%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU244+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n013.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 08:48:05 EDT 2022 % Result : Theorem 2.68s 1.28s % Output : Proof 3.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SEU244+1 : TPTP v8.1.0. Released v3.3.0. % 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n013.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jun 20 10:09:14 EDT 2022 % 0.13/0.33 % CPUTime : % 0.58/0.58 ____ _ % 0.58/0.58 ___ / __ \_____(_)___ ________ __________ % 0.58/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.58 % 0.58/0.58 A Theorem Prover for First-Order Logic % 0.58/0.58 (ePrincess v.1.0) % 0.58/0.58 % 0.58/0.58 (c) Philipp Rümmer, 2009-2015 % 0.58/0.58 (c) Peter Backeman, 2014-2015 % 0.58/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.58 Bug reports to peter@backeman.se % 0.58/0.58 % 0.58/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.58 % 0.58/0.58 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 % 1.45/0.91 Prover 0: Preprocessing ... % 1.94/1.12 Prover 0: Constructing countermodel ... % 2.22/1.28 Prover 0: proved (645ms) % 2.68/1.28 % 2.68/1.28 No countermodel exists, formula is valid % 2.68/1.28 % SZS status Theorem for theBenchmark % 2.68/1.28 % 2.68/1.28 Generating proof ... found it (size 29) % 3.33/1.53 % 3.33/1.53 % SZS output start Proof for theBenchmark % 3.33/1.53 Assumed formulas after preprocessing and simplification: % 3.33/1.53 | (0) ? [v0] : ? [v1] : (relation_field(v0) = v1 & relation(v0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (set_union2(v5, v4) = v3) | ~ (set_union2(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v2) = v3) | ~ (relation_rng(v2) = v4) | ~ (set_union2(v3, v4) = v5) | ~ relation(v2) | relation_field(v2) = v5) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (relation_dom(v4) = v3) | ~ (relation_dom(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (relation_rng(v4) = v3) | ~ (relation_rng(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (relation_field(v4) = v3) | ~ (relation_field(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v3, v2) = v4) | set_union2(v2, v3) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v2, v3) = v4) | set_union2(v3, v2) = v4) & ! [v2] : ! [v3] : (v3 = v2 | ~ (set_union2(v2, v2) = v3)) & ! [v2] : ! [v3] : ( ~ (relation_field(v2) = v3) | ~ is_well_founded_in(v2, v3) | ~ relation(v2) | well_founded_relation(v2)) & ! [v2] : ! [v3] : ( ~ (relation_field(v2) = v3) | ~ is_reflexive_in(v2, v3) | ~ relation(v2) | reflexive(v2)) & ! [v2] : ! [v3] : ( ~ (relation_field(v2) = v3) | ~ well_founded_relation(v2) | ~ relation(v2) | is_well_founded_in(v2, v3)) & ! [v2] : ! [v3] : ( ~ (relation_field(v2) = v3) | ~ reflexive(v2) | ~ relation(v2) | is_reflexive_in(v2, v3)) & ! [v2] : ! [v3] : ( ~ (relation_field(v2) = v3) | ~ is_transitive_in(v2, v3) | ~ relation(v2) | transitive(v2)) & ! [v2] : ! [v3] : ( ~ (relation_field(v2) = v3) | ~ transitive(v2) | ~ relation(v2) | is_transitive_in(v2, v3)) & ! [v2] : ! [v3] : ( ~ (relation_field(v2) = v3) | ~ is_connected_in(v2, v3) | ~ relation(v2) | connected(v2)) & ! [v2] : ! [v3] : ( ~ (relation_field(v2) = v3) | ~ connected(v2) | ~ relation(v2) | is_connected_in(v2, v3)) & ! [v2] : ! [v3] : ( ~ (relation_field(v2) = v3) | ~ is_antisymmetric_in(v2, v3) | ~ relation(v2) | antisymmetric(v2)) & ! [v2] : ! [v3] : ( ~ (relation_field(v2) = v3) | ~ antisymmetric(v2) | ~ relation(v2) | is_antisymmetric_in(v2, v3)) & ! [v2] : ! [v3] : ( ~ (relation_field(v2) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (relation_dom(v2) = v4 & relation_rng(v2) = v5 & set_union2(v4, v5) = v3)) & ! [v2] : ! [v3] : ( ~ is_well_founded_in(v2, v3) | ~ is_reflexive_in(v2, v3) | ~ is_transitive_in(v2, v3) | ~ is_connected_in(v2, v3) | ~ is_antisymmetric_in(v2, v3) | ~ relation(v2) | well_orders(v2, v3)) & ! [v2] : ! [v3] : ( ~ well_orders(v2, v3) | ~ relation(v2) | is_well_founded_in(v2, v3)) & ! [v2] : ! [v3] : ( ~ well_orders(v2, v3) | ~ relation(v2) | is_reflexive_in(v2, v3)) & ! [v2] : ! [v3] : ( ~ well_orders(v2, v3) | ~ relation(v2) | is_transitive_in(v2, v3)) & ! [v2] : ! [v3] : ( ~ well_orders(v2, v3) | ~ relation(v2) | is_connected_in(v2, v3)) & ! [v2] : ! [v3] : ( ~ well_orders(v2, v3) | ~ relation(v2) | is_antisymmetric_in(v2, v3)) & ! [v2] : ( ~ well_founded_relation(v2) | ~ reflexive(v2) | ~ transitive(v2) | ~ connected(v2) | ~ antisymmetric(v2) | ~ relation(v2) | well_ordering(v2)) & ! [v2] : ( ~ well_ordering(v2) | ~ relation(v2) | well_founded_relation(v2)) & ! [v2] : ( ~ well_ordering(v2) | ~ relation(v2) | reflexive(v2)) & ! [v2] : ( ~ well_ordering(v2) | ~ relation(v2) | transitive(v2)) & ! [v2] : ( ~ well_ordering(v2) | ~ relation(v2) | connected(v2)) & ! [v2] : ( ~ well_ordering(v2) | ~ relation(v2) | antisymmetric(v2)) & ((well_orders(v0, v1) & ~ well_ordering(v0)) | (well_ordering(v0) & ~ well_orders(v0, v1)))) % 3.61/1.57 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 3.61/1.57 | (1) relation_field(all_0_1_1) = all_0_0_0 & relation(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v0) = v1) | ~ (relation_rng(v0) = v2) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_well_founded_in(v0, v1) | ~ relation(v0) | well_founded_relation(v0)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_reflexive_in(v0, v1) | ~ relation(v0) | reflexive(v0)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ well_founded_relation(v0) | ~ relation(v0) | is_well_founded_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ reflexive(v0) | ~ relation(v0) | is_reflexive_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_transitive_in(v0, v1) | ~ relation(v0) | transitive(v0)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ transitive(v0) | ~ relation(v0) | is_transitive_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_connected_in(v0, v1) | ~ relation(v0) | connected(v0)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ connected(v0) | ~ relation(v0) | is_connected_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_antisymmetric_in(v0, v1) | ~ relation(v0) | antisymmetric(v0)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ antisymmetric(v0) | ~ relation(v0) | is_antisymmetric_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v0) = v2 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1)) & ! [v0] : ! [v1] : ( ~ is_well_founded_in(v0, v1) | ~ is_reflexive_in(v0, v1) | ~ is_transitive_in(v0, v1) | ~ is_connected_in(v0, v1) | ~ is_antisymmetric_in(v0, v1) | ~ relation(v0) | well_orders(v0, v1)) & ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_well_founded_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_reflexive_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_transitive_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_connected_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_antisymmetric_in(v0, v1)) & ! [v0] : ( ~ well_founded_relation(v0) | ~ reflexive(v0) | ~ transitive(v0) | ~ connected(v0) | ~ antisymmetric(v0) | ~ relation(v0) | well_ordering(v0)) & ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | well_founded_relation(v0)) & ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | reflexive(v0)) & ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | transitive(v0)) & ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | connected(v0)) & ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | antisymmetric(v0)) & ((well_orders(all_0_1_1, all_0_0_0) & ~ well_ordering(all_0_1_1)) | (well_ordering(all_0_1_1) & ~ well_orders(all_0_1_1, all_0_0_0))) % 3.61/1.58 | % 3.61/1.58 | Applying alpha-rule on (1) yields: % 3.61/1.58 | (2) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | connected(v0)) % 3.61/1.58 | (3) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_transitive_in(v0, v1) | ~ relation(v0) | transitive(v0)) % 3.61/1.58 | (4) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_reflexive_in(v0, v1) | ~ relation(v0) | reflexive(v0)) % 3.61/1.58 | (5) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ transitive(v0) | ~ relation(v0) | is_transitive_in(v0, v1)) % 3.61/1.58 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 3.68/1.58 | (7) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v0) = v2 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1)) % 3.68/1.58 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 3.68/1.58 | (9) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_reflexive_in(v0, v1)) % 3.68/1.58 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 3.68/1.58 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 3.68/1.58 | (12) ! [v0] : ( ~ well_founded_relation(v0) | ~ reflexive(v0) | ~ transitive(v0) | ~ connected(v0) | ~ antisymmetric(v0) | ~ relation(v0) | well_ordering(v0)) % 3.68/1.58 | (13) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_well_founded_in(v0, v1)) % 3.68/1.58 | (14) relation(all_0_1_1) % 3.68/1.58 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v0) = v1) | ~ (relation_rng(v0) = v2) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3) % 3.68/1.58 | (16) relation_field(all_0_1_1) = all_0_0_0 % 3.68/1.58 | (17) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_connected_in(v0, v1)) % 3.68/1.58 | (18) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | well_founded_relation(v0)) % 3.68/1.58 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 3.68/1.58 | (20) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ antisymmetric(v0) | ~ relation(v0) | is_antisymmetric_in(v0, v1)) % 3.68/1.58 | (21) ! [v0] : ! [v1] : ( ~ is_well_founded_in(v0, v1) | ~ is_reflexive_in(v0, v1) | ~ is_transitive_in(v0, v1) | ~ is_connected_in(v0, v1) | ~ is_antisymmetric_in(v0, v1) | ~ relation(v0) | well_orders(v0, v1)) % 3.68/1.59 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 3.68/1.59 | (23) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ reflexive(v0) | ~ relation(v0) | is_reflexive_in(v0, v1)) % 3.68/1.59 | (24) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_transitive_in(v0, v1)) % 3.68/1.59 | (25) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_connected_in(v0, v1) | ~ relation(v0) | connected(v0)) % 3.68/1.59 | (26) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ well_founded_relation(v0) | ~ relation(v0) | is_well_founded_in(v0, v1)) % 3.68/1.59 | (27) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_antisymmetric_in(v0, v1) | ~ relation(v0) | antisymmetric(v0)) % 3.68/1.59 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 