TSTP Solution File: SEU173+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU173+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 08:47:18 EDT 2022
% Result : Theorem 4.92s 1.85s
% Output : Proof 13.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU173+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.07 % Command : ePrincess-casc -timeout=%d %s
% 0.06/0.26 % Computer : n029.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 600
% 0.06/0.26 % DateTime : Sun Jun 19 16:24:44 EDT 2022
% 0.06/0.26 % CPUTime :
% 0.11/0.51 ____ _
% 0.11/0.51 ___ / __ \_____(_)___ ________ __________
% 0.11/0.51 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.11/0.51 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.11/0.51 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.11/0.51
% 0.11/0.51 A Theorem Prover for First-Order Logic
% 0.11/0.51 (ePrincess v.1.0)
% 0.11/0.51
% 0.11/0.51 (c) Philipp Rümmer, 2009-2015
% 0.11/0.51 (c) Peter Backeman, 2014-2015
% 0.11/0.51 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.11/0.51 Free software under GNU Lesser General Public License (LGPL).
% 0.11/0.51 Bug reports to peter@backeman.se
% 0.11/0.51
% 0.11/0.51 For more information, visit http://user.uu.se/~petba168/breu/
% 0.11/0.51
% 0.11/0.51 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.56/0.56 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.40/0.84 Prover 0: Preprocessing ...
% 1.64/0.98 Prover 0: Warning: ignoring some quantifiers
% 1.82/1.00 Prover 0: Constructing countermodel ...
% 2.62/1.25 Prover 0: gave up
% 2.62/1.25 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.62/1.27 Prover 1: Preprocessing ...
% 2.85/1.34 Prover 1: Warning: ignoring some quantifiers
% 2.85/1.35 Prover 1: Constructing countermodel ...
% 3.88/1.65 Prover 1: gave up
% 3.88/1.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.26/1.67 Prover 2: Preprocessing ...
% 4.36/1.73 Prover 2: Warning: ignoring some quantifiers
% 4.36/1.73 Prover 2: Constructing countermodel ...
% 4.92/1.85 Prover 2: proved (191ms)
% 4.92/1.85
% 4.92/1.85 No countermodel exists, formula is valid
% 4.92/1.85 % SZS status Theorem for theBenchmark
% 4.92/1.85
% 4.92/1.85 Generating proof ... Warning: ignoring some quantifiers
% 13.00/3.75 found it (size 59)
% 13.00/3.75
% 13.00/3.75 % SZS output start Proof for theBenchmark
% 13.00/3.75 Assumed formulas after preprocessing and simplification:
% 13.00/3.75 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v5 = 0) & ~ (v3 = 0) & empty(v6) = 0 & empty(v4) = v5 & empty(empty_set) = 0 & element(v0, v2) = v3 & powerset(v1) = v2 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (powerset(v7) = v8) | ~ (subset(v9, v7) = v10) | ? [v11] : ( ~ (v11 = 0) & in(v9, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (powerset(v7) = v8) | ~ (in(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v9, v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v7, v8) = 0) | ~ (in(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & in(v9, v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (element(v10, v9) = v8) | ~ (element(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (in(v10, v9) = v8) | ~ (in(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & in(v10, v8) = v11 & in(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (empty(v9) = v8) | ~ (empty(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (powerset(v9) = v8) | ~ (powerset(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (element(v8, v7) = v9) | ? [v10] : ((v10 = 0 & empty(v7) = 0) | (( ~ (v9 = 0) | (v10 = 0 & in(v8, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & in(v8, v7) = v10))))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (element(v8, v7) = v9) | ? [v10] : (( ~ (v10 = 0) & empty(v7) = v10) | (( ~ (v9 = 0) | (v10 = 0 & empty(v8) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & empty(v8) = v10))))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v7) = v8) | ~ (subset(v9, v7) = 0) | in(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v7) = v8) | ~ (in(v9, v8) = 0) | subset(v9, v7) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (in(v9, v7) = 