TSTP Solution File: KLE160+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : KLE160+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.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 : Sun Jul 17 01:51:41 EDT 2022
% Result : Theorem 32.53s 9.33s
% Output : Proof 48.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE160+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.33 % Computer : n005.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Thu Jun 16 07:26:08 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.58 ____ _
% 0.20/0.58 ___ / __ \_____(_)___ ________ __________
% 0.20/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.20/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.20/0.58
% 0.20/0.58 A Theorem Prover for First-Order Logic
% 0.20/0.59 (ePrincess v.1.0)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2015
% 0.20/0.59 (c) Peter Backeman, 2014-2015
% 0.20/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.59 Bug reports to peter@backeman.se
% 0.20/0.59
% 0.20/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.59
% 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.68/0.95 Prover 0: Preprocessing ...
% 2.38/1.21 Prover 0: Constructing countermodel ...
% 19.22/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.22/5.96 Prover 1: Preprocessing ...
% 19.58/6.06 Prover 1: Constructing countermodel ...
% 29.25/8.53 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 29.25/8.54 Prover 2: Preprocessing ...
% 29.42/8.58 Prover 2: Warning: ignoring some quantifiers
% 29.42/8.58 Prover 2: Constructing countermodel ...
% 32.53/9.33 Prover 2: proved (802ms)
% 32.53/9.33 Prover 1: stopped
% 32.53/9.33 Prover 0: stopped
% 32.53/9.33
% 32.53/9.33 No countermodel exists, formula is valid
% 32.53/9.33 % SZS status Theorem for theBenchmark
% 32.53/9.33
% 32.53/9.33 Generating proof ... Warning: ignoring some quantifiers
% 47.98/16.35 found it (size 506)
% 47.98/16.35
% 47.98/16.35 % SZS output start Proof for theBenchmark
% 47.98/16.36 Assumed formulas after preprocessing and simplification:
% 47.98/16.36 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & leq(v6, v8) = v9 & leq(v3, v4) = 0 & star(v2) = v7 & star(v0) = v5 & multiplication(v5, v1) = v6 & multiplication(v1, v7) = v8 & multiplication(v1, v2) = v4 & multiplication(v0, v1) = v3 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (strong_iteration(v10) = v13) | ~ (leq(v12, v14) = v15) | ~ (multiplication(v13, v11) = v14) | ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = 0) & leq(v12, v17) = v18 & multiplication(v10, v12) = v16 & addition(v16, v11) = v17)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (leq(v14, v12) = v15) | ~ (star(v10) = v13) | ~ (multiplication(v13, v11) = v14) | ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = 0) & leq(v17, v12) = v18 & multiplication(v10, v12) = v16 & addition(v16, v11) = v17)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (leq(v14, v12) = v15) | ~ (star(v10) = v13) | ~ (multiplication(v11, v13) = v14) | ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = 0) & leq(v17, v12) = v18 & multiplication(v12, v10) = v16 & addition(v16, v11) = v17)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (multiplication(v11, v12) = v14) | ~ (multiplication(v10, v12) = v13) | ~ (addition(v13, v14) = v15) | ? [v16] : (multiplication(v16, v12) = v15 & addition(v10, v11) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (multiplication(v10, v12) = v14) | ~ (multiplication(v10, v11) = v13) | ~ (addition(v13, v14) = v15) | ? [v16] : (multiplication(v10, v16) = v15 & addition(v11, v12) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (multiplication(v13, v12) = v14) | ~ (multiplication(v10, v11) = v13) | ? [v15] : (multiplication(v11, v12) = v15 & multiplication(v10, v15) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (multiplication(v13, v12) = v14) | ~ (addition(v10, v11) = v13) | ? [v15] : ? [v16] : (multiplication(v11, v12) = v16 & multiplication(v10, v12) = v15 & addition(v15, v16) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (multiplication(v12, v10) = v13) | ~ (addition(v13, v11) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & leq(v16, v12) = 0 & star(v10) = v15 & multiplication(v11, v15) = v16) | ( ~ (v15 = 0) & leq(v14, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (multiplication(v11, v12) = v13) | ~ (multiplication(v10, v13) = v14) | ? [v15] : (multiplication(v15, v12) = v14 & multiplication(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (multiplication(v10, v13) = v14) | ~ (addition(v11, v12) = v13) | ? [v15] : ? [v16] : (multiplication(v10, v12) = v16 & multiplication(v10, v11) = v15 & addition(v15, v16) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (multiplication(v10, v12) = v13) | ~ (addition(v13, v11) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & strong_iteration(v10) = v15 & leq(v12, v16) = 0 & multiplication(v15, v11) = v16) | ( ~ (v15 = 0) & leq(v12, v14) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (multiplication(v10, v12) = v13) | ~ (addition(v13, v11) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & leq(v16, v12) = 0 & star(v10) = v15 & multiplication(v15, v11) = v16) | ( ~ (v15 = 0) & leq(v14, v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (addition(v13, v10) = v14) | ~ (addition(v12, v11) = v13) | ? [v15] : (addition(v12, v15) = v14 & addition(v11, v10) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (addition(v12, v13) = v14) | ~ (addition(v11, v10) = v13) | ? [v15] : (addition(v15, v10) = v14 & addition(v12, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (leq(v13, v12) = v11) | ~ (leq(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (multiplication(v13, v12) = v11) | ~ (multiplication(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (addition(v13, v12) = v11) | ~ (addition(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (addition(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & leq(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (leq(v10, v11) = v12) | ? [v13] : ( ~ (v13 = v11) & addition(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (strong_iteration(v12) = v11) | ~ (strong_iteration(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (star(v12) = v11) | ~ (star(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (addition(v11, v10) = v12) | addition(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (addition(v10, v11) = v12) | addition(v11, v10) = v12) & ! [v10] : ! [v11] : (v11 = v10 | ~ (multiplication(v10, one) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (multiplication(one, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (addition(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (addition(v10, zero) = v11)) & ! [v10] : ! [v11] : (v11 = zero | ~ (multiplication(zero, v10) = v11)) & ! [v10] : ! [v11] : ( ~ (strong_iteration(v10) = v11) | ? [v12] : ? [v13] : (star(v10) = v12 & multiplication(v11, zero) = v13 & addition(v12, v13) = v11)) & ! [v10] : ! [v11] : ( ~ (strong_iteration(v10) = v11) | ? [v12] : (multiplication(v10, v11) = v12 & addition(v12, one) = v11)) & ! [v10] : ! [v11] : ( ~ (leq(v10, v11) = 0) | addition(v10, v11) = v11) & ! [v10] : ! [v11] : ( ~ (star(v10) = v11) | ? [v12] : ? [v13] : (strong_iteration(v10) = v12 & multiplication(v12, zero) = v13 & addition(v11, v13) = v12)) & ! [v10] : ! [v11] : ( ~ (star(v10) = v11) | ? [v12] : (multiplication(v11, v10) = v12 & addition(one, v12) = v11)) & ! [v10] : ! [v11] : ( ~ (star(v10) = v11) | ? [v12] : (multiplication(v10, v11) = v12 & addition(one, v12) = v11)) & ! [v10] : ! [v11] : ( ~ (addition(v10, v11) = v11) | leq(v10, v11) = 0) & ? [v10] : ? [v11] : ? [v12] : leq(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : multiplication(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : addition(v11, v10) = v12 & ? [v10] : ? [v11] : strong_iteration(v10) = v11 & ? [v10] : ? [v11] : star(v10) = v11)
% 48.28/16.40 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 48.28/16.40 | (1) ~ (all_0_0_0 = 0) & leq(all_0_3_3, all_0_1_1) = all_0_0_0 & leq(all_0_6_6, all_0_5_5) = 0 & star(all_0_7_7) = all_0_2_2 & star(all_0_9_9) = all_0_4_4 & multiplication(all_0_4_4, all_0_8_8) = all_0_3_3 & multiplication(all_0_8_8, all_0_2_2) = all_0_1_1 & multiplication(all_0_8_8, all_0_7_7) = all_0_5_5 & multiplication(all_0_9_9, all_0_8_8) = all_0_6_6 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (strong_iteration(v0) = v3) | ~ (leq(v2, v4) = v5) | ~ (multiplication(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v2, v7) = v8 & multiplication(v0, v2) = v6 & addition(v6, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v4, v2) = v5) | ~ (star(v0) = v3) | ~ (multiplication(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v7, v2) = v8 & multiplication(v0, v2) = v6 & addition(v6, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v4, v2) = v5) | ~ (star(v0) = v3) | ~ (multiplication(v1, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v7, v2) = v8 & multiplication(v2, v0) = v6 & addition(v6, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ? [v5] : ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v2, v0) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & leq(v6, v2) = 0 & star(v0) = v5 & multiplication(v1, v5) = v6) | ( ~ (v5 = 0) & leq(v4, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ? [v5] : ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & strong_iteration(v0) = v5 & leq(v2, v6) = 0 & multiplication(v5, v1) = v6) | ( ~ (v5 = 0) & leq(v2, v4) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & leq(v6, v2) = 0 & star(v0) = v5 & multiplication(v5, v1) = v6) | ( ~ (v5 = 0) & leq(v4, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~ (strong_iteration(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1)) & ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1)) & ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) & ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : ? [v3] : (strong_iteration(v0) = v2 & multiplication(v2, zero) = v3 & addition(v1, v3) = v2)) & ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) & ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2 & ? [v0] : ? [v1] : strong_iteration(v0) = v1 & ? [v0] : ? [v1] : star(v0) = v1
