%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU156+3 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 : Tue Jul 19 08:47:05 EDT 2022 % Result : Theorem 2.66s 1.35s % Output : Proof 3.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU156+3 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n026.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jun 19 01:58:40 EDT 2022 % 0.12/0.34 % CPUTime : % 0.47/0.59 ____ _ % 0.47/0.59 ___ / __ \_____(_)___ ________ __________ % 0.47/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.47/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.47/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.47/0.59 % 0.47/0.59 A Theorem Prover for First-Order Logic % 0.47/0.59 (ePrincess v.1.0) % 0.47/0.59 % 0.47/0.59 (c) Philipp Rümmer, 2009-2015 % 0.47/0.59 (c) Peter Backeman, 2014-2015 % 0.47/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.47/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.47/0.59 Bug reports to peter@backeman.se % 0.47/0.59 % 0.47/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.47/0.59 % 0.47/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.46/0.93 Prover 0: Preprocessing ... % 1.86/1.12 Prover 0: Warning: ignoring some quantifiers % 1.86/1.13 Prover 0: Constructing countermodel ... % 2.66/1.34 Prover 0: proved (705ms) % 2.66/1.35 % 2.66/1.35 No countermodel exists, formula is valid % 2.66/1.35 % SZS status Theorem for theBenchmark % 2.66/1.35 % 2.66/1.35 Generating proof ... Warning: ignoring some quantifiers % 3.81/1.63 found it (size 84) % 3.81/1.63 % 3.81/1.63 % SZS output start Proof for theBenchmark % 3.81/1.63 Assumed formulas after preprocessing and simplification: % 3.81/1.63 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v2, v3) = v4 & ordered_pair(v0, v1) = v4 & empty(v6) & ~ empty(v5) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v7 | v9 = v7 | ~ (unordered_pair(v9, v10) = v11) | ~ (unordered_pair(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (singleton(v7) = v10) | ~ (unordered_pair(v9, v10) = v11) | ~ (unordered_pair(v7, v8) = v9) | ordered_pair(v7, v8) = v11) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v7) = v10) | ~ (unordered_pair(v8, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (singleton(v8) = v10) | ~ (singleton(v7) = v9) | ~ subset(v9, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (singleton(v7) = v10) | ~ (unordered_pair(v8, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (ordered_pair(v10, v9) = v8) | ~ (ordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ empty(v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ? [v10] : ? [v11] : (singleton(v7) = v11 & unordered_pair(v10, v11) = v9 & unordered_pair(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v8, v7) = v9) | unordered_pair(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | unordered_pair(v8, v7) = v9) & ! [v7] : ! [v8] : ( ~ (singleton(v7) = v8) | unordered_pair(v7, v7) = v8) & ! [v7] : ! [v8] : ( ~ (unordered_pair(v7, v7) = v8) | singleton(v7) = v8) & ? [v7] : subset(v7, v7) & ( ~ (v3 = v1) | ~ (v2 = v0))) % 3.96/1.67 | 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 yields: % 3.96/1.67 | (1) ordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2 & ordered_pair(all_0_6_6, all_0_5_5) = all_0_2_2 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ? [v0] : subset(v0, v0) & ( ~ (all_0_3_3 = all_0_5_5) | ~ (all_0_4_4 = all_0_6_6)) % 3.96/1.68 | % 3.96/1.68 | Applying alpha-rule on (1) yields: % 3.96/1.68 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) % 3.96/1.68 | (3) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) % 3.96/1.68 | (4) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) % 3.96/1.68 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 3.96/1.68 | (6) ordered_pair(all_0_6_6, all_0_5_5) = all_0_2_2 % 3.96/1.68 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 3.96/1.68 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 3.96/1.68 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 3.96/1.68 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 3.96/1.68 | (11) ~ (all_0_3_3 = all_0_5_5) | ~ (all_0_4_4 = all_0_6_6) % 3.96/1.68 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3)) % 3.96/1.68 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 3.96/1.68 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 3.96/1.68 | (15) ? [v0] : subset(v0, v0) % 3.96/1.68 | (16) ~ empty(all_0_1_1) % 3.96/1.68 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 3.96/1.68 | (18) ordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2 % 3.96/1.68 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 3.96/1.68 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 3.96/1.68 | (21) empty(all_0_0_0) % 3.96/1.68 | % 3.96/1.68 | Instantiating formula (13) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms ordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2, yields: % 3.96/1.68 | (22) ? [v0] : ? [v1] : (singleton(all_0_4_4) = v1 & unordered_pair(v0, v1) = all_0_2_2 & unordered_pair(all_0_4_4, all_0_3_3) = v0) % 3.96/1.68 | % 3.96/1.68 | Instantiating formula (13) with all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms ordered_pair(all_0_6_6, all_0_5_5) = all_0_2_2, yields: % 3.96/1.68 | (23) ? [v0] : ? [v1] : (singleton(all_0_6_6) = v1 & unordered_pair(v0, v1) = all_0_2_2 & unordered_pair(all_0_6_6, all_0_5_5) = v0) % 3.96/1.68 | % 3.96/1.68 | Instantiating (23) with all_10_0_8, all_10_1_9 yields: % 3.96/1.68 | (24) singleton(all_0_6_6) = all_10_0_8 & unordered_pair(all_10_1_9, all_10_0_8) = all_0_2_2 & unordered_pair(all_0_6_6, all_0_5_5) = all_10_1_9 % 3.96/1.68 | % 3.96/1.68 | Applying alpha-rule on (24) yields: % 3.96/1.68 | (25) singleton(all_0_6_6) = all_10_0_8 % 3.96/1.68 | (26) unordered_pair(all_10_1_9, all_10_0_8) = all_0_2_2 % 3.96/1.69 | (27) unordered_pair(all_0_6_6, all_0_5_5) = all_10_1_9 % 3.96/1.69 | % 3.96/1.69 | Instantiating (22) with all_12_0_10, all_12_1_11 yields: % 3.96/1.69 | (28) singleton(all_0_4_4) = all_12_0_10 & unordered_pair(all_12_1_11, all_12_0_10) = all_0_2_2 & unordered_pair(all_0_4_4, all_0_3_3) = all_12_1_11 % 3.96/1.69 | % 3.96/1.69 | Applying alpha-rule on (28) yields: % 3.96/1.69 | (29) singleton(all_0_4_4) = all_12_0_10 % 3.96/1.69 | (30) unordered_pair(all_12_1_11, all_12_0_10) = all_0_2_2 % 3.96/1.69 | (31) unordered_pair(all_0_4_4, all_0_3_3) = all_12_1_11 % 3.96/1.69 | % 3.96/1.69 | Instantiating formula (4) with all_12_0_10, all_0_4_4 and discharging atoms singleton(all_0_4_4) = all_12_0_10, yields: % 3.96/1.69 | (32) unordered_pair(all_0_4_4, all_0_4_4) = all_12_0_10 % 3.96/1.69 | % 3.96/1.69 | Instantiating formula (8) with all_0_2_2, all_12_1_11, all_12_0_10 and discharging atoms unordered_pair(all_12_1_11, all_12_0_10) = all_0_2_2, yields: % 3.96/1.69 | (33) unordered_pair(all_12_0_10, all_12_1_11) = all_0_2_2 % 3.96/1.69 | % 3.96/1.69 | Instantiating formula (8) with all_0_2_2, all_10_1_9, all_10_0_8 and discharging atoms unordered_pair(all_10_1_9, all_10_0_8) = all_0_2_2, yields: % 3.96/1.69 | (34) unordered_pair(all_10_0_8, all_10_1_9) = all_0_2_2 % 3.96/1.69 | % 3.96/1.69 | Instantiating formula (8) with all_12_1_11, all_0_4_4, all_0_3_3 and discharging atoms unordered_pair(all_0_4_4, all_0_3_3) = all_12_1_11, yields: % 3.96/1.69 | (35) unordered_pair(all_0_3_3, all_0_4_4) = all_12_1_11 % 3.96/1.69 | % 3.96/1.69 | Instantiating formula (8) with all_10_1_9, all_0_6_6, all_0_5_5 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_10_1_9, yields: % 3.96/1.69 | (36) unordered_pair(all_0_5_5, all_0_6_6) = all_10_1_9 % 3.96/1.69 | % 3.96/1.69 | Instantiating formula (2) with all_0_2_2, all_12_1_11, all_12_0_10, all_10_0_8, all_10_1_9 and discharging atoms unordered_pair(all_12_0_10, all_12_1_11) = all_0_2_2, unordered_pair(all_10_1_9, all_10_0_8) = all_0_2_2, yields: % 3.96/1.69 | (37) all_12_0_10 = all_10_1_9 | all_12_1_11 = all_10_1_9 % 3.96/1.69 | % 3.96/1.69 | Instantiating formula (2) with all_0_2_2, all_10_1_9, all_10_0_8, all_12_0_10, all_12_1_11 and discharging atoms unordered_pair(all_12_1_11, all_12_0_10) = all_0_2_2, unordered_pair(all_10_0_8, all_10_1_9) = all_0_2_2, yields: % 3.96/1.69 | (38) all_12_1_11 = all_10_0_8 | all_12_1_11 = all_10_1_9 % 3.96/1.69 | % 3.96/1.69 | Instantiating formula (2) with all_0_2_2, all_12_1_11, all_12_0_10, all_10_1_9, all_10_0_8 and discharging atoms unordered_pair(all_12_0_10, all_12_1_11) = all_0_2_2, unordered_pair(all_10_0_8, all_10_1_9) = all_0_2_2, yields: % 3.96/1.69 | (39) all_12_0_10 = all_10_0_8 | all_12_1_11 = all_10_0_8 % 3.96/1.69 | % 3.96/1.69 +-Applying beta-rule and splitting (11), into two cases. % 3.96/1.69 |-Branch one: % 3.96/1.69 | (40) ~ (all_0_3_3 = all_0_5_5) % 3.96/1.69 | % 3.96/1.69 +-Applying beta-rule and splitting (38), into two cases. % 3.96/1.69 |-Branch one: % 3.96/1.69 | (41) all_12_1_11 = all_10_0_8 % 3.96/1.69 | % 3.96/1.69 | From (41) and (35) follows: % 3.96/1.69 | (42) unordered_pair(all_0_3_3, all_0_4_4) = all_10_0_8 % 3.96/1.69 | % 3.96/1.69 | From (41) and (31) follows: % 3.96/1.69 | (43) unordered_pair(all_0_4_4, all_0_3_3) = all_10_0_8 % 3.96/1.69 | % 3.96/1.69 | Instantiating formula (9) with