%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SYN551+1 : TPTP v8.1.0. Bugfixed v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n008.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 : Thu Jul 21 05:03:41 EDT 2022 % Result : Theorem 2.25s 1.25s % Output : Proof 3.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN551+1 : TPTP v8.1.0. Bugfixed v3.1.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.34 % Computer : n008.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Mon Jul 11 23:04:53 EDT 2022 % 0.14/0.34 % CPUTime : % 0.48/0.59 ____ _ % 0.48/0.59 ___ / __ \_____(_)___ ________ __________ % 0.48/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.48/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.48/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.48/0.59 % 0.48/0.59 A Theorem Prover for First-Order Logic % 0.48/0.59 (ePrincess v.1.0) % 0.48/0.59 % 0.48/0.59 (c) Philipp Rümmer, 2009-2015 % 0.48/0.59 (c) Peter Backeman, 2014-2015 % 0.48/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.48/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.48/0.59 Bug reports to peter@backeman.se % 0.48/0.59 % 0.48/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.48/0.59 % 0.48/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.33/0.86 Prover 0: Preprocessing ... % 1.54/0.98 Prover 0: Warning: ignoring some quantifiers % 1.54/1.00 Prover 0: Constructing countermodel ... % 2.01/1.11 Prover 0: gave up % 2.01/1.11 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.01/1.13 Prover 1: Preprocessing ... % 2.25/1.18 Prover 1: Constructing countermodel ... % 2.25/1.25 Prover 1: proved (141ms) % 2.25/1.25 % 2.25/1.25 No countermodel exists, formula is valid % 2.25/1.25 % SZS status Theorem for theBenchmark % 2.25/1.25 % 2.25/1.25 Generating proof ... found it (size 57) % 3.24/1.53 % 3.24/1.53 % SZS output start Proof for theBenchmark % 3.24/1.53 Assumed formulas after preprocessing and simplification: % 3.24/1.53 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (g(v11) = v10) | ~ (g(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (f(v11) = v10) | ~ (f(v11) = v9)) & ((v8 = v6 & g(v7) = v6 & f(v6) = v7 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (f(v10) = v12) | ~ (f(v9) = v11) | ? [v13] : ? [v14] : (g(v12) = v14 & g(v11) = v13 & ( ~ (v14 = v10) | ~ (v13 = v9)))) & ( ! [v9] : ! [v10] : ( ~ (g(v9) = v10) | ? [v11] : ( ~ (v11 = v9) & f(v10) = v11)) | (v5 = v1 & v3 = v0 & ~ (v1 = v0) & g(v1) = v4 & g(v0) = v2 & f(v4) = v1 & f(v2) = v0))) | (v8 = v6 & g(v6) = v7 & f(v7) = v6 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (g(v10) = v12) | ~ (g(v9) = v11) | ? [v13] : ? [v14] : (f(v12) = v14 & f(v11) = v13 & ( ~ (v14 = v10) | ~ (v13 = v9)))) & ( ! [v9] : ! [v10] : ( ~ (f(v9) = v10) | ? [v11] : ( ~ (v11 = v9) & g(v10) = v11)) | (v5 = v1 & v3 = v0 & ~ (v1 = v0) & g(v4) = v1 & g(v2) = v0 & f(v1) = v4 & f(v0) = v2))))) % 3.45/1.56 | 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 yields: % 3.45/1.56 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (g(v2) = v1) | ~ (g(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) & ((all_0_0_0 = all_0_2_2 & g(all_0_1_1) = all_0_2_2 & f(all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (f(v1) = v3) | ~ (f(v0) = v2) | ? [v4] : ? [v5] : (g(v3) = v5 & g(v2) = v4 & ( ~ (v5 = v1) | ~ (v4 = v0)))) & ( ! [v0] : ! [v1] : ( ~ (g(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & f(v1) = v2)) | (all_0_3_3 = all_0_7_7 & all_0_5_5 = all_0_8_8 & ~ (all_0_7_7 = all_0_8_8) & g(all_0_7_7) = all_0_4_4 & g(all_0_8_8) = all_0_6_6 & f(all_0_4_4) = all_0_7_7 & f(all_0_6_6) = all_0_8_8))) | (all_0_0_0 = all_0_2_2 & g(all_0_2_2) = all_0_1_1 & f(all_0_1_1) = all_0_2_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (g(v1) = v3) | ~ (g(v0) = v2) | ? [v4] : ? [v5] : (f(v3) = v5 & f(v2) = v4 & ( ~ (v5 = v1) | ~ (v4 = v0)))) & ( ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & g(v1) = v2)) | (all_0_3_3 = all_0_7_7 & all_0_5_5 = all_0_8_8 & ~ (all_0_7_7 = all_0_8_8) & g(all_0_4_4) = all_0_7_7 & g(all_0_6_6) = all_0_8_8 & f(all_0_7_7) = all_0_4_4 & f(all_0_8_8) = all_0_6_6)))) % 3.45/1.57 | % 3.45/1.57 | Applying alpha-rule on (1) yields: % 3.45/1.57 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (g(v2) = v1) | ~ (g(v2) = v0)) % 3.45/1.57 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) % 3.45/1.57 | (4) (all_0_0_0 = all_0_2_2 & g(all_0_1_1) = all_0_2_2 & f(all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (f(v1) = v3) | ~ (f(v0) = v2) | ? [v4] : ? [v5] : (g(v3) = v5 & g(v2) = v4 & ( ~ (v5 = v1) | ~ (v4 = v0)))) & ( ! [v0] : ! [v1] : ( ~ (g(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & f(v1) = v2)) | (all_0_3_3 = all_0_7_7 & all_0_5_5 = all_0_8_8 & ~ (all_0_7_7 = all_0_8_8) & g(all_0_7_7) = all_0_4_4 & g(all_0_8_8) = all_0_6_6 & f(all_0_4_4) = all_0_7_7 & f(all_0_6_6) = all_0_8_8))) | (all_0_0_0 = all_0_2_2 & g(all_0_2_2) = all_0_1_1 & f(all_0_1_1) = all_0_2_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (g(v1) = v3) | ~ (g(v0) = v2) | ? [v4] : ? [v5] : (f(v3) = v5 & f(v2) = v4 & ( ~ (v5 = v1) | ~ (v4 = v0)))) & ( ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & g(v1) = v2)) | (all_0_3_3 = all_0_7_7 & all_0_5_5 = all_0_8_8 & ~ (all_0_7_7 = all_0_8_8) & g(all_0_4_4) = all_0_7_7 & g(all_0_6_6) = all_0_8_8 & f(all_0_7_7) = all_0_4_4 & f(all_0_8_8) = all_0_6_6))) % 3.45/1.57 | % 3.45/1.57 +-Applying beta-rule and splitting (4), into two cases. % 3.45/1.57 |-Branch one: % 3.45/1.57 | (5) all_0_0_0 = all_0_2_2 & g(all_0_1_1) = all_0_2_2 & f(all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (f(v1) = v3) | ~ (f(v0) = v2) | ? [v4] : ? [v5] : (g(v3) = v5 & g(v2) = v4 & ( ~ (v5 = v1) | ~ (v4 = v0)))) & ( ! [v0] : ! [v1] : ( ~ (g(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & f(v1) = v2)) | (all_0_3_3 = all_0_7_7 & all_0_5_5 = all_0_8_8 & ~ (all_0_7_7 = all_0_8_8) & g(all_0_7_7) = all_0_4_4 & g(all_0_8_8) = all_0_6_6 & f(all_0_4_4) = all_0_7_7 & f(all_0_6_6) = all_0_8_8)) % 3.45/1.57 | % 3.45/1.57 | Applying alpha-rule on (5) yields: % 3.45/1.57 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (f(v1) = v3) | ~ (f(v0) = v2) | ? [v4] : ? [v5] : (g(v3) = v5 & g(v2) = v4 & ( ~ (v5 = v1) | ~ (v4 = v0)))) % 3.45/1.58 | (7) g(all_0_1_1) = all_0_2_2 % 3.45/1.58 | (8) ! [v0] : ! [v1] : ( ~ (g(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & f(v1) = v2)) | (all_0_3_3 = all_0_7_7 & all_0_5_5 = all_0_8_8 & ~ (all_0_7_7 = all_0_8_8) & g(all_0_7_7) = all_0_4_4 & g(all_0_8_8) = all_0_6_6 & f(all_0_4_4) = all_0_7_7 & f(all_0_6_6) = all_0_8_8) % 3.45/1.58 | (9) f(all_0_2_2) = all_0_1_1 % 3.45/1.58 | (10) all_0_0_0 = all_0_2_2 % 3.45/1.58 | % 3.45/1.58 +-Applying beta-rule and splitting (8), into two cases. % 3.45/1.58 |-Branch one: % 3.45/1.58 | (11) ! [v0] : ! [v1] : ( ~ (g(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & f(v1) = v2)) % 3.45/1.58 | % 3.45/1.58 | Instantiating formula (11) with all_0_2_2, all_0_1_1 and discharging atoms g(all_0_1_1) = all_0_2_2, yields: % 3.45/1.58 | (12) ? [v0] : ( ~ (v0 = all_0_1_1) & f(all_0_2_2) = v0) % 3.45/1.58 | % 3.45/1.58 | Instantiating (12) with all_14_0_9 yields: % 3.45/1.58 | (13) ~ (all_14_0_9 = all_0_1_1) & f(all_0_2_2) = all_14_0_9 % 3.45/1.58 | % 3.45/1.58 | Applying alpha-rule on (13) yields: % 3.45/1.58 | (14) ~ (all_14_0_9 = all_0_1_1) % 3.45/1.58 | (15) f(all_0_2_2) = all_14_0_9 % 3.45/1.58 | % 3.45/1.58 | Instantiating formula (3) with all_0_2_2, all_14_0_9, all_0_1_1 and discharging atoms f(all_0_2_2) = all_14_0_9, f(all_0_2_2) = all_0_1_1, yields: % 3.45/1.58 | (16) all_14_0_9 = all_0_1_1 % 3.45/1.58 | % 3.45/1.58 | Equations (16) can reduce 14 to: % 3.45/1.58 | (17) $false % 3.45/1.58 | % 3.45/1.58 |-The branch is then unsatisfiable % 3.45/1.58 |-Branch two: % 3.45/1.58 | (18) all_0_3_3 = all_0_7_7 & all_0_5_5 = all_0_8_8 & ~ (all_0_7_7 = all_0_8_8) & g(all_0_7_7) = all_0_4_4 & g(all_0_8_8) = all_0_6_6 & f(all_0_4_4) = all_0_7_7 & f(all_0_6_6) = all_0_8_8 % 3.45/1.58 | % 3.45/1.58 | Applying alpha-rule on (18) yields: % 3.45/1.58 | (19) g(all_0_8_8) = all_0_6_6 % 3.45/1.58 | (20) all_0_3_3 = all_0_7_7 % 3.45/1.58 | (21) f(all_0_4_4) = all_0_7_7 % 3.45/1.58 | (22) ~ (all_0_7_7 = all_0_8_8) % 3.45/1.58 | (23) f(all_0_6_6) = all_0_8_8 % 3.45/1.58 | (24) all_0_5_5 = all_0_8_8 % 3.45/1.58 | (25) g(all_0_7_7) = all_0_4_4 % 3.45/1.58 | % 3.45/1.58 | Instantiating formula (3) with all_0_6_6, all_0_8_8, all_0_7_7 and discharging atoms f(all_0_6_6) = all_0_8_8, yields: % 3.45/1.58 | (26) all_0_7_7 = all_0_8_8 | ~ (f(all_0_6_6) = all_0_7_7) % 3.45/1.58 | % 3.45/1.58 | Instantiating formula (6) with all_0_7_7, all_0_8_8, all_0_4_4, all_0_6_6 and discharging atoms