0) | in(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (in(v8, v7) = v9) | ? [v10] : ((v10 = 0 & empty(v7) = 0) | (( ~ (v9 = 0) | (v10 = 0 & element(v8, v7) = 0)) & (v9 = 0 | ( ~ (v10 = 0) & element(v8, v7) = v10))))) & ? [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (powerset(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (((v12 = 0 & subset(v10, v8) = 0) | (v11 = 0 & in(v10, v7) = 0)) & (( ~ (v12 = 0) & subset(v10, v8) = v12) | ( ~ (v11 = 0) & in(v10, v7) = v11)))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (empty(v8) = 0) | ~ (empty(v7) = 0)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (empty(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = 0) & empty(v10) = v11 & element(v10, v9) = 0 & powerset(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (in(v7, v1) = v8) | ? [v9] : ( ~ (v9 = 0) & in(v7, v0) = v9)) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & ~ (v11 = 0) & empty(v9) = v11 & element(v9, v8) = 0) | (v9 = 0 & empty(v7) = 0))) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ? [v9] : ( ~ (v9 = 0) & empty(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ? [v9] : (empty(v9) = 0 & element(v9, v8) = 0)) & ! [v7] : ! [v8] : ( ~ (in(v8, v7) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & empty(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9)) & ! [v7] : (v7 = empty_set | ~ (empty(v7) = 0)) & ! [v7] : ( ~ (in(v7, v0) = 0) | in(v7, v1) = 0) & ? [v7] : ? [v8] : ? [v9] : element(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : subset(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : in(v8, v7) = v9 & ? [v7] : ? [v8] : empty(v7) = v8 & ? [v7] : ? [v8] : element(v8, v7) = 0 & ? [v7] : ? [v8] : powerset(v7) = v8)
% 13.00/3.79 | 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 yields:
% 13.00/3.79 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_3_3 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & element(all_0_6_6, all_0_4_4) = all_0_3_3 & powerset(all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | (( ~ (v2 = 0) | (v3 = 0 & in(v1, v0) = 0)) & (v2 = 0 | ( ~ (v3 = 0) & in(v1, v0) = v3))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v0) = v2) | ? [v3] : (( ~ (v3 = 0) & empty(v0) = v3) | (( ~ (v2 = 0) | (v3 = 0 & empty(v1) = 0)) & (v2 = 0 | ( ~ (v3 = 0) & empty(v1) = v3))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | subset(v2, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (in(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | (( ~ (v2 = 0) | (v3 = 0 & element(v1, v0) = 0)) & (v2 = 0 | ( ~ (v3 = 0) & element(v1, v0) = v3))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & subset(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v5 = 0) & subset(v3, v1) = v5) | ( ~ (v4 = 0) & in(v3, v0) = v4)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & empty(v3) = v4 & element(v3, v2) = 0 & powerset(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_0_5_5) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_6_6) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (in(v0, all_0_6_6) = 0) | in(v0, all_0_5_5) = 0) & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : empty(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : powerset(v0) = v1
% 13.37/3.80 |
% 13.37/3.80 | Applying alpha-rule on (1) yields:
% 13.37/3.80 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v2, v0) = v4))
% 13.37/3.80 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 13.37/3.80 | (4) ? [v0] : ? [v1] : powerset(v0) = v1
% 13.37/3.80 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 13.37/3.80 | (6) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 13.37/3.80 | (7) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & subset(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v5 = 0) & subset(v3, v1) = v5) | ( ~ (v4 = 0) & in(v3, v0) = v4))))
% 13.37/3.80 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | subset(v2, v0) = 0)
% 13.37/3.81 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0)
% 13.37/3.81 | (10) empty(all_0_0_0) = 0
% 13.37/3.81 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 13.37/3.81 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 13.37/3.81 | (13) ~ (all_0_1_1 = 0)
