TSTP Solution File: GRP775+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GRP775+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n006.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 : Sat Jul 16 08:43:56 EDT 2022
% Result : Theorem 12.36s 3.60s
% Output : Proof 41.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP775+1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n006.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 : Tue Jun 14 13:25:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.60/0.58 ____ _
% 0.60/0.58 ___ / __ \_____(_)___ ________ __________
% 0.60/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.60/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.60/0.58
% 0.60/0.58 A Theorem Prover for First-Order Logic
% 0.60/0.58 (ePrincess v.1.0)
% 0.60/0.58
% 0.60/0.58 (c) Philipp Rümmer, 2009-2015
% 0.60/0.58 (c) Peter Backeman, 2014-2015
% 0.60/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.58 Bug reports to peter@backeman.se
% 0.60/0.58
% 0.60/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.58
% 0.60/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.60/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.34/0.87 Prover 0: Preprocessing ...
% 1.77/1.06 Prover 0: Constructing countermodel ...
% 9.63/2.99 Prover 0: gave up
% 9.63/2.99 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 9.63/3.01 Prover 1: Preprocessing ...
% 10.10/3.04 Prover 1: Constructing countermodel ...
% 10.66/3.17 Prover 1: gave up
% 10.66/3.17 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 10.66/3.19 Prover 2: Preprocessing ...
% 10.66/3.23 Prover 2: Warning: ignoring some quantifiers
% 10.66/3.24 Prover 2: Constructing countermodel ...
% 12.36/3.60 Prover 2: proved (427ms)
% 12.36/3.60
% 12.36/3.60 No countermodel exists, formula is valid
% 12.36/3.60 % SZS status Theorem for theBenchmark
% 12.36/3.60
% 12.36/3.60 Generating proof ... Warning: ignoring some quantifiers
% 40.75/14.08 found it (size 557)
% 40.75/14.08
% 40.75/14.08 % SZS output start Proof for theBenchmark
% 40.75/14.08 Assumed formulas after preprocessing and simplification:
% 40.75/14.08 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (d(v0, v1) = v2 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (product(v10, v7) = v11) | ~ (product(v9, v8) = v10) | ? [v12] : (product(v9, v12) = v11 & product(v8, v7) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (product(v9, v10) = v11) | ~ (product(v8, v7) = v10) | ? [v12] : (product(v12, v7) = v11 & product(v9, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (d(v7, v8) = v9) | ~ (r(v7, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & l(v10, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (d(v7, v8) = v9) | ~ (l(v10, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & r(v7, v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (d(v10, v9) = v8) | ~ (d(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (r(v10, v9) = v8) | ~ (r(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (l(v10, v9) = v8) | ~ (l(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (product(v10, v9) = v8) | ~ (product(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (r(v7, v8) = v9) | ? [v10] : (( ~ (v10 = v8) & product(v7, v8) = v10) | ( ~ (v10 = v7) & product(v8, v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (l(v7, v8) = v9) | ? [v10] : (( ~ (v10 = v8) & product(v8, v7) = v10) | ( ~ (v10 = v7) & product(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (product(v8, v7) = v9) | ? [v10] : ((v10 = v8 & v9 = v7 & product(v7, v8) = v8) | ( ~ (v10 = 0) & r(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (product(v8, v7) = v9) | ? [v10] : ((v10 = v7 & v9 = v8 & product(v7, v8) = v7) | ( ~ (v10 = 0) & l(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (product(v7, v8) = v9) | ? [v10] : ((v10 = v8 & v9 = v7 & product(v8, v7) = v8) | ( ~ (v10 = 0) & l(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (product(v7, v8) = v9) | ? [v10] : ((v10 = v7 & v9 = v8 & product(v8, v7) = v7) | ( ~ (v10 = 0) & r(v7, v8) = v10))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (product(v7, v7) = v8)) & ! [v7] : ! [v8] : ( ~ (d(v7, v8) = 0) | ? [v9] : (r(v7, v9) = 0 & l(v9, v8) = 0)) & ! [v7] : ! [v8] : ( ~ (r(v7, v8) = 0) | (product(v8, v7) = v7 & product(v7, v8) = v8)) & ! [v7] : ! [v8] : ( ~ (l(v7, v8) = 0) | (product(v8, v7) = v8 & product(v7, v8) = v7)) & ! [v7] : ! [v8] : ( ~ (product(v8, v7) = v8) | ? [v9] : ((v9 = 0 & l(v7, v8) = 0) | ( ~ (v9 = v7) & product(v7, v8) = v9))) & ! [v7] : ! [v8] : ( ~ (product(v8, v7) = v7) | ? [v9] : ((v9 = 0 & r(v7, v8) = 0) | ( ~ (v9 = v8) & product(v7, v8) = v9))) & ! [v7] : ! [v8] : ( ~ (product(v7, v8) = v8) | ? [v9] : ((v9 = 0 & r(v7, v8) = 0) | ( ~ (v9 = v7) & product(v8, v7) = v9))) & ! [v7] : ! [v8] : ( ~ (product(v7, v8) = v7) | ? [v9] : ((v9 = 0 & l(v7, v8) = 0) | ( ~ (v9 = v8) & product(v8, v7) = v9))) & ? [v7] : ? [v8] : ? [v9] : d(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : r(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : l(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : product(v8, v7) = v9 & ((v6 = v1 & v4 = v0 & ~ (v2 = 0) & product(v1, v5) = v1 & product(v1, v0) = v3 & product(v0, v3) = v0 & product(v0, v1) = v5) | (v2 = 0 & (( ~ (v6 = v1) & product(v1, v5) = v6 & product(v0, v1) = v5) | ( ~ (v4 = v0) & product(v1, v0) = v3 & product(v0, v3) = v4)))))
% 40.88/14.12 | 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:
% 40.88/14.12 | (1) d(all_0_6_6, all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (product(v3, v0) = v4) | ~ (product(v2, v1) = v3) | ? [v5] : (product(v2, v5) = v4 & product(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (product(v2, v3) = v4) | ~ (product(v1, v0) = v3) | ? [v5] : (product(v5, v0) = v4 & product(v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (d(v0, v1) = v2) | ~ (r(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & l(v3, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (d(v0, v1) = v2) | ~ (l(v3, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & r(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (d(v3, v2) = v1) | ~ (d(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (r(v3, v2) = v1) | ~ (r(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (l(v3, v2) = v1) | ~ (l(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (product(v3, v2) = v1) | ~ (product(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (r(v0, v1) = v2) | ? [v3] : (( ~ (v3 = v1) & product(v0, v1) = v3) | ( ~ (v3 = v0) & product(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (l(v0, v1) = v2) | ? [v3] : (( ~ (v3 = v1) & product(v1, v0) = v3) | ( ~ (v3 = v0) & product(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (product(v1, v0) = v2) | ? [v3] : ((v3 = v1 & v2 = v0 & product(v0, v1) = v1) | ( ~ (v3 = 0) & r(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (product(v1, v0) = v2) | ? [v3] : ((v3 = v0 & v2 = v1 & product(v0, v1) = v0) | ( ~ (v3 = 0) & l(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (product(v0, v1) = v2) | ? [v3] : ((v3 = v1 & v2 = v0 & product(v1, v0) = v1) | ( ~ (v3 = 0) & l(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (product(v0, v1) = v2) | ? [v3] : ((v3 = v0 & v2 = v1 & product(v1, v0) = v0) | ( ~ (v3 = 0) & r(v0, v1) = v3))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (product(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (d(v0, v1) = 0) | ? [v2] : (r(v0, v2) = 0 & l(v2, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (r(v0, v1) = 0) | (product(v1, v0) = v0 & product(v0, v1) = v1)) & ! [v0] : ! [v1] : ( ~ (l(v0, v1) = 0) | (product(v1, v0) = v1 & product(v0, v1) = v0)) & ! [v0] : ! [v1] : ( ~ (product(v1, v0) = v1) | ? [v2] : ((v2 = 0 & l(v0, v1) = 0) | ( ~ (v2 = v0) & product(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (product(v1, v0) = v0) | ? [v2] : ((v2 = 0 & r(v0, v1) = 0) | ( ~ (v2 = v1) & product(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (product(v0, v1) = v1) | ? [v2] : ((v2 = 0 & r(v0, v1) = 0) | ( ~ (v2 = v0) & product(v1, v0) = v2))) & ! [v0] : ! [v1] : ( ~ (product(v0, v1) = v0) | ? [v2] : ((v2 = 0 & l(v0, v1) = 0) | ( ~ (v2 = v1) & product(v1, v0) = v2))) & ? [v0] : ? [v1] : ? [v2] : d(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : r(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : l(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : product(v1, v0) = v2 & ((all_0_0_0 = all_0_5_5 & all_0_2_2 = all_0_6_6 & ~ (all_0_4_4 = 0) & product(all_0_5_5, all_0_1_1) = all_0_5_5 & product(all_0_5_5, all_0_6_6) = all_0_3_3 & product(all_0_6_6, all_0_3_3) = all_0_6_6 & product(all_0_6_6, all_0_5_5) = all_0_1_1) | (all_0_4_4 = 0 & (( ~ (all_0_0_0 = all_0_5_5) & product(all_0_5_5, all_0_1_1) = all_0_0_0 & product(all_0_6_6, all_0_5_5) = all_0_1_1) | ( ~ (all_0_2_2 = all_0_6_6) & product(all_0_5_5, all_0_6_6) = all_0_3_3 & product(all_0_6_6, all_0_3_3) = all_0_2_2))))
% 40.88/14.14 |
% 40.88/14.14 | Applying alpha-rule on (1) yields:
% 40.88/14.14 | (2) ! [v0] : ! [v1] : ( ~ (r(v0, v1) = 0) | (product(v1, v0) = v0 & product(v0, v1) = v1))
% 40.88/14.14 | (3) ? [v0] : ? [v1] : ? [v2] : product(v1, v0) = v2
% 40.88/14.14 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (product(v0, v1) = v2) | ? [v3] : ((v3 = v0 & v2 = v1 & product(v1, v0) = v0) | ( ~ (v3 = 0) & r(v0, v1) = v3)))
% 40.88/14.14 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ (product(v0, v0) = v1))
% 40.88/14.14 | (6) ? [v0] : ? [v1] : ? [v2] : r(v1, v0) = v2
% 40.88/14.14 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (l(v0, v1) = v2) | ? [v3] : (( ~ (v3 = v1) & product(v1, v0) = v3) | ( ~ (v3 = v0) & product(v0, v1) = v3)))
% 40.88/14.14 | (8) ? [v0] : ? [v1] : ? [v2] : d(v1, v0) = v2
% 40.88/14.14 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (r(v3, v2) = v1) | ~ (r(v3, v2) = v0))
% 40.88/14.14 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (product(v2, v3) = v4) | ~ (product(v1, v0) = v3) | ? [v5] : (product(v5, v0) = v4 & product(v2, v1) = v5))
% 40.88/14.14 | (11) ? [v0] : ? [v1] : ? [v2] : l(v1, v0) = v2
% 40.88/14.14 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (product(v0, v1) = v2) | ? [v3] : ((v3 = v1 & v2 = v0 & product(v1, v0) = v1) | ( ~ (v3 = 0) & l(v0, v1) = v3)))
% 40.88/14.14 | (13) ! [v0] : ! [v1] : ( ~ (l(v0, v1) = 0) | (product(v1, v0) = v1 & product(v0, v1) = v0))
% 40.88/14.14 | (14) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (r(v0, v1) = v2) | ? [v3] : (( ~ (v3 = v1) & product(v0, v1) = v3) | ( ~ (v3 = v0) & product(v1, v0) = v3)))
% 40.88/14.14 | (15) d(all_0_6_6, all_0_5_5) = all_0_4_4
% 40.88/14.14 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (product(v3, v2) = v1) | ~ (product(v3, v2) = v0))
% 40.88/14.14 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (l(v3, v2) = v1) | ~ (l(v3, v2) = v0))
% 40.88/14.14 | (18) (all_0_0_0 = all_0_5_5 & all_0_2_2 = all_0_6_6 & ~ (all_0_4_4 = 0) & product(all_0_5_5, all_0_1_1) = all_0_5_5 & product(all_0_5_5, all_0_6_6) = all_0_3_3 & product(all_0_6_6, all_0_3_3) = all_0_6_6 & product(all_0_6_6, all_0_5_5) = all_0_1_1) | (all_0_4_4 = 0 & (( ~ (all_0_0_0 = all_0_5_5) & product(all_0_5_5, all_0_1_1) = all_0_0_0 & product(all_0_6_6, all_0_5_5) = all_0_1_1) | ( ~ (all_0_2_2 = all_0_6_6) & product(all_0_5_5, all_0_6_6) = all_0_3_3 & product(all_0_6_6, all_0_3_3) = all_0_2_2)))
% 40.88/14.15 | (19) ! [v0] : ! [v1] : ( ~ (d(v0, v1) = 0) | ? [v2] : (r(v0, v2) = 0 & l(v2, v1) = 0))
% 40.88/14.15 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (product(v1, v0) = v2) | ? [v3] : ((v3 = v0 & v2 = v1 & product(v0, v1) = v0) | ( ~ (v3 = 0) & l(v0, v1) = v3)))
% 40.88/14.15 | (21) ! [v0] : ! [v1] : ( ~ (product(v1, v0) = v0) | ? [v2] : ((v2 = 0 & r(v0, v1) = 0) | ( ~ (v2 = v1) & product(v0, v1) = v2)))
% 40.88/14.15 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (product(v3, v0) = v4) | ~ (product(v2, v1) = v3) | ? [v5] : (product(v2, v5) = v4 & product(v1, v0) = v5))
% 40.88/14.15 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (d(v0, v1) = v2) | ~ (r(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & l(v3, v1) = v4))
% 40.88/14.15 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (d(v3, v2) = v1) | ~ (d(v3, v2) = v0))
% 40.88/14.15 | (25) ! [v0] : ! [v1] : ( ~ (product(v0, v1) = v0) | ? [v2] : ((v2 = 0 & l(v0, v1) = 0) | ( ~ (v2 = v1) & product(v1, v0) = v2)))
% 40.88/14.15 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (product(v1, v0) = v2) | ? [v3] : ((v3 = v1 & v2 = v0 & product(v0, v1) = v1) | ( ~ (v3 = 0) & r(v0, v1) = v3)))
% 40.88/14.15 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (d(v0, v1) = v2) | ~ (l(v3, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & r(v0, v3) = v4))
% 40.88/14.15 | (28) ! [v0] : ! [v1] : ( ~ (product(v0, v1) = v1) | ? [v2] : ((v2 = 0 & r(v0, v1) = 0) | ( ~ (v2 = v0) & product(v1, v0) = v2)))
% 40.88/14.15 | (29) ! [v0] : ! [v1] : ( ~ (product(v1, v0) = v1) | ? [v2] : ((v2 = 0 & l(v0, v1) = 0) | ( ~ (v2 = v0) & product(v0, v1) = v2)))
% 41.19/14.15 |
% 41.19/14.15 +-Applying beta-rule and splitting (18), into two cases.
% 41.19/14.15 |-Branch one:
% 41.19/14.15 | (30) all_0_0_0 = all_0_5_5 & all_0_2_2 = all_0_6_6 & ~ (all_0_4_4 = 0) & product(all_0_5_5, all_0_1_1) = all_0_5_5 & product(all_0_5_5, all_0_6_6) = all_0_3_3 & product(all_0_6_6, all_0_3_3) = all_0_6_6 & product(all_0_6_6, all_0_5_5) = all_0_1_1
% 41.19/14.15 |
% 41.19/14.15 | Applying alpha-rule on (30) yields:
% 41.19/14.15 | (31) all_0_2_2 = all_0_6_6
% 41.19/14.15 | (32) product(all_0_6_6, all_0_5_5) = all_0_1_1
% 41.19/14.15 | (33) ~ (all_0_4_4 = 0)
% 41.19/14.15 | (34) product(all_0_6_6, all_0_3_3) = all_0_6_6
% 41.19/14.15 | (35) product(all_0_5_5, all_0_1_1) = all_0_5_5
% 41.19/14.15 | (36) all_0_0_0 = all_0_5_5
% 41.19/14.15 | (37) product(all_0_5_5, all_0_6_6) = all_0_3_3
% 41.19/14.15 |
% 41.19/14.15 | Instantiating formula (29) with all_0_5_5, all_0_1_1 and discharging atoms product(all_0_5_5, all_0_1_1) = all_0_5_5, yields:
% 41.19/14.15 | (38) ? [v0] : ((v0 = 0 & l(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = all_0_1_1) & product(all_0_1_1, all_0_5_5) = v0))
% 41.19/14.15 |
% 41.19/14.15 | Instantiating formula (25) with all_0_1_1, all_0_5_5 and discharging atoms product(all_0_5_5, all_0_1_1) = all_0_5_5, yields:
% 41.19/14.15 | (39) ? [v0] : ((v0 = 0 & l(all_0_5_5, all_0_1_1) = 0) | ( ~ (v0 = all_0_1_1) & product(all_0_1_1, all_0_5_5) = v0))
% 41.19/14.16 |
% 41.19/14.16 | Instantiating formula (20) with all_0_5_5, all_0_5_5, all_0_1_1 and discharging atoms product(all_0_5_5, all_0_1_1) = all_0_5_5, yields:
% 41.19/14.16 | (40) ? [v0] : ((v0 = all_0_1_1 & product(all_0_1_1, all_0_5_5) = all_0_1_1) | ( ~ (v0 = 0) & l(all_0_1_1, all_0_5_5) = v0))
% 41.19/14.16 |
% 41.19/14.16 | Instantiating formula (12) with all_0_5_5, all_0_1_1, all_0_5_5 and discharging atoms product(all_0_5_5, all_0_1_1) = all_0_5_5, yields:
% 41.19/14.16 | (41) ? [v0] : ((v0 = all_0_1_1 & product(all_0_1_1, all_0_5_5) = all_0_1_1) | ( ~ (v0 = 0) & l(all_0_5_5, all_0_1_1) = v0))
% 41.19/14.16 |
% 41.19/14.16 | Instantiating formula (22) with all_0_3_3, all_0_5_5, all_0_5_5, all_0_1_1, all_0_6_6 and discharging atoms product(all_0_5_5, all_0_1_1) = all_0_5_5, product(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 41.19/14.16 | (42) ? [v0] : (product(all_0_1_1, all_0_6_6) = v0 & product(all_0_5_5, v0) = all_0_3_3)
% 41.19/14.16 |
% 41.19/14.16 | Instantiating formula (10) with all_0_6_6, all_0_3_3, all_0_6_6, all_0_5_5, all_0_6_6 and discharging atoms product(all_0_5_5, all_0_6_6) = all_0_3_3, product(all_0_6_6, all_0_3_3) = all_0_6_6, yields:
% 41.19/14.16 | (43) ? [v0] : (product(v0, all_0_6_6) = all_0_6_6 & product(all_0_6_6, all_0_5_5) = v0)
% 41.19/14.16 |
% 41.19/14.16 | Instantiating formula (10) with all_0_3_3, all_0_6_6, all_0_5_5, all_0_6_6, all_0_3_3 and discharging atoms product(all_0_5_5, all_0_6_6) = all_0_3_3, product(all_0_6_6, all_0_3_3) = all_0_6_6, yields:
% 41.19/14.16 | (44) ? [v0] : (product(v0, all_0_3_3) = all_0_3_3 & product(all_0_5_5, all_0_6_6) = v0)
% 41.19/14.16 |
% 41.19/14.16 | Instantiating formula (22) with all_0_6_6, all_0_6_6, all_0_6_6, all_0_3_3, all_0_3_3 and discharging atoms product(all_0_6_6, all_0_3_3) = all_0_6_6, yields:
% 41.19/14.16 | (45) ? [v0] : (product(all_0_3_3, all_0_3_3) = v0 & product(all_0_6_6, v0) = all_0_6_6)
% 41.19/14.16 |
% 41.19/14.16 | Instantiating formula (29) with all_0_6_6, all_0_3_3 and discharging atoms product(all_0_6_6, all_0_3_3) = all_0_6_6, yields:
% 41.19/14.16 | (46) ? [v0] : ((v0 = 0 & l(all_0_3_3, all_0_6_6) = 0) | ( ~ (v0 = all_0_3_3) & product(all_0_3_3, all_0_6_6) = v0))
% 41.19/14.16 |
% 41.19/14.16 | Instantiating formula (25) with all_0_3_3, all_0_6_6 and discharging atoms product(all_0_6_6, all_0_3_3) = all_0_6_6, yields:
% 41.19/14.16 | (47) ? [v0] : ((v0 = 0 & l(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = all_0_3_3) & product(all_0_3_3, all_0_6_6) = v0))
% 41.19/14.16 |
% 41.19/14.16 | Instantiating formula (20) with all_0_6_6, all_0_6_6, all_0_3_3 and discharging atoms product(all_0_6_6, all_0_3_3) = all_0_6_6, yields:
% 41.19/14.16 | (48) ? [v0] : ((v0 = all_0_3_3 & product(all_0_3_3, all_0_6_6) = all_0_3_3) | ( ~ (v0 = 0) & l(all_0_3_3, all_0_6_6) = v0))
% 41.19/14.16 |
% 41.19/14.16 | Instantiating formula (12) with all_0_6_6, all_0_3_3, all_0_6_6 and discharging atoms product(all_0_6_6, all_0_3_3) = all_0_6_6, yields:
% 41.19/14.16 | (49) ? [v0] : ((v0 = all_0_3_3 & product(all_0_3_3, all_0_6_6) = all_0_3_3) | ( ~ (v0 = 0) & l(all_0_6_6, all_0_3_3) = v0))
% 41.19/14.16 |
% 41.19/14.16 | Instantiating formula (10) with all_0_1_1, all_0_5_5, all_0_6_6, all_0_5_5, all_0_1_1 and discharging atoms product(all_0_5_5, all_0_1_1) = all_0_5_5, product(all_0_6_6, all_0_5_5) = all_0_1_1, yields:
% 41.24/14.16 | (50) ? [v0] : (product(v0, all_0_1_1) = all_0_1_1 & product(all_0_6_6, all_0_5_5) = v0)
% 41.24/14.16 |
% 41.24/14.16 | Instantiating formula (10) with all_0_5_5, all_0_1_1, all_0_5_5, all_0_6_6, all_0_5_5 and discharging atoms product(all_0_5_5, all_0_1_1) = all_0_5_5, product(all_0_6_6, all_0_5_5) = all_0_1_1, yields:
% 41.24/14.16 | (51) ? [v0] : (product(v0, all_0_5_5) = all_0_5_5 & product(all_0_5_5, all_0_6_6) = v0)
% 41.24/14.16 |
% 41.24/14.16 | Instantiating formula (22) with all_0_1_1, all_0_6_6, all_0_6_6, all_0_3_3, all_0_5_5 and discharging atoms product(all_0_6_6, all_0_3_3) = all_0_6_6, product(all_0_6_6, all_0_5_5) = all_0_1_1, yields:
% 41.24/14.16 | (52) ? [v0] : (product(all_0_3_3, all_0_5_5) = v0 & product(all_0_6_6, v0) = all_0_1_1)
% 41.24/14.16 |
% 41.24/14.16 | Instantiating (46) with all_27_0_23 yields:
% 41.24/14.16 | (53) (all_27_0_23 = 0 & l(all_0_3_3, all_0_6_6) = 0) | ( ~ (all_27_0_23 = all_0_3_3) & product(all_0_3_3, all_0_6_6) = all_27_0_23)
% 41.24/14.16 |
% 41.24/14.16 | Instantiating (45) with all_28_0_24 yields:
% 41.24/14.16 | (54) product(all_0_3_3, all_0_3_3) = all_28_0_24 & product(all_0_6_6, all_28_0_24) = all_0_6_6
% 41.24/14.16 |
% 41.24/14.16 | Applying alpha-rule on (54) yields:
% 41.24/14.16 | (55) product(all_0_3_3, all_0_3_3) = all_28_0_24
% 41.24/14.16 | (56) product(all_0_6_6, all_28_0_24) = all_0_6_6
% 41.24/14.16 |
% 41.24/14.16 | Instantiating (44) with all_30_0_25 yields:
% 41.24/14.16 | (57) product(all_30_0_25, all_0_3_3) = all_0_3_3 & product(all_0_5_5, all_0_6_6) = all_30_0_25
% 41.24/14.16 |
% 41.24/14.16 | Applying alpha-rule on (57) yields:
% 41.24/14.16 | (58) product(all_30_0_25, all_0_3_3) = all_0_3_3
% 41.24/14.16 | (59) product(all_0_5_5, all_0_6_6) = all_30_0_25
% 41.24/14.16 |
% 41.24/14.16 | Instantiating (43) with all_32_0_26 yields:
% 41.24/14.16 | (60) product(all_32_0_26, all_0_6_6) = all_0_6_6 & product(all_0_6_6, all_0_5_5) = all_32_0_26
% 41.24/14.16 |
% 41.24/14.16 | Applying alpha-rule on (60) yields:
% 41.24/14.16 | (61) product(all_32_0_26, all_0_6_6) = all_0_6_6
% 41.24/14.16 | (62) product(all_0_6_6, all_0_5_5) = all_32_0_26
% 41.24/14.16 |
% 41.24/14.16 | Instantiating (42) with all_34_0_27 yields:
% 41.24/14.16 | (63) product(all_0_1_1, all_0_6_6) = all_34_0_27 & product(all_0_5_5, all_34_0_27) = all_0_3_3
% 41.24/14.16 |
% 41.24/14.16 | Applying alpha-rule on (63) yields:
% 41.24/14.16 | (64) product(all_0_1_1, all_0_6_6) = all_34_0_27
% 41.24/14.16 | (65) product(all_0_5_5, all_34_0_27) = all_0_3_3
% 41.24/14.16 |
% 41.24/14.16 | Instantiating (41) with all_36_0_28 yields:
% 41.24/14.16 | (66) (all_36_0_28 = all_0_1_1 & product(all_0_1_1, all_0_5_5) = all_0_1_1) | ( ~ (all_36_0_28 = 0) & l(all_0_5_5, all_0_1_1) = all_36_0_28)
% 41.24/14.16 |
% 41.24/14.16 | Instantiating (40) with all_37_0_29 yields:
% 41.24/14.16 | (67) (all_37_0_29 = all_0_1_1 & product(all_0_1_1, all_0_5_5) = all_0_1_1) | ( ~ (all_37_0_29 = 0) & l(all_0_1_1, all_0_5_5) = all_37_0_29)
% 41.24/14.17 |
% 41.24/14.17 | Instantiating (39) with all_40_0_32 yields:
% 41.24/14.17 | (68) (all_40_0_32 = 0 & l(all_0_5_5, all_0_1_1) = 0) | ( ~ (all_40_0_32 = all_0_1_1) & product(all_0_1_1, all_0_5_5) = all_40_0_32)
% 41.24/14.17 |
% 41.24/14.17 | Instantiating (38) with all_41_0_33 yields:
% 41.24/14.17 | (69) (all_41_0_33 = 0 & l(all_0_1_1, all_0_5_5) = 0) | ( ~ (all_41_0_33 = all_0_1_1) & product(all_0_1_1, all_0_5_5) = all_41_0_33)
% 41.24/14.17 |
% 41.24/14.17 | Instantiating (52) with all_42_0_34 yields:
% 41.24/14.17 | (70) product(all_0_3_3, all_0_5_5) = all_42_0_34 & product(all_0_6_6, all_42_0_34) = all_0_1_1
% 41.24/14.17 |
% 41.24/14.17 | Applying alpha-rule on (70) yields:
% 41.24/14.17 | (71) product(all_0_3_3, all_0_5_5) = all_42_0_34
% 41.24/14.17 | (72) product(all_0_6_6, all_42_0_34) = all_0_1_1
% 41.24/14.17 |
% 41.24/14.17 | Instantiating (50) with all_44_0_35 yields:
% 41.24/14.17 | (73) product(all_44_0_35, all_0_1_1) = all_0_1_1 & product(all_0_6_6, all_0_5_5) = all_44_0_35
% 41.24/14.17 |
% 41.24/14.17 | Applying alpha-rule on (73) yields:
% 41.24/14.17 | (74) product(all_44_0_35, all_0_1_1) = all_0_1_1
% 41.24/14.17 | (75) product(all_0_6_6, all_0_5_5) = all_44_0_35
% 41.24/14.17 |
% 41.24/14.17 | Instantiating (51) with all_49_0_38 yields:
% 41.24/14.17 | (76) product(all_49_0_38, all_0_5_5) = all_0_5_5 & product(all_0_5_5, all_0_6_6) = all_49_0_38
% 41.24/14.17 |
% 41.24/14.17 | Applying alpha-rule on (76) yields:
% 41.24/14.17 | (77) product(all_49_0_38, all_0_5_5) = all_0_5_5
% 41.24/14.17 | (78) product(all_0_5_5, all_0_6_6) = all_49_0_38
% 41.24/14.17 |
% 41.24/14.17 | Instantiating (49) with all_54_0_42 yields:
% 41.24/14.17 | (79) (all_54_0_42 = all_0_3_3 & product(all_0_3_3, all_0_6_6) = all_0_3_3) | ( ~ (all_54_0_42 = 0) & l(all_0_6_6, all_0_3_3) = all_54_0_42)
% 41.24/14.17 |
% 41.24/14.17 | Instantiating (48) with all_55_0_43 yields:
% 41.24/14.17 | (80) (all_55_0_43 = all_0_3_3 & product(all_0_3_3, all_0_6_6) = all_0_3_3) | ( ~ (all_55_0_43 = 0) & l(all_0_3_3, all_0_6_6) = all_55_0_43)
% 41.24/14.17 |
% 41.24/14.17 | Instantiating (47) with all_57_0_45 yields:
% 41.24/14.17 | (81) (all_57_0_45 = 0 & l(all_0_6_6, all_0_3_3) = 0) | ( ~ (all_57_0_45 = all_0_3_3) & product(all_0_3_3, all_0_6_6) = all_57_0_45)
% 41.24/14.17 |
% 41.24/14.17 | Instantiating formula (5) with all_28_0_24, all_0_3_3 and discharging atoms product(all_0_3_3, all_0_3_3) = all_28_0_24, yields:
% 41.24/14.17 | (82) all_28_0_24 = all_0_3_3
% 41.24/14.17 |
% 41.24/14.17 | Instantiating formula (16) with all_0_5_5, all_0_6_6, all_49_0_38, all_0_3_3 and discharging atoms product(all_0_5_5, all_0_6_6) = all_49_0_38, product(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 41.24/14.17 | (83) all_49_0_38 = all_0_3_3
% 41.24/14.17 |
% 41.24/14.17 | Instantiating formula (16) with all_0_5_5, all_0_6_6, all_30_0_25, all_49_0_38 and discharging atoms product(all_0_5_5, all_0_6_6) = all_49_0_38, product(all_0_5_5, all_0_6_6) = all_30_0_25, yields:
% 41.24/14.17 | (84) all_49_0_38 = all_30_0_25
% 41.24/14.17 |
% 41.24/14.17 | Instantiating formula (16) with all_0_6_6, all_0_5_5, all_44_0_35, all_0_1_1 and discharging atoms product(all_0_6_6, all_0_5_5) = all_44_0_35, product(all_0_6_6, all_0_5_5) = all_0_1_1, yields:
% 41.24/14.17 | (85) all_44_0_35 = all_0_1_1
% 41.24/14.17 |
% 41.24/14.17 | Instantiating formula (16) with all_0_6_6, all_0_5_5, all_32_0_26, all_44_0_35 and discharging atoms product(all_0_6_6, all_0_5_5) = all_44_0_35, product(all_0_6_6, all_0_5_5) = all_32_0_26, yields:
% 41.24/14.17 | (86) all_44_0_35 = all_32_0_26
% 41.24/14.17 |
% 41.24/14.17 | Combining equations (83,84) yields a new equation:
% 41.24/14.17 | (87) all_30_0_25 = all_0_3_3
% 41.24/14.17 |
% 41.24/14.17 | Combining equations (86,85) yields a new equation:
% 41.24/14.17 | (88) all_32_0_26 = all_0_1_1
% 41.24/14.17 |
% 41.24/14.17 | Simplifying 88 yields:
% 41.24/14.17 | (89) all_32_0_26 = all_0_1_1
% 41.24/14.17 |
% 41.24/14.17 | Combining equations (87,84) yields a new equation:
% 41.24/14.17 | (83) all_49_0_38 = all_0_3_3
% 41.24/14.17 |
% 41.24/14.17 | From (83) and (77) follows:
% 41.24/14.17 | (91) product(all_0_3_3, all_0_5_5) = all_0_5_5
% 41.24/14.17 |
% 41.24/14.17 | From (89) and (61) follows:
% 41.24/14.17 | (92) product(all_0_1_1, all_0_6_6) = all_0_6_6
% 41.24/14.17 |
% 41.24/14.17 | From (82) and (56) follows:
% 41.24/14.17 | (34) product(all_0_6_6, all_0_3_3) = all_0_6_6
% 41.24/14.17 |
% 41.24/14.17 | Instantiating formula (16) with all_0_1_1, all_0_6_6, all_0_6_6, all_34_0_27 and discharging atoms product(all_0_1_1, all_0_6_6) = all_34_0_27, product(all_0_1_1, all_0_6_6) = all_0_6_6, yields:
% 41.24/14.17 | (94) all_34_0_27 = all_0_6_6
% 41.24/14.17 |
% 41.24/14.17 | Instantiating formula (16) with all_0_3_3, all_0_5_5, all_0_5_5, all_42_0_34 and discharging atoms product(all_0_3_3, all_0_5_5) = all_42_0_34, product(all_0_3_3, all_0_5_5) = all_0_5_5, yields:
% 41.24/14.17 | (95) all_42_0_34 = all_0_5_5
% 41.24/14.17 |
% 41.24/14.17 | From (94) and (64) follows:
% 41.24/14.17 | (92) product(all_0_1_1, all_0_6_6) = all_0_6_6
% 41.24/14.17 |
% 41.24/14.17 | From (95) and (71) follows:
% 41.24/14.17 | (91) product(all_0_3_3, all_0_5_5) = all_0_5_5
% 41.24/14.17 |
% 41.24/14.17 | From (94) and (65) follows:
% 41.24/14.17 | (37) product(all_0_5_5, all_0_6_6) = all_0_3_3
% 41.24/14.17 |
% 41.24/14.17 | From (95) and (72) follows:
% 41.24/14.17 | (32) product(all_0_6_6, all_0_5_5) = all_0_1_1
% 41.24/14.17 |
% 41.24/14.17 | Instantiating formula (21) with all_0_1_1, all_0_6_6 and discharging atoms product(all_0_1_1, all_0_6_6) = all_0_6_6, yields:
% 41.24/14.17 | (100) ? [v0] : ((v0 = 0 & r(all_0_6_6, all_0_1_1) = 0) | ( ~ (v0 = all_0_1_1) & product(all_0_6_6, all_0_1_1) = v0))
% 41.24/14.17 |
% 41.24/14.17 | Instantiating formula (28) with all_0_6_6, all_0_1_1 and discharging atoms product(all_0_1_1, all_0_6_6) = all_0_6_6, yields:
% 41.24/14.17 | (101) ? [v0] : ((v0 = 0 & r(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = all_0_1_1) & product(all_0_6_6, all_0_1_1) = v0))
% 41.24/14.17 |
% 41.24/14.17 | Instantiating formula (4) with all_0_6_6, all_0_6_6, all_0_1_1 and discharging atoms product(all_0_1_1, all_0_6_6) = all_0_6_6, yields:
% 41.24/14.17 | (102) ? [v0] : ((v0 = all_0_1_1 & product(all_0_6_6, all_0_1_1) = all_0_1_1) | ( ~ (v0 = 0) & r(all_0_1_1, all_0_6_6) = v0))
% 41.24/14.17 |
% 41.24/14.17 | Instantiating formula (21) with all_0_3_3, all_0_5_5 and discharging atoms product(all_0_3_3, all_0_5_5) = all_0_5_5, yields:
% 41.24/14.17 | (103) ? [v0] : ((v0 = 0 & r(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = all_0_3_3) & product(all_0_5_5, all_0_3_3) = v0))
% 41.24/14.17 |
% 41.24/14.17 | Instantiating formula (28) with all_0_5_5, all_0_3_3 and discharging atoms product(all_0_3_3, all_0_5_5) = all_0_5_5, yields:
% 41.24/14.17 | (104) ? [v0] : ((v0 = 0 & r(all_0_3_3, all_0_5_5) = 0) | ( ~ (v0 = all_0_3_3) & product(all_0_5_5, all_0_3_3) = v0))
% 41.24/14.17 |
% 41.24/14.17 | Instantiating formula (26) with all_0_5_5, all_0_3_3, all_0_5_5 and discharging atoms product(all_0_3_3, all_0_5_5) = all_0_5_5, yields:
% 41.24/14.17 | (105) ? [v0] : ((v0 = all_0_3_3 & product(all_0_5_5, all_0_3_3) = all_0_3_3) | ( ~ (v0 = 0) & r(all_0_5_5, all_0_3_3) = v0))
% 41.24/14.17 |
% 41.24/14.17 | Instantiating formula (4) with all_0_5_5, all_0_5_5, all_0_3_3 and discharging atoms product(all_0_3_3, all_0_5_5) = all_0_5_5, yields:
% 41.24/14.18 | (106) ? [v0] : ((v0 = all_0_3_3 & product(all_0_5_5, all_0_3_3) = all_0_3_3) | ( ~ (v0 = 0) & r(all_0_3_3, all_0_5_5) = v0))
% 41.24/14.18 |
% 41.24/14.18 | Instantiating (106) with all_72_0_47 yields:
% 41.24/14.18 | (107) (all_72_0_47 = all_0_3_3 & product(all_0_5_5, all_0_3_3) = all_0_3_3) | ( ~ (all_72_0_47 = 0) & r(all_0_3_3, all_0_5_5) = all_72_0_47)
% 41.24/14.18 |
% 41.24/14.18 | Instantiating (105) with all_74_0_49 yields:
% 41.24/14.18 | (108) (all_74_0_49 = all_0_3_3 & product(all_0_5_5, all_0_3_3) = all_0_3_3) | ( ~ (all_74_0_49 = 0) & r(all_0_5_5, all_0_3_3) = all_74_0_49)
% 41.24/14.18 |
% 41.24/14.18 | Instantiating (104) with all_76_0_51 yields:
% 41.24/14.18 | (109) (all_76_0_51 = 0 & r(all_0_3_3, all_0_5_5) = 0) | ( ~ (all_76_0_51 = all_0_3_3) & product(all_0_5_5, all_0_3_3) = all_76_0_51)
% 41.24/14.18 |
% 41.24/14.18 | Instantiating (103) with all_77_0_52 yields:
% 41.24/14.18 | (110) (all_77_0_52 = 0 & r(all_0_5_5, all_0_3_3) = 0) | ( ~ (all_77_0_52 = all_0_3_3) & product(all_0_5_5, all_0_3_3) = all_77_0_52)
% 41.24/14.18 |
% 41.24/14.18 | Instantiating (101) with all_86_0_61 yields:
% 41.24/14.18 | (111) (all_86_0_61 = 0 & r(all_0_1_1, all_0_6_6) = 0) | ( ~ (all_86_0_61 = all_0_1_1) & product(all_0_6_6, all_0_1_1) = all_86_0_61)
% 41.24/14.18 |
% 41.24/14.18 | Instantiating (102) with all_87_0_62 yields:
% 41.24/14.18 | (112) (all_87_0_62 = all_0_1_1 & product(all_0_6_6, all_0_1_1) = all_0_1_1) | ( ~ (all_87_0_62 = 0) & r(all_0_1_1, all_0_6_6) = all_87_0_62)
% 41.24/14.18 |
% 41.24/14.18 | Instantiating (100) with all_88_0_63 yields:
% 41.24/14.18 | (113) (all_88_0_63 = 0 & r(all_0_6_6, all_0_1_1) = 0) | ( ~ (all_88_0_63 = all_0_1_1) & product(all_0_6_6, all_0_1_1) = all_88_0_63)
% 41.24/14.18 |
% 41.24/14.18 +-Applying beta-rule and splitting (53), into two cases.
% 41.24/14.18 |-Branch one:
% 41.24/14.18 | (114) all_27_0_23 = 0 & l(all_0_3_3, all_0_6_6) = 0
% 41.24/14.18 |
% 41.24/14.18 | Applying alpha-rule on (114) yields:
% 41.24/14.18 | (115) all_27_0_23 = 0
% 41.24/14.18 | (116) l(all_0_3_3, all_0_6_6) = 0
% 41.24/14.18 |
% 41.24/14.18 +-Applying beta-rule and splitting (80), into two cases.
% 41.24/14.18 |-Branch one:
% 41.24/14.18 | (117) all_55_0_43 = all_0_3_3 & product(all_0_3_3, all_0_6_6) = all_0_3_3
% 41.24/14.18 |
% 41.24/14.18 | Applying alpha-rule on (117) yields:
% 41.24/14.18 | (118) all_55_0_43 = all_0_3_3
% 41.24/14.18 | (119) product(all_0_3_3, all_0_6_6) = all_0_3_3
% 41.24/14.18 |
% 41.24/14.18 +-Applying beta-rule and splitting (81), into two cases.
% 41.24/14.18 |-Branch one:
% 41.24/14.18 | (120) all_57_0_45 = 0 & l(all_0_6_6, all_0_3_3) = 0
% 41.24/14.18 |
% 41.24/14.18 | Applying alpha-rule on (120) yields:
% 41.24/14.18 | (121) all_57_0_45 = 0
% 41.24/14.18 | (122) l(all_0_6_6, all_0_3_3) = 0
% 41.24/14.18 |
% 41.24/14.18 +-Applying beta-rule and splitting (79), into two cases.