% 48.28/16.42 |
% 48.28/16.42 | Applying alpha-rule on (1) yields:
% 48.28/16.42 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0))
% 48.28/16.42 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1))
% 48.28/16.42 | (4) multiplication(all_0_8_8, all_0_2_2) = all_0_1_1
% 48.28/16.42 | (5) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1))
% 48.28/16.42 | (6) star(all_0_7_7) = all_0_2_2
% 48.28/16.42 | (7) multiplication(all_0_8_8, all_0_7_7) = all_0_5_5
% 48.28/16.42 | (8) ? [v0] : ? [v1] : star(v0) = v1
% 48.28/16.42 | (9) ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2
% 48.28/16.42 | (10) leq(all_0_3_3, all_0_1_1) = all_0_0_0
% 48.28/16.42 | (11) ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2
% 48.28/16.42 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 48.28/16.42 | (13) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1))
% 48.28/16.42 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 48.28/16.42 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 48.28/16.42 | (16) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : ? [v3] : (strong_iteration(v0) = v2 & multiplication(v2, zero) = v3 & addition(v1, v3) = v2))
% 48.28/16.42 | (17) ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1))
% 48.28/16.42 | (18) multiplication(all_0_4_4, all_0_8_8) = all_0_3_3
% 48.28/16.42 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 48.28/16.42 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ? [v5] : ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4))
% 48.28/16.42 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 48.28/16.42 | (22) leq(all_0_6_6, all_0_5_5) = 0
% 48.28/16.42 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 48.28/16.42 | (24) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1))
% 48.28/16.42 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 48.28/16.42 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (strong_iteration(v0) = v3) | ~ (leq(v2, v4) = v5) | ~ (multiplication(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v2, v7) = v8 & multiplication(v0, v2) = v6 & addition(v6, v1) = v7))
% 48.28/16.42 | (27) ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2
% 48.28/16.42 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v4, v2) = v5) | ~ (star(v0) = v3) | ~ (multiplication(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v7, v2) = v8 & multiplication(v0, v2) = v6 & addition(v6, v1) = v7))
% 48.28/16.42 | (29) ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1))
% 48.28/16.42 | (30) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1))
% 48.28/16.42 | (31) ~ (all_0_0_0 = 0)
% 48.28/16.42 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 48.28/16.42 | (33) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1))
% 48.28/16.42 | (34) multiplication(all_0_9_9, all_0_8_8) = all_0_6_6
% 48.28/16.42 | (35) ? [v0] : ? [v1] : strong_iteration(v0) = v1
% 48.28/16.42 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 48.28/16.42 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ? [v5] : ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4))
% 48.28/16.43 | (38) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0)
% 48.28/16.43 | (39) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 48.28/16.43 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 48.28/16.43 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6))
% 48.28/16.43 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0))
% 48.28/16.43 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & strong_iteration(v0) = v5 & leq(v2, v6) = 0 & multiplication(v5, v1) = v6) | ( ~ (v5 = 0) & leq(v2, v4) = v5)))
% 48.28/16.43 | (44) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1))
% 48.28/16.43 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v2, v0) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & leq(v6, v2) = 0 & star(v0) = v5 & multiplication(v1, v5) = v6) | ( ~ (v5 = 0) & leq(v4, v2) = v5)))
% 48.28/16.43 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & leq(v6, v2) = 0 & star(v0) = v5 & multiplication(v5, v1) = v6) | ( ~ (v5 = 0) & leq(v4, v2) = v5)))
% 48.28/16.43 | (47) star(all_0_9_9) = all_0_4_4
% 48.28/16.43 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6))
% 48.28/16.43 | (49) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~ (strong_iteration(v2) = v0))
% 48.28/16.43 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v4, v2) = v5) | ~ (star(v0) = v3) | ~ (multiplication(v1, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v7, v2) = v8 & multiplication(v2, v0) = v6 & addition(v6, v1) = v7))
% 48.28/16.43 |
% 48.28/16.43 | Instantiating formula (12) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms leq(all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 48.28/16.43 | (51) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = all_0_1_1) & addition(all_0_3_3, all_0_1_1) = v0)
% 48.28/16.43 |
% 48.28/16.43 | Instantiating formula (39) with all_0_5_5, all_0_6_6 and discharging atoms leq(all_0_6_6, all_0_5_5) = 0, yields:
% 48.28/16.43 | (52) addition(all_0_6_6, all_0_5_5) = all_0_5_5
% 48.28/16.43 |
% 48.28/16.43 | Instantiating formula (13) with all_0_2_2, all_0_7_7 and discharging atoms star(all_0_7_7) = all_0_2_2, yields:
% 48.28/16.43 | (53) ? [v0] : (multiplication(all_0_2_2, all_0_7_7) = v0 & addition(one, v0) = all_0_2_2)
% 48.28/16.43 |
% 48.28/16.43 | Instantiating formula (33) with all_0_2_2, all_0_7_7 and discharging atoms star(all_0_7_7) = all_0_2_2, yields:
% 48.28/16.43 | (54) ? [v0] : (multiplication(all_0_7_7, all_0_2_2) = v0 & addition(one, v0) = all_0_2_2)
% 48.28/16.43 |
% 48.28/16.43 | Instantiating formula (13) with all_0_4_4, all_0_9_9 and discharging atoms star(all_0_9_9) = all_0_4_4, yields:
% 48.28/16.43 | (55) ? [v0] : (multiplication(all_0_4_4, all_0_9_9) = v0 & addition(one, v0) = all_0_4_4)
% 48.28/16.43 |
% 48.28/16.43 | Instantiating formula (33) with all_0_4_4, all_0_9_9 and discharging atoms star(all_0_9_9) = all_0_4_4, yields:
% 48.28/16.43 | (56) ? [v0] : (multiplication(all_0_9_9, all_0_4_4) = v0 & addition(one, v0) = all_0_4_4)
% 48.28/16.43 |
% 48.28/16.43 | Instantiating formula (28) with all_0_0_0, all_0_3_3, all_0_4_4, all_0_1_1, all_0_8_8, all_0_9_9 and discharging atoms leq(all_0_3_3, all_0_1_1) = all_0_0_0, star(all_0_9_9) = all_0_4_4, multiplication(all_0_4_4, all_0_8_8) = all_0_3_3, yields:
% 48.28/16.43 | (57) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & leq(v1, all_0_1_1) = v2 & multiplication(all_0_9_9, all_0_1_1) = v0 & addition(v0, all_0_8_8) = v1)
% 48.28/16.43 |
% 48.28/16.43 | Instantiating (53) with all_19_0_23 yields:
% 48.28/16.43 | (58) multiplication(all_0_2_2, all_0_7_7) = all_19_0_23 & addition(one, all_19_0_23) = all_0_2_2
% 48.28/16.43 |
% 48.28/16.43 | Applying alpha-rule on (58) yields:
% 48.28/16.43 | (59) multiplication(all_0_2_2, all_0_7_7) = all_19_0_23
% 48.28/16.43 | (60) addition(one, all_19_0_23) = all_0_2_2
% 48.28/16.43 |
% 48.28/16.43 | Instantiating (56) with all_23_0_26 yields:
% 48.28/16.43 | (61) multiplication(all_0_9_9, all_0_4_4) = all_23_0_26 & addition(one, all_23_0_26) = all_0_4_4
% 48.28/16.43 |
% 48.28/16.43 | Applying alpha-rule on (61) yields:
% 48.28/16.43 | (62) multiplication(all_0_9_9, all_0_4_4) = all_23_0_26
% 48.28/16.43 | (63) addition(one, all_23_0_26) = all_0_4_4
% 48.28/16.44 |
% 48.28/16.44 | Instantiating (54) with all_27_0_29 yields:
% 48.28/16.44 | (64) multiplication(all_0_7_7, all_0_2_2) = all_27_0_29 & addition(one, all_27_0_29) = all_0_2_2
% 48.28/16.44 |
% 48.28/16.44 | Applying alpha-rule on (64) yields:
% 48.28/16.44 | (65) multiplication(all_0_7_7, all_0_2_2) = all_27_0_29
% 48.28/16.44 | (66) addition(one, all_27_0_29) = all_0_2_2
% 48.28/16.44 |
% 48.28/16.44 | Instantiating (55) with all_29_0_30 yields:
% 48.28/16.44 | (67) multiplication(all_0_4_4, all_0_9_9) = all_29_0_30 & addition(one, all_29_0_30) = all_0_4_4
% 48.28/16.44 |
% 48.28/16.44 | Applying alpha-rule on (67) yields:
% 48.28/16.44 | (68) multiplication(all_0_4_4, all_0_9_9) = all_29_0_30
% 48.28/16.44 | (69) addition(one, all_29_0_30) = all_0_4_4
% 48.28/16.44 |
% 48.28/16.44 +-Applying beta-rule and splitting (57), into two cases.
