TSTP Solution File: SET934+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET934+1 : TPTP v8.1.0. Released v3.2.0.
% 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 00:23:17 EDT 2022
% Result : Theorem 7.33s 2.43s
% Output : Proof 9.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET934+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n019.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 : Mon Jul 11 10:31:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.55/0.58 ____ _
% 0.55/0.58 ___ / __ \_____(_)___ ________ __________
% 0.55/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.58
% 0.55/0.58 A Theorem Prover for First-Order Logic
% 0.55/0.59 (ePrincess v.1.0)
% 0.55/0.59
% 0.55/0.59 (c) Philipp Rümmer, 2009-2015
% 0.55/0.59 (c) Peter Backeman, 2014-2015
% 0.55/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.59 Bug reports to peter@backeman.se
% 0.55/0.59
% 0.55/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.59
% 0.55/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.40/0.92 Prover 0: Preprocessing ...
% 1.87/1.10 Prover 0: Warning: ignoring some quantifiers
% 1.87/1.11 Prover 0: Constructing countermodel ...
% 5.13/1.92 Prover 0: gave up
% 5.13/1.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.13/1.94 Prover 1: Preprocessing ...
% 5.51/2.00 Prover 1: Warning: ignoring some quantifiers
% 5.51/2.01 Prover 1: Constructing countermodel ...
% 6.54/2.27 Prover 1: gave up
% 6.54/2.27 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.54/2.29 Prover 2: Preprocessing ...
% 6.92/2.36 Prover 2: Warning: ignoring some quantifiers
% 6.92/2.36 Prover 2: Constructing countermodel ...
% 7.33/2.43 Prover 2: proved (154ms)
% 7.33/2.43
% 7.33/2.43 No countermodel exists, formula is valid
% 7.33/2.43 % SZS status Theorem for theBenchmark
% 7.33/2.43
% 7.33/2.43 Generating proof ... Warning: ignoring some quantifiers
% 8.66/2.76 found it (size 57)
% 8.66/2.76
% 8.66/2.76 % SZS output start Proof for theBenchmark
% 8.66/2.76 Assumed formulas after preprocessing and simplification:
% 8.66/2.77 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v9 = 0) & ~ (v7 = 0) & empty(v10) = 0 & empty(v8) = v9 & powerset(v5) = v6 & powerset(v1) = v3 & powerset(v0) = v2 & subset(v4, v6) = v7 & set_union2(v2, v3) = v4 & set_union2(v0, v1) = v5 & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (set_union2(v11, v12) = v13) | ~ (in(v14, v13) = v15) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & ~ (v16 = 0) & in(v14, v12) = v17 & in(v14, v11) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (set_union2(v11, v12) = v13) | ~ (in(v14, v12) = v15) | ? [v16] : ((v16 = 0 & in(v14, v11) = 0) | ( ~ (v16 = 0) & in(v14, v13) = v16))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (set_union2(v11, v12) = v13) | ~ (in(v14, v11) = v15) | ? [v16] : ((v16 = 0 & in(v14, v12) = 0) | ( ~ (v16 = 0) & in(v14, v13) = v16))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v11, v12) = v13) | ~ (in(v14, v12) = v15) | ? [v16] : ((v16 = 0 & in(v14, v13) = 0) | ( ~ (v16 = 0) & ~ (v15 = 0) & in(v14, v11) = v16))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v11, v12) = v13) | ~ (in(v14, v11) = v15) | ? [v16] : ((v16 = 0 & in(v14, v13) = 0) | ( ~ (v16 = 0) & ~ (v15 = 0) & in(v14, v12) = v16))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (powerset(v11) = v12) | ~ (subset(v13, v11) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v13, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (powerset(v11) = v12) | ~ (in(v13, v12) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v13, v11) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v12, v13) = 0) | ~ (subset(v11, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v11, v13) = v14) | ~ (subset(v11, v12) = 0) | ? [v15] : ( ~ (v15 = 0) & subset(v12, v13) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v11, v12) = 0) | ~ (in(v13, v12) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v13, v11) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (subset(v14, v13) = v12) | ~ (subset(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (set_union2(v14, v13) = v12) | ~ (set_union2(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (in(v14, v13) = v12) | ~ (in(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v11, v12) = v13) | ~ (in(v14, v13) = 0) | ? [v15] : ((v15 = 0 & in(v14, v12) = 0) | (v15 = 0 & in(v14, v11) = 0))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (set_union2(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (((v18 = 0 & in(v15, v13) = 0) | (v17 = 0 & in(v15, v12) = 0) | (v16 = 0 & in(v15, v11) = 0)) & (( ~ (v18 = 0) & ~ (v17 = 0) & in(v15, v13) = v18 & in(v15, v12) = v17) | ( ~ (v16 = 0) & in(v15, v11) = v16)))) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v11, v12) = v13) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & in(v14, v12) = v15 & in(v14, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (empty(v13) = v12) | ~ (empty(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (powerset(v13) = v12) | ~ (powerset(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v11) = v12) | ~ (subset(v13, v11) = 0) | in(v13, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v11) = v12) | ~ (in(v13, v12) = 0) | subset(v13, v11) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (subset(v12, v13) = 0) | ~ (subset(v11, v12) = 0) | subset(v11, v13) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (subset(v11, v12) = 0) | ~ (in(v13, v11) = 0) | in(v13, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v12, v11) = v13) | set_union2(v11, v12) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v12, v11) = v13) | ? [v14] : ((v14 = 0 & empty(v11) = 0) | ( ~ (v14 = 0) & empty(v13) = v14))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | subset(v11, v13) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | set_union2(v12, v11) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | ? [v14] : ((v14 = 0 & empty(v11) = 0) | ( ~ (v14 = 0) & empty(v13) = v14))) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (powerset(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (((v16 = 0 & subset(v14, v12) = 0) | (v15 = 0 & in(v14, v11) = 0)) & (( ~ (v16 = 0) & subset(v14, v12) = v16) | ( ~ (v15 = 0) & in(v14, v11) = v15)))) & ! [v11] : ! [v12] : (v12 = v11 | ~ (set_union2(v11, v11) = v12)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v11, v11) = v12)) & ! [v11] : ! [v12] : ( ~ (in(v12, v11) = 0) | ? [v13] : ( ~ (v13 = 0) & in(v11, v12) = v13)) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & in(v12, v11) = v13)) & ? [v11] : ? [v12] : ? [v13] : subset(v12, v11) = v13 & ? [v11] : ? [v12] : ? [v13] : set_union2(v12, v11) = v13 & ? [v11] : ? [v12] : ? [v13] : in(v12, v11) = v13 & ? [v11] : ? [v12] : empty(v11) = v12 & ? [v11] : ? [v12] : powerset(v11) = v12)
% 9.09/2.81 | 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, all_0_10_10 yields:
% 9.09/2.81 | (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 & powerset(all_0_5_5) = all_0_4_4 & powerset(all_0_9_9) = all_0_7_7 & powerset(all_0_10_10) = all_0_8_8 & subset(all_0_6_6, all_0_4_4) = all_0_3_3 & set_union2(all_0_8_8, all_0_7_7) = all_0_6_6 & set_union2(all_0_10_10, all_0_9_9) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v1) = v5))) & ! [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(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = 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 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ((v4 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | (v6 = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & ~ (v6 = 0) & in(v4, v2) = v7 & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) & ! [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] : ( ~ (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(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = 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 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : empty(v0) = v1 & ? [v0] : ? [v1] : powerset(v0) = v1
