%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE009+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n011.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 01:50:49 EDT 2022 % Result : Theorem 3.52s 1.54s % Output : Proof 5.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KLE009+1 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n011.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Thu Jun 16 08:18:36 EDT 2022 % 0.13/0.35 % CPUTime : % 0.45/0.60 ____ _ % 0.45/0.60 ___ / __ \_____(_)___ ________ __________ % 0.45/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.45/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.45/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.45/0.60 % 0.45/0.60 A Theorem Prover for First-Order Logic % 0.45/0.60 (ePrincess v.1.0) % 0.45/0.60 % 0.45/0.60 (c) Philipp Rümmer, 2009-2015 % 0.45/0.60 (c) Peter Backeman, 2014-2015 % 0.45/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.45/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.45/0.60 Bug reports to peter@backeman.se % 0.45/0.60 % 0.45/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.45/0.60 % 0.45/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.61/0.96 Prover 0: Preprocessing ... % 2.56/1.29 Prover 0: Constructing countermodel ... % 3.52/1.54 Prover 0: proved (889ms) % 3.52/1.54 % 3.52/1.54 No countermodel exists, formula is valid % 3.52/1.54 % SZS status Theorem for theBenchmark % 3.52/1.54 % 3.52/1.54 Generating proof ... found it (size 40) % 4.73/1.86 % 4.73/1.86 % SZS output start Proof for theBenchmark % 4.73/1.86 Assumed formulas after preprocessing and simplification: % 4.73/1.86 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = one) & c(v1) = v3 & c(v0) = v6 & multiplication(v6, v3) = v9 & multiplication(v6, v1) = v7 & multiplication(v0, v3) = v4 & multiplication(v0, v1) = v2 & addition(v8, v9) = v10 & addition(v5, v7) = v8 & addition(v2, v4) = v5 & test(v1) & test(v0) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (multiplication(v12, v13) = v15) | ~ (multiplication(v11, v13) = v14) | ~ (addition(v14, v15) = v16) | ? [v17] : (multiplication(v17, v13) = v16 & addition(v11, v12) = v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (multiplication(v11, v13) = v15) | ~ (multiplication(v11, v12) = v14) | ~ (addition(v14, v15) = v16) | ? [v17] : (multiplication(v11, v17) = v16 & addition(v12, v13) = v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (multiplication(v14, v13) = v15) | ~ (multiplication(v11, v12) = v14) | ? [v16] : (multiplication(v12, v13) = v16 & multiplication(v11, v16) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (multiplication(v14, v13) = v15) | ~ (addition(v11, v12) = v14) | ? [v16] : ? [v17] : (multiplication(v12, v13) = v17 & multiplication(v11, v13) = v16 & addition(v16, v17) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (multiplication(v12, v13) = v14) | ~ (multiplication(v11, v14) = v15) | ? [v16] : (multiplication(v16, v13) = v15 & multiplication(v11, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (multiplication(v11, v14) = v15) | ~ (addition(v12, v13) = v14) | ? [v16] : ? [v17] : (multiplication(v11, v13) = v17 & multiplication(v11, v12) = v16 & addition(v16, v17) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (addition(v14, v11) = v15) | ~ (addition(v13, v12) = v14) | ? [v16] : (addition(v13, v16) = v15 & addition(v12, v11) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (addition(v13, v14) = v15) | ~ (addition(v12, v11) = v14) | ? [v16] : (addition(v16, v11) = v15 & addition(v13, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (multiplication(v14, v13) = v12) | ~ (multiplication(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (addition(v14, v13) = v12) | ~ (addition(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (c(v11) = v13) | ~ complement(v11, v12) | ~ test(v11)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (addition(v11, v12) = v13) | ~ leq(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : (v13 = one | ~ (addition(v11, v12) = v13) | ~ complement(v12, v11)) & ! [v11] : ! [v12] : ! [v13] : (v13 = zero | ~ (multiplication(v12, v11) = v13) | ~ complement(v12, v11)) & ! [v11] : ! [v12] : ! [v13] : (v13 = zero | ~ (multiplication(v11, v12) = v13) | ~ complement(v12, v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (c(v13) = v12) | ~ (c(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (multiplication(v12, v11) = v13) | ~ complement(v12, v11) | (multiplication(v11, v12) = zero & addition(v11, v12) = one)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (multiplication(v11, v12) = v13) | ~ complement(v12, v11) | (multiplication(v12, v11) = zero & addition(v11, v12) = one)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (addition(v12, v11) = v13) | addition(v11, v12) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (addition(v11, v12) = v13) | ~ complement(v12, v11) | (multiplication(v12, v11) = zero & multiplication(v11, v12) = zero)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (addition(v11, v12) = v13) | addition(v12, v11) = v13) & ! [v11] : ! [v12] : (v12 = v11 | ~ (multiplication(v11, one) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (multiplication(one, v11) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (addition(v11, v11) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (addition(v11, zero) = v12)) & ! [v11] : ! [v12] : (v12 = zero | ~ (c(v11) = v12) | test(v11)) & ! [v11] : ! [v12] : (v12 = zero | ~ (multiplication(v11, zero) = v12)) & ! [v11] : ! [v12] : (v12 = zero | ~ (multiplication(zero, v11) = v12)) & ! [v11] : ! [v12] : ( ~ (c(v11) = v12) | ~ test(v11) | complement(v11, v12)) & ! [v11] : ! [v12] : ( ~ (multiplication(v12, v11) = zero) | complement(v12, v11) | ? [v13] : ? [v14] : (multiplication(v11, v12) = v13 & addition(v11, v12) = v14 & ( ~ (v14 = one) | ~ (v13 = zero)))) & ! [v11] : ! [v12] : ( ~ (multiplication(v11, v12) = zero) | complement(v12, v11) | ? [v13] : ? [v14] : (multiplication(v12, v11) = v13 & addition(v11, v12) = v14 & ( ~ (v14 = one) | ~ (v13 = zero)))) & ! [v11] : ! [v12] : ( ~ (addition(v11, v12) = v12) | leq(v11, v12)) & ! [v11] : ! [v12] : ( ~ (addition(v11, v12) = one) | complement(v12, v11) | ? [v13] : ? [v14] : (multiplication(v12, v11) = v14 & multiplication(v11, v12) = v13 & ( ~ (v14 = zero) | ~ (v13 = zero)))) & ! [v11] : ! [v12] : ( ~ complement(v12, v11) | test(v11)) & ! [v11] : ( ~ test(v11) | ? [v12] : complement(v12, v11))) % 4.96/1.91 | 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, all_0_8_8, all_0_9_9, all_0_10_10 yields: % 4.96/1.91 | (1) ~ (all_0_0_0 = one) & c(all_0_9_9) = all_0_7_7 & c(all_0_10_10) = all_0_4_4 & multiplication(all_0_4_4, all_0_7_7) = all_0_1_1 & multiplication(all_0_4_4, all_0_9_9) = all_0_3_3 & multiplication(all_0_10_10, all_0_7_7) = all_0_6_6 & multiplication(all_0_10_10, all_0_9_9) = all_0_8_8 & addition(all_0_2_2, all_0_1_1) = all_0_0_0 & addition(all_0_5_5, all_0_3_3) = all_0_2_2 & addition(all_0_8_8, all_0_6_6) = all_0_5_5 & test(all_0_9_9) & test(all_0_10_10) & ! [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] : ( ~ (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] : ( ~ (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) | 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)) % 4.96/1.92 | % 4.96/1.92 | Applying alpha-rule on (1) yields: % 4.96/1.92 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 4.96/1.92 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 4.96/1.92 | (4) ! [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)) % 4.96/1.92 | (5) ~ (all_0_0_0 = one) % 4.96/1.92 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 4.96/1.92 | (7) ! [v0] : ! [v1] : ( ~ (multiplication(v0, v1) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) % 4.96/1.92 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) % 4.96/1.92 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero)) % 4.96/1.92 | (10) c(all_0_9_9) = all_0_7_7 % 4.96/1.92 | (11) multiplication(all_0_10_10, all_0_7_7) = all_0_6_6 % 4.96/1.92 | (12) multiplication(all_0_4_4, all_0_9_9) = all_0_3_3 % 4.96/1.92 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 4.96/1.92 | (14) test(all_0_9_9) % 4.96/1.92 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 4.96/1.92 | (16) ! [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)) % 4.96/1.93 | (17) addition(all_0_5_5, all_0_3_3) = all_0_2_2 % 4.96/1.93 | (18) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 4.96/1.93 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 4.96/1.93 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 4.96/1.93 | (21) test(all_0_10_10) % 4.96/1.93 | (22) c(all_0_10_10) = all_0_4_4 % 4.96/1.93 | (23) ! [v0] : ( ~ test(v0) | ? [v1] : complement(v1, v0)) % 4.96/1.93 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (c(v2) = v1) | ~ (c(v2) = v0)) % 4.96/1.93 | (25) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) % 4.96/1.93 | (26) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 4.96/1.93 | (27) ! [v0] : ! [v1] : (v1 = zero | ~ (c(v0) = v1) | test(v0)) % 4.96/1.93 | (28) multiplication(all_0_4_4, all_0_7_7) = all_0_1_1 % 4.96/1.93 | (29) ! [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)) % 4.96/1.93 | (30) ! [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)) % 4.96/1.93 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (c(v0) = v2) | ~ complement(v0, v1) | ~ test(v0)) % 4.96/1.93 | (32) ! [v0] : ! [v1] : ( ~ (c(v0) = v1) | ~ test(v0) | complement(v0, v1)) % 4.96/1.93 | (33) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = one) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) | ~ (v2 = zero)))) % 4.96/1.93 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0) | (multiplication(v1, v0) = zero & addition(v0, v1) = one)) % 4.96/1.93 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) = one)) % 4.96/1.93 | (36) multiplication(all_0_10_10, all_0_9_9) = all_0_8_8 % 4.96/1.93 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 4.96/1.93 | (38) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 4.96/1.93 | (39) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v0, v1) = v2) | ~ complement(v1, v0)) % 4.96/1.93 | (40) addition(all_0_8_8, all_0_6_6) = all_0_5_5 % 4.96/1.93 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 4.96/1.93 | (42) ! [v0] : ! [v1] : ( ~ (multiplication(v1, v0) = zero) | complement(v1, v0) | ? [v2] : ? [v3] : (multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) | ~ (v2 = zero)))) % 4.96/1.93 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = zero | ~ (multiplication(v1, v0) = v2) | ~ complement(v1, v0)) % 4.96/1.94 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 4.96/1.94 | (45) ! [v0] : ! [v1] : ! [v2] : (v2 = one | ~ (addition(v0, v1) = v2) | ~ complement(v1, v0)) % 4.96/1.94 | (46) ! [v0] : ! [v1] : ( ~ complement(v1, v0) | test(v0)) % 4.96/1.94 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 4.96/1.94 | (48) addition(all_0_2_2, all_0_1_1) = all_0_0_0 % 4.96/1.94 | % 4.96/1.94 | Instantiating formula (3) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms addition(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 4.96/1.94 | (49) addition(all_0_1_1, all_0_2_2) = all_0_0_0 % 4.96/1.94 | % 4.96/1.94 | Instantiating formula (44) with all_0_0_0, all_0_2_2, all_0_5_5, all_0_3_3, all_0_1_1 and discharging atoms addition(all_0_2_2, all_0_1_1) = all_0_0_0, addition(all_0_5_5, all_0_3_3) = all_0_2_2, yields: % 4.96/1.94 | (50) ? [v0] : (addition(all_0_3_3, all_0_1_1) = v0 & addition(all_0_5_5, v0) = all_0_0_0) % 4.96/1.94 | % 4.96/1.94 | Instantiating formula (3) with all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms addition(all_0_5_5, all_0_3_3) = all_0_2_2, yields: % 4.96/1.94 | (51) addition(all_0_3_3, all_0_5_5) = all_0_2_2 % 4.96/1.94 | % 4.96/1.94 | Instantiating formula (29) with all_0_5_5, all_0_6_6, all_0_8_8, all_0_7_7, all_0_9_9, all_0_10_10 and discharging atoms multiplication(all_0_10_10, all_0_7_7) = all_0_6_6, multiplication(all_0_10_10, all_0_9_9) = all_0_8_8, addition(all_0_8_8, all_0_6_6) = all_0_5_5, yields: % 4.96/1.94 | (52) ? [v0] : (multiplication(all_0_10_10, v0) = all_0_5_5 & addition(all_0_9_9, all_0_7_7) = v0) % 4.96/1.94 | % 4.96/1.94 | Instantiating formula (3) with all_0_5_5, all_0_8_8, all_0_6_6 and discharging atoms addition(all_0_8_8, all_0_6_6) = all_0_5_5, yields: % 4.96/1.94 | (53) addition(all_0_6_6, all_0_8_8) = all_0_5_5 % 4.96/1.94 | % 4.96/1.94 | Instantiating formula (32) with all_0_7_7, all_0_9_9 and discharging atoms c(all_0_9_9) = all_0_7_7, test(all_0_9_9), yields: % 4.96/1.94 | (54) complement(all_0_9_9, all_0_7_7) % 4.96/1.94 | % 4.96/1.94 | Instantiating formula (32) with all_0_4_4, all_0_10_10 and discharging atoms c(all_0_10_10) = all_0_4_4, test(all_0_10_10), yields: % 4.96/1.94 | (55) complement(all_0_10_10, all_0_4_4) % 4.96/1.94 | % 4.96/1.94 | Instantiating (52) with all_11_0_12 yields: % 4.96/1.94 | (56) multiplication(all_0_10_10, all_11_0_12) = all_0_5_5 & addition(all_0_9_9, all_0_7_7) = all_11_0_12 % 4.96/1.94 | % 4.96/1.94 | Applying alpha-rule on (56) yields: % 4.96/1.94 | (57) multiplication(all_0_10_10, all_11_0_12) = all_0_5_5 % 4.96/1.94 | (58) addition(all_0_9_9, all_0_7_7) = all_11_0_12 % 4.96/1.94 | % 4.96/1.94 | Instantiating (50) with all_13_0_13 yields: % 4.96/1.94 | (59) addition(all_0_3_3, all_0_1_1) = all_13_0_13 & addition(all_0_5_5, all_13_0_13) = all_0_0_0 % 4.96/1.94 | % 4.96/1.94 | Applying alpha-rule on (59) yields: % 4.96/1.94 | (60) addition(all_0_3_3, all_0_1_1) = all_13_0_13 % 4.96/1.94 | (61) addition(all_0_5_5, all_13_0_13) = all_0_0_0 % 4.96/1.94 | % 4.96/1.94 | Instantiating formula (29) with all_13_0_13, all_0_1_1, all_0_3_3, all_0_7_7, all_0_9_9, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_7_7) = all_0_1_1, multiplication(all_0_4_4, all_0_9_9) = all_0_3_3, addition(all_0_3_3, all_0_1_1) = all_13_0_13, yields: % 4.96/1.94 | (62) ? [v0] : (multiplication(all_0_4_4, v0) = all_13_0_13 & addition(all_0_9_9, all_0_7_7) = v0) % 4.96/1.94 | % 4.96/1.94 | Instantiating formula (3) with all_13_0_13, all_0_3_3, all_0_1_1 and discharging atoms addition(all_0_3_3, all_0_1_1) = all_13_0_13, yields: % 4.96/1.94 | (63) addition(all_0_1_1, all_0_3_3) = all_13_0_13 % 4.96/1.94 | % 4.96/1.94 | Instantiating formula (13) with all_0_0_0, all_0_2_2, all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms addition(all_0_1_1, all_0_2_2) = all_0_0_0, addition(all_0_3_3, all_0_5_5) = all_0_2_2, yields: % 4.96/1.94 | (64) ? [v0] : (addition(v0, all_0_5_5) = all_0_0_0 & addition(all_0_1_1, all_0_3_3) = v0) % 4.96/1.94 | % 4.96/1.94 | Instantiating formula (29) with all_0_5_5, all_0_8_8, all_0_6_6, all_0_9_9, all_0_7_7, all_0_10_10 and discharging atoms multiplication(all_0_10_10, all_0_7_7) = all_0_6_6, multiplication(all_0_10_10, all_0_9_9) = all_0_8_8, addition(all_0_6_6, all_0_8_8) = all_0_5_5, yields: % 4.96/1.95 | (65) ? [v0] : (multiplication(all_0_10_10, v0) = all_0_5_5 & addition(all_0_7_7, all_0_9_9) = v0) % 4.96/1.95 | % 4.96/1.95 | Instantiating formula (3) with all_11_0_12, all_0_9_9, all_0_7_7 and discharging atoms addition(all_0_9_9, all_0_7_7) = all_11_0_12, yields: % 4.96/1.95 | (66) addition(all_0_7_7, all_0_9_9) = all_11_0_12 % 4.96/1.95 | % 4.96/1.95 | Instantiating (62) with all_29_0_18 yields: % 4.96/1.95 | (67) multiplication(all_0_4_4, all_29_0_18) = all_13_0_13 & addition(all_0_9_9, all_0_7_7) = all_29_0_18 % 4.96/1.95 | % 4.96/1.95 | Applying alpha-rule on (67) yields: % 4.96/1.95 | (68) multiplication(all_0_4_4, all_29_0_18) = all_13_0_13 % 4.96/1.95 | (69) addition(all_0_9_9, all_0_7_7) = all_29_0_18 % 4.96/1.95 | % 4.96/1.95 | Instantiating (64) with all_39_0_23 yields: % 4.96/1.95 | (70) addition(all_39_0_23, all_0_5_5) = all_0_0_0 & addition(all_0_1_1, all_0_3_3) = all_39_0_23 % 4.96/1.95 | % 4.96/1.95 | Applying alpha-rule on (70) yields: % 4.96/1.95 | (71) addition(all_39_0_23, all_0_5_5) = all_0_0_0 % 4.96/1.95 | (72) addition(all_0_1_1, all_0_3_3) = all_39_0_23 % 4.96/1.95 | % 4.96/1.95 | Instantiating (65) with all_45_0_26 yields: % 4.96/1.95 | (73) multiplication(all_0_10_10, all_45_0_26) = all_0_5_5 & addition(all_0_7_7, all_0_9_9) = all_45_0_26 % 4.96/1.95 | % 4.96/1.95 | Applying alpha-rule on (73) yields: % 4.96/1.95 | (74) multiplication(all_0_10_10, all_45_0_26) = all_0_5_5 % 4.96/1.95 | (75) addition(all_0_7_7, all_0_9_9) = all_45_0_26 % 4.96/1.95 | % 4.96/1.95 | Instantiating formula (15) with all_0_1_1, all_0_3_3, all_13_0_13, all_39_0_23 and discharging atoms addition(all_0_1_1, all_0_3_3) = all_39_0_23, addition(all_0_1_1, all_0_3_3) = all_13_0_13, yields: % 4.96/1.95 | (76) all_39_0_23 = all_13_0_13 % 4.96/1.95 | % 4.96/1.95 | Instantiating formula (45) with all_45_0_26, all_0_9_9, all_0_7_7 and discharging atoms addition(all_0_7_7, all_0_9_9) = all_45_0_26, complement(all_0_9_9, all_0_7_7), yields: % 4.96/1.95 | (77) all_45_0_26 = one % 5.32/1.95 | % 5.32/1.95 | Instantiating formula (15) with all_0_7_7, all_0_9_9, all_11_0_12, all_45_0_26 and discharging atoms addition(all_0_7_7, all_0_9_9) = all_45_0_26, addition(all_0_7_7, all_0_9_9) = all_11_0_12, yields: % 5.32/1.95 | (78) all_45_0_26 = all_11_0_12 % 5.32/1.95 | % 5.32/1.95 | Instantiating formula (15) with all_0_9_9, all_0_7_7, all_29_0_18, all_11_0_12 and discharging atoms addition(all_0_9_9, all_0_7_7) = all_29_0_18, addition(all_0_9_9, all_0_7_7) = all_11_0_12, yields: % 5.32/1.95 | (79) all_29_0_18 = all_11_0_12 % 5.32/1.95 | % 5.32/1.95 | Combining equations (78,77) yields a new equation: % 5.32/1.95 | (80) all_11_0_12 = one % 5.32/1.95 | % 5.32/1.95 | Simplifying 80 yields: % 5.32/1.95 | (81) all_11_0_12 = one % 5.32/1.95 | % 5.32/1.95 | Combining equations (81,79) yields a new equation: % 5.32/1.95 | (82) all_29_0_18 = one % 5.32/1.95 | % 5.32/1.95 | From (82) and (68) follows: % 5.32/1.95 | (83) multiplication(all_0_4_4, one) = all_13_0_13 % 5.32/1.95 | % 5.32/1.95 | From (81) and (57) follows: % 5.32/1.95 | (84) multiplication(all_0_10_10, one) = all_0_5_5 % 5.32/1.95 | % 5.32/1.95 | From (76) and (71) follows: % 5.32/1.95 | (85) addition(all_13_0_13, all_0_5_5) = all_0_0_0 % 5.32/1.95 | % 5.32/1.95 | Instantiating formula (38) with all_13_0_13, all_0_4_4 and discharging atoms multiplication(all_0_4_4, one) = all_13_0_13, yields: % 5.32/1.95 | (86) all_13_0_13 = all_0_4_4 % 5.32/1.95 | % 5.32/1.95 | Instantiating formula (38) with all_0_5_5, all_0_10_10 and discharging atoms multiplication(all_0_10_10, one) = all_0_5_5, yields: % 5.32/1.95 | (87) all_0_5_5 = all_0_10_10 % 5.32/1.95 | % 5.32/1.95 | From (86)(87) and (85) follows: % 5.32/1.95 | (88) addition(all_0_4_4, all_0_10_10) = all_0_0_0 % 5.32/1.96 | % 5.32/1.96 | Instantiating formula (45) with all_0_0_0, all_0_10_10, all_0_4_4 and discharging atoms addition(all_0_4_4, all_0_10_10) = all_0_0_0, complement(all_0_10_10, all_0_4_4), yields: % 5.32/1.96 | (89) all_0_0_0 = one % 5.32/1.96 | % 5.32/1.96 | Equations (89) can reduce 5 to: % 5.32/1.96 | (90) $false % 5.32/1.96 | % 5.32/1.96 |-The branch is then unsatisfiable % 5.32/1.96 % SZS output end Proof for theBenchmark % 5.32/1.96 % 5.32/1.96 1346ms %------------------------------------------------------------------------------