f(all_0_4_4) = all_0_7_7, f(all_0_6_6) = all_0_8_8, yields: % 3.45/1.58 | (27) all_0_4_4 = all_0_6_6 | ? [v0] : ? [v1] : (g(all_0_7_7) = v1 & g(all_0_8_8) = v0 & ( ~ (v1 = all_0_4_4) | ~ (v0 = all_0_6_6))) % 3.45/1.58 | % 3.45/1.58 +-Applying beta-rule and splitting (26), into two cases. % 3.45/1.58 |-Branch one: % 3.45/1.58 | (28) ~ (f(all_0_6_6) = all_0_7_7) % 3.45/1.58 | % 3.45/1.58 +-Applying beta-rule and splitting (27), into two cases. % 3.45/1.58 |-Branch one: % 3.45/1.58 | (29) all_0_4_4 = all_0_6_6 % 3.45/1.58 | % 3.45/1.58 | From (29) and (21) follows: % 3.45/1.58 | (30) f(all_0_6_6) = all_0_7_7 % 3.45/1.58 | % 3.45/1.58 | Using (30) and (28) yields: % 3.45/1.58 | (31) $false % 3.45/1.59 | % 3.45/1.59 |-The branch is then unsatisfiable % 3.45/1.59 |-Branch two: % 3.45/1.59 | (32) ~ (all_0_4_4 = all_0_6_6) % 3.45/1.59 | (33) ? [v0] : ? [v1] : (g(all_0_7_7) = v1 & g(all_0_8_8) = v0 & ( ~ (v1 = all_0_4_4) | ~ (v0 = all_0_6_6))) % 3.45/1.59 | % 3.45/1.59 | Instantiating (33) with all_25_0_10, all_25_1_11 yields: % 3.45/1.59 | (34) g(all_0_7_7) = all_25_0_10 & g(all_0_8_8) = all_25_1_11 & ( ~ (all_25_0_10 = all_0_4_4) | ~ (all_25_1_11 = all_0_6_6)) % 3.45/1.59 | % 3.45/1.59 | Applying alpha-rule on (34) yields: % 3.45/1.59 | (35) g(all_0_7_7) = all_25_0_10 % 3.45/1.59 | (36) g(all_0_8_8) = all_25_1_11 % 3.45/1.59 | (37) ~ (all_25_0_10 = all_0_4_4) | ~ (all_25_1_11 = all_0_6_6) % 3.45/1.59 | % 3.45/1.59 | Instantiating formula (2) with all_0_7_7, all_25_0_10, all_0_4_4 and discharging atoms g(all_0_7_7) = all_25_0_10, g(all_0_7_7) = all_0_4_4, yields: % 3.45/1.59 | (38) all_25_0_10 = all_0_4_4 % 3.45/1.59 | % 3.45/1.59 | Instantiating formula (2) with all_0_8_8, all_25_1_11, all_0_6_6 and discharging atoms g(all_0_8_8) = all_25_1_11, g(all_0_8_8) = all_0_6_6, yields: % 3.45/1.59 | (39) all_25_1_11 = all_0_6_6 % 3.45/1.59 | % 3.45/1.59 +-Applying beta-rule and splitting (37), into two cases. % 3.45/1.59 |-Branch one: % 3.45/1.59 | (40) ~ (all_25_0_10 = all_0_4_4) % 3.45/1.59 | % 3.45/1.59 | Equations (38) can reduce 40 to: % 3.45/1.59 | (17) $false % 3.45/1.59 | % 3.45/1.59 |-The branch is then unsatisfiable % 3.45/1.59 |-Branch two: % 3.45/1.59 | (38) all_25_0_10 = all_0_4_4 % 3.45/1.59 | (43) ~ (all_25_1_11 = all_0_6_6) % 3.45/1.59 | % 3.45/1.59 | Equations (39) can reduce 43 to: % 3.45/1.59 | (17) $false % 3.45/1.59 | % 3.45/1.59 |-The branch is then unsatisfiable % 3.45/1.59 |-Branch two: % 3.45/1.59 | (30) f(all_0_6_6) = all_0_7_7 % 3.45/1.59 | (46) all_0_7_7 = all_0_8_8 % 3.45/1.59 | % 3.45/1.59 | Equations (46) can reduce 22 to: % 3.45/1.59 | (17) $false % 3.45/1.59 | % 3.45/1.59 |-The branch is then unsatisfiable % 3.45/1.59 |-Branch two: % 3.45/1.59 | (48) all_0_0_0 = all_0_2_2 & g(all_0_2_2) = all_0_1_1 & f(all_0_1_1) = all_0_2_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (g(v1) = v3) | ~ (g(v0) = v2) | ? [v4] : ? [v5] : (f(v3) = v5 & f(v2) = v4 & ( ~ (v5 = v1) | ~ (v4 = v0)))) & ( ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & g(v1) = v2)) | (all_0_3_3 = all_0_7_7 & all_0_5_5 = all_0_8_8 & ~ (all_0_7_7 = all_0_8_8) & g(all_0_4_4) = all_0_7_7 & g(all_0_6_6) = all_0_8_8 & f(all_0_7_7) = all_0_4_4 & f(all_0_8_8) = all_0_6_6)) % 3.45/1.59 | % 3.45/1.59 | Applying alpha-rule on (48) yields: % 3.45/1.59 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (g(v1) = v3) | ~ (g(v0) = v2) | ? [v4] : ? [v5] : (f(v3) = v5 & f(v2) = v4 & ( ~ (v5 = v1) | ~ (v4 = v0)))) % 3.45/1.59 | (50) f(all_0_1_1) = all_0_2_2 % 3.45/1.59 | (51) g(all_0_2_2) = all_0_1_1 % 3.45/1.59 | (52) ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & g(v1) = v2)) | (all_0_3_3 = all_0_7_7 & all_0_5_5 = all_0_8_8 & ~ (all_0_7_7 = all_0_8_8) & g(all_0_4_4) = all_0_7_7 & g(all_0_6_6) = all_0_8_8 & f(all_0_7_7) = all_0_4_4 & f(all_0_8_8) = all_0_6_6) % 3.45/1.59 | (10) all_0_0_0 = all_0_2_2 % 3.45/1.59 | % 3.45/1.59 +-Applying beta-rule and splitting (52), into two cases. % 3.45/1.59 |-Branch one: % 3.45/1.59 | (54) ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & g(v1) = v2)) % 3.45/1.59 | % 3.45/1.59 | Instantiating formula (54) with all_0_2_2, all_0_1_1 and discharging atoms f(all_0_1_1) = all_0_2_2, yields: % 3.45/1.59 | (55) ? [v0] : ( ~ (v0 = all_0_1_1) & g(all_0_2_2) = v0) % 3.45/1.59 | % 3.45/1.59 | Instantiating (55) with all_14_0_14 yields: % 3.45/1.59 | (56) ~ (all_14_0_14 = all_0_1_1) & g(all_0_2_2) = all_14_0_14 % 3.45/1.59 | % 3.45/1.59 | Applying alpha-rule on (56) yields: % 3.45/1.59 | (57) ~ (all_14_0_14 = all_0_1_1) % 3.45/1.59 | (58) g(all_0_2_2) = all_14_0_14 % 3.45/1.59 | % 3.45/1.59 | Instantiating formula (2) with all_0_2_2, all_14_0_14, all_0_1_1 and discharging atoms g(all_0_2_2) = all_14_0_14, g(all_0_2_2) = all_0_1_1, yields: % 3.45/1.59 | (59) all_14_0_14 = all_0_1_1 % 3.45/1.59 | % 3.45/1.59 | Equations (59) can reduce 57 to: % 3.45/1.59 | (17) $false % 3.45/1.59 | % 3.45/1.59 |-The branch is then unsatisfiable % 3.45/1.59 |-Branch two: % 3.45/1.59 | (61) all_0_3_3 = all_0_7_7 & all_0_5_5 = all_0_8_8 & ~ (all_0_7_7 = all_0_8_8) & g(all_0_4_4) = all_0_7_7 & g(all_0_6_6) = all_0_8_8 & f(all_0_7_7) = all_0_4_4 & f(all_0_8_8) = all_0_6_6 % 3.45/1.59 | % 3.45/1.59 | Applying alpha-rule on (61) yields: % 3.45/1.60 | (62) g(all_0_4_4) = all_0_7_7 % 3.45/1.60 | (20) all_0_3_3 = all_0_7_7 % 3.45/1.60 | (64) g(all_0_6_6) = all_0_8_8 % 3.45/1.60 | (22) ~ (all_0_7_7 = all_0_8_8) % 3.45/1.60 | (66) f(all_0_7_7) = all_0_4_4 % 3.45/1.60 | (67) f(all_0_8_8) = all_0_6_6 % 3.45/1.60 | (24) all_0_5_5 = all_0_8_8 % 3.45/1.60 | % 3.45/1.60 | Instantiating formula (2) with all_0_6_6, all_0_8_8, all_0_7_7 and discharging atoms g(all_0_6_6) = all_0_8_8, yields: % 3.45/1.60 | (69) all_0_7_7 = all_0_8_8 | ~ (g(all_0_6_6) = all_0_7_7) % 3.45/1.60 | % 3.45/1.60 | Instantiating formula (49) with