TSTP Solution File: SEU359+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU359+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 08:49:10 EDT 2022
% Result : Theorem 2.74s 1.40s
% Output : Proof 3.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU359+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n011.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 09:33:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.61/0.62 ____ _
% 0.61/0.62 ___ / __ \_____(_)___ ________ __________
% 0.61/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.61/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.61/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.61/0.62
% 0.61/0.62 A Theorem Prover for First-Order Logic
% 0.61/0.62 (ePrincess v.1.0)
% 0.61/0.62
% 0.61/0.62 (c) Philipp Rümmer, 2009-2015
% 0.61/0.62 (c) Peter Backeman, 2014-2015
% 0.61/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.62 Bug reports to peter@backeman.se
% 0.61/0.62
% 0.61/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.62
% 0.61/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.48/0.98 Prover 0: Preprocessing ...
% 1.85/1.15 Prover 0: Warning: ignoring some quantifiers
% 1.85/1.17 Prover 0: Constructing countermodel ...
% 2.74/1.40 Prover 0: proved (707ms)
% 2.74/1.40
% 2.74/1.40 No countermodel exists, formula is valid
% 2.74/1.40 % SZS status Theorem for theBenchmark
% 2.74/1.40
% 2.74/1.40 Generating proof ... Warning: ignoring some quantifiers
% 3.58/1.69 found it (size 37)
% 3.58/1.69
% 3.58/1.69 % SZS output start Proof for theBenchmark
% 3.58/1.69 Assumed formulas after preprocessing and simplification:
% 3.58/1.69 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (the_carrier(v0) = v1 & join_on_relstr(v0, v3) = v4 & antisymmetric_relstr(v0) & one_sorted_str(v6) & element(v2, v1) & rel_str(v7) & rel_str(v0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (the_carrier(v8) = v9) | ~ (join_on_relstr(v8, v10) = v12) | ~ relstr_set_smaller(v8, v10, v11) | ~ ex_sup_of_relstr_set(v8, v10) | ~ element(v11, v9) | ~ rel_str(v8) | ? [v13] : (relstr_set_smaller(v8, v10, v13) & element(v13, v9) & ~ related(v8, v11, v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (the_carrier(v8) = v9) | ~ (join_on_relstr(v8, v10) = v11) | ~ relstr_set_smaller(v8, v10, v12) | ~ ex_sup_of_relstr_set(v8, v10) | ~ element(v12, v9) | ~ element(v11, v9) | ~ rel_str(v8) | related(v8, v11, v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (join_on_relstr(v11, v10) = v9) | ~ (join_on_relstr(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (the_carrier(v8) = v9) | ~ (join_on_relstr(v8, v10) = v11) | ~ ex_sup_of_relstr_set(v8, v10) | ~ element(v11, v9) | ~ rel_str(v8) | relstr_set_smaller(v8, v10, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (the_carrier(v8) = v9) | ~ antisymmetric_relstr(v8) | ~ relstr_set_smaller(v8, v10, v11) | ~ element(v11, v9) | ~ rel_str(v8) | ex_sup_of_relstr_set(v8, v10) | ? [v12] : (relstr_set_smaller(v8, v10, v12) & element(v12, v9) & ~ related(v8, v11, v12))) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (the_carrier(v10) = v9) | ~ (the_carrier(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (the_carrier(v8) = v9) | ~ antisymmetric_relstr(v8) | ~ ex_sup_of_relstr_set(v8, v10) | ~ rel_str(v8) | ? [v11] : (relstr_set_smaller(v8, v10, v11) & element(v11, v9) & ! [v12] : ( ~ relstr_set_smaller(v8, v10, v12) | ~ element(v12, v9) | related(v8, v11, v12)))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (join_on_relstr(v8, v9) = v10) | ~ rel_str(v8) | ? [v11] : (the_carrier(v8) = v11 & element(v10, v11))) & ! [v8] : ( ~ rel_str(v8) | one_sorted_str(v8)) & ? [v8] : ? [v9] : element(v9, v8) & ((v4 = v2 & ex_sup_of_relstr_set(v0, v3) & ( ~ relstr_set_smaller(v0, v3, v2) | (relstr_set_smaller(v0, v3, v5) & element(v5, v1) & ~ related(v0, v2, v5)))) | (relstr_set_smaller(v0, v3, v2) & ! [v8] : ( ~ relstr_set_smaller(v0, v3, v8) | ~ element(v8, v1) | related(v0, v2, v8)) & ( ~ (v4 = v2) | ~ ex_sup_of_relstr_set(v0, v3)))))
% 3.91/1.73 | 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:
% 3.91/1.73 | (1) the_carrier(all_0_7_7) = all_0_6_6 & join_on_relstr(all_0_7_7, all_0_4_4) = all_0_3_3 & antisymmetric_relstr(all_0_7_7) & one_sorted_str(all_0_1_1) & element(all_0_5_5, all_0_6_6) & rel_str(all_0_0_0) & rel_str(all_0_7_7) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v2) = v4) | ~ relstr_set_smaller(v0, v2, v3) | ~ ex_sup_of_relstr_set(v0, v2) | ~ element(v3, v1) | ~ rel_str(v0) | ? [v5] : (relstr_set_smaller(v0, v2, v5) & element(v5, v1) & ~ related(v0, v3, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v2) = v3) | ~ relstr_set_smaller(v0, v2, v4) | ~ ex_sup_of_relstr_set(v0, v2) | ~ element(v4, v1) | ~ element(v3, v1) | ~ rel_str(v0) | related(v0, v3, 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, v2) = v3) | ~ ex_sup_of_relstr_set(v0, v2) | ~ element(v3, v1) | ~ rel_str(v0) | relstr_set_smaller(v0, v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v1) | ~ antisymmetric_relstr(v0) | ~ relstr_set_smaller(v0, v2, v3) | ~ element(v3, v1) | ~ rel_str(v0) | ex_sup_of_relstr_set(v0, v2) | ? [v4] : (relstr_set_smaller(v0, v2, v4) & element(v4, v1) & ~ related(v0, v3, v4))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (the_carrier(v0) = v1) | ~ antisymmetric_relstr(v0) | ~ ex_sup_of_relstr_set(v0, v2) | ~ rel_str(v0) | ? [v3] : (relstr_set_smaller(v0, v2, v3) & element(v3, v1) & ! [v4] : ( ~ relstr_set_smaller(v0, v2, v4) | ~ element(v4, v1) | related(v0, v3, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (join_on_relstr(v0, v1) = v2) | ~ rel_str(v0) | ? [v3] : (the_carrier(v0) = v3 & element(v2, v3))) & ! [v0] : ( ~ rel_str(v0) | one_sorted_str(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ((all_0_3_3 = all_0_5_5 & ex_sup_of_relstr_set(all_0_7_7, all_0_4_4) & ( ~ relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_5_5) | (relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_2_2) & element(all_0_2_2, all_0_6_6) & ~ related(all_0_7_7, all_0_5_5, all_0_2_2)))) | (relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_5_5) & ! [v0] : ( ~ relstr_set_smaller(all_0_7_7, all_0_4_4, v0) | ~ element(v0, all_0_6_6) | related(all_0_7_7, all_0_5_5, v0)) & ( ~ (all_0_3_3 = all_0_5_5) | ~ ex_sup_of_relstr_set(all_0_7_7, all_0_4_4))))
% 3.91/1.73 |
% 3.91/1.73 | Applying alpha-rule on (1) yields:
% 3.91/1.73 | (2) one_sorted_str(all_0_1_1)
% 3.91/1.73 | (3) ? [v0] : ? [v1] : element(v1, v0)
% 3.91/1.73 | (4) ! [v0] : ( ~ rel_str(v0) | one_sorted_str(v0))
% 3.91/1.73 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (join_on_relstr(v3, v2) = v1) | ~ (join_on_relstr(v3, v2) = v0))
% 3.91/1.73 | (6) join_on_relstr(all_0_7_7, all_0_4_4) = all_0_3_3