% 48.28/16.44 |-Branch one:
% 48.28/16.44 | (70) all_0_0_0 = 0
% 48.28/16.44 |
% 48.28/16.44 | Equations (70) can reduce 31 to:
% 48.28/16.44 | (71) $false
% 48.28/16.44 |
% 48.28/16.44 |-The branch is then unsatisfiable
% 48.28/16.44 |-Branch two:
% 48.28/16.44 | (31) ~ (all_0_0_0 = 0)
% 48.28/16.44 | (73) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & leq(v1, all_0_1_1) = v2 & multiplication(all_0_9_9, all_0_1_1) = v0 & addition(v0, all_0_8_8) = v1)
% 48.28/16.44 |
% 48.28/16.44 | Instantiating (73) with all_35_0_31, all_35_1_32, all_35_2_33 yields:
% 48.28/16.44 | (74) ~ (all_35_0_31 = 0) & leq(all_35_1_32, all_0_1_1) = all_35_0_31 & multiplication(all_0_9_9, all_0_1_1) = all_35_2_33 & addition(all_35_2_33, all_0_8_8) = all_35_1_32
% 48.28/16.44 |
% 48.28/16.44 | Applying alpha-rule on (74) yields:
% 48.28/16.44 | (75) ~ (all_35_0_31 = 0)
% 48.28/16.44 | (76) leq(all_35_1_32, all_0_1_1) = all_35_0_31
% 48.28/16.44 | (77) multiplication(all_0_9_9, all_0_1_1) = all_35_2_33
% 48.28/16.44 | (78) addition(all_35_2_33, all_0_8_8) = all_35_1_32
% 48.28/16.44 |
% 48.28/16.44 +-Applying beta-rule and splitting (51), into two cases.
% 48.28/16.44 |-Branch one:
% 48.28/16.44 | (70) all_0_0_0 = 0
% 48.28/16.44 |
% 48.28/16.44 | Equations (70) can reduce 31 to:
% 48.28/16.44 | (71) $false
% 48.28/16.44 |
% 48.28/16.44 |-The branch is then unsatisfiable
% 48.28/16.44 |-Branch two:
% 48.28/16.44 | (31) ~ (all_0_0_0 = 0)
% 48.28/16.44 | (82) ? [v0] : ( ~ (v0 = all_0_1_1) & addition(all_0_3_3, all_0_1_1) = v0)
% 48.28/16.44 |
% 48.28/16.44 | Instantiating (82) with all_40_0_34 yields:
% 48.28/16.44 | (83) ~ (all_40_0_34 = all_0_1_1) & addition(all_0_3_3, all_0_1_1) = all_40_0_34
% 48.28/16.44 |
% 48.28/16.44 | Applying alpha-rule on (83) yields:
% 48.28/16.44 | (84) ~ (all_40_0_34 = all_0_1_1)
% 48.28/16.44 | (85) addition(all_0_3_3, all_0_1_1) = all_40_0_34
% 48.28/16.44 |
% 48.28/16.44 | Instantiating formula (12) with all_35_0_31, all_0_1_1, all_35_1_32 and discharging atoms leq(all_35_1_32, all_0_1_1) = all_35_0_31, yields:
% 48.28/16.44 | (86) all_35_0_31 = 0 | ? [v0] : ( ~ (v0 = all_0_1_1) & addition(all_35_1_32, all_0_1_1) = v0)
% 48.28/16.44 |
% 48.28/16.44 | Instantiating formula (40) with all_35_2_33, all_0_1_1, all_0_2_2, all_0_8_8, all_0_9_9 and discharging atoms multiplication(all_0_8_8, all_0_2_2) = all_0_1_1, multiplication(all_0_9_9, all_0_1_1) = all_35_2_33, yields:
% 48.28/16.44 | (87) ? [v0] : (multiplication(v0, all_0_2_2) = all_35_2_33 & multiplication(all_0_9_9, all_0_8_8) = v0)
% 48.28/16.44 |
% 48.28/16.44 | Instantiating formula (15) with all_35_1_32, all_35_2_33, all_0_8_8 and discharging atoms addition(all_35_2_33, all_0_8_8) = all_35_1_32, yields:
% 48.28/16.44 | (88) addition(all_0_8_8, all_35_2_33) = all_35_1_32
% 48.28/16.44 |
% 48.28/16.44 | Instantiating formula (15) with all_40_0_34, all_0_3_3, all_0_1_1 and discharging atoms addition(all_0_3_3, all_0_1_1) = all_40_0_34, yields:
% 48.28/16.44 | (89) addition(all_0_1_1, all_0_3_3) = all_40_0_34
% 48.28/16.44 |
% 48.28/16.44 | Instantiating formula (25) with all_0_5_5, all_0_5_5, all_0_6_6, all_0_6_6, all_0_5_5 and discharging atoms addition(all_0_6_6, all_0_5_5) = all_0_5_5, yields:
% 48.28/16.44 | (90) ? [v0] : (addition(v0, all_0_5_5) = all_0_5_5 & addition(all_0_6_6, all_0_6_6) = v0)
% 48.28/16.44 |
% 48.28/16.44 | Instantiating formula (15) with all_0_5_5, all_0_6_6, all_0_5_5 and discharging atoms addition(all_0_6_6, all_0_5_5) = all_0_5_5, yields:
% 48.28/16.44 | (91) addition(all_0_5_5, all_0_6_6) = all_0_5_5
% 48.28/16.44 |
% 48.28/16.44 | Instantiating formula (37) with all_0_3_3, all_0_4_4, all_0_8_8, all_29_0_30, one and discharging atoms multiplication(all_0_4_4, all_0_8_8) = all_0_3_3, addition(one, all_29_0_30) = all_0_4_4, yields:
% 48.28/16.44 | (92) ? [v0] : ? [v1] : (multiplication(all_29_0_30, all_0_8_8) = v1 & multiplication(one, all_0_8_8) = v0 & addition(v0, v1) = all_0_3_3)
% 48.28/16.44 |
% 48.28/16.44 | Instantiating formula (37) with all_29_0_30, all_0_4_4, all_0_9_9, all_29_0_30, one and discharging atoms multiplication(all_0_4_4, all_0_9_9) = all_29_0_30, addition(one, all_29_0_30) = all_0_4_4, yields:
% 48.28/16.44 | (93) ? [v0] : ? [v1] : (multiplication(all_29_0_30, all_0_9_9) = v1 & multiplication(one, all_0_9_9) = v0 & addition(v0, v1) = all_29_0_30)
% 48.28/16.44 |
% 48.28/16.44 | Instantiating formula (20) with all_23_0_26, all_0_4_4, all_29_0_30, one, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_4_4) = all_23_0_26, addition(one, all_29_0_30) = all_0_4_4, yields:
% 48.28/16.44 | (94) ? [v0] : ? [v1] : (multiplication(all_0_9_9, all_29_0_30) = v1 & multiplication(all_0_9_9, one) = v0 & addition(v0, v1) = all_23_0_26)
% 48.28/16.44 |
% 48.28/16.44 | Instantiating formula (15) with all_0_4_4, one, all_29_0_30 and discharging atoms addition(one, all_29_0_30) = all_0_4_4, yields:
% 48.28/16.44 | (95) addition(all_29_0_30, one) = all_0_4_4
% 48.28/16.44 |
% 48.28/16.44 | Instantiating formula (20) with all_0_1_1, all_0_2_2, all_27_0_29, one, all_0_8_8 and discharging atoms multiplication(all_0_8_8, all_0_2_2) = all_0_1_1, addition(one, all_27_0_29) = all_0_2_2, yields:
% 48.28/16.44 | (96) ? [v0] : ? [v1] : (multiplication(all_0_8_8, all_27_0_29) = v1 & multiplication(all_0_8_8, one) = v0 & addition(v0, v1) = all_0_1_1)
% 48.28/16.44 |
% 48.28/16.44 | Instantiating formula (37) with all_19_0_23, all_0_2_2, all_0_7_7, all_27_0_29, one and discharging atoms multiplication(all_0_2_2, all_0_7_7) = all_19_0_23, addition(one, all_27_0_29) = all_0_2_2, yields:
% 48.28/16.44 | (97) ? [v0] : ? [v1] : (multiplication(all_27_0_29, all_0_7_7) = v1 & multiplication(one, all_0_7_7) = v0 & addition(v0, v1) = all_19_0_23)
% 48.28/16.44 |
% 48.28/16.44 | Instantiating formula (20) with all_27_0_29, all_0_2_2, all_27_0_29, one, all_0_7_7 and discharging atoms multiplication(all_0_7_7, all_0_2_2) = all_27_0_29, addition(one, all_27_0_29) = all_0_2_2, yields:
% 48.28/16.45 | (98) ? [v0] : ? [v1] : (multiplication(all_0_7_7, all_27_0_29) = v1 & multiplication(all_0_7_7, one) = v0 & addition(v0, v1) = all_27_0_29)
% 48.28/16.45 |
% 48.28/16.45 | Instantiating formula (15) with all_0_2_2, one, all_27_0_29 and discharging atoms addition(one, all_27_0_29) = all_0_2_2, yields:
% 48.28/16.45 | (99) addition(all_27_0_29, one) = all_0_2_2
% 48.28/16.45 |
% 48.28/16.45 | Instantiating formula (37) with all_0_3_3, all_0_4_4, all_0_8_8, all_23_0_26, one and discharging atoms multiplication(all_0_4_4, all_0_8_8) = all_0_3_3, addition(one, all_23_0_26) = all_0_4_4, yields:
% 48.28/16.45 | (100) ? [v0] : ? [v1] : (multiplication(all_23_0_26, all_0_8_8) = v1 & multiplication(one, all_0_8_8) = v0 & addition(v0, v1) = all_0_3_3)
% 48.28/16.45 |
% 48.28/16.45 | Instantiating formula (37) with all_29_0_30, all_0_4_4, all_0_9_9, all_23_0_26, one and discharging atoms multiplication(all_0_4_4, all_0_9_9) = all_29_0_30, addition(one, all_23_0_26) = all_0_4_4, yields:
% 48.28/16.45 | (101) ? [v0] : ? [v1] : (multiplication(all_23_0_26, all_0_9_9) = v1 & multiplication(one, all_0_9_9) = v0 & addition(v0, v1) = all_29_0_30)
% 48.28/16.45 |
% 48.28/16.45 | Instantiating formula (20) with all_23_0_26, all_0_4_4, all_23_0_26, one, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_4_4) = all_23_0_26, addition(one, all_23_0_26) = all_0_4_4, yields:
% 48.28/16.45 | (102) ? [v0] : ? [v1] : (multiplication(all_0_9_9, all_23_0_26) = v1 & multiplication(all_0_9_9, one) = v0 & addition(v0, v1) = all_23_0_26)
% 48.28/16.45 |
% 48.28/16.45 | Instantiating formula (15) with all_0_4_4, one, all_23_0_26 and discharging atoms addition(one, all_23_0_26) = all_0_4_4, yields:
% 48.28/16.45 | (103) addition(all_23_0_26, one) = all_0_4_4
% 48.28/16.45 |
% 48.28/16.45 | Instantiating formula (20) with all_0_1_1, all_0_2_2, all_19_0_23, one, all_0_8_8 and discharging atoms multiplication(all_0_8_8, all_0_2_2) = all_0_1_1, addition(one, all_19_0_23) = all_0_2_2, yields:
% 48.28/16.45 | (104) ? [v0] : ? [v1] : (multiplication(all_0_8_8, all_19_0_23) = v1 & multiplication(all_0_8_8, one) = v0 & addition(v0, v1) = all_0_1_1)
% 48.28/16.45 |
% 48.28/16.45 | Instantiating formula (37) with all_19_0_23, all_0_2_2, all_0_7_7, all_19_0_23, one and discharging atoms multiplication(all_0_2_2, all_0_7_7) = all_19_0_23, addition(one, all_19_0_23) = all_0_2_2, yields:
% 48.28/16.45 | (105) ? [v0] : ? [v1] : (multiplication(all_19_0_23, all_0_7_7) = v1 & multiplication(one, all_0_7_7) = v0 & addition(v0, v1) = all_19_0_23)
% 48.28/16.45 |
% 48.28/16.45 | Instantiating formula (20) with all_27_0_29, all_0_2_2, all_19_0_23, one, all_0_7_7 and discharging atoms multiplication(all_0_7_7, all_0_2_2) = all_27_0_29, addition(one, all_19_0_23) = all_0_2_2, yields:
% 48.28/16.45 | (106) ? [v0] : ? [v1] : (multiplication(all_0_7_7, all_19_0_23) = v1 & multiplication(all_0_7_7, one) = v0 & addition(v0, v1) = all_27_0_29)
% 48.28/16.45 |
% 48.28/16.45 | Instantiating formula (15) with all_0_2_2, one, all_19_0_23 and discharging atoms addition(one, all_19_0_23) = all_0_2_2, yields:
% 48.28/16.45 | (107) addition(all_19_0_23, one) = all_0_2_2
% 48.28/16.45 |
% 48.28/16.45 | Instantiating (87) with all_48_0_35 yields:
% 48.28/16.45 | (108) multiplication(all_48_0_35, all_0_2_2) = all_35_2_33 & multiplication(all_0_9_9, all_0_8_8) = all_48_0_35
% 48.28/16.45 |
% 48.28/16.45 | Applying alpha-rule on (108) yields:
% 48.28/16.45 | (109) multiplication(all_48_0_35, all_0_2_2) = all_35_2_33
% 48.28/16.45 | (110) multiplication(all_0_9_9, all_0_8_8) = all_48_0_35
% 48.28/16.45 |
% 48.28/16.45 | Instantiating (98) with all_52_0_37, all_52_1_38 yields:
% 48.28/16.45 | (111) multiplication(all_0_7_7, all_27_0_29) = all_52_0_37 & multiplication(all_0_7_7, one) = all_52_1_38 & addition(all_52_1_38, all_52_0_37) = all_27_0_29
% 48.28/16.45 |
% 48.28/16.45 | Applying alpha-rule on (111) yields:
% 48.28/16.45 | (112) multiplication(all_0_7_7, all_27_0_29) = all_52_0_37
% 48.28/16.45 | (113) multiplication(all_0_7_7, one) = all_52_1_38
% 48.28/16.45 | (114) addition(all_52_1_38, all_52_0_37) = all_27_0_29
% 48.28/16.45 |
% 48.28/16.45 | Instantiating (90) with all_54_0_39 yields:
% 48.28/16.45 | (115) addition(all_54_0_39, all_0_5_5) = all_0_5_5 & addition(all_0_6_6, all_0_6_6) = all_54_0_39
% 48.28/16.45 |
% 48.28/16.45 | Applying alpha-rule on (115) yields:
% 48.28/16.45 | (116) addition(all_54_0_39, all_0_5_5) = all_0_5_5
% 48.28/16.45 | (117) addition(all_0_6_6, all_0_6_6) = all_54_0_39
% 48.28/16.45 |
% 48.28/16.45 | Instantiating (104) with all_58_0_41, all_58_1_42 yields:
% 48.28/16.45 | (118) multiplication(all_0_8_8, all_19_0_23) = all_58_0_41 & multiplication(all_0_8_8, one) = all_58_1_42 & addition(all_58_1_42, all_58_0_41) = all_0_1_1
% 48.28/16.45 |
% 48.28/16.45 | Applying alpha-rule on (118) yields:
% 48.28/16.45 | (119) multiplication(all_0_8_8, all_19_0_23) = all_58_0_41
% 48.28/16.45 | (120) multiplication(all_0_8_8, one) = all_58_1_42
% 48.28/16.45 | (121) addition(all_58_1_42, all_58_0_41) = all_0_1_1