all_0_7_7, all_0_8_8, all_0_4_4, all_0_6_6 and discharging atoms g(all_0_4_4) = all_0_7_7, g(all_0_6_6) = all_0_8_8, yields: % 3.45/1.60 | (70) all_0_4_4 = all_0_6_6 | ? [v0] : ? [v1] : (f(all_0_7_7) = v1 & f(all_0_8_8) = v0 & ( ~ (v1 = all_0_4_4) | ~ (v0 = all_0_6_6))) % 3.45/1.60 | % 3.45/1.60 +-Applying beta-rule and splitting (70), into two cases. % 3.45/1.60 |-Branch one: % 3.45/1.60 | (29) all_0_4_4 = all_0_6_6 % 3.45/1.60 | % 3.45/1.60 | From (29) and (62) follows: % 3.45/1.60 | (72) g(all_0_6_6) = all_0_7_7 % 3.45/1.60 | % 3.45/1.60 +-Applying beta-rule and splitting (69), into two cases. % 3.45/1.60 |-Branch one: % 3.45/1.60 | (73) ~ (g(all_0_6_6) = all_0_7_7) % 3.45/1.60 | % 3.45/1.60 | Using (72) and (73) yields: % 3.45/1.60 | (31) $false % 3.45/1.60 | % 3.45/1.60 |-The branch is then unsatisfiable % 3.45/1.60 |-Branch two: % 3.45/1.60 | (72) g(all_0_6_6) = all_0_7_7 % 3.45/1.60 | (46) all_0_7_7 = all_0_8_8 % 3.45/1.60 | % 3.45/1.60 | Equations (46) can reduce 22 to: % 3.45/1.60 | (17) $false % 3.45/1.60 | % 3.45/1.60 |-The branch is then unsatisfiable % 3.45/1.60 |-Branch two: % 3.45/1.60 | (32) ~ (all_0_4_4 = all_0_6_6) % 3.45/1.60 | (79) ? [v0] : ? [v1] : (f(all_0_7_7) = v1 & f(all_0_8_8) = v0 & ( ~ (v1 = all_0_4_4) | ~ (v0 = all_0_6_6))) % 3.45/1.60 | % 3.45/1.60 | Instantiating (79) with all_25_0_15, all_25_1_16 yields: % 3.45/1.60 | (80) f(all_0_7_7) = all_25_0_15 & f(all_0_8_8) = all_25_1_16 & ( ~ (all_25_0_15 = all_0_4_4) | ~ (all_25_1_16 = all_0_6_6)) % 3.45/1.60 | % 3.45/1.60 | Applying alpha-rule on (80) yields: % 3.45/1.60 | (81) f(all_0_7_7) = all_25_0_15 % 3.45/1.60 | (82) f(all_0_8_8) = all_25_1_16 % 3.45/1.60 | (83) ~ (all_25_0_15 = all_0_4_4) | ~ (all_25_1_16 = all_0_6_6) % 3.45/1.60 | % 3.45/1.60 | Instantiating formula (3) with all_0_7_7, all_25_0_15, all_0_4_4 and discharging atoms f(all_0_7_7) = all_25_0_15, f(all_0_7_7) = all_0_4_4, yields: % 3.45/1.60 | (84) all_25_0_15 = all_0_4_4 % 3.45/1.60 | % 3.45/1.60 | Instantiating formula (3) with all_0_8_8, all_25_1_16, all_0_6_6 and discharging atoms f(all_0_8_8) = all_25_1_16, f(all_0_8_8) = all_0_6_6, yields: % 3.45/1.60 | (85) all_25_1_16 = all_0_6_6 % 3.45/1.60 | % 3.45/1.60 +-Applying beta-rule and splitting (83), into two cases. % 3.45/1.60 |-Branch one: % 3.45/1.60 | (86) ~ (all_25_0_15 = all_0_4_4) % 3.45/1.60 | % 3.45/1.60 | Equations (84) can reduce 86 to: % 3.45/1.60 | (17) $false % 3.45/1.60 | % 3.45/1.60 |-The branch is then unsatisfiable % 3.45/1.60 |-Branch two: % 3.45/1.60 | (84) all_25_0_15 = all_0_4_4 % 3.45/1.60 | (89) ~ (all_25_1_16 = all_0_6_6) % 3.45/1.60 | % 3.45/1.60 | Equations (85) can reduce 89 to: % 3.45/1.60 | (17) $false % 3.45/1.60 | % 3.45/1.60 |-The branch is then unsatisfiable % 3.45/1.60 % SZS output end Proof for theBenchmark % 3.45/1.60 % 3.45/1.60 999ms %------------------------------------------------------------------------------