%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GRP665+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n007.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 : Sat Jul 16 08:43:31 EDT 2022 % Result : Theorem 2.57s 1.25s % Output : Proof 4.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRP665+1 : TPTP v8.1.0. Released v4.0.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n007.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 : Tue Jun 14 00:39:24 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.58 ____ _ % 0.18/0.58 ___ / __ \_____(_)___ ________ __________ % 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.58 % 0.18/0.58 A Theorem Prover for First-Order Logic % 0.18/0.58 (ePrincess v.1.0) % 0.18/0.58 % 0.18/0.58 (c) Philipp Rümmer, 2009-2015 % 0.18/0.58 (c) Peter Backeman, 2014-2015 % 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.58 Bug reports to peter@backeman.se % 0.18/0.58 % 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.58 % 0.18/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.65/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.36/0.88 Prover 0: Preprocessing ... % 1.76/1.07 Prover 0: Constructing countermodel ... % 2.57/1.25 Prover 0: proved (617ms) % 2.57/1.25 % 2.57/1.25 No countermodel exists, formula is valid % 2.57/1.25 % SZS status Theorem for theBenchmark % 2.57/1.25 % 2.57/1.25 Generating proof ... found it (size 81) % 3.71/1.59 % 3.71/1.59 % SZS output start Proof for theBenchmark % 3.71/1.59 Assumed formulas after preprocessing and simplification: % 3.71/1.59 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (mult(v6, v1) = v7 & mult(v4, v1) = v5 & mult(v2, op_c) = v10 & mult(v1, op_c) = v11 & mult(v0, v11) = v12 & mult(v0, v8) = v9 & mult(v0, v1) = v2 & mult(v0, op_c) = v6 & mult(op_c, v2) = v3 & mult(op_c, v1) = v8 & mult(op_c, v0) = v4 & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (rd(v16, v15) = v17) | ~ (mult(v17, v18) = v19) | ~ (mult(v15, v14) = v16) | ~ (mult(v15, v13) = v18) | ? [v20] : (mult(v15, v20) = v19 & mult(v14, v13) = v20)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (ld(v13, v17) = v18) | ~ (mult(v16, v18) = v19) | ~ (mult(v15, v13) = v16) | ~ (mult(v14, v13) = v17) | ? [v20] : (mult(v20, v13) = v19 & mult(v15, v14) = v20)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (mult(v16, v13) = v17) | ~ (mult(v15, v14) = v16) | ? [v18] : ? [v19] : ? [v20] : (ld(v13, v19) = v20 & mult(v18, v20) = v17 & mult(v15, v13) = v18 & mult(v14, v13) = v19)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (mult(v15, v16) = v17) | ~ (mult(v14, v13) = v16) | ? [v18] : ? [v19] : ? [v20] : (rd(v18, v15) = v19 & mult(v19, v20) = v17 & mult(v15, v14) = v18 & mult(v15, v13) = v20)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v14 | ~ (rd(v15, v13) = v16) | ~ (mult(v14, v13) = v15)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v14 | ~ (rd(v14, v13) = v15) | ~ (mult(v15, v13) = v16)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v13 | ~ (ld(v14, v15) = v16) | ~ (mult(v14, v13) = v15)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v13 | ~ (ld(v14, v13) = v15) | ~ (mult(v14, v15) = v16)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (rd(v16, v15) = v14) | ~ (rd(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (ld(v16, v15) = v14) | ~ (ld(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (mult(v16, v15) = v14) | ~ (mult(v16, v15) = v13)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (mult(v13, unit) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (mult(unit, v13) = v14)) & ! [v13] : ! [v14] : ( ~ (mult(v13, op_c) = v14) | mult(op_c, v13) = v14) & ! [v13] : ! [v14] : ( ~ (mult(op_c, v13) = v14) | mult(v13, op_c) = v14) & ( ~ (v12 = v10) | ~ (v9 = v7) | ~ (v5 = v3))) % 3.97/1.63 | 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, all_0_11_11, all_0_12_12 yields: % 3.97/1.63 | (1) mult(all_0_6_6, all_0_11_11) = all_0_5_5 & mult(all_0_8_8, all_0_11_11) = all_0_7_7 & mult(all_0_10_10, op_c) = all_0_2_2 & mult(all_0_11_11, op_c) = all_0_1_1 & mult(all_0_12_12, all_0_1_1) = all_0_0_0 & mult(all_0_12_12, all_0_4_4) = all_0_3_3 & mult(all_0_12_12, all_0_11_11) = all_0_10_10 & mult(all_0_12_12, op_c) = all_0_6_6 & mult(op_c, all_0_10_10) = all_0_9_9 & mult(op_c, all_0_11_11) = all_0_4_4 & mult(op_c, all_0_12_12) = all_0_8_8 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rd(v3, v2) = v4) | ~ (mult(v4, v5) = v6) | ~ (mult(v2, v1) = v3) | ~ (mult(v2, v0) = v5) | ? [v7] : (mult(v2, v7) = v6 & mult(v1, v0) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (ld(v0, v4) = v5) | ~ (mult(v3, v5) = v6) | ~ (mult(v2, v0) = v3) | ~ (mult(v1, v0) = v4) | ? [v7] : (mult(v7, v0) = v6 & mult(v2, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (mult(v3, v0) = v4) | ~ (mult(v2, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (ld(v0, v6) = v7 & mult(v5, v7) = v4 & mult(v2, v0) = v5 & mult(v1, v0) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (mult(v2, v3) = v4) | ~ (mult(v1, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (rd(v5, v2) = v6 & mult(v6, v7) = v4 & mult(v2, v1) = v5 & mult(v2, v0) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (rd(v2, v0) = v3) | ~ (mult(v1, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (rd(v1, v0) = v2) | ~ (mult(v2, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ld(v1, v2) = v3) | ~ (mult(v1, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ld(v1, v0) = v2) | ~ (mult(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rd(v3, v2) = v1) | ~ (rd(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ld(v3, v2) = v1) | ~ (ld(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (mult(v3, v2) = v1) | ~ (mult(v3, v2) = v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (mult(v0, unit) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (mult(unit, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (mult(v0, op_c) = v1) | mult(op_c, v0) = v1) & ! [v0] : ! [v1] : ( ~ (mult(op_c, v0) = v1) | mult(v0, op_c) = v1) & ( ~ (all_0_0_0 = all_0_2_2) | ~ (all_0_3_3 = all_0_5_5) | ~ (all_0_7_7 = all_0_9_9)) % 3.97/1.64 | % 3.97/1.64 | Applying alpha-rule on (1) yields: % 3.97/1.64 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (rd(v1, v0) = v2) | ~ (mult(v2, v0) = v3)) % 3.97/1.64 | (3) mult(all_0_6_6, all_0_11_11) = all_0_5_5 % 3.97/1.64 | (4) mult(all_0_11_11, op_c) = all_0_1_1 % 3.97/1.64 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (rd(v2, v0) = v3) | ~ (mult(v1, v0) = v2)) % 3.97/1.64 | (6) ~ (all_0_0_0 = all_0_2_2) | ~ (all_0_3_3 = all_0_5_5) | ~ (all_0_7_7 = all_0_9_9) % 3.97/1.64 | (7) mult(op_c, all_0_11_11) = all_0_4_4 % 3.97/1.64 | (8) mult(all_0_12_12, all_0_4_4) = all_0_3_3 % 3.97/1.64 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ (mult(v0, unit) = v1)) % 3.97/1.64 | (10) mult(op_c, all_0_12_12) = all_0_8_8 % 3.97/1.64 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (mult(v3, v2) = v1) | ~ (mult(v3, v2) = v0)) % 3.97/1.64 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (mult(unit, v0) = v1)) % 3.97/1.64 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ld(v1, v0) = v2) | ~ (mult(v1, v2) = v3)) % 3.97/1.65 | (14) mult(all_0_12_12, all_0_1_1) = all_0_0_0 % 3.97/1.65 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ld(v1, v2) = v3) | ~ (mult(v1, v0) = v2)) % 3.97/1.65 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ld(v3, v2) = v1) | ~ (ld(v3, v2) = v0)) % 3.97/1.65 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rd(v3, v2) = v1) | ~ (rd(v3, v2) = v0)) % 3.97/1.65 | (18) mult(all_0_12_12, all_0_11_11) = all_0_10_10 % 3.97/1.65 | (19) ! [v0] : ! [v1] : ( ~ (mult(op_c, v0) = v1) | mult(v0, op_c) = v1) % 3.97/1.65 | (20) ! [v0] : ! [v1] : ( ~ (mult(v0, op_c) = v1) | mult(op_c, v0) = v1) % 3.97/1.65 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (ld(v0, v4) = v5) | ~ (mult(v3, v5) = v6) | ~ (mult(v2, v0) = v3) | ~ (mult(v1, v0) = v4) | ? [v7] : (mult(v7, v0) = v6 & mult(v2, v1) = v7)) % 3.97/1.65 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (mult(v3, v0) = v4) | ~ (mult(v2, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (ld(v0, v6) = v7 & mult(v5, v7) = v4 & mult(v2, v0) = v5 & mult(v1, v0) = v6)) % 3.97/1.65 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rd(v3, v2) = v4) | ~ (mult(v4, v5) = v6) | ~ (mult(v2, v1) = v3) | ~ (mult(v2, v0) = v5) | ? [v7] : (mult(v2, v7) = v6 & mult(v1, v0) = v7)) % 3.97/1.65 | (24) mult(op_c, all_0_10_10) = all_0_9_9 % 3.97/1.65 | (25) mult(all_0_10_10, op_c) = all_0_2_2 % 3.97/1.65 | (26) mult(all_0_8_8, all_0_11_11) = all_0_7_7 % 3.97/1.65 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (mult(v2, v3) = v4) | ~ (mult(v1, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : (rd(v5, v2) = v6 & mult(v6, v7) = v4 & mult(v2, v1) = v5 & mult(v2, v0) = v7)) % 3.97/1.65 | (28) mult(all_0_12_12, op_c) = all_0_6_6 % 3.97/1.65 | % 3.97/1.65 | Instantiating formula (20) with all_0_2_2, all_0_10_10 and discharging atoms mult(all_0_10_10, op_c) = all_0_2_2, yields: % 3.97/1.65 | (29) mult(op_c, all_0_10_10) = all_0_2_2 % 3.97/1.65 | % 3.97/1.65 | Instantiating formula (20) with all_0_1_1, all_0_11_11 and discharging atoms mult(all_0_11_11, op_c) = all_0_1_1, yields: % 3.97/1.65 | (30) mult(op_c, all_0_11_11) = all_0_1_1 % 3.97/1.65 | % 3.97/1.65 | Instantiating formula (27) with