% 41.24/14.18 |-Branch one:
% 41.24/14.18 | (123) all_54_0_42 = all_0_3_3 & product(all_0_3_3, all_0_6_6) = all_0_3_3
% 41.24/14.18 |
% 41.24/14.18 | Applying alpha-rule on (123) yields:
% 41.24/14.18 | (124) all_54_0_42 = all_0_3_3
% 41.24/14.18 | (119) product(all_0_3_3, all_0_6_6) = all_0_3_3
% 41.24/14.18 |
% 41.24/14.18 | Instantiating formula (10) with all_0_3_3, all_0_6_6, all_0_3_3, all_0_1_1, all_0_6_6 and discharging atoms product(all_0_1_1, all_0_6_6) = all_0_6_6, product(all_0_3_3, all_0_6_6) = all_0_3_3, yields:
% 41.24/14.18 | (126) ? [v0] : (product(v0, all_0_6_6) = all_0_3_3 & product(all_0_3_3, all_0_1_1) = v0)
% 41.24/14.18 |
% 41.24/14.18 | Instantiating formula (22) with all_0_5_5, all_0_3_3, all_0_3_3, all_0_6_6, all_0_5_5 and discharging atoms product(all_0_3_3, all_0_5_5) = all_0_5_5, product(all_0_3_3, all_0_6_6) = all_0_3_3, yields:
% 41.24/14.18 | (127) ? [v0] : (product(all_0_3_3, v0) = all_0_5_5 & product(all_0_6_6, all_0_5_5) = v0)
% 41.24/14.18 |
% 41.24/14.18 | Instantiating formula (22) with all_0_3_3, all_0_3_3, all_0_5_5, all_0_6_6, all_0_6_6 and discharging atoms product(all_0_3_3, all_0_6_6) = all_0_3_3, product(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 41.24/14.18 | (128) ? [v0] : (product(all_0_5_5, v0) = all_0_3_3 & product(all_0_6_6, all_0_6_6) = v0)
% 41.24/14.18 |
% 41.24/14.18 | Instantiating formula (10) with all_0_6_6, all_0_3_3, all_0_6_6, all_0_3_3, all_0_6_6 and discharging atoms product(all_0_3_3, all_0_6_6) = all_0_3_3, product(all_0_6_6, all_0_3_3) = all_0_6_6, yields:
% 41.24/14.18 | (129) ? [v0] : (product(v0, all_0_6_6) = all_0_6_6 & product(all_0_6_6, all_0_3_3) = v0)
% 41.24/14.18 |
% 41.24/14.18 | Instantiating formula (22) with all_0_3_3, all_0_3_3, all_0_3_3, all_0_6_6, all_0_6_6 and discharging atoms product(all_0_3_3, all_0_6_6) = all_0_3_3, yields:
% 41.24/14.18 | (130) ? [v0] : (product(all_0_3_3, v0) = all_0_3_3 & product(all_0_6_6, all_0_6_6) = v0)
% 41.24/14.18 |
% 41.24/14.18 | Instantiating (130) with all_173_0_82 yields:
% 41.24/14.18 | (131) product(all_0_3_3, all_173_0_82) = all_0_3_3 & product(all_0_6_6, all_0_6_6) = all_173_0_82
% 41.24/14.18 |
% 41.24/14.18 | Applying alpha-rule on (131) yields:
% 41.24/14.18 | (132) product(all_0_3_3, all_173_0_82) = all_0_3_3
% 41.24/14.18 | (133) product(all_0_6_6, all_0_6_6) = all_173_0_82
% 41.24/14.18 |
% 41.24/14.18 | Instantiating (129) with all_175_0_83 yields:
% 41.24/14.18 | (134) product(all_175_0_83, all_0_6_6) = all_0_6_6 & product(all_0_6_6, all_0_3_3) = all_175_0_83
% 41.24/14.18 |
% 41.24/14.18 | Applying alpha-rule on (134) yields:
% 41.24/14.18 | (135) product(all_175_0_83, all_0_6_6) = all_0_6_6
% 41.24/14.18 | (136) product(all_0_6_6, all_0_3_3) = all_175_0_83
% 41.24/14.18 |
% 41.24/14.18 | Instantiating (126) with all_177_0_84 yields:
% 41.24/14.18 | (137) product(all_177_0_84, all_0_6_6) = all_0_3_3 & product(all_0_3_3, all_0_1_1) = all_177_0_84
% 41.24/14.18 |
% 41.24/14.18 | Applying alpha-rule on (137) yields:
% 41.24/14.18 | (138) product(all_177_0_84, all_0_6_6) = all_0_3_3
% 41.24/14.18 | (139) product(all_0_3_3, all_0_1_1) = all_177_0_84
% 41.24/14.18 |
% 41.24/14.18 | Instantiating (128) with all_179_0_85 yields:
% 41.24/14.18 | (140) product(all_0_5_5, all_179_0_85) = all_0_3_3 & product(all_0_6_6, all_0_6_6) = all_179_0_85
% 41.24/14.18 |
% 41.24/14.18 | Applying alpha-rule on (140) yields:
% 41.24/14.18 | (141) product(all_0_5_5, all_179_0_85) = all_0_3_3
% 41.24/14.18 | (142) product(all_0_6_6, all_0_6_6) = all_179_0_85
% 41.24/14.18 |
% 41.24/14.18 | Instantiating (127) with all_181_0_86 yields:
% 41.24/14.18 | (143) product(all_0_3_3, all_181_0_86) = all_0_5_5 & product(all_0_6_6, all_0_5_5) = all_181_0_86
% 41.24/14.18 |
% 41.24/14.18 | Applying alpha-rule on (143) yields:
% 41.24/14.18 | (144) product(all_0_3_3, all_181_0_86) = all_0_5_5
% 41.24/14.18 | (145) product(all_0_6_6, all_0_5_5) = all_181_0_86
% 41.24/14.18 |
% 41.24/14.18 | Instantiating formula (16) with all_0_6_6, all_0_3_3, all_175_0_83, all_0_6_6 and discharging atoms product(all_0_6_6, all_0_3_3) = all_175_0_83, product(all_0_6_6, all_0_3_3) = all_0_6_6, yields:
% 41.24/14.18 | (146) all_175_0_83 = all_0_6_6
% 41.24/14.18 |
% 41.24/14.18 | Instantiating formula (16) with all_0_6_6, all_0_5_5, all_181_0_86, all_0_1_1 and discharging atoms product(all_0_6_6, all_0_5_5) = all_181_0_86, product(all_0_6_6, all_0_5_5) = all_0_1_1, yields:
% 41.24/14.18 | (147) all_181_0_86 = all_0_1_1
% 41.24/14.18 |
% 41.24/14.18 | Instantiating formula (5) with all_179_0_85, all_0_6_6 and discharging atoms product(all_0_6_6, all_0_6_6) = all_179_0_85, yields:
% 41.24/14.18 | (148) all_179_0_85 = all_0_6_6
% 41.24/14.18 |
% 41.24/14.18 | Instantiating formula (16) with all_0_6_6, all_0_6_6, all_173_0_82, all_179_0_85 and discharging atoms product(all_0_6_6, all_0_6_6) = all_179_0_85, product(all_0_6_6, all_0_6_6) = all_173_0_82, yields:
% 41.24/14.19 | (149) all_179_0_85 = all_173_0_82
% 41.24/14.19 |
% 41.24/14.19 | Combining equations (148,149) yields a new equation:
% 41.24/14.19 | (150) all_173_0_82 = all_0_6_6
% 41.24/14.19 |
% 41.24/14.19 | From (147) and (144) follows:
% 41.24/14.19 | (151) product(all_0_3_3, all_0_1_1) = all_0_5_5
% 41.24/14.19 |
% 41.24/14.19 | From (150) and (132) follows:
% 41.24/14.19 | (119) product(all_0_3_3, all_0_6_6) = all_0_3_3
% 41.24/14.19 |
% 41.24/14.19 | From (146) and (136) follows:
% 41.24/14.19 | (34) product(all_0_6_6, all_0_3_3) = all_0_6_6
% 41.24/14.19 |
% 41.24/14.19 | From (147) and (145) follows:
% 41.24/14.19 | (32) product(all_0_6_6, all_0_5_5) = all_0_1_1
% 41.24/14.19 |
% 41.24/14.19 | From (150) and (133) follows:
% 41.24/14.19 | (155) product(all_0_6_6, all_0_6_6) = all_0_6_6
% 41.24/14.19 |
% 41.24/14.19 | Instantiating formula (16) with all_0_3_3, all_0_1_1, all_0_5_5, all_177_0_84 and discharging atoms product(all_0_3_3, all_0_1_1) = all_177_0_84, product(all_0_3_3, all_0_1_1) = all_0_5_5, yields:
% 41.24/14.19 | (156) all_177_0_84 = all_0_5_5
% 41.24/14.19 |
% 41.24/14.19 | From (156) and (138) follows:
% 41.24/14.19 | (37) product(all_0_5_5, all_0_6_6) = all_0_3_3
% 41.24/14.19 |
% 41.24/14.19 | From (156) and (139) follows:
% 41.24/14.19 | (151) product(all_0_3_3, all_0_1_1) = all_0_5_5
% 41.24/14.19 |
% 41.24/14.19 +-Applying beta-rule and splitting (66), into two cases.
% 41.24/14.19 |-Branch one:
% 41.24/14.19 | (159) all_36_0_28 = all_0_1_1 & product(all_0_1_1, all_0_5_5) = all_0_1_1
% 41.24/14.19 |
% 41.24/14.19 | Applying alpha-rule on (159) yields:
% 41.24/14.19 | (160) all_36_0_28 = all_0_1_1
% 41.24/14.19 | (161) product(all_0_1_1, all_0_5_5) = all_0_1_1
% 41.24/14.19 |
% 41.24/14.19 +-Applying beta-rule and splitting (69), into two cases.
% 41.24/14.19 |-Branch one:
% 41.24/14.19 | (162) all_41_0_33 = 0 & l(all_0_1_1, all_0_5_5) = 0
% 41.24/14.19 |
% 41.24/14.19 | Applying alpha-rule on (162) yields:
% 41.24/14.19 | (163) all_41_0_33 = 0
% 41.24/14.19 | (164) l(all_0_1_1, all_0_5_5) = 0
% 41.24/14.19 |
% 41.24/14.19 +-Applying beta-rule and splitting (67), into two cases.
% 41.24/14.19 |-Branch one:
% 41.24/14.19 | (165) all_37_0_29 = all_0_1_1 & product(all_0_1_1, all_0_5_5) = all_0_1_1
% 41.24/14.19 |
% 41.24/14.19 | Applying alpha-rule on (165) yields:
% 41.24/14.19 | (166) all_37_0_29 = all_0_1_1
% 41.24/14.19 | (161) product(all_0_1_1, all_0_5_5) = all_0_1_1
% 41.24/14.19 |
% 41.24/14.19 +-Applying beta-rule and splitting (107), into two cases.
% 41.24/14.19 |-Branch one:
% 41.24/14.19 | (168) all_72_0_47 = all_0_3_3 & product(all_0_5_5, all_0_3_3) = all_0_3_3
% 41.24/14.19 |
% 41.24/14.19 | Applying alpha-rule on (168) yields:
% 41.24/14.19 | (169) all_72_0_47 = all_0_3_3
% 41.24/14.19 | (170) product(all_0_5_5, all_0_3_3) = all_0_3_3
% 41.24/14.19 |
% 41.24/14.19 +-Applying beta-rule and splitting (110), into two cases.
% 41.24/14.19 |-Branch one:
% 41.24/14.19 | (171) all_77_0_52 = 0 & r(all_0_5_5, all_0_3_3) = 0
% 41.24/14.19 |
% 41.24/14.19 | Applying alpha-rule on (171) yields:
% 41.24/14.19 | (172) all_77_0_52 = 0
% 41.24/14.19 | (173) r(all_0_5_5, all_0_3_3) = 0
% 41.24/14.19 |
% 41.24/14.19 +-Applying beta-rule and splitting (108), into two cases.
% 41.24/14.19 |-Branch one:
% 41.24/14.19 | (174) all_74_0_49 = all_0_3_3 & product(all_0_5_5, all_0_3_3) = all_0_3_3
% 41.24/14.19 |
% 41.24/14.19 | Applying alpha-rule on (174) yields:
% 41.24/14.19 | (175) all_74_0_49 = all_0_3_3
% 41.24/14.19 | (170) product(all_0_5_5, all_0_3_3) = all_0_3_3
% 41.24/14.19 |
% 41.24/14.19 | Instantiating formula (27) with all_0_1_1, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms d(all_0_6_6, all_0_5_5) = all_0_4_4, l(all_0_1_1, all_0_5_5) = 0, yields:
% 41.24/14.19 | (177) all_0_4_4 = 0 | ? [v0] : ( ~ (v0 = 0) & r(all_0_6_6, all_0_1_1) = v0)
% 41.24/14.19 |
% 41.24/14.19 | Instantiating formula (22) with all_0_5_5, all_0_3_3, all_0_3_3, all_0_6_6, all_0_1_1 and discharging atoms product(all_0_3_3, all_0_1_1) = all_0_5_5, product(all_0_3_3, all_0_6_6) = all_0_3_3, yields:
% 41.24/14.19 | (178) ? [v0] : (product(all_0_3_3, v0) = all_0_5_5 & product(all_0_6_6, all_0_1_1) = v0)
% 41.24/14.19 |
% 41.24/14.19 | Instantiating formula (22) with all_0_5_5, all_0_3_3, all_0_5_5, all_0_6_6, all_0_1_1 and discharging atoms product(all_0_3_3, all_0_1_1) = all_0_5_5, product(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 41.24/14.19 | (179) ? [v0] : (product(all_0_5_5, v0) = all_0_5_5 & product(all_0_6_6, all_0_1_1) = v0)
% 41.24/14.19 |
% 41.24/14.19 | Instantiating formula (10) with all_0_6_6, all_0_3_3, all_0_6_6, all_0_5_5, all_0_3_3 and discharging atoms product(all_0_5_5, all_0_3_3) = all_0_3_3, product(all_0_6_6, all_0_3_3) = all_0_6_6, yields:
% 41.24/14.19 | (180) ? [v0] : (product(v0, all_0_3_3) = all_0_6_6 & product(all_0_6_6, all_0_5_5) = v0)
% 41.24/14.19 |
% 41.24/14.19 | Instantiating formula (10) with all_0_6_6, all_0_6_6, all_0_6_6, all_0_1_1, all_0_6_6 and discharging atoms product(all_0_1_1, all_0_6_6) = all_0_6_6, product(all_0_6_6, all_0_6_6) = all_0_6_6, yields:
% 41.24/14.19 | (181) ? [v0] : (product(v0, all_0_6_6) = all_0_6_6 & product(all_0_6_6, all_0_1_1) = v0)
% 41.24/14.19 |
% 41.24/14.19 | Instantiating formula (22) with all_0_1_1, all_0_6_6, all_0_6_6, all_0_6_6, all_0_5_5 and discharging atoms product(all_0_6_6, all_0_5_5) = all_0_1_1, product(all_0_6_6, all_0_6_6) = all_0_6_6, yields:
% 41.24/14.19 | (182) ? [v0] : (product(all_0_6_6, v0) = all_0_1_1 & product(all_0_6_6, all_0_5_5) = v0)
% 41.24/14.19 |
% 41.24/14.19 | Instantiating (181) with all_320_0_95 yields:
% 41.24/14.19 | (183) product(all_320_0_95, all_0_6_6) = all_0_6_6 & product(all_0_6_6, all_0_1_1) = all_320_0_95
% 41.24/14.19 |
% 41.24/14.19 | Applying alpha-rule on (183) yields:
% 41.24/14.19 | (184) product(all_320_0_95, all_0_6_6) = all_0_6_6
% 41.24/14.19 | (185) product(all_0_6_6, all_0_1_1) = all_320_0_95
% 41.24/14.19 |
% 41.24/14.19 | Instantiating (182) with all_337_0_106 yields:
% 41.24/14.19 | (186) product(all_0_6_6, all_337_0_106) = all_0_1_1 & product(all_0_6_6, all_0_5_5) = all_337_0_106
% 41.24/14.19 |
% 41.24/14.19 | Applying alpha-rule on (186) yields:
% 41.24/14.19 | (187) product(all_0_6_6, all_337_0_106) = all_0_1_1
% 41.24/14.19 | (188) product(all_0_6_6, all_0_5_5) = all_337_0_106
% 41.24/14.19 |
% 41.24/14.19 | Instantiating (178) with all_342_0_109 yields:
% 41.24/14.19 | (189) product(all_0_3_3, all_342_0_109) = all_0_5_5 & product(all_0_6_6, all_0_1_1) = all_342_0_109
% 41.24/14.19 |
% 41.24/14.19 | Applying alpha-rule on (189) yields:
% 41.24/14.19 | (190) product(all_0_3_3, all_342_0_109) = all_0_5_5
% 41.24/14.19 | (191) product(all_0_6_6, all_0_1_1) = all_342_0_109
% 41.24/14.19 |
% 41.24/14.19 | Instantiating (179) with all_348_0_112 yields:
% 41.24/14.19 | (192) product(all_0_5_5, all_348_0_112) = all_0_5_5 & product(all_0_6_6, all_0_1_1) = all_348_0_112
% 41.24/14.19 |
% 41.24/14.19 | Applying alpha-rule on (192) yields:
% 41.24/14.19 | (193) product(all_0_5_5, all_348_0_112) = all_0_5_5
% 41.24/14.19 | (194) product(all_0_6_6, all_0_1_1) = all_348_0_112
% 41.24/14.20 |
% 41.24/14.20 | Instantiating (180) with all_362_0_120 yields:
% 41.24/14.20 | (195) product(all_362_0_120, all_0_3_3) = all_0_6_6 & product(all_0_6_6, all_0_5_5) = all_362_0_120
% 41.24/14.20 |
% 41.24/14.20 | Applying alpha-rule on (195) yields:
% 41.24/14.20 | (196) product(all_362_0_120, all_0_3_3) = all_0_6_6
% 41.24/14.20 | (197) product(all_0_6_6, all_0_5_5) = all_362_0_120
% 41.24/14.20 |
% 41.24/14.20 +-Applying beta-rule and splitting (177), into two cases.
% 41.24/14.20 |-Branch one:
% 41.24/14.20 | (198) all_0_4_4 = 0
% 41.24/14.20 |
% 41.24/14.20 | Equations (198) can reduce 33 to:
% 41.24/14.20 | (199) $false
% 41.24/14.20 |
% 41.24/14.20 |-The branch is then unsatisfiable
% 41.24/14.20 |-Branch two:
% 41.24/14.20 | (33) ~ (all_0_4_4 = 0)
% 41.24/14.20 | (201) ? [v0] : ( ~ (v0 = 0) & r(all_0_6_6, all_0_1_1) = v0)
% 41.24/14.20 |
% 41.24/14.20 | Instantiating (201) with all_405_0_127 yields:
% 41.24/14.20 | (202) ~ (all_405_0_127 = 0) & r(all_0_6_6, all_0_1_1) = all_405_0_127
% 41.24/14.20 |
% 41.24/14.20 | Applying alpha-rule on (202) yields:
% 41.24/14.20 | (203) ~ (all_405_0_127 = 0)
% 41.24/14.20 | (204) r(all_0_6_6, all_0_1_1) = all_405_0_127
% 41.24/14.20 |
% 41.24/14.20 +-Applying beta-rule and splitting (113), into two cases.
% 41.24/14.20 |-Branch one:
% 41.24/14.20 | (205) all_88_0_63 = 0 & r(all_0_6_6, all_0_1_1) = 0
% 41.24/14.20 |
% 41.24/14.20 | Applying alpha-rule on (205) yields:
% 41.24/14.20 | (206) all_88_0_63 = 0
% 41.24/14.20 | (207) r(all_0_6_6, all_0_1_1) = 0
% 41.24/14.20 |
% 41.24/14.20 | Instantiating formula (9) with all_0_6_6, all_0_1_1, 0, all_405_0_127 and discharging atoms r(all_0_6_6, all_0_1_1) = all_405_0_127, r(all_0_6_6, all_0_1_1) = 0, yields:
% 41.24/14.20 | (208) all_405_0_127 = 0
% 41.24/14.20 |
% 41.24/14.20 | Equations (208) can reduce 203 to:
% 41.24/14.20 | (199) $false
% 41.24/14.20 |
% 41.24/14.20 |-The branch is then unsatisfiable
% 41.24/14.20 |-Branch two:
% 41.24/14.20 | (210) ~ (all_88_0_63 = all_0_1_1) & product(all_0_6_6, all_0_1_1) = all_88_0_63
% 41.24/14.20 |
% 41.24/14.20 | Applying alpha-rule on (210) yields:
% 41.24/14.20 | (211) ~ (all_88_0_63 = all_0_1_1)
% 41.24/14.20 | (212) product(all_0_6_6, all_0_1_1) = all_88_0_63
% 41.24/14.20 |
% 41.24/14.20 +-Applying beta-rule and splitting (112), into two cases.
% 41.24/14.20 |-Branch one:
% 41.24/14.20 | (213) all_87_0_62 = all_0_1_1 & product(all_0_6_6, all_0_1_1) = all_0_1_1
% 41.24/14.20 |
% 41.24/14.20 | Applying alpha-rule on (213) yields:
% 41.24/14.20 | (214) all_87_0_62 = all_0_1_1
% 41.24/14.20 | (215) product(all_0_6_6, all_0_1_1) = all_0_1_1
% 41.24/14.20 |
% 41.24/14.20 | Instantiating formula (16) with all_0_6_6, all_0_1_1, all_342_0_109, all_348_0_112 and discharging atoms product(all_0_6_6, all_0_1_1) = all_348_0_112, product(all_0_6_6, all_0_1_1) = all_342_0_109, yields:
% 41.24/14.20 | (216) all_348_0_112 = all_342_0_109
% 41.24/14.20 |
% 41.24/14.20 | Instantiating formula (16) with all_0_6_6, all_0_1_1, all_320_0_95, all_342_0_109 and discharging atoms product(all_0_6_6, all_0_1_1) = all_342_0_109, product(all_0_6_6, all_0_1_1) = all_320_0_95, yields:
% 41.24/14.20 | (217) all_342_0_109 = all_320_0_95
% 41.24/14.20 |
% 41.24/14.20 | Instantiating formula (16) with all_0_6_6, all_0_1_1, all_88_0_63, all_320_0_95 and discharging atoms product(all_0_6_6, all_0_1_1) = all_320_0_95, product(all_0_6_6, all_0_1_1) = all_88_0_63, yields:
% 41.24/14.20 | (218) all_320_0_95 = all_88_0_63
% 41.24/14.20 |
% 41.24/14.20 | Instantiating formula (16) with all_0_6_6, all_0_1_1, all_0_1_1, all_348_0_112 and discharging atoms product(all_0_6_6, all_0_1_1) = all_348_0_112, product(all_0_6_6, all_0_1_1) = all_0_1_1, yields:
% 41.24/14.20 | (219) all_348_0_112 = all_0_1_1
% 41.24/14.20 |
% 41.24/14.20 | Combining equations (216,219) yields a new equation:
% 41.24/14.20 | (220) all_342_0_109 = all_0_1_1
% 41.24/14.20 |
% 41.24/14.20 | Simplifying 220 yields:
% 41.24/14.20 | (221) all_342_0_109 = all_0_1_1
% 41.24/14.20 |
% 41.24/14.20 | Combining equations (217,221) yields a new equation:
% 41.24/14.20 | (222) all_320_0_95 = all_0_1_1
% 41.24/14.20 |
% 41.24/14.20 | Simplifying 222 yields:
% 41.24/14.20 | (223) all_320_0_95 = all_0_1_1
% 41.24/14.20 |
% 41.24/14.20 | Combining equations (218,223) yields a new equation:
% 41.24/14.20 | (224) all_88_0_63 = all_0_1_1
% 41.24/14.20 |
% 41.24/14.20 | Simplifying 224 yields:
% 41.24/14.20 | (225) all_88_0_63 = all_0_1_1
% 41.24/14.20 |
% 41.24/14.20 | Equations (225) can reduce 211 to:
% 41.24/14.20 | (199) $false
% 41.24/14.20 |
% 41.24/14.20 |-The branch is then unsatisfiable
% 41.24/14.20 |-Branch two:
% 41.24/14.20 | (227) ~ (all_87_0_62 = 0) & r(all_0_1_1, all_0_6_6) = all_87_0_62
% 41.24/14.20 |
% 41.24/14.20 | Applying alpha-rule on (227) yields:
% 41.24/14.20 | (228) ~ (all_87_0_62 = 0)
% 41.24/14.20 | (229) r(all_0_1_1, all_0_6_6) = all_87_0_62
% 41.24/14.20 |
% 41.24/14.20 +-Applying beta-rule and splitting (111), into two cases.
