TSTP Solution File: SEU361+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU361+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.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 08:49:11 EDT 2022
% Result : Theorem 2.91s 1.40s
% Output : Proof 4.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU361+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 22:47:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.57/0.62 ____ _
% 0.57/0.62 ___ / __ \_____(_)___ ________ __________
% 0.57/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.62
% 0.57/0.62 A Theorem Prover for First-Order Logic
% 0.57/0.62 (ePrincess v.1.0)
% 0.57/0.62
% 0.57/0.62 (c) Philipp Rümmer, 2009-2015
% 0.57/0.62 (c) Peter Backeman, 2014-2015
% 0.57/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.62 Bug reports to peter@backeman.se
% 0.57/0.62
% 0.57/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.62
% 0.57/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.66/1.01 Prover 0: Preprocessing ...
% 2.22/1.22 Prover 0: Warning: ignoring some quantifiers
% 2.27/1.24 Prover 0: Constructing countermodel ...
% 2.91/1.40 Prover 0: proved (704ms)
% 2.91/1.40
% 2.91/1.40 No countermodel exists, formula is valid
% 2.91/1.40 % SZS status Theorem for theBenchmark
% 2.91/1.40
% 2.91/1.40 Generating proof ... Warning: ignoring some quantifiers
% 3.83/1.67 found it (size 13)
% 3.83/1.67
% 3.83/1.67 % SZS output start Proof for theBenchmark
% 3.83/1.67 Assumed formulas after preprocessing and simplification:
% 3.83/1.67 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (the_carrier(v0) = v1 & bottom_of_relstr(v0) = v2 & lower_bounded_relstr(v0) & antisymmetric_relstr(v0) & one_sorted_str(v8) & one_sorted_str(v4) & element(v3, v1) & rel_str(v9) & rel_str(v0) & finite(v7) & empty(v6) & empty(empty_set) & ~ related(v0, v2, v3) & ~ empty_carrier(v4) & ~ empty_carrier(v0) & ~ empty(v7) & ~ empty(v5) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (the_carrier(v10) = v11) | ~ (join_on_relstr(v10, v13) = v14) | ~ relstr_set_smaller(v10, v13, v12) | ~ antisymmetric_relstr(v10) | ~ element(v12, v11) | ~ rel_str(v10) | ? [v15] : (relstr_set_smaller(v10, v13, v15) & element(v15, v11) & ~ related(v10, v12, v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (the_carrier(v10) = v11) | ~ (join_on_relstr(v10, v13) = v14) | ~ relstr_set_smaller(v10, v13, v12) | ~ antisymmetric_relstr(v10) | ~ element(v12, v11) | ~ rel_str(v10) | ex_sup_of_relstr_set(v10, v13) | ? [v15] : (relstr_set_smaller(v10, v13, v15) & element(v15, v11) & ~ related(v10, v12, v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (the_carrier(v10) = v11) | ~ (join_on_relstr(v10, v13) = v12) | ~ relstr_set_smaller(v10, v13, v14) | ~ ex_sup_of_relstr_set(v10, v13) | ~ antisymmetric_relstr(v10) | ~ element(v14, v11) | ~ element(v12, v11) | ~ rel_str(v10) | related(v10, v12, v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (join_on_relstr(v13, v12) = v11) | ~ (join_on_relstr(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (the_carrier(v10) = v11) | ~ (join_on_relstr(v10, v13) = v12) | ~ ex_sup_of_relstr_set(v10, v13) | ~ antisymmetric_relstr(v10) | ~ element(v12, v11) | ~ rel_str(v10) | relstr_set_smaller(v10, v13, v12)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (the_carrier(v12) = v11) | ~ (the_carrier(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (bottom_of_relstr(v12) = v11) | ~ (bottom_of_relstr(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (the_carrier(v10) = v11) | ~ element(v12, v11) | ~ rel_str(v10) | relstr_element_smaller(v10, empty_set, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (the_carrier(v10) = v11) | ~ element(v12, v11) | ~ rel_str(v10) | relstr_set_smaller(v10, empty_set, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (join_on_relstr(v10, v11) = v12) | ~ rel_str(v10) | ? [v13] : (the_carrier(v10) = v13 & element(v12, v13))) & ! [v10] : ! [v11] : (v11 = v10 | ~ empty(v11) | ~ empty(v10)) & ! [v10] : ! [v11] : ( ~ (the_carrier(v10) = v11) | ~ lower_bounded_relstr(v10) | ~ antisymmetric_relstr(v10) | ~ rel_str(v10) | ex_inf_of_relstr_set(v10, v11) | empty_carrier(v10)) & ! [v10] : ! [v11] : ( ~ (the_carrier(v10) = v11) | ~ lower_bounded_relstr(v10) | ~ antisymmetric_relstr(v10) | ~ rel_str(v10) | ex_sup_of_relstr_set(v10, empty_set) | empty_carrier(v10)) & ! [v10] : ! [v11] : ( ~ (the_carrier(v10) = v11) | ~ one_sorted_str(v10) | ~ empty(v11) | empty_carrier(v10)) & ! [v10] : ! [v11] : ( ~ (the_carrier(v10) = v11) | ~ rel_str(v10) | ? [v12] : (bottom_of_relstr(v10) = v12 & element(v12, v11))) & ! [v10] : ! [v11] : ( ~ (bottom_of_relstr(v10) = v11) | ~ rel_str(v10) | join_on_relstr(v10, empty_set) = v11) & ! [v10] : ! [v11] : ( ~ (bottom_of_relstr(v10) = v11) | ~ rel_str(v10) | ? [v12] : (the_carrier(v10) = v12 & element(v11, v12))) & ! [v10] : ! [v11] : ( ~ (join_on_relstr(v10, empty_set) = v11) | ~ rel_str(v10) | bottom_of_relstr(v10) = v11) & ! [v10] : ! [v11] : ( ~ element(v10, v11) | empty(v11) | in(v10, v11)) & ! [v10] : ! [v11] : ( ~ empty(v11) | ~ in(v10, v11)) & ! [v10] : ! [v11] : ( ~ in(v11, v10) | ~ in(v10, v11)) & ! [v10] : ! [v11] : ( ~ in(v10, v11) | element(v10, v11)) & ! [v10] : (v10 = empty_set | ~ empty(v10)) & ! [v10] : ( ~ rel_str(v10) | one_sorted_str(v10)) & ! [v10] : ( ~ empty(v10) | finite(v10)) & ? [v10] : ? [v11] : element(v11, v10))
% 4.16/1.71 | 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, all_0_9_9 yields:
% 4.16/1.71 | (1) the_carrier(all_0_9_9) = all_0_8_8 & bottom_of_relstr(all_0_9_9) = all_0_7_7 & lower_bounded_relstr(all_0_9_9) & antisymmetric_relstr(all_0_9_9) & one_sorted_str(all_0_1_1) & one_sorted_str(all_0_5_5) & element(all_0_6_6, all_0_8_8) & rel_str(all_0_0_0) & rel_str(all_0_9_9) & finite(all_0_2_2) & empty(all_0_3_3) & empty(empty_set) & ~ related(all_0_9_9, all_0_7_7, all_0_6_6) & ~ empty_carrier(all_0_5_5) & ~ empty_carrier(all_0_9_9) & ~ empty(all_0_2_2) & ~ empty(all_0_4_4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v3) = v4) | ~ relstr_set_smaller(v0, v3, v2) | ~ antisymmetric_relstr(v0) | ~ element(v2, v1) | ~ rel_str(v0) | ? [v5] : (relstr_set_smaller(v0, v3, v5) & element(v5, v1) & ~ related(v0, v2, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v3) = v4) | ~ relstr_set_smaller(v0, v3, v2) | ~ antisymmetric_relstr(v0) | ~ element(v2, v1) | ~ rel_str(v0) | ex_sup_of_relstr_set(v0, v3) | ? [v5] : (relstr_set_smaller(v0, v3, v5) & element(v5, v1) & ~ related(v0, v2, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v3) = v2) | ~ relstr_set_smaller(v0, v3, v4) | ~ ex_sup_of_relstr_set(v0, v3) | ~ antisymmetric_relstr(v0) | ~ element(v4, v1) | ~ element(v2, v1) | ~ rel_str(v0) | related(v0, v2, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (join_on_relstr(v3, v2) = v1) | ~ (join_on_relstr(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v3) = v2) | ~ ex_sup_of_relstr_set(v0, v3) | ~ antisymmetric_relstr(v0) | ~ element(v2, v1) | ~ rel_str(v0) | relstr_set_smaller(v0, v3, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (bottom_of_relstr(v2) = v1) | ~ (bottom_of_relstr(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (the_carrier(v0) = v1) | ~ element(v2, v1) | ~ rel_str(v0) | relstr_element_smaller(v0, empty_set, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (the_carrier(v0) = v1) | ~ element(v2, v1) | ~ rel_str(v0) | relstr_set_smaller(v0, empty_set, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (join_on_relstr(v0, v1) = v2) | ~ rel_str(v0) | ? [v3] : (the_carrier(v0) = v3 & element(v2, v3))) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ lower_bounded_relstr(v0) | ~ antisymmetric_relstr(v0) | ~ rel_str(v0) | ex_inf_of_relstr_set(v0, v1) | empty_carrier(v0)) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ lower_bounded_relstr(v0) | ~ antisymmetric_relstr(v0) | ~ rel_str(v0) | ex_sup_of_relstr_set(v0, empty_set) | empty_carrier(v0)) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ~ empty(v1) | empty_carrier(v0)) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ rel_str(v0) | ? [v2] : (bottom_of_relstr(v0) = v2 & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ (bottom_of_relstr(v0) = v1) | ~ rel_str(v0) | join_on_relstr(v0, empty_set) = v1) & ! [v0] : ! [v1] : ( ~ (bottom_of_relstr(v0) = v1) | ~ rel_str(v0) | ? [v2] : (the_carrier(v0) = v2 & element(v1, v2))) & ! [v0] : ! [v1] : ( ~ (join_on_relstr(v0, empty_set) = v1) | ~ rel_str(v0) | bottom_of_relstr(v0) = v1) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ rel_str(v0) | one_sorted_str(v0)) & ! [v0] : ( ~ empty(v0) | finite(v0)) & ? [v0] : ? [v1] : element(v1, v0)
% 4.16/1.72 |
% 4.16/1.72 | Applying alpha-rule on (1) yields:
% 4.16/1.72 | (2) ~ related(all_0_9_9, all_0_7_7, all_0_6_6)
% 4.16/1.72 | (3) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ~ empty(v1) | empty_carrier(v0))
% 4.16/1.72 | (4) element(all_0_6_6, all_0_8_8)
% 4.16/1.72 | (5) ! [v0] : ! [v1] : ( ~ (join_on_relstr(v0, empty_set) = v1) | ~ rel_str(v0) | bottom_of_relstr(v0) = v1)
% 4.16/1.72 | (6) finite(all_0_2_2)
% 4.16/1.72 | (7) one_sorted_str(all_0_5_5)
% 4.16/1.72 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v3) = v4) | ~ relstr_set_smaller(v0, v3, v2) | ~ antisymmetric_relstr(v0) | ~ element(v2, v1) | ~ rel_str(v0) | ? [v5] : (relstr_set_smaller(v0, v3, v5) & element(v5, v1) & ~ related(v0, v2, v5)))