% 48.28/16.45 |
% 48.28/16.45 | Instantiating (97) with all_63_0_52, all_63_1_53 yields:
% 48.28/16.45 | (122) multiplication(all_27_0_29, all_0_7_7) = all_63_0_52 & multiplication(one, all_0_7_7) = all_63_1_53 & addition(all_63_1_53, all_63_0_52) = all_19_0_23
% 48.28/16.45 |
% 48.28/16.45 | Applying alpha-rule on (122) yields:
% 48.28/16.45 | (123) multiplication(all_27_0_29, all_0_7_7) = all_63_0_52
% 48.28/16.45 | (124) multiplication(one, all_0_7_7) = all_63_1_53
% 48.28/16.45 | (125) addition(all_63_1_53, all_63_0_52) = all_19_0_23
% 48.28/16.45 |
% 48.28/16.45 | Instantiating (102) with all_71_0_63, all_71_1_64 yields:
% 48.28/16.45 | (126) multiplication(all_0_9_9, all_23_0_26) = all_71_0_63 & multiplication(all_0_9_9, one) = all_71_1_64 & addition(all_71_1_64, all_71_0_63) = all_23_0_26
% 48.28/16.45 |
% 48.28/16.45 | Applying alpha-rule on (126) yields:
% 48.28/16.45 | (127) multiplication(all_0_9_9, all_23_0_26) = all_71_0_63
% 48.28/16.45 | (128) multiplication(all_0_9_9, one) = all_71_1_64
% 48.28/16.45 | (129) addition(all_71_1_64, all_71_0_63) = all_23_0_26
% 48.28/16.45 |
% 48.28/16.45 | Instantiating (106) with all_73_0_65, all_73_1_66 yields:
% 48.28/16.45 | (130) multiplication(all_0_7_7, all_19_0_23) = all_73_0_65 & multiplication(all_0_7_7, one) = all_73_1_66 & addition(all_73_1_66, all_73_0_65) = all_27_0_29
% 48.28/16.45 |
% 48.28/16.45 | Applying alpha-rule on (130) yields:
% 48.28/16.45 | (131) multiplication(all_0_7_7, all_19_0_23) = all_73_0_65
% 48.28/16.45 | (132) multiplication(all_0_7_7, one) = all_73_1_66
% 48.28/16.45 | (133) addition(all_73_1_66, all_73_0_65) = all_27_0_29
% 48.28/16.46 |
% 48.28/16.46 | Instantiating (100) with all_75_0_67, all_75_1_68 yields:
% 48.28/16.46 | (134) multiplication(all_23_0_26, all_0_8_8) = all_75_0_67 & multiplication(one, all_0_8_8) = all_75_1_68 & addition(all_75_1_68, all_75_0_67) = all_0_3_3
% 48.28/16.46 |
% 48.28/16.46 | Applying alpha-rule on (134) yields:
% 48.28/16.46 | (135) multiplication(all_23_0_26, all_0_8_8) = all_75_0_67
% 48.28/16.46 | (136) multiplication(one, all_0_8_8) = all_75_1_68
% 48.28/16.46 | (137) addition(all_75_1_68, all_75_0_67) = all_0_3_3
% 48.28/16.46 |
% 48.28/16.46 | Instantiating (105) with all_77_0_69, all_77_1_70 yields:
% 48.28/16.46 | (138) multiplication(all_19_0_23, all_0_7_7) = all_77_0_69 & multiplication(one, all_0_7_7) = all_77_1_70 & addition(all_77_1_70, all_77_0_69) = all_19_0_23
% 48.28/16.46 |
% 48.28/16.46 | Applying alpha-rule on (138) yields:
% 48.28/16.46 | (139) multiplication(all_19_0_23, all_0_7_7) = all_77_0_69
% 48.28/16.46 | (140) multiplication(one, all_0_7_7) = all_77_1_70
% 48.28/16.46 | (141) addition(all_77_1_70, all_77_0_69) = all_19_0_23
% 48.28/16.46 |
% 48.28/16.46 | Instantiating (101) with all_79_0_71, all_79_1_72 yields:
% 48.28/16.46 | (142) multiplication(all_23_0_26, all_0_9_9) = all_79_0_71 & multiplication(one, all_0_9_9) = all_79_1_72 & addition(all_79_1_72, all_79_0_71) = all_29_0_30
% 48.28/16.46 |
% 48.28/16.46 | Applying alpha-rule on (142) yields:
% 48.28/16.46 | (143) multiplication(all_23_0_26, all_0_9_9) = all_79_0_71
% 48.28/16.46 | (144) multiplication(one, all_0_9_9) = all_79_1_72
% 48.28/16.46 | (145) addition(all_79_1_72, all_79_0_71) = all_29_0_30
% 48.28/16.46 |
% 48.28/16.46 | Instantiating (92) with all_86_0_78, all_86_1_79 yields:
% 48.28/16.46 | (146) multiplication(all_29_0_30, all_0_8_8) = all_86_0_78 & multiplication(one, all_0_8_8) = all_86_1_79 & addition(all_86_1_79, all_86_0_78) = all_0_3_3
% 48.28/16.46 |
% 48.28/16.46 | Applying alpha-rule on (146) yields:
% 48.28/16.46 | (147) multiplication(all_29_0_30, all_0_8_8) = all_86_0_78
% 48.28/16.46 | (148) multiplication(one, all_0_8_8) = all_86_1_79
% 48.28/16.46 | (149) addition(all_86_1_79, all_86_0_78) = all_0_3_3
% 48.28/16.46 |
% 48.28/16.46 | Instantiating (96) with all_88_0_80, all_88_1_81 yields:
% 48.28/16.46 | (150) multiplication(all_0_8_8, all_27_0_29) = all_88_0_80 & multiplication(all_0_8_8, one) = all_88_1_81 & addition(all_88_1_81, all_88_0_80) = all_0_1_1
% 48.28/16.46 |
% 48.28/16.46 | Applying alpha-rule on (150) yields:
% 48.28/16.46 | (151) multiplication(all_0_8_8, all_27_0_29) = all_88_0_80
% 48.28/16.46 | (152) multiplication(all_0_8_8, one) = all_88_1_81
% 48.28/16.46 | (153) addition(all_88_1_81, all_88_0_80) = all_0_1_1
% 48.28/16.46 |
% 48.28/16.46 | Instantiating (94) with all_92_0_83, all_92_1_84 yields:
% 48.28/16.46 | (154) multiplication(all_0_9_9, all_29_0_30) = all_92_0_83 & multiplication(all_0_9_9, one) = all_92_1_84 & addition(all_92_1_84, all_92_0_83) = all_23_0_26
% 48.28/16.46 |
% 48.28/16.46 | Applying alpha-rule on (154) yields:
% 48.28/16.46 | (155) multiplication(all_0_9_9, all_29_0_30) = all_92_0_83
% 48.28/16.46 | (156) multiplication(all_0_9_9, one) = all_92_1_84
% 48.28/16.46 | (157) addition(all_92_1_84, all_92_0_83) = all_23_0_26
% 48.28/16.46 |
% 48.28/16.46 | Instantiating (93) with all_96_0_87, all_96_1_88 yields:
% 48.28/16.46 | (158) multiplication(all_29_0_30, all_0_9_9) = all_96_0_87 & multiplication(one, all_0_9_9) = all_96_1_88 & addition(all_96_1_88, all_96_0_87) = all_29_0_30
% 48.28/16.46 |
% 48.28/16.46 | Applying alpha-rule on (158) yields:
% 48.28/16.46 | (159) multiplication(all_29_0_30, all_0_9_9) = all_96_0_87
% 48.28/16.46 | (160) multiplication(one, all_0_9_9) = all_96_1_88
% 48.28/16.46 | (161) addition(all_96_1_88, all_96_0_87) = all_29_0_30
% 48.28/16.46 |
% 48.28/16.46 +-Applying beta-rule and splitting (86), into two cases.
