%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SYN940+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n014.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 05:05:59 EDT 2022 % Result : Theorem 3.43s 1.57s % Output : Proof 5.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SYN940+1 : TPTP v8.1.0. Released v3.1.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.35 % Computer : n014.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Tue Jul 12 06:29:34 EDT 2022 % 0.14/0.35 % CPUTime : % 0.46/0.61 ____ _ % 0.46/0.61 ___ / __ \_____(_)___ ________ __________ % 0.46/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.46/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.46/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.46/0.61 % 0.46/0.61 A Theorem Prover for First-Order Logic % 0.46/0.61 (ePrincess v.1.0) % 0.46/0.61 % 0.46/0.61 (c) Philipp Rümmer, 2009-2015 % 0.46/0.61 (c) Peter Backeman, 2014-2015 % 0.46/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.46/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.46/0.61 Bug reports to peter@backeman.se % 0.46/0.61 % 0.46/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.46/0.61 % 0.46/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.70/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.23/0.88 Prover 0: Preprocessing ... % 1.43/0.96 Prover 0: Warning: ignoring some quantifiers % 1.43/0.97 Prover 0: Constructing countermodel ... % 1.82/1.11 Prover 0: gave up % 1.82/1.11 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 1.98/1.14 Prover 1: Preprocessing ... % 2.11/1.22 Prover 1: Constructing countermodel ... % 2.29/1.26 Prover 1: gave up % 2.29/1.26 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.29/1.27 Prover 2: Preprocessing ... % 2.41/1.33 Prover 2: Warning: ignoring some quantifiers % 2.41/1.33 Prover 2: Constructing countermodel ... % 2.69/1.38 Prover 2: gave up % 2.69/1.38 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.69/1.38 Prover 3: Preprocessing ... % 2.69/1.39 Prover 3: Warning: ignoring some quantifiers % 2.69/1.40 Prover 3: Constructing countermodel ... % 2.90/1.43 Prover 3: gave up % 2.90/1.43 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 2.90/1.44 Prover 4: Preprocessing ... % 3.01/1.48 Prover 4: Warning: ignoring some quantifiers % 3.01/1.49 Prover 4: Constructing countermodel ... % 3.43/1.57 Prover 4: proved (140ms) % 3.43/1.57 % 3.43/1.57 No countermodel exists, formula is valid % 3.43/1.57 % SZS status Theorem for theBenchmark % 3.43/1.57 % 3.43/1.57 Generating proof ... Warning: ignoring some quantifiers % 4.52/1.93 found it (size 35) % 4.52/1.93 % 4.52/1.93 % SZS output start Proof for theBenchmark % 4.52/1.93 Assumed formulas after preprocessing and simplification: % 4.52/1.93 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (r(v5) = v7 & r(v4) = v6 & r(v1) = v3 & r(v0) = v2 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (p(v10) = v11) | ~ (p(v8) = v12) | ~ (f(v9) = v10) | ? [v13] : ? [v14] : (r(v9) = v13 & q(v8) = v14 & ( ~ (v14 = 0) | (v11 = 0 & ( ~ (v12 = 0) | (v13 = 0 & ( ~ (v7 = 0) | ~ (v6 = 0)))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (p(v10) = v11) | ~ (f(v9) = v10) | ~ (q(v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (p(v10) = v11) | ~ (f(v9) = v10) | ~ (q(v8) = 0) | ? [v12] : ? [v13] : (p(v8) = v12 & r(v9) = v13 & ( ~ (v12 = 0) | (v13 = 0 & ( ~ (v7 = 0) | ~ (v6 = 0)))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (p(v8) = v10) | ~ (r(v9) = v11) | ? [v12] : ? [v13] : ? [v14] : (p(v12) = v13 & f(v9) = v12 & q(v8) = v14 & ( ~ (v14 = 0) | (v13 = 0 & ( ~ (v10 = 0) | (v11 = 0 & ( ~ (v7 = 0) | ~ (v6 = 0)))))))) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (p(v10) = v9) | ~ (p(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (r(v10) = v9) | ~ (r(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (f(v10) = v9) | ~ (f(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (q(v10) = v9) | ~ (q(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (r(v9) = v10) | ~ (q(v8) = 0) | ? [v11] : ? [v12] : (p(v11) = 0 & p(v8) = v12 & f(v9) = v11 & ( ~ (v12 = 0) | (v10 = 0 & ( ~ (v7 = 0) | ~ (v6 = 0)))))) & ! [v8] : ! [v9] : ( ~ (f(v8) = v9) | q(v9) = 0) & ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (p(v10) = v11 & p(v8) = v12 & r(v9) = v13 & f(v9) = v10 & q(v8) = v14 & ( ~ (v14 = 0) | (v11 = 0 & ( ~ (v12 = 0) | (v13 = 0 & ( ~ (v3 = 0) | ~ (v2 = 0))))))) & ? [v8] : ? [v9] : (f(v8) = v9 & q(v9) = 0)) % 4.88/1.96 | 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 yields: % 4.88/1.96 | (1) r(all_0_2_2) = all_0_0_0 & r(all_0_3_3) = all_0_1_1 & r(all_0_6_6) = all_0_4_4 & r(all_0_7_7) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (p(v2) = v3) | ~ (p(v0) = v4) | ~ (f(v1) = v2) | ? [v5] : ? [v6] : (r(v1) = v5 & q(v0) = v6 & ( ~ (v6 = 0) | (v3 = 0 & ( ~ (v4 = 0) | (v5 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (p(v2) = v3) | ~ (f(v1) = v2) | ~ (q(v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (p(v2) = v3) | ~ (f(v1) = v2) | ~ (q(v0) = 0) | ? [v4] : ? [v5] : (p(v0) = v4 & r(v1) = v5 & ( ~ (v4 = 0) | (v5 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (p(v0) = v2) | ~ (r(v1) = v3) | ? [v4] : ? [v5] : ? [v6] : (p(v4) = v5 & f(v1) = v4 & q(v0) = v6 & ( ~ (v6 = 0) | (v5 = 0 & ( ~ (v2 = 0) | (v3 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)))))))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (r(v2) = v1) | ~ (r(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (r(v1) = v2) | ~ (q(v0) = 0) | ? [v3] : ? [v4] : (p(v3) = 0 & p(v0) = v4 & f(v1) = v3 & ( ~ (v4 = 0) | (v2 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)))))) & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | q(v1) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (p(v2) = v3 & p(v0) = v4 & r(v1) = v5 & f(v1) = v2 & q(v0) = v6 & ( ~ (v6 = 0) | (v3 = 0 & ( ~ (v4 = 0) | (v5 = 0 & ( ~ (all_0_4_4 = 0) | ~ (all_0_5_5 = 0))))))) & ? [v0] : ? [v1] : (f(v0) = v1 & q(v1) = 0) % 4.88/1.97 | % 4.88/1.97 | Applying alpha-rule on (1) yields: % 4.88/1.97 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (p(v0) = v2) | ~ (r(v1) = v3) | ? [v4] : ? [v5] : ? [v6] : (p(v4) = v5 & f(v1) = v4 & q(v0) = v6 & ( ~ (v6 = 0) | (v5 = 0 & ( ~ (v2 = 0) | (v3 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)))))))) % 4.88/1.97 | (3) r(all_0_6_6) = all_0_4_4 % 4.88/1.97 | (4) ? [v0] : ? [v1] : (f(v0) = v1 & q(v1) = 0) % 4.88/1.97 | (5) r(all_0_7_7) = all_0_5_5 % 4.88/1.97 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (r(v2) = v1) | ~ (r(v2) = v0)) % 4.88/1.97 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (p(v2) = v3) | ~ (f(v1) = v2) | ~ (q(v0) = 0)) % 4.88/1.98 | (8) ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | q(v1) = 0) % 4.88/1.98 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (p(v2) = v3) | ~ (f(v1) = v2) | ~ (q(v0) = 0) | ? [v4] : ? [v5] : (p(v0) = v4 & r(v1) = v5 & ( ~ (v4 = 0) | (v5 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)))))) % 4.88/1.98 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (r(v1) = v2) | ~ (q(v0) = 0) | ? [v3] : ? [v4] : (p(v3) = 0 & p(v0) = v4 & f(v1) = v3 & ( ~ (v4 = 0) | (v2 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)))))) % 4.88/1.98 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (p(v2) = v3) | ~ (p(v0) = v4) | ~ (f(v1) = v2) | ? [v5] : ? [v6] : (r(v1) = v5 & q(v0) = v6 & ( ~ (v6 = 0) | (v3 = 0 & ( ~ (v4 = 0) | (v5 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)))))))) % 5.04/1.98 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) % 5.04/1.98 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) % 5.04/1.98 | (14) r(all_0_3_3) = all_0_1_1 % 5.04/1.98 | (15) r(all_0_2_2) = all_0_0_0 % 5.04/1.98 | (16) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (p(v2) = v3 & p(v0) = v4 & r(v1) = v5 & f(v1) = v2 & q(v0) = v6 & ( ~ (v6 = 0) | (v3 = 0 & ( ~ (v4 = 0) | (v5 = 0 & ( ~ (all_0_4_4 = 0) | ~ (all_0_5_5 = 0))))))) % 5.04/1.98 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0)) % 5.04/1.98 | % 5.04/1.98 | Instantiating (4) with all_3_0_8, all_3_1_9 yields: % 5.04/1.98 | (18) f(all_3_1_9) = all_3_0_8 & q(all_3_0_8) = 0 % 5.04/1.98 | % 5.04/1.98 | Applying alpha-rule on (18) yields: % 5.04/1.98 | (19) f(all_3_1_9) = all_3_0_8 % 5.04/1.98 | (20) q(all_3_0_8) = 0 % 5.04/1.98 | % 5.04/1.98 | Instantiating (16) with all_5_0_10, all_5_1_11, all_5_2_12, all_5_3_13, all_5_4_14, all_5_5_15, all_5_6_16 yields: % 5.04/1.98 | (21) p(all_5_4_14) = all_5_3_13 & p(all_5_6_16) = all_5_2_12 & r(all_5_5_15) = all_5_1_11 & f(all_5_5_15) = all_5_4_14 & q(all_5_6_16) = all_5_0_10 & ( ~ (all_5_0_10 = 0) | (all_5_3_13 = 0 & ( ~ (all_5_2_12 = 0) | (all_5_1_11 = 0 & ( ~ (all_0_4_4 = 0) | ~ (all_0_5_5 = 0)))))) % 5.04/1.98 | % 5.04/1.98 | Applying alpha-rule on (21) yields: % 5.04/1.98 | (22) r(all_5_5_15) = all_5_1_11 % 5.04/1.98 | (23) ~ (all_5_0_10 = 