% 4.16/1.72 | (9) one_sorted_str(all_0_1_1)
% 4.16/1.72 | (10) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ lower_bounded_relstr(v0) | ~ antisymmetric_relstr(v0) | ~ rel_str(v0) | ex_sup_of_relstr_set(v0, empty_set) | empty_carrier(v0))
% 4.16/1.72 | (11) ! [v0] : ( ~ empty(v0) | finite(v0))
% 4.16/1.72 | (12) rel_str(all_0_9_9)
% 4.16/1.72 | (13) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 4.16/1.72 | (14) rel_str(all_0_0_0)
% 4.16/1.72 | (15) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 4.16/1.72 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v3) = v4) | ~ relstr_set_smaller(v0, v3, v2) | ~ antisymmetric_relstr(v0) | ~ element(v2, v1) | ~ rel_str(v0) | ex_sup_of_relstr_set(v0, v3) | ? [v5] : (relstr_set_smaller(v0, v3, v5) & element(v5, v1) & ~ related(v0, v2, v5)))
% 4.16/1.72 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (bottom_of_relstr(v2) = v1) | ~ (bottom_of_relstr(v2) = v0))
% 4.16/1.72 | (18) ! [v0] : ! [v1] : ( ~ (bottom_of_relstr(v0) = v1) | ~ rel_str(v0) | join_on_relstr(v0, empty_set) = v1)
% 4.16/1.72 | (19) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ lower_bounded_relstr(v0) | ~ antisymmetric_relstr(v0) | ~ rel_str(v0) | ex_inf_of_relstr_set(v0, v1) | empty_carrier(v0))
% 4.16/1.73 | (20) bottom_of_relstr(all_0_9_9) = all_0_7_7
% 4.16/1.73 | (21) ! [v0] : ! [v1] : ( ~ (bottom_of_relstr(v0) = v1) | ~ rel_str(v0) | ? [v2] : (the_carrier(v0) = v2 & element(v1, v2)))
% 4.16/1.73 | (22) ~ empty_carrier(all_0_9_9)
% 4.16/1.73 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 4.16/1.73 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (the_carrier(v0) = v1) | ~ element(v2, v1) | ~ rel_str(v0) | relstr_element_smaller(v0, empty_set, v2))
% 4.16/1.73 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v3) = v2) | ~ ex_sup_of_relstr_set(v0, v3) | ~ antisymmetric_relstr(v0) | ~ element(v2, v1) | ~ rel_str(v0) | relstr_set_smaller(v0, v3, v2))
% 4.16/1.73 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (join_on_relstr(v0, v1) = v2) | ~ rel_str(v0) | ? [v3] : (the_carrier(v0) = v3 & element(v2, v3)))
% 4.16/1.73 | (27) ~ empty_carrier(all_0_5_5)
% 4.16/1.73 | (28) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 4.16/1.73 | (29) empty(all_0_3_3)
% 4.16/1.73 | (30) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 4.16/1.73 | (31) ! [v0] : ( ~ rel_str(v0) | one_sorted_str(v0))
% 4.16/1.73 | (32) ~ empty(all_0_4_4)
% 4.16/1.73 | (33) the_carrier(all_0_9_9) = all_0_8_8
% 4.16/1.73 | (34) empty(empty_set)
% 4.16/1.73 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (the_carrier(v0) = v1) | ~ element(v2, v1) | ~ rel_str(v0) | relstr_set_smaller(v0, empty_set, v2))
% 4.16/1.73 | (36) ? [v0] : ? [v1] : element(v1, v0)
% 4.16/1.73 | (37) ~ empty(all_0_2_2)
% 4.16/1.73 | (38) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 4.16/1.73 | (39) antisymmetric_relstr(all_0_9_9)
% 4.16/1.73 | (40) lower_bounded_relstr(all_0_9_9)
% 4.16/1.73 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v3) = v2) | ~ relstr_set_smaller(v0, v3, v4) | ~ ex_sup_of_relstr_set(v0, v3) | ~ antisymmetric_relstr(v0) | ~ element(v4, v1) | ~ element(v2, v1) | ~ rel_str(v0) | related(v0, v2, v4))
% 4.16/1.73 | (42) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 4.16/1.73 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (join_on_relstr(v3, v2) = v1) | ~ (join_on_relstr(v3, v2) = v0))
% 4.16/1.73 | (44) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ rel_str(v0) | ? [v2] : (bottom_of_relstr(v0) = v2 & element(v2, v1)))
% 4.16/1.73 |
% 4.16/1.73 | Instantiating formula (35) with all_0_6_6, all_0_8_8, all_0_9_9 and discharging atoms the_carrier(all_0_9_9) = all_0_8_8, element(all_0_6_6, all_0_8_8), rel_str(all_0_9_9), yields:
% 4.16/1.73 | (45) relstr_set_smaller(all_0_9_9, empty_set, all_0_6_6)
% 4.16/1.73 |
% 4.16/1.73 | Instantiating formula (10) with all_0_8_8, all_0_9_9 and discharging atoms the_carrier(all_0_9_9) = all_0_8_8, lower_bounded_relstr(all_0_9_9), antisymmetric_relstr(all_0_9_9), rel_str(all_0_9_9), ~ empty_carrier(all_0_9_9), yields:
% 4.16/1.73 | (46) ex_sup_of_relstr_set(all_0_9_9, empty_set)
% 4.16/1.73 |
% 4.16/1.73 | Instantiating formula (18) with all_0_7_7, all_0_9_9 and discharging atoms bottom_of_relstr(all_0_9_9) = all_0_7_7, rel_str(all_0_9_9), yields:
% 4.16/1.74 | (47) join_on_relstr(all_0_9_9, empty_set) = all_0_7_7
% 4.16/1.74 |
% 4.16/1.74 | Instantiating formula (21) with all_0_7_7, all_0_9_9 and discharging atoms bottom_of_relstr(all_0_9_9) = all_0_7_7, rel_str(all_0_9_9), yields:
% 4.16/1.74 | (48) ? [v0] : (the_carrier(all_0_9_9) = v0 & element(all_0_7_7, v0))
% 4.16/1.74 |
% 4.16/1.74 | Instantiating (48) with all_17_0_13 yields:
% 4.16/1.74 | (49) the_carrier(all_0_9_9) = all_17_0_13 & element(all_0_7_7, all_17_0_13)
% 4.16/1.74 |
% 4.16/1.74 | Applying alpha-rule on (49) yields:
% 4.16/1.74 | (50) the_carrier(all_0_9_9) = all_17_0_13
% 4.16/1.74 | (51) element(all_0_7_7, all_17_0_13)
% 4.16/1.74 |
% 4.16/1.74 | Instantiating formula (23) with all_0_9_9, all_17_0_13, all_0_8_8 and discharging atoms the_carrier(all_0_9_9) = all_17_0_13, the_carrier(all_0_9_9) = all_0_8_8, yields:
% 4.16/1.74 | (52) all_17_0_13 = all_0_8_8
% 4.16/1.74 |
% 4.16/1.74 | From (52) and (50) follows:
% 4.16/1.74 | (33) the_carrier(all_0_9_9) = all_0_8_8
% 4.16/1.74 |
% 4.16/1.74 | From (52) and (51) follows:
% 4.16/1.74 | (54) element(all_0_7_7, all_0_8_8)
% 4.16/1.74 |
% 4.16/1.74 | Instantiating formula (41) with all_0_6_6, empty_set, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms the_carrier(all_0_9_9) = all_0_8_8, join_on_relstr(all_0_9_9, empty_set) = all_0_7_7, relstr_set_smaller(all_0_9_9, empty_set, all_0_6_6), ex_sup_of_relstr_set(all_0_9_9, empty_set), antisymmetric_relstr(all_0_9_9), element(all_0_6_6, all_0_8_8), element(all_0_7_7, all_0_8_8), rel_str(all_0_9_9), ~ related(all_0_9_9, all_0_7_7, all_0_6_6), yields:
% 4.16/1.74 | (55) $false
% 4.16/1.74 |
% 4.16/1.74 |-The branch is then unsatisfiable
% 4.16/1.74 % SZS output end Proof for theBenchmark
% 4.16/1.74
% 4.16/1.74 1104ms
%------------------------------------------------------------------------------