% 41.24/14.20 |-Branch one:
% 41.24/14.20 | (230) all_86_0_61 = 0 & r(all_0_1_1, all_0_6_6) = 0
% 41.24/14.20 |
% 41.24/14.20 | Applying alpha-rule on (230) yields:
% 41.24/14.20 | (231) all_86_0_61 = 0
% 41.24/14.20 | (232) r(all_0_1_1, all_0_6_6) = 0
% 41.24/14.20 |
% 41.24/14.20 | Instantiating formula (9) with all_0_1_1, all_0_6_6, 0, all_87_0_62 and discharging atoms r(all_0_1_1, all_0_6_6) = all_87_0_62, r(all_0_1_1, all_0_6_6) = 0, yields:
% 41.24/14.20 | (233) all_87_0_62 = 0
% 41.24/14.20 |
% 41.24/14.20 | Equations (233) can reduce 228 to:
% 41.24/14.20 | (199) $false
% 41.24/14.20 |
% 41.24/14.20 |-The branch is then unsatisfiable
% 41.24/14.20 |-Branch two:
% 41.24/14.20 | (235) ~ (all_86_0_61 = all_0_1_1) & product(all_0_6_6, all_0_1_1) = all_86_0_61
% 41.24/14.20 |
% 41.24/14.20 | Applying alpha-rule on (235) yields:
% 41.24/14.20 | (236) ~ (all_86_0_61 = all_0_1_1)
% 41.24/14.20 | (237) product(all_0_6_6, all_0_1_1) = all_86_0_61
% 41.24/14.20 |
% 41.24/14.20 | Instantiating formula (16) with all_0_6_6, all_0_1_1, all_320_0_95, all_348_0_112 and discharging atoms product(all_0_6_6, all_0_1_1) = all_348_0_112, product(all_0_6_6, all_0_1_1) = all_320_0_95, yields:
% 41.45/14.21 | (238) all_348_0_112 = all_320_0_95
% 41.45/14.21 |
% 41.45/14.21 | Instantiating formula (16) with all_0_6_6, all_0_1_1, all_320_0_95, all_342_0_109 and discharging atoms product(all_0_6_6, all_0_1_1) = all_342_0_109, product(all_0_6_6, all_0_1_1) = all_320_0_95, yields:
% 41.45/14.21 | (217) all_342_0_109 = all_320_0_95
% 41.45/14.21 |
% 41.45/14.21 | Instantiating formula (16) with all_0_6_6, all_0_1_1, all_88_0_63, all_342_0_109 and discharging atoms product(all_0_6_6, all_0_1_1) = all_342_0_109, product(all_0_6_6, all_0_1_1) = all_88_0_63, yields:
% 41.45/14.21 | (240) all_342_0_109 = all_88_0_63
% 41.45/14.21 |
% 41.45/14.21 | Instantiating formula (16) with all_0_6_6, all_0_1_1, all_86_0_61, all_348_0_112 and discharging atoms product(all_0_6_6, all_0_1_1) = all_348_0_112, product(all_0_6_6, all_0_1_1) = all_86_0_61, yields:
% 41.45/14.21 | (241) all_348_0_112 = all_86_0_61
% 41.45/14.21 |
% 41.45/14.21 | Instantiating formula (16) with all_0_6_6, all_0_5_5, all_362_0_120, all_0_1_1 and discharging atoms product(all_0_6_6, all_0_5_5) = all_362_0_120, product(all_0_6_6, all_0_5_5) = all_0_1_1, yields:
% 41.45/14.21 | (242) all_362_0_120 = all_0_1_1
% 41.45/14.21 |
% 41.45/14.21 | Instantiating formula (16) with all_0_6_6, all_0_5_5, all_337_0_106, all_362_0_120 and discharging atoms product(all_0_6_6, all_0_5_5) = all_362_0_120, product(all_0_6_6, all_0_5_5) = all_337_0_106, yields:
% 41.45/14.21 | (243) all_362_0_120 = all_337_0_106
% 41.45/14.21 |
% 41.45/14.21 | Combining equations (242,243) yields a new equation:
% 41.45/14.21 | (244) all_337_0_106 = all_0_1_1
% 41.45/14.21 |
% 41.45/14.21 | Combining equations (238,241) yields a new equation:
% 41.45/14.21 | (245) all_320_0_95 = all_86_0_61
% 41.45/14.21 |
% 41.45/14.21 | Simplifying 245 yields:
% 41.45/14.21 | (246) all_320_0_95 = all_86_0_61
% 41.45/14.21 |
% 41.45/14.21 | Combining equations (217,240) yields a new equation:
% 41.45/14.21 | (247) all_320_0_95 = all_88_0_63
% 41.45/14.21 |
% 41.45/14.21 | Simplifying 247 yields:
% 41.45/14.21 | (218) all_320_0_95 = all_88_0_63
% 41.45/14.21 |
% 41.45/14.21 | Combining equations (218,246) yields a new equation:
% 41.45/14.21 | (249) all_88_0_63 = all_86_0_61
% 41.45/14.21 |
% 41.45/14.21 | Simplifying 249 yields:
% 41.45/14.21 | (250) all_88_0_63 = all_86_0_61
% 41.45/14.21 |
% 41.45/14.21 | Equations (250) can reduce 211 to:
% 41.45/14.21 | (236) ~ (all_86_0_61 = all_0_1_1)
% 41.45/14.21 |
% 41.45/14.21 | From (244) and (187) follows:
% 41.45/14.21 | (215) product(all_0_6_6, all_0_1_1) = all_0_1_1
% 41.45/14.21 |
% 41.45/14.21 | From (250) and (212) follows:
% 41.45/14.21 | (237) product(all_0_6_6, all_0_1_1) = all_86_0_61
% 41.45/14.21 |
% 41.45/14.21 | Instantiating formula (16) with all_0_6_6, all_0_1_1, all_0_1_1, all_86_0_61 and discharging atoms product(all_0_6_6, all_0_1_1) = all_86_0_61, product(all_0_6_6, all_0_1_1) = all_0_1_1, yields:
% 41.45/14.21 | (254) all_86_0_61 = all_0_1_1
% 41.45/14.21 |
% 41.45/14.21 | Equations (254) can reduce 236 to:
% 41.45/14.21 | (199) $false
% 41.45/14.21 |
% 41.45/14.21 |-The branch is then unsatisfiable
% 41.45/14.21 |-Branch two:
% 41.45/14.21 | (256) ~ (all_74_0_49 = 0) & r(all_0_5_5, all_0_3_3) = all_74_0_49
% 41.45/14.21 |
% 41.45/14.21 | Applying alpha-rule on (256) yields:
% 41.45/14.21 | (257) ~ (all_74_0_49 = 0)
% 41.45/14.21 | (258) r(all_0_5_5, all_0_3_3) = all_74_0_49
% 41.45/14.21 |
% 41.45/14.21 | Instantiating formula (9) with all_0_5_5, all_0_3_3, 0, all_74_0_49 and discharging atoms r(all_0_5_5, all_0_3_3) = all_74_0_49, r(all_0_5_5, all_0_3_3) = 0, yields:
% 41.45/14.21 | (259) all_74_0_49 = 0
% 41.45/14.21 |
% 41.45/14.21 | Equations (259) can reduce 257 to:
% 41.45/14.21 | (199) $false
% 41.45/14.21 |
% 41.45/14.21 |-The branch is then unsatisfiable
% 41.45/14.21 |-Branch two:
% 41.45/14.21 | (261) ~ (all_77_0_52 = all_0_3_3) & product(all_0_5_5, all_0_3_3) = all_77_0_52
% 41.45/14.21 |
% 41.45/14.21 | Applying alpha-rule on (261) yields:
% 41.45/14.21 | (262) ~ (all_77_0_52 = all_0_3_3)
% 41.45/14.21 | (263) product(all_0_5_5, all_0_3_3) = all_77_0_52
% 41.45/14.21 |
% 41.45/14.21 | Instantiating formula (16) with all_0_5_5, all_0_3_3, all_0_3_3, all_77_0_52 and discharging atoms product(all_0_5_5, all_0_3_3) = all_77_0_52, product(all_0_5_5, all_0_3_3) = all_0_3_3, yields:
% 41.45/14.21 | (264) all_77_0_52 = all_0_3_3
% 41.45/14.21 |
% 41.45/14.21 | Equations (264) can reduce 262 to:
% 41.45/14.21 | (199) $false
% 41.45/14.21 |
% 41.45/14.21 |-The branch is then unsatisfiable
% 41.45/14.21 |-Branch two:
% 41.45/14.21 | (266) ~ (all_72_0_47 = 0) & r(all_0_3_3, all_0_5_5) = all_72_0_47
% 41.45/14.21 |
% 41.45/14.21 | Applying alpha-rule on (266) yields:
% 41.45/14.21 | (267) ~ (all_72_0_47 = 0)
% 41.45/14.21 | (268) r(all_0_3_3, all_0_5_5) = all_72_0_47
% 41.45/14.21 |
% 41.45/14.21 +-Applying beta-rule and splitting (109), into two cases.
% 41.45/14.21 |-Branch one:
% 41.45/14.21 | (269) all_76_0_51 = 0 & r(all_0_3_3, all_0_5_5) = 0
% 41.45/14.21 |
% 41.45/14.21 | Applying alpha-rule on (269) yields:
% 41.45/14.21 | (270) all_76_0_51 = 0
% 41.45/14.21 | (271) r(all_0_3_3, all_0_5_5) = 0
% 41.45/14.21 |
% 41.45/14.21 | Instantiating formula (9) with all_0_3_3, all_0_5_5, 0, all_72_0_47 and discharging atoms r(all_0_3_3, all_0_5_5) = all_72_0_47, r(all_0_3_3, all_0_5_5) = 0, yields:
% 41.45/14.21 | (272) all_72_0_47 = 0
% 41.45/14.21 |
% 41.45/14.21 | Equations (272) can reduce 267 to:
% 41.45/14.21 | (199) $false
% 41.45/14.21 |
% 41.45/14.21 |-The branch is then unsatisfiable
% 41.45/14.21 |-Branch two:
% 41.45/14.21 | (274) ~ (all_76_0_51 = all_0_3_3) & product(all_0_5_5, all_0_3_3) = all_76_0_51
% 41.45/14.21 |
% 41.45/14.21 | Applying alpha-rule on (274) yields:
% 41.45/14.21 | (275) ~ (all_76_0_51 = all_0_3_3)
% 41.45/14.21 | (276) product(all_0_5_5, all_0_3_3) = all_76_0_51
% 41.45/14.21 |
% 41.45/14.21 +-Applying beta-rule and splitting (108), into two cases.
% 41.45/14.21 |-Branch one:
% 41.45/14.21 | (174) all_74_0_49 = all_0_3_3 & product(all_0_5_5, all_0_3_3) = all_0_3_3
% 41.45/14.21 |
% 41.45/14.21 | Applying alpha-rule on (174) yields:
% 41.45/14.21 | (175) all_74_0_49 = all_0_3_3
% 41.45/14.21 | (170) product(all_0_5_5, all_0_3_3) = all_0_3_3
% 41.45/14.21 |
% 41.45/14.21 | Instantiating formula (16) with all_0_5_5, all_0_3_3, all_0_3_3, all_76_0_51 and discharging atoms product(all_0_5_5, all_0_3_3) = all_76_0_51, product(all_0_5_5, all_0_3_3) = all_0_3_3, yields:
% 41.45/14.21 | (280) all_76_0_51 = all_0_3_3
% 41.45/14.21 |
% 41.45/14.21 | Equations (280) can reduce 275 to:
% 41.45/14.22 | (199) $false
% 41.45/14.22 |
% 41.45/14.22 |-The branch is then unsatisfiable
% 41.45/14.22 |-Branch two:
% 41.45/14.22 | (256) ~ (all_74_0_49 = 0) & r(all_0_5_5, all_0_3_3) = all_74_0_49
% 41.45/14.22 |
% 41.45/14.22 | Applying alpha-rule on (256) yields:
% 41.45/14.22 | (257) ~ (all_74_0_49 = 0)
% 41.45/14.22 | (258) r(all_0_5_5, all_0_3_3) = all_74_0_49
% 41.45/14.22 |
% 41.45/14.22 +-Applying beta-rule and splitting (110), into two cases.
% 41.45/14.22 |-Branch one:
% 41.45/14.22 | (171) all_77_0_52 = 0 & r(all_0_5_5, all_0_3_3) = 0
% 41.45/14.22 |
% 41.45/14.22 | Applying alpha-rule on (171) yields:
% 41.45/14.22 | (172) all_77_0_52 = 0
% 41.45/14.22 | (173) r(all_0_5_5, all_0_3_3) = 0
% 41.45/14.22 |
% 41.45/14.22 | Instantiating formula (9) with all_0_5_5, all_0_3_3, 0, all_74_0_49 and discharging atoms r(all_0_5_5, all_0_3_3) = all_74_0_49, r(all_0_5_5, all_0_3_3) = 0, yields:
% 41.45/14.22 | (259) all_74_0_49 = 0
% 41.45/14.22 |
% 41.45/14.22 | Equations (259) can reduce 257 to:
% 41.45/14.22 | (199) $false
% 41.45/14.22 |
% 41.45/14.22 |-The branch is then unsatisfiable
% 41.45/14.22 |-Branch two:
% 41.45/14.22 | (261) ~ (all_77_0_52 = all_0_3_3) & product(all_0_5_5, all_0_3_3) = all_77_0_52
% 41.45/14.22 |
% 41.45/14.22 | Applying alpha-rule on (261) yields:
% 41.45/14.22 | (262) ~ (all_77_0_52 = all_0_3_3)
% 41.45/14.22 | (263) product(all_0_5_5, all_0_3_3) = all_77_0_52
% 41.45/14.22 |
% 41.45/14.22 | Instantiating formula (16) with all_0_5_5, all_0_3_3, all_76_0_51, all_77_0_52 and discharging atoms product(all_0_5_5, all_0_3_3) = all_77_0_52, product(all_0_5_5, all_0_3_3) = all_76_0_51, yields:
% 41.45/14.22 | (293) all_77_0_52 = all_76_0_51
% 41.45/14.22 |
% 41.45/14.22 | Equations (293) can reduce 262 to:
% 41.45/14.22 | (275) ~ (all_76_0_51 = all_0_3_3)
% 41.45/14.22 |
% 41.45/14.22 | From (293) and (263) follows:
% 41.45/14.22 | (276) product(all_0_5_5, all_0_3_3) = all_76_0_51
% 41.45/14.22 |
% 41.45/14.22 | Instantiating formula (22) with all_0_6_6, all_0_1_1, all_0_1_1, all_0_5_5, all_0_6_6 and discharging atoms product(all_0_1_1, all_0_5_5) = all_0_1_1, product(all_0_1_1, all_0_6_6) = all_0_6_6, yields:
% 41.45/14.22 | (296) ? [v0] : (product(all_0_1_1, v0) = all_0_6_6 & product(all_0_5_5, all_0_6_6) = v0)
% 41.45/14.22 |
% 41.45/14.22 | Instantiating formula (10) with all_76_0_51, all_0_3_3, all_0_5_5, all_0_5_5, all_0_6_6 and discharging atoms product(all_0_5_5, all_0_3_3) = all_76_0_51, product(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 41.45/14.22 | (297) ? [v0] : (product(v0, all_0_6_6) = all_76_0_51 & product(all_0_5_5, all_0_5_5) = v0)
% 41.45/14.22 |
% 41.45/14.22 | Instantiating (296) with all_338_0_139 yields:
% 41.45/14.22 | (298) product(all_0_1_1, all_338_0_139) = all_0_6_6 & product(all_0_5_5, all_0_6_6) = all_338_0_139
% 41.45/14.22 |
% 41.45/14.22 | Applying alpha-rule on (298) yields:
% 41.45/14.22 | (299) product(all_0_1_1, all_338_0_139) = all_0_6_6
% 41.45/14.22 | (300) product(all_0_5_5, all_0_6_6) = all_338_0_139
% 41.45/14.22 |
% 41.45/14.22 | Instantiating (297) with all_360_0_153 yields:
% 41.45/14.22 | (301) product(all_360_0_153, all_0_6_6) = all_76_0_51 & product(all_0_5_5, all_0_5_5) = all_360_0_153
% 41.45/14.22 |
% 41.45/14.22 | Applying alpha-rule on (301) yields:
% 41.45/14.22 | (302) product(all_360_0_153, all_0_6_6) = all_76_0_51
% 41.45/14.22 | (303) product(all_0_5_5, all_0_5_5) = all_360_0_153
% 41.45/14.22 |
% 41.45/14.22 | Instantiating formula (5) with all_360_0_153, all_0_5_5 and discharging atoms product(all_0_5_5, all_0_5_5) = all_360_0_153, yields:
% 41.45/14.22 | (304) all_360_0_153 = all_0_5_5
% 41.45/14.22 |
% 41.45/14.22 | Instantiating formula (16) with all_0_5_5, all_0_6_6, all_338_0_139, all_0_3_3 and discharging atoms product(all_0_5_5, all_0_6_6) = all_338_0_139, product(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 41.45/14.22 | (305) all_338_0_139 = all_0_3_3
% 41.45/14.22 |
% 41.45/14.22 | From (304) and (302) follows:
% 41.45/14.22 | (306) product(all_0_5_5, all_0_6_6) = all_76_0_51
% 41.45/14.22 |
% 41.45/14.22 | From (305) and (300) follows:
% 41.45/14.22 | (37) product(all_0_5_5, all_0_6_6) = all_0_3_3
% 41.45/14.22 |
% 41.45/14.22 | Instantiating formula (16) with all_0_5_5, all_0_6_6, all_76_0_51, all_0_3_3 and discharging atoms product(all_0_5_5, all_0_6_6) = all_76_0_51, product(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 41.45/14.22 | (280) all_76_0_51 = all_0_3_3
% 41.45/14.22 |
% 41.45/14.22 | Equations (280) can reduce 275 to:
% 41.45/14.22 | (199) $false
% 41.45/14.22 |
% 41.45/14.22 |-The branch is then unsatisfiable
% 41.45/14.22 |-Branch two:
% 41.45/14.22 | (310) ~ (all_37_0_29 = 0) & l(all_0_1_1, all_0_5_5) = all_37_0_29
% 41.45/14.22 |
% 41.45/14.22 | Applying alpha-rule on (310) yields:
% 41.45/14.22 | (311) ~ (all_37_0_29 = 0)
% 41.45/14.22 | (312) l(all_0_1_1, all_0_5_5) = all_37_0_29
% 41.45/14.22 |
% 41.45/14.22 | Instantiating formula (17) with all_0_1_1, all_0_5_5, 0, all_37_0_29 and discharging atoms l(all_0_1_1, all_0_5_5) = all_37_0_29, l(all_0_1_1, all_0_5_5) = 0, yields:
% 41.45/14.22 | (313) all_37_0_29 = 0
% 41.45/14.22 |
% 41.45/14.22 | Equations (313) can reduce 311 to:
% 41.45/14.22 | (199) $false
% 41.45/14.22 |
% 41.45/14.22 |-The branch is then unsatisfiable
% 41.45/14.22 |-Branch two:
% 41.45/14.22 | (315) ~ (all_41_0_33 = all_0_1_1) & product(all_0_1_1, all_0_5_5) = all_41_0_33
% 41.45/14.22 |
% 41.45/14.22 | Applying alpha-rule on (315) yields:
% 41.45/14.22 | (316) ~ (all_41_0_33 = all_0_1_1)
% 41.45/14.22 | (317) product(all_0_1_1, all_0_5_5) = all_41_0_33
% 41.45/14.22 |
% 41.45/14.22 | Instantiating formula (16) with all_0_1_1, all_0_5_5, all_0_1_1, all_41_0_33 and discharging atoms product(all_0_1_1, all_0_5_5) = all_41_0_33, product(all_0_1_1, all_0_5_5) = all_0_1_1, yields:
% 41.45/14.22 | (318) all_41_0_33 = all_0_1_1
% 41.45/14.22 |
% 41.45/14.22 | Equations (318) can reduce 316 to:
% 41.45/14.22 | (199) $false
% 41.45/14.22 |
% 41.45/14.22 |-The branch is then unsatisfiable
% 41.45/14.22 |-Branch two:
% 41.45/14.22 | (320) ~ (all_36_0_28 = 0) & l(all_0_5_5, all_0_1_1) = all_36_0_28
% 41.45/14.22 |
% 41.45/14.23 | Applying alpha-rule on (320) yields:
% 41.45/14.23 | (321) ~ (all_36_0_28 = 0)
% 41.45/14.23 | (322) l(all_0_5_5, all_0_1_1) = all_36_0_28
% 41.45/14.23 |
% 41.45/14.23 +-Applying beta-rule and splitting (68), into two cases.
% 41.45/14.23 |-Branch one:
% 41.45/14.23 | (323) all_40_0_32 = 0 & l(all_0_5_5, all_0_1_1) = 0
% 41.45/14.23 |
% 41.45/14.23 | Applying alpha-rule on (323) yields:
% 41.45/14.23 | (324) all_40_0_32 = 0
% 41.45/14.23 | (325) l(all_0_5_5, all_0_1_1) = 0
% 41.45/14.23 |
% 41.45/14.23 | Instantiating formula (17) with all_0_5_5, all_0_1_1, 0, all_36_0_28 and discharging atoms l(all_0_5_5, all_0_1_1) = all_36_0_28, l(all_0_5_5, all_0_1_1) = 0, yields:
% 41.45/14.23 | (326) all_36_0_28 = 0
% 41.45/14.23 |
% 41.45/14.23 | Equations (326) can reduce 321 to:
% 41.45/14.23 | (199) $false
% 41.45/14.23 |
% 41.45/14.23 |-The branch is then unsatisfiable
% 41.45/14.23 |-Branch two:
% 41.45/14.23 | (328) ~ (all_40_0_32 = all_0_1_1) & product(all_0_1_1, all_0_5_5) = all_40_0_32
% 41.45/14.23 |
% 41.45/14.23 | Applying alpha-rule on (328) yields:
% 41.45/14.23 | (329) ~ (all_40_0_32 = all_0_1_1)
% 41.45/14.23 | (330) product(all_0_1_1, all_0_5_5) = all_40_0_32
% 41.45/14.23 |
% 41.45/14.23 +-Applying beta-rule and splitting (67), into two cases.