% 48.28/16.46 |-Branch one:
% 48.28/16.46 | (162) all_35_0_31 = 0
% 48.28/16.46 |
% 48.28/16.46 | Equations (162) can reduce 75 to:
% 48.28/16.46 | (71) $false
% 48.28/16.46 |
% 48.28/16.46 |-The branch is then unsatisfiable
% 48.28/16.46 |-Branch two:
% 48.28/16.46 | (75) ~ (all_35_0_31 = 0)
% 48.28/16.46 | (165) ? [v0] : ( ~ (v0 = all_0_1_1) & addition(all_35_1_32, all_0_1_1) = v0)
% 48.28/16.46 |
% 48.28/16.46 | Instantiating (165) with all_104_0_95 yields:
% 48.28/16.46 | (166) ~ (all_104_0_95 = all_0_1_1) & addition(all_35_1_32, all_0_1_1) = all_104_0_95
% 48.28/16.46 |
% 48.28/16.46 | Applying alpha-rule on (166) yields:
% 48.28/16.46 | (167) ~ (all_104_0_95 = all_0_1_1)
% 48.28/16.46 | (168) addition(all_35_1_32, all_0_1_1) = all_104_0_95
% 48.28/16.46 |
% 48.28/16.46 | Instantiating formula (3) with all_73_1_66, all_0_7_7 and discharging atoms multiplication(all_0_7_7, one) = all_73_1_66, yields:
% 48.28/16.46 | (169) all_73_1_66 = all_0_7_7
% 48.28/16.46 |
% 48.28/16.46 | Instantiating formula (42) with all_0_7_7, one, all_52_1_38, all_73_1_66 and discharging atoms multiplication(all_0_7_7, one) = all_73_1_66, multiplication(all_0_7_7, one) = all_52_1_38, yields:
% 48.28/16.46 | (170) all_73_1_66 = all_52_1_38
% 48.28/16.46 |
% 48.28/16.46 | Instantiating formula (3) with all_88_1_81, all_0_8_8 and discharging atoms multiplication(all_0_8_8, one) = all_88_1_81, yields:
% 48.28/16.46 | (171) all_88_1_81 = all_0_8_8
% 48.28/16.46 |
% 48.28/16.46 | Instantiating formula (42) with all_0_8_8, one, all_58_1_42, all_88_1_81 and discharging atoms multiplication(all_0_8_8, one) = all_88_1_81, multiplication(all_0_8_8, one) = all_58_1_42, yields:
% 48.28/16.46 | (172) all_88_1_81 = all_58_1_42
% 48.28/16.46 |
% 48.28/16.46 | Instantiating formula (42) with all_0_9_9, all_0_8_8, all_48_0_35, all_0_6_6 and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_48_0_35, multiplication(all_0_9_9, all_0_8_8) = all_0_6_6, yields:
% 48.28/16.46 | (173) all_48_0_35 = all_0_6_6
% 48.28/16.46 |
% 48.28/16.46 | Instantiating formula (3) with all_92_1_84, all_0_9_9 and discharging atoms multiplication(all_0_9_9, one) = all_92_1_84, yields:
% 48.28/16.46 | (174) all_92_1_84 = all_0_9_9
% 48.28/16.46 |
% 48.28/16.46 | Instantiating formula (42) with all_0_9_9, one, all_71_1_64, all_92_1_84 and discharging atoms multiplication(all_0_9_9, one) = all_92_1_84, multiplication(all_0_9_9, one) = all_71_1_64, yields:
% 48.28/16.47 | (175) all_92_1_84 = all_71_1_64
% 48.28/16.47 |
% 48.28/16.47 | Instantiating formula (30) with all_77_1_70, all_0_7_7 and discharging atoms multiplication(one, all_0_7_7) = all_77_1_70, yields:
% 48.28/16.47 | (176) all_77_1_70 = all_0_7_7
% 48.28/16.47 |
% 48.28/16.47 | Instantiating formula (42) with one, all_0_7_7, all_63_1_53, all_77_1_70 and discharging atoms multiplication(one, all_0_7_7) = all_77_1_70, multiplication(one, all_0_7_7) = all_63_1_53, yields:
% 48.28/16.47 | (177) all_77_1_70 = all_63_1_53
% 48.28/16.47 |
% 48.28/16.47 | Instantiating formula (30) with all_86_1_79, all_0_8_8 and discharging atoms multiplication(one, all_0_8_8) = all_86_1_79, yields:
% 48.28/16.47 | (178) all_86_1_79 = all_0_8_8
% 48.28/16.47 |
% 48.28/16.47 | Instantiating formula (42) with one, all_0_8_8, all_75_1_68, all_86_1_79 and discharging atoms multiplication(one, all_0_8_8) = all_86_1_79, multiplication(one, all_0_8_8) = all_75_1_68, yields:
% 48.28/16.47 | (179) all_86_1_79 = all_75_1_68
% 48.28/16.47 |
% 48.28/16.47 | Instantiating formula (30) with all_96_1_88, all_0_9_9 and discharging atoms multiplication(one, all_0_9_9) = all_96_1_88, yields:
% 48.28/16.47 | (180) all_96_1_88 = all_0_9_9
% 48.28/16.47 |
% 48.28/16.47 | Instantiating formula (42) with one, all_0_9_9, all_79_1_72, all_96_1_88 and discharging atoms multiplication(one, all_0_9_9) = all_96_1_88, multiplication(one, all_0_9_9) = all_79_1_72, yields:
% 48.28/16.47 | (181) all_96_1_88 = all_79_1_72
% 48.28/16.47 |
% 48.28/16.47 | Instantiating formula (44) with all_54_0_39, all_0_6_6 and discharging atoms addition(all_0_6_6, all_0_6_6) = all_54_0_39, yields:
% 48.28/16.47 | (182) all_54_0_39 = all_0_6_6
% 48.28/16.47 |
% 48.28/16.47 | Combining equations (180,181) yields a new equation:
% 48.28/16.47 | (183) all_79_1_72 = all_0_9_9
% 48.28/16.47 |
% 48.28/16.47 | Combining equations (174,175) yields a new equation:
% 48.28/16.47 | (184) all_71_1_64 = all_0_9_9
% 48.28/16.47 |
% 48.28/16.47 | Combining equations (172,171) yields a new equation:
% 48.28/16.47 | (185) all_58_1_42 = all_0_8_8
% 48.28/16.47 |
% 48.28/16.47 | Simplifying 185 yields:
% 48.28/16.47 | (186) all_58_1_42 = all_0_8_8
% 48.28/16.47 |
% 48.28/16.47 | Combining equations (179,178) yields a new equation:
% 48.28/16.47 | (187) all_75_1_68 = all_0_8_8
% 48.28/16.47 |
% 48.28/16.47 | Simplifying 187 yields:
% 48.28/16.47 | (188) all_75_1_68 = all_0_8_8
% 48.28/16.47 |
% 48.28/16.47 | Combining equations (176,177) yields a new equation:
% 48.28/16.47 | (189) all_63_1_53 = all_0_7_7
% 48.28/16.47 |
% 48.28/16.47 | Combining equations (169,170) yields a new equation:
% 48.28/16.47 | (190) all_52_1_38 = all_0_7_7
% 48.28/16.47 |
% 48.28/16.47 | Combining equations (190,170) yields a new equation:
% 48.28/16.47 | (169) all_73_1_66 = all_0_7_7
% 48.28/16.47 |
% 48.28/16.47 | Combining equations (189,177) yields a new equation:
% 48.28/16.47 | (176) all_77_1_70 = all_0_7_7
% 48.28/16.47 |
% 48.28/16.47 | Combining equations (184,175) yields a new equation:
% 48.28/16.47 | (174) all_92_1_84 = all_0_9_9
% 48.28/16.47 |
% 48.28/16.47 | Combining equations (183,181) yields a new equation:
% 48.28/16.47 | (180) all_96_1_88 = all_0_9_9
% 48.28/16.47 |
% 48.28/16.47 | From (173) and (109) follows:
% 48.28/16.47 | (195) multiplication(all_0_6_6, all_0_2_2) = all_35_2_33
% 48.28/16.47 |
% 48.28/16.47 | From (190) and (113) follows:
% 48.68/16.47 | (196) multiplication(all_0_7_7, one) = all_0_7_7
% 48.68/16.47 |
% 48.68/16.47 | From (186) and (120) follows:
% 48.68/16.47 | (197) multiplication(all_0_8_8, one) = all_0_8_8
% 48.68/16.47 |
% 48.68/16.47 | From (173) and (110) follows:
% 48.68/16.47 | (34) multiplication(all_0_9_9, all_0_8_8) = all_0_6_6
