TSTP Solution File: SEU125+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU125+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n012.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 08:46:45 EDT 2022
% Result : Theorem 4.15s 1.78s
% Output : Proof 5.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU125+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 19:22:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.57/0.62 ____ _
% 0.57/0.62 ___ / __ \_____(_)___ ________ __________
% 0.57/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.62
% 0.57/0.62 A Theorem Prover for First-Order Logic
% 0.57/0.63 (ePrincess v.1.0)
% 0.57/0.63
% 0.57/0.63 (c) Philipp Rümmer, 2009-2015
% 0.57/0.63 (c) Peter Backeman, 2014-2015
% 0.57/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.63 Bug reports to peter@backeman.se
% 0.66/0.63
% 0.66/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.66/0.63
% 0.66/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.45/0.98 Prover 0: Preprocessing ...
% 1.79/1.14 Prover 0: Warning: ignoring some quantifiers
% 1.79/1.16 Prover 0: Constructing countermodel ...
% 2.50/1.34 Prover 0: gave up
% 2.50/1.34 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.50/1.36 Prover 1: Preprocessing ...
% 2.78/1.44 Prover 1: Warning: ignoring some quantifiers
% 2.78/1.44 Prover 1: Constructing countermodel ...
% 3.74/1.65 Prover 1: gave up
% 3.74/1.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.74/1.66 Prover 2: Preprocessing ...
% 4.15/1.73 Prover 2: Warning: ignoring some quantifiers
% 4.15/1.73 Prover 2: Constructing countermodel ...
% 4.15/1.78 Prover 2: proved (132ms)
% 4.15/1.78
% 4.15/1.78 No countermodel exists, formula is valid
% 4.15/1.78 % SZS status Theorem for theBenchmark
% 4.15/1.78
% 4.15/1.78 Generating proof ... Warning: ignoring some quantifiers
% 5.34/2.00 found it (size 32)
% 5.34/2.00
% 5.34/2.00 % SZS output start Proof for theBenchmark
% 5.34/2.00 Assumed formulas after preprocessing and simplification:
% 5.34/2.00 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v6 = 0) & ~ (v4 = 0) & empty(v7) = 0 & empty(v5) = v6 & empty(empty_set) = 0 & subset(v3, v1) = v4 & subset(v2, v1) = 0 & subset(v0, v1) = 0 & set_union2(v0, v2) = v3 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v10) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & ~ (v13 = 0) & in(v11, v9) = v14 & in(v11, v8) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v9) = v12) | ? [v13] : ((v13 = 0 & in(v11, v8) = 0) | ( ~ (v13 = 0) & in(v11, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ((v13 = 0 & in(v11, v9) = 0) | ( ~ (v13 = 0) & in(v11, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v9) = v12) | ? [v13] : ((v13 = 0 & in(v11, v10) = 0) | ( ~ (v13 = 0) & ~ (v12 = 0) & in(v11, v8) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ((v13 = 0 & in(v11, v10) = 0) | ( ~ (v13 = 0) & ~ (v12 = 0) & in(v11, v9) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v8, v9) = 0) | ~ (in(v10, v9) = v11) | ? [v12] : ( ~ (v12 = 0) & in(v10, v8) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset(v11, v10) = v9) | ~ (subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_union2(v11, v10) = v9) | ~ (set_union2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (in(v11, v10) = v9) | ~ (in(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v10) = 0) | ? [v12] : ((v12 = 0 & in(v11, v9) = 0) | (v12 = 0 & in(v11, v8) = 0))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_union2(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (((v15 = 0 & in(v12, v10) = 0) | (v14 = 0 & in(v12, v9) = 0) | (v13 = 0 & in(v12, v8) = 0)) & (( ~ (v15 = 0) & ~ (v14 = 0) & in(v12, v10) = v15 & in(v12, v9) = v14) | ( ~ (v13 = 0) & in(v12, v8) = v13)))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & in(v11, v9) = v12 & in(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (empty(v10) = v9) | ~ (empty(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = 0) | ~ (in(v10, v8) = 0) | in(v10, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v9, v8) = v10) | set_union2(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v9, v8) = v10) | ? [v11] : ((v11 = 0 & empty(v8) = 0) | ( ~ (v11 = 0) & empty(v10) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | set_union2(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | ? [v11] : ((v11 = 0 & empty(v8) = 0) | ( ~ (v11 = 0) & empty(v10) = v11))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (empty(v9) = 0) | ~ (empty(v8) = 0)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v8, empty_set) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v8, v8) = v9)) & ! [v8] : ! [v9] : ( ~ (in(v9, v8) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (in(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & empty(v9) = v10)) & ! [v8] : ! [v9] : ( ~ (in(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v9, v8) = v10)) & ! [v8] : (v8 = empty_set | ~ (empty(v8) = 0)) & ? [v8] : ? [v9] : ? [v10] : subset(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : set_union2(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : in(v9, v8) = v10 & ? [v8] : ? [v9] : empty(v8) = v9)