all_10_0_8, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_10_0_8, unordered_pair(all_0_3_3, all_0_4_4) = all_10_0_8, yields: % 3.96/1.69 | (44) all_0_3_3 = all_0_6_6 % 3.96/1.69 | % 3.96/1.69 | Instantiating formula (19) with all_10_0_8, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_10_0_8, unordered_pair(all_0_4_4, all_0_3_3) = all_10_0_8, yields: % 3.96/1.69 | (45) all_0_3_3 = all_0_4_4 % 3.96/1.69 | % 3.96/1.69 | Combining equations (45,44) yields a new equation: % 3.96/1.69 | (46) all_0_4_4 = all_0_6_6 % 3.96/1.69 | % 3.96/1.69 | Simplifying 46 yields: % 3.96/1.69 | (47) all_0_4_4 = all_0_6_6 % 3.96/1.69 | % 3.96/1.69 | Equations (44) can reduce 40 to: % 3.96/1.69 | (48) ~ (all_0_5_5 = all_0_6_6) % 3.96/1.69 | % 3.96/1.69 | Simplifying 48 yields: % 3.96/1.69 | (49) ~ (all_0_5_5 = all_0_6_6) % 3.96/1.69 | % 3.96/1.69 | From (47)(44) and (43) follows: % 3.96/1.69 | (50) unordered_pair(all_0_6_6, all_0_6_6) = all_10_0_8 % 3.96/1.69 | % 3.96/1.69 | From (47)(47) and (32) follows: % 3.96/1.69 | (51) unordered_pair(all_0_6_6, all_0_6_6) = all_12_0_10 % 3.96/1.69 | % 3.96/1.69 | Instantiating formula (17) with all_0_6_6, all_0_6_6, all_12_0_10, all_10_0_8 and discharging atoms unordered_pair(all_0_6_6, all_0_6_6) = all_12_0_10, unordered_pair(all_0_6_6, all_0_6_6) = all_10_0_8, yields: % 3.96/1.69 | (52) all_12_0_10 = all_10_0_8 % 3.96/1.70 | % 3.96/1.70 | From (52) and (51) follows: % 3.96/1.70 | (50) unordered_pair(all_0_6_6, all_0_6_6) = all_10_0_8 % 3.96/1.70 | % 3.96/1.70 +-Applying beta-rule and splitting (37), into two cases. % 3.96/1.70 |-Branch one: % 3.96/1.70 | (54) all_12_0_10 = all_10_1_9 % 3.96/1.70 | % 3.96/1.70 | Combining equations (54,52) yields a new equation: % 3.96/1.70 | (55) all_10_0_8 = all_10_1_9 % 3.96/1.70 | % 3.96/1.70 | From (55) and (50) follows: % 3.96/1.70 | (56) unordered_pair(all_0_6_6, all_0_6_6) = all_10_1_9 % 3.96/1.70 | % 3.96/1.70 | Instantiating formula (2) with all_10_1_9, all_0_6_6, all_0_6_6, all_0_6_6, all_0_5_5 and discharging atoms unordered_pair(all_0_5_5, all_0_6_6) = all_10_1_9, unordered_pair(all_0_6_6, all_0_6_6) = all_10_1_9, yields: % 3.96/1.70 | (57) all_0_5_5 = all_0_6_6 % 3.96/1.70 | % 3.96/1.70 | Equations (57) can reduce 49 to: % 3.96/1.70 | (58) $false % 3.96/1.70 | % 3.96/1.70 |-The branch is then unsatisfiable % 3.96/1.70 |-Branch two: % 3.96/1.70 | (59) ~ (all_12_0_10 = all_10_1_9) % 3.96/1.70 | (60) all_12_1_11 = all_10_1_9 % 3.96/1.70 | % 3.96/1.70 | Combining equations (41,60) yields a new equation: % 3.96/1.70 | (61) all_10_0_8 = all_10_1_9 % 3.96/1.70 | % 3.96/1.70 | Simplifying 61 yields: % 3.96/1.70 | (55) all_10_0_8 = all_10_1_9 % 3.96/1.70 | % 3.96/1.70 | Combining equations (55,52) yields a new equation: % 3.96/1.70 | (54) all_12_0_10 = all_10_1_9 % 3.96/1.70 | % 3.96/1.70 | Equations (54) can reduce 59 to: % 3.96/1.70 | (58) $false % 3.96/1.70 | % 3.96/1.70 |-The branch is then unsatisfiable % 3.96/1.70 |-Branch two: % 3.96/1.70 | (65) ~ (all_12_1_11 = all_10_0_8) % 3.96/1.70 | (60) all_12_1_11 = all_10_1_9 % 3.96/1.70 | % 