% 9.25/2.82 |
% 9.25/2.83 | Applying alpha-rule on (1) yields:
% 9.25/2.83 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0)
% 9.25/2.83 | (3) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | (v6 = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & ~ (v6 = 0) & in(v4, v2) = v7 & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5))))
% 9.25/2.83 | (4) set_union2(all_0_8_8, all_0_7_7) = all_0_6_6
% 9.25/2.83 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | subset(v2, v0) = 0)
% 9.25/2.83 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0)
% 9.25/2.83 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v2, v0) = v4))
% 9.25/2.83 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 9.25/2.83 | (9) ~ (all_0_3_3 = 0)
% 9.25/2.83 | (10) ? [v0] : ? [v1] : powerset(v0) = v1
% 9.25/2.83 | (11) empty(all_0_0_0) = 0
% 9.25/2.83 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 9.25/2.83 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 9.25/2.83 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 9.25/2.83 | (15) powerset(all_0_10_10) = all_0_8_8
% 9.25/2.83 | (16) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 9.25/2.83 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ((v4 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)))
% 9.25/2.83 | (18) empty(all_0_2_2) = all_0_1_1
% 9.25/2.83 | (19) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2
% 9.25/2.83 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 9.25/2.83 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0)
% 9.25/2.83 | (22) set_union2(all_0_10_10, all_0_9_9) = all_0_5_5
% 9.25/2.83 | (23) powerset(all_0_9_9) = all_0_7_7
% 9.25/2.83 | (24) powerset(all_0_5_5) = all_0_4_4
% 9.25/2.83 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 9.25/2.83 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 9.25/2.83 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 9.25/2.84 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5))
% 9.25/2.84 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 9.25/2.84 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v1) = v5)))
% 9.25/2.84 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & in(v3, v0) = v5)))
% 9.25/2.84 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 9.25/2.84 | (33) ~ (all_0_1_1 = 0)
% 9.25/2.84 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 9.25/2.84 | (35) ? [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))))
% 9.25/2.84 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4))
% 9.25/2.84 | (37) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 9.25/2.84 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 9.25/2.84 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 9.25/2.84 | (40) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 9.25/2.84 | (41) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 9.25/2.84 | (42) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 9.25/2.84 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 9.25/2.84 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 9.25/2.84 | (45) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 9.25/2.84 | (46) subset(all_0_6_6, all_0_4_4) = all_0_3_3
% 9.25/2.84 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 9.25/2.84 | (48) ? [v0] : ? [v1] : empty(v0) = v1
% 9.25/2.84 |
% 9.25/2.84 | Instantiating formula (13) with all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_4_4) = all_0_3_3, yields:
% 9.25/2.84 | (49) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_6_6) = 0)
% 9.25/2.85 |
% 9.25/2.85 | Instantiating formula (39) with all_0_6_6, all_0_8_8, all_0_7_7 and discharging atoms set_union2(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 9.25/2.85 | (50) set_union2(all_0_7_7, all_0_8_8) = all_0_6_6
% 9.25/2.85 |
% 9.25/2.85 | Instantiating formula (39) with all_0_5_5, all_0_10_10, all_0_9_9 and discharging atoms set_union2(all_0_10_10, all_0_9_9) = all_0_5_5, yields:
% 9.25/2.85 | (51) set_union2(all_0_9_9, all_0_10_10) = all_0_5_5
% 9.25/2.85 |
% 9.25/2.85 | Instantiating formula (2) with all_0_5_5, all_0_9_9, all_0_10_10 and discharging atoms set_union2(all_0_10_10, all_0_9_9) = all_0_5_5, yields:
% 9.25/2.85 | (52) subset(all_0_10_10, all_0_5_5) = 0
% 9.25/2.85 |
% 9.25/2.85 +-Applying beta-rule and splitting (49), into two cases.
% 9.25/2.85 |-Branch one:
% 9.25/2.85 | (53) all_0_3_3 = 0
% 9.25/2.85 |
% 9.25/2.85 | Equations (53) can reduce 9 to:
% 9.25/2.85 | (54) $false
% 9.25/2.85 |
% 9.25/2.85 |-The branch is then unsatisfiable
% 9.25/2.85 |-Branch two:
% 9.25/2.85 | (9) ~ (all_0_3_3 = 0)
% 9.25/2.85 | (56) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_6_6) = 0)
% 9.25/2.85 |
% 9.25/2.85 | Instantiating (56) with all_31_0_30, all_31_1_31 yields:
% 9.25/2.85 | (57) ~ (all_31_0_30 = 0) & in(all_31_1_31, all_0_4_4) = all_31_0_30 & in(all_31_1_31, all_0_6_6) = 0
% 9.25/2.85 |
% 9.25/2.85 | Applying alpha-rule on (57) yields:
% 9.25/2.85 | (58) ~ (all_31_0_30 = 0)
% 9.25/2.85 | (59) in(all_31_1_31, all_0_4_4) = all_31_0_30
% 9.25/2.85 | (60) in(all_31_1_31, all_0_6_6) = 0
% 9.25/2.85 |
% 9.25/2.85 | Instantiating formula (2) with all_0_5_5, all_0_10_10, all_0_9_9 and discharging atoms set_union2(all_0_9_9, all_0_10_10) = all_0_5_5, yields:
% 9.25/2.85 | (61) subset(all_0_9_9, all_0_5_5) = 0
% 9.25/2.85 |
% 9.25/2.85 | Instantiating formula (7) with all_31_0_30, all_31_1_31, all_0_4_4, all_0_5_5 and discharging atoms powerset(all_0_5_5) = all_0_4_4, in(all_31_1_31, all_0_4_4) = all_31_0_30, yields:
% 9.25/2.85 | (62) all_31_0_30 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_31_1_31, all_0_5_5) = v0)
% 9.25/2.85 |
% 9.25/2.85 | Instantiating formula (17) with all_31_1_31, all_0_6_6, all_0_8_8, all_0_7_7 and discharging atoms set_union2(all_0_7_7, all_0_8_8) = all_0_6_6, in(all_31_1_31, all_0_6_6) = 0, yields:
% 9.25/2.85 | (63) ? [v0] : ((v0 = 0 & in(all_31_1_31, all_0_7_7) = 0) | (v0 = 0 & in(all_31_1_31, all_0_8_8) = 0))
% 9.25/2.85 |
% 9.25/2.85 | Instantiating (63) with all_43_0_35 yields:
% 9.25/2.85 | (64) (all_43_0_35 = 0 & in(all_31_1_31, all_0_7_7) = 0) | (all_43_0_35 = 0 & in(all_31_1_31, all_0_8_8) = 0)
% 9.25/2.85 |
% 9.25/2.85 +-Applying beta-rule and splitting (62), into two cases.
% 9.25/2.85 |-Branch one:
% 9.25/2.85 | (65) all_31_0_30 = 0
% 9.25/2.85 |
% 9.25/2.85 | Equations (65) can reduce 58 to:
% 9.25/2.85 | (54) $false
% 9.25/2.85 |
% 9.25/2.85 |-The branch is then unsatisfiable
% 9.25/2.85 |-Branch two:
% 9.25/2.85 | (58) ~ (all_31_0_30 = 0)
% 9.25/2.85 | (68) ? [v0] : ( ~ (v0 = 0) & subset(all_31_1_31, all_0_5_5) = v0)
% 9.25/2.85 |
% 9.25/2.85 | Instantiating (68) with all_50_0_38 yields:
% 9.25/2.85 | (69) ~ (all_50_0_38 = 0) & subset(all_31_1_31, all_0_5_5) = all_50_0_38
% 9.25/2.85 |
% 9.25/2.85 | Applying alpha-rule on (69) yields:
% 9.25/2.85 | (70) ~ (all_50_0_38 = 0)
% 9.25/2.85 | (71) subset(all_31_1_31, all_0_5_5) = all_50_0_38
% 9.25/2.85 |
% 9.25/2.85 | Instantiating formula (32) with all_50_0_38, all_0_5_5, all_0_10_10, all_31_1_31 and discharging atoms subset(all_31_1_31, all_0_5_5) = all_50_0_38, subset(all_0_10_10, all_0_5_5) = 0, yields:
% 9.25/2.85 | (72) all_50_0_38 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_31_1_31, all_0_10_10) = v0)
% 9.25/2.85 |
% 9.25/2.85 | Instantiating formula (13) with all_50_0_38, all_0_5_5, all_31_1_31 and discharging atoms subset(all_31_1_31, all_0_5_5) = all_50_0_38, yields:
% 9.25/2.85 | (73) all_50_0_38 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_31_1_31) = 0 & in(v0, all_0_5_5) = v1)
% 9.25/2.85 |
% 9.25/2.85 | Instantiating formula (32) with all_50_0_38, all_0_5_5, all_0_9_9, all_31_1_31 and discharging atoms subset(all_31_1_31, all_0_5_5) = all_50_0_38, subset(all_0_9_9, all_0_5_5) = 0, yields:
% 9.25/2.85 | (74) all_50_0_38 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_31_1_31, all_0_9_9) = v0)
% 9.25/2.85 |
% 9.25/2.85 +-Applying beta-rule and splitting (73), into two cases.