all_0_0_0, all_0_1_1, all_0_12_12, all_0_11_11, op_c and discharging atoms mult(all_0_11_11, op_c) = all_0_1_1, mult(all_0_12_12, all_0_1_1) = all_0_0_0, yields: % 3.97/1.65 | (31) ? [v0] : ? [v1] : ? [v2] : (rd(v0, all_0_12_12) = v1 & mult(v1, v2) = all_0_0_0 & mult(all_0_12_12, all_0_11_11) = v0 & mult(all_0_12_12, op_c) = v2) % 3.97/1.65 | % 3.97/1.65 | Instantiating formula (22) with all_0_2_2, all_0_10_10, all_0_12_12, all_0_11_11, op_c and discharging atoms mult(all_0_10_10, op_c) = all_0_2_2, mult(all_0_12_12, all_0_11_11) = all_0_10_10, yields: % 3.97/1.65 | (32) ? [v0] : ? [v1] : ? [v2] : (ld(op_c, v1) = v2 & mult(v0, v2) = all_0_2_2 & mult(all_0_11_11, op_c) = v1 & mult(all_0_12_12, op_c) = v0) % 3.97/1.66 | % 3.97/1.66 | Instantiating formula (22) with all_0_5_5, all_0_6_6, all_0_12_12, op_c, all_0_11_11 and discharging atoms mult(all_0_6_6, all_0_11_11) = all_0_5_5, mult(all_0_12_12, op_c) = all_0_6_6, yields: % 3.97/1.66 | (33) ? [v0] : ? [v1] : ? [v2] : (ld(all_0_11_11, v1) = v2 & mult(v0, v2) = all_0_5_5 & mult(all_0_12_12, all_0_11_11) = v0 & mult(op_c, all_0_11_11) = v1) % 3.97/1.66 | % 3.97/1.66 | Instantiating formula (20) with all_0_6_6, all_0_12_12 and discharging atoms mult(all_0_12_12, op_c) = all_0_6_6, yields: % 3.97/1.66 | (34) mult(op_c, all_0_12_12) = all_0_6_6 % 3.97/1.66 | % 3.97/1.66 | Instantiating formula (27) with all_0_9_9, all_0_10_10, op_c, all_0_12_12, all_0_11_11 and discharging atoms mult(all_0_12_12, all_0_11_11) = all_0_10_10, mult(op_c, all_0_10_10) = all_0_9_9, yields: % 3.97/1.66 | (35) ? [v0] : ? [v1] : ? [v2] : (rd(v0, op_c) = v1 & mult(v1, v2) = all_0_9_9 & mult(op_c, all_0_11_11) = v2 & mult(op_c, all_0_12_12) = v0) % 3.97/1.66 | % 3.97/1.66 | Instantiating formula (27) with all_0_3_3, all_0_4_4, all_0_12_12, op_c, all_0_11_11 and discharging atoms mult(all_0_12_12, all_0_4_4) = all_0_3_3, mult(op_c, all_0_11_11) = all_0_4_4, yields: % 3.97/1.66 | (36) ? [v0] : ? [v1] : ? [v2] : (rd(v0, all_0_12_12) = v1 & mult(v1, v2) = all_0_3_3 & mult(all_0_12_12, all_0_11_11) = v2 & mult(all_0_12_12, op_c) = v0) % 3.97/1.66 | % 3.97/1.66 | Instantiating formula (22) with all_0_7_7, all_0_8_8, op_c, all_0_12_12, all_0_11_11 and discharging atoms mult(all_0_8_8, all_0_11_11) = all_0_7_7, mult(op_c, all_0_12_12) = all_0_8_8, yields: % 3.97/1.66 | (37) ? [v0] : ? [v1] : ? [v2] : (ld(all_0_11_11, v1) = v2 & mult(v0, v2) = all_0_7_7 & mult(all_0_12_12, all_0_11_11) = v1 & mult(op_c, all_0_11_11) = v0) % 3.97/1.66 | % 3.97/1.66 | Instantiating (35) with all_9_0_13, all_9_1_14, all_9_2_15 yields: % 3.97/1.66 | (38) rd(all_9_2_15, op_c) = all_9_1_14 & mult(all_9_1_14, all_9_0_13) = all_0_9_9 & mult(op_c, all_0_11_11) = all_9_0_13 & mult(op_c, all_0_12_12) = all_9_2_15 % 3.97/1.66 | % 3.97/1.66 | Applying alpha-rule on (38) yields: % 3.97/1.66 | (39) rd(all_9_2_15, op_c) = all_9_1_14 % 3.97/1.66 | (40) mult(all_9_1_14, all_9_0_13) = all_0_9_9 % 3.97/1.66 | (41) mult(op_c, all_0_11_11) = all_9_0_13 % 3.97/1.66 | (42) mult(op_c, all_0_12_12) = all_9_2_15 % 3.97/1.66 | % 3.97/1.66 | Instantiating (31) with all_11_0_16, all_11_1_17, all_11_2_18 yields: % 3.97/1.66 | (43) rd(all_11_2_18, all_0_12_12) = all_11_1_17 & mult(all_11_1_17, all_11_0_16) = all_0_0_0 & mult(all_0_12_12, all_0_11_11) = all_11_2_18 & mult(all_0_12_12, op_c) = all_11_0_16 % 3.97/1.66 | % 3.97/1.66 | Applying alpha-rule on (43) yields: % 3.97/1.66 | (44) rd(all_11_2_18, all_0_12_12) = all_11_1_17 % 3.97/1.66 | (45) mult(all_11_1_17, all_11_0_16) = all_0_0_0 % 3.97/1.66 | (46) mult(all_0_12_12, all_0_11_11) = all_11_2_18 % 3.97/1.66 | (47) mult(all_0_12_12, op_c) = all_11_0_16 % 3.97/1.66 | % 3.97/1.66 | Instantiating (36) with all_13_0_19, all_13_1_20, all_13_2_21 yields: % 3.97/1.66 | (48) rd(all_13_2_21, all_0_12_12) = all_13_1_20 & mult(all_13_1_20, all_13_0_19) = all_0_3_3 & mult(all_0_12_12, all_0_11_11) = all_13_0_19 & mult(all_0_12_12, op_c) = all_13_2_21 % 3.97/1.66 | % 3.97/1.66 | Applying alpha-rule on (48) yields: % 3.97/1.66 | (49) rd(all_13_2_21, all_0_12_12) = all_13_1_20 % 3.97/1.66 | (50) mult(all_13_1_20, all_13_0_19) = all_0_3_3 % 3.97/1.66 | (51) mult(all_0_12_12, all_0_11_11) = all_13_0_19 % 3.97/1.66 | (52) mult(all_0_12_12, op_c) = all_13_2_21 % 3.97/1.66 | % 3.97/1.66 | Instantiating (33) with all_15_0_22, all_15_1_23, all_15_2_24 yields: % 3.97/1.66 | (53) ld(all_0_11_11, all_15_1_23) = all_15_0_22 & mult(all_15_2_24, all_15_0_22) = all_0_5_5 & mult(all_0_12_12, all_0_11_11) = all_15_2_24 & mult(op_c, all_0_11_11) = all_15_1_23 % 3.97/1.66 | % 3.97/1.66 | Applying alpha-rule on (53) yields: % 3.97/1.66 | (54) ld(all_0_11_11, all_15_1_23) = all_15_0_22 % 3.97/1.66 | (55) mult(all_15_2_24, all_15_0_22) = all_0_5_5 % 3.97/1.66 | (56) mult(all_0_12_12, all_0_11_11) = all_15_2_24 % 3.97/1.66 | (57) mult(op_c, all_0_11_11) = all_15_1_23 % 3.97/1.66 | % 3.97/1.66 | Instantiating (32) with all_17_0_25, all_17_1_26, all_17_2_27 yields: % 3.97/1.66 | (58) ld(op_c, all_17_1_26) = all_17_0_25 & mult(all_17_2_27, all_17_0_25) = all_0_2_2 & mult(all_0_11_11, op_c) = all_17_1_26 & mult(all_0_12_12, op_c) = all_17_2_27 % 3.97/1.66 | % 3.97/1.66 | Applying alpha-rule on (58) yields: % 3.97/1.66 | (59) ld(op_c, all_17_1_26) = all_17_0_25 % 3.97/1.67 | (60) mult(all_17_2_27, all_17_0_25) = all_0_2_2 % 3.97/1.67 | (61) mult(all_0_11_11, op_c) = all_17_1_26 % 3.97/1.67 | (62) mult(all_0_12_12, op_c) = all_17_2_27 % 3.97/1.67 | % 3.97/1.67 | Instantiating (37) with all_19_0_28, all_19_1_29, all_19_2_30 yields: % 3.97/1.67 | (63) ld(all_0_11_11, all_19_1_29) = all_19_0_28 & mult(all_19_2_30, all_19_0_28) = all_0_7_7 & mult(all_0_12_12, all_0_11_11) = all_19_1_29 & mult(op_c, all_0_11_11) = all_19_2_30 % 3.97/1.67 | % 3.97/1.67 | Applying alpha-rule on (63) yields: % 3.97/1.67 | (64) ld(all_0_11_11, all_19_1_29) = all_19_0_28 % 3.97/1.67 | (65) mult(all_19_2_30, all_19_0_28) = all_0_7_7 % 3.97/1.67 | (66) mult(all_0_12_12, all_0_11_11) = all_19_1_29 % 3.97/1.67 | (67) mult(op_c, all_0_11_11) = all_19_2_30 % 3.97/1.67 | % 3.97/1.67 | Instantiating formula (11) with all_0_12_12, all_0_11_11, all_15_2_24, all_19_1_29 and discharging atoms mult(all_0_12_12, all_0_11_11) = all_19_1_29, mult(all_0_12_12, all_0_11_11) = all_15_2_24, yields: % 