3.96/1.70 | Equations (60) can reduce 65 to: % 3.96/1.70 | (67) ~ (all_10_0_8 = all_10_1_9) % 3.96/1.70 | % 3.96/1.70 | Simplifying 67 yields: % 3.96/1.70 | (68) ~ (all_10_0_8 = all_10_1_9) % 3.96/1.70 | % 3.96/1.70 | From (60) and (35) follows: % 3.96/1.70 | (69) unordered_pair(all_0_3_3, all_0_4_4) = all_10_1_9 % 3.96/1.70 | % 3.96/1.70 | From (60) and (31) follows: % 3.96/1.70 | (70) unordered_pair(all_0_4_4, all_0_3_3) = all_10_1_9 % 3.96/1.70 | % 3.96/1.70 +-Applying beta-rule and splitting (39), into two cases. % 3.96/1.70 |-Branch one: % 3.96/1.70 | (52) all_12_0_10 = all_10_0_8 % 3.96/1.70 | % 3.96/1.70 | From (52) and (32) follows: % 3.96/1.70 | (72) unordered_pair(all_0_4_4, all_0_4_4) = all_10_0_8 % 3.96/1.70 | % 3.96/1.70 | Instantiating formula (2) with all_10_1_9, all_0_5_5, all_0_6_6, all_0_4_4, all_0_3_3 and discharging atoms unordered_pair(all_0_3_3, all_0_4_4) = all_10_1_9, unordered_pair(all_0_6_6, all_0_5_5) = all_10_1_9, yields: % 3.96/1.70 | (73) all_0_3_3 = all_0_5_5 | all_0_3_3 = all_0_6_6 % 3.96/1.70 | % 3.96/1.70 | Instantiating formula (2) with all_10_1_9, all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms unordered_pair(all_0_4_4, all_0_3_3) = all_10_1_9, unordered_pair(all_0_5_5, all_0_6_6) = all_10_1_9, yields: % 3.96/1.70 | (74) all_0_3_3 = all_0_5_5 | all_0_4_4 = all_0_5_5 % 3.96/1.70 | % 3.96/1.70 | Instantiating formula (9) with all_10_0_8, all_0_4_4, all_0_4_4, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_10_0_8, unordered_pair(all_0_4_4, all_0_4_4) = all_10_0_8, yields: % 3.96/1.70 | (47) all_0_4_4 = all_0_6_6 % 3.96/1.70 | % 3.96/1.70 +-Applying beta-rule and splitting (73), into two cases. % 3.96/1.70 |-Branch one: % 3.96/1.70 | (76) all_0_3_3 = all_0_5_5 % 3.96/1.70 | % 3.96/1.70 | Equations (76) can reduce 40 to: % 3.96/1.70 | (58) $false % 3.96/1.70 | % 3.96/1.70 |-The branch is then unsatisfiable % 3.96/1.70 |-Branch two: % 3.96/1.70 | (40) ~ (all_0_3_3 = all_0_5_5) % 3.96/1.70 | (44) all_0_3_3 = all_0_6_6 % 3.96/1.70 | % 3.96/1.70 | Equations (44) can reduce 40 to: % 3.96/1.70 | (48) ~ (all_0_5_5 = all_0_6_6) % 3.96/1.70 | % 3.96/1.70 | Simplifying 48 yields: % 3.96/1.70 | (49) ~ (all_0_5_5 = all_0_6_6) % 3.96/1.70 | % 3.96/1.70 +-Applying beta-rule and splitting (74), into two cases. % 3.96/1.70 |-Branch one: % 3.96/1.70 | (76) all_0_3_3 = all_0_5_5 % 3.96/1.70 | % 3.96/1.70 | Combining equations (44,76) yields a new equation: % 3.96/1.70 | (57) all_0_5_5 = all_0_6_6 % 3.96/1.70 | % 3.96/1.70 | Equations (57) can reduce 49 to: % 3.96/1.70 | (58) $false % 3.96/1.70 | % 3.96/1.70 |-The branch is then unsatisfiable % 3.96/1.70 |-Branch two: % 3.96/1.70 | (40) ~ (all_0_3_3 = all_0_5_5) % 3.96/1.70 | (86) all_0_4_4 = all_0_5_5 % 3.96/1.70 | % 3.96/1.70 | Combining equations (86,47) yields a new equation: % 3.96/1.70 | (87) all_0_5_5 = all_0_6_6 % 3.96/1.70 | % 3.96/1.70 | Simplifying 87 yields: % 3.96/1.70 | (57) all_0_5_5 = all_0_6_6 % 3.96/1.70 | % 3.96/1.70 | Equations (57) can reduce 49 to: % 3.96/1.70 | (58) $false % 3.96/1.70 | % 3.96/1.70 |-The