% 13.37/3.81 | (14) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 13.37/3.81 | (15) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0)))
% 13.37/3.81 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | (( ~ (v2 = 0) | (v3 = 0 & in(v1, v0) = 0)) & (v2 = 0 | ( ~ (v3 = 0) & in(v1, v0) = v3)))))
% 13.37/3.81 | (17) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 13.37/3.81 | (18) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 13.37/3.81 | (19) ~ (all_0_3_3 = 0)
% 13.37/3.81 | (20) powerset(all_0_5_5) = all_0_4_4
% 13.37/3.81 | (21) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 13.37/3.81 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 13.37/3.81 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 13.37/3.81 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 13.37/3.81 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 13.37/3.81 | (26) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0))
% 13.37/3.81 | (27) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & empty(v3) = v4 & element(v3, v2) = 0 & powerset(v0) = v2))
% 13.37/3.81 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (in(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | (( ~ (v2 = 0) | (v3 = 0 & element(v1, v0) = 0)) & (v2 = 0 | ( ~ (v3 = 0) & element(v1, v0) = v3)))))
% 13.37/3.81 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 13.37/3.81 | (30) element(all_0_6_6, all_0_4_4) = all_0_3_3
% 13.37/3.81 | (31) empty(all_0_2_2) = all_0_1_1
% 13.37/3.81 | (32) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 13.37/3.81 | (33) ? [v0] : ? [v1] : element(v1, v0) = 0
% 13.37/3.81 | (34) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 13.37/3.81 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v0) = v2) | ? [v3] : (( ~ (v3 = 0) & empty(v0) = v3) | (( ~ (v2 = 0) | (v3 = 0 & empty(v1) = 0)) & (v2 = 0 | ( ~ (v3 = 0) & empty(v1) = v3)))))
% 13.37/3.81 | (36) empty(empty_set) = 0
% 13.37/3.81 | (37) ? [v0] : ? [v1] : empty(v0) = v1
% 13.37/3.81 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4))
% 13.37/3.81 | (39) ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_0_5_5) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_0_6_6) = v2))
% 13.37/3.81 | (40) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 13.37/3.81 | (41) ! [v0] : ( ~ (in(v0, all_0_6_6) = 0) | in(v0, all_0_5_5) = 0)
% 13.37/3.81 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 13.37/3.81 |
% 13.37/3.81 | Instantiating formula (16) with all_0_3_3, all_0_6_6, all_0_4_4 and discharging atoms element(all_0_6_6, all_0_4_4) = all_0_3_3, yields:
% 13.37/3.81 | (43) ? [v0] : ((v0 = 0 & empty(all_0_4_4) = 0) | (( ~ (all_0_3_3 = 0) | (v0 = 0 & in(all_0_6_6, all_0_4_4) = 0)) & (all_0_3_3 = 0 | ( ~ (v0 = 0) & in(all_0_6_6, all_0_4_4) = v0))))
% 13.37/3.81 |
% 13.37/3.81 | Instantiating formula (34) with all_0_4_4, all_0_5_5 and discharging atoms powerset(all_0_5_5) = all_0_4_4, yields:
% 13.37/3.81 | (44) ? [v0] : ( ~ (v0 = 0) & empty(all_0_4_4) = v0)
% 13.37/3.81 |
% 13.37/3.81 | Instantiating formula (26) with all_0_4_4, all_0_5_5 and discharging atoms powerset(all_0_5_5) = all_0_4_4, yields:
% 13.37/3.81 | (45) ? [v0] : (empty(v0) = 0 & element(v0, all_0_4_4) = 0)
% 13.37/3.81 |
% 13.37/3.81 | Instantiating (45) with all_26_0_23 yields:
% 13.37/3.81 | (46) empty(all_26_0_23) = 0 & element(all_26_0_23, all_0_4_4) = 0
% 13.37/3.81 |
% 13.37/3.82 | Applying alpha-rule on (46) yields:
% 13.37/3.82 | (47) empty(all_26_0_23) = 0
% 13.37/3.82 | (48) element(all_26_0_23, all_0_4_4) = 0
% 13.37/3.82 |
% 13.37/3.82 | Instantiating (44) with all_28_0_24 yields:
% 13.37/3.82 | (49) ~ (all_28_0_24 = 0) & empty(all_0_4_4) = all_28_0_24
% 13.37/3.82 |
% 13.37/3.82 | Applying alpha-rule on (49) yields:
% 13.37/3.82 | (50) ~ (all_28_0_24 = 0)
% 13.37/3.82 | (51) empty(all_0_4_4) = all_28_0_24
% 13.37/3.82 |
% 13.37/3.82 | Instantiating (43) with all_32_0_29 yields:
% 13.37/3.82 | (52) (all_32_0_29 = 0 & empty(all_0_4_4) = 0) | (( ~ (all_0_3_3 = 0) | (all_32_0_29 = 0 & in(all_0_6_6, all_0_4_4) = 0)) & (all_0_3_3 = 0 | ( ~ (all_32_0_29 = 0) & in(all_0_6_6, all_0_4_4) = all_32_0_29)))
% 13.37/3.82 |
% 13.37/3.82 +-Applying beta-rule and splitting (52), into two cases.
