%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KRS181+1 : TPTP v8.1.0. Bugfixed v5.4.0. % 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 02:56:49 EDT 2022 % Result : Theorem 12.36s 3.60s % Output : Proof 13.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KRS181+1 : TPTP v8.1.0. Bugfixed v5.4.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n025.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 07:22:48 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 % 1.39/0.92 Prover 0: Preprocessing ... % 2.03/1.07 Prover 0: Warning: ignoring some quantifiers % 2.09/1.09 Prover 0: Constructing countermodel ... % 12.11/3.47 Prover 0: gave up % 12.11/3.47 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 12.16/3.50 Prover 1: Preprocessing ... % 12.36/3.57 Prover 1: Constructing countermodel ... % 12.36/3.60 Prover 1: proved (130ms) % 12.36/3.60 % 12.36/3.60 No countermodel exists, formula is valid % 12.36/3.60 % SZS status Theorem for theBenchmark % 12.36/3.61 % 12.36/3.61 Generating proof ... found it (size 13) % 13.76/3.83 % 13.76/3.83 % SZS output start Proof for theBenchmark % 13.76/3.83 Assumed formulas after preprocessing and simplification: % 13.76/3.83 | (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] : ? [v26] : ? [v27] : ( ~ (v25 = 0) & ~ (v14 = 0) & ~ (v12 = 0) & ~ (v7 = 0) & ~ (v3 = 0) & model(v26, v23) = 0 & model(v24, v23) = v25 & model(v21, v17) = 0 & model(v21, v16) = 0 & model(v18, v17) = v20 & model(v18, v16) = v19 & model(v15, v9) = 0 & model(v13, v10) = 0 & model(v13, v9) = v14 & model(v11, v10) = v12 & model(v8, v6) = 0 & model(v4, v6) = v7 & model(v4, v5) = 0 & nota(v1, v2) = v3 & nota(v0, v2) = 0 & isa(v0, v1) = 0 & ! [v28] : ! [v29] : ! [v30] : ! [v31] : ! [v32] : (v32 = 0 | ~ (xora(v28, v29) = 0) | ~ (status(v30, v31, v28) = v32) | status(v30, v31, v29) = 0) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : ! [v32] : (v30 = 0 | ~ (nota(v28, v29) = v30) | ~ (status(v31, v32, v28) = 0) | status(v31, v32, v29) = 0) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : ! [v32] : (v30 = 0 | ~ (mighta(v28, v29) = v30) | ~ (status(v31, v32, v28) = 0) | ? [v33] : ( ~ (v33 = 0) & status(v31, v32, v29) = v33)) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : ! [v32] : (v29 = v28 | ~ (status(v32, v31, v30) = v29) | ~ (status(v32, v31, v30) = v28)) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : (v31 = 0 | ~ (not(v29) = v30) | ~ (model(v28, v30) = v31) | model(v28, v29) = 0) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : (v29 = v28 | ~ (model(v31, v30) = v29) | ~ (model(v31, v30) = v28)) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : (v29 = v28 | ~ (xora(v31, v30) = v29) | ~ (xora(v31, v30) = v28)) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : (v29 = v28 | ~ (nevera(v31, v30) = v29) | ~ (nevera(v31, v30) = v28)) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : (v29 = v28 | ~ (nota(v31, v30) = v29) | ~ (nota(v31, v30) = v28)) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : (v29 = v28 | ~ (isa(v31, v30) = v29) | ~ (isa(v31, v30) = v28)) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : (v29 = v28 | ~ (mighta(v31, v30) = v29) | ~ (mighta(v31, v30) = v28)) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : ( ~ (xora(v28, v29) = 0) | ~ (status(v30, v31, v28) = 0) | ? [v32] : ( ~ (v32 = 0) & status(v30, v31, v29) = v32)) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : ( ~ (nevera(v28, v29) = 0) | ~ (status(v30, v31, v28) = 0) | ? [v32] : ( ~ (v32 = 0) & status(v30, v31, v29) = v32)) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : ( ~ (isa(v28, v29) = 0) | ~ (status(v30, v31, v28) = 0) | status(v30, v31, v29) = 0) & ! [v28] : ! [v29] : ! [v30] : (v30 = 0 | ~ (xora(v28, v29) = v30) | ? [v31] : ? [v32] : ? [v33] : ? [v34] : (status(v31, v32, v29) = v34 & status(v31, v32, v28) = v33 & ( ~ (v34 = 0) | v33 = 0) & ( ~ (v33 = 0) | v34 = 0))) & ! [v28] : ! [v29] : ! [v30] : (v30 = 0 | ~ (nevera(v28, v29) = v30) | ? [v31] : ? [v32] : (status(v31, v32, v29) = 0 & status(v31, v32, v28) = 0)) & ! [v28] : ! [v29] : ! [v30] : (v30 = 0 | ~ (isa(v28, v29) = v30) | ? [v31] : ? [v32] : ? [v33] : ( ~ (v33 = 0) & status(v31, v32, v29) = v33 & status(v31, v32, v28) = 0)) & ! [v28] : ! [v29] : ! [v30] : (v29 = v28 | ~ (not(v30) = v29) | ~ (not(v30) = v28)) & ! [v28] : ! [v29] : ! [v30] : ( ~ (not(v29) = v30) | ~ (model(v28, v30) = 0) | ? [v31] : ( ~ (v31 = 0) & model(v28, v29) = v31)) & ! [v28] : ! [v29] : (v29 = 0 | ~ (model(v28, v27) = v29)) & ! [v28] : ! [v29] : ( ~ (nota(v28, v29) = 0) | ? [v30] : ? [v31] : ? [v32] : ( ~ (v32 = 0) & status(v30, v31, v29) = v32 & status(v30, v31, v28) = 0)) & ! [v28] : ! [v29] : ( ~ (mighta(v28, v29) = 0) | ? [v30] : ? [v31] : (status(v30, v31, v29) = 0 & status(v30, v31, v28) = 0)) & ! [v28] : ~ (model(v28, v22) = 0) & ! [v28] : ( ~ (model(v28, v9) = 0) | model(v28, v10) = 0) & ( ~ (v20 = 0) | ~ (v19 = 0))) % 13.85/3.86 | 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, all_0_26_26, all_0_27_27 yields: % 13.85/3.86 | (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 & nota(all_0_26_26, all_0_25_25) = all_0_24_24 & nota(all_0_27_27, all_0_25_25) = 0 & isa(all_0_27_27, all_0_26_26) = 0 & ! [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)) % 13.85/3.87 | % 13.85/3.87 | Applying alpha-rule on (1) yields: % 13.85/3.87 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (status(v4, v3, v2) = v1) | ~ (status(v4, v3, v2) = v0)) % 13.85/3.87 | (3) ! [v0] : ! [v1] : ( ~ (mighta(v0, v1) = 0) | ? [v2] : ? [v3] : (status(v2, v3, v1) = 0 & status(v2, v3, v0) = 0)) % 13.85/3.87 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (not(v1) = v2) | ~ (model(v0, v2) = v3) | model(v0, v1) = 0) % 13.85/3.87 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (not(v2) = v1) | ~ (not(v2) = v0)) % 13.85/3.87 | (6) ~ (all_0_7_7 = 0) | ~ (all_0_8_8 = 0) % 13.85/3.87 | (7) model(all_0_9_9, all_0_10_10) = all_0_7_7 % 13.85/3.87 | (8) model(all_0_9_9, all_0_11_11) = all_0_8_8 % 13.85/3.87 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (nevera(v0, v1) = 