% 9.25/2.85 |-Branch one:
% 9.25/2.85 | (75) all_50_0_38 = 0
% 9.25/2.85 |
% 9.25/2.85 | Equations (75) can reduce 70 to:
% 9.25/2.85 | (54) $false
% 9.25/2.85 |
% 9.25/2.85 |-The branch is then unsatisfiable
% 9.25/2.85 |-Branch two:
% 9.25/2.85 | (70) ~ (all_50_0_38 = 0)
% 9.25/2.86 | (78) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_31_1_31) = 0 & in(v0, all_0_5_5) = v1)
% 9.25/2.86 |
% 9.25/2.86 +-Applying beta-rule and splitting (74), into two cases.
% 9.25/2.86 |-Branch one:
% 9.25/2.86 | (75) all_50_0_38 = 0
% 9.25/2.86 |
% 9.25/2.86 | Equations (75) can reduce 70 to:
% 9.25/2.86 | (54) $false
% 9.25/2.86 |
% 9.25/2.86 |-The branch is then unsatisfiable
% 9.25/2.86 |-Branch two:
% 9.25/2.86 | (70) ~ (all_50_0_38 = 0)
% 9.25/2.86 | (82) ? [v0] : ( ~ (v0 = 0) & subset(all_31_1_31, all_0_9_9) = v0)
% 9.25/2.86 |
% 9.25/2.86 | Instantiating (82) with all_69_0_42 yields:
% 9.25/2.86 | (83) ~ (all_69_0_42 = 0) & subset(all_31_1_31, all_0_9_9) = all_69_0_42
% 9.25/2.86 |
% 9.25/2.86 | Applying alpha-rule on (83) yields:
% 9.25/2.86 | (84) ~ (all_69_0_42 = 0)
% 9.25/2.86 | (85) subset(all_31_1_31, all_0_9_9) = all_69_0_42
% 9.25/2.86 |
% 9.25/2.86 +-Applying beta-rule and splitting (72), into two cases.
% 9.25/2.86 |-Branch one:
% 9.25/2.86 | (75) all_50_0_38 = 0
% 9.25/2.86 |
% 9.25/2.86 | Equations (75) can reduce 70 to:
% 9.25/2.86 | (54) $false
% 9.25/2.86 |
% 9.25/2.86 |-The branch is then unsatisfiable
% 9.25/2.86 |-Branch two:
% 9.25/2.86 | (70) ~ (all_50_0_38 = 0)
% 9.25/2.86 | (89) ? [v0] : ( ~ (v0 = 0) & subset(all_31_1_31, all_0_10_10) = v0)
% 9.25/2.86 |
% 9.25/2.86 | Instantiating (89) with all_74_0_43 yields:
% 9.25/2.86 | (90) ~ (all_74_0_43 = 0) & subset(all_31_1_31, all_0_10_10) = all_74_0_43
% 9.25/2.86 |
% 9.25/2.86 | Applying alpha-rule on (90) yields:
% 9.25/2.86 | (91) ~ (all_74_0_43 = 0)
% 9.25/2.86 | (92) subset(all_31_1_31, all_0_10_10) = all_74_0_43
% 9.25/2.86 |
% 9.25/2.86 | Instantiating formula (36) with all_69_0_42, all_31_1_31, all_0_7_7, all_0_9_9 and discharging atoms powerset(all_0_9_9) = all_0_7_7, subset(all_31_1_31, all_0_9_9) = all_69_0_42, yields:
% 9.25/2.86 | (93) all_69_0_42 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_31_1_31, all_0_7_7) = v0)
% 9.25/2.86 |
% 9.25/2.86 | Instantiating formula (36) with all_74_0_43, all_31_1_31, all_0_8_8, all_0_10_10 and discharging atoms powerset(all_0_10_10) = all_0_8_8, subset(all_31_1_31, all_0_10_10) = all_74_0_43, yields:
% 9.25/2.86 | (94) all_74_0_43 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_31_1_31, all_0_8_8) = v0)
% 9.25/2.86 |
% 9.25/2.86 +-Applying beta-rule and splitting (93), into two cases.
% 9.25/2.86 |-Branch one:
% 9.25/2.86 | (95) all_69_0_42 = 0
% 9.25/2.86 |
% 9.25/2.86 | Equations (95) can reduce 84 to:
% 9.25/2.86 | (54) $false
% 9.25/2.86 |
% 9.25/2.86 |-The branch is then unsatisfiable
% 9.25/2.86 |-Branch two:
% 9.25/2.86 | (84) ~ (all_69_0_42 = 0)
% 9.25/2.86 | (98) ? [v0] : ( ~ (v0 = 0) & in(all_31_1_31, all_0_7_7) = v0)
% 9.25/2.86 |
% 9.25/2.86 | Instantiating (98) with all_109_0_52 yields:
% 9.25/2.86 | (99) ~ (all_109_0_52 = 0) & in(all_31_1_31, all_0_7_7) = all_109_0_52
% 9.25/2.86 |
% 9.25/2.86 | Applying alpha-rule on (99) yields:
% 9.25/2.86 | (100) ~ (all_109_0_52 = 0)
% 9.25/2.86 | (101) in(all_31_1_31, all_0_7_7) = all_109_0_52
% 9.25/2.86 |
% 9.25/2.86 +-Applying beta-rule and splitting (94), into two cases.
% 9.25/2.86 |-Branch one:
% 9.25/2.86 | (102) all_74_0_43 = 0
% 9.25/2.86 |
% 9.25/2.86 | Equations (102) can reduce 91 to:
% 9.25/2.86 | (54) $false
% 9.25/2.86 |
% 9.25/2.86 |-The branch is then unsatisfiable
% 9.25/2.86 |-Branch two:
% 9.25/2.86 | (91) ~ (all_74_0_43 = 0)
% 9.25/2.86 | (105) ? [v0] : ( ~ (v0 = 0) & in(all_31_1_31, all_0_8_8) = v0)
% 9.25/2.86 |
% 9.25/2.86 | Instantiating (105) with all_119_0_55 yields:
% 9.25/2.86 | (106) ~ (all_119_0_55 = 0) & in(all_31_1_31, all_0_8_8) = all_119_0_55
% 9.25/2.86 |
% 9.25/2.86 | Applying alpha-rule on (106) yields:
% 9.25/2.86 | (107) ~ (all_119_0_55 = 0)
% 9.25/2.86 | (108) in(all_31_1_31, all_0_8_8) = all_119_0_55
% 9.25/2.86 |
% 9.25/2.86 +-Applying beta-rule and splitting (64), into two cases.
% 9.25/2.86 |-Branch one:
% 9.25/2.86 | (109) all_43_0_35 = 0 & in(all_31_1_31, all_0_7_7) = 0
% 9.25/2.86 |
% 9.25/2.86 | Applying alpha-rule on (109) yields:
% 9.25/2.86 | (110) all_43_0_35 = 0
% 9.25/2.86 | (111) in(all_31_1_31, all_0_7_7) = 0
% 9.25/2.86 |
% 9.25/2.86 | Instantiating formula (44) with all_31_1_31, all_0_7_7, 0, all_109_0_52 and discharging atoms in(all_31_1_31, all_0_7_7) = all_109_0_52, in(all_31_1_31, all_0_7_7) = 0, yields:
% 9.25/2.86 | (112) all_109_0_52 = 0
% 9.25/2.86 |
% 9.25/2.86 | Equations (112) can reduce 100 to:
% 9.25/2.86 | (54) $false
% 9.25/2.86 |
% 9.25/2.86 |-The branch is then unsatisfiable
% 9.25/2.86 |-Branch two:
% 9.25/2.86 | (114) all_43_0_35 = 0 & in(all_31_1_31, all_0_8_8) = 0
% 9.25/2.86 |
% 9.25/2.86 | Applying alpha-rule on (114) yields:
% 9.25/2.86 | (110) all_43_0_35 = 0
% 9.25/2.86 | (116) in(all_31_1_31, all_0_8_8) = 0
% 9.25/2.87 |
% 9.25/2.87 | Instantiating formula (44) with all_31_1_31, all_0_8_8, 0, all_119_0_55 and discharging atoms in(all_31_1_31, all_0_8_8) = all_119_0_55, in(all_31_1_31, all_0_8_8) = 0, yields:
% 9.25/2.87 | (117) all_119_0_55 = 0
% 9.25/2.87 |
% 9.25/2.87 | Equations (117) can reduce 107 to:
% 9.25/2.87 | (54) $false
% 9.25/2.87 |
% 9.25/2.87 |-The branch is then unsatisfiable
% 9.25/2.87 % SZS output end Proof for theBenchmark
% 9.25/2.87
% 9.25/2.87 2270ms
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