3.97/1.67 | (68) all_19_1_29 = all_15_2_24 % 3.97/1.67 | % 3.97/1.67 | Instantiating formula (11) with all_0_12_12, all_0_11_11, all_13_0_19, all_0_10_10 and discharging atoms mult(all_0_12_12, all_0_11_11) = all_13_0_19, mult(all_0_12_12, all_0_11_11) = all_0_10_10, yields: % 3.97/1.67 | (69) all_13_0_19 = all_0_10_10 % 3.97/1.67 | % 3.97/1.67 | Instantiating formula (11) with all_0_12_12, all_0_11_11, all_13_0_19, all_15_2_24 and discharging atoms mult(all_0_12_12, all_0_11_11) = all_15_2_24, mult(all_0_12_12, all_0_11_11) = all_13_0_19, yields: % 3.97/1.67 | (70) all_15_2_24 = all_13_0_19 % 3.97/1.67 | % 3.97/1.67 | Instantiating formula (11) with all_0_12_12, all_0_11_11, all_11_2_18, all_19_1_29 and discharging atoms mult(all_0_12_12, all_0_11_11) = all_19_1_29, mult(all_0_12_12, all_0_11_11) = all_11_2_18, yields: % 3.97/1.67 | (71) all_19_1_29 = all_11_2_18 % 3.97/1.67 | % 3.97/1.67 | Instantiating formula (11) with all_0_12_12, op_c, all_17_2_27, all_0_6_6 and discharging atoms mult(all_0_12_12, op_c) = all_17_2_27, mult(all_0_12_12, op_c) = all_0_6_6, yields: % 3.97/1.67 | (72) all_17_2_27 = all_0_6_6 % 3.97/1.67 | % 3.97/1.67 | Instantiating formula (11) with all_0_12_12, op_c, all_13_2_21, all_17_2_27 and discharging atoms mult(all_0_12_12, op_c) = all_17_2_27, mult(all_0_12_12, op_c) = all_13_2_21, yields: % 3.97/1.67 | (73) all_17_2_27 = all_13_2_21 % 3.97/1.67 | % 3.97/1.67 | Instantiating formula (11) with op_c, all_0_10_10, all_0_2_2, all_0_9_9 and discharging atoms mult(op_c, all_0_10_10) = all_0_2_2, mult(op_c, all_0_10_10) = all_0_9_9, yields: % 3.97/1.67 | (74) all_0_2_2 = all_0_9_9 % 3.97/1.67 | % 3.97/1.67 | Instantiating formula (11) with op_c, all_0_11_11, all_19_2_30, all_0_4_4 and discharging atoms mult(op_c, all_0_11_11) = all_19_2_30, mult(op_c, all_0_11_11) = all_0_4_4, yields: % 3.97/1.67 | (75) all_19_2_30 = all_0_4_4 % 3.97/1.67 | % 3.97/1.67 | Instantiating formula (11) with op_c, all_0_11_11, all_15_1_23, all_19_2_30 and discharging atoms mult(op_c, all_0_11_11) = all_19_2_30, mult(op_c, all_0_11_11) = all_15_1_23, yields: % 3.97/1.67 | (76) all_19_2_30 = all_15_1_23 % 3.97/1.67 | % 3.97/1.67 | Instantiating formula (11) with op_c, all_0_11_11, all_9_0_13, all_15_1_23 and discharging atoms mult(op_c, all_0_11_11) = all_15_1_23, mult(op_c, all_0_11_11) = all_9_0_13, yields: % 3.97/1.67 | (77) all_15_1_23 = all_9_0_13 % 3.97/1.67 | % 3.97/1.67 | Instantiating formula (11) with op_c, all_0_11_11, all_0_1_1, all_9_0_13 and discharging atoms mult(op_c, all_0_11_11) = all_9_0_13, mult(op_c, all_0_11_11) = all_0_1_1, yields: % 3.97/1.67 | (78) all_9_0_13 = all_0_1_1 % 3.97/1.67 | % 3.97/1.67 | Instantiating formula (11) with op_c, all_0_12_12, all_9_2_15, all_0_8_8 and discharging atoms mult(op_c, all_0_12_12) = all_9_2_15, mult(op_c, all_0_12_12) = all_0_8_8, yields: % 3.97/1.67 | (79) all_9_2_15 = all_0_8_8 % 3.97/1.67 | % 3.97/1.67 | Instantiating formula (11) with op_c, all_0_12_12, all_0_6_6, all_9_2_15 and discharging atoms mult(op_c, all_0_12_12) = all_9_2_15, mult(op_c, all_0_12_12) = all_0_6_6, yields: % 3.97/1.67 | (80) all_9_2_15 = all_0_6_6 % 3.97/1.67 | % 3.97/1.67 | Combining equations (68,71) yields a new equation: % 3.97/1.67 | (81) all_15_2_24 = all_11_2_18 % 3.97/1.67 | % 3.97/1.67 | Simplifying 81 yields: % 3.97/1.67 | (82) all_15_2_24 = all_11_2_18 % 3.97/1.67 | % 3.97/1.67 | Combining equations (76,75) yields a new equation: % 3.97/1.67 | (83) all_15_1_23 = all_0_4_4 % 3.97/1.67 | % 3.97/1.67 | Simplifying 83 yields: % 3.97/1.67 | (84) all_15_1_23 = all_0_4_4 % 3.97/1.67 | % 3.97/1.67 | Combining equations (73,72) yields a new equation: % 3.97/1.68 | (85) all_13_2_21 = all_0_6_6 % 3.97/1.68 | % 3.97/1.68 | Simplifying 85 yields: % 3.97/1.68 | (86) all_13_2_21 = all_0_6_6 % 3.97/1.68 | % 3.97/1.68 | Combining equations (77,84) yields a new equation: % 3.97/1.68 | (87) all_9_0_13 = all_0_4_4 % 3.97/1.68 | % 3.97/1.68 | Simplifying 87 yields: % 3.97/1.68 | (88) all_9_0_13 = all_0_4_4 % 3.97/1.68 | % 3.97/1.68 | Combining equations (70,82) yields a new equation: % 3.97/1.68 | (89) all_13_0_19 = all_11_2_18 % 3.97/1.68 | % 3.97/1.68 | Simplifying 89 yields: % 3.97/1.68 | (90) all_13_0_19 = all_11_2_18 % 3.97/1.68 | % 3.97/1.68 | Combining equations (90,69) yields a new equation: % 3.97/1.68 | (91) all_11_2_18 = all_0_10_10 % 3.97/1.68 | % 3.97/1.68 | Simplifying 91 yields: % 3.97/1.68 | (92) all_11_2_18 = all_0_10_10 % 3.97/1.68 | % 3.97/1.68 | Combining equations (78,88) yields a new equation: % 3.97/1.68 | (93) all_0_1_1 = all_0_4_4 % 3.97/1.68 | % 3.97/1.68 | Simplifying 93 yields: % 3.97/1.68 | (94) all_0_1_1 = all_0_4_4 % 3.97/1.68 | % 3.97/1.68 | Combining equations (79,80) yields a new equation: % 3.97/1.68 | (95) all_0_6_6 = all_0_8_8 % 3.97/1.68 | % 3.97/1.68 | Combining equations (95,86) yields a new equation: % 3.97/1.68 | (96) all_13_2_21 = all_0_8_8 % 3.97/1.68 | % 3.97/1.68 | Combining equations (92,82) yields a new equation: % 3.97/1.68 | (97) all_15_2_24 = all_0_10_10 % 3.97/1.68 | % 3.97/1.68 | From (96) and (49) follows: % 3.97/1.68 | (98) rd(all_0_8_8, all_0_12_12) = all_13_1_20 % 3.97/1.68 | % 3.97/1.68 | From (84) and (54) follows: % 3.97/1.68 | (99) ld(all_0_11_11, all_0_4_4) = all_15_0_22 % 3.97/1.68 | % 3.97/1.68 | From (97) and (55) follows: % 3.97/1.68 | (100) mult(all_0_10_10, all_15_0_22) = all_0_5_5 % 3.97/1.68 | % 3.97/1.68 | From (69) and (50) follows: % 3.97/1.68 | (101) mult(all_13_1_20, all_0_10_10) = all_0_3_3 % 3.97/1.68 | % 3.97/1.68 | From (95) and (3) follows: % 4.17/1.68 | (102) mult(all_0_8_8, all_0_11_11) = all_0_5_5 % 4.17/1.68 | % 4.17/1.68 | From (74) and (25) follows: % 4.17/1.68 | (103) mult(all_0_10_10, op_c) = all_0_9_9 % 4.17/1.68 | % 4.17/1.68 | From (94) and (4) follows: % 4.17/1.68 | (104) mult(all_0_11_11, op_c) = all_0_4_4 % 4.17/1.68 | % 4.17/1.68 | From (94) and (14) follows: % 4.17/1.68 | (105) mult(all_0_12_12, all_0_4_4) = all_0_0_0 % 4.17/1.68 | % 4.17/1.68 | From (74) and (29) follows: % 4.17/1.68 | (24) mult(op_c, all_0_10_10) = all_0_9_9 % 4.17/1.68 | % 4.17/1.68 | From (95) and (34) follows: % 4.17/1.68 | (10) mult(op_c, all_0_12_12) = all_0_8_8 % 4.17/1.68 | % 4.17/1.68 | Instantiating formula (5) with all_13_1_20, all_0_8_8, op_c, all_0_12_12 and discharging atoms rd(all_0_8_8, all_0_12_12) = all_13_1_20, mult(op_c, all_0_12_12) = all_0_8_8, yields: % 4.17/1.68 | (108) all_13_1_20 = op_c % 4.17/1.68 | % 4.17/1.68 | Instantiating formula (15) with all_15_0_22, all_0_4_4, all_0_11_11, op_c and discharging atoms ld(all_0_11_11, all_0_4_4) = all_15_0_22, mult(all_0_11_11, op_c) = all_0_4_4, yields: % 4.17/1.68 | (109) all_15_0_22 = op_c % 4.17/1.68 | % 4.17/1.68 | Instantiating formula (11) with all_0_8_8, all_0_11_11, all_0_5_5, all_0_7_7 and discharging atoms mult(all_0_8_8, all_0_11_11) = all_0_5_5, mult(all_0_8_8, all_0_11_11) = all_0_7_7, yields: % 4.17/1.68 | (110) all_0_5_5 = all_0_7_7 % 4.17/1.68 | % 4.17/1.68 | Instantiating formula (11) with all_0_12_12, all_0_4_4, all_0_0_0, all_0_3_3 and discharging atoms mult(all_0_12_12, all_0_4_4) = all_0_0_0, mult(all_0_12_12, all_0_4_4) = all_0_3_3, yields: % 4.17/1.68 | (111) all_0_0_0 = all_0_3_3 % 4.17/1.68 | % 4.17/1.68 | From (108) and (101) follows: % 4.17/1.68 | (112) mult(op_c, all_0_10_10) = all_0_3_3 % 4.17/1.68 | % 4.17/1.68 | From (109)(110) and (100) follows: % 4.17/1.68 | (113) mult(all_0_10_10, op_c) = all_0_7_7 % 4.17/1.68 | % 4.17/1.68 | Instantiating formula (11) with all_0_10_10, op_c, all_0_7_7, all_0_9_9 and discharging atoms mult(all_0_10_10, op_c) = all_0_7_7, mult(all_0_10_10, op_c) = all_0_9_9, yields: % 4.17/1.69 | (114) all_0_7_7 = all_0_9_9 % 4.17/1.69 | % 4.17/1.69 | Instantiating formula (11) with op_c, all_0_10_10, all_0_3_3, all_0_9_9 and discharging atoms mult(op_c, all_0_10_10) = all_0_3_3, mult(op_c, all_0_10_10) = all_0_9_9, yields: % 4.17/1.69 | (115) all_0_3_3 = all_0_9_9 % 4.17/1.69 | % 4.17/1.69 | Combining equations (114,110) yields a new equation: % 4.17/1.69 | (116) all_0_5_5 = all_0_9_9 % 4.17/1.69 | % 4.17/1.69 | Combining equations (115,111) yields a new equation: % 4.17/1.69 | (117) all_0_0_0 = all_0_9_9 % 4.17/1.69 | % 4.17/1.69 +-Applying beta-rule and splitting (6), into two cases. % 4.17/1.69 |-Branch one: % 4.17/1.69 | (118) ~ (all_0_0_0 = all_0_2_2) % 4.17/1.69 | % 4.17/1.69 | Equations (117,74) can reduce 118 to: % 4.17/1.69 | (119) $false % 4.17/1.69 | % 4.17/1.69 |-The branch is then unsatisfiable % 4.17/1.69 |-Branch two: % 4.17/1.69 | (120) all_0_0_0 = all_0_2_2 % 4.17/1.69 | (121) ~ (all_0_3_3 = all_0_5_5) | ~ (all_0_7_7 = all_0_9_9) % 4.17/1.69 | % 4.17/1.69 +-Applying beta-rule and splitting (121), into two cases. % 4.17/1.69 |-Branch one: % 4.17/1.69 | (122) ~ (all_0_3_3 = all_0_5_5) % 4.17/1.69 | % 4.17/1.69 | Equations (115,116) can reduce 122 to: % 4.17/1.69 | (119) $false % 4.17/1.69 | % 4.17/1.69 |-The branch is then unsatisfiable % 4.17/1.69 |-Branch two: % 4.17/1.69 | (124) all_0_3_3 = all_0_5_5 % 4.17/1.69 | (125) ~ (all_0_7_7 = all_0_9_9) % 4.17/1.69 | % 4.17/1.69 | Equations (114) can reduce 125 to: % 4.17/1.69 | (119) $false % 4.17/1.69 | % 4.17/1.69 |-The branch is then unsatisfiable % 4.17/1.69 % SZS output end Proof for theBenchmark % 4.17/1.69 % 4.17/1.69 1100ms %------------------------------------------------------------------------------