0) | (all_5_3_13 = 0 & ( ~ (all_5_2_12 = 0) | (all_5_1_11 = 0 & ( ~ (all_0_4_4 = 0) | ~ (all_0_5_5 = 0))))) % 5.04/1.98 | (24) p(all_5_6_16) = all_5_2_12 % 5.04/1.98 | (25) p(all_5_4_14) = all_5_3_13 % 5.04/1.98 | (26) q(all_5_6_16) = all_5_0_10 % 5.04/1.98 | (27) f(all_5_5_15) = all_5_4_14 % 5.04/1.98 | % 5.04/1.98 | Instantiating formula (7) with all_5_3_13, all_5_4_14, all_5_5_15, all_3_0_8 and discharging atoms p(all_5_4_14) = all_5_3_13, f(all_5_5_15) = all_5_4_14, q(all_3_0_8) = 0, yields: % 5.04/1.98 | (28) all_5_3_13 = 0 % 5.04/1.99 | % 5.04/1.99 | From (28) and (25) follows: % 5.04/1.99 | (29) p(all_5_4_14) = 0 % 5.04/1.99 | % 5.04/1.99 | Instantiating formula (8) with all_5_4_14, all_5_5_15 and discharging atoms f(all_5_5_15) = all_5_4_14, yields: % 5.04/1.99 | (30) q(all_5_4_14) = 0 % 5.04/1.99 | % 5.04/1.99 | Instantiating formula (9) with 0, all_5_4_14, all_5_5_15, all_3_0_8 and discharging atoms p(all_5_4_14) = 0, f(all_5_5_15) = all_5_4_14, q(all_3_0_8) = 0, yields: % 5.04/1.99 | (31) ? [v0] : ? [v1] : (p(all_3_0_8) = v0 & r(all_5_5_15) = v1 & ( ~ (v0 = 0) | (v1 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))))) % 5.04/1.99 | % 5.04/1.99 | Instantiating formula (10) with all_0_0_0, all_0_2_2, all_3_0_8 and discharging atoms r(all_0_2_2) = all_0_0_0, q(all_3_0_8) = 0, yields: % 5.04/1.99 | (32) ? [v0] : ? [v1] : (p(v0) = 0 & p(all_3_0_8) = v1 & f(all_0_2_2) = v0 & ( ~ (v1 = 0) | (all_0_0_0 = 0 & ~ (all_0_1_1 = 0)))) % 5.04/1.99 | % 5.04/1.99 | Instantiating formula (10) with all_0_1_1, all_0_3_3, all_3_0_8 and discharging atoms r(all_0_3_3) = all_0_1_1, q(all_3_0_8) = 0, yields: % 5.04/1.99 | (33) ? [v0] : ? [v1] : (p(v0) = 0 & p(all_3_0_8) = v1 & f(all_0_3_3) = v0 & ( ~ (v1 = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)))) % 5.04/1.99 | % 5.04/1.99 | Instantiating (33) with all_23_0_23, all_23_1_24 yields: % 5.04/1.99 | (34) p(all_23_1_24) = 0 & p(all_3_0_8) = all_23_0_23 & f(all_0_3_3) = all_23_1_24 & ( ~ (all_23_0_23 = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0))) % 5.04/1.99 | % 5.04/1.99 | Applying alpha-rule on (34) yields: % 5.04/1.99 | (35) p(all_23_1_24) = 0 % 5.04/1.99 | (36) p(all_3_0_8) = all_23_0_23 % 5.04/1.99 | (37) f(all_0_3_3) = all_23_1_24 % 5.04/1.99 | (38) ~ (all_23_0_23 = 0) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)) % 5.04/1.99 | % 5.04/1.99 | Instantiating (31) with all_31_0_33, all_31_1_34 yields: % 5.04/1.99 | (39) p(all_3_0_8) = all_31_1_34 & r(all_5_5_15) = all_31_0_33 & ( ~ (all_31_1_34 = 0) | (all_31_0_33 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0)))) % 5.04/1.99 | % 5.04/1.99 | Applying alpha-rule on (39) yields: % 5.04/1.99 | (40) p(all_3_0_8) = all_31_1_34 % 5.04/1.99 | (41) r(all_5_5_15) = all_31_0_33 % 5.04/1.99 | (42) ~ (all_31_1_34 = 0) | (all_31_0_33 = 0 & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0))) % 5.04/1.99 | % 5.04/1.99 | Instantiating (32) with all_33_0_35, all_33_1_36 yields: % 5.04/1.99 | (43) p(all_33_1_36) = 0 & p(all_3_0_8) = all_33_0_35 & f(all_0_2_2) = all_33_1_36 & ( ~ (all_33_0_35 = 0) | (all_0_0_0 = 0 & ~ (all_0_1_1 = 0))) % 5.04/1.99 | % 5.04/1.99 | Applying alpha-rule on (43) yields: % 5.04/1.99 | (44) p(all_33_1_36) = 0 % 5.04/1.99 | (45) p(all_3_0_8) = all_33_0_35 % 5.04/1.99 | (46) f(all_0_2_2) = all_33_1_36 % 5.04/1.99 | (47) ~ (all_33_0_35 = 0) | (all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) % 5.04/1.99 | % 5.04/1.99 | Instantiating formula (12) with all_3_0_8, all_31_1_34, all_33_0_35 and discharging atoms p(all_3_0_8) = all_33_0_35, p(all_3_0_8) = all_31_1_34, yields: % 5.04/1.99 | (48) all_33_0_35 = all_31_1_34 % 5.04/1.99 | % 5.04/1.99 | Instantiating formula (12) with all_3_0_8, all_23_0_23, all_31_1_34 and discharging atoms p(all_3_0_8) = all_31_1_34, p(all_3_0_8) = all_23_0_23, yields: % 5.04/1.99 | (49) all_31_1_34 = all_23_0_23 % 5.04/1.99 | % 5.04/1.99 | Instantiating formula (7) with all_33_0_35, all_3_0_8, all_3_1_9, all_5_4_14 and discharging atoms p(all_3_0_8) = all_33_0_35, f(all_3_1_9) = all_3_0_8, q(all_5_4_14) = 0, yields: % 5.04/1.99 | (50) all_33_0_35 = 0 % 5.04/1.99 | % 5.04/1.99 | Combining equations (48,50) yields a new equation: % 5.04/1.99 | (51) all_31_1_34 = 0 % 5.04/1.99 | % 5.04/1.99 | Simplifying 51 yields: % 5.04/1.99 | (52) all_31_1_34 = 0 % 5.04/1.99 | % 5.04/1.99 | Combining equations (49,52) yields a new equation: % 5.04/1.99 | (53) all_23_0_23 = 0 % 5.04/1.99 | % 5.04/1.99 | Simplifying 53 yields: % 5.04/1.99 | (54) all_23_0_23 = 0 % 5.04/1.99 | % 5.04/1.99 +-Applying beta-rule and splitting (47), into two cases. % 5.04/1.99 |-Branch one: % 5.04/1.99 | (55) ~ (all_33_0_35 = 0) % 5.04/1.99 | % 5.04/2.00 | Equations (50) can reduce 55 to: % 5.04/2.00 | (56) $false % 5.04/2.00 | % 5.04/2.00 |-The branch is then unsatisfiable % 5.04/2.00 |-Branch two: % 5.04/2.00 | (50) all_33_0_35 = 0 % 5.04/2.00 | (58) all_0_0_0 = 0 & ~ (all_0_1_1 = 0) % 5.04/2.00 | % 5.04/2.00 | Applying alpha-rule on (58) yields: % 5.04/2.00 | (59) all_0_0_0 = 0 % 5.04/2.00 | (60) ~ (all_0_1_1 = 0) % 5.04/2.00 | % 5.04/2.00 +-Applying beta-rule and splitting (38), into two cases. % 5.04/2.00 |-Branch one: % 5.04/2.00 | (61) ~ (all_23_0_23 = 0) % 5.04/2.00 | % 5.04/2.00 | Equations (54) can reduce 61 to: % 5.04/2.00 | (56) $false % 5.04/2.00 | % 5.04/2.00 |-The branch is then unsatisfiable % 5.04/2.00 |-Branch two: % 5.04/2.00 | (54) all_23_0_23 = 0 % 5.04/2.00 | (64) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) % 5.04/2.00 | % 5.04/2.00 | Applying alpha-rule on (64) yields: % 5.04/2.00 | (65) all_0_1_1 = 0 % 5.04/2.00 | (66) ~ (all_0_0_0 = 0) % 5.04/2.00 | % 5.04/2.00 | Equations (65) can reduce 60 to: % 5.04/2.00 | (56) $false % 5.04/2.00 | % 5.04/2.00 |-The branch is then unsatisfiable % 5.04/2.00 % SZS output end Proof for theBenchmark % 5.04/2.00 % 5.04/2.00 1379ms %------------------------------------------------------------------------------