branch is then unsatisfiable % 3.96/1.71 |-Branch two: % 3.96/1.71 | (90) ~ (all_12_0_10 = all_10_0_8) % 3.96/1.71 | (41) all_12_1_11 = all_10_0_8 % 3.96/1.71 | % 3.96/1.71 | Combining equations (41,60) yields a new equation: % 3.96/1.71 | (61) all_10_0_8 = all_10_1_9 % 3.96/1.71 | % 3.96/1.71 | Simplifying 61 yields: % 3.96/1.71 | (55) all_10_0_8 = all_10_1_9 % 3.96/1.71 | % 3.96/1.71 | Equations (55) can reduce 68 to: % 3.96/1.71 | (58) $false % 3.96/1.71 | % 3.96/1.71 |-The branch is then unsatisfiable % 3.96/1.71 |-Branch two: % 3.96/1.71 | (76) all_0_3_3 = all_0_5_5 % 3.96/1.71 | (96) ~ (all_0_4_4 = all_0_6_6) % 3.96/1.71 | % 3.96/1.71 | From (76) and (31) follows: % 3.96/1.71 | (97) unordered_pair(all_0_4_4, all_0_5_5) = all_12_1_11 % 3.96/1.71 | % 3.96/1.71 +-Applying beta-rule and splitting (38), into two cases. % 3.96/1.71 |-Branch one: % 3.96/1.71 | (41) all_12_1_11 = all_10_0_8 % 3.96/1.71 | % 3.96/1.71 | From (41) and (97) follows: % 3.96/1.71 | (99) unordered_pair(all_0_4_4, all_0_5_5) = all_10_0_8 % 3.96/1.71 | % 3.96/1.71 | Instantiating formula (9) with all_10_0_8, all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_10_0_8, unordered_pair(all_0_4_4, all_0_5_5) = all_10_0_8, yields: % 3.96/1.71 | (47) all_0_4_4 = all_0_6_6 % 3.96/1.71 | % 3.96/1.71 | Equations (47) can reduce 96 to: % 3.96/1.71 | (58) $false % 3.96/1.71 | % 3.96/1.71 |-The branch is then unsatisfiable % 3.96/1.71 |-Branch two: % 3.96/1.71 | (65) ~ (all_12_1_11 = all_10_0_8) % 3.96/1.71 | (60) all_12_1_11 = all_10_1_9 % 3.96/1.71 | % 3.96/1.71 | Equations (60) can reduce 65 to: % 3.96/1.71 | (67) ~ (all_10_0_8 = all_10_1_9) % 3.96/1.71 | % 3.96/1.71 | Simplifying 67 yields: % 3.96/1.71 | (68) ~ (all_10_0_8 = all_10_1_9) % 3.96/1.71 | % 3.96/1.71 +-Applying beta-rule and splitting (39), into two cases. % 3.96/1.71 |-Branch one: % 3.96/1.71 | (52) all_12_0_10 = all_10_0_8 % 3.96/1.71 | % 3.96/1.71 | From (52) and (32) follows: % 3.96/1.71 | (72) unordered_pair(all_0_4_4, all_0_4_4) = all_10_0_8 % 3.96/1.71 | % 3.96/1.71 | Instantiating formula (9) with all_10_0_8, all_0_4_4, all_0_4_4, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_10_0_8, unordered_pair(all_0_4_4, all_0_4_4) = all_10_0_8, yields: % 3.96/1.71 | (47) all_0_4_4 = all_0_6_6 % 3.96/1.71 | % 3.96/1.71 | Equations (47) can reduce 96 to: % 3.96/1.71 | (58) $false % 3.96/1.71 | % 3.96/1.71 |-The branch is then unsatisfiable % 3.96/1.71 |-Branch two: % 3.96/1.71 | (90) ~ (all_12_0_10 = all_10_0_8) % 3.96/1.71 | (41) all_12_1_11 = all_10_0_8 % 3.96/1.71 | % 3.96/1.71 | Combining equations (41,60) yields a new equation: % 3.96/1.71 | (61) all_10_0_8 = all_10_1_9 % 3.96/1.71 | % 3.96/1.71 | Simplifying 61 yields: % 3.96/1.71 | (55) all_10_0_8 = all_10_1_9 % 3.96/1.71 | % 3.96/1.71 | Equations (55) can reduce 68 to: % 3.96/1.71 | (58) $false % 3.96/1.71 | % 3.96/1.71 |-The branch is then unsatisfiable % 3.96/1.71 % SZS output end Proof for theBenchmark % 3.96/1.71 % 3.96/1.71 1111ms %------------------------------------------------------------------------------