TSTP Solution File: SEU118+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU118+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.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 08:46:41 EDT 2022
% Result : Theorem 2.55s 1.31s
% Output : Proof 4.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU118+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n020.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 : Sat Jun 18 22:27:18 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.54/0.59 ____ _
% 0.54/0.59 ___ / __ \_____(_)___ ________ __________
% 0.54/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.59
% 0.54/0.59 A Theorem Prover for First-Order Logic
% 0.54/0.60 (ePrincess v.1.0)
% 0.54/0.60
% 0.54/0.60 (c) Philipp Rümmer, 2009-2015
% 0.54/0.60 (c) Peter Backeman, 2014-2015
% 0.54/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.60 Bug reports to peter@backeman.se
% 0.54/0.60
% 0.54/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.60
% 0.54/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.56/0.92 Prover 0: Preprocessing ...
% 2.05/1.12 Prover 0: Warning: ignoring some quantifiers
% 2.05/1.14 Prover 0: Constructing countermodel ...
% 2.55/1.31 Prover 0: proved (662ms)
% 2.55/1.31
% 2.55/1.31 No countermodel exists, formula is valid
% 2.55/1.31 % SZS status Theorem for theBenchmark
% 2.55/1.31
% 2.55/1.31 Generating proof ... Warning: ignoring some quantifiers
% 3.83/1.58 found it (size 8)
% 3.83/1.58
% 3.83/1.58 % SZS output start Proof for theBenchmark
% 3.83/1.58 Assumed formulas after preprocessing and simplification:
% 3.83/1.59 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (finite_subsets(v0) = v3 & powerset(v0) = v2 & cap_closed(v6) & element(v1, v2) & diff_closed(v6) & cup_closed(v6) & preboolean(v6) & finite(v7) & finite(v0) & empty(v5) & empty(empty_set) & ~ element(v1, v3) & ~ empty(v7) & ~ empty(v6) & ~ empty(v4) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ element(v9, v11) | ~ empty(v10) | ~ in(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ element(v9, v11) | ~ in(v8, v9) | element(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (finite_subsets(v8) = v10) | ~ preboolean(v9) | ? [v11] : (( ~ subset(v11, v8) | ~ finite(v11) | ~ in(v11, v9)) & (in(v11, v9) | (subset(v11, v8) & finite(v11))))) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (finite_subsets(v10) = v9) | ~ (finite_subsets(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (powerset(v10) = v9) | ~ (powerset(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (finite_subsets(v8) = v10) | ~ element(v9, v10) | finite(v9)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (finite_subsets(v8) = v9) | ~ subset(v10, v8) | ~ preboolean(v9) | ~ finite(v10) | in(v10, v9)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (finite_subsets(v8) = v9) | ~ preboolean(v9) | ~ in(v10, v9) | subset(v10, v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (finite_subsets(v8) = v9) | ~ preboolean(v9) | ~ in(v10, v9) | finite(v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ subset(v8, v9) | element(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ element(v8, v10) | subset(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v8) = v9) | ~ element(v10, v9) | ~ finite(v8) | finite(v10)) & ! [v8] : ! [v9] : (v9 = v8 | ~ empty(v9) | ~ empty(v8)) & ! [v8] : ! [v9] : ( ~ (finite_subsets(v8) = v9) | ~ empty(v9)) & ! [v8] : ! [v9] : ( ~ (finite_subsets(v8) = v9) | diff_closed(v9)) & ! [v8] : ! [v9] : ( ~ (finite_subsets(v8) = v9) | cup_closed(v9)) & ! [v8] : ! [v9] : ( ~ (finite_subsets(v8) = v9) | preboolean(v9)) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ~ empty(v9)) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | diff_closed(v9)) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | cup_closed(v9)) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | preboolean(v9)) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | empty(v8) | ? [v10] : (element(v10, v9) & finite(v10) & ~ empty(v10))) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | empty(v8) | ? [v10] : (element(v10, v9) & ~ empty(v10))) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ? [v10] : (natural(v10) & ordinal(v10) & epsilon_connected(v10) & epsilon_transitive(v10) & one_to_one(v10) & function(v10) & relation(v10) & element(v10, v9) & finite(v10) & empty(v10))) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ? [v10] : (element(v10, v9) & empty(v10))) & ! [v8] : ! [v9] : ( ~ subset(v8, v9) | ~ finite(v9) | finite(v8)) & ! [v8] : ! [v9] : ( ~ element(v8, v9) | empty(v9) | in(v8, v9)) & ! [v8] : ! [v9] : ( ~ empty(v9) | ~ in(v8, v9)) & ! [v8] : ! [v9] : ( ~ in(v9, v8) | ~ in(v8, v9)) & ! [v8] : ! [v9] : ( ~ in(v8, v9) | element(v8, v9)) & ! [v8] : (v8 = empty_set | ~ empty(v8)) & ! [v8] : ( ~ diff_closed(v8) | ~ cup_closed(v8) | preboolean(v8)) & ! [v8] : ( ~ preboolean(v8) | diff_closed(v8)) & ! [v8] : ( ~ preboolean(v8) | cup_closed(v8)) & ! [v8] : ( ~ empty(v8) | finite(v8)) & ? [v8] : ? [v9] : element(v9, v8) & ? [v8] : subset(v8, v8))
% 4.15/1.63 | 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:
% 4.15/1.63 | (1) finite_subsets(all_0_7_7) = all_0_4_4 & powerset(all_0_7_7) = all_0_5_5 & cap_closed(all_0_1_1) & element(all_0_6_6, all_0_5_5) & diff_closed(all_0_1_1) & cup_closed(all_0_1_1) & preboolean(all_0_1_1) & finite(all_0_0_0) & finite(all_0_7_7) & empty(all_0_2_2) & empty(empty_set) & ~ element(all_0_6_6, all_0_4_4) & ~ empty(all_0_0_0) & ~ empty(all_0_1_1) & ~ empty(all_0_3_3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (finite_subsets(v0) = v2) | ~ preboolean(v1) | ? [v3] : (( ~ subset(v3, v0) | ~ finite(v3) | ~ in(v3, v1)) & (in(v3, v1) | (subset(v3, v0) & finite(v3))))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite_subsets(v2) = v1) | ~ (finite_subsets(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v2) | ~ element(v1, v2) | finite(v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ subset(v2, v0) | ~ preboolean(v1) | ~ finite(v2) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ preboolean(v1) | ~ in(v2, v1) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ preboolean(v1) | ~ in(v2, v1) | finite(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ finite(v0) | finite(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | diff_closed(v1)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | cup_closed(v1)) & ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | preboolean(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & finite(v2) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (natural(v2) & ordinal(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & one_to_one(v2) & function(v2) & relation(v2) & element(v2, v1) & finite(v2) & empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ finite(v1) | finite(v0)) & ! [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] : ( ~ diff_closed(v0) | ~ cup_closed(v0) | preboolean(v0)) & ! [v0] : ( ~ preboolean(v0) | diff_closed(v0)) & ! [v0] : ( ~ preboolean(v0) | cup_closed(v0)) & ! [v0] : ( ~ empty(v0) | finite(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0)
% 4.15/1.64 |
% 4.15/1.64 | Applying alpha-rule on (1) yields:
% 4.15/1.64 | (2) finite(all_0_0_0)
% 4.15/1.64 | (3) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1))
% 4.15/1.64 | (4) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & finite(v2) & ~ empty(v2)))
% 4.15/1.64 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v2) | ~ element(v1, v2) | finite(v1))
% 4.15/1.64 | (6) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | diff_closed(v1))
% 4.15/1.64 | (7) empty(empty_set)
% 4.15/1.64 | (8) finite_subsets(all_0_7_7) = all_0_4_4
% 4.15/1.64 | (9) ! [v0] : ( ~ empty(v0) | finite(v0))
% 4.15/1.64 | (10) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ finite(v1) | finite(v0))
% 4.15/1.64 | (11) ~ element(all_0_6_6, all_0_4_4)
% 4.15/1.64 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (finite_subsets(v0) = v2) | ~ preboolean(v1) | ? [v3] : (( ~ subset(v3, v0) | ~ finite(v3) | ~ in(v3, v1)) & (in(v3, v1) | (subset(v3, v0) & finite(v3)))))
% 4.15/1.64 | (13) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1))
% 4.15/1.64 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ preboolean(v1) | ~ in(v2, v1) | subset(v2, v0))
