TSTP Solution File: SEU129+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU129+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n009.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 08:46:47 EDT 2022
% Result : Theorem 5.43s 2.00s
% Output : Proof 6.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU129+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 12:27:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.54/0.58 ____ _
% 0.54/0.58 ___ / __ \_____(_)___ ________ __________
% 0.54/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.58
% 0.54/0.58 A Theorem Prover for First-Order Logic
% 0.54/0.58 (ePrincess v.1.0)
% 0.54/0.58
% 0.54/0.58 (c) Philipp Rümmer, 2009-2015
% 0.54/0.58 (c) Peter Backeman, 2014-2015
% 0.54/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.58 Bug reports to peter@backeman.se
% 0.54/0.58
% 0.54/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.58
% 0.54/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.60/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.36/0.90 Prover 0: Preprocessing ...
% 1.66/1.05 Prover 0: Warning: ignoring some quantifiers
% 1.66/1.07 Prover 0: Constructing countermodel ...
% 2.31/1.29 Prover 0: gave up
% 2.31/1.29 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.31/1.31 Prover 1: Preprocessing ...
% 2.69/1.37 Prover 1: Warning: ignoring some quantifiers
% 2.69/1.38 Prover 1: Constructing countermodel ...
% 4.65/1.88 Prover 1: gave up
% 4.65/1.88 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.65/1.89 Prover 2: Preprocessing ...
% 5.07/1.94 Prover 2: Warning: ignoring some quantifiers
% 5.07/1.95 Prover 2: Constructing countermodel ...
% 5.43/2.00 Prover 2: proved (118ms)
% 5.43/2.00
% 5.43/2.00 No countermodel exists, formula is valid
% 5.43/2.00 % SZS status Theorem for theBenchmark
% 5.43/2.00
% 5.43/2.00 Generating proof ... Warning: ignoring some quantifiers
% 6.00/2.22 found it (size 31)
% 6.00/2.22
% 6.00/2.22 % SZS output start Proof for theBenchmark
% 6.00/2.22 Assumed formulas after preprocessing and simplification:
% 6.00/2.22 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v7 = 0) & ~ (v5 = 0) & empty(v8) = 0 & empty(v6) = v7 & empty(empty_set) = 0 & subset(v3, v4) = v5 & subset(v0, v1) = 0 & set_intersection2(v1, v2) = v4 & set_intersection2(v0, v2) = v3 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (set_intersection2(v9, v10) = v11) | ~ (in(v12, v11) = v13) | ? [v14] : (( ~ (v14 = 0) & in(v12, v10) = v14) | ( ~ (v14 = 0) & in(v12, v9) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v9, v10) = v11) | ~ (in(v12, v10) = v13) | ? [v14] : ((v14 = 0 & v13 = 0 & in(v12, v9) = 0) | ( ~ (v14 = 0) & in(v12, v11) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v9, v10) = v11) | ~ (in(v12, v9) = v13) | ? [v14] : ((v14 = 0 & v13 = 0 & in(v12, v10) = 0) | ( ~ (v14 = 0) & in(v12, v11) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v9, v10) = 0) | ~ (in(v11, v10) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v11, v9) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (subset(v12, v11) = v10) | ~ (subset(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (set_intersection2(v12, v11) = v10) | ~ (set_intersection2(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (in(v12, v11) = v10) | ~ (in(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v9, v10) = v11) | ~ (in(v12, v11) = 0) | (in(v12, v10) = 0 & in(v12, v9) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v9, v10) = v11) | ~ (in(v12, v10) = 0) | ? [v13] : ((v13 = 0 & in(v12, v11) = 0) | ( ~ (v13 = 0) & in(v12, v9) = v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v9, v10) = v11) | ~ (in(v12, v9) = 0) | ? [v13] : ((v13 = 0 & in(v12, v11) = 0) | ( ~ (v13 = 0) & in(v12, v10) = v13))) & ? [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (set_intersection2(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (((v16 = 0 & v15 = 0 & in(v13, v11) = 0 & in(v13, v10) = 0) | (v14 = 0 & in(v13, v9) = 0)) & (( ~ (v16 = 0) & in(v13, v11) = v16) | ( ~ (v15 = 0) & in(v13, v10) = v15) | ( ~ (v14 = 0) & in(v13, v9) = v14)))) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v9, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & in(v12, v10) = v13 & in(v12, v9) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (empty(v11) = v10) | ~ (empty(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset(v9, v10) = 0) | ~ (in(v11, v9) = 0) | in(v11, v10) = 0) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | set_intersection2(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | set_intersection2(v10, v9) = v11) & ! [v9] : ! [v10] : (v10 = v9 | ~ (empty(v10) = 0) | ~ (empty(v9) = 0)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_intersection2(v9, v9) = v10)) & ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_intersection2(v9, empty_set) = v10)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v9, v9) = v10)) & ! [v9] : ! [v10] : ( ~ (in(v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & in(v9, v10) = v11)) & ! [v9] : ! [v10] : ( ~ (in(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & empty(v10) = v11)) & ! [v9] : ! [v10] : ( ~ (in(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & in(v10, v9) = v11)) & ! [v9] : (v9 = empty_set | ~ (empty(v9) = 0)) & ? [v9] : ? [v10] : ? [v11] : subset(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : set_intersection2(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : in(v10, v9) = v11 & ? [v9] : ? [v10] : empty(v9) = v10)
% 6.47/2.25 | 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 yields:
% 6.47/2.25 | (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 & subset(all_0_5_5, all_0_4_4) = all_0_3_3 & subset(all_0_8_8, all_0_7_7) = 0 & set_intersection2(all_0_7_7, all_0_6_6) = all_0_4_4 & set_intersection2(all_0_8_8, all_0_6_6) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [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_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v1) = v4))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v4, v2) = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & in(v4, v2) = v7) | ( ~ (v6 = 0) & 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] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = 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) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : empty(v0) = v1
% 6.47/2.27 |
% 6.47/2.27 | Applying alpha-rule on (1) yields:
% 6.47/2.27 | (2) empty(all_0_2_2) = all_0_1_1
% 6.47/2.27 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 6.47/2.27 | (4) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 6.47/2.27 | (5) subset(all_0_5_5, all_0_4_4) = all_0_3_3
% 6.47/2.27 | (6) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 6.47/2.27 | (7) empty(empty_set) = 0
% 6.47/2.27 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 6.47/2.27 | (9) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 6.47/2.27 | (10) ~ (all_0_1_1 = 0)
% 6.47/2.27 | (11) ~ (all_0_3_3 = 0)
% 6.47/2.27 | (12) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 6.47/2.27 | (13) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 6.47/2.27 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v0) = v5)))
% 6.47/2.27 | (15) set_intersection2(all_0_7_7, all_0_6_6) = all_0_4_4
% 6.47/2.27 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 6.47/2.27 | (17) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v6 = 0 & in(v4, v2) = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & in(v4, v2) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5))))
% 6.47/2.27 | (18) empty(all_0_0_0) = 0
% 6.47/2.27 | (19) ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2
% 6.47/2.27 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 6.47/2.27 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 6.47/2.27 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 6.47/2.27 | (23) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 6.47/2.27 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v1) = v4)))
% 6.47/2.27 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 6.47/2.27 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 6.47/2.27 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4)))
% 6.47/2.27 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 6.47/2.27 | (29) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 6.47/2.27 | (30) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 6.47/2.27 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 6.47/2.27 | (32) set_intersection2(all_0_8_8, all_0_6_6) = all_0_5_5
% 6.47/2.28 | (33) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 6.47/2.28 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0))
% 6.47/2.28 | (35) ? [v0] : ? [v1] : empty(v0) = v1
% 6.47/2.28 | (36) subset(all_0_8_8, all_0_7_7) = 0
% 6.47/2.28 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 6.47/2.28 | (38) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 6.47/2.28 |
% 6.47/2.28 | Instantiating formula (22) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 6.47/2.28 | (39) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0)
% 6.47/2.28 |
% 6.47/2.28 | Instantiating formula (26) with all_0_4_4, all_0_7_7, all_0_6_6 and discharging atoms set_intersection2(all_0_7_7, all_0_6_6) = all_0_4_4, yields:
% 6.47/2.28 | (40) set_intersection2(all_0_6_6, all_0_7_7) = all_0_4_4
% 6.47/2.28 |
% 6.47/2.28 | Instantiating formula (26) with all_0_5_5, all_0_8_8, all_0_6_6 and discharging atoms set_intersection2(all_0_8_8, all_0_6_6) = all_0_5_5, yields:
% 6.47/2.28 | (41) set_intersection2(all_0_6_6, all_0_8_8) = all_0_5_5
% 6.47/2.28 |
% 6.47/2.28 +-Applying beta-rule and splitting (39), into two cases.
% 6.47/2.28 |-Branch one:
% 6.47/2.28 | (42) all_0_3_3 = 0
% 6.47/2.28 |
% 6.47/2.28 | Equations (42) can reduce 11 to:
% 6.47/2.28 | (43) $false
% 6.47/2.28 |
% 6.47/2.28 |-The branch is then unsatisfiable
% 6.47/2.28 |-Branch two:
% 6.47/2.28 | (11) ~ (all_0_3_3 = 0)
% 6.47/2.28 | (45) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0)
% 6.47/2.28 |
% 6.47/2.28 | Instantiating (45) with all_27_0_21, all_27_1_22 yields:
% 6.47/2.28 | (46) ~ (all_27_0_21 = 0) & in(all_27_1_22, all_0_4_4) = all_27_0_21 & in(all_27_1_22, all_0_5_5) = 0
% 6.47/2.28 |
% 6.47/2.28 | Applying alpha-rule on (46) yields:
% 6.47/2.28 | (47) ~ (all_27_0_21 = 0)
% 6.47/2.28 | (48) in(all_27_1_22, all_0_4_4) = all_27_0_21
% 6.47/2.28 | (49) in(all_27_1_22, all_0_5_5) = 0
% 6.47/2.28 |
% 6.47/2.28 | Instantiating formula (14) with all_27_0_21, all_27_1_22, all_0_4_4, all_0_7_7, all_0_6_6 and discharging atoms set_intersection2(all_0_6_6, all_0_7_7) = all_0_4_4, in(all_27_1_22, all_0_4_4) = all_27_0_21, yields:
% 6.47/2.28 | (50) all_27_0_21 = 0 | ? [v0] : (( ~ (v0 = 0) & in(all_27_1_22, all_0_6_6) = v0) | ( ~ (v0 = 0) & in(all_27_1_22, all_0_7_7) = v0))
% 6.47/2.28 |
% 6.47/2.28 | Instantiating formula (34) with all_27_1_22, all_0_5_5, all_0_8_8, all_0_6_6 and discharging atoms set_intersection2(all_0_6_6, all_0_8_8) = all_0_5_5, in(all_27_1_22, all_0_5_5) = 0, yields:
% 6.47/2.28 | (51) in(all_27_1_22, all_0_6_6) = 0 & in(all_27_1_22, all_0_8_8) = 0
% 6.47/2.28 |
% 6.47/2.28 | Applying alpha-rule on (51) yields:
% 6.47/2.28 | (52) in(all_27_1_22, all_0_6_6) = 0
% 6.47/2.28 | (53) in(all_27_1_22, all_0_8_8) = 0
% 6.47/2.28 |
% 6.47/2.28 +-Applying beta-rule and splitting (50), into two cases.
% 6.47/2.28 |-Branch one:
% 6.47/2.28 | (54) all_27_0_21 = 0
% 6.47/2.28 |
% 6.47/2.28 | Equations (54) can reduce 47 to:
% 6.47/2.28 | (43) $false
% 6.47/2.28 |
% 6.47/2.28 |-The branch is then unsatisfiable
% 6.47/2.28 |-Branch two:
% 6.47/2.28 | (47) ~ (all_27_0_21 = 0)
% 6.47/2.28 | (57) ? [v0] : (( ~ (v0 = 0) & in(all_27_1_22, all_0_6_6) = v0) | ( ~ (v0 = 0) & in(all_27_1_22, all_0_7_7) = v0))
% 6.47/2.28 |
% 6.47/2.28 | Instantiating (57) with all_43_0_25 yields:
% 6.47/2.28 | (58) ( ~ (all_43_0_25 = 0) & in(all_27_1_22, all_0_6_6) = all_43_0_25) | ( ~ (all_43_0_25 = 0) & in(all_27_1_22, all_0_7_7) = all_43_0_25)
% 6.47/2.28 |
% 6.47/2.28 +-Applying beta-rule and splitting (58), into two cases.
% 6.47/2.28 |-Branch one:
% 6.47/2.28 | (59) ~ (all_43_0_25 = 0) & in(all_27_1_22, all_0_6_6) = all_43_0_25
% 6.47/2.28 |
% 6.47/2.28 | Applying alpha-rule on (59) yields:
% 6.47/2.28 | (60) ~ (all_43_0_25 = 0)
% 6.47/2.28 | (61) in(all_27_1_22, all_0_6_6) = all_43_0_25
% 6.47/2.29 |
% 6.47/2.29 | Instantiating formula (20) with all_27_1_22, all_0_6_6, 0, all_43_0_25 and discharging atoms in(all_27_1_22, all_0_6_6) = all_43_0_25, in(all_27_1_22, all_0_6_6) = 0, yields:
% 6.47/2.29 | (62) all_43_0_25 = 0
% 6.47/2.29 |
% 6.47/2.29 | Equations (62) can reduce 60 to:
% 6.47/2.29 | (43) $false
% 6.47/2.29 |
% 6.47/2.29 |-The branch is then unsatisfiable
% 6.47/2.29 |-Branch two:
% 6.47/2.29 | (64) ~ (all_43_0_25 = 0) & in(all_27_1_22, all_0_7_7) = all_43_0_25
% 6.47/2.29 |
% 6.47/2.29 | Applying alpha-rule on (64) yields:
% 6.47/2.29 | (60) ~ (all_43_0_25 = 0)
% 6.47/2.29 | (66) in(all_27_1_22, all_0_7_7) = all_43_0_25
% 6.47/2.29 |
% 6.47/2.29 | Instantiating formula (28) with all_43_0_25, all_27_1_22, all_0_7_7, all_0_8_8 and discharging atoms subset(all_0_8_8, all_0_7_7) = 0, in(all_27_1_22, all_0_7_7) = all_43_0_25, yields:
% 6.47/2.29 | (67) all_43_0_25 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_27_1_22, all_0_8_8) = v0)
% 6.47/2.29 |
% 6.47/2.29 | Instantiating formula (16) with all_27_1_22, all_0_7_7, all_0_8_8 and discharging atoms subset(all_0_8_8, all_0_7_7) = 0, in(all_27_1_22, all_0_8_8) = 0, yields:
% 6.47/2.29 | (68) in(all_27_1_22, all_0_7_7) = 0
% 6.47/2.29 |
% 6.47/2.29 +-Applying beta-rule and splitting (67), into two cases.
% 6.47/2.29 |-Branch one:
% 6.47/2.29 | (62) all_43_0_25 = 0
% 6.47/2.29 |
% 6.47/2.29 | Equations (62) can reduce 60 to:
% 6.47/2.29 | (43) $false
% 6.47/2.29 |
% 6.47/2.29 |-The branch is then unsatisfiable
% 6.47/2.29 |-Branch two:
% 6.47/2.29 | (60) ~ (all_43_0_25 = 0)
% 6.47/2.29 | (72) ? [v0] : ( ~ (v0 = 0) & in(all_27_1_22, all_0_8_8) = v0)
% 6.47/2.29 |
% 6.47/2.29 | Instantiating formula (20) with all_27_1_22, all_0_7_7, 0, all_43_0_25 and discharging atoms in(all_27_1_22, all_0_7_7) = all_43_0_25, in(all_27_1_22, all_0_7_7) = 0, yields:
% 6.47/2.29 | (62) all_43_0_25 = 0
% 6.47/2.29 |
% 6.47/2.29 | Equations (62) can reduce 60 to:
% 6.47/2.29 | (43) $false
% 6.47/2.29 |
% 6.47/2.29 |-The branch is then unsatisfiable
% 6.47/2.29 % SZS output end Proof for theBenchmark
% 6.47/2.29
% 6.47/2.29 1702ms
%------------------------------------------------------------------------------