% 41.45/14.23 |-Branch one:
% 41.45/14.23 | (165) all_37_0_29 = all_0_1_1 & product(all_0_1_1, all_0_5_5) = all_0_1_1
% 41.45/14.23 |
% 41.45/14.23 | Applying alpha-rule on (165) yields:
% 41.45/14.23 | (166) all_37_0_29 = all_0_1_1
% 41.45/14.23 | (161) product(all_0_1_1, all_0_5_5) = all_0_1_1
% 41.45/14.23 |
% 41.45/14.23 | Instantiating formula (16) with all_0_1_1, all_0_5_5, all_0_1_1, all_40_0_32 and discharging atoms product(all_0_1_1, all_0_5_5) = all_40_0_32, product(all_0_1_1, all_0_5_5) = all_0_1_1, yields:
% 41.45/14.23 | (334) all_40_0_32 = all_0_1_1
% 41.45/14.23 |
% 41.45/14.23 | Equations (334) can reduce 329 to:
% 41.45/14.23 | (199) $false
% 41.45/14.23 |
% 41.45/14.23 |-The branch is then unsatisfiable
% 41.45/14.23 |-Branch two:
% 41.45/14.23 | (310) ~ (all_37_0_29 = 0) & l(all_0_1_1, all_0_5_5) = all_37_0_29
% 41.45/14.23 |
% 41.45/14.23 | Applying alpha-rule on (310) yields:
% 41.45/14.23 | (311) ~ (all_37_0_29 = 0)
% 41.45/14.23 | (312) l(all_0_1_1, all_0_5_5) = all_37_0_29
% 41.45/14.23 |
% 41.45/14.23 +-Applying beta-rule and splitting (69), into two cases.
% 41.45/14.23 |-Branch one:
% 41.45/14.23 | (162) all_41_0_33 = 0 & l(all_0_1_1, all_0_5_5) = 0
% 41.45/14.23 |
% 41.45/14.23 | Applying alpha-rule on (162) yields:
% 41.45/14.23 | (163) all_41_0_33 = 0
% 41.45/14.23 | (164) l(all_0_1_1, all_0_5_5) = 0
% 41.45/14.23 |
% 41.45/14.23 | Instantiating formula (17) with all_0_1_1, all_0_5_5, 0, all_37_0_29 and discharging atoms l(all_0_1_1, all_0_5_5) = all_37_0_29, l(all_0_1_1, all_0_5_5) = 0, yields:
% 41.45/14.23 | (313) all_37_0_29 = 0
% 41.45/14.23 |
% 41.45/14.23 | Equations (313) can reduce 311 to:
% 41.45/14.23 | (199) $false
% 41.45/14.23 |
% 41.45/14.23 |-The branch is then unsatisfiable
% 41.45/14.23 |-Branch two:
% 41.45/14.23 | (315) ~ (all_41_0_33 = all_0_1_1) & product(all_0_1_1, all_0_5_5) = all_41_0_33
% 41.45/14.23 |
% 41.45/14.23 | Applying alpha-rule on (315) yields:
% 41.45/14.23 | (316) ~ (all_41_0_33 = all_0_1_1)
% 41.45/14.23 | (317) product(all_0_1_1, all_0_5_5) = all_41_0_33
% 41.45/14.23 |
% 41.45/14.23 | Instantiating formula (16) with all_0_1_1, all_0_5_5, all_40_0_32, all_41_0_33 and discharging atoms product(all_0_1_1, all_0_5_5) = all_41_0_33, product(all_0_1_1, all_0_5_5) = all_40_0_32, yields:
% 41.45/14.23 | (347) all_41_0_33 = all_40_0_32
% 41.45/14.23 |
% 41.45/14.23 | Equations (347) can reduce 316 to:
% 41.45/14.23 | (329) ~ (all_40_0_32 = all_0_1_1)
% 41.45/14.23 |
% 41.45/14.23 | From (347) and (317) follows:
% 41.45/14.23 | (330) product(all_0_1_1, all_0_5_5) = all_40_0_32
% 41.45/14.23 |
% 41.45/14.23 | Instantiating formula (22) with all_40_0_32, all_0_1_1, all_0_6_6, all_0_5_5, all_0_5_5 and discharging atoms product(all_0_1_1, all_0_5_5) = all_40_0_32, product(all_0_6_6, all_0_5_5) = all_0_1_1, yields:
% 41.45/14.23 | (350) ? [v0] : (product(all_0_5_5, all_0_5_5) = v0 & product(all_0_6_6, v0) = all_40_0_32)
% 41.45/14.23 |
% 41.45/14.23 | Instantiating formula (22) with all_0_1_1, all_0_6_6, all_0_6_6, all_0_6_6, all_0_5_5 and discharging atoms product(all_0_6_6, all_0_5_5) = all_0_1_1, product(all_0_6_6, all_0_6_6) = all_0_6_6, yields:
% 41.45/14.23 | (182) ? [v0] : (product(all_0_6_6, v0) = all_0_1_1 & product(all_0_6_6, all_0_5_5) = v0)
% 41.45/14.23 |
% 41.45/14.23 | Instantiating (182) with all_332_0_219 yields:
% 41.45/14.23 | (352) product(all_0_6_6, all_332_0_219) = all_0_1_1 & product(all_0_6_6, all_0_5_5) = all_332_0_219
% 41.45/14.23 |
% 41.45/14.23 | Applying alpha-rule on (352) yields:
% 41.45/14.23 | (353) product(all_0_6_6, all_332_0_219) = all_0_1_1
% 41.45/14.23 | (354) product(all_0_6_6, all_0_5_5) = all_332_0_219
% 41.45/14.23 |
% 41.45/14.23 | Instantiating (350) with all_356_0_233 yields:
% 41.45/14.23 | (355) product(all_0_5_5, all_0_5_5) = all_356_0_233 & product(all_0_6_6, all_356_0_233) = all_40_0_32
% 41.45/14.23 |
% 41.45/14.23 | Applying alpha-rule on (355) yields:
% 41.45/14.23 | (356) product(all_0_5_5, all_0_5_5) = all_356_0_233
% 41.45/14.23 | (357) product(all_0_6_6, all_356_0_233) = all_40_0_32
% 41.45/14.23 |
% 41.45/14.23 | Instantiating formula (5) with all_356_0_233, all_0_5_5 and discharging atoms product(all_0_5_5, all_0_5_5) = all_356_0_233, yields:
% 41.45/14.23 | (358) all_356_0_233 = all_0_5_5
% 41.45/14.23 |
% 41.45/14.23 | Instantiating formula (16) with all_0_6_6, all_0_5_5, all_332_0_219, all_0_1_1 and discharging atoms product(all_0_6_6, all_0_5_5) = all_332_0_219, product(all_0_6_6, all_0_5_5) = all_0_1_1, yields:
% 41.45/14.23 | (359) all_332_0_219 = all_0_1_1
% 41.45/14.23 |
% 41.45/14.23 | From (358) and (357) follows:
% 41.45/14.23 | (360) product(all_0_6_6, all_0_5_5) = all_40_0_32
% 41.45/14.23 |
% 41.45/14.23 | From (359) and (354) follows:
% 41.45/14.23 | (32) product(all_0_6_6, all_0_5_5) = all_0_1_1
% 41.45/14.23 |
% 41.45/14.23 | Instantiating formula (16) with all_0_6_6, all_0_5_5, all_40_0_32, all_0_1_1 and discharging atoms product(all_0_6_6, all_0_5_5) = all_40_0_32, product(all_0_6_6, all_0_5_5) = all_0_1_1, yields:
% 41.45/14.23 | (334) all_40_0_32 = all_0_1_1
% 41.45/14.23 |
% 41.45/14.23 | Equations (334) can reduce 329 to:
% 41.45/14.23 | (199) $false
% 41.45/14.23 |
% 41.45/14.23 |-The branch is then unsatisfiable
% 41.45/14.24 |-Branch two:
% 41.45/14.24 | (364) ~ (all_54_0_42 = 0) & l(all_0_6_6, all_0_3_3) = all_54_0_42
% 41.45/14.24 |
% 41.45/14.24 | Applying alpha-rule on (364) yields:
% 41.45/14.24 | (365) ~ (all_54_0_42 = 0)
% 41.45/14.24 | (366) l(all_0_6_6, all_0_3_3) = all_54_0_42
% 41.45/14.24 |
% 41.45/14.24 | Instantiating formula (17) with all_0_6_6, all_0_3_3, 0, all_54_0_42 and discharging atoms l(all_0_6_6, all_0_3_3) = all_54_0_42, l(all_0_6_6, all_0_3_3) = 0, yields:
% 41.45/14.24 | (367) all_54_0_42 = 0
% 41.45/14.24 |
% 41.45/14.24 | Equations (367) can reduce 365 to:
% 41.45/14.24 | (199) $false
% 41.45/14.24 |
% 41.45/14.24 |-The branch is then unsatisfiable
% 41.45/14.24 |-Branch two:
% 41.45/14.24 | (369) ~ (all_57_0_45 = all_0_3_3) & product(all_0_3_3, all_0_6_6) = all_57_0_45
% 41.45/14.24 |
% 41.45/14.24 | Applying alpha-rule on (369) yields:
% 41.45/14.24 | (370) ~ (all_57_0_45 = all_0_3_3)
% 41.45/14.24 | (371) product(all_0_3_3, all_0_6_6) = all_57_0_45
% 41.45/14.24 |
% 41.45/14.24 | Instantiating formula (16) with all_0_3_3, all_0_6_6, all_0_3_3, all_57_0_45 and discharging atoms product(all_0_3_3, all_0_6_6) = all_57_0_45, product(all_0_3_3, all_0_6_6) = all_0_3_3, yields:
% 41.45/14.24 | (372) all_57_0_45 = all_0_3_3
% 41.45/14.24 |
% 41.45/14.24 | Equations (372) can reduce 370 to:
% 41.45/14.24 | (199) $false
% 41.45/14.24 |
% 41.45/14.24 |-The branch is then unsatisfiable
% 41.45/14.24 |-Branch two:
% 41.45/14.24 | (374) ~ (all_55_0_43 = 0) & l(all_0_3_3, all_0_6_6) = all_55_0_43
% 41.45/14.24 |
% 41.45/14.24 | Applying alpha-rule on (374) yields:
% 41.45/14.24 | (375) ~ (all_55_0_43 = 0)
% 41.45/14.24 | (376) l(all_0_3_3, all_0_6_6) = all_55_0_43
% 41.45/14.24 |
% 41.45/14.24 | Instantiating formula (17) with all_0_3_3, all_0_6_6, 0, all_55_0_43 and discharging atoms l(all_0_3_3, all_0_6_6) = all_55_0_43, l(all_0_3_3, all_0_6_6) = 0, yields:
% 41.45/14.24 | (377) all_55_0_43 = 0
% 41.45/14.24 |
% 41.45/14.24 | Equations (377) can reduce 375 to:
% 41.45/14.24 | (199) $false
% 41.45/14.24 |
% 41.45/14.24 |-The branch is then unsatisfiable
% 41.45/14.24 |-Branch two:
% 41.45/14.24 | (379) ~ (all_27_0_23 = all_0_3_3) & product(all_0_3_3, all_0_6_6) = all_27_0_23
% 41.45/14.24 |
% 41.45/14.24 | Applying alpha-rule on (379) yields:
% 41.45/14.24 | (380) ~ (all_27_0_23 = all_0_3_3)
% 41.45/14.24 | (381) product(all_0_3_3, all_0_6_6) = all_27_0_23
% 41.45/14.24 |
% 41.45/14.24 +-Applying beta-rule and splitting (79), into two cases.
% 41.45/14.24 |-Branch one:
% 41.45/14.24 | (123) all_54_0_42 = all_0_3_3 & product(all_0_3_3, all_0_6_6) = all_0_3_3
% 41.45/14.24 |
% 41.45/14.24 | Applying alpha-rule on (123) yields:
% 41.45/14.24 | (124) all_54_0_42 = all_0_3_3
% 41.45/14.24 | (119) product(all_0_3_3, all_0_6_6) = all_0_3_3
% 41.45/14.24 |
% 41.45/14.24 | Instantiating formula (16) with all_0_3_3, all_0_6_6, all_0_3_3, all_27_0_23 and discharging atoms product(all_0_3_3, all_0_6_6) = all_27_0_23, product(all_0_3_3, all_0_6_6) = all_0_3_3, yields:
% 41.45/14.24 | (385) all_27_0_23 = all_0_3_3
% 41.45/14.24 |
% 41.45/14.24 | Equations (385) can reduce 380 to:
% 41.45/14.24 | (199) $false
% 41.63/14.24 |
% 41.63/14.24 |-The branch is then unsatisfiable
% 41.63/14.24 |-Branch two:
% 41.63/14.24 | (364) ~ (all_54_0_42 = 0) & l(all_0_6_6, all_0_3_3) = all_54_0_42
% 41.63/14.24 |
% 41.63/14.24 | Applying alpha-rule on (364) yields:
% 41.63/14.24 | (365) ~ (all_54_0_42 = 0)
% 41.63/14.24 | (366) l(all_0_6_6, all_0_3_3) = all_54_0_42
% 41.63/14.24 |
% 41.63/14.24 +-Applying beta-rule and splitting (81), into two cases.
% 41.63/14.24 |-Branch one:
% 41.63/14.24 | (120) all_57_0_45 = 0 & l(all_0_6_6, all_0_3_3) = 0
% 41.63/14.24 |
% 41.63/14.24 | Applying alpha-rule on (120) yields:
% 41.63/14.24 | (121) all_57_0_45 = 0
% 41.63/14.24 | (122) l(all_0_6_6, all_0_3_3) = 0
% 41.63/14.24 |
% 41.63/14.24 | Instantiating formula (17) with all_0_6_6, all_0_3_3, 0, all_54_0_42 and discharging atoms l(all_0_6_6, all_0_3_3) = all_54_0_42, l(all_0_6_6, all_0_3_3) = 0, yields:
% 41.63/14.24 | (367) all_54_0_42 = 0
% 41.63/14.24 |
% 41.63/14.24 | Equations (367) can reduce 365 to:
% 41.63/14.24 | (199) $false
% 41.63/14.24 |
% 41.63/14.24 |-The branch is then unsatisfiable
% 41.63/14.24 |-Branch two:
% 41.63/14.24 | (369) ~ (all_57_0_45 = all_0_3_3) & product(all_0_3_3, all_0_6_6) = all_57_0_45
% 41.63/14.24 |
% 41.63/14.24 | Applying alpha-rule on (369) yields:
% 41.63/14.24 | (370) ~ (all_57_0_45 = all_0_3_3)
% 41.63/14.24 | (371) product(all_0_3_3, all_0_6_6) = all_57_0_45
% 41.63/14.24 |
% 41.63/14.24 | Instantiating formula (16) with all_0_3_3, all_0_6_6, all_27_0_23, all_57_0_45 and discharging atoms product(all_0_3_3, all_0_6_6) = all_57_0_45, product(all_0_3_3, all_0_6_6) = all_27_0_23, yields:
% 41.63/14.24 | (398) all_57_0_45 = all_27_0_23
% 41.63/14.24 |
% 41.63/14.25 | Equations (398) can reduce 370 to:
% 41.63/14.25 | (380) ~ (all_27_0_23 = all_0_3_3)
% 41.63/14.25 |
% 41.63/14.25 | From (398) and (371) follows:
% 41.63/14.25 | (381) product(all_0_3_3, all_0_6_6) = all_27_0_23
% 41.63/14.25 |
% 41.63/14.25 | Instantiating formula (22) with all_27_0_23, all_0_3_3, all_0_5_5, all_0_6_6, all_0_6_6 and discharging atoms product(all_0_3_3, all_0_6_6) = all_27_0_23, product(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 41.63/14.25 | (401) ? [v0] : (product(all_0_5_5, v0) = all_27_0_23 & product(all_0_6_6, all_0_6_6) = v0)
% 41.63/14.25 |
% 41.63/14.25 | Instantiating (401) with all_182_0_262 yields:
% 41.63/14.25 | (402) product(all_0_5_5, all_182_0_262) = all_27_0_23 & product(all_0_6_6, all_0_6_6) = all_182_0_262
% 41.63/14.25 |
% 41.63/14.25 | Applying alpha-rule on (402) yields:
% 41.63/14.25 | (403) product(all_0_5_5, all_182_0_262) = all_27_0_23
% 41.63/14.25 | (404) product(all_0_6_6, all_0_6_6) = all_182_0_262
% 41.63/14.25 |
% 41.63/14.25 | Instantiating formula (5) with all_182_0_262, all_0_6_6 and discharging atoms product(all_0_6_6, all_0_6_6) = all_182_0_262, yields:
% 41.63/14.25 | (405) all_182_0_262 = all_0_6_6
% 41.63/14.25 |
% 41.63/14.25 | From (405) and (403) follows:
% 41.63/14.25 | (406) product(all_0_5_5, all_0_6_6) = all_27_0_23
% 41.63/14.25 |
% 41.63/14.25 | Instantiating formula (16) with all_0_5_5, all_0_6_6, all_27_0_23, all_0_3_3 and discharging atoms product(all_0_5_5, all_0_6_6) = all_27_0_23, product(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 41.63/14.25 | (385) all_27_0_23 = all_0_3_3
% 41.63/14.25 |
% 41.63/14.25 | Equations (385) can reduce 380 to:
% 41.63/14.25 | (199) $false
% 41.63/14.25 |
% 41.63/14.25 |-The branch is then unsatisfiable
% 41.63/14.25 |-Branch two:
% 41.63/14.25 | (409) all_0_4_4 = 0 & (( ~ (all_0_0_0 = all_0_5_5) & product(all_0_5_5, all_0_1_1) = all_0_0_0 & product(all_0_6_6, all_0_5_5) = all_0_1_1) | ( ~ (all_0_2_2 = all_0_6_6) & product(all_0_5_5, all_0_6_6) = all_0_3_3 & product(all_0_6_6, all_0_3_3) = all_0_2_2))
% 41.63/14.25 |
% 41.63/14.25 | Applying alpha-rule on (409) yields:
% 41.63/14.25 | (198) all_0_4_4 = 0
% 41.63/14.25 | (411) ( ~ (all_0_0_0 = all_0_5_5) & product(all_0_5_5, all_0_1_1) = all_0_0_0 & product(all_0_6_6, all_0_5_5) = all_0_1_1) | ( ~ (all_0_2_2 = all_0_6_6) & product(all_0_5_5, all_0_6_6) = all_0_3_3 & product(all_0_6_6, all_0_3_3) = all_0_2_2)
% 41.63/14.25 |
% 41.63/14.25 | From (198) and (15) follows:
% 41.63/14.25 | (412) d(all_0_6_6, all_0_5_5) = 0
% 41.63/14.25 |
% 41.63/14.25 | Instantiating formula (19) with all_0_5_5, all_0_6_6 and discharging atoms d(all_0_6_6, all_0_5_5) = 0, yields:
% 41.63/14.25 | (413) ? [v0] : (r(all_0_6_6, v0) = 0 & l(v0, all_0_5_5) = 0)
% 41.63/14.25 |
% 41.63/14.25 | Instantiating (413) with all_23_0_267 yields:
% 41.63/14.25 | (414) r(all_0_6_6, all_23_0_267) = 0 & l(all_23_0_267, all_0_5_5) = 0
% 41.63/14.25 |
% 41.63/14.25 | Applying alpha-rule on (414) yields:
% 41.63/14.25 | (415) r(all_0_6_6, all_23_0_267) = 0
% 41.63/14.25 | (416) l(all_23_0_267, all_0_5_5) = 0
% 41.63/14.25 |
% 41.63/14.25 | Instantiating formula (2) with all_23_0_267, all_0_6_6 and discharging atoms r(all_0_6_6, all_23_0_267) = 0, yields:
% 41.63/14.25 | (417) product(all_23_0_267, all_0_6_6) = all_0_6_6 & product(all_0_6_6, all_23_0_267) = all_23_0_267
% 41.63/14.25 |
% 41.63/14.25 | Applying alpha-rule on (417) yields:
% 41.63/14.25 | (418) product(all_23_0_267, all_0_6_6) = all_0_6_6
% 41.63/14.25 | (419) product(all_0_6_6, all_23_0_267) = all_23_0_267
% 41.63/14.25 |
% 41.63/14.25 | Instantiating formula (13) with all_0_5_5, all_23_0_267 and discharging atoms l(all_23_0_267, all_0_5_5) = 0, yields:
% 41.63/14.25 | (420) product(all_23_0_267, all_0_5_5) = all_23_0_267 & product(all_0_5_5, all_23_0_267) = all_0_5_5
% 41.63/14.25 |
% 41.63/14.25 | Applying alpha-rule on (420) yields:
% 41.63/14.25 | (421) product(all_23_0_267, all_0_5_5) = all_23_0_267
% 41.63/14.25 | (422) product(all_0_5_5, all_23_0_267) = all_0_5_5
% 41.63/14.25 |
% 41.63/14.25 | Instantiating formula (22) with all_23_0_267, all_23_0_267, all_23_0_267, all_0_5_5, all_0_5_5 and discharging atoms product(all_23_0_267, all_0_5_5) = all_23_0_267, yields:
% 41.63/14.25 | (423) ? [v0] : (product(all_23_0_267, v0) = all_23_0_267 & product(all_0_5_5, all_0_5_5) = v0)
% 41.63/14.25 |
% 41.63/14.25 | Instantiating formula (22) with all_0_6_6, all_23_0_267, all_23_0_267, all_0_5_5, all_0_6_6 and discharging atoms product(all_23_0_267, all_0_5_5) = all_23_0_267, product(all_23_0_267, all_0_6_6) = all_0_6_6, yields:
% 41.63/14.25 | (424) ? [v0] : (product(all_23_0_267, v0) = all_0_6_6 & product(all_0_5_5, all_0_6_6) = v0)
% 41.63/14.25 |
% 41.63/14.25 | Instantiating formula (4) with all_0_6_6, all_0_6_6, all_23_0_267 and discharging atoms product(all_23_0_267, all_0_6_6) = all_0_6_6, yields:
% 41.63/14.25 | (425) ? [v0] : ((v0 = all_23_0_267 & product(all_0_6_6, all_23_0_267) = all_23_0_267) | ( ~ (v0 = 0) & r(all_23_0_267, all_0_6_6) = v0))
% 41.63/14.25 |
% 41.63/14.25 | Instantiating formula (10) with all_23_0_267, all_0_5_5, all_23_0_267, all_0_5_5, all_23_0_267 and discharging atoms product(all_23_0_267, all_0_5_5) = all_23_0_267, product(all_0_5_5, all_23_0_267) = all_0_5_5, yields:
% 41.63/14.25 | (426) ? [v0] : (product(v0, all_23_0_267) = all_23_0_267 & product(all_23_0_267, all_0_5_5) = v0)
% 41.63/14.25 |
% 41.63/14.25 | Instantiating formula (25) with all_23_0_267, all_0_5_5 and discharging atoms product(all_0_5_5, all_23_0_267) = all_0_5_5, yields:
% 41.63/14.25 | (427) ? [v0] : ((v0 = 0 & l(all_0_5_5, all_23_0_267) = 0) | ( ~ (v0 = all_23_0_267) & product(all_23_0_267, all_0_5_5) = v0))
% 41.63/14.25 |
% 41.63/14.25 | Instantiating formula (12) with all_0_5_5, all_23_0_267, all_0_5_5 and discharging atoms product(all_0_5_5, all_23_0_267) = all_0_5_5, yields:
% 41.63/14.25 | (428) ? [v0] : ((v0 = all_23_0_267 & product(all_23_0_267, all_0_5_5) = all_23_0_267) | ( ~ (v0 = 0) & l(all_0_5_5, all_23_0_267) = v0))
% 41.63/14.25 |
% 41.63/14.25 | Instantiating formula (22) with all_0_6_6, all_23_0_267, all_0_6_6, all_23_0_267, all_0_6_6 and discharging atoms product(all_23_0_267, all_0_6_6) = all_0_6_6, product(all_0_6_6, all_23_0_267) = all_23_0_267, yields:
% 41.63/14.25 | (429) ? [v0] : (product(all_23_0_267, all_0_6_6) = v0 & product(all_0_6_6, v0) = all_0_6_6)
% 41.63/14.25 |
% 41.63/14.25 | Instantiating formula (10) with all_0_5_5, all_23_0_267, all_0_5_5, all_0_6_6, all_23_0_267 and discharging atoms product(all_0_5_5, all_23_0_267) = all_0_5_5, product(all_0_6_6, all_23_0_267) = all_23_0_267, yields:
% 41.63/14.26 | (430) ? [v0] : (product(v0, all_23_0_267) = all_0_5_5 & product(all_0_5_5, all_0_6_6) = v0)
% 41.63/14.26 |
% 41.63/14.26 | Instantiating formula (10) with all_23_0_267, all_23_0_267, all_0_6_6, all_0_6_6, all_23_0_267 and discharging atoms product(all_0_6_6, all_23_0_267) = all_23_0_267, yields:
% 41.63/14.26 | (431) ? [v0] : (product(v0, all_23_0_267) = all_23_0_267 & product(all_0_6_6, all_0_6_6) = v0)
% 41.63/14.26 |
% 41.63/14.26 | Instantiating formula (21) with all_0_6_6, all_23_0_267 and discharging atoms product(all_0_6_6, all_23_0_267) = all_23_0_267, yields:
% 41.63/14.26 | (432) ? [v0] : ((v0 = 0 & r(all_23_0_267, all_0_6_6) = 0) | ( ~ (v0 = all_0_6_6) & product(all_23_0_267, all_0_6_6) = v0))
% 41.63/14.26 |
% 41.63/14.26 | Instantiating formula (26) with all_23_0_267, all_0_6_6, all_23_0_267 and discharging atoms product(all_0_6_6, all_23_0_267) = all_23_0_267, yields:
% 41.63/14.26 | (433) ? [v0] : ((v0 = all_0_6_6 & product(all_23_0_267, all_0_6_6) = all_0_6_6) | ( ~ (v0 = 0) & r(all_23_0_267, all_0_6_6) = v0))
% 41.63/14.26 |
% 41.63/14.26 | Instantiating (433) with all_36_0_268 yields:
% 41.63/14.26 | (434) (all_36_0_268 = all_0_6_6 & product(all_23_0_267, all_0_6_6) = all_0_6_6) | ( ~ (all_36_0_268 = 0) & r(all_23_0_267, all_0_6_6) = all_36_0_268)
% 41.63/14.26 |
% 41.63/14.26 | Instantiating (432) with all_37_0_269 yields:
% 41.63/14.26 | (435) (all_37_0_269 = 0 & r(all_23_0_267, all_0_6_6) = 0) | ( ~ (all_37_0_269 = all_0_6_6) & product(all_23_0_267, all_0_6_6) = all_37_0_269)
% 41.63/14.26 |
% 41.63/14.26 | Instantiating (431) with all_38_0_270 yields:
% 41.63/14.26 | (436) product(all_38_0_270, all_23_0_267) = all_23_0_267 & product(all_0_6_6, all_0_6_6) = all_38_0_270
% 41.63/14.26 |
% 41.63/14.26 | Applying alpha-rule on (436) yields:
% 41.63/14.26 | (437) product(all_38_0_270, all_23_0_267) = all_23_0_267
% 41.63/14.26 | (438) product(all_0_6_6, all_0_6_6) = all_38_0_270
% 41.63/14.26 |
% 41.63/14.26 | Instantiating (427) with all_40_0_271 yields:
% 41.63/14.26 | (439) (all_40_0_271 = 0 & l(all_0_5_5, all_23_0_267) = 0) | ( ~ (all_40_0_271 = all_23_0_267) & product(all_23_0_267, all_0_5_5) = all_40_0_271)
% 41.63/14.26 |
% 41.63/14.26 | Instantiating (426) with all_43_0_273 yields:
% 41.63/14.26 | (440) product(all_43_0_273, all_23_0_267) = all_23_0_267 & product(all_23_0_267, all_0_5_5) = all_43_0_273
% 41.63/14.26 |
% 41.63/14.26 | Applying alpha-rule on (440) yields:
% 41.63/14.26 | (441) product(all_43_0_273, all_23_0_267) = all_23_0_267
% 41.63/14.26 | (442) product(all_23_0_267, all_0_5_5) = all_43_0_273
% 41.63/14.26 |
% 41.63/14.26 | Instantiating (424) with all_47_0_275 yields:
% 41.63/14.26 | (443) product(all_23_0_267, all_47_0_275) = all_0_6_6 & product(all_0_5_5, all_0_6_6) = all_47_0_275
% 41.63/14.26 |
% 41.63/14.26 | Applying alpha-rule on (443) yields:
% 41.63/14.26 | (444) product(all_23_0_267, all_47_0_275) = all_0_6_6
% 41.63/14.26 | (445) product(all_0_5_5, all_0_6_6) = all_47_0_275
% 41.63/14.26 |
% 41.63/14.26 | Instantiating (423) with all_50_0_277 yields:
% 41.63/14.26 | (446) product(all_23_0_267, all_50_0_277) = all_23_0_267 & product(all_0_5_5, all_0_5_5) = all_50_0_277
% 41.63/14.26 |
% 41.63/14.26 | Applying alpha-rule on (446) yields:
% 41.63/14.26 | (447) product(all_23_0_267, all_50_0_277) = all_23_0_267
% 41.63/14.26 | (448) product(all_0_5_5, all_0_5_5) = all_50_0_277
% 41.63/14.26 |
% 41.63/14.26 | Instantiating (430) with all_54_0_279 yields:
% 41.63/14.26 | (449) product(all_54_0_279, all_23_0_267) = all_0_5_5 & product(all_0_5_5, all_0_6_6) = all_54_0_279
% 41.63/14.26 |
% 41.63/14.26 | Applying alpha-rule on (449) yields:
% 41.63/14.26 | (450) product(all_54_0_279, all_23_0_267) = all_0_5_5
% 41.63/14.26 | (451) product(all_0_5_5, all_0_6_6) = all_54_0_279
% 41.63/14.26 |
% 41.63/14.26 | Instantiating (429) with all_56_0_280 yields:
% 41.63/14.26 | (452) product(all_23_0_267, all_0_6_6) = all_56_0_280 & product(all_0_6_6, all_56_0_280) = all_0_6_6
% 41.63/14.26 |
% 41.63/14.26 | Applying alpha-rule on (452) yields:
% 41.63/14.26 | (453) product(all_23_0_267, all_0_6_6) = all_56_0_280
% 41.63/14.26 | (454) product(all_0_6_6, all_56_0_280) = all_0_6_6
% 41.63/14.26 |
% 41.63/14.26 | Instantiating (428) with all_60_0_282 yields:
% 41.63/14.26 | (455) (all_60_0_282 = all_23_0_267 & product(all_23_0_267, all_0_5_5) = all_23_0_267) | ( ~ (all_60_0_282 = 0) & l(all_0_5_5, all_23_0_267) = all_60_0_282)
% 41.63/14.26 |
% 41.63/14.26 | Instantiating (425) with all_63_0_285 yields:
% 41.63/14.26 | (456) (all_63_0_285 = all_23_0_267 & product(all_0_6_6, all_23_0_267) = all_23_0_267) | ( ~ (all_63_0_285 = 0) & r(all_23_0_267, all_0_6_6) = all_63_0_285)
% 41.63/14.26 |
% 41.63/14.26 | Instantiating formula (16) with all_23_0_267, all_0_5_5, all_43_0_273, all_23_0_267 and discharging atoms product(all_23_0_267, all_0_5_5) = all_43_0_273, product(all_23_0_267, all_0_5_5) = all_23_0_267, yields:
% 41.63/14.26 | (457) all_43_0_273 = all_23_0_267
% 41.63/14.26 |
% 41.63/14.26 | Instantiating formula (16) with all_23_0_267, all_0_6_6, all_56_0_280, all_0_6_6 and discharging atoms product(all_23_0_267, all_0_6_6) = all_56_0_280, product(all_23_0_267, all_0_6_6) = all_0_6_6, yields:
% 41.63/14.26 | (458) all_56_0_280 = all_0_6_6
% 41.63/14.26 |
% 41.63/14.26 | Instantiating formula (5) with all_50_0_277, all_0_5_5 and discharging atoms product(all_0_5_5, all_0_5_5) = all_50_0_277, yields:
% 41.63/14.26 | (459) all_50_0_277 = all_0_5_5
% 41.63/14.26 |
% 41.63/14.26 | Instantiating formula (16) with all_0_5_5, all_0_6_6, all_47_0_275, all_54_0_279 and discharging atoms product(all_0_5_5, all_0_6_6) = all_54_0_279, product(all_0_5_5, all_0_6_6) = all_47_0_275, yields:
% 41.63/14.26 | (460) all_54_0_279 = all_47_0_275
% 41.63/14.26 |
% 41.63/14.26 | Instantiating formula (5) with all_38_0_270, all_0_6_6 and discharging atoms product(all_0_6_6, all_0_6_6) = all_38_0_270, yields:
% 41.63/14.26 | (461) all_38_0_270 = all_0_6_6
% 41.63/14.26 |
% 41.63/14.26 | From (460) and (450) follows:
% 41.63/14.26 | (462) product(all_47_0_275, all_23_0_267) = all_0_5_5
% 41.63/14.26 |
% 41.63/14.26 | From (457) and (442) follows:
% 41.63/14.26 | (421) product(all_23_0_267, all_0_5_5) = all_23_0_267
% 41.63/14.26 |
% 41.63/14.26 | From (458) and (453) follows:
% 41.63/14.26 | (418) product(all_23_0_267, all_0_6_6) = all_0_6_6
% 41.63/14.26 |
% 41.63/14.26 | From (459) and (448) follows:
% 41.63/14.26 | (465) product(all_0_5_5, all_0_5_5) = all_0_5_5
% 41.63/14.26 |
% 41.63/14.26 | From (460) and (451) follows:
% 41.63/14.26 | (445) product(all_0_5_5, all_0_6_6) = all_47_0_275
% 41.63/14.26 |
% 41.63/14.26 | From (461) and (438) follows:
% 41.63/14.26 | (155) product(all_0_6_6, all_0_6_6) = all_0_6_6
% 41.63/14.26 |
% 41.63/14.26 +-Applying beta-rule and splitting (455), into two cases.
% 41.63/14.26 |-Branch one:
% 41.63/14.26 | (468) all_60_0_282 = all_23_0_267 & product(all_23_0_267, all_0_5_5) = all_23_0_267
% 41.63/14.26 |
% 41.63/14.26 | Applying alpha-rule on (468) yields:
% 41.63/14.26 | (469) all_60_0_282 = all_23_0_267
% 41.63/14.26 | (421) product(all_23_0_267, all_0_5_5) = all_23_0_267
% 41.63/14.26 |
% 41.63/14.26 +-Applying beta-rule and splitting (435), into two cases.
% 41.63/14.26 |-Branch one:
% 41.63/14.26 | (471) all_37_0_269 = 0 & r(all_23_0_267, all_0_6_6) = 0
% 41.63/14.26 |
% 41.63/14.26 | Applying alpha-rule on (471) yields:
% 41.63/14.26 | (472) all_37_0_269 = 0
% 41.63/14.26 | (473) r(all_23_0_267, all_0_6_6) = 0
% 41.63/14.26 |
% 41.63/14.26 +-Applying beta-rule and splitting (434), into two cases.
% 41.63/14.26 |-Branch one:
% 41.63/14.26 | (474) all_36_0_268 = all_0_6_6 & product(all_23_0_267, all_0_6_6) = all_0_6_6
% 41.63/14.26 |
% 41.63/14.26 | Applying alpha-rule on (474) yields:
% 41.63/14.26 | (475) all_36_0_268 = all_0_6_6
% 41.63/14.26 | (418) product(all_23_0_267, all_0_6_6) = all_0_6_6
% 41.63/14.26 |
% 41.63/14.26 +-Applying beta-rule and splitting (456), into two cases.
% 41.63/14.26 |-Branch one:
% 41.63/14.26 | (477) all_63_0_285 = all_23_0_267 & product(all_0_6_6, all_23_0_267) = all_23_0_267
% 41.63/14.26 |
% 41.63/14.26 | Applying alpha-rule on (477) yields:
% 41.63/14.26 | (478) all_63_0_285 = all_23_0_267
% 41.63/14.26 | (419) product(all_0_6_6, all_23_0_267) = all_23_0_267
% 41.63/14.26 |
% 41.63/14.26 | Instantiating formula (10) with all_0_5_5, all_23_0_267, all_47_0_275, all_0_6_6, all_23_0_267 and discharging atoms product(all_47_0_275, all_23_0_267) = all_0_5_5, product(all_0_6_6, all_23_0_267) = all_23_0_267, yields:
% 41.63/14.27 | (480) ? [v0] : (product(v0, all_23_0_267) = all_0_5_5 & product(all_47_0_275, all_0_6_6) = v0)
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (22) with all_0_6_6, all_23_0_267, all_23_0_267, all_0_5_5, all_47_0_275 and discharging atoms product(all_23_0_267, all_47_0_275) = all_0_6_6, product(all_23_0_267, all_0_5_5) = all_23_0_267, yields:
% 41.63/14.27 | (481) ? [v0] : (product(all_23_0_267, v0) = all_0_6_6 & product(all_0_5_5, all_47_0_275) = v0)
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (10) with all_0_5_5, all_0_5_5, all_0_5_5, all_47_0_275, all_23_0_267 and discharging atoms product(all_47_0_275, all_23_0_267) = all_0_5_5, product(all_0_5_5, all_0_5_5) = all_0_5_5, yields:
% 41.63/14.27 | (482) ? [v0] : (product(v0, all_23_0_267) = all_0_5_5 & product(all_0_5_5, all_47_0_275) = v0)
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (22) with all_47_0_275, all_0_5_5, all_47_0_275, all_23_0_267, all_0_6_6 and discharging atoms product(all_47_0_275, all_23_0_267) = all_0_5_5, product(all_0_5_5, all_0_6_6) = all_47_0_275, yields:
% 41.63/14.27 | (483) ? [v0] : (product(all_47_0_275, v0) = all_47_0_275 & product(all_23_0_267, all_0_6_6) = v0)
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (22) with all_47_0_275, all_0_5_5, all_0_5_5, all_0_5_5, all_0_6_6 and discharging atoms product(all_0_5_5, all_0_5_5) = all_0_5_5, product(all_0_5_5, all_0_6_6) = all_47_0_275, yields:
% 41.63/14.27 | (484) ? [v0] : (product(all_0_5_5, v0) = all_47_0_275 & product(all_0_5_5, all_0_6_6) = v0)
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (22) with all_0_6_6, all_0_6_6, all_23_0_267, all_47_0_275, all_0_6_6 and discharging atoms product(all_23_0_267, all_47_0_275) = all_0_6_6, product(all_0_6_6, all_0_6_6) = all_0_6_6, yields:
% 41.63/14.27 | (485) ? [v0] : (product(all_47_0_275, all_0_6_6) = v0 & product(all_23_0_267, v0) = all_0_6_6)
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (10) with all_47_0_275, all_0_6_6, all_0_5_5, all_0_6_6, all_0_6_6 and discharging atoms product(all_0_5_5, all_0_6_6) = all_47_0_275, product(all_0_6_6, all_0_6_6) = all_0_6_6, yields:
% 41.63/14.27 | (486) ? [v0] : (product(v0, all_0_6_6) = all_47_0_275 & product(all_0_5_5, all_0_6_6) = v0)
% 41.63/14.27 |
% 41.63/14.27 | Instantiating (484) with all_112_0_293 yields:
% 41.63/14.27 | (487) product(all_0_5_5, all_112_0_293) = all_47_0_275 & product(all_0_5_5, all_0_6_6) = all_112_0_293
% 41.63/14.27 |
% 41.63/14.27 | Applying alpha-rule on (487) yields:
% 41.63/14.27 | (488) product(all_0_5_5, all_112_0_293) = all_47_0_275
% 41.63/14.27 | (489) product(all_0_5_5, all_0_6_6) = all_112_0_293
% 41.63/14.27 |
% 41.63/14.27 | Instantiating (481) with all_120_0_299 yields:
% 41.63/14.27 | (490) product(all_23_0_267, all_120_0_299) = all_0_6_6 & product(all_0_5_5, all_47_0_275) = all_120_0_299
% 41.63/14.27 |
% 41.63/14.27 | Applying alpha-rule on (490) yields:
% 41.63/14.27 | (491) product(all_23_0_267, all_120_0_299) = all_0_6_6
% 41.63/14.27 | (492) product(all_0_5_5, all_47_0_275) = all_120_0_299
% 41.63/14.27 |
% 41.63/14.27 | Instantiating (482) with all_124_0_302 yields:
% 41.63/14.27 | (493) product(all_124_0_302, all_23_0_267) = all_0_5_5 & product(all_0_5_5, all_47_0_275) = all_124_0_302
% 41.63/14.27 |
% 41.63/14.27 | Applying alpha-rule on (493) yields:
% 41.63/14.27 | (494) product(all_124_0_302, all_23_0_267) = all_0_5_5
% 41.63/14.27 | (495) product(all_0_5_5, all_47_0_275) = all_124_0_302
% 41.63/14.27 |
% 41.63/14.27 | Instantiating (486) with all_132_0_309 yields:
% 41.63/14.27 | (496) product(all_132_0_309, all_0_6_6) = all_47_0_275 & product(all_0_5_5, all_0_6_6) = all_132_0_309
% 41.63/14.27 |
% 41.63/14.27 | Applying alpha-rule on (496) yields:
% 41.63/14.27 | (497) product(all_132_0_309, all_0_6_6) = all_47_0_275
% 41.63/14.27 | (498) product(all_0_5_5, all_0_6_6) = all_132_0_309
% 41.63/14.27 |
% 41.63/14.27 | Instantiating (485) with all_134_0_310 yields:
% 41.63/14.27 | (499) product(all_47_0_275, all_0_6_6) = all_134_0_310 & product(all_23_0_267, all_134_0_310) = all_0_6_6
% 41.63/14.27 |
% 41.63/14.27 | Applying alpha-rule on (499) yields:
% 41.63/14.27 | (500) product(all_47_0_275, all_0_6_6) = all_134_0_310
% 41.63/14.27 | (501) product(all_23_0_267, all_134_0_310) = all_0_6_6
% 41.63/14.27 |
% 41.63/14.27 | Instantiating (483) with all_139_0_314 yields:
% 41.63/14.27 | (502) product(all_47_0_275, all_139_0_314) = all_47_0_275 & product(all_23_0_267, all_0_6_6) = all_139_0_314
% 41.63/14.27 |
% 41.63/14.27 | Applying alpha-rule on (502) yields:
% 41.63/14.27 | (503) product(all_47_0_275, all_139_0_314) = all_47_0_275
% 41.63/14.27 | (504) product(all_23_0_267, all_0_6_6) = all_139_0_314
% 41.63/14.27 |
% 41.63/14.27 | Instantiating (480) with all_142_0_316 yields:
% 41.63/14.27 | (505) product(all_142_0_316, all_23_0_267) = all_0_5_5 & product(all_47_0_275, all_0_6_6) = all_142_0_316
% 41.63/14.27 |
% 41.63/14.27 | Applying alpha-rule on (505) yields:
% 41.63/14.27 | (506) product(all_142_0_316, all_23_0_267) = all_0_5_5
% 41.63/14.27 | (507) product(all_47_0_275, all_0_6_6) = all_142_0_316
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (16) with all_47_0_275, all_0_6_6, all_134_0_310, all_142_0_316 and discharging atoms product(all_47_0_275, all_0_6_6) = all_142_0_316, product(all_47_0_275, all_0_6_6) = all_134_0_310, yields:
% 41.63/14.27 | (508) all_142_0_316 = all_134_0_310
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (16) with all_23_0_267, all_0_6_6, all_139_0_314, all_0_6_6 and discharging atoms product(all_23_0_267, all_0_6_6) = all_139_0_314, product(all_23_0_267, all_0_6_6) = all_0_6_6, yields:
% 41.63/14.27 | (509) all_139_0_314 = all_0_6_6
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (16) with all_0_5_5, all_47_0_275, all_120_0_299, all_124_0_302 and discharging atoms product(all_0_5_5, all_47_0_275) = all_124_0_302, product(all_0_5_5, all_47_0_275) = all_120_0_299, yields:
% 41.63/14.27 | (510) all_124_0_302 = all_120_0_299
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (16) with all_0_5_5, all_0_6_6, all_132_0_309, all_47_0_275 and discharging atoms product(all_0_5_5, all_0_6_6) = all_132_0_309, product(all_0_5_5, all_0_6_6) = all_47_0_275, yields:
% 41.63/14.27 | (511) all_132_0_309 = all_47_0_275
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (16) with all_0_5_5, all_0_6_6, all_112_0_293, all_132_0_309 and discharging atoms product(all_0_5_5, all_0_6_6) = all_132_0_309, product(all_0_5_5, all_0_6_6) = all_112_0_293, yields:
% 41.63/14.27 | (512) all_132_0_309 = all_112_0_293
% 41.63/14.27 |
% 41.63/14.27 | Combining equations (511,512) yields a new equation:
% 41.63/14.27 | (513) all_112_0_293 = all_47_0_275
% 41.63/14.27 |
% 41.63/14.27 | From (510) and (494) follows:
% 41.63/14.27 | (514) product(all_120_0_299, all_23_0_267) = all_0_5_5
% 41.63/14.27 |
% 41.63/14.27 | From (509) and (503) follows:
% 41.63/14.27 | (515) product(all_47_0_275, all_0_6_6) = all_47_0_275
% 41.63/14.27 |
% 41.63/14.27 | From (508) and (507) follows:
% 41.63/14.27 | (500) product(all_47_0_275, all_0_6_6) = all_134_0_310
% 41.63/14.27 |
% 41.63/14.27 | From (513) and (488) follows:
% 41.63/14.27 | (517) product(all_0_5_5, all_47_0_275) = all_47_0_275
% 41.63/14.27 |
% 41.63/14.27 | From (510) and (495) follows:
% 41.63/14.27 | (492) product(all_0_5_5, all_47_0_275) = all_120_0_299
% 41.63/14.27 |
% 41.63/14.27 | From (513) and (489) follows:
% 41.63/14.27 | (445) product(all_0_5_5, all_0_6_6) = all_47_0_275
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (16) with all_47_0_275, all_0_6_6, all_47_0_275, all_134_0_310 and discharging atoms product(all_47_0_275, all_0_6_6) = all_134_0_310, product(all_47_0_275, all_0_6_6) = all_47_0_275, yields:
% 41.63/14.27 | (520) all_134_0_310 = all_47_0_275
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (16) with all_0_5_5, all_47_0_275, all_47_0_275, all_120_0_299 and discharging atoms product(all_0_5_5, all_47_0_275) = all_120_0_299, product(all_0_5_5, all_47_0_275) = all_47_0_275, yields:
% 41.63/14.27 | (521) all_120_0_299 = all_47_0_275
% 41.63/14.27 |
% 41.63/14.27 | From (521) and (514) follows:
% 41.63/14.27 | (462) product(all_47_0_275, all_23_0_267) = all_0_5_5
% 41.63/14.27 |
% 41.63/14.27 | From (520) and (500) follows:
% 41.63/14.27 | (515) product(all_47_0_275, all_0_6_6) = all_47_0_275
% 41.63/14.27 |
% 41.63/14.27 | From (521) and (491) follows:
% 41.63/14.27 | (444) product(all_23_0_267, all_47_0_275) = all_0_6_6
% 41.63/14.27 |
% 41.63/14.27 | From (521) and (492) follows:
% 41.63/14.27 | (517) product(all_0_5_5, all_47_0_275) = all_47_0_275
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (29) with all_47_0_275, all_0_6_6 and discharging atoms product(all_47_0_275, all_0_6_6) = all_47_0_275, yields:
% 41.63/14.27 | (526) ? [v0] : ((v0 = 0 & l(all_0_6_6, all_47_0_275) = 0) | ( ~ (v0 = all_0_6_6) & product(all_0_6_6, all_47_0_275) = v0))
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (25) with all_0_6_6, all_47_0_275 and discharging atoms product(all_47_0_275, all_0_6_6) = all_47_0_275, yields:
% 41.63/14.27 | (527) ? [v0] : ((v0 = 0 & l(all_47_0_275, all_0_6_6) = 0) | ( ~ (v0 = all_0_6_6) & product(all_0_6_6, all_47_0_275) = v0))
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (20) with all_47_0_275, all_47_0_275, all_0_6_6 and discharging atoms product(all_47_0_275, all_0_6_6) = all_47_0_275, yields:
% 41.63/14.27 | (528) ? [v0] : ((v0 = all_0_6_6 & product(all_0_6_6, all_47_0_275) = all_0_6_6) | ( ~ (v0 = 0) & l(all_0_6_6, all_47_0_275) = v0))
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (12) with all_47_0_275, all_0_6_6, all_47_0_275 and discharging atoms product(all_47_0_275, all_0_6_6) = all_47_0_275, yields:
% 41.63/14.27 | (529) ? [v0] : ((v0 = all_0_6_6 & product(all_0_6_6, all_47_0_275) = all_0_6_6) | ( ~ (v0 = 0) & l(all_47_0_275, all_0_6_6) = v0))
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (21) with all_0_5_5, all_47_0_275 and discharging atoms product(all_0_5_5, all_47_0_275) = all_47_0_275, yields:
% 41.63/14.27 | (530) ? [v0] : ((v0 = 0 & r(all_47_0_275, all_0_5_5) = 0) | ( ~ (v0 = all_0_5_5) & product(all_47_0_275, all_0_5_5) = v0))
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (28) with all_47_0_275, all_0_5_5 and discharging atoms product(all_0_5_5, all_47_0_275) = all_47_0_275, yields:
% 41.63/14.27 | (531) ? [v0] : ((v0 = 0 & r(all_0_5_5, all_47_0_275) = 0) | ( ~ (v0 = all_0_5_5) & product(all_47_0_275, all_0_5_5) = v0))
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (26) with all_47_0_275, all_0_5_5, all_47_0_275 and discharging atoms product(all_0_5_5, all_47_0_275) = all_47_0_275, yields:
% 41.63/14.27 | (532) ? [v0] : ((v0 = all_0_5_5 & product(all_47_0_275, all_0_5_5) = all_0_5_5) | ( ~ (v0 = 0) & r(all_47_0_275, all_0_5_5) = v0))
% 41.63/14.27 |
% 41.63/14.27 | Instantiating formula (4) with all_47_0_275, all_47_0_275, all_0_5_5 and discharging atoms product(all_0_5_5, all_47_0_275) = all_47_0_275, yields:
% 41.63/14.27 | (533) ? [v0] : ((v0 = all_0_5_5 & product(all_47_0_275, all_0_5_5) = all_0_5_5) | ( ~ (v0 = 0) & r(all_0_5_5, all_47_0_275) = v0))
% 41.63/14.27 |
% 41.63/14.27 | Instantiating (533) with all_210_0_322 yields:
% 41.63/14.27 | (534) (all_210_0_322 = all_0_5_5 & product(all_47_0_275, all_0_5_5) = all_0_5_5) | ( ~ (all_210_0_322 = 0) & r(all_0_5_5, all_47_0_275) = all_210_0_322)
% 41.63/14.27 |
% 41.63/14.27 | Instantiating (532) with all_212_0_324 yields:
% 41.63/14.27 | (535) (all_212_0_324 = all_0_5_5 & product(all_47_0_275, all_0_5_5) = all_0_5_5) | ( ~ (all_212_0_324 = 0) & r(all_47_0_275, all_0_5_5) = all_212_0_324)
% 41.63/14.27 |
% 41.63/14.27 | Instantiating (531) with all_214_0_326 yields:
% 41.63/14.27 | (536) (all_214_0_326 = 0 & r(all_0_5_5, all_47_0_275) = 0) | ( ~ (all_214_0_326 = all_0_5_5) & product(all_47_0_275, all_0_5_5) = all_214_0_326)
% 41.63/14.27 |
% 41.63/14.27 | Instantiating (530) with all_215_0_327 yields:
% 41.63/14.27 | (537) (all_215_0_327 = 0 & r(all_47_0_275, all_0_5_5) = 0) | ( ~ (all_215_0_327 = all_0_5_5) & product(all_47_0_275, all_0_5_5) = all_215_0_327)
% 41.63/14.27 |
% 41.63/14.27 | Instantiating (528) with all_216_0_328 yields:
% 41.63/14.27 | (538) (all_216_0_328 = all_0_6_6 & product(all_0_6_6, all_47_0_275) = all_0_6_6) | ( ~ (all_216_0_328 = 0) & l(all_0_6_6, all_47_0_275) = all_216_0_328)
% 41.63/14.27 |
% 41.63/14.27 | Instantiating (527) with all_218_0_330 yields:
% 41.63/14.27 | (539) (all_218_0_330 = 0 & l(all_47_0_275, all_0_6_6) = 0) | ( ~ (all_218_0_330 = all_0_6_6) & product(all_0_6_6, all_47_0_275) = all_218_0_330)
% 41.63/14.27 |
% 41.63/14.27 | Instantiating (529) with all_220_0_332 yields:
% 41.63/14.27 | (540) (all_220_0_332 = all_0_6_6 & product(all_0_6_6, all_47_0_275) = all_0_6_6) | ( ~ (all_220_0_332 = 0) & l(all_47_0_275, all_0_6_6) = all_220_0_332)
% 41.63/14.28 |
% 41.63/14.28 | Instantiating (526) with all_221_0_333 yields:
% 41.63/14.28 | (541) (all_221_0_333 = 0 & l(all_0_6_6, all_47_0_275) = 0) | ( ~ (all_221_0_333 = all_0_6_6) & product(all_0_6_6, all_47_0_275) = all_221_0_333)
% 41.63/14.28 |
% 41.63/14.28 +-Applying beta-rule and splitting (411), into two cases.
% 41.63/14.28 |-Branch one:
% 41.63/14.28 | (542) ~ (all_0_0_0 = all_0_5_5) & product(all_0_5_5, all_0_1_1) = all_0_0_0 & product(all_0_6_6, all_0_5_5) = all_0_1_1
% 41.63/14.28 |
% 41.63/14.28 | Applying alpha-rule on (542) yields:
% 41.63/14.28 | (543) ~ (all_0_0_0 = all_0_5_5)
% 41.63/14.28 | (544) product(all_0_5_5, all_0_1_1) = all_0_0_0
% 41.63/14.28 | (32) product(all_0_6_6, all_0_5_5) = all_0_1_1
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (10) with all_0_1_1, all_0_5_5, all_0_6_6, all_47_0_275, all_23_0_267 and discharging atoms product(all_47_0_275, all_23_0_267) = all_0_5_5, product(all_0_6_6, all_0_5_5) = all_0_1_1, yields:
% 41.63/14.28 | (546) ? [v0] : (product(v0, all_23_0_267) = all_0_1_1 & product(all_0_6_6, all_47_0_275) = v0)
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (22) with all_0_1_1, all_0_6_6, all_23_0_267, all_47_0_275, all_0_5_5 and discharging atoms product(all_23_0_267, all_47_0_275) = all_0_6_6, product(all_0_6_6, all_0_5_5) = all_0_1_1, yields:
% 41.63/14.28 | (547) ? [v0] : (product(all_47_0_275, all_0_5_5) = v0 & product(all_23_0_267, v0) = all_0_1_1)
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (10) with all_0_0_0, all_0_1_1, all_0_5_5, all_0_6_6, all_0_5_5 and discharging atoms product(all_0_5_5, all_0_1_1) = all_0_0_0, product(all_0_6_6, all_0_5_5) = all_0_1_1, yields:
% 41.63/14.28 | (548) ? [v0] : (product(v0, all_0_5_5) = all_0_0_0 & product(all_0_5_5, all_0_6_6) = v0)
% 41.63/14.28 |
% 41.63/14.28 | Instantiating (547) with all_274_0_337 yields:
% 41.63/14.28 | (549) product(all_47_0_275, all_0_5_5) = all_274_0_337 & product(all_23_0_267, all_274_0_337) = all_0_1_1
% 41.63/14.28 |
% 41.63/14.28 | Applying alpha-rule on (549) yields:
% 41.63/14.28 | (550) product(all_47_0_275, all_0_5_5) = all_274_0_337
% 41.63/14.28 | (551) product(all_23_0_267, all_274_0_337) = all_0_1_1
% 41.63/14.28 |
% 41.63/14.28 | Instantiating (546) with all_276_0_338 yields:
% 41.63/14.28 | (552) product(all_276_0_338, all_23_0_267) = all_0_1_1 & product(all_0_6_6, all_47_0_275) = all_276_0_338
% 41.63/14.28 |
% 41.63/14.28 | Applying alpha-rule on (552) yields:
% 41.63/14.28 | (553) product(all_276_0_338, all_23_0_267) = all_0_1_1
% 41.63/14.28 | (554) product(all_0_6_6, all_47_0_275) = all_276_0_338
% 41.63/14.28 |
% 41.63/14.28 | Instantiating (548) with all_292_0_348 yields:
% 41.63/14.28 | (555) product(all_292_0_348, all_0_5_5) = all_0_0_0 & product(all_0_5_5, all_0_6_6) = all_292_0_348
% 41.63/14.28 |
% 41.63/14.28 | Applying alpha-rule on (555) yields:
% 41.63/14.28 | (556) product(all_292_0_348, all_0_5_5) = all_0_0_0
% 41.63/14.28 | (557) product(all_0_5_5, all_0_6_6) = all_292_0_348
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (16) with all_0_5_5, all_0_6_6, all_292_0_348, all_47_0_275 and discharging atoms product(all_0_5_5, all_0_6_6) = all_292_0_348, product(all_0_5_5, all_0_6_6) = all_47_0_275, yields:
% 41.63/14.28 | (558) all_292_0_348 = all_47_0_275
% 41.63/14.28 |
% 41.63/14.28 | From (558) and (556) follows:
% 41.63/14.28 | (559) product(all_47_0_275, all_0_5_5) = all_0_0_0
% 41.63/14.28 |
% 41.63/14.28 +-Applying beta-rule and splitting (534), into two cases.
% 41.63/14.28 |-Branch one:
% 41.63/14.28 | (560) all_210_0_322 = all_0_5_5 & product(all_47_0_275, all_0_5_5) = all_0_5_5
% 41.63/14.28 |
% 41.63/14.28 | Applying alpha-rule on (560) yields:
% 41.63/14.28 | (561) all_210_0_322 = all_0_5_5
% 41.63/14.28 | (562) product(all_47_0_275, all_0_5_5) = all_0_5_5
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (16) with all_47_0_275, all_0_5_5, all_0_0_0, all_274_0_337 and discharging atoms product(all_47_0_275, all_0_5_5) = all_274_0_337, product(all_47_0_275, all_0_5_5) = all_0_0_0, yields:
% 41.63/14.28 | (563) all_274_0_337 = all_0_0_0
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (16) with all_47_0_275, all_0_5_5, all_0_5_5, all_274_0_337 and discharging atoms product(all_47_0_275, all_0_5_5) = all_274_0_337, product(all_47_0_275, all_0_5_5) = all_0_5_5, yields:
% 41.63/14.28 | (564) all_274_0_337 = all_0_5_5
% 41.63/14.28 |
% 41.63/14.28 | Combining equations (564,563) yields a new equation:
% 41.63/14.28 | (36) all_0_0_0 = all_0_5_5
% 41.63/14.28 |
% 41.63/14.28 | Equations (36) can reduce 543 to:
% 41.63/14.28 | (199) $false
% 41.63/14.28 |
% 41.63/14.28 |-The branch is then unsatisfiable
% 41.63/14.28 |-Branch two:
% 41.63/14.28 | (567) ~ (all_210_0_322 = 0) & r(all_0_5_5, all_47_0_275) = all_210_0_322
% 41.63/14.28 |
% 41.63/14.28 | Applying alpha-rule on (567) yields:
% 41.63/14.28 | (568) ~ (all_210_0_322 = 0)
% 41.63/14.28 | (569) r(all_0_5_5, all_47_0_275) = all_210_0_322
% 41.63/14.28 |
% 41.63/14.28 +-Applying beta-rule and splitting (535), into two cases.
% 41.63/14.28 |-Branch one:
% 41.63/14.28 | (570) all_212_0_324 = all_0_5_5 & product(all_47_0_275, all_0_5_5) = all_0_5_5
% 41.63/14.28 |
% 41.63/14.28 | Applying alpha-rule on (570) yields:
% 41.63/14.28 | (571) all_212_0_324 = all_0_5_5
% 41.63/14.28 | (562) product(all_47_0_275, all_0_5_5) = all_0_5_5
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (16) with all_47_0_275, all_0_5_5, all_0_0_0, all_274_0_337 and discharging atoms product(all_47_0_275, all_0_5_5) = all_274_0_337, product(all_47_0_275, all_0_5_5) = all_0_0_0, yields:
% 41.63/14.28 | (563) all_274_0_337 = all_0_0_0
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (16) with all_47_0_275, all_0_5_5, all_0_5_5, all_274_0_337 and discharging atoms product(all_47_0_275, all_0_5_5) = all_274_0_337, product(all_47_0_275, all_0_5_5) = all_0_5_5, yields:
% 41.63/14.28 | (564) all_274_0_337 = all_0_5_5
% 41.63/14.28 |
% 41.63/14.28 | Combining equations (563,564) yields a new equation:
% 41.63/14.28 | (575) all_0_0_0 = all_0_5_5
% 41.63/14.28 |
% 41.63/14.28 | Simplifying 575 yields:
% 41.63/14.28 | (36) all_0_0_0 = all_0_5_5
% 41.63/14.28 |
% 41.63/14.28 | Equations (36) can reduce 543 to:
% 41.63/14.28 | (199) $false
% 41.63/14.28 |
% 41.63/14.28 |-The branch is then unsatisfiable
% 41.63/14.28 |-Branch two:
% 41.63/14.28 | (578) ~ (all_212_0_324 = 0) & r(all_47_0_275, all_0_5_5) = all_212_0_324
% 41.63/14.28 |
% 41.63/14.28 | Applying alpha-rule on (578) yields:
% 41.63/14.28 | (579) ~ (all_212_0_324 = 0)
% 41.63/14.28 | (580) r(all_47_0_275, all_0_5_5) = all_212_0_324
% 41.63/14.28 |
% 41.63/14.28 +-Applying beta-rule and splitting (537), into two cases.
% 41.63/14.28 |-Branch one:
% 41.63/14.28 | (581) all_215_0_327 = 0 & r(all_47_0_275, all_0_5_5) = 0
% 41.63/14.28 |
% 41.63/14.28 | Applying alpha-rule on (581) yields:
% 41.63/14.28 | (582) all_215_0_327 = 0
% 41.63/14.28 | (583) r(all_47_0_275, all_0_5_5) = 0
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (9) with all_47_0_275, all_0_5_5, 0, all_212_0_324 and discharging atoms r(all_47_0_275, all_0_5_5) = all_212_0_324, r(all_47_0_275, all_0_5_5) = 0, yields:
% 41.63/14.28 | (584) all_212_0_324 = 0
% 41.63/14.28 |
% 41.63/14.28 | Equations (584) can reduce 579 to:
% 41.63/14.28 | (199) $false
% 41.63/14.28 |
% 41.63/14.28 |-The branch is then unsatisfiable
% 41.63/14.28 |-Branch two:
% 41.63/14.28 | (586) ~ (all_215_0_327 = all_0_5_5) & product(all_47_0_275, all_0_5_5) = all_215_0_327
% 41.63/14.28 |
% 41.63/14.28 | Applying alpha-rule on (586) yields:
% 41.63/14.28 | (587) ~ (all_215_0_327 = all_0_5_5)
% 41.63/14.28 | (588) product(all_47_0_275, all_0_5_5) = all_215_0_327
% 41.63/14.28 |
% 41.63/14.28 +-Applying beta-rule and splitting (536), into two cases.
