%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KRS178+1 : TPTP v8.1.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n023.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 02:56:48 EDT 2022 % Result : Theorem 5.79s 1.99s % Output : Proof 7.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KRS178+1 : TPTP v8.1.0. Bugfixed v5.4.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n023.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 7 17:29:08 EDT 2022 % 0.12/0.33 % CPUTime : % 0.65/0.63 ____ _ % 0.65/0.63 ___ / __ \_____(_)___ ________ __________ % 0.65/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.65/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.65/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.65/0.63 % 0.65/0.63 A Theorem Prover for First-Order Logic % 0.65/0.63 (ePrincess v.1.0) % 0.65/0.63 % 0.65/0.63 (c) Philipp Rümmer, 2009-2015 % 0.65/0.63 (c) Peter Backeman, 2014-2015 % 0.65/0.63 (contributions by Angelo Brillout, Peter Baumgartner) % 0.65/0.63 Free software under GNU Lesser General Public License (LGPL). % 0.65/0.63 Bug reports to peter@backeman.se % 0.65/0.63 % 0.65/0.63 For more information, visit http://user.uu.se/~petba168/breu/ % 0.65/0.63 % 0.65/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.65/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.61/0.95 Prover 0: Preprocessing ... % 2.02/1.10 Prover 0: Warning: ignoring some quantifiers % 2.11/1.12 Prover 0: Constructing countermodel ... % 4.95/1.86 Prover 0: gave up % 4.95/1.86 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 5.19/1.88 Prover 1: Preprocessing ... % 5.63/1.96 Prover 1: Constructing countermodel ... % 5.79/1.99 Prover 1: proved (135ms) % 5.79/1.99 % 5.79/1.99 No countermodel exists, formula is valid % 5.79/1.99 % SZS status Theorem for theBenchmark % 5.79/1.99 % 5.79/1.99 Generating proof ... found it (size 11) % 6.65/2.22 % 6.65/2.22 % SZS output start Proof for theBenchmark % 6.65/2.22 Assumed formulas after preprocessing and simplification: % 6.65/2.22 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ( ~ (v23 = 0) & ~ (v12 = 0) & ~ (v10 = 0) & ~ (v5 = 0) & ~ (v1 = 0) & model(v24, v21) = 0 & model(v22, v21) = v23 & model(v19, v15) = 0 & model(v19, v14) = 0 & model(v16, v15) = v18 & model(v16, v14) = v17 & model(v13, v7) = 0 & model(v11, v8) = 0 & model(v11, v7) = v12 & model(v9, v8) = v10 & model(v6, v4) = 0 & model(v2, v4) = v5 & model(v2, v3) = 0 & isa(v0, v0) = v1 & ! [v26] : ! [v27] : ! [v28] : ! [v29] : ! [v30] : (v30 = 0 | ~ (xora(v26, v27) = 0) | ~ (status(v28, v29, v26) = v30) | status(v28, v29, v27) = 0) & ! [v26] : ! [v27] : ! [v28] : ! [v29] : ! [v30] : (v28 = 0 | ~ (nota(v26, v27) = v28) | ~ (status(v29, v30, v26) = 0) | status(v29, v30, v27) = 0) & ! [v26] : ! [v27] : ! [v28] : ! [v29] : ! [v30] : (v28 = 0 | ~ (mighta(v26, v27) = v28) | ~ (status(v29, v30, v26) = 0) | ? [v31] : ( ~ (v31 = 0) & status(v29, v30, v27) = v31)) & ! [v26] : ! [v27] : ! [v28] : ! [v29] : ! [v30] : (v27 = v26 | ~ (status(v30, v29, v28) = v27) | ~ (status(v30, v29, v28) = v26)) & ! [v26] : ! [v27] : ! [v28] : ! [v29] : (v29 = 0 | ~ (not(v27) = v28) | ~ (model(v26, v28) = v29) | model(v26, v27) = 0) & ! [v26] : ! [v27] : ! [v28] : ! [v29] : (v27 = v26 | ~ (model(v29, v28) = v27) | ~ (model(v29, v28) = v26)) & ! [v26] : ! [v27] : ! [v28] : ! [v29] : (v27 = v26 | ~ (xora(v29, v28) = v27) | ~ (xora(v29, v28) = v26)) & ! [v26] : ! [v27] : ! [v28] : ! [v29] : (v27 = v26 | ~ (nevera(v29, v28) = v27) | ~ (nevera(v29, v28) = v26)) & ! [v26] : ! [v27] : ! [v28] : ! [v29] : (v27 = v26 | ~ (nota(v29, v28) = v27) | ~ (nota(v29, v28) = v26)) & ! [v26] : ! [v27] : ! [v28] : ! [v29] : (v27 = v26 | ~ (isa(v29, v28) = v27) | ~ (isa(v29, v28) = v26)) & ! [v26] : ! [v27] : ! [v28] : ! [v29] : (v27 = v26 | ~ (mighta(v29, v28) = v27) | ~ (mighta(v29, v28) = v26)) & ! [v26] : ! [v27] : ! [v28] : ! [v29] : ( ~ (xora(v26, v27) = 0) | ~ (status(v28, v29, v26) = 0) | ? [v30] : ( ~ (v30 = 0) & status(v28, v29, v27) = v30)) & ! [v26] : ! [v27] : ! [v28] : ! [v29] : ( ~ (nevera(v26, v27) = 0) | ~ (status(v28, v29, v26) = 0) | ? [v30] : ( ~ (v30 = 0) & status(v28, v29, v27) = v30)) & ! [v26] : ! [v27] : ! [v28] : ! [v29] : ( ~ (isa(v26, v27) = 0) | ~ (status(v28, v29, v26) = 0) | status(v28, v29, v27) = 0) & ! [v26] : ! [v27] : ! [v28] : (v28 = 0 | ~ (xora(v26, v27) = v28) | ? [v29] : ? [v30] : ? [v31] : ? [v32] : (status(v29, v30, v27) = v32 & status(v29, v30, v26) = v31 & ( ~ (v32 = 0) | v31 = 0) & ( ~ (v31 = 0) | v32 = 0))) & ! [v26] : ! [v27] : ! [v28] : (v28 = 0 | ~ (nevera(v26, v27) = v28) | ? [v29] : ? [v30] : (status(v29, v30, v27) = 0 & status(v29, v30, v26) = 0)) & ! [v26] : ! [v27] : ! [v28] : (v28 = 0 | ~ (isa(v26, v27) = v28) | ? [v29] : ? [v30] : ? [v31] : ( ~ (v31 = 0) & status(v29, v30, v27) = v31 & status(v29, v30, v26) = 0)) & ! [v26] : ! [v27] : ! [v28] : (v27 = v26 | ~ (not(v28) = v27) | ~ (not(v28) = v26)) & ! [v26] : ! [v27] : ! [v28] : ( ~ (not(v27) = v28) | ~ (model(v26, v28) = 0) | ? [v29] : ( ~ (v29 = 0) & model(v26, v27) = v29)) & ! [v26] : ! [v27] : (v27 = 0 | ~ (model(v26, v25) = v27)) & ! [v26] : ! [v27] : ( ~ (nota(v26, v27) = 0) | ? [v28] : ? [v29] : ? [v30] : ( ~ (v30 = 0) & status(v28, v29, v27) = v30 & status(v28, v29, v26) = 0)) & ! [v26] : ! [v27] : ( ~ (mighta(v26, v27) = 0) | ? [v28] : ? [v29] : (status(v28, v29, v27) = 0 & status(v28, v29, v26) = 0)) & ! [v26] : ~ (model(v26, v20) = 0) & ! [v26] : ( ~ (model(v26, v7) = 0) | model(v26, v8) = 0) & ( ~ (v18 = 0) | ~ (v17 = 0))) % 6.65/2.26 | 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, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19, all_0_20_20, all_0_21_21, all_0_22_22, all_0_23_23, all_0_24_24, all_0_25_25 yields: % 6.65/2.26 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_13_13 = 0) & ~ (all_0_15_15 = 0) & ~ (all_0_20_20 = 0) & ~ (all_0_24_24 = 0) & model(all_0_1_1, all_0_4_4) = 0 & model(all_0_3_3, all_0_4_4) = all_0_2_2 & model(all_0_6_6, all_0_10_10) = 0 & model(all_0_6_6, all_0_11_11) = 0 & model(all_0_9_9, all_0_10_10) = all_0_7_7 & model(all_0_9_9, all_0_11_11) = all_0_8_8 & model(all_0_12_12, all_0_18_18) = 0 & model(all_0_14_14, all_0_17_17) = 0 & model(all_0_14_14, all_0_18_18) = all_0_13_13 & model(all_0_16_16, all_0_17_17) = all_0_15_15 & model(all_0_19_19, all_0_21_21) = 0 & model(all_0_23_23, all_0_21_21) = all_0_20_20 & model(all_0_23_23, all_0_22_22) = 0 & isa(all_0_25_25, all_0_25_25) = all_0_24_24 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (xora(v0, v1) = 0) | ~ (status(v2, v3, v0) = v4) | status(v2, v3, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = 0 | ~ (nota(v0, v1) = v2) | ~ (status(v3, v4, v0) = 0) | status(v3, v4, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = 0 | ~ (mighta(v0, v1) = v2) | ~ (status(v3, v4, v0) = 0) | ? [v5] : ( ~ (v5 = 0) & status(v3, v4, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (status(v4, v3, v2) = v1) | ~ (status(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (not(v1) = v2) | ~ (model(v0, v2) = v3) | model(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (model(v3, v2) = v1) | ~ (model(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (xora(v3, v2) = v1) | ~ (xora(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (nevera(v3, v2) = v1) | ~ (nevera(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (nota(v3, v2) = v1) | ~ (nota(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (isa(v3, v2) = v1) | ~ (isa(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (mighta(v3, v2) = v1) | ~ (mighta(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (xora(v0, v1) = 0) | ~ (status(v2, v3, v0) = 0) | ? [v4] : ( ~ (v4 = 0) & status(v2, v3, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (nevera(v0, v1) = 0) | ~ (status(v2, v3, v0) = 0) | ? [v4] : ( ~ (v4 = 0) & status(v2, v3, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (isa(v0, v1) = 0) | ~ (status(v2, v3, v0) = 0) | status(v2, v3, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (xora(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (status(v3, v4, v1) = v6 & status(v3, v4, v0) = v5 & ( ~ (v6 = 0) | v5 = 0) & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (nevera(v0, v1) = v2) | ? [v3] : ? [v4] : (status(v3, v4, v1) = 0 & status(v3, v4, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (isa(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & status(v3, v4, v1) = v5 & status(v3, v4, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (not(v1) = v2) | ~ (model(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & model(v0, v1) = v3)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (model(v0, all_0_0_0) = v1)) & ! [v0] : ! [v1] : ( ~ (nota(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & status(v2, v3, v1) = v4 & status(v2, v3, v0) = 0)) & ! [v0] : ! [v1] : ( ~ (mighta(v0, v1) = 0) | ? [v2] : ? [v3] : (status(v2, v3, v1) = 0 & status(v2, v3, v0) = 0)) & ! [v0] : ~ (model(v0, all_0_5_5) = 0) & ! [v0] : ( ~ (model(v0, all_0_18_18) = 0) | model(v0, all_0_17_17) = 0) & ( ~ (all_0_7_7 = 0) | ~ (all_0_8_8 = 0)) % 7.09/2.27 | % 7.09/2.27 | Applying alpha-rule on (1) yields: % 7.09/2.27 | (2) ! [v0] : ! [v1] : ( ~ (nota(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & status(v2, v3, v1) = v4 & status(v2, v3, v0) = 0)) % 7.09/2.27 | (3) ~ (all_0_13_13 = 0) % 7.09/2.27 | (4) model(all_0_12_12, all_0_18_18) = 0 % 7.09/2.27 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (mighta(v3, v2) = v1) | ~ (mighta(v3, v2) = v0)) % 7.09/2.27 | (6) model(all_0_19_19, all_0_21_21) = 0 % 7.09/2.27 | (7) model(all_0_9_9, all_0_10_10) = all_0_7_7 % 7.09/2.27 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (isa(v0, v1) = 0) | ~ (status(v2, v3, v0) = 0) | status(v2, v3, v1) = 0) % 7.09/2.27 | (9) model(all_0_3_3, all_0_4_4) = all_0_2_2 % 7.09/2.27 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (xora(v3, v2) = v1) | ~ (xora(v3, v2) = v0)) % 7.09/2.27 | (11) model(all_0_14_14, all_0_18_18) = all_0_13_13 % 7.09/2.27 | (12) model(all_0_6_6, all_0_11_11) = 0 % 7.09/2.27 | (13) ~ (all_0_15_15 = 0) % 7.09/2.27 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (nota(v3, v2) = v1) | ~ (nota(v3, v2) = v0)) % 7.09/2.27 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = 0 | ~ (nota(v0, v1) = v2) | ~ (status(v3, v4, v0) = 0) | status(v3, v4, v1) = 0) % 7.09/2.27 | (16) ! [v0] : ~ (model(v0, all_0_5_5) = 0) % 7.09/2.27 | (17) ~ (all_0_2_2 = 0) % 7.09/2.27 | (18) model(all_0_16_16, all_0_17_17) = all_0_15_15 % 7.09/2.27 | (19) model(all_0_6_6, all_0_10_10) = 0 % 7.09/2.27 | (20) model(all_0_9_9, all_0_11_11) = all_0_8_8 % 7.09/2.27 | (21) ! [v0] : ! [v1] : ( ~ (mighta(v0, v1) = 0) | ? [v2] : ? [v3] : (status(v2, v3, v1) = 0 & status(v2, v3, v0) = 0)) % 7.09/2.27 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (xora(v0, v1) = 0) | ~ (status(v2, v3, v0) = v4) | status(v2, v3, v1) = 0) % 7.09/2.27 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (not(v1) = v2) | ~ (model(v0, v2) = v3) | model(v0, v1) = 0) % 7.09/2.27 | (24) model(all_0_1_1, all_0_4_4) = 0 % 7.09/2.27 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (isa(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & status(v3, v4, v1) = v5 & status(v3, v4, v0) = 0)) % 7.09/2.27 | (26) model(all_0_23_23, all_0_21_21) = all_0_20_20 % 7.09/2.27 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (status(v4, v3, v2) = v1) | ~ (status(v4, v3, v2) = v0)) % 7.09/2.27 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = 0 | ~ (mighta(v0, v1) = v2) | ~ (status(v3, v4, v0) = 0) | ? [v5] : ( ~ (v5 = 0) & status(v3, v4, v1) = v5)) % 7.09/2.28 | (29) ~ (all_0_24_24 = 0) % 7.09/2.28 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (not(v1) = v2) | ~ (model(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & model(v0, v1) = v3)) % 7.09/2.28 | (31) isa(all_0_25_25, all_0_25_25) = all_0_24_24 % 7.09/2.28 | (32) model(all_0_23_23, all_0_22_22) = 0 % 7.09/2.28 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (model(v3, v2) = v1) | ~ (model(v3, v2) = v0)) % 7.09/2.28 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (xora(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (status(v3, v4, v1) = v6 & status(v3, v4, v0) = v5 & ( ~ (v6 = 0) | v5 = 0) & ( ~ (v5 = 0) | v6 = 0))) % 7.09/2.28 | (35) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (nevera(v0, v1) = v2) | ? [v3] : ? [v4] : (status(v3, v4, v1) = 0 & status(v3, v4, v0) = 0)) % 7.09/2.28 | (36) model(all_0_14_14, all_0_17_17) = 0 % 7.09/2.28 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (nevera(v3, v2) = v1) | ~ (nevera(v3, v2) = v0)) % 7.09/2.28 | (38) ! [v0] : ! [v1] : (v1 = 0 | ~ (model(v0, all_0_0_0) = v1)) % 7.09/2.28 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (nevera(v0, v1) = 0) | ~ (status(v2, v3, v0) = 0) | ? [v4] : ( ~ (v4 = 0) & status(v2, v3, v1) = v4)) % 7.09/2.28 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (xora(v0, v1) = 0) | ~ (status(v2, v3, v0) = 0) | ? [v4] : ( ~ (v4 = 0) & status(v2, v3, v1) = v4)) % 7.09/2.28 | (41) ! [v0] : ( ~ (model(v0, all_0_18_18) = 0) | model(v0, all_0_17_17) = 0) % 7.09/2.28 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (isa(v3, v2) = v1) | ~ (isa(v3, v2) = v0)) % 7.09/2.28 | (43) ~ (all_0_7_7 = 0) | ~ (all_0_8_8 = 0) % 7.09/2.28 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) % 7.09/2.28 | (45) ~ (all_0_20_20 = 0) % 7.09/2.28 | % 7.09/2.28 | Instantiating formula (25) with all_0_24_24, all_0_25_25, all_0_25_25 and discharging atoms isa(all_0_25_25, all_0_25_25) = all_0_24_24, yields: % 7.09/2.28 | (46) all_0_24_24 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & status(v0, v1, all_0_25_25) = v2 & status(v0, v1, all_0_25_25) = 0) % 7.09/2.28 | % 7.09/2.28 +-Applying beta-rule and splitting (46), into two cases. % 7.09/2.28 |-Branch one: % 7.09/2.28 | (47) all_0_24_24 = 0 % 7.09/2.28 | % 7.09/2.28 | Equations (47) can reduce 29 to: % 7.09/2.28 | (48) $false % 7.09/2.28 | % 7.09/2.28 |-The branch is then unsatisfiable % 7.09/2.28 |-Branch two: % 7.09/2.28 | (29) ~ (all_0_24_24 = 0) % 7.09/2.28 | (50) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & status(v0, v1, all_0_25_25) = v2 & status(v0, v1, all_0_25_25) = 0) % 7.09/2.28 | % 7.09/2.28 | Instantiating (50) with all_37_0_26, all_37_1_27, all_37_2_28 yields: % 7.09/2.28 | (51) ~ (all_37_0_26 = 0) & status(all_37_2_28, all_37_1_27, all_0_25_25) = all_37_0_26 & status(all_37_2_28, all_37_1_27, all_0_25_25) = 0 % 7.09/2.28 | % 7.09/2.28 | Applying alpha-rule on (51) yields: % 7.09/2.28 | (52) ~ (all_37_0_26 = 0) % 7.09/2.28 | (53) status(all_37_2_28, all_37_1_27, all_0_25_25) = all_37_0_26 % 7.09/2.28 | (54) status(all_37_2_28, all_37_1_27, all_0_25_25) = 0 % 7.09/2.28 | % 7.09/2.28 | Instantiating formula (27) with all_37_2_28, all_37_1_27, all_0_25_25, 0, all_37_0_26 and discharging atoms status(all_37_2_28, all_37_1_27, all_0_25_25) = all_37_0_26, status(all_37_2_28, all_37_1_27, all_0_25_25) = 0, yields: % 7.09/2.29 | (55) all_37_0_26 = 0 % 7.09/2.29 | % 7.09/2.29 | Equations (55) can reduce 52 to: % 7.09/2.29 | (48) $false % 7.09/2.29 | % 7.09/2.29 |-The branch is then unsatisfiable % 7.09/2.29 % SZS output end Proof for theBenchmark % 7.09/2.29 % 7.09/2.29 1648ms %------------------------------------------------------------------------------