% 13.37/3.82 |-Branch one:
% 13.37/3.82 | (53) all_32_0_29 = 0 & empty(all_0_4_4) = 0
% 13.37/3.82 |
% 13.37/3.82 | Applying alpha-rule on (53) yields:
% 13.37/3.82 | (54) all_32_0_29 = 0
% 13.37/3.82 | (55) empty(all_0_4_4) = 0
% 13.37/3.82 |
% 13.37/3.82 | Instantiating formula (3) with all_0_4_4, 0, all_28_0_24 and discharging atoms empty(all_0_4_4) = all_28_0_24, empty(all_0_4_4) = 0, yields:
% 13.37/3.82 | (56) all_28_0_24 = 0
% 13.37/3.82 |
% 13.37/3.82 | Equations (56) can reduce 50 to:
% 13.37/3.82 | (57) $false
% 13.37/3.82 |
% 13.37/3.82 |-The branch is then unsatisfiable
% 13.37/3.82 |-Branch two:
% 13.37/3.82 | (58) ( ~ (all_0_3_3 = 0) | (all_32_0_29 = 0 & in(all_0_6_6, all_0_4_4) = 0)) & (all_0_3_3 = 0 | ( ~ (all_32_0_29 = 0) & in(all_0_6_6, all_0_4_4) = all_32_0_29))
% 13.37/3.82 |
% 13.37/3.82 | Applying alpha-rule on (58) yields:
% 13.37/3.82 | (59) ~ (all_0_3_3 = 0) | (all_32_0_29 = 0 & in(all_0_6_6, all_0_4_4) = 0)
% 13.37/3.82 | (60) all_0_3_3 = 0 | ( ~ (all_32_0_29 = 0) & in(all_0_6_6, all_0_4_4) = all_32_0_29)
% 13.37/3.82 |
% 13.37/3.82 +-Applying beta-rule and splitting (60), into two cases.
% 13.37/3.82 |-Branch one:
% 13.37/3.82 | (61) all_0_3_3 = 0
% 13.37/3.82 |
% 13.37/3.82 | Equations (61) can reduce 19 to:
% 13.37/3.82 | (57) $false
% 13.37/3.82 |
% 13.37/3.82 |-The branch is then unsatisfiable
% 13.37/3.82 |-Branch two:
% 13.37/3.82 | (19) ~ (all_0_3_3 = 0)
% 13.37/3.82 | (64) ~ (all_32_0_29 = 0) & in(all_0_6_6, all_0_4_4) = all_32_0_29
% 13.37/3.82 |
% 13.37/3.82 | Applying alpha-rule on (64) yields:
% 13.37/3.82 | (65) ~ (all_32_0_29 = 0)
% 13.37/3.82 | (66) in(all_0_6_6, all_0_4_4) = all_32_0_29
% 13.37/3.82 |
% 13.37/3.82 | Instantiating formula (32) with all_26_0_23 and discharging atoms empty(all_26_0_23) = 0, yields:
% 13.37/3.82 | (67) all_26_0_23 = empty_set
% 13.37/3.82 |
% 13.37/3.82 | From (67) and (48) follows:
% 13.37/3.82 | (68) element(empty_set, all_0_4_4) = 0
% 13.37/3.82 |
% 13.37/3.82 | Instantiating formula (27) with all_28_0_24, all_0_4_4 and discharging atoms empty(all_0_4_4) = all_28_0_24, yields:
% 13.37/3.82 | (69) all_28_0_24 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2 & element(v1, v0) = 0 & powerset(all_0_4_4) = v0)
% 13.37/3.82 |
% 13.37/3.82 | Instantiating formula (16) with 0, empty_set, all_0_4_4 and discharging atoms element(empty_set, all_0_4_4) = 0, yields:
% 13.37/3.82 | (70) ? [v0] : ((v0 = 0 & empty(all_0_4_4) = 0) | (v0 = 0 & in(empty_set, all_0_4_4) = 0))
% 13.37/3.82 |
% 13.37/3.82 | Instantiating formula (2) with all_32_0_29, all_0_6_6, all_0_4_4, all_0_5_5 and discharging atoms powerset(all_0_5_5) = all_0_4_4, in(all_0_6_6, all_0_4_4) = all_32_0_29, yields:
% 13.37/3.82 | (71) all_32_0_29 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_6_6, all_0_5_5) = v0)
% 13.37/3.82 |
% 13.37/3.82 | Instantiating (70) with all_63_0_46 yields:
% 13.37/3.82 | (72) (all_63_0_46 = 0 & empty(all_0_4_4) = 0) | (all_63_0_46 = 0 & in(empty_set, all_0_4_4) = 0)
% 13.37/3.82 |
% 13.37/3.82 +-Applying beta-rule and splitting (71), into two cases.
