%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE007+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n003.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 01:50:48 EDT 2022 % Result : Theorem 3.16s 1.39s % Output : Proof 4.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : KLE007+3 : TPTP v8.1.0. Released v4.0.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n003.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 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Thu Jun 16 11:57:11 EDT 2022 % 0.12/0.33 % CPUTime : % 0.49/0.58 ____ _ % 0.49/0.58 ___ / __ \_____(_)___ ________ __________ % 0.49/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.49/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.49/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.49/0.58 % 0.49/0.58 A Theorem Prover for First-Order Logic % 0.49/0.58 (ePrincess v.1.0) % 0.49/0.58 % 0.49/0.58 (c) Philipp Rümmer, 2009-2015 % 0.49/0.58 (c) Peter Backeman, 2014-2015 % 0.49/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.49/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.49/0.58 Bug reports to peter@backeman.se % 0.49/0.58 % 0.49/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.49/0.58 % 0.49/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.35/0.93 Prover 0: Preprocessing ... % 2.38/1.22 Prover 0: Constructing countermodel ... % 3.16/1.39 Prover 0: proved (760ms) % 3.16/1.39 % 3.16/1.39 No countermodel exists, formula is valid % 3.16/1.39 % SZS status Theorem for theBenchmark % 3.16/1.39 % 3.16/1.39 Generating proof ... found it (size 15) % 4.19/1.60 % 4.19/1.60 % SZS output start Proof for theBenchmark % 4.19/1.61 Assumed formulas after preprocessing and simplification: % 4.19/1.61 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = one) & c(v1) = v5 & c(v0) = v2 & multiplication(v3, v5) = v6 & multiplication(v3, v1) = v4 & addition(v4, v6) = v7 & addition(v0, v2) = v3 & test(v1) & test(v0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (multiplication(v9, v10) = v12) | ~ (multiplication(v8, v10) = v11) | ~ (addition(v11, v12) = v13) | ? [v14] : (multiplication(v14, v10) = v13 & addition(v8, v9) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (multiplication(v8, v10) = v12) | ~ (multiplication(v8, v9) = v11) | ~ (addition(v11, v12) = v13) | ? [v14] : (multiplication(v8, v14) = v13 & addition(v9, v10) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (c(v9) = v11) | ~ (c(v8) = v10) | ~ (multiplication(v10, v11) = v12) | ~ test(v9) | ~ test(v8) | ? [v13] : (c(v13) = v12 & addition(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (c(v9) = v11) | ~ (c(v8) = v10) | ~ (addition(v10, v11) = v12) | ~ test(v9) | ~ test(v8) | ? [v13] : (c(v13) = v12 & multiplication(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (multiplication(v11, v10) = v12) | ~ (multiplication(v8, v9) = v11) | ? [v13] : (multiplication(v9, v10) = v13 & multiplication(v8, v13) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (multiplication(v11, v10) = v12) | ~ (addition(v8, v9) = v11) | ? [v13] : ? [v14] : (multiplication(v9, v10) = v14 & multiplication(v8, v10) = v13 & addition(v13, v14) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (multiplication(v9, v10) = v11) | ~ (multiplication(v8, v11) = v12) | ? [v13] : (multiplication(v13, v10) = v12 & multiplication(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (multiplication(v8, v11) = v12) | ~ (addition(v9, v10) = v11) | ? [v13] : ? [v14] : (multiplication(v8, v10) = v14 & multiplication(v8, v9) = v13 & addition(v13, v14) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (addition(v11, v8) = v12) | ~ (addition(v10, v9) = v11) | ? [v13] : (addition(v10, v13) = v12 & addition(v9, v8) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (addition(v10, v11) = v12) | ~ (addition(v9, v8) = v11) | ? [v13] : (addition(v13, v8) = v12 & addition(v10, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (multiplication(v11, v10) = v9) | ~ (multiplication(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (addition(v11, v10) = v9) | ~ (addition(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (c(v8) = v10) | ~ complement(v8, v9) | ~ test(v8)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (addition(v8, v9) = v10) | ~ leq(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : (v10 = one | ~ (addition(v8, v9) = v10) | ~ complement(v9, v8)) & ! [v8] : ! [v9] : ! [v10] : (v10 = zero | ~ (multiplication(v9, v8) = v10) | ~ complement(v9, v8)) & ! [v8] : ! [v9] : ! [v10] : (v10 = zero | ~ (multiplication(v8, v9) = v10) | ~ complement(v9, v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (c(v10) = v9) | ~ (c(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v9, v8) = v10) | ~ complement(v9, v8) | (multiplication(v8, v9) = zero & addition(v8, v9) = one)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v8, v9) = v10) | ~ complement(v9, v8) | (multiplication(v9, v8) = zero & addition(v8, v9) = one)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v8, v9) = v10) | ~ test(v9) | ~ test(v8) | ? [v11] : ? [v12] : ? [v13] : (c(v10) = v11 & c(v9) = v13 & c(v8) = v12 & addition(v12, v13) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (addition(v9, v8) = v10) | addition(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (addition(v8, v9) = v10) | ~ complement(v9, v8) | (multiplication(v9, v8) = zero & multiplication(v8, v9) = zero)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (addition(v8, v9) = v10) | ~ test(v9) | ~ test(v8) | ? [v11] : ? [v12] : ? [v13] : (c(v10) = v11 & c(v9) = v13 & c(v8) = v12 & multiplication(v12, v13) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (addition(v8, v9) = v10) | addition(v9, v8) = v10) & ! [v8] : ! [v9] : (v9 = v8 | ~ (multiplication(v8, one) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (multiplication(one, v8) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (addition(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (addition(v8, zero) = v9)) & ! [v8] : ! [v9] : (v9 = zero | ~ (c(v8) = v9) | test(v8)) & ! [v8] : ! [v9] : (v9 = zero | ~ (multiplication(v8, zero) = v9)) & ! [v8] : ! [v9] : (v9 = zero | ~ (multiplication(zero, v8) = v9)) & ! [v8] : ! [v9] : ( ~ (c(v8) = v9) | ~ test(v8) | complement(v8, v9)) & ! [v8] : ! [v9] : ( ~ (multiplication(v9, v8) = zero) | complement(v9, v8) | ? [v10] : ? [v11] : (multiplication(v8, v9) = v10 & addition(v8, v9) = v11 & ( ~ (v11 = one) | ~ (v10 = zero)))) & ! [v8] : ! [v9] : ( ~ (multiplication(v8, v9) = zero) | complement(v9, v8) | ? [v10] : ? [v11] : (multiplication(v9, v8) = v10 & addition(v8, v9) = v11 & ( ~ (v11 = one) | ~ (v10 = zero)))) & ! [v8] : ! [v9] : ( ~ (addition(v8, v9) = v9) | leq(v8, v9)) & ! [v8] : ! [v9] : ( ~ (addition(v8, v9) = one) | complement(v9, v8) | ? [v10] : ? [v11] : (multiplication(v9, v8) = v11 & multiplication(v8, v9) = v10 & ( ~ (v11 = zero) | ~ (v10 = zero)))) & ! [v8] : ! [v9] : ( ~ complement(v9, v8) | test(v8)) & ! [v8] : ( ~ test(v8) | ? [v9] : complement(v9, v8))) % 4.19/1.65 | 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, all_0_6_6, all_0_7_7 yields: % 4.19/1.65 | (1) ~ (all_0_0_0 = one) & c(all_0_6_6) = all_0_2_2 & c(all_0_7_7) = all_0_5_5 & multiplication(all_0_4_4, all_0_2_2) = all_0_1_1 & multiplication(all_0_4_4, all_0_6_6) = all_0_3_3 & addition(all_0_3_3, all_0_1_1) = all_0_0_0 & addition(all_0_7_7, all_0_5_5) = all_0_4_4 & test(all_0_6_6) & test(all_0_7_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)) & ! [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)) % 4.19/1.66 | % 4.19/1.66 | Applying alpha-rule on (1) yields: % 4.19/1.66 | (2) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 4.19/1.66 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 4.55/1.66 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (c(v0) = v2) | ~ complement(v0, v1) | ~ test(v0)) % 4.55/1.66 | (5) ! [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)) % 4.55/1.66 | (6) c(all_0_6_6) = all_0_2_2 % 4.55/1.66 | (7) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 4.55/1.66 | (8) addition(all_0_7_7, all_0_5_5) = all_0_4_4 % 4.55/1.66 | (9) ! [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)) % 4.55/1.66 | (10) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) % 4.55/1.66 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0)) % 4.55/1.66 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) % 4.55/1.66 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 4.55/1.66 | (14) ! [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)) % 4.55/1.67 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 4.55/1.67 | (16) test(all_0_7_7) % 4.55/1.67 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero)) % 4.55/1.67 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) % 4.55/1.67 | (19) addition(all_0_3_3, all_0_1_1) = all_0_0_0 % 4.55/1.67 | (20) c(all_0_7_7) = all_0_5_5 % 4.55/1.67 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 4.55/1.67 | (22) ! [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)) % 4.55/1.67 | (23) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 4.55/1.67 | (24) ~ (all_0_0_0 = one) % 4.55/1.67 | (25) multiplication(all_0_4_4, all_0_6_6) = all_0_3_3 % 4.55/1.67 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 4.55/1.67 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 4.55/1.67 | (28) ! [v0] : ( ~ test(v0) | ? [v1] : complement(v1, v0)) % 4.55/1.67 | (29) ! [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)) % 4.55/1.67 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 4.55/1.67 | (31) test(all_0_6_6) % 4.55/1.67 | (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)) % 4.55/1.67 | (33) ! [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)) % 4.55/1.67 | (34) ! [v0] : ! [v1] : (v1 = zero | ~ (c(v0) = v1) | test(v0)) % 4.55/1.67 | (35) ! [v0] : ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) % 4.55/1.67 | (36) multiplication(all_0_4_4, all_0_2_2) = all_0_1_1 % 4.55/1.67 | (37) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) | ~ (v2 = zero)))) % 4.55/1.67 | (38) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 4.55/1.67 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one)) % 4.55/1.68 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one)) % 4.55/1.68 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 4.55/1.68 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 4.55/1.68 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0)) % 4.55/1.68 | (44) ! [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)) % 4.55/1.68 | (45) ! [v0] : ! [v1] : ! [v2] : (v2 = one | ~ (addition(v0, v1) = v2) | ~ complement(v1, v0)) % 4.55/1.68 | (46) ! [v0] : ! [v1] : ( ~ (c(v0) = v1) | ~ test(v0) | complement(v0, v1)) % 4.55/1.68 | (47) ! [v0] : ! [v1] : ( ~ complement(v1, v0) | test(v0)) % 4.55/1.68 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 4.55/1.68 | (49) ! [v0] : ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) % 4.55/1.68 | % 4.55/1.68 | Instantiating formula (42) 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: % 4.55/1.68 | (50) addition(all_0_1_1, all_0_3_3) = all_0_0_0 % 4.65/1.68 | % 4.65/1.68 | Instantiating formula (42) with all_0_4_4, all_0_7_7, all_0_5_5 and discharging atoms addition(all_0_7_7, all_0_5_5) = all_0_4_4, yields: % 4.65/1.68 | (51) addition(all_0_5_5, all_0_7_7) = all_0_4_4 % 4.65/1.68 | % 4.65/1.68 | Instantiating formula (46) with all_0_2_2, all_0_6_6 and discharging atoms c(all_0_6_6) = all_0_2_2, test(all_0_6_6), yields: % 4.65/1.68 | (52) complement(all_0_6_6, all_0_2_2) % 4.65/1.68 | % 4.65/1.68 | Instantiating formula (46) with all_0_5_5, all_0_7_7 and discharging atoms c(all_0_7_7) = all_0_5_5, test(all_0_7_7), yields: % 4.65/1.68 | (53) complement(all_0_7_7, all_0_5_5) % 4.65/1.68 | % 4.65/1.68 | Instantiating formula (45) with all_0_4_4, all_0_7_7, all_0_5_5 and discharging atoms addition(all_0_5_5, all_0_7_7) = all_0_4_4, complement(all_0_7_7, all_0_5_5), yields: % 4.65/1.68 | (54) all_0_4_4 = one % 4.65/1.68 | % 4.65/1.68 | From (54) and (36) follows: % 4.65/1.68 | (55) multiplication(one, all_0_2_2) = all_0_1_1 % 4.65/1.68 | % 4.65/1.68 | From (54) and (25) follows: % 4.65/1.68 | (56) multiplication(one, all_0_6_6) = all_0_3_3 % 4.65/1.68 | % 4.65/1.68 | Instantiating formula (26) with all_0_1_1, all_0_2_2 and discharging atoms multiplication(one, all_0_2_2) = all_0_1_1, yields: % 4.65/1.68 | (57) all_0_1_1 = all_0_2_2 % 4.65/1.68 | % 4.65/1.68 | Instantiating formula (26) with all_0_3_3, all_0_6_6 and discharging atoms multiplication(one, all_0_6_6) = all_0_3_3, yields: % 4.65/1.68 | (58) all_0_3_3 = all_0_6_6 % 4.65/1.68 | % 4.65/1.68 | From (57)(58) and (50) follows: % 4.65/1.68 | (59) addition(all_0_2_2, all_0_6_6) = all_0_0_0 % 4.65/1.69 | % 4.65/1.69 | Instantiating formula (45) with all_0_0_0, all_0_6_6, all_0_2_2 and discharging atoms addition(all_0_2_2, all_0_6_6) = all_0_0_0, complement(all_0_6_6, all_0_2_2), yields: % 4.65/1.69 | (60) all_0_0_0 = one % 4.65/1.69 | % 4.65/1.69 | Equations (60) can reduce 24 to: % 4.65/1.69 | (61) $false % 4.65/1.69 | % 4.65/1.69 |-The branch is then unsatisfiable % 4.65/1.69 % SZS output end Proof for theBenchmark % 4.65/1.69 % 4.65/1.69 1093ms %------------------------------------------------------------------------------