% 5.34/2.03 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields:
% 5.34/2.03 | (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_4_4, all_0_6_6) = all_0_3_3 & subset(all_0_5_5, all_0_6_6) = 0 & subset(all_0_7_7, all_0_6_6) = 0 & set_union2(all_0_7_7, all_0_5_5) = all_0_4_4 & ! [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 | ~ (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] : ( ~ (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) | 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] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(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_union2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : empty(v0) = v1
% 5.34/2.04 |
% 5.34/2.04 | Applying alpha-rule on (1) yields:
% 5.34/2.05 | (2) empty(empty_set) = 0
% 5.34/2.05 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 5.34/2.05 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 5.34/2.05 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 5.34/2.05 | (6) ! [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)))
% 5.34/2.05 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 5.34/2.05 | (8) subset(all_0_7_7, all_0_6_6) = 0
% 5.34/2.05 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 5.34/2.05 | (10) subset(all_0_4_4, all_0_6_6) = all_0_3_3
% 5.34/2.05 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 5.34/2.05 | (12) ! [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)))
% 5.34/2.05 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 5.34/2.05 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 5.34/2.05 | (15) ? [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))))
% 5.34/2.05 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 5.34/2.05 | (17) ! [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)))
% 5.34/2.05 | (18) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 5.34/2.05 | (19) ! [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))
% 5.34/2.05 | (20) ! [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)))
% 5.34/2.05 | (21) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 5.34/2.05 | (22) ~ (all_0_3_3 = 0)
% 5.34/2.05 | (23) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 5.34/2.06 | (24) ! [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)))
% 5.34/2.06 | (25) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 5.34/2.06 | (26) ? [v0] : ? [v1] : empty(v0) = v1
% 5.34/2.06 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 5.34/2.06 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 5.34/2.06 | (29) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 5.34/2.06 | (30) ~ (all_0_1_1 = 0)
% 5.34/2.06 | (31) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 5.34/2.06 | (32) set_union2(all_0_7_7, all_0_5_5) = all_0_4_4
% 5.34/2.06 | (33) empty(all_0_2_2) = all_0_1_1
% 5.34/2.06 | (34) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 5.34/2.06 | (35) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 5.34/2.06 | (36) empty(all_0_0_0) = 0
% 5.34/2.06 | (37) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 5.34/2.06 | (38) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 5.34/2.06 | (39) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2
% 5.34/2.06 | (40) subset(all_0_5_5, all_0_6_6) = 0
% 5.34/2.06 |
% 5.34/2.06 | Instantiating formula (35) with all_0_3_3, all_0_6_6, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_6_6) = all_0_3_3, yields:
% 5.34/2.06 | (41) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = v1)
% 5.34/2.06 |
% 5.34/2.06 | Instantiating formula (14) with all_0_4_4, all_0_7_7, all_0_5_5 and discharging atoms set_union2(all_0_7_7, all_0_5_5) = all_0_4_4, yields:
% 5.34/2.06 | (42) set_union2(all_0_5_5, all_0_7_7) = all_0_4_4
% 5.34/2.06 |
% 5.34/2.06 +-Applying beta-rule and splitting (41), into two cases.
% 5.34/2.06 |-Branch one:
% 5.34/2.06 | (43) all_0_3_3 = 0
% 5.34/2.06 |
% 5.34/2.06 | Equations (43) can reduce 22 to:
% 5.34/2.06 | (44) $false
% 5.34/2.06 |
% 5.34/2.06 |-The branch is then unsatisfiable
% 5.34/2.06 |-Branch two:
% 5.34/2.06 | (22) ~ (all_0_3_3 = 0)
% 5.34/2.06 | (46) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = v1)
% 5.34/2.06 |
% 5.34/2.06 | Instantiating (46) with all_29_0_22, all_29_1_23 yields:
% 5.34/2.06 | (47) ~ (all_29_0_22 = 0) & in(all_29_1_23, all_0_4_4) = 0 & in(all_29_1_23, all_0_6_6) = all_29_0_22
% 5.34/2.06 |
% 5.34/2.06 | Applying alpha-rule on (47) yields:
% 5.34/2.06 | (48) ~ (all_29_0_22 = 0)
% 5.34/2.07 | (49) in(all_29_1_23, all_0_4_4) = 0
% 5.34/2.07 | (50) in(all_29_1_23, all_0_6_6) = all_29_0_22
% 5.34/2.07 |
% 5.34/2.07 | Instantiating formula (20) with all_29_1_23, all_0_4_4, all_0_7_7, all_0_5_5 and discharging atoms set_union2(all_0_5_5, all_0_7_7) = all_0_4_4, in(all_29_1_23, all_0_4_4) = 0, yields:
% 5.34/2.07 | (51) ? [v0] : ((v0 = 0 & in(all_29_1_23, all_0_5_5) = 0) | (v0 = 0 & in(all_29_1_23, all_0_7_7) = 0))
% 5.34/2.07 |
% 5.34/2.07 | Instantiating formula (3) with all_29_0_22, all_29_1_23, all_0_6_6, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_6_6) = 0, in(all_29_1_23, all_0_6_6) = all_29_0_22, yields:
% 5.34/2.07 | (52) all_29_0_22 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_29_1_23, all_0_5_5) = v0)
% 5.34/2.07 |
% 5.34/2.07 | Instantiating formula (3) with all_29_0_22, all_29_1_23, all_0_6_6, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_6_6) = 0, in(all_29_1_23, all_0_6_6) = all_29_0_22, yields:
% 5.34/2.07 | (53) all_29_0_22 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_29_1_23, all_0_7_7) = v0)
% 5.34/2.07 |
% 5.34/2.07 | Instantiating (51) with all_40_0_26 yields:
% 5.34/2.07 | (54) (all_40_0_26 = 0 & in(all_29_1_23, all_0_5_5) = 0) | (all_40_0_26 = 0 & in(all_29_1_23, all_0_7_7) = 0)
% 5.34/2.07 |
% 5.34/2.07 +-Applying beta-rule and splitting (52), into two cases.
% 5.34/2.07 |-Branch one:
% 5.34/2.07 | (55) all_29_0_22 = 0
% 5.34/2.07 |
% 5.34/2.07 | Equations (55) can reduce 48 to:
% 5.34/2.07 | (44) $false
% 5.34/2.07 |
% 5.34/2.07 |-The branch is then unsatisfiable
% 5.34/2.07 |-Branch two:
% 5.34/2.07 | (48) ~ (all_29_0_22 = 0)
% 5.34/2.07 | (58) ? [v0] : ( ~ (v0 = 0) & in(all_29_1_23, all_0_5_5) = v0)
% 5.34/2.07 |
% 5.34/2.07 | Instantiating (58) with all_47_0_29 yields:
% 5.34/2.07 | (59) ~ (all_47_0_29 = 0) & in(all_29_1_23, all_0_5_5) = all_47_0_29
% 5.34/2.07 |
% 5.34/2.07 | Applying alpha-rule on (59) yields:
% 5.34/2.07 | (60) ~ (all_47_0_29 = 0)
% 5.34/2.07 | (61) in(all_29_1_23, all_0_5_5) = all_47_0_29
% 5.34/2.07 |
% 5.34/2.07 +-Applying beta-rule and splitting (53), into two cases.