% 13.37/3.82 |-Branch one:
% 13.37/3.82 | (54) all_32_0_29 = 0
% 13.37/3.82 |
% 13.37/3.82 | Equations (54) can reduce 65 to:
% 13.37/3.82 | (57) $false
% 13.37/3.82 |
% 13.37/3.82 |-The branch is then unsatisfiable
% 13.37/3.82 |-Branch two:
% 13.37/3.82 | (65) ~ (all_32_0_29 = 0)
% 13.37/3.82 | (76) ? [v0] : ( ~ (v0 = 0) & subset(all_0_6_6, all_0_5_5) = v0)
% 13.37/3.82 |
% 13.37/3.82 | Instantiating (76) with all_71_0_47 yields:
% 13.37/3.82 | (77) ~ (all_71_0_47 = 0) & subset(all_0_6_6, all_0_5_5) = all_71_0_47
% 13.37/3.82 |
% 13.37/3.82 | Applying alpha-rule on (77) yields:
% 13.37/3.82 | (78) ~ (all_71_0_47 = 0)
% 13.37/3.82 | (79) subset(all_0_6_6, all_0_5_5) = all_71_0_47
% 13.37/3.82 |
% 13.37/3.82 +-Applying beta-rule and splitting (72), into two cases.
% 13.37/3.82 |-Branch one:
% 13.37/3.82 | (80) all_63_0_46 = 0 & empty(all_0_4_4) = 0
% 13.37/3.82 |
% 13.37/3.82 | Applying alpha-rule on (80) yields:
% 13.37/3.82 | (81) all_63_0_46 = 0
% 13.37/3.82 | (55) empty(all_0_4_4) = 0
% 13.37/3.82 |
% 13.37/3.82 +-Applying beta-rule and splitting (69), into two cases.
% 13.37/3.82 |-Branch one:
% 13.37/3.82 | (56) all_28_0_24 = 0
% 13.37/3.82 |
% 13.37/3.82 | Equations (56) can reduce 50 to:
% 13.37/3.82 | (57) $false
% 13.37/3.82 |
% 13.37/3.82 |-The branch is then unsatisfiable
% 13.37/3.82 |-Branch two:
% 13.37/3.82 | (50) ~ (all_28_0_24 = 0)
% 13.37/3.82 | (86) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2 & element(v1, v0) = 0 & powerset(all_0_4_4) = v0)
% 13.37/3.82 |
% 13.37/3.82 | Instantiating formula (3) with all_0_4_4, 0, all_28_0_24 and discharging atoms empty(all_0_4_4) = all_28_0_24, empty(all_0_4_4) = 0, yields:
% 13.37/3.82 | (56) all_28_0_24 = 0
% 13.37/3.82 |
% 13.37/3.82 | Equations (56) can reduce 50 to:
% 13.37/3.82 | (57) $false
% 13.37/3.82 |
% 13.37/3.82 |-The branch is then unsatisfiable
% 13.37/3.82 |-Branch two:
% 13.37/3.82 | (89) all_63_0_46 = 0 & in(empty_set, all_0_4_4) = 0
% 13.37/3.82 |
% 13.37/3.82 | Applying alpha-rule on (89) yields:
% 13.37/3.82 | (81) all_63_0_46 = 0
% 13.37/3.82 | (91) in(empty_set, all_0_4_4) = 0
% 13.37/3.82 |
% 13.37/3.82 | Instantiating formula (24) with all_71_0_47, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = all_71_0_47, yields:
% 13.37/3.82 | (92) all_71_0_47 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_5_5) = v1 & in(v0, all_0_6_6) = 0)
% 13.37/3.82 |
% 13.37/3.82 | Instantiating formula (8) with empty_set, all_0_4_4, all_0_5_5 and discharging atoms powerset(all_0_5_5) = all_0_4_4, in(empty_set, all_0_4_4) = 0, yields:
% 13.37/3.82 | (93) subset(empty_set, all_0_5_5) = 0
% 13.37/3.82 |
% 13.37/3.82 +-Applying beta-rule and splitting (92), into two cases.
