%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE064+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n016.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 01:51:12 EDT 2022 % Result : Theorem 3.38s 1.46s % Output : Proof 5.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : KLE064+1 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n016.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % 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 10:03:04 EDT 2022 % 0.12/0.34 % CPUTime : % 0.53/0.59 ____ _ % 0.53/0.59 ___ / __ \_____(_)___ ________ __________ % 0.53/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.53/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.53/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.53/0.59 % 0.53/0.59 A Theorem Prover for First-Order Logic % 0.53/0.59 (ePrincess v.1.0) % 0.53/0.59 % 0.53/0.59 (c) Philipp Rümmer, 2009-2015 % 0.53/0.59 (c) Peter Backeman, 2014-2015 % 0.53/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.53/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.53/0.59 Bug reports to peter@backeman.se % 0.53/0.59 % 0.53/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.53/0.59 % 0.53/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.47/0.92 Prover 0: Preprocessing ... % 2.32/1.18 Prover 0: Constructing countermodel ... % 3.38/1.45 Prover 0: proved (814ms) % 3.38/1.46 % 3.38/1.46 No countermodel exists, formula is valid % 3.38/1.46 % SZS status Theorem for theBenchmark % 3.38/1.46 % 3.38/1.46 Generating proof ... found it (size 28) % 5.39/1.95 % 5.39/1.95 % SZS output start Proof for theBenchmark % 5.39/1.95 Assumed formulas after preprocessing and simplification: % 5.39/1.95 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & domain(v1) = v3 & domain(v0) = v2 & domain(zero) = zero & multiplication(v3, v0) = v4 & addition(v2, v3) = v3 & addition(v0, v4) = v5 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (multiplication(v7, v8) = v10) | ~ (multiplication(v6, v8) = v9) | ~ (addition(v9, v10) = v11) | ? [v12] : (multiplication(v12, v8) = v11 & addition(v6, v7) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (multiplication(v6, v8) = v10) | ~ (multiplication(v6, v7) = v9) | ~ (addition(v9, v10) = v11) | ? [v12] : (multiplication(v6, v12) = v11 & addition(v7, v8) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (domain(v7) = v9) | ~ (domain(v6) = v8) | ~ (addition(v8, v9) = v10) | ? [v11] : (domain(v11) = v10 & addition(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v9, v8) = v10) | ~ (multiplication(v6, v7) = v9) | ? [v11] : (multiplication(v7, v8) = v11 & multiplication(v6, v11) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v9, v8) = v10) | ~ (addition(v6, v7) = v9) | ? [v11] : ? [v12] : (multiplication(v7, v8) = v12 & multiplication(v6, v8) = v11 & addition(v11, v12) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v7, v8) = v9) | ~ (multiplication(v6, v9) = v10) | ? [v11] : (multiplication(v11, v8) = v10 & multiplication(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v6, v9) = v10) | ~ (addition(v7, v8) = v9) | ? [v11] : ? [v12] : (multiplication(v6, v8) = v12 & multiplication(v6, v7) = v11 & addition(v11, v12) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (addition(v9, v6) = v10) | ~ (addition(v8, v7) = v9) | ? [v11] : (addition(v8, v11) = v10 & addition(v7, v6) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (addition(v8, v9) = v10) | ~ (addition(v7, v6) = v9) | ? [v11] : (addition(v11, v6) = v10 & addition(v8, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | ~ (domain(v6) = v7) | ~ (multiplication(v7, v6) = v8) | ~ (addition(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (multiplication(v9, v8) = v7) | ~ (multiplication(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (addition(v9, v8) = v7) | ~ (addition(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (domain(v7) = v8) | ~ (multiplication(v6, v8) = v9) | ? [v10] : ? [v11] : (domain(v10) = v11 & domain(v9) = v11 & multiplication(v6, v7) = v10)) & ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (addition(v6, v7) = v8) | ~ leq(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (domain(v8) = v7) | ~ (domain(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (domain(v6) = v7) | ~ (multiplication(v7, v6) = v8) | addition(v6, v8) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (domain(v11) = v9 & domain(v8) = v9 & domain(v7) = v10 & multiplication(v6, v10) = v11)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v7, v6) = v8) | addition(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v6, v7) = v8) | addition(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (domain(v8) = v9 & domain(v7) = v11 & domain(v6) = v10 & addition(v10, v11) = v9)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (multiplication(v6, one) = v7)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (multiplication(one, v6) = v7)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (addition(v6, v6) = v7)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (addition(v6, zero) = v7)) & ! [v6] : ! [v7] : (v7 = zero | ~ (multiplication(v6, zero) = v7)) & ! [v6] : ! [v7] : (v7 = zero | ~ (multiplication(zero, v6) = v7)) & ! [v6] : ! [v7] : ( ~ (domain(v6) = v7) | addition(v7, one) = one) & ! [v6] : ! [v7] : ( ~ (addition(v6, v7) = v7) | leq(v6, v7))) % 5.71/1.99 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields: % 5.71/1.99 | (1) ~ (all_0_0_0 = all_0_1_1) & domain(all_0_4_4) = all_0_2_2 & domain(all_0_5_5) = all_0_3_3 & domain(zero) = zero & multiplication(all_0_2_2, all_0_5_5) = all_0_1_1 & addition(all_0_3_3, all_0_2_2) = all_0_2_2 & addition(all_0_5_5, all_0_1_1) = 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] : ( ~ (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)) % 5.71/2.00 | % 5.71/2.00 | Applying alpha-rule on (1) yields: % 5.71/2.00 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3)) % 5.71/2.00 | (3) ~ (all_0_0_0 = all_0_1_1) % 5.71/2.00 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 5.71/2.00 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 5.71/2.00 | (6) domain(zero) = zero % 5.71/2.00 | (7) domain(all_0_5_5) = all_0_3_3 % 5.71/2.00 | (8) domain(all_0_4_4) = all_0_2_2 % 5.71/2.00 | (9) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 5.71/2.00 | (10) addition(all_0_3_3, all_0_2_2) = all_0_2_2 % 5.71/2.00 | (11) ! [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)) % 5.71/2.00 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 5.71/2.00 | (13) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) % 5.71/2.00 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 5.71/2.01 | (15) addition(all_0_5_5, all_0_1_1) = all_0_0_0 % 5.71/2.01 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 5.71/2.01 | (17) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 5.71/2.01 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) % 5.71/2.01 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 5.71/2.01 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 5.71/2.01 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5)) % 5.71/2.01 | (22) multiplication(all_0_2_2, all_0_5_5) = all_0_1_1 % 5.71/2.01 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 5.71/2.01 | (24) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 5.71/2.01 | (25) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 5.71/2.01 | (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)) % 5.71/2.01 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (domain(v1) = v2) | ~ (multiplication(v0, v2) = v3) | ? [v4] : ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4)) % 5.71/2.01 | (28) ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one) % 5.71/2.01 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) % 5.71/2.01 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5)) % 5.71/2.01 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (domain(v0) = v1) | ~ (multiplication(v1, v0) = v2) | addition(v0, v2) = v2) % 5.71/2.01 | (32) ! [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)) % 5.71/2.01 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (domain(v0) = v1) | ~ (multiplication(v1, v0) = v2) | ~ (addition(v0, v2) = v3)) % 5.71/2.01 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 5.71/2.01 | (35) ! [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)) % 5.71/2.01 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 5.71/2.01 | % 5.71/2.01 | Instantiating formula (21) with all_0_1_1, all_0_5_5, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_5_5) = all_0_1_1, yields: % 5.71/2.01 | (37) ? [v0] : ? [v1] : ? [v2] : (domain(v2) = v0 & domain(all_0_1_1) = v0 & domain(all_0_5_5) = v1 & multiplication(all_0_2_2, v1) = v2) % 5.71/2.01 | % 5.71/2.01 | Instantiating formula (11) with all_0_1_1, all_0_2_2, all_0_5_5, all_0_2_2, all_0_3_3 and discharging atoms multiplication(all_0_2_2, all_0_5_5) = all_0_1_1, addition(all_0_3_3, all_0_2_2) = all_0_2_2, yields: % 5.71/2.01 | (38) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_0_5_5) = v1 & multiplication(all_0_3_3, all_0_5_5) = v0 & addition(v0, v1) = all_0_1_1) % 5.71/2.02 | % 5.71/2.02 | Instantiating formula (2) with all_0_0_0, all_0_1_1, all_0_5_5 and discharging atoms addition(all_0_5_5, all_0_1_1) = all_0_0_0, yields: % 5.71/2.02 | (39) ? [v0] : ? [v1] : ? [v2] : (domain(all_0_0_0) = v0 & domain(all_0_1_1) = v2 & domain(all_0_5_5) = v1 & addition(v1, v2) = v0) % 5.71/2.02 | % 5.71/2.02 | Instantiating (39) with all_11_0_7, all_11_1_8, all_11_2_9 yields: % 5.71/2.02 | (40) domain(all_0_0_0) = all_11_2_9 & domain(all_0_1_1) = all_11_0_7 & domain(all_0_5_5) = all_11_1_8 & addition(all_11_1_8, all_11_0_7) = all_11_2_9 % 5.71/2.02 | % 5.71/2.02 | Applying alpha-rule on (40) yields: % 5.71/2.02 | (41) domain(all_0_0_0) = all_11_2_9 % 5.71/2.02 | (42) domain(all_0_1_1) = all_11_0_7 % 5.71/2.02 | (43) domain(all_0_5_5) = all_11_1_8 % 5.71/2.02 | (44) addition(all_11_1_8, all_11_0_7) = all_11_2_9 % 5.71/2.02 | % 5.71/2.02 | Instantiating (38) with all_15_0_11, all_15_1_12 yields: % 5.71/2.02 | (45) multiplication(all_0_2_2, all_0_5_5) = all_15_0_11 & multiplication(all_0_3_3, all_0_5_5) = all_15_1_12 & addition(all_15_1_12, all_15_0_11) = all_0_1_1 % 5.71/2.02 | % 5.71/2.02 | Applying alpha-rule on (45) yields: % 5.71/2.02 | (46) multiplication(all_0_2_2, all_0_5_5) = all_15_0_11 % 5.71/2.02 | (47) multiplication(all_0_3_3, all_0_5_5) = all_15_1_12 % 5.71/2.02 | (48) addition(all_15_1_12, all_15_0_11) = all_0_1_1 % 5.71/2.02 | % 5.71/2.02 | Instantiating (37) with all_17_0_13, all_17_1_14, all_17_2_15 yields: % 5.71/2.02 | (49) domain(all_17_0_13) = all_17_2_15 & domain(all_0_1_1) = all_17_2_15 & domain(all_0_5_5) = all_17_1_14 & multiplication(all_0_2_2, all_17_1_14) = all_17_0_13 % 5.71/2.02 | % 5.71/2.02 | Applying alpha-rule on (49) yields: % 5.71/2.02 | (50) domain(all_17_0_13) = all_17_2_15 % 5.71/2.02 | (51) domain(all_0_1_1) = all_17_2_15 % 5.71/2.02 | (52) domain(all_0_5_5) = all_17_1_14 % 5.71/2.02 | (53) multiplication(all_0_2_2, all_17_1_14) = all_17_0_13 % 5.71/2.02 | % 5.71/2.02 | Instantiating formula (18) with all_0_5_5, all_17_1_14, all_0_3_3 and discharging atoms domain(all_0_5_5) = all_17_1_14, domain(all_0_5_5) = all_0_3_3, yields: % 5.71/2.02 | (54) all_17_1_14 = all_0_3_3 % 5.71/2.02 | % 5.71/2.02 | Instantiating formula (18) with all_0_5_5, all_11_1_8, all_17_1_14 and discharging atoms domain(all_0_5_5) = all_17_1_14, domain(all_0_5_5) = all_11_1_8, yields: % 5.71/2.02 | (55) all_17_1_14 = all_11_1_8 % 5.71/2.02 | % 5.71/2.02 | Instantiating formula (16) with all_0_2_2, all_0_5_5, all_15_0_11, all_0_1_1 and discharging atoms multiplication(all_0_2_2, all_0_5_5) = all_15_0_11, multiplication(all_0_2_2, all_0_5_5) = all_0_1_1, yields: % 5.71/2.02 | (56) all_15_0_11 = all_0_1_1 % 5.71/2.02 | % 5.71/2.02 | Combining equations (55,54) yields a new equation: % 5.71/2.02 | (57) all_11_1_8 = all_0_3_3 % 5.71/2.02 | % 5.71/2.02 | Simplifying 57 yields: % 5.71/2.02 | (58) all_11_1_8 = all_0_3_3 % 5.71/2.02 | % 5.71/2.02 | From (58) and (43) follows: % 5.71/2.02 | (7) domain(all_0_5_5) = all_0_3_3 % 5.71/2.02 | % 5.71/2.02 | From (56) and (48) follows: % 5.71/2.02 | (60) addition(all_15_1_12, all_0_1_1) = all_0_1_1 % 5.71/2.02 | % 5.71/2.02 | Instantiating formula (31) with all_15_1_12, all_0_3_3, all_0_5_5 and discharging atoms domain(all_0_5_5) = all_0_3_3, multiplication(all_0_3_3, all_0_5_5) = all_15_1_12, yields: % 5.71/2.02 | (61) addition(all_0_5_5, all_15_1_12) = all_15_1_12 % 5.71/2.02 | % 5.71/2.02 | Instantiating formula (23) with all_0_0_0, all_0_1_1, all_0_5_5, all_15_1_12, all_0_1_1 and discharging atoms addition(all_15_1_12, all_0_1_1) = all_0_1_1, addition(all_0_5_5, all_0_1_1) = all_0_0_0, yields: % 5.71/2.02 | (62) ? [v0] : (addition(v0, all_0_1_1) = all_0_0_0 & addition(all_0_5_5, all_15_1_12) = v0) % 5.71/2.02 | % 5.71/2.02 | Instantiating formula (25) with all_0_1_1, all_15_1_12 and discharging atoms addition(all_15_1_12, all_0_1_1) = all_0_1_1, yields: % 5.71/2.02 | (63) leq(all_15_1_12, all_0_1_1) % 5.71/2.02 | % 5.71/2.02 | Instantiating (62) with all_71_0_56 yields: % 5.71/2.02 | (64) addition(all_71_0_56, all_0_1_1) = all_0_0_0 & addition(all_0_5_5, all_15_1_12) = all_71_0_56 % 5.71/2.02 | % 5.71/2.02 | Applying alpha-rule on (64) yields: % 5.71/2.02 | (65) addition(all_71_0_56, all_0_1_1) = all_0_0_0 % 5.71/2.02 | (66) addition(all_0_5_5, all_15_1_12) = all_71_0_56 % 5.71/2.02 | % 5.71/2.02 | Instantiating formula (4) with all_0_5_5, all_15_1_12, all_15_1_12, all_71_0_56 and discharging atoms addition(all_0_5_5, all_15_1_12) = all_71_0_56, addition(all_0_5_5, all_15_1_12) = all_15_1_12, yields: % 5.71/2.02 | (67) all_71_0_56 = all_15_1_12 % 5.71/2.02 | % 5.71/2.02 | From (67) and (65) follows: % 5.71/2.02 | (68) addition(all_15_1_12, all_0_1_1) = all_0_0_0 % 5.71/2.02 | % 5.71/2.02 | Instantiating formula (29) with all_0_0_0, all_0_1_1, all_15_1_12 and discharging atoms addition(all_15_1_12, all_0_1_1) = all_0_0_0, leq(all_15_1_12, all_0_1_1), yields: % 5.71/2.02 | (69) all_0_0_0 = all_0_1_1 % 5.71/2.02 | % 5.71/2.02 | Equations (69) can reduce 3 to: % 5.71/2.02 | (70) $false % 5.71/2.02 | % 5.71/2.03 |-The branch is then unsatisfiable % 5.71/2.03 % SZS output end Proof for theBenchmark % 5.71/2.03 % 5.71/2.03 1424ms %------------------------------------------------------------------------------