% 3.91/1.74 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (the_carrier(v0) = v1) | ~ antisymmetric_relstr(v0) | ~ ex_sup_of_relstr_set(v0, v2) | ~ rel_str(v0) | ? [v3] : (relstr_set_smaller(v0, v2, v3) & element(v3, v1) & ! [v4] : ( ~ relstr_set_smaller(v0, v2, v4) | ~ element(v4, v1) | related(v0, v3, v4))))
% 3.91/1.74 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v1) | ~ antisymmetric_relstr(v0) | ~ relstr_set_smaller(v0, v2, v3) | ~ element(v3, v1) | ~ rel_str(v0) | ex_sup_of_relstr_set(v0, v2) | ? [v4] : (relstr_set_smaller(v0, v2, v4) & element(v4, v1) & ~ related(v0, v3, v4)))
% 3.91/1.74 | (9) the_carrier(all_0_7_7) = all_0_6_6
% 3.91/1.74 | (10) element(all_0_5_5, all_0_6_6)
% 3.91/1.74 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v2) = v3) | ~ ex_sup_of_relstr_set(v0, v2) | ~ element(v3, v1) | ~ rel_str(v0) | relstr_set_smaller(v0, v2, v3))
% 3.91/1.74 | (12) rel_str(all_0_0_0)
% 3.91/1.74 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 3.91/1.74 | (14) (all_0_3_3 = all_0_5_5 & ex_sup_of_relstr_set(all_0_7_7, all_0_4_4) & ( ~ relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_5_5) | (relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_2_2) & element(all_0_2_2, all_0_6_6) & ~ related(all_0_7_7, all_0_5_5, all_0_2_2)))) | (relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_5_5) & ! [v0] : ( ~ relstr_set_smaller(all_0_7_7, all_0_4_4, v0) | ~ element(v0, all_0_6_6) | related(all_0_7_7, all_0_5_5, v0)) & ( ~ (all_0_3_3 = all_0_5_5) | ~ ex_sup_of_relstr_set(all_0_7_7, all_0_4_4)))
% 3.91/1.74 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (join_on_relstr(v0, v1) = v2) | ~ rel_str(v0) | ? [v3] : (the_carrier(v0) = v3 & element(v2, v3)))
% 3.91/1.74 | (16) antisymmetric_relstr(all_0_7_7)
% 3.91/1.74 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v2) = v4) | ~ relstr_set_smaller(v0, v2, v3) | ~ ex_sup_of_relstr_set(v0, v2) | ~ element(v3, v1) | ~ rel_str(v0) | ? [v5] : (relstr_set_smaller(v0, v2, v5) & element(v5, v1) & ~ related(v0, v3, v5)))
% 3.91/1.74 | (18) rel_str(all_0_7_7)
% 3.91/1.74 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (the_carrier(v0) = v1) | ~ (join_on_relstr(v0, v2) = v3) | ~ relstr_set_smaller(v0, v2, v4) | ~ ex_sup_of_relstr_set(v0, v2) | ~ element(v4, v1) | ~ element(v3, v1) | ~ rel_str(v0) | related(v0, v3, v4))
% 3.91/1.74 |
% 3.91/1.74 | Instantiating formula (15) with all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms join_on_relstr(all_0_7_7, all_0_4_4) = all_0_3_3, rel_str(all_0_7_7), yields:
% 3.91/1.74 | (20) ? [v0] : (the_carrier(all_0_7_7) = v0 & element(all_0_3_3, v0))
% 3.91/1.74 |
% 3.91/1.74 | Instantiating (20) with all_11_0_10 yields:
% 3.91/1.74 | (21) the_carrier(all_0_7_7) = all_11_0_10 & element(all_0_3_3, all_11_0_10)
% 3.91/1.74 |
% 3.91/1.74 | Applying alpha-rule on (21) yields:
% 3.91/1.74 | (22) the_carrier(all_0_7_7) = all_11_0_10
% 3.91/1.74 | (23) element(all_0_3_3, all_11_0_10)
% 3.91/1.74 |
% 3.91/1.74 | Instantiating formula (13) with all_0_7_7, all_11_0_10, all_0_6_6 and discharging atoms the_carrier(all_0_7_7) = all_11_0_10, the_carrier(all_0_7_7) = all_0_6_6, yields:
% 3.91/1.74 | (24) all_11_0_10 = all_0_6_6
% 3.91/1.74 |
% 3.91/1.74 | From (24) and (22) follows:
% 3.91/1.75 | (9) the_carrier(all_0_7_7) = all_0_6_6
% 3.91/1.75 |
% 3.91/1.75 | From (24) and (23) follows:
% 3.91/1.75 | (26) element(all_0_3_3, all_0_6_6)
% 3.91/1.75 |
% 3.91/1.75 +-Applying beta-rule and splitting (14), into two cases.
% 3.91/1.75 |-Branch one:
% 3.91/1.75 | (27) all_0_3_3 = all_0_5_5 & ex_sup_of_relstr_set(all_0_7_7, all_0_4_4) & ( ~ relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_5_5) | (relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_2_2) & element(all_0_2_2, all_0_6_6) & ~ related(all_0_7_7, all_0_5_5, all_0_2_2)))
% 3.91/1.75 |
% 3.91/1.75 | Applying alpha-rule on (27) yields:
% 3.91/1.75 | (28) all_0_3_3 = all_0_5_5
% 3.91/1.75 | (29) ex_sup_of_relstr_set(all_0_7_7, all_0_4_4)
% 3.91/1.75 | (30) ~ relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_5_5) | (relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_2_2) & element(all_0_2_2, all_0_6_6) & ~ related(all_0_7_7, all_0_5_5, all_0_2_2))
% 3.91/1.75 |
% 3.91/1.75 | From (28) and (6) follows:
% 3.91/1.75 | (31) join_on_relstr(all_0_7_7, all_0_4_4) = all_0_5_5
% 3.91/1.75 |
% 3.91/1.75 | From (28) and (26) follows:
% 3.91/1.75 | (10) element(all_0_5_5, all_0_6_6)
% 3.91/1.75 |
% 3.91/1.75 | Instantiating formula (11) with all_0_5_5, all_0_4_4, all_0_6_6, all_0_7_7 and discharging atoms the_carrier(all_0_7_7) = all_0_6_6, join_on_relstr(all_0_7_7, all_0_4_4) = all_0_5_5, ex_sup_of_relstr_set(all_0_7_7, all_0_4_4), element(all_0_5_5, all_0_6_6), rel_str(all_0_7_7), yields:
% 3.91/1.75 | (33) relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_5_5)
% 3.91/1.75 |
% 3.91/1.75 +-Applying beta-rule and splitting (30), into two cases.
% 3.91/1.75 |-Branch one:
% 3.91/1.75 | (34) ~ relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_5_5)
% 3.91/1.75 |
% 3.91/1.75 | Using (33) and (34) yields:
% 3.91/1.75 | (35) $false
% 3.91/1.75 |
% 3.91/1.75 |-The branch is then unsatisfiable
% 3.91/1.75 |-Branch two:
% 3.91/1.75 | (33) relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_5_5)
% 3.91/1.75 | (37) relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_2_2) & element(all_0_2_2, all_0_6_6) & ~ related(all_0_7_7, all_0_5_5, all_0_2_2)
% 3.91/1.75 |
% 3.91/1.75 | Applying alpha-rule on (37) yields:
% 3.91/1.75 | (38) relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_2_2)
% 3.91/1.75 | (39) element(all_0_2_2, all_0_6_6)
% 3.91/1.75 | (40) ~ related(all_0_7_7, all_0_5_5, all_0_2_2)
% 3.91/1.75 |
% 3.91/1.75 | Instantiating formula (19) with all_0_2_2, all_0_5_5, all_0_4_4, all_0_6_6, all_0_7_7 and discharging atoms the_carrier(all_0_7_7) = all_0_6_6, join_on_relstr(all_0_7_7, all_0_4_4) = all_0_5_5, relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_2_2), ex_sup_of_relstr_set(all_0_7_7, all_0_4_4), element(all_0_2_2, all_0_6_6), element(all_0_5_5, all_0_6_6), rel_str(all_0_7_7), ~ related(all_0_7_7, all_0_5_5, all_0_2_2), yields:
% 3.91/1.75 | (35) $false
% 3.91/1.75 |
% 3.91/1.75 |-The branch is then unsatisfiable
% 3.91/1.75 |-Branch two:
% 3.91/1.75 | (42) relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_5_5) & ! [v0] : ( ~ relstr_set_smaller(all_0_7_7, all_0_4_4, v0) | ~ element(v0, all_0_6_6) | related(all_0_7_7, all_0_5_5, v0)) & ( ~ (all_0_3_3 = all_0_5_5) | ~ ex_sup_of_relstr_set(all_0_7_7, all_0_4_4))
% 3.91/1.75 |
% 3.91/1.75 | Applying alpha-rule on (42) yields:
% 3.91/1.75 | (33) relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_5_5)
% 3.91/1.75 | (44) ! [v0] : ( ~ relstr_set_smaller(all_0_7_7, all_0_4_4, v0) | ~ element(v0, all_0_6_6) | related(all_0_7_7, all_0_5_5, v0))
% 3.91/1.75 | (45) ~ (all_0_3_3 = all_0_5_5) | ~ ex_sup_of_relstr_set(all_0_7_7, all_0_4_4)
% 3.91/1.75 |
% 3.91/1.75 | Instantiating formula (8) with all_0_5_5, all_0_4_4, all_0_6_6, all_0_7_7 and discharging atoms the_carrier(all_0_7_7) = all_0_6_6, antisymmetric_relstr(all_0_7_7), relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_5_5), element(all_0_5_5, all_0_6_6), rel_str(all_0_7_7), yields:
% 3.91/1.75 | (46) ex_sup_of_relstr_set(all_0_7_7, all_0_4_4) | ? [v0] : (relstr_set_smaller(all_0_7_7, all_0_4_4, v0) & element(v0, all_0_6_6) & ~ related(all_0_7_7, all_0_5_5, v0))
% 3.91/1.75 |
% 3.91/1.75 +-Applying beta-rule and splitting (45), into two cases.
% 3.91/1.75 |-Branch one:
% 3.91/1.75 | (47) ~ ex_sup_of_relstr_set(all_0_7_7, all_0_4_4)
% 3.91/1.75 |
% 3.91/1.75 +-Applying beta-rule and splitting (46), into two cases.
% 3.91/1.75 |-Branch one:
% 3.91/1.75 | (29) ex_sup_of_relstr_set(all_0_7_7, all_0_4_4)
% 3.91/1.75 |
% 3.91/1.75 | Using (29) and (47) yields:
% 3.91/1.75 | (35) $false
% 3.91/1.75 |
% 3.91/1.75 |-The branch is then unsatisfiable
% 3.91/1.75 |-Branch two:
% 3.91/1.75 | (47) ~ ex_sup_of_relstr_set(all_0_7_7, all_0_4_4)
% 3.91/1.75 | (51) ? [v0] : (relstr_set_smaller(all_0_7_7, all_0_4_4, v0) & element(v0, all_0_6_6) & ~ related(all_0_7_7, all_0_5_5, v0))
% 3.91/1.76 |
% 3.91/1.76 | Instantiating (51) with all_42_0_12 yields:
% 3.91/1.76 | (52) relstr_set_smaller(all_0_7_7, all_0_4_4, all_42_0_12) & element(all_42_0_12, all_0_6_6) & ~ related(all_0_7_7, all_0_5_5, all_42_0_12)
% 3.91/1.76 |
% 3.91/1.76 | Applying alpha-rule on (52) yields:
% 3.91/1.76 | (53) relstr_set_smaller(all_0_7_7, all_0_4_4, all_42_0_12)
% 3.91/1.76 | (54) element(all_42_0_12, all_0_6_6)
% 3.91/1.76 | (55) ~ related(all_0_7_7, all_0_5_5, all_42_0_12)
% 3.91/1.76 |
% 3.91/1.76 | Instantiating formula (44) with all_42_0_12 and discharging atoms relstr_set_smaller(all_0_7_7, all_0_4_4, all_42_0_12), element(all_42_0_12, all_0_6_6), ~ related(all_0_7_7, all_0_5_5, all_42_0_12), yields:
% 3.91/1.76 | (35) $false
% 3.91/1.76 |
% 3.91/1.76 |-The branch is then unsatisfiable
% 3.91/1.76 |-Branch two:
% 3.91/1.76 | (29) ex_sup_of_relstr_set(all_0_7_7, all_0_4_4)
% 3.91/1.76 | (58) ~ (all_0_3_3 = all_0_5_5)
% 3.91/1.76 |
% 3.91/1.76 | Instantiating formula (17) with all_0_3_3, all_0_5_5, all_0_4_4, all_0_6_6, all_0_7_7 and discharging atoms the_carrier(all_0_7_7) = all_0_6_6, join_on_relstr(all_0_7_7, all_0_4_4) = all_0_3_3, relstr_set_smaller(all_0_7_7, all_0_4_4, all_0_5_5), ex_sup_of_relstr_set(all_0_7_7, all_0_4_4), element(all_0_5_5, all_0_6_6), rel_str(all_0_7_7), yields:
% 3.91/1.76 | (59) all_0_3_3 = all_0_5_5 | ? [v0] : (relstr_set_smaller(all_0_7_7, all_0_4_4, v0) & element(v0, all_0_6_6) & ~ related(all_0_7_7, all_0_5_5, v0))
% 3.91/1.76 |
% 3.91/1.76 +-Applying beta-rule and splitting (59), into two cases.
% 3.91/1.76 |-Branch one:
% 3.91/1.76 | (28) all_0_3_3 = all_0_5_5
% 3.91/1.76 |
% 3.91/1.76 | Equations (28) can reduce 58 to:
% 3.91/1.76 | (61) $false
% 3.91/1.76 |
% 3.91/1.76 |-The branch is then unsatisfiable
% 3.91/1.76 |-Branch two:
% 3.91/1.76 | (58) ~ (all_0_3_3 = all_0_5_5)
% 3.91/1.76 | (51) ? [v0] : (relstr_set_smaller(all_0_7_7, all_0_4_4, v0) & element(v0, all_0_6_6) & ~ related(all_0_7_7, all_0_5_5, v0))
% 3.91/1.76 |
% 3.91/1.76 | Instantiating (51) with all_52_0_14 yields:
% 3.91/1.76 | (64) relstr_set_smaller(all_0_7_7, all_0_4_4, all_52_0_14) & element(all_52_0_14, all_0_6_6) & ~ related(all_0_7_7, all_0_5_5, all_52_0_14)
% 3.91/1.76 |
% 3.91/1.76 | Applying alpha-rule on (64) yields:
% 3.91/1.76 | (65) relstr_set_smaller(all_0_7_7, all_0_4_4, all_52_0_14)
% 3.91/1.76 | (66) element(all_52_0_14, all_0_6_6)
% 3.91/1.76 | (67) ~ related(all_0_7_7, all_0_5_5, all_52_0_14)
% 3.91/1.76 |
% 3.91/1.76 | Instantiating formula (44) with all_52_0_14 and discharging atoms relstr_set_smaller(all_0_7_7, all_0_4_4, all_52_0_14), element(all_52_0_14, all_0_6_6), ~ related(all_0_7_7, all_0_5_5, all_52_0_14), yields:
% 3.91/1.76 | (35) $false
% 3.91/1.76 |
% 3.91/1.76 |-The branch is then unsatisfiable
% 3.91/1.76 % SZS output end Proof for theBenchmark
% 3.91/1.76
% 3.91/1.76 1125ms
%------------------------------------------------------------------------------