% 13.37/3.82 |-Branch one:
% 13.37/3.82 | (94) all_71_0_47 = 0
% 13.37/3.82 |
% 13.37/3.82 | Equations (94) can reduce 78 to:
% 13.37/3.82 | (57) $false
% 13.37/3.82 |
% 13.37/3.83 |-The branch is then unsatisfiable
% 13.37/3.83 |-Branch two:
% 13.37/3.83 | (78) ~ (all_71_0_47 = 0)
% 13.37/3.83 | (97) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_5_5) = v1 & in(v0, all_0_6_6) = 0)
% 13.37/3.83 |
% 13.37/3.83 | Instantiating (97) with all_149_0_229, all_149_1_230 yields:
% 13.37/3.83 | (98) ~ (all_149_0_229 = 0) & in(all_149_1_230, all_0_5_5) = all_149_0_229 & in(all_149_1_230, all_0_6_6) = 0
% 13.37/3.83 |
% 13.37/3.83 | Applying alpha-rule on (98) yields:
% 13.37/3.83 | (99) ~ (all_149_0_229 = 0)
% 13.37/3.83 | (100) in(all_149_1_230, all_0_5_5) = all_149_0_229
% 13.37/3.83 | (101) in(all_149_1_230, all_0_6_6) = 0
% 13.37/3.83 |
% 13.37/3.83 | Instantiating formula (42) with all_149_0_229, all_149_1_230, all_0_5_5, empty_set and discharging atoms subset(empty_set, all_0_5_5) = 0, in(all_149_1_230, all_0_5_5) = all_149_0_229, yields:
% 13.37/3.83 | (102) all_149_0_229 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_149_1_230, empty_set) = v0)
% 13.37/3.83 |
% 13.37/3.83 | Instantiating formula (39) with all_149_0_229, all_149_1_230 and discharging atoms in(all_149_1_230, all_0_5_5) = all_149_0_229, yields:
% 13.37/3.83 | (103) all_149_0_229 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_149_1_230, all_0_6_6) = v0)
% 13.37/3.83 |
% 13.37/3.83 | Instantiating formula (41) with all_149_1_230 and discharging atoms in(all_149_1_230, all_0_6_6) = 0, yields:
% 13.37/3.83 | (104) in(all_149_1_230, all_0_5_5) = 0
% 13.37/3.83 |
% 13.37/3.83 +-Applying beta-rule and splitting (103), into two cases.
% 13.37/3.83 |-Branch one:
% 13.37/3.83 | (105) all_149_0_229 = 0
% 13.37/3.83 |
% 13.37/3.83 | Equations (105) can reduce 99 to:
% 13.37/3.83 | (57) $false
% 13.37/3.83 |
% 13.37/3.83 |-The branch is then unsatisfiable
% 13.37/3.83 |-Branch two:
% 13.37/3.83 | (99) ~ (all_149_0_229 = 0)
% 13.37/3.83 | (108) ? [v0] : ( ~ (v0 = 0) & in(all_149_1_230, all_0_6_6) = v0)
% 13.37/3.83 |
% 13.37/3.83 +-Applying beta-rule and splitting (102), into two cases.
% 13.37/3.83 |-Branch one:
% 13.37/3.83 | (105) all_149_0_229 = 0
% 13.37/3.83 |
% 13.37/3.83 | Equations (105) can reduce 99 to:
% 13.37/3.83 | (57) $false
% 13.37/3.83 |
% 13.37/3.83 |-The branch is then unsatisfiable
% 13.37/3.83 |-Branch two:
% 13.37/3.83 | (99) ~ (all_149_0_229 = 0)
% 13.37/3.83 | (112) ? [v0] : ( ~ (v0 = 0) & in(all_149_1_230, empty_set) = v0)
% 13.37/3.83 |
% 13.37/3.83 | Instantiating formula (11) with all_149_1_230, all_0_5_5, 0, all_149_0_229 and discharging atoms in(all_149_1_230, all_0_5_5) = all_149_0_229, in(all_149_1_230, all_0_5_5) = 0, yields:
% 13.37/3.83 | (105) all_149_0_229 = 0
% 13.37/3.83 |
% 13.37/3.83 | Equations (105) can reduce 99 to:
% 13.37/3.83 | (57) $false
% 13.37/3.83 |
% 13.37/3.83 |-The branch is then unsatisfiable
% 13.37/3.83 % SZS output end Proof for theBenchmark
% 13.37/3.83
% 13.37/3.83 3311ms
%------------------------------------------------------------------------------