% 41.63/14.28 |-Branch one:
% 41.63/14.28 | (589) all_214_0_326 = 0 & r(all_0_5_5, all_47_0_275) = 0
% 41.63/14.28 |
% 41.63/14.28 | Applying alpha-rule on (589) yields:
% 41.63/14.28 | (590) all_214_0_326 = 0
% 41.63/14.28 | (591) r(all_0_5_5, all_47_0_275) = 0
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (9) with all_0_5_5, all_47_0_275, 0, all_210_0_322 and discharging atoms r(all_0_5_5, all_47_0_275) = all_210_0_322, r(all_0_5_5, all_47_0_275) = 0, yields:
% 41.63/14.28 | (592) all_210_0_322 = 0
% 41.63/14.28 |
% 41.63/14.28 | Equations (592) can reduce 568 to:
% 41.63/14.28 | (199) $false
% 41.63/14.28 |
% 41.63/14.28 |-The branch is then unsatisfiable
% 41.63/14.28 |-Branch two:
% 41.63/14.28 | (594) ~ (all_214_0_326 = all_0_5_5) & product(all_47_0_275, all_0_5_5) = all_214_0_326
% 41.63/14.28 |
% 41.63/14.28 | Applying alpha-rule on (594) yields:
% 41.63/14.28 | (595) ~ (all_214_0_326 = all_0_5_5)
% 41.63/14.28 | (596) product(all_47_0_275, all_0_5_5) = all_214_0_326
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (16) with all_47_0_275, all_0_5_5, all_215_0_327, all_274_0_337 and discharging atoms product(all_47_0_275, all_0_5_5) = all_274_0_337, product(all_47_0_275, all_0_5_5) = all_215_0_327, yields:
% 41.63/14.28 | (597) all_274_0_337 = all_215_0_327
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (16) with all_47_0_275, all_0_5_5, all_214_0_326, all_274_0_337 and discharging atoms product(all_47_0_275, all_0_5_5) = all_274_0_337, product(all_47_0_275, all_0_5_5) = all_214_0_326, yields:
% 41.63/14.28 | (598) all_274_0_337 = all_214_0_326
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (16) with all_47_0_275, all_0_5_5, all_0_0_0, all_274_0_337 and discharging atoms product(all_47_0_275, all_0_5_5) = all_274_0_337, product(all_47_0_275, all_0_5_5) = all_0_0_0, yields:
% 41.63/14.28 | (563) all_274_0_337 = all_0_0_0
% 41.63/14.28 |
% 41.63/14.28 | Combining equations (563,597) yields a new equation:
% 41.63/14.28 | (600) all_215_0_327 = all_0_0_0
% 41.63/14.28 |
% 41.63/14.28 | Combining equations (598,597) yields a new equation:
% 41.63/14.28 | (601) all_215_0_327 = all_214_0_326
% 41.63/14.28 |
% 41.63/14.28 | Combining equations (600,601) yields a new equation:
% 41.63/14.28 | (602) all_214_0_326 = all_0_0_0
% 41.63/14.28 |
% 41.63/14.28 | Equations (602) can reduce 595 to:
% 41.63/14.28 | (543) ~ (all_0_0_0 = all_0_5_5)
% 41.63/14.28 |
% 41.63/14.28 | From (602) and (596) follows:
% 41.63/14.28 | (559) product(all_47_0_275, all_0_5_5) = all_0_0_0
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (10) with all_0_0_0, all_0_5_5, all_47_0_275, all_47_0_275, all_23_0_267 and discharging atoms product(all_47_0_275, all_23_0_267) = all_0_5_5, product(all_47_0_275, all_0_5_5) = all_0_0_0, yields:
% 41.63/14.28 | (605) ? [v0] : (product(v0, all_23_0_267) = all_0_0_0 & product(all_47_0_275, all_47_0_275) = v0)
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (22) with all_276_0_338, all_0_6_6, all_23_0_267, all_47_0_275, all_47_0_275 and discharging atoms product(all_23_0_267, all_47_0_275) = all_0_6_6, product(all_0_6_6, all_47_0_275) = all_276_0_338, yields:
% 41.63/14.28 | (606) ? [v0] : (product(all_47_0_275, all_47_0_275) = v0 & product(all_23_0_267, v0) = all_276_0_338)
% 41.63/14.28 |
% 41.63/14.28 | Instantiating (605) with all_494_0_401 yields:
% 41.63/14.28 | (607) product(all_494_0_401, all_23_0_267) = all_0_0_0 & product(all_47_0_275, all_47_0_275) = all_494_0_401
% 41.63/14.28 |
% 41.63/14.28 | Applying alpha-rule on (607) yields:
% 41.63/14.28 | (608) product(all_494_0_401, all_23_0_267) = all_0_0_0
% 41.63/14.28 | (609) product(all_47_0_275, all_47_0_275) = all_494_0_401
% 41.63/14.28 |
% 41.63/14.28 | Instantiating (606) with all_514_0_415 yields:
% 41.63/14.28 | (610) product(all_47_0_275, all_47_0_275) = all_514_0_415 & product(all_23_0_267, all_514_0_415) = all_276_0_338
% 41.63/14.28 |
% 41.63/14.28 | Applying alpha-rule on (610) yields:
% 41.63/14.28 | (611) product(all_47_0_275, all_47_0_275) = all_514_0_415
% 41.63/14.28 | (612) product(all_23_0_267, all_514_0_415) = all_276_0_338
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (5) with all_514_0_415, all_47_0_275 and discharging atoms product(all_47_0_275, all_47_0_275) = all_514_0_415, yields:
% 41.63/14.28 | (613) all_514_0_415 = all_47_0_275
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (16) with all_47_0_275, all_47_0_275, all_494_0_401, all_514_0_415 and discharging atoms product(all_47_0_275, all_47_0_275) = all_514_0_415, product(all_47_0_275, all_47_0_275) = all_494_0_401, yields:
% 41.63/14.28 | (614) all_514_0_415 = all_494_0_401
% 41.63/14.28 |
% 41.63/14.28 | Combining equations (613,614) yields a new equation:
% 41.63/14.28 | (615) all_494_0_401 = all_47_0_275
% 41.63/14.28 |
% 41.63/14.28 | From (615) and (608) follows:
% 41.63/14.28 | (616) product(all_47_0_275, all_23_0_267) = all_0_0_0
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (16) with all_47_0_275, all_23_0_267, all_0_0_0, all_0_5_5 and discharging atoms product(all_47_0_275, all_23_0_267) = all_0_0_0, product(all_47_0_275, all_23_0_267) = all_0_5_5, yields:
% 41.63/14.28 | (36) all_0_0_0 = all_0_5_5
% 41.63/14.28 |
% 41.63/14.28 | Equations (36) can reduce 543 to:
% 41.63/14.28 | (199) $false
% 41.63/14.28 |
% 41.63/14.28 |-The branch is then unsatisfiable
% 41.63/14.28 |-Branch two:
% 41.63/14.28 | (619) ~ (all_0_2_2 = all_0_6_6) & product(all_0_5_5, all_0_6_6) = all_0_3_3 & product(all_0_6_6, all_0_3_3) = all_0_2_2
% 41.63/14.28 |
% 41.63/14.28 | Applying alpha-rule on (619) yields:
% 41.63/14.28 | (620) ~ (all_0_2_2 = all_0_6_6)
% 41.63/14.28 | (37) product(all_0_5_5, all_0_6_6) = all_0_3_3
% 41.63/14.28 | (622) product(all_0_6_6, all_0_3_3) = all_0_2_2
% 41.63/14.28 |
% 41.63/14.28 | Instantiating formula (16) with all_0_5_5, all_0_6_6, all_0_3_3, all_47_0_275 and discharging atoms product(all_0_5_5, all_0_6_6) = all_47_0_275, product(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 41.63/14.28 | (623) all_47_0_275 = all_0_3_3
% 41.63/14.28 |
% 41.63/14.28 | From (623) and (444) follows:
% 41.63/14.28 | (624) product(all_23_0_267, all_0_3_3) = all_0_6_6
% 41.63/14.28 |
% 41.63/14.28 +-Applying beta-rule and splitting (538), into two cases.
% 41.63/14.28 |-Branch one:
% 41.63/14.28 | (625) all_216_0_328 = all_0_6_6 & product(all_0_6_6, all_47_0_275) = all_0_6_6
% 41.63/14.28 |
% 41.63/14.28 | Applying alpha-rule on (625) yields:
% 41.63/14.28 | (626) all_216_0_328 = all_0_6_6
% 41.63/14.28 | (627) product(all_0_6_6, all_47_0_275) = all_0_6_6
% 41.63/14.28 |
% 41.63/14.28 | From (623) and (627) follows:
% 41.63/14.28 | (34) product(all_0_6_6, all_0_3_3) = all_0_6_6
% 41.63/14.28 |
% 41.63/14.29 | Instantiating formula (16) with all_0_6_6, all_0_3_3, all_0_6_6, all_0_2_2 and discharging atoms product(all_0_6_6, all_0_3_3) = all_0_2_2, product(all_0_6_6, all_0_3_3) = all_0_6_6, yields:
% 41.63/14.29 | (31) all_0_2_2 = all_0_6_6
% 41.63/14.29 |
% 41.63/14.29 | Equations (31) can reduce 620 to:
% 41.63/14.29 | (199) $false
% 41.63/14.29 |
% 41.63/14.29 |-The branch is then unsatisfiable
% 41.63/14.29 |-Branch two:
% 41.63/14.29 | (631) ~ (all_216_0_328 = 0) & l(all_0_6_6, all_47_0_275) = all_216_0_328
% 41.63/14.29 |
% 41.63/14.29 | Applying alpha-rule on (631) yields:
% 41.63/14.29 | (632) ~ (all_216_0_328 = 0)
% 41.63/14.29 | (633) l(all_0_6_6, all_47_0_275) = all_216_0_328
% 41.63/14.29 |
% 41.63/14.29 | From (623) and (633) follows:
% 41.63/14.29 | (634) l(all_0_6_6, all_0_3_3) = all_216_0_328
% 41.63/14.29 |
% 41.63/14.29 +-Applying beta-rule and splitting (541), into two cases.
% 41.63/14.29 |-Branch one:
% 41.63/14.29 | (635) all_221_0_333 = 0 & l(all_0_6_6, all_47_0_275) = 0
% 41.63/14.29 |
% 41.63/14.29 | Applying alpha-rule on (635) yields:
% 41.63/14.29 | (636) all_221_0_333 = 0
% 41.63/14.29 | (637) l(all_0_6_6, all_47_0_275) = 0
% 41.63/14.29 |
% 41.63/14.29 | From (623) and (637) follows:
% 41.63/14.29 | (122) l(all_0_6_6, all_0_3_3) = 0
% 41.63/14.29 |
% 41.63/14.29 | Instantiating formula (17) with all_0_6_6, all_0_3_3, 0, all_216_0_328 and discharging atoms l(all_0_6_6, all_0_3_3) = all_216_0_328, l(all_0_6_6, all_0_3_3) = 0, yields:
% 41.63/14.29 | (639) all_216_0_328 = 0
% 41.63/14.29 |
% 41.63/14.29 | Equations (639) can reduce 632 to:
% 41.63/14.29 | (199) $false
% 41.63/14.29 |
% 41.63/14.29 |-The branch is then unsatisfiable
% 41.63/14.29 |-Branch two:
% 41.63/14.29 | (641) ~ (all_221_0_333 = all_0_6_6) & product(all_0_6_6, all_47_0_275) = all_221_0_333
% 41.63/14.29 |
% 41.63/14.29 | Applying alpha-rule on (641) yields:
% 41.63/14.29 | (642) ~ (all_221_0_333 = all_0_6_6)
% 41.63/14.29 | (643) product(all_0_6_6, all_47_0_275) = all_221_0_333
% 41.63/14.29 |
% 41.63/14.29 | From (623) and (643) follows:
% 41.63/14.29 | (644) product(all_0_6_6, all_0_3_3) = all_221_0_333
% 41.63/14.29 |
% 41.63/14.29 +-Applying beta-rule and splitting (540), into two cases.
% 41.63/14.29 |-Branch one:
% 41.63/14.29 | (645) all_220_0_332 = all_0_6_6 & product(all_0_6_6, all_47_0_275) = all_0_6_6
% 41.63/14.29 |
% 41.63/14.29 | Applying alpha-rule on (645) yields:
% 41.63/14.29 | (646) all_220_0_332 = all_0_6_6
% 41.63/14.29 | (627) product(all_0_6_6, all_47_0_275) = all_0_6_6
% 41.63/14.29 |
% 41.63/14.29 | From (623) and (627) follows:
% 41.63/14.29 | (34) product(all_0_6_6, all_0_3_3) = all_0_6_6
% 41.63/14.29 |
% 41.63/14.29 | Instantiating formula (16) with all_0_6_6, all_0_3_3, all_221_0_333, all_0_2_2 and discharging atoms product(all_0_6_6, all_0_3_3) = all_221_0_333, product(all_0_6_6, all_0_3_3) = all_0_2_2, yields:
% 41.63/14.29 | (649) all_221_0_333 = all_0_2_2
% 41.63/14.29 |
% 41.63/14.29 | Instantiating formula (16) with all_0_6_6, all_0_3_3, all_0_6_6, all_221_0_333 and discharging atoms product(all_0_6_6, all_0_3_3) = all_221_0_333, product(all_0_6_6, all_0_3_3) = all_0_6_6, yields:
% 41.63/14.29 | (650) all_221_0_333 = all_0_6_6
% 41.63/14.29 |
% 41.63/14.29 | Combining equations (649,650) yields a new equation:
% 41.63/14.29 | (651) all_0_2_2 = all_0_6_6
% 41.63/14.29 |
% 41.63/14.29 | Simplifying 651 yields:
% 41.63/14.29 | (31) all_0_2_2 = all_0_6_6
% 41.63/14.29 |
% 41.63/14.29 | Equations (31) can reduce 620 to:
% 41.63/14.29 | (199) $false
% 41.63/14.29 |
% 41.63/14.29 |-The branch is then unsatisfiable
% 41.63/14.29 |-Branch two:
% 41.63/14.29 | (654) ~ (all_220_0_332 = 0) & l(all_47_0_275, all_0_6_6) = all_220_0_332
% 41.63/14.29 |
% 41.63/14.29 | Applying alpha-rule on (654) yields:
% 41.63/14.29 | (655) ~ (all_220_0_332 = 0)
% 41.63/14.29 | (656) l(all_47_0_275, all_0_6_6) = all_220_0_332
% 41.63/14.29 |
% 41.63/14.29 | From (623) and (656) follows:
% 41.63/14.29 | (657) l(all_0_3_3, all_0_6_6) = all_220_0_332
% 41.63/14.29 |
% 41.63/14.29 +-Applying beta-rule and splitting (539), into two cases.
% 41.63/14.29 |-Branch one:
% 41.63/14.29 | (658) all_218_0_330 = 0 & l(all_47_0_275, all_0_6_6) = 0
% 41.63/14.29 |
% 41.63/14.29 | Applying alpha-rule on (658) yields:
% 41.63/14.29 | (659) all_218_0_330 = 0
% 41.63/14.29 | (660) l(all_47_0_275, all_0_6_6) = 0
% 41.63/14.29 |
% 41.63/14.29 | From (623) and (660) follows:
% 41.63/14.29 | (116) l(all_0_3_3, all_0_6_6) = 0
% 41.63/14.29 |
% 41.63/14.29 | Instantiating formula (17) with all_0_3_3, all_0_6_6, 0, all_220_0_332 and discharging atoms l(all_0_3_3, all_0_6_6) = all_220_0_332, l(all_0_3_3, all_0_6_6) = 0, yields:
% 41.63/14.29 | (662) all_220_0_332 = 0
% 41.63/14.29 |
% 41.63/14.29 | Equations (662) can reduce 655 to:
% 41.63/14.29 | (199) $false
% 41.63/14.29 |
% 41.63/14.29 |-The branch is then unsatisfiable
% 41.63/14.29 |-Branch two:
% 41.63/14.29 | (664) ~ (all_218_0_330 = all_0_6_6) & product(all_0_6_6, all_47_0_275) = all_218_0_330
% 41.63/14.29 |
% 41.63/14.29 | Applying alpha-rule on (664) yields:
% 41.63/14.29 | (665) ~ (all_218_0_330 = all_0_6_6)
% 41.63/14.29 | (666) product(all_0_6_6, all_47_0_275) = all_218_0_330
% 41.63/14.29 |
% 41.63/14.29 | From (623) and (666) follows:
% 41.63/14.29 | (667) product(all_0_6_6, all_0_3_3) = all_218_0_330
% 41.63/14.29 |
% 41.63/14.29 | Instantiating formula (16) with all_0_6_6, all_0_3_3, all_221_0_333, all_0_2_2 and discharging atoms product(all_0_6_6, all_0_3_3) = all_221_0_333, product(all_0_6_6, all_0_3_3) = all_0_2_2, yields:
% 41.63/14.29 | (649) all_221_0_333 = all_0_2_2
% 41.63/14.29 |
% 41.63/14.29 | Instantiating formula (16) with all_0_6_6, all_0_3_3, all_218_0_330, all_221_0_333 and discharging atoms product(all_0_6_6, all_0_3_3) = all_221_0_333, product(all_0_6_6, all_0_3_3) = all_218_0_330, yields:
% 41.63/14.29 | (669) all_221_0_333 = all_218_0_330
% 41.63/14.29 |
% 41.63/14.29 | Combining equations (649,669) yields a new equation:
% 41.63/14.29 | (670) all_218_0_330 = all_0_2_2
% 41.63/14.29 |
% 41.63/14.29 | Equations (670) can reduce 665 to:
% 41.63/14.29 | (620) ~ (all_0_2_2 = all_0_6_6)
% 41.63/14.29 |
% 41.63/14.29 | From (670) and (667) follows:
% 41.63/14.29 | (622) product(all_0_6_6, all_0_3_3) = all_0_2_2
% 41.63/14.29 |
% 41.63/14.29 | Instantiating formula (22) with all_0_2_2, all_0_6_6, all_23_0_267, all_0_3_3, all_0_3_3 and discharging atoms product(all_23_0_267, all_0_3_3) = all_0_6_6, product(all_0_6_6, all_0_3_3) = all_0_2_2, yields:
% 41.63/14.29 | (673) ? [v0] : (product(all_23_0_267, v0) = all_0_2_2 & product(all_0_3_3, all_0_3_3) = v0)
% 41.63/14.29 |
% 41.63/14.29 | Instantiating (673) with all_300_0_504 yields:
% 41.63/14.29 | (674) product(all_23_0_267, all_300_0_504) = all_0_2_2 & product(all_0_3_3, all_0_3_3) = all_300_0_504
% 41.63/14.29 |
% 41.63/14.29 | Applying alpha-rule on (674) yields:
% 41.63/14.29 | (675) product(all_23_0_267, all_300_0_504) = all_0_2_2
% 41.63/14.29 | (676) product(all_0_3_3, all_0_3_3) = all_300_0_504
% 41.63/14.29 |
% 41.63/14.29 | Instantiating formula (5) with all_300_0_504, all_0_3_3 and discharging atoms product(all_0_3_3, all_0_3_3) = all_300_0_504, yields:
% 41.63/14.29 | (677) all_300_0_504 = all_0_3_3
% 41.63/14.29 |
% 41.63/14.29 | From (677) and (675) follows:
% 41.63/14.29 | (678) product(all_23_0_267, all_0_3_3) = all_0_2_2
% 41.63/14.29 |
% 41.63/14.29 | Instantiating formula (16) with all_23_0_267, all_0_3_3, all_0_2_2, all_0_6_6 and discharging atoms product(all_23_0_267, all_0_3_3) = all_0_2_2, product(all_23_0_267, all_0_3_3) = all_0_6_6, yields:
% 41.63/14.29 | (31) all_0_2_2 = all_0_6_6
% 41.63/14.29 |
% 41.63/14.29 | Equations (31) can reduce 620 to:
% 41.63/14.29 | (199) $false
% 41.63/14.29 |
% 41.63/14.29 |-The branch is then unsatisfiable
% 41.63/14.29 |-Branch two:
% 41.63/14.29 | (681) ~ (all_63_0_285 = 0) & r(all_23_0_267, all_0_6_6) = all_63_0_285
% 41.63/14.29 |
% 41.63/14.29 | Applying alpha-rule on (681) yields:
% 41.63/14.29 | (682) ~ (all_63_0_285 = 0)
% 41.63/14.29 | (683) r(all_23_0_267, all_0_6_6) = all_63_0_285
% 41.63/14.29 |
% 41.63/14.29 | Instantiating formula (9) with all_23_0_267, all_0_6_6, 0, all_63_0_285 and discharging atoms r(all_23_0_267, all_0_6_6) = all_63_0_285, r(all_23_0_267, all_0_6_6) = 0, yields:
% 41.63/14.29 | (684) all_63_0_285 = 0
% 41.63/14.29 |
% 41.63/14.29 | Equations (684) can reduce 682 to:
% 41.63/14.29 | (199) $false
% 41.63/14.29 |
% 41.63/14.29 |-The branch is then unsatisfiable
% 41.63/14.29 |-Branch two:
% 41.63/14.29 | (686) ~ (all_36_0_268 = 0) & r(all_23_0_267, all_0_6_6) = all_36_0_268
% 41.63/14.29 |
% 41.63/14.29 | Applying alpha-rule on (686) yields:
% 41.63/14.29 | (687) ~ (all_36_0_268 = 0)
% 41.63/14.29 | (688) r(all_23_0_267, all_0_6_6) = all_36_0_268
% 41.63/14.29 |
% 41.63/14.29 | Instantiating formula (9) with all_23_0_267, all_0_6_6, 0, all_36_0_268 and discharging atoms r(all_23_0_267, all_0_6_6) = all_36_0_268, r(all_23_0_267, all_0_6_6) = 0, yields:
% 41.63/14.29 | (689) all_36_0_268 = 0
% 41.63/14.29 |
% 41.63/14.29 | Equations (689) can reduce 687 to:
% 41.63/14.29 | (199) $false
% 41.63/14.29 |
% 41.63/14.29 |-The branch is then unsatisfiable
% 41.63/14.29 |-Branch two:
% 41.63/14.29 | (691) ~ (all_37_0_269 = all_0_6_6) & product(all_23_0_267, all_0_6_6) = all_37_0_269
% 41.63/14.29 |
% 41.63/14.29 | Applying alpha-rule on (691) yields:
% 41.63/14.29 | (692) ~ (all_37_0_269 = all_0_6_6)
% 41.63/14.29 | (693) product(all_23_0_267, all_0_6_6) = all_37_0_269
% 41.63/14.29 |
% 41.63/14.29 | Instantiating formula (16) with all_23_0_267, all_0_6_6, all_37_0_269, all_0_6_6 and discharging atoms product(all_23_0_267, all_0_6_6) = all_37_0_269, product(all_23_0_267, all_0_6_6) = all_0_6_6, yields:
% 41.63/14.29 | (694) all_37_0_269 = all_0_6_6
% 41.63/14.29 |
% 41.63/14.29 | Equations (694) can reduce 692 to:
% 41.63/14.29 | (199) $false
% 41.63/14.29 |
% 41.63/14.29 |-The branch is then unsatisfiable
% 41.63/14.29 |-Branch two:
% 41.63/14.29 | (696) ~ (all_60_0_282 = 0) & l(all_0_5_5, all_23_0_267) = all_60_0_282
% 41.63/14.29 |
% 41.63/14.29 | Applying alpha-rule on (696) yields:
% 41.63/14.29 | (697) ~ (all_60_0_282 = 0)
% 41.63/14.29 | (698) l(all_0_5_5, all_23_0_267) = all_60_0_282
% 41.63/14.29 |
% 41.63/14.29 +-Applying beta-rule and splitting (439), into two cases.
% 41.63/14.29 |-Branch one:
% 41.63/14.29 | (699) all_40_0_271 = 0 & l(all_0_5_5, all_23_0_267) = 0
% 41.63/14.29 |
% 41.63/14.29 | Applying alpha-rule on (699) yields:
% 41.63/14.29 | (700) all_40_0_271 = 0
% 41.63/14.29 | (701) l(all_0_5_5, all_23_0_267) = 0
% 41.63/14.29 |
% 41.63/14.29 | Instantiating formula (17) with all_0_5_5, all_23_0_267, 0, all_60_0_282 and discharging atoms l(all_0_5_5, all_23_0_267) = all_60_0_282, l(all_0_5_5, all_23_0_267) = 0, yields:
% 41.63/14.29 | (702) all_60_0_282 = 0
% 41.63/14.29 |
% 41.63/14.29 | Equations (702) can reduce 697 to:
% 41.63/14.29 | (199) $false
% 41.63/14.29 |
% 41.63/14.29 |-The branch is then unsatisfiable
% 41.63/14.29 |-Branch two:
% 41.63/14.29 | (704) ~ (all_40_0_271 = all_23_0_267) & product(all_23_0_267, all_0_5_5) = all_40_0_271
% 41.63/14.29 |
% 41.63/14.29 | Applying alpha-rule on (704) yields:
% 41.63/14.29 | (705) ~ (all_40_0_271 = all_23_0_267)
% 41.63/14.29 | (706) product(all_23_0_267, all_0_5_5) = all_40_0_271
% 41.63/14.29 |
% 41.63/14.29 | Instantiating formula (16) with all_23_0_267, all_0_5_5, all_40_0_271, all_23_0_267 and discharging atoms product(all_23_0_267, all_0_5_5) = all_40_0_271, product(all_23_0_267, all_0_5_5) = all_23_0_267, yields:
% 41.63/14.29 | (707) all_40_0_271 = all_23_0_267
% 41.63/14.29 |
% 41.63/14.29 | Equations (707) can reduce 705 to:
% 41.63/14.29 | (199) $false
% 41.63/14.29 |
% 41.63/14.29 |-The branch is then unsatisfiable
% 41.63/14.29 % SZS output end Proof for theBenchmark
% 41.63/14.29
% 41.63/14.29 13702ms
%------------------------------------------------------------------------------