0) | ~ (status(v2, v3, v0) = 0) | ? [v4] : ( ~ (v4 = 0) & status(v2, v3, v1) = v4)) % 13.85/3.87 | (10) ! [v0] : ~ (model(v0, all_0_5_5) = 0) % 13.85/3.87 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (mighta(v3, v2) = v1) | ~ (mighta(v3, v2) = v0)) % 13.85/3.87 | (12) model(all_0_14_14, all_0_17_17) = 0 % 13.85/3.87 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (model(v0, all_0_0_0) = v1)) % 13.85/3.87 | (14) nota(all_0_26_26, all_0_25_25) = all_0_24_24 % 13.85/3.87 | (15) model(all_0_19_19, all_0_21_21) = 0 % 13.85/3.87 | (16) ~ (all_0_24_24 = 0) % 13.85/3.87 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = 0 | ~ (mighta(v0, v1) = v2) | ~ (status(v3, v4, v0) = 0) | ? [v5] : ( ~ (v5 = 0) & status(v3, v4, v1) = v5)) % 13.85/3.87 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (nevera(v0, v1) = v2) | ? [v3] : ? [v4] : (status(v3, v4, v1) = 0 & status(v3, v4, v0) = 0)) % 13.85/3.87 | (19) ! [v0] : ( ~ (model(v0, all_0_18_18) = 0) | model(v0, all_0_17_17) = 0) % 13.85/3.87 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (model(v3, v2) = v1) | ~ (model(v3, v2) = v0)) % 13.85/3.87 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (xora(v3, v2) = v1) | ~ (xora(v3, v2) = v0)) % 13.85/3.87 | (22) model(all_0_6_6, all_0_11_11) = 0 % 13.85/3.87 | (23) isa(all_0_27_27, all_0_26_26) = 0 % 13.85/3.87 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (xora(v0, v1) = 0) | ~ (status(v2, v3, v0) = 0) | ? [v4] : ( ~ (v4 = 0) & status(v2, v3, v1) = v4)) % 13.85/3.88 | (25) model(all_0_12_12, all_0_18_18) = 0 % 13.85/3.88 | (26) model(all_0_3_3, all_0_4_4) = all_0_2_2 % 13.85/3.88 | (27) nota(all_0_27_27, all_0_25_25) = 0 % 13.85/3.88 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (xora(v0, v1) = 0) | ~ (status(v2, v3, v0) = v4) | status(v2, v3, v1) = 0) % 13.85/3.88 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (nevera(v3, v2) = v1) | ~ (nevera(v3, v2) = v0)) % 13.85/3.88 | (30) model(all_0_16_16, all_0_17_17) = all_0_15_15 % 13.85/3.88 | (31) ~ (all_0_2_2 = 0) % 13.85/3.88 | (32) ! [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))) % 13.85/3.88 | (33) model(all_0_1_1, all_0_4_4) = 0 % 13.85/3.88 | (34) model(all_0_14_14, all_0_18_18) = all_0_13_13 % 13.85/3.88 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (isa(v0, v1) = 0) | ~ (status(v2, v3, v0) = 0) | status(v2, v3, v1) = 0) % 13.85/3.88 | (36) ~ (all_0_15_15 = 0) % 13.85/3.88 | (37) ~ (all_0_13_13 = 0) % 13.85/3.88 | (38) ~ (all_0_20_20 = 0) % 13.85/3.88 | (39) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (isa(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & status(v3, v4, v1) = v5 & status(v3, v4, v0) = 0)) % 13.85/3.88 | (40) model(all_0_6_6, all_0_10_10) = 0 % 13.85/3.88 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (isa(v3, v2) = v1) | ~ (isa(v3, v2) = v0)) % 13.85/3.88 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (not(v1) = v2) | ~ (model(v0, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & model(v0, v1) = v3)) % 13.85/3.88 