & domain(v6) = v9 & multiplication(v5, v9) = v10)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (addition(v6, v5) = v7) | addition(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (addition(v5, v6) = v7) | addition(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (addition(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : (domain(v7) = v8 & domain(v6) = v10 & domain(v5) = v9 & addition(v9, v10) = v8)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (multiplication(v5, one) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (multiplication(one, v5) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (addition(v5, v5) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (addition(v5, zero) = v6)) & ! [v5] : ! [v6] : (v6 = zero | ~ (multiplication(v5, zero) = v6)) & ! [v5] : ! [v6] : (v6 = zero | ~ (multiplication(zero, v5) = v6)) & ! [v5] : ! [v6] : ( ~ (domain(v5) = v6) | addition(v6, one) = one) & ! [v5] : ! [v6] : ( ~ (addition(v5, v6) = v6) | leq(v5, v6))) % 3.95/1.57 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 3.95/1.57 | (1) ~ (all_0_0_0 = all_0_1_1) & domain(all_0_3_3) = all_0_1_1 & domain(all_0_4_4) = all_0_2_2 & domain(zero) = zero & addition(all_0_2_2, all_0_1_1) = all_0_0_0 & addition(all_0_4_4, all_0_3_3) = all_0_3_3 & ! [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] : ( ~ (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ? [v5] : ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ? [v5] : ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (domain(v0) = v1) | ~ (multiplication(v1, v0) = v2) | ~ (addition(v0, v2) = v3)) & ! [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] : ! [v3] : ( ~ (domain(v1) = v2) | ~ (multiplication(v0, v2) = v3) | ? [v4] : ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (domain(v0) = v1) | ~ (multiplication(v1, v0) = v2) | addition(v0, v2) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3)) & ! [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(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 3.95/1.58 | % 3.95/1.58 | Applying alpha-rule on (1) yields: % 3.95/1.58 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (domain(v0) = v1) | ~ (multiplication(v1, v0) = v2) | ~ (addition(v0, v2) = v3)) % 3.95/1.58 | (3) ! [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)) % 3.95/1.58 | (4) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 3.95/1.58 | (5) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) % 3.95/1.58 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 3.95/1.58 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 3.95/1.58 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5)) % 3.95/1.58 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (domain(v1) = v2) | ~ (multiplication(v0, v2) = v3) | ? [v4] : ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4)) % 3.95/1.58 | (10) domain(all_0_4_4) = all_0_2_2 % 3.95/1.58 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 3.95/1.58 | (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)) % 3.95/1.58 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) % 3.95/1.58 | (14) ! [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)) % 3.95/1.58 | (15) addition(all_0_2_2, all_0_1_1) = all_0_0_0 % 3.95/1.58 | (16) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 3.95/1.58 | (17) ~ (all_0_0_0 = all_0_1_1) % 3.95/1.58 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 3.95/1.58 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 3.95/1.58 | (20) domain(all_0_3_3) = all_0_1_1 % 3.95/1.58 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) % 3.95/1.58 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 3.95/1.58 | (23) ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one) % 3.95/1.58 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 3.95/1.59 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 3.95/1.59 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 3.95/1.59 | (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)) % 3.95/1.59 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3)) % 3.95/1.59 | (29) domain(zero) = zero % 3.95/1.59 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 3.95/1.59 | (31) addition(all_0_4_4, all_0_3_3) = all_0_3_3 % 3.95/1.59 | (32) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 3.95/1.59 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (domain(v0) = v1) | ~ (multiplication(v1, v0) = v2) | addition(v0, v2) = v2) % 3.95/1.59 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5)) % 3.95/1.59 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 3.95/1.59 | % 3.95/1.59 | Instantiating formula (28) with all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms addition(all_0_4_4, all_0_3_3) = all_0_3_3, yields: % 3.95/1.59 | (36) ? [v0] : ? [v1] : ? [v2] : (domain(all_0_3_3) = v2 & domain(all_0_3_3) = v0 & domain(all_0_4_4) = v1 & addition(v1, v2) = v0) % 3.95/1.59 | % 3.95/1.59 | Instantiating (36) with all_11_0_6, all_11_1_7, all_11_2_8 yields: % 3.95/1.59 | (37) domain(all_0_3_3) = all_11_0_6 & domain(all_0_3_3) = all_11_2_8 & domain(all_0_4_4) = all_11_1_7 & addition(all_11_1_7, all_11_0_6) = all_11_2_8 % 3.95/1.59 | % 3.95/1.59 | Applying alpha-rule on (37) yields: % 3.95/1.59 | (38) domain(all_0_3_3) = all_11_0_6 % 3.95/1.59 | (39) domain(all_0_3_3) = all_11_2_8 % 3.95/1.59 | (40) domain(all_0_4_4) = all_11_1_7 % 3.95/1.59 | (41) addition(all_11_1_7, all_11_0_6) = all_11_2_8 % 3.95/1.59 | % 3.95/1.59 | Instantiating formula (13) with all_0_3_3, all_11_0_6, all_0_1_1 and discharging atoms domain(all_0_3_3) = all_11_0_6, domain(all_0_3_3) = all_0_1_1, yields: % 3.95/1.59 | (42) all_11_0_6 = all_0_1_1 % 3.95/1.59 | % 3.95/1.59 | Instantiating formula (13) with all_0_3_3, all_11_2_8, all_11_0_6 and discharging atoms domain(all_0_3_3) = all_11_0_6, domain(all_0_3_3) = all_11_2_8, yields: % 3.95/1.59 | (43) all_11_0_6 = all_11_2_8 % 3.95/1.59 | % 3.95/1.59 | Instantiating formula (13) with all_0_4_4, all_11_1_7, all_0_2_2 and discharging atoms domain(all_0_4_4) = all_11_1_7, domain(all_0_4_4) = all_0_2_2, yields: % 3.95/1.59 | (44) all_11_1_7 = all_0_2_2 % 3.95/1.59 | % 3.95/1.59 | Combining equations (42,43) yields a new equation: % 3.95/1.59 | (45) all_11_2_8 = all_0_1_1 % 3.95/1.59 | % 3.95/1.59 | Combining equations (45,43) yields a new equation: % 3.95/1.59 | (42) all_11_0_6 = all_0_1_1 % 3.95/1.59 | % 3.95/1.59 | From (44)(42)(45) and (41) follows: % 3.95/1.60 | (47) addition(all_0_2_2, all_0_1_1) = all_0_1_1 % 3.95/1.60 | % 3.95/1.60 | Instantiating formula (7) with all_0_2_2, all_0_1_1, all_0_1_1, all_0_0_0 and discharging atoms addition(all_0_2_2, all_0_1_1) = all_0_0_0, addition(all_0_2_2, all_0_1_1) = all_0_1_1, yields: % 3.95/1.60 | (48) all_0_0_0 = all_0_1_1 % 3.95/1.60 | % 3.95/1.60 | Equations (48) can reduce 17 to: % 3.95/1.60 | (49) $false % 3.95/1.60 | % 3.95/1.60 |-The branch is then unsatisfiable % 3.95/1.60 % SZS output end Proof for theBenchmark % 3.95/1.60 % 3.95/1.60 1003ms %------------------------------------------------------------------------------