% 4.15/1.64 | (15) ! [v0] : ( ~ preboolean(v0) | cup_closed(v0))
% 4.15/1.64 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ subset(v2, v0) | ~ preboolean(v1) | ~ finite(v2) | in(v2, v1))
% 4.15/1.65 | (17) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 4.15/1.65 | (18) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2)))
% 4.15/1.65 | (19) ~ empty(all_0_1_1)
% 4.15/1.65 | (20) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 4.15/1.65 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 4.15/1.65 | (22) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 4.15/1.65 | (23) cup_closed(all_0_1_1)
% 4.15/1.65 | (24) cap_closed(all_0_1_1)
% 4.15/1.65 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (finite_subsets(v0) = v1) | ~ preboolean(v1) | ~ in(v2, v1) | finite(v2))
% 4.15/1.65 | (26) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 4.15/1.65 | (27) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 4.15/1.65 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite_subsets(v2) = v1) | ~ (finite_subsets(v2) = v0))
% 4.15/1.65 | (29) ? [v0] : ? [v1] : element(v1, v0)
% 4.15/1.65 | (30) empty(all_0_2_2)
% 4.15/1.65 | (31) ~ empty(all_0_3_3)
% 4.15/1.65 | (32) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 4.15/1.65 | (33) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | cup_closed(v1))
% 4.15/1.65 | (34) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | ~ empty(v1))
% 4.15/1.65 | (35) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1))
% 4.15/1.65 | (36) ! [v0] : ( ~ preboolean(v0) | diff_closed(v0))
% 4.15/1.65 | (37) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 4.15/1.65 | (38) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (natural(v2) & ordinal(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & one_to_one(v2) & function(v2) & relation(v2) & element(v2, v1) & finite(v2) & empty(v2)))
% 4.15/1.65 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 4.15/1.65 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 4.15/1.65 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 4.15/1.65 | (42) diff_closed(all_0_1_1)
% 4.15/1.65 | (43) ~ empty(all_0_0_0)
% 4.15/1.65 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ finite(v0) | finite(v2))
% 4.15/1.65 | (45) ! [v0] : ( ~ diff_closed(v0) | ~ cup_closed(v0) | preboolean(v0))
% 4.15/1.65 | (46) ! [v0] : ! [v1] : ( ~ (finite_subsets(v0) = v1) | preboolean(v1))
% 4.15/1.65 | (47) finite(all_0_7_7)
% 4.15/1.65 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 4.15/1.65 | (49) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 4.15/1.65 | (50) ? [v0] : subset(v0, v0)
% 4.15/1.65 | (51) element(all_0_6_6, all_0_5_5)
% 4.15/1.65 | (52) preboolean(all_0_1_1)
% 4.15/1.66 | (53) powerset(all_0_7_7) = all_0_5_5
% 4.15/1.66 |
% 4.15/1.66 | Instantiating formula (46) with all_0_4_4, all_0_7_7 and discharging atoms finite_subsets(all_0_7_7) = all_0_4_4, yields:
% 4.15/1.66 | (54) preboolean(all_0_4_4)
% 4.15/1.66 |
% 4.15/1.66 | Instantiating formula (40) with all_0_5_5, all_0_7_7, all_0_6_6 and discharging atoms powerset(all_0_7_7) = all_0_5_5, element(all_0_6_6, all_0_5_5), yields:
% 4.15/1.66 | (55) subset(all_0_6_6, all_0_7_7)
% 4.15/1.66 |
% 4.15/1.66 | Instantiating formula (44) with all_0_6_6, all_0_5_5, all_0_7_7 and discharging atoms powerset(all_0_7_7) = all_0_5_5, element(all_0_6_6, all_0_5_5), finite(all_0_7_7), yields:
% 4.15/1.66 | (56) finite(all_0_6_6)
% 4.15/1.66 |
% 4.15/1.66 | Instantiating formula (16) with all_0_6_6, all_0_4_4, all_0_7_7 and discharging atoms finite_subsets(all_0_7_7) = all_0_4_4, subset(all_0_6_6, all_0_7_7), preboolean(all_0_4_4), finite(all_0_6_6), yields:
% 4.15/1.66 | (57) in(all_0_6_6, all_0_4_4)
% 4.15/1.66 |
% 4.15/1.66 | Instantiating formula (20) with all_0_4_4, all_0_6_6 and discharging atoms in(all_0_6_6, all_0_4_4), ~ element(all_0_6_6, all_0_4_4), yields:
% 4.15/1.66 | (58) $false
% 4.15/1.66 |
% 4.15/1.66 |-The branch is then unsatisfiable
% 4.15/1.66 % SZS output end Proof for theBenchmark
% 4.15/1.66
% 4.15/1.66 1052ms
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