% 48.68/16.47 |
% 48.68/16.47 | From (184) and (128) follows:
% 48.68/16.47 | (199) multiplication(all_0_9_9, one) = all_0_9_9
% 48.68/16.47 |
% 48.68/16.47 | From (189) and (124) follows:
% 48.68/16.47 | (200) multiplication(one, all_0_7_7) = all_0_7_7
% 48.68/16.47 |
% 48.68/16.47 | From (188) and (136) follows:
% 48.68/16.47 | (201) multiplication(one, all_0_8_8) = all_0_8_8
% 48.68/16.47 |
% 48.68/16.47 | From (183) and (144) follows:
% 48.68/16.48 | (202) multiplication(one, all_0_9_9) = all_0_9_9
% 48.68/16.48 |
% 48.68/16.48 | From (180) and (161) follows:
% 48.68/16.48 | (203) addition(all_0_9_9, all_96_0_87) = all_29_0_30
% 48.68/16.48 |
% 48.68/16.48 | From (174) and (157) follows:
% 48.68/16.48 | (204) addition(all_0_9_9, all_92_0_83) = all_23_0_26
% 48.68/16.48 |
% 48.68/16.48 | From (171) and (153) follows:
% 48.68/16.48 | (205) addition(all_0_8_8, all_88_0_80) = all_0_1_1
% 48.68/16.48 |
% 48.68/16.48 | From (178) and (149) follows:
% 48.68/16.48 | (206) addition(all_0_8_8, all_86_0_78) = all_0_3_3
% 48.68/16.48 |
% 48.68/16.48 | From (183) and (145) follows:
% 48.68/16.48 | (207) addition(all_0_9_9, all_79_0_71) = all_29_0_30
% 48.68/16.48 |
% 48.68/16.48 | From (176) and (141) follows:
% 48.68/16.48 | (208) addition(all_0_7_7, all_77_0_69) = all_19_0_23
% 48.68/16.48 |
% 48.68/16.48 | From (188) and (137) follows:
% 48.68/16.48 | (209) addition(all_0_8_8, all_75_0_67) = all_0_3_3
% 48.68/16.48 |
% 48.68/16.48 | From (169) and (133) follows:
% 48.68/16.48 | (210) addition(all_0_7_7, all_73_0_65) = all_27_0_29
% 48.68/16.48 |
% 48.68/16.48 | From (184) and (129) follows:
% 48.68/16.48 | (211) addition(all_0_9_9, all_71_0_63) = all_23_0_26
% 48.68/16.48 |
% 48.68/16.48 | From (189) and (125) follows:
% 48.68/16.48 | (212) addition(all_0_7_7, all_63_0_52) = all_19_0_23
% 48.68/16.48 |
% 48.68/16.48 | From (186) and (121) follows:
% 48.68/16.48 | (213) addition(all_0_8_8, all_58_0_41) = all_0_1_1
% 48.68/16.48 |
% 48.68/16.48 | From (182) and (116) follows:
% 48.68/16.48 | (52) addition(all_0_6_6, all_0_5_5) = all_0_5_5
% 48.68/16.48 |
% 48.68/16.48 | From (182) and (117) follows:
% 48.68/16.48 | (215) addition(all_0_6_6, all_0_6_6) = all_0_6_6
% 48.68/16.48 |
% 48.68/16.48 | Instantiating formula (36) with all_86_0_78, all_29_0_30, all_0_8_8, all_0_9_9, all_0_4_4 and discharging atoms multiplication(all_29_0_30, all_0_8_8) = all_86_0_78, multiplication(all_0_4_4, all_0_9_9) = all_29_0_30, yields:
% 48.68/16.48 | (216) ? [v0] : (multiplication(all_0_4_4, v0) = all_86_0_78 & multiplication(all_0_9_9, all_0_8_8) = v0)
% 48.68/16.48 |
% 48.68/16.48 | Instantiating formula (36) with all_63_0_52, all_27_0_29, all_0_7_7, all_0_2_2, all_0_7_7 and discharging atoms multiplication(all_27_0_29, all_0_7_7) = all_63_0_52, multiplication(all_0_7_7, all_0_2_2) = all_27_0_29, yields:
% 48.68/16.48 | (217) ? [v0] : (multiplication(all_0_2_2, all_0_7_7) = v0 & multiplication(all_0_7_7, v0) = all_63_0_52)
% 48.68/16.48 |
% 48.68/16.48 | Instantiating formula (36) with all_79_0_71, all_23_0_26, all_0_9_9, all_0_4_4, all_0_9_9 and discharging atoms multiplication(all_23_0_26, all_0_9_9) = all_79_0_71, multiplication(all_0_9_9, all_0_4_4) = all_23_0_26, yields:
% 48.68/16.48 | (218) ? [v0] : (multiplication(all_0_4_4, all_0_9_9) = v0 & multiplication(all_0_9_9, v0) = all_79_0_71)
% 48.68/16.48 |
% 48.68/16.48 | Instantiating formula (20) with all_35_2_33, all_0_2_2, all_27_0_29, one, all_0_6_6 and discharging atoms multiplication(all_0_6_6, all_0_2_2) = all_35_2_33, addition(one, all_27_0_29) = all_0_2_2, yields:
% 48.68/16.48 | (219) ? [v0] : ? [v1] : (multiplication(all_0_6_6, all_27_0_29) = v1 & multiplication(all_0_6_6, one) = v0 & addition(v0, v1) = all_35_2_33)
% 48.68/16.48 |
% 48.68/16.48 | Instantiating formula (20) with all_35_2_33, all_0_2_2, all_19_0_23, one, all_0_6_6 and discharging atoms multiplication(all_0_6_6, all_0_2_2) = all_35_2_33, addition(one, all_19_0_23) = all_0_2_2, yields:
% 48.68/16.48 | (220) ? [v0] : ? [v1] : (multiplication(all_0_6_6, all_19_0_23) = v1 & multiplication(all_0_6_6, one) = v0 & addition(v0, v1) = all_35_2_33)
% 48.68/16.48 |
% 48.68/16.48 | Instantiating formula (40) with all_19_0_23, all_0_7_7, one, all_0_7_7, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_7_7) = all_19_0_23, multiplication(all_0_7_7, one) = all_0_7_7, yields:
% 48.68/16.48 | (221) ? [v0] : (multiplication(v0, one) = all_19_0_23 & multiplication(all_0_2_2, all_0_7_7) = v0)
% 48.68/16.48 |
% 48.68/16.48 | Instantiating formula (40) with all_0_5_5, all_0_7_7, one, all_0_7_7, all_0_8_8 and discharging atoms multiplication(all_0_7_7, one) = all_0_7_7, multiplication(all_0_8_8, all_0_7_7) = all_0_5_5, yields:
% 48.68/16.48 | (222) ? [v0] : (multiplication(v0, one) = all_0_5_5 & multiplication(all_0_8_8, all_0_7_7) = v0)
% 48.68/16.48 |
% 48.68/16.48 | Instantiating formula (40) with all_88_0_80, all_27_0_29, all_0_2_2, all_0_7_7, all_0_8_8 and discharging atoms multiplication(all_0_7_7, all_0_2_2) = all_27_0_29, multiplication(all_0_8_8, all_27_0_29) = all_88_0_80, yields:
% 48.68/16.48 | (223) ? [v0] : (multiplication(v0, all_0_2_2) = all_88_0_80 & multiplication(all_0_8_8, all_0_7_7) = v0)
% 48.68/16.48 |
% 48.68/16.48 | Instantiating formula (40) with all_0_6_6, all_0_8_8, one, all_0_8_8, all_0_9_9 and discharging atoms multiplication(all_0_8_8, one) = all_0_8_8, multiplication(all_0_9_9, all_0_8_8) = all_0_6_6, yields:
% 48.68/16.48 | (224) ? [v0] : (multiplication(v0, one) = all_0_6_6 & multiplication(all_0_9_9, all_0_8_8) = v0)
% 48.68/16.48 |
% 48.68/16.48 | Instantiating formula (40) with all_86_0_78, all_0_8_8, one, all_0_8_8, all_29_0_30 and discharging atoms multiplication(all_29_0_30, all_0_8_8) = all_86_0_78, multiplication(all_0_8_8, one) = all_0_8_8, yields:
% 48.68/16.48 | (225) ? [v0] : (multiplication(v0, one) = all_86_0_78 & multiplication(all_29_0_30, all_0_8_8) = v0)
% 48.68/16.48 |
% 48.68/16.48 | Instantiating formula (40) with all_29_0_30, all_0_9_9, one, all_0_9_9, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_9_9) = all_29_0_30, multiplication(all_0_9_9, one) = all_0_9_9, yields:
% 48.68/16.49 | (226) ? [v0] : (multiplication(v0, one) = all_29_0_30 & multiplication(all_0_4_4, all_0_9_9) = v0)
% 48.68/16.49 |
% 48.68/16.49 | Instantiating formula (36) with all_35_2_33, all_0_9_9, all_0_1_1, one, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_1_1) = all_35_2_33, multiplication(all_0_9_9, one) = all_0_9_9, yields:
% 48.72/16.49 | (227) ? [v0] : (multiplication(all_0_9_9, v0) = all_35_2_33 & multiplication(one, all_0_1_1) = v0)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (40) with all_19_0_23, all_0_7_7, all_0_7_7, one, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_7_7) = all_19_0_23, multiplication(one, all_0_7_7) = all_0_7_7, yields:
% 48.72/16.49 | (228) ? [v0] : (multiplication(v0, all_0_7_7) = all_19_0_23 & multiplication(all_0_2_2, one) = v0)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (36) with all_73_0_65, all_0_7_7, all_19_0_23, all_0_7_7, one and discharging atoms multiplication(all_0_7_7, all_19_0_23) = all_73_0_65, multiplication(one, all_0_7_7) = all_0_7_7, yields:
% 48.72/16.49 | (229) ? [v0] : (multiplication(all_0_7_7, all_19_0_23) = v0 & multiplication(one, v0) = all_73_0_65)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (36) with all_0_5_5, all_0_8_8, all_0_7_7, all_0_8_8, one and discharging atoms multiplication(all_0_8_8, all_0_7_7) = all_0_5_5, multiplication(one, all_0_8_8) = all_0_8_8, yields:
% 48.72/16.49 | (230) ? [v0] : (multiplication(all_0_8_8, all_0_7_7) = v0 & multiplication(one, v0) = all_0_5_5)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (36) with all_0_6_6, all_0_9_9, all_0_8_8, all_0_9_9, one and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_0_6_6, multiplication(one, all_0_9_9) = all_0_9_9, yields:
% 48.72/16.49 | (231) ? [v0] : (multiplication(all_0_9_9, all_0_8_8) = v0 & multiplication(one, v0) = all_0_6_6)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (36) with all_92_0_83, all_0_9_9, all_29_0_30, all_0_9_9, one and discharging atoms multiplication(all_0_9_9, all_29_0_30) = all_92_0_83, multiplication(one, all_0_9_9) = all_0_9_9, yields:
% 48.72/16.49 | (232) ? [v0] : (multiplication(all_0_9_9, all_29_0_30) = v0 & multiplication(one, v0) = all_92_0_83)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (32) with all_104_0_95, all_35_1_32, all_35_2_33, all_0_8_8, all_0_1_1 and discharging atoms addition(all_35_1_32, all_0_1_1) = all_104_0_95, addition(all_35_2_33, all_0_8_8) = all_35_1_32, yields:
% 48.72/16.49 | (233) ? [v0] : (addition(all_35_2_33, v0) = all_104_0_95 & addition(all_0_8_8, all_0_1_1) = v0)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (15) with all_104_0_95, all_35_1_32, all_0_1_1 and discharging atoms addition(all_35_1_32, all_0_1_1) = all_104_0_95, yields:
% 48.72/16.49 | (234) addition(all_0_1_1, all_35_1_32) = all_104_0_95
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (37) with all_0_3_3, all_0_4_4, all_0_8_8, one, all_29_0_30 and discharging atoms multiplication(all_0_4_4, all_0_8_8) = all_0_3_3, addition(all_29_0_30, one) = all_0_4_4, yields:
% 48.72/16.49 | (235) ? [v0] : ? [v1] : (multiplication(all_29_0_30, all_0_8_8) = v0 & multiplication(one, all_0_8_8) = v1 & addition(v0, v1) = all_0_3_3)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (20) with all_23_0_26, all_0_4_4, one, all_29_0_30, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_4_4) = all_23_0_26, addition(all_29_0_30, one) = all_0_4_4, yields:
% 48.72/16.49 | (236) ? [v0] : ? [v1] : (multiplication(all_0_9_9, all_29_0_30) = v0 & multiplication(all_0_9_9, one) = v1 & addition(v0, v1) = all_23_0_26)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (20) with all_0_1_1, all_0_2_2, one, all_27_0_29, all_0_8_8 and discharging atoms multiplication(all_0_8_8, all_0_2_2) = all_0_1_1, addition(all_27_0_29, one) = all_0_2_2, yields:
% 48.72/16.49 | (237) ? [v0] : ? [v1] : (multiplication(all_0_8_8, all_27_0_29) = v0 & multiplication(all_0_8_8, one) = v1 & addition(v0, v1) = all_0_1_1)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (20) with all_35_2_33, all_0_2_2, one, all_27_0_29, all_0_6_6 and discharging atoms multiplication(all_0_6_6, all_0_2_2) = all_35_2_33, addition(all_27_0_29, one) = all_0_2_2, yields:
% 48.72/16.49 | (238) ? [v0] : ? [v1] : (multiplication(all_0_6_6, all_27_0_29) = v0 & multiplication(all_0_6_6, one) = v1 & addition(v0, v1) = all_35_2_33)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (37) with all_0_3_3, all_0_4_4, all_0_8_8, one, all_23_0_26 and discharging atoms multiplication(all_0_4_4, all_0_8_8) = all_0_3_3, addition(all_23_0_26, one) = all_0_4_4, yields:
% 48.72/16.49 | (239) ? [v0] : ? [v1] : (multiplication(all_23_0_26, all_0_8_8) = v0 & multiplication(one, all_0_8_8) = v1 & addition(v0, v1) = all_0_3_3)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (20) with all_27_0_29, all_0_2_2, one, all_19_0_23, all_0_7_7 and discharging atoms multiplication(all_0_7_7, all_0_2_2) = all_27_0_29, addition(all_19_0_23, one) = all_0_2_2, yields:
% 48.72/16.49 | (240) ? [v0] : ? [v1] : (multiplication(all_0_7_7, all_19_0_23) = v0 & multiplication(all_0_7_7, one) = v1 & addition(v0, v1) = all_27_0_29)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (20) with all_35_2_33, all_0_2_2, one, all_19_0_23, all_0_6_6 and discharging atoms multiplication(all_0_6_6, all_0_2_2) = all_35_2_33, addition(all_19_0_23, one) = all_0_2_2, yields:
% 48.72/16.49 | (241) ? [v0] : ? [v1] : (multiplication(all_0_6_6, all_19_0_23) = v0 & multiplication(all_0_6_6, one) = v1 & addition(v0, v1) = all_35_2_33)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (48) with all_0_6_6, all_0_6_6, all_0_6_6, all_0_8_8, all_0_8_8, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_0_6_6, addition(all_0_6_6, all_0_6_6) = all_0_6_6, yields:
% 48.72/16.49 | (242) ? [v0] : (multiplication(all_0_9_9, v0) = all_0_6_6 & addition(all_0_8_8, all_0_8_8) = v0)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (37) with all_35_2_33, all_0_6_6, all_0_2_2, all_0_6_6, all_0_6_6 and discharging atoms multiplication(all_0_6_6, all_0_2_2) = all_35_2_33, addition(all_0_6_6, all_0_6_6) = all_0_6_6, yields:
% 48.72/16.49 | (243) ? [v0] : ? [v1] : (multiplication(all_0_6_6, all_0_2_2) