TSTP Solution File: SEU132+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU132+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 08:46:49 EDT 2022
% Result : Theorem 4.22s 1.76s
% Output : Proof 5.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU132+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jun 18 23:02:44 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.59 ____ _
% 0.19/0.59 ___ / __ \_____(_)___ ________ __________
% 0.19/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic
% 0.19/0.59 (ePrincess v.1.0)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2015
% 0.19/0.59 (c) Peter Backeman, 2014-2015
% 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.59 Bug reports to peter@backeman.se
% 0.19/0.59
% 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.40/0.91 Prover 0: Preprocessing ...
% 1.68/1.05 Prover 0: Warning: ignoring some quantifiers
% 1.68/1.06 Prover 0: Constructing countermodel ...
% 2.43/1.25 Prover 0: gave up
% 2.43/1.25 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.43/1.27 Prover 1: Preprocessing ...
% 2.79/1.34 Prover 1: Warning: ignoring some quantifiers
% 2.79/1.34 Prover 1: Constructing countermodel ...
% 3.90/1.63 Prover 1: gave up
% 3.90/1.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.90/1.64 Prover 2: Preprocessing ...
% 4.22/1.70 Prover 2: Warning: ignoring some quantifiers
% 4.22/1.70 Prover 2: Constructing countermodel ...
% 4.22/1.75 Prover 2: proved (129ms)
% 4.22/1.76
% 4.22/1.76 No countermodel exists, formula is valid
% 4.22/1.76 % SZS status Theorem for theBenchmark
% 4.22/1.76
% 4.22/1.76 Generating proof ... Warning: ignoring some quantifiers
% 5.22/1.95 found it (size 30)
% 5.22/1.95
% 5.22/1.95 % SZS output start Proof for theBenchmark
% 5.22/1.95 Assumed formulas after preprocessing and simplification:
% 5.22/1.95 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v7 = 0) & ~ (v5 = 0) & empty(v8) = 0 & empty(v6) = v7 & empty(empty_set) = 0 & set_difference(v1, v2) = v4 & set_difference(v0, v2) = v3 & subset(v3, v4) = v5 & subset(v0, v1) = 0 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (set_difference(v9, v10) = v11) | ~ (in(v12, v11) = v13) | ? [v14] : ((v14 = 0 & in(v12, v10) = 0) | ( ~ (v14 = 0) & in(v12, v9) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (set_difference(v9, v10) = v11) | ~ (in(v12, v10) = v13) | ? [v14] : ((v14 = 0 & in(v12, v11) = 0) | ( ~ (v14 = 0) & in(v12, v9) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(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_difference(v9, v10) = v11) | ~ (in(v12, v9) = v13) | ? [v14] : ((v13 = 0 & ~ (v14 = 0) & in(v12, v10) = v14) | ( ~ (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 | ~ (set_difference(v12, v11) = v10) | ~ (set_difference(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (subset(v12, v11) = v10) | ~ (subset(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (in(v12, v11) = v10) | ~ (in(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v9, v10) = v11) | ~ (in(v12, v11) = 0) | ? [v13] : ( ~ (v13 = 0) & in(v12, v10) = v13 & in(v12, v9) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v9, v10) = v11) | ~ (in(v12, v9) = 0) | ? [v13] : ((v13 = 0 & in(v12, v11) = 0) | (v13 = 0 & in(v12, v10) = 0))) & ? [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (set_difference(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (((v16 = 0 & in(v13, v11) = 0) | ( ~ (v15 = 0) & in(v13, v10) = v15) | ( ~ (v14 = 0) & in(v13, v9) = v14)) & ((v15 = 0 & ~ (v16 = 0) & in(v13, v11) = v16 & in(v13, v10) = 0) | (v14 = 0 & in(v13, v9) = 0)))) & ! [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] : (v10 = v9 | ~ (empty(v10) = 0) | ~ (empty(v9) = 0)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_difference(v9, empty_set) = v10)) & ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_difference(empty_set, v9) = 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] : set_difference(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : subset(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : in(v10, v9) = v11 & ? [v9] : ? [v10] : empty(v9) = v10)
% 5.52/1.99 | 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:
% 5.52/1.99 | (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 & set_difference(all_0_7_7, all_0_6_6) = all_0_4_4 & set_difference(all_0_8_8, all_0_6_6) = all_0_5_5 & subset(all_0_5_5, all_0_4_4) = all_0_3_3 & subset(all_0_8_8, all_0_7_7) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(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_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v4 = 0 & ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (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 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(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] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v4 = 0 & in(v3, v1) = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)) & ((v6 = 0 & ~ (v7 = 0) & in(v4, v2) = v7 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)))) & ! [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] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, 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) & 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] : set_difference(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : empty(v0) = v1
% 5.52/2.00 |
% 5.52/2.00 | Applying alpha-rule on (1) yields:
% 5.52/2.00 | (2) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 5.52/2.00 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5)))
% 5.52/2.00 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5)))
% 5.52/2.00 | (5) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 5.52/2.00 | (6) empty(empty_set) = 0
% 5.52/2.00 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 5.52/2.00 | (8) ~ (all_0_3_3 = 0)
% 5.52/2.00 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ((v5 = 0 & ~ (v4 = 0) & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 5.52/2.00 | (10) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 5.52/2.00 | (11) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 5.52/2.00 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 5.52/2.00 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 5.52/2.00 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 5.52/2.00 | (15) empty(all_0_0_0) = 0
% 5.52/2.00 | (16) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)) & ((v6 = 0 & ~ (v7 = 0) & in(v4, v2) = v7 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0))))
% 5.52/2.00 | (17) set_difference(all_0_7_7, all_0_6_6) = all_0_4_4
% 5.52/2.00 | (18) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 5.52/2.00 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 5.52/2.00 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 5.52/2.00 | (21) ? [v0] : ? [v1] : empty(v0) = v1
% 5.52/2.00 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v4 = 0 & in(v3, v1) = 0)))
% 5.52/2.00 | (23) subset(all_0_8_8, all_0_7_7) = 0
% 5.52/2.00 | (24) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 5.52/2.00 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ((v4 = 0 & ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 5.52/2.00 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 5.52/2.00 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 5.52/2.01 | (28) set_difference(all_0_8_8, all_0_6_6) = all_0_5_5
% 5.52/2.01 | (29) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 5.52/2.01 | (30) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 5.52/2.01 | (31) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 5.52/2.01 | (32) ? [v0] : ? [v1] : ? [v2] : set_difference(v1, v0) = v2
% 5.52/2.01 | (33) ~ (all_0_1_1 = 0)
% 5.52/2.01 | (34) subset(all_0_5_5, all_0_4_4) = all_0_3_3
% 5.52/2.01 | (35) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 5.52/2.01 | (36) empty(all_0_2_2) = all_0_1_1
% 5.52/2.01 |
% 5.52/2.01 | Instantiating formula (20) 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:
% 5.52/2.01 | (37) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0)
% 5.52/2.01 |
% 5.52/2.01 +-Applying beta-rule and splitting (37), into two cases.
% 5.52/2.01 |-Branch one:
% 5.52/2.01 | (38) all_0_3_3 = 0
% 5.52/2.01 |
% 5.52/2.01 | Equations (38) can reduce 8 to:
% 5.52/2.01 | (39) $false
% 5.52/2.01 |
% 5.52/2.01 |-The branch is then unsatisfiable
% 5.52/2.01 |-Branch two:
% 5.52/2.01 | (8) ~ (all_0_3_3 = 0)
% 5.52/2.01 | (41) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_5_5) = 0)
% 5.52/2.01 |
% 5.52/2.01 | Instantiating (41) with all_24_0_21, all_24_1_22 yields:
% 5.52/2.01 | (42) ~ (all_24_0_21 = 0) & in(all_24_1_22, all_0_4_4) = all_24_0_21 & in(all_24_1_22, all_0_5_5) = 0
% 5.52/2.01 |
% 5.52/2.01 | Applying alpha-rule on (42) yields:
% 5.52/2.01 | (43) ~ (all_24_0_21 = 0)
% 5.52/2.01 | (44) in(all_24_1_22, all_0_4_4) = all_24_0_21
% 5.52/2.01 | (45) in(all_24_1_22, all_0_5_5) = 0
% 5.52/2.01 |
% 5.52/2.01 | Instantiating formula (3) with all_24_0_21, all_24_1_22, all_0_4_4, all_0_6_6, all_0_7_7 and discharging atoms set_difference(all_0_7_7, all_0_6_6) = all_0_4_4, in(all_24_1_22, all_0_4_4) = all_24_0_21, yields:
% 5.52/2.01 | (46) all_24_0_21 = 0 | ? [v0] : ((v0 = 0 & in(all_24_1_22, all_0_6_6) = 0) | ( ~ (v0 = 0) & in(all_24_1_22, all_0_7_7) = v0))
% 5.52/2.01 |
% 5.52/2.01 | Instantiating formula (7) with all_24_1_22, all_0_5_5, all_0_6_6, all_0_8_8 and discharging atoms set_difference(all_0_8_8, all_0_6_6) = all_0_5_5, in(all_24_1_22, all_0_5_5) = 0, yields:
% 5.52/2.01 | (47) ? [v0] : ( ~ (v0 = 0) & in(all_24_1_22, all_0_6_6) = v0 & in(all_24_1_22, all_0_8_8) = 0)
% 5.52/2.01 |
% 5.52/2.01 | Instantiating (47) with all_33_0_24 yields:
% 5.52/2.01 | (48) ~ (all_33_0_24 = 0) & in(all_24_1_22, all_0_6_6) = all_33_0_24 & in(all_24_1_22, all_0_8_8) = 0
% 5.52/2.01 |
% 5.52/2.01 | Applying alpha-rule on (48) yields:
% 5.52/2.01 | (49) ~ (all_33_0_24 = 0)
% 5.52/2.01 | (50) in(all_24_1_22, all_0_6_6) = all_33_0_24
% 5.52/2.01 | (51) in(all_24_1_22, all_0_8_8) = 0
% 5.52/2.01 |
% 5.52/2.01 +-Applying beta-rule and splitting (46), into two cases.
% 5.52/2.01 |-Branch one:
% 5.52/2.01 | (52) all_24_0_21 = 0
% 5.52/2.01 |
% 5.52/2.01 | Equations (52) can reduce 43 to:
% 5.52/2.01 | (39) $false
% 5.52/2.01 |
% 5.52/2.01 |-The branch is then unsatisfiable
% 5.52/2.01 |-Branch two:
% 5.52/2.01 | (43) ~ (all_24_0_21 = 0)
% 5.52/2.01 | (55) ? [v0] : ((v0 = 0 & in(all_24_1_22, all_0_6_6) = 0) | ( ~ (v0 = 0) & in(all_24_1_22, all_0_7_7) = v0))
% 5.52/2.01 |
% 5.52/2.01 | Instantiating (55) with all_41_0_26 yields:
% 5.52/2.01 | (56) (all_41_0_26 = 0 & in(all_24_1_22, all_0_6_6) = 0) | ( ~ (all_41_0_26 = 0) & in(all_24_1_22, all_0_7_7) = all_41_0_26)
% 5.52/2.01 |
% 5.52/2.01 +-Applying beta-rule and splitting (56), into two cases.
% 5.52/2.01 |-Branch one:
% 5.52/2.01 | (57) all_41_0_26 = 0 & in(all_24_1_22, all_0_6_6) = 0
% 5.52/2.01 |
% 5.52/2.01 | Applying alpha-rule on (57) yields:
% 5.52/2.01 | (58) all_41_0_26 = 0
% 5.52/2.01 | (59) in(all_24_1_22, all_0_6_6) = 0
% 5.52/2.01 |
% 5.52/2.01 | Instantiating formula (26) with all_24_1_22, all_0_6_6, 0, all_33_0_24 and discharging atoms in(all_24_1_22, all_0_6_6) = all_33_0_24, in(all_24_1_22, all_0_6_6) = 0, yields:
% 5.52/2.01 | (60) all_33_0_24 = 0
% 5.52/2.01 |
% 5.52/2.01 | Equations (60) can reduce 49 to:
% 5.52/2.01 | (39) $false
% 5.52/2.01 |
% 5.52/2.01 |-The branch is then unsatisfiable
% 5.52/2.01 |-Branch two:
% 5.52/2.01 | (62) ~ (all_41_0_26 = 0) & in(all_24_1_22, all_0_7_7) = all_41_0_26
% 5.52/2.01 |
% 5.52/2.01 | Applying alpha-rule on (62) yields:
% 5.52/2.01 | (63) ~ (all_41_0_26 = 0)
% 5.52/2.01 | (64) in(all_24_1_22, all_0_7_7) = all_41_0_26
% 5.52/2.01 |
% 5.52/2.01 | Instantiating formula (12) with all_41_0_26, all_24_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_24_1_22, all_0_7_7) = all_41_0_26, yields:
% 5.52/2.02 | (65) all_41_0_26 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_24_1_22, all_0_8_8) = v0)
% 5.52/2.02 |
% 5.52/2.02 | Instantiating formula (19) with all_24_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_24_1_22, all_0_8_8) = 0, yields:
% 5.52/2.02 | (66) in(all_24_1_22, all_0_7_7) = 0
% 5.52/2.02 |
% 5.52/2.02 +-Applying beta-rule and splitting (65), into two cases.
% 5.52/2.02 |-Branch one:
% 5.52/2.02 | (58) all_41_0_26 = 0
% 5.52/2.02 |
% 5.52/2.02 | Equations (58) can reduce 63 to:
% 5.52/2.02 | (39) $false
% 5.52/2.02 |
% 5.52/2.02 |-The branch is then unsatisfiable
% 5.52/2.02 |-Branch two:
% 5.52/2.02 | (63) ~ (all_41_0_26 = 0)
% 5.52/2.02 | (70) ? [v0] : ( ~ (v0 = 0) & in(all_24_1_22, all_0_8_8) = v0)
% 5.52/2.02 |
% 5.52/2.02 | Instantiating formula (26) with all_24_1_22, all_0_7_7, 0, all_41_0_26 and discharging atoms in(all_24_1_22, all_0_7_7) = all_41_0_26, in(all_24_1_22, all_0_7_7) = 0, yields:
% 5.52/2.02 | (58) all_41_0_26 = 0
% 5.52/2.02 |
% 5.52/2.02 | Equations (58) can reduce 63 to:
% 5.52/2.02 | (39) $false
% 5.52/2.02 |
% 5.52/2.02 |-The branch is then unsatisfiable
% 5.52/2.02 % SZS output end Proof for theBenchmark
% 5.52/2.02
% 5.52/2.02 1409ms
%------------------------------------------------------------------------------