%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE021+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n025.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 01:50:56 EDT 2022 % Result : Theorem 3.12s 1.42s % Output : Proof 4.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : KLE021+3 : TPTP v8.1.0. Released v4.0.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.15/0.35 % Computer : n025.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 600 % 0.15/0.35 % DateTime : Thu Jun 16 10:25:26 EDT 2022 % 0.15/0.35 % CPUTime : % 0.56/0.61 ____ _ % 0.56/0.61 ___ / __ \_____(_)___ ________ __________ % 0.56/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.56/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.56/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.56/0.61 % 0.56/0.61 A Theorem Prover for First-Order Logic % 0.56/0.61 (ePrincess v.1.0) % 0.56/0.61 % 0.56/0.61 (c) Philipp Rümmer, 2009-2015 % 0.56/0.61 (c) Peter Backeman, 2014-2015 % 0.56/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.56/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.56/0.61 Bug reports to peter@backeman.se % 0.56/0.61 % 0.56/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.56/0.61 % 0.56/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.68/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.60/0.97 Prover 0: Preprocessing ... % 2.51/1.27 Prover 0: Constructing countermodel ... % 3.12/1.42 Prover 0: proved (751ms) % 3.12/1.42 % 3.12/1.42 No countermodel exists, formula is valid % 3.12/1.42 % SZS status Theorem for theBenchmark % 3.12/1.42 % 3.12/1.42 Generating proof ... found it (size 19) % 4.39/1.70 % 4.39/1.70 % SZS output start Proof for theBenchmark % 4.39/1.70 Assumed formulas after preprocessing and simplification: % 4.39/1.70 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v0) & c(v1) = v3 & multiplication(v3, v0) = v4 & multiplication(v1, v0) = v2 & addition(v2, v4) = v5 & test(v1) & ! [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] : ( ~ (c(v7) = v9) | ~ (c(v6) = v8) | ~ (multiplication(v8, v9) = v10) | ~ test(v7) | ~ test(v6) | ? [v11] : (c(v11) = v10 & addition(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (c(v7) = v9) | ~ (c(v6) = v8) | ~ (addition(v8, v9) = v10) | ~ test(v7) | ~ test(v6) | ? [v11] : (c(v11) = v10 & multiplication(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] : (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] : (v8 = v7 | ~ (c(v6) = v8) | ~ complement(v6, v7) | ~ test(v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (addition(v6, v7) = v8) | ~ leq(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : (v8 = one | ~ (addition(v6, v7) = v8) | ~ complement(v7, v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = zero | ~ (multiplication(v7, v6) = v8) | ~ complement(v7, v6)) & ! [v6] : ! [v7] : ! [v8] : (v8 = zero | ~ (multiplication(v6, v7) = v8) | ~ complement(v7, v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (c(v8) = v7) | ~ (c(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v7, v6) = v8) | ~ complement(v7, v6) | (multiplication(v6, v7) = zero & addition(v6, v7) = one)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v6, v7) = v8) | ~ complement(v7, v6) | (multiplication(v7, v6) = zero & addition(v6, v7) = one)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v6, v7) = v8) | ~ test(v7) | ~ test(v6) | ? [v9] : ? [v10] : ? [v11] : (c(v8) = v9 & c(v7) = v11 & c(v6) = v10 & addition(v10, v11) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v7, v6) = v8) | addition(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v6, v7) = v8) | ~ complement(v7, v6) | (multiplication(v7, v6) = zero & multiplication(v6, v7) = zero)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v6, v7) = v8) | ~ test(v7) | ~ test(v6) | ? [v9] : ? [v10] : ? [v11] : (c(v8) = v9 & c(v7) = v11 & c(v6) = v10 & multiplication(v10, v11) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v6, v7) = v8) | addition(v7, v6) = v8) & ! [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 | ~ (c(v6) = v7) | test(v6)) & ! [v6] : ! [v7] : (v7 = zero | ~ (multiplication(v6, zero) = v7)) & ! [v6] : ! [v7] : (v7 = zero | ~ (multiplication(zero, v6) = v7)) & ! [v6] : ! [v7] : ( ~ (c(v6) = v7) | ~ test(v6) | complement(v6, v7)) & ! [v6] : ! [v7] : ( ~ (multiplication(v7, v6) = zero) | complement(v7, v6) | ? [v8] : ? [v9] : (multiplication(v6, v7) = v8 & addition(v6, v7) = v9 & ( ~ (v9 = one) | ~ (v8 = zero)))) & ! [v6] : ! [v7] : ( ~ (multiplication(v6, v7) = zero) | complement(v7, v6) | ? [v8] : ? [v9] : (multiplication(v7, v6) = v8 & addition(v6, v7) = v9 & ( ~ (v9 = one) | ~ (v8 = zero)))) & ! [v6] : ! [v7] : ( ~ (addition(v6, v7) = v7) | leq(v6, v7)) & ! [v6] : ! [v7] : ( ~ (addition(v6, v7) = one) | complement(v7, v6) | ? [v8] : ? [v9] : (multiplication(v7, v6) = v9 & multiplication(v6, v7) = v8 & ( ~ (v9 = zero) | ~ (v8 = zero)))) & ! [v6] : ! [v7] : ( ~ complement(v7, v6) | test(v6)) & ! [v6] : ( ~ test(v6) | ? [v7] : complement(v7, v6))) % 4.39/1.75 | 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: % 4.39/1.75 | (1) ~ (all_0_0_0 = all_0_5_5) & c(all_0_4_4) = all_0_2_2 & multiplication(all_0_2_2, all_0_5_5) = all_0_1_1 & multiplication(all_0_4_4, all_0_5_5) = all_0_3_3 & addition(all_0_3_3, all_0_1_1) = all_0_0_0 & test(all_0_4_4) & ! [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] : ( ~ (c(v1) = v3) | ~ (c(v0) = v2) | ~ (multiplication(v2, v3) = v4) | ~ test(v1) | ~ test(v0) | ? [v5] : (c(v5) = v4 & addition(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (c(v1) = v3) | ~ (c(v0) = v2) | ~ (addition(v2, v3) = v4) | ~ test(v1) | ~ test(v0) | ? [v5] : (c(v5) = v4 & multiplication(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] : (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 | ~ (c(v0) = v2) | ~ complement(v0, v1) | ~ test(v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = one | ~ (addition(v0, v1) = v2) | ~ complement(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ~ test(v1) | ~ test(v0) | ? [v3] : ? [v4] : ? [v5] : (c(v2) = v3 & c(v1) = v5 & c(v0) = v4 & addition(v4, v5) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ~ test(v1) | ~ test(v0) | ? [v3] : ? [v4] : ? [v5] : (c(v2) = v3 & c(v1) = v5 & c(v0) = v4 & multiplication(v4, v5) = v3)) & ! [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 | ~ (c(v0) = v1) | test(v0)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (c(v0) = v1) | ~ test(v0) | complement(v0, v1)) & ! [v0] : ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) & ! [v0] : ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) | ~ (v2 = zero)))) & ! [v0] : ! [v1] : ( ~ complement(v1, v0) | test(v0)) & ! [v0] : ( ~ test(v0) | ? [v1] : complement(v1, v0)) % 4.39/1.76 | % 4.39/1.76 | Applying alpha-rule on (1) yields: % 4.39/1.76 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) % 4.39/1.76 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 4.39/1.76 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ~ test(v1) | ~ test(v0) | ? [v3] : ? [v4] : ? [v5] : (c(v2) = v3 & c(v1) = v5 & c(v0) = v4 & addition(v4, v5) = v3)) % 4.39/1.76 | (5) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) % 4.39/1.76 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 4.39/1.76 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ~ test(v1) | ~ test(v0) | ? [v3] : ? [v4] : ? [v5] : (c(v2) = v3 & c(v1) = v5 & c(v0) = v4 & multiplication(v4, v5) = v3)) % 4.39/1.76 | (8) c(all_0_4_4) = all_0_2_2 % 4.39/1.76 | (9) ! [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)) % 4.39/1.76 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0)) % 4.39/1.76 | (11) ! [v0] : ! [v1] : (v1 = zero | ~ (c(v0) = v1) | test(v0)) % 4.39/1.76 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (c(v1) = v3) | ~ (c(v0) = v2) | ~ (addition(v2, v3) = v4) | ~ test(v1) | ~ test(v0) | ? [v5] : (c(v5) = v4 & multiplication(v0, v1) = v5)) % 4.39/1.77 | (13) multiplication(all_0_2_2, all_0_5_5) = all_0_1_1 % 4.39/1.77 | (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)) % 4.39/1.77 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 4.39/1.77 | (16) ! [v0] : ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) % 4.39/1.77 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 4.39/1.77 | (18) ! [v0] : ( ~ test(v0) | ? [v1] : complement(v1, v0)) % 4.39/1.77 | (19) ~ (all_0_0_0 = all_0_5_5) % 4.39/1.77 | (20) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 4.39/1.77 | (21) test(all_0_4_4) % 4.39/1.77 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 4.39/1.77 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) % 4.39/1.77 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = one | ~ (addition(v0, v1) = v2) | ~ complement(v1, v0)) % 4.39/1.77 | (25) ! [v0] : ! [v1] : ( ~ (c(v0) = v1) | ~ test(v0) | complement(v0, v1)) % 4.39/1.77 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (c(v0) = v2) | ~ complement(v0, v1) | ~ test(v0)) % 4.39/1.77 | (27) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) | ~ (v2 = zero)))) % 4.39/1.77 | (28) ! [v0] : ! [v1] : ( ~ complement(v1, v0) | test(v0)) % 4.39/1.77 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 4.39/1.77 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 4.39/1.77 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (c(v1) = v3) | ~ (c(v0) = v2) | ~ (multiplication(v2, v3) = v4) | ~ test(v1) | ~ test(v0) | ? [v5] : (c(v5) = v4 & addition(v0, v1) = v5)) % 4.39/1.77 | (32) ! [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)) % 4.39/1.77 | (33) ! [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)) % 4.39/1.77 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 4.39/1.77 | (35) multiplication(all_0_4_4, all_0_5_5) = all_0_3_3 % 4.39/1.77 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 4.39/1.77 | (37) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 4.39/1.77 | (38) addition(all_0_3_3, all_0_1_1) = all_0_0_0 % 4.39/1.77 | (39) ! [v0] : ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) % 4.39/1.78 | (40) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0)) % 4.39/1.78 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero)) % 4.76/1.78 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 4.76/1.78 | (43) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 4.76/1.78 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one)) % 4.76/1.78 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one)) % 4.76/1.78 | (46) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 4.76/1.78 | % 4.76/1.78 | Instantiating formula (32) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_5_5, all_0_2_2, all_0_4_4 and discharging atoms multiplication(all_0_2_2, all_0_5_5) = all_0_1_1, multiplication(all_0_4_4, all_0_5_5) = all_0_3_3, addition(all_0_3_3, all_0_1_1) = all_0_0_0, yields: % 4.76/1.78 | (47) ? [v0] : (multiplication(v0, all_0_5_5) = all_0_0_0 & addition(all_0_4_4, all_0_2_2) = v0) % 4.76/1.78 | % 4.76/1.78 | Instantiating formula (30) with all_0_0_0, all_0_3_3, all_0_1_1 and discharging atoms addition(all_0_3_3, all_0_1_1) = all_0_0_0, yields: % 4.76/1.78 | (48) addition(all_0_1_1, all_0_3_3) = all_0_0_0 % 4.76/1.78 | % 4.76/1.78 | Instantiating formula (25) with all_0_2_2, all_0_4_4 and discharging atoms c(all_0_4_4) = all_0_2_2, test(all_0_4_4), yields: % 4.76/1.78 | (49) complement(all_0_4_4, all_0_2_2) % 4.76/1.78 | % 4.76/1.78 | Instantiating (47) with all_11_0_7 yields: % 4.76/1.78 | (50) multiplication(all_11_0_7, all_0_5_5) = all_0_0_0 & addition(all_0_4_4, all_0_2_2) = all_11_0_7 % 4.76/1.78 | % 4.76/1.78 | Applying alpha-rule on (50) yields: % 4.76/1.78 | (51) multiplication(all_11_0_7, all_0_5_5) = all_0_0_0 % 4.76/1.78 | (52) addition(all_0_4_4, all_0_2_2) = all_11_0_7 % 4.76/1.78 | % 4.76/1.78 | Instantiating formula (32) with all_0_0_0, all_0_3_3, all_0_1_1, all_0_5_5, all_0_4_4, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_5_5) = all_0_1_1, multiplication(all_0_4_4, all_0_5_5) = all_0_3_3, addition(all_0_1_1, all_0_3_3) = all_0_0_0, yields: % 4.76/1.78 | (53) ? [v0] : (multiplication(v0, all_0_5_5) = all_0_0_0 & addition(all_0_2_2, all_0_4_4) = v0) % 4.76/1.78 | % 4.76/1.78 | Instantiating formula (30) with all_11_0_7, all_0_4_4, all_0_2_2 and discharging atoms addition(all_0_4_4, all_0_2_2) = all_11_0_7, yields: % 4.76/1.78 | (54) addition(all_0_2_2, all_0_4_4) = all_11_0_7 % 4.76/1.78 | % 4.76/1.78 | Instantiating (53) with all_19_0_8 yields: % 4.76/1.78 | (55) multiplication(all_19_0_8, all_0_5_5) = all_0_0_0 & addition(all_0_2_2, all_0_4_4) = all_19_0_8 % 4.76/1.78 | % 4.76/1.78 | Applying alpha-rule on (55) yields: % 4.76/1.78 | (56) multiplication(all_19_0_8, all_0_5_5) = all_0_0_0 % 4.76/1.78 | (57) addition(all_0_2_2, all_0_4_4) = all_19_0_8 % 4.76/1.78 | % 4.76/1.78 | Instantiating formula (24) with all_19_0_8, all_0_4_4, all_0_2_2 and discharging atoms addition(all_0_2_2, all_0_4_4) = all_19_0_8, complement(all_0_4_4, all_0_2_2), yields: % 4.76/1.78 | (58) all_19_0_8 = one % 4.76/1.78 | % 4.76/1.78 | Instantiating formula (6) with all_0_2_2, all_0_4_4, all_11_0_7, all_19_0_8 and discharging atoms addition(all_0_2_2, all_0_4_4) = all_19_0_8, addition(all_0_2_2, all_0_4_4) = all_11_0_7, yields: % 4.76/1.78 | (59) all_19_0_8 = all_11_0_7 % 4.76/1.78 | % 4.76/1.78 | Combining equations (59,58) yields a new equation: % 4.76/1.78 | (60) all_11_0_7 = one % 4.76/1.78 | % 4.76/1.78 | Simplifying 60 yields: % 4.76/1.78 | (61) all_11_0_7 = one % 4.76/1.78 | % 4.76/1.78 | From (61) and (51) follows: % 4.76/1.79 | (62) multiplication(one, all_0_5_5) = all_0_0_0 % 4.76/1.79 | % 4.76/1.79 | Instantiating formula (46) with all_0_0_0, all_0_5_5 and discharging atoms multiplication(one, all_0_5_5) = all_0_0_0, yields: % 4.76/1.79 | (63) all_0_0_0 = all_0_5_5 % 4.76/1.79 | % 4.76/1.79 | Equations (63) can reduce 19 to: % 4.76/1.79 | (64) $false % 4.76/1.79 | % 4.76/1.79 |-The branch is then unsatisfiable % 4.76/1.79 % SZS output end Proof for theBenchmark % 4.76/1.79 % 4.76/1.79 1162ms %------------------------------------------------------------------------------