% 5.34/2.07 |-Branch one:
% 5.34/2.07 | (55) all_29_0_22 = 0
% 5.34/2.07 |
% 5.34/2.07 | Equations (55) can reduce 48 to:
% 5.34/2.07 | (44) $false
% 5.34/2.07 |
% 5.34/2.07 |-The branch is then unsatisfiable
% 5.34/2.07 |-Branch two:
% 5.34/2.07 | (48) ~ (all_29_0_22 = 0)
% 5.34/2.07 | (65) ? [v0] : ( ~ (v0 = 0) & in(all_29_1_23, all_0_7_7) = v0)
% 5.34/2.07 |
% 5.34/2.07 | Instantiating (65) with all_52_0_30 yields:
% 5.34/2.07 | (66) ~ (all_52_0_30 = 0) & in(all_29_1_23, all_0_7_7) = all_52_0_30
% 5.34/2.07 |
% 5.34/2.07 | Applying alpha-rule on (66) yields:
% 5.34/2.07 | (67) ~ (all_52_0_30 = 0)
% 5.34/2.07 | (68) in(all_29_1_23, all_0_7_7) = all_52_0_30
% 5.34/2.07 |
% 5.34/2.07 +-Applying beta-rule and splitting (54), into two cases.
% 5.34/2.07 |-Branch one:
% 5.34/2.07 | (69) all_40_0_26 = 0 & in(all_29_1_23, all_0_5_5) = 0
% 5.34/2.07 |
% 5.34/2.07 | Applying alpha-rule on (69) yields:
% 5.34/2.07 | (70) all_40_0_26 = 0
% 5.34/2.07 | (71) in(all_29_1_23, all_0_5_5) = 0
% 5.34/2.07 |
% 5.34/2.07 | Instantiating formula (9) with all_29_1_23, all_0_5_5, 0, all_47_0_29 and discharging atoms in(all_29_1_23, all_0_5_5) = all_47_0_29, in(all_29_1_23, all_0_5_5) = 0, yields:
% 5.34/2.07 | (72) all_47_0_29 = 0
% 5.34/2.07 |
% 5.34/2.07 | Equations (72) can reduce 60 to:
% 5.34/2.07 | (44) $false
% 5.34/2.07 |
% 5.34/2.07 |-The branch is then unsatisfiable
% 5.34/2.07 |-Branch two:
% 5.34/2.07 | (74) all_40_0_26 = 0 & in(all_29_1_23, all_0_7_7) = 0
% 5.34/2.07 |
% 5.34/2.07 | Applying alpha-rule on (74) yields:
% 5.34/2.07 | (70) all_40_0_26 = 0
% 5.34/2.07 | (76) in(all_29_1_23, all_0_7_7) = 0
% 5.34/2.07 |
% 5.34/2.07 | Instantiating formula (9) with all_29_1_23, all_0_7_7, 0, all_52_0_30 and discharging atoms in(all_29_1_23, all_0_7_7) = all_52_0_30, in(all_29_1_23, all_0_7_7) = 0, yields:
% 5.34/2.07 | (77) all_52_0_30 = 0
% 5.34/2.07 |
% 5.34/2.07 | Equations (77) can reduce 67 to:
% 5.34/2.07 | (44) $false
% 5.34/2.07 |
% 5.34/2.07 |-The branch is then unsatisfiable
% 5.34/2.07 % SZS output end Proof for theBenchmark
% 5.34/2.07
% 5.34/2.07 1431ms
%------------------------------------------------------------------------------