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (nota(v3, v2) = v1) | ~ (nota(v3, v2) = v0)) % 13.85/3.88 | (44) model(all_0_23_23, all_0_21_21) = all_0_20_20 % 13.85/3.88 | (45) model(all_0_23_23, all_0_22_22) = 0 % 13.85/3.88 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = 0 | ~ (nota(v0, v1) = v2) | ~ (status(v3, v4, v0) = 0) | status(v3, v4, v1) = 0) % 13.85/3.88 | (47) ! [v0] : ! [v1] : ( ~ (nota(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & status(v2, v3, v1) = v4 & status(v2, v3, v0) = 0)) % 13.85/3.88 | % 13.85/3.88 | Instantiating formula (47) with all_0_25_25, all_0_27_27 and discharging atoms nota(all_0_27_27, all_0_25_25) = 0, yields: % 13.85/3.88 | (48) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & status(v0, v1, all_0_25_25) = v2 & status(v0, v1, all_0_27_27) = 0) % 13.85/3.88 | % 13.85/3.88 | Instantiating (48) with all_33_0_28, all_33_1_29, all_33_2_30 yields: % 13.85/3.88 | (49) ~ (all_33_0_28 = 0) & status(all_33_2_30, all_33_1_29, all_0_25_25) = all_33_0_28 & status(all_33_2_30, all_33_1_29, all_0_27_27) = 0 % 13.85/3.88 | % 13.85/3.88 | Applying alpha-rule on (49) yields: % 13.85/3.88 | (50) ~ (all_33_0_28 = 0) % 13.85/3.88 | (51) status(all_33_2_30, all_33_1_29, all_0_25_25) = all_33_0_28 % 13.85/3.88 | (52) status(all_33_2_30, all_33_1_29, all_0_27_27) = 0 % 13.85/3.88 | % 13.85/3.88 | Instantiating formula (35) with all_33_1_29, all_33_2_30, all_0_26_26, all_0_27_27 and discharging atoms isa(all_0_27_27, all_0_26_26) = 0, status(all_33_2_30, all_33_1_29, all_0_27_27) = 0, yields: % 13.85/3.88 | (53) status(all_33_2_30, all_33_1_29, all_0_26_26) = 0 % 13.85/3.88 | % 13.85/3.88 | Instantiating formula (46) with all_33_1_29, all_33_2_30, all_0_24_24, all_0_25_25, all_0_26_26 and discharging atoms nota(all_0_26_26, all_0_25_25) = all_0_24_24, status(all_33_2_30, all_33_1_29, all_0_26_26) = 0, yields: % 13.85/3.88 | (54) all_0_24_24 = 0 | status(all_33_2_30, all_33_1_29, all_0_25_25) = 0 % 13.85/3.88 | % 13.85/3.88 +-Applying beta-rule and splitting (54), into two cases. % 13.85/3.88 |-Branch one: % 13.85/3.88 | (55) status(all_33_2_30, all_33_1_29, all_0_25_25) = 0 % 13.85/3.88 | % 13.85/3.88 | Instantiating formula (2) with all_33_2_30, all_33_1_29, all_0_25_25, 0, all_33_0_28 and discharging atoms status(all_33_2_30, all_33_1_29, all_0_25_25) = all_33_0_28, status(all_33_2_30, all_33_1_29, all_0_25_25) = 0, yields: % 13.85/3.88 | (56) all_33_0_28 = 0 % 13.85/3.88 | % 13.85/3.88 | Equations (56) can reduce 50 to: % 13.85/3.88 | (57) $false % 13.85/3.88 | % 13.85/3.89 |-The branch is then unsatisfiable % 13.85/3.89 |-Branch two: % 13.85/3.89 | (58) ~ (status(all_33_2_30, all_33_1_29, all_0_25_25) = 0) % 13.85/3.89 | (59) all_0_24_24 = 0 % 13.85/3.89 | % 13.85/3.89 | Equations (59) can reduce 16 to: % 13.85/3.89 | (57) $false % 13.85/3.89 | % 13.85/3.89 |-The branch is then unsatisfiable % 13.85/3.89 % SZS output end Proof for theBenchmark % 13.85/3.89 % 13.85/3.89 3297ms %------------------------------------------------------------------------------