%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : TOP021+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n017.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 21:24:38 EDT 2022 % Result : Theorem 1.82s 1.14s % Output : Proof 2.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.11 % Problem : TOP021+1 : TPTP v8.1.0. Released v3.1.0. % 0.09/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n017.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 : Sun May 29 04:02:38 EDT 2022 % 0.12/0.33 % CPUTime : % 0.60/0.59 ____ _ % 0.60/0.59 ___ / __ \_____(_)___ ________ __________ % 0.60/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.60/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.60/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.60/0.59 % 0.60/0.59 A Theorem Prover for First-Order Logic % 0.60/0.59 (ePrincess v.1.0) % 0.60/0.59 % 0.60/0.59 (c) Philipp Rümmer, 2009-2015 % 0.60/0.59 (c) Peter Backeman, 2014-2015 % 0.60/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.60/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.60/0.59 Bug reports to peter@backeman.se % 0.60/0.59 % 0.60/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.60/0.59 % 0.60/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.68/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.31/0.90 Prover 0: Preprocessing ... % 1.62/1.03 Prover 0: Constructing countermodel ... % 1.82/1.14 Prover 0: proved (492ms) % 1.82/1.14 % 1.82/1.14 No countermodel exists, formula is valid % 1.82/1.14 % SZS status Theorem for theBenchmark % 1.82/1.14 % 1.82/1.14 Generating proof ... found it (size 12) % 2.39/1.29 % 2.39/1.29 % SZS output start Proof for theBenchmark % 2.39/1.30 Assumed formulas after preprocessing and simplification: % 2.39/1.30 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (the_product_top_space_over(v0, v1) = v2 & apply(v0, v3) = v4 & a_locally_compact_top_space(v2) & ~ a_locally_compact_top_space(v4) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (the_projection_function(v5, v6, v7) = v9) | ~ (the_product_top_space_over(v8, v7) = v10) | ? [v11] : (apply(v8, v5) = v11 & an_open_function_from_onto(v9, v10, v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (the_projection_function(v5, v6, v7) = v9) | ~ (apply(v8, v5) = v10) | ? [v11] : (the_product_top_space_over(v8, v7) = v11 & an_open_function_from_onto(v9, v11, v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (the_projection_function(v9, v8, v7) = v6) | ~ (the_projection_function(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (the_product_top_space_over(v6, v7) = v8) | ~ (apply(v6, v5) = v9) | ? [v10] : (the_projection_function(v5, v6, v7) = v10 & a_continuous_function_from_onto(v10, v8, v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (the_product_top_space_over(v8, v7) = v6) | ~ (the_product_top_space_over(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (apply(v8, v7) = v6) | ~ (apply(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (the_projection_function(v5, v6, v7) = v8) | ? [v9] : ? [v10] : (the_product_top_space_over(v6, v7) = v9 & apply(v6, v5) = v10 & a_continuous_function_from_onto(v8, v9, v10))) & ! [v5] : ! [v6] : ! [v7] : ( ~ a_locally_compact_top_space(v6) | ~ an_open_function_from_onto(v5, v6, v7) | ~ a_continuous_function_from_onto(v5, v6, v7) | a_locally_compact_top_space(v7))) % 2.59/1.33 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 2.59/1.33 | (1) the_product_top_space_over(all_0_4_4, all_0_3_3) = all_0_2_2 & apply(all_0_4_4, all_0_1_1) = all_0_0_0 & a_locally_compact_top_space(all_0_2_2) & ~ a_locally_compact_top_space(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (the_projection_function(v0, v1, v2) = v4) | ~ (the_product_top_space_over(v3, v2) = v5) | ? [v6] : (apply(v3, v0) = v6 & an_open_function_from_onto(v4, v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (the_projection_function(v0, v1, v2) = v4) | ~ (apply(v3, v0) = v5) | ? [v6] : (the_product_top_space_over(v3, v2) = v6 & an_open_function_from_onto(v4, v6, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (the_projection_function(v4, v3, v2) = v1) | ~ (the_projection_function(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (the_product_top_space_over(v1, v2) = v3) | ~ (apply(v1, v0) = v4) | ? [v5] : (the_projection_function(v0, v1, v2) = v5 & a_continuous_function_from_onto(v5, v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (the_product_top_space_over(v3, v2) = v1) | ~ (the_product_top_space_over(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_projection_function(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (the_product_top_space_over(v1, v2) = v4 & apply(v1, v0) = v5 & a_continuous_function_from_onto(v3, v4, v5))) & ! [v0] : ! [v1] : ! [v2] : ( ~ a_locally_compact_top_space(v1) | ~ an_open_function_from_onto(v0, v1, v2) | ~ a_continuous_function_from_onto(v0, v1, v2) | a_locally_compact_top_space(v2)) % 2.59/1.34 | % 2.59/1.34 | Applying alpha-rule on (1) yields: % 2.59/1.34 | (2) a_locally_compact_top_space(all_0_2_2) % 2.59/1.34 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (the_product_top_space_over(v1, v2) = v3) | ~ (apply(v1, v0) = v4) | ? [v5] : (the_projection_function(v0, v1, v2) = v5 & a_continuous_function_from_onto(v5, v3, v4))) % 2.59/1.34 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_projection_function(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (the_product_top_space_over(v1, v2) = v4 & apply(v1, v0) = v5 & a_continuous_function_from_onto(v3, v4, v5))) % 2.59/1.34 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (the_projection_function(v4, v3, v2) = v1) | ~ (the_projection_function(v4, v3, v2) = v0)) % 2.59/1.34 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ a_locally_compact_top_space(v1) | ~ an_open_function_from_onto(v0, v1, v2) | ~ a_continuous_function_from_onto(v0, v1, v2) | a_locally_compact_top_space(v2)) % 2.59/1.34 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (the_projection_function(v0, v1, v2) = v4) | ~ (apply(v3, v0) = v5) | ? [v6] : (the_product_top_space_over(v3, v2) = v6 & an_open_function_from_onto(v4, v6, v5))) % 2.59/1.34 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (the_projection_function(v0, v1, v2) = v4) | ~ (the_product_top_space_over(v3, v2) = v5) | ? [v6] : (apply(v3, v0) = v6 & an_open_function_from_onto(v4, v5, v6))) % 2.59/1.34 | (9) ~ a_locally_compact_top_space(all_0_0_0) % 2.59/1.34 | (10) the_product_top_space_over(all_0_4_4, all_0_3_3) = all_0_2_2 % 2.59/1.34 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 2.59/1.34 | (12) apply(all_0_4_4, all_0_1_1) = all_0_0_0 % 2.59/1.34 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (the_product_top_space_over(v3, v2) = v1) | ~ (the_product_top_space_over(v3, v2) = v0)) % 2.59/1.35 | % 2.59/1.35 | Instantiating formula (3) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4, all_0_1_1 and discharging atoms the_product_top_space_over(all_0_4_4, all_0_3_3) = all_0_2_2, apply(all_0_4_4, all_0_1_1) = all_0_0_0, yields: % 2.59/1.35 | (14) ? [v0] : (the_projection_function(all_0_1_1, all_0_4_4, all_0_3_3) = v0 & a_continuous_function_from_onto(v0, all_0_2_2, all_0_0_0)) % 2.59/1.35 | % 2.59/1.35 | Instantiating (14) with all_8_0_5 yields: % 2.59/1.35 | (15) the_projection_function(all_0_1_1, all_0_4_4, all_0_3_3) = all_8_0_5 & a_continuous_function_from_onto(all_8_0_5, all_0_2_2, all_0_0_0) % 2.59/1.35 | % 2.59/1.35 | Applying alpha-rule on (15) yields: % 2.59/1.35 | (16) the_projection_function(all_0_1_1, all_0_4_4, all_0_3_3) = all_8_0_5 % 2.59/1.35 | (17) a_continuous_function_from_onto(all_8_0_5, all_0_2_2, all_0_0_0) % 2.59/1.35 | % 2.59/1.35 | Instantiating formula (8) with all_0_2_2, all_8_0_5, all_0_4_4, all_0_3_3, all_0_4_4, all_0_1_1 and discharging atoms the_projection_function(all_0_1_1, all_0_4_4, all_0_3_3) = all_8_0_5, the_product_top_space_over(all_0_4_4, all_0_3_3) = all_0_2_2, yields: % 2.59/1.35 | (18) ? [v0] : (apply(all_0_4_4, all_0_1_1) = v0 & an_open_function_from_onto(all_8_0_5, all_0_2_2, v0)) % 2.59/1.35 | % 2.59/1.35 | Instantiating (18) with all_17_0_7 yields: % 2.59/1.35 | (19) apply(all_0_4_4, all_0_1_1) = all_17_0_7 & an_open_function_from_onto(all_8_0_5, all_0_2_2, all_17_0_7) % 2.59/1.35 | % 2.59/1.35 | Applying alpha-rule on (19) yields: % 2.59/1.35 | (20) apply(all_0_4_4, all_0_1_1) = all_17_0_7 % 2.59/1.35 | (21) an_open_function_from_onto(all_8_0_5, all_0_2_2, all_17_0_7) % 2.59/1.35 | % 2.59/1.35 | Instantiating formula (11) with all_0_4_4, all_0_1_1, all_17_0_7, all_0_0_0 and discharging atoms apply(all_0_4_4, all_0_1_1) = all_17_0_7, apply(all_0_4_4, all_0_1_1) = all_0_0_0, yields: % 2.59/1.35 | (22) all_17_0_7 = all_0_0_0 % 2.59/1.35 | % 2.59/1.35 | From (22) and (21) follows: % 2.59/1.35 | (23) an_open_function_from_onto(all_8_0_5, all_0_2_2, all_0_0_0) % 2.59/1.35 | % 2.59/1.35 | Instantiating formula (6) with all_0_0_0, all_0_2_2, all_8_0_5 and discharging atoms a_locally_compact_top_space(all_0_2_2), an_open_function_from_onto(all_8_0_5, all_0_2_2, all_0_0_0), a_continuous_function_from_onto(all_8_0_5, all_0_2_2, all_0_0_0), ~ a_locally_compact_top_space(all_0_0_0), yields: % 2.59/1.35 | (24) $false % 2.59/1.35 | % 2.59/1.35 |-The branch is then unsatisfiable % 2.59/1.35 % SZS output end Proof for theBenchmark % 2.59/1.35 % 2.59/1.35 748ms %------------------------------------------------------------------------------