3.68/1.59 | (29) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_well_founded_in(v0, v1) | ~ relation(v0) | well_founded_relation(v0)) % 3.68/1.59 | (30) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | transitive(v0)) % 3.68/1.59 | (31) (well_orders(all_0_1_1, all_0_0_0) & ~ well_ordering(all_0_1_1)) | (well_ordering(all_0_1_1) & ~ well_orders(all_0_1_1, all_0_0_0)) % 3.68/1.59 | (32) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | antisymmetric(v0)) % 3.68/1.59 | (33) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | reflexive(v0)) % 3.68/1.59 | (34) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ connected(v0) | ~ relation(v0) | is_connected_in(v0, v1)) % 3.68/1.59 | (35) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_antisymmetric_in(v0, v1)) % 3.68/1.59 | % 3.68/1.59 +-Applying beta-rule and splitting (31), into two cases. % 3.68/1.59 |-Branch one: % 3.68/1.59 | (36) well_orders(all_0_1_1, all_0_0_0) & ~ well_ordering(all_0_1_1) % 3.68/1.59 | % 3.68/1.59 | Applying alpha-rule on (36) yields: % 3.68/1.59 | (37) well_orders(all_0_1_1, all_0_0_0) % 3.68/1.59 | (38) ~ well_ordering(all_0_1_1) % 3.68/1.59 | % 3.68/1.59 | Instantiating formula (13) with all_0_0_0, all_0_1_1 and discharging atoms well_orders(all_0_1_1, all_0_0_0), relation(all_0_1_1), yields: % 3.68/1.59 | (39) is_well_founded_in(all_0_1_1, all_0_0_0) % 3.68/1.59 | % 3.68/1.59 | Instantiating formula (9) with all_0_0_0, all_0_1_1 and discharging atoms well_orders(all_0_1_1, all_0_0_0), relation(all_0_1_1), yields: % 3.68/1.59 | (40) is_reflexive_in(all_0_1_1, all_0_0_0) % 3.68/1.59 | % 3.68/1.59 | Instantiating formula (24) with all_0_0_0, all_0_1_1 and discharging atoms well_orders(all_0_1_1, all_0_0_0), relation(all_0_1_1), yields: % 3.68/1.59 | (41) is_transitive_in(all_0_1_1, all_0_0_0) % 3.68/1.59 | % 3.68/1.59 | Instantiating formula (17) with all_0_0_0, all_0_1_1 and discharging atoms well_orders(all_0_1_1, all_0_0_0), relation(all_0_1_1), yields: % 3.68/1.59 | (42) is_connected_in(all_0_1_1, all_0_0_0) % 3.68/1.59 | % 3.68/1.59 | Instantiating formula (35) with all_0_0_0, all_0_1_1 and discharging atoms well_orders(all_0_1_1, all_0_0_0), relation(all_0_1_1), yields: % 3.68/1.59 | (43) is_antisymmetric_in(all_0_1_1, all_0_0_0) % 3.68/1.59 | % 3.68/1.59 | Instantiating formula (29) with all_0_0_0, all_0_1_1 and discharging atoms relation_field(all_0_1_1) = all_0_0_0, is_well_founded_in(all_0_1_1, all_0_0_0), relation(all_0_1_1), yields: % 3.68/1.59 | (44) well_founded_relation(all_0_1_1) % 3.68/1.59 | % 3.68/1.59 | Instantiating formula (4) with all_0_0_0, all_0_1_1 and discharging atoms relation_field(all_0_1_1) = all_0_0_0, is_reflexive_in(all_0_1_1, all_0_0_0), relation(all_0_1_1), yields: % 3.68/1.59 | (45) reflexive(all_0_1_1) % 3.68/1.59 | % 3.68/1.59 | Instantiating formula (3) with all_0_0_0, all_0_1_1 and discharging atoms relation_field(all_0_1_1) = all_0_0_0, is_transitive_in(all_0_1_1, all_0_0_0), relation(all_0_1_1), yields: % 3.68/1.59 | (46) transitive(all_0_1_1) % 3.68/1.59 | % 3.68/1.59 | Instantiating formula (25) with all_0_0_0, all_0_1_1 and discharging atoms relation_field(all_0_1_1) = all_0_0_0, is_connected_in(all_0_1_1, all_0_0_0), relation(all_0_1_1), yields: % 3.68/1.60 | (47) connected(all_0_1_1) % 3.68/1.60 | % 3.68/1.60 | Instantiating formula (27) with all_0_0_0, all_0_1_1 and discharging atoms relation_field(all_0_1_1) = all_0_0_0, is_antisymmetric_in(all_0_1_1, all_0_0_0), relation(all_0_1_1), yields: % 3.68/1.60 | (48) antisymmetric(all_0_1_1) % 3.68/1.60 | % 3.68/1.60 | Instantiating formula (12) with all_0_1_1 and discharging atoms well_founded_relation(all_0_1_1), reflexive(all_0_1_1), transitive(all_0_1_1), connected(all_0_1_1), antisymmetric(all_0_1_1), relation(all_0_1_1), ~ well_ordering(all_0_1_1), yields: % 3.68/1.60 | (49) $false % 3.68/1.60 | % 3.68/1.60 |-The branch is then unsatisfiable % 3.68/1.60 |-Branch two: % 3.68/1.60 | (50) well_ordering(all_0_1_1) & ~ well_orders(all_0_1_1, all_0_0_0) % 3.68/1.60 | % 3.68/1.60 | Applying alpha-rule on (50) yields: % 3.68/1.60 | (51) well_ordering(all_0_1_1) % 3.68/1.60 | (52) ~ well_orders(all_0_1_1, all_0_0_0) % 3.68/1.60 | % 3.68/1.60 | Instantiating formula (18) with all_0_1_1 and discharging atoms well_ordering(all_0_1_1), relation(all_0_1_1), yields: % 3.68/1.60 | (44) well_founded_relation(all_0_1_1) % 3.68/1.60 | % 3.68/1.60 | Instantiating formula (33) with all_0_1_1 and discharging atoms well_ordering(all_0_1_1), relation(all_0_1_1), yields: % 3.68/1.60 | (45) reflexive(all_0_1_1) % 3.68/1.60 | % 3.68/1.60 | Instantiating formula (30) with all_0_1_1 and discharging atoms well_ordering(all_0_1_1), relation(all_0_1_1), yields: % 3.68/1.60 | (46) transitive(all_0_1_1) % 3.68/1.60 | % 3.68/1.60 | Instantiating formula (2) with all_0_1_1 and discharging atoms well_ordering(all_0_1_1), relation(all_0_1_1), yields: % 3.68/1.60 | (47) connected(all_0_1_1) % 3.68/1.60 | % 3.68/1.60 | Instantiating formula (32) with all_0_1_1 and discharging atoms well_ordering(all_0_1_1), relation(all_0_1_1), yields: % 3.68/1.60 | (48) antisymmetric(all_0_1_1) % 3.68/1.60 | % 3.68/1.60 | Instantiating formula (26) with all_0_0_0, all_0_1_1 and discharging atoms relation_field(all_0_1_1) = all_0_0_0, well_founded_relation(all_0_1_1), relation(all_0_1_1), yields: % 3.68/1.60 | (39) is_well_founded_in(all_0_1_1, all_0_0_0) % 3.68/1.60 | % 3.68/1.60 | Instantiating formula (23) with all_0_0_0, all_0_1_1 and discharging atoms relation_field(all_0_1_1) = all_0_0_0, reflexive(all_0_1_1), relation(all_0_1_1), yields: % 3.68/1.60 | (40) is_reflexive_in(all_0_1_1, all_0_0_0) % 3.68/1.60 | % 3.68/1.60 | Instantiating formula (5) with all_0_0_0, all_0_1_1 and discharging atoms relation_field(all_0_1_1) = all_0_0_0, transitive(all_0_1_1), relation(all_0_1_1), yields: % 3.68/1.60 | (41) is_transitive_in(all_0_1_1, all_0_0_0) % 3.68/1.60 | % 3.68/1.60 | Instantiating formula (34) with all_0_0_0, all_0_1_1 and discharging atoms relation_field(all_0_1_1) = all_0_0_0, connected(all_0_1_1), relation(all_0_1_1), yields: % 3.68/1.60 | (42) is_connected_in(all_0_1_1, all_0_0_0) % 3.68/1.60 | % 3.68/1.60 | Instantiating formula (20) with all_0_0_0, all_0_1_1 and discharging atoms relation_field(all_0_1_1) = all_0_0_0, antisymmetric(all_0_1_1), relation(all_0_1_1), yields: % 3.68/1.60 | (43) is_antisymmetric_in(all_0_1_1, all_0_0_0) % 3.68/1.60 | % 3.68/1.60 | Instantiating formula (21) with all_0_0_0, all_0_1_1 and discharging atoms is_well_founded_in(all_0_1_1, all_0_0_0), is_reflexive_in(all_0_1_1, all_0_0_0), is_transitive_in(all_0_1_1, all_0_0_0), is_connected_in(all_0_1_1, all_0_0_0), is_antisymmetric_in(all_0_1_1, all_0_0_0), relation(all_0_1_1), ~ well_orders(all_0_1_1, all_0_0_0), yields: % 3.68/1.60 | (49) $false % 3.68/1.60 | % 3.68/1.60 |-The branch is then unsatisfiable % 3.68/1.60 % SZS output end Proof for theBenchmark % 3.68/1.60 % 3.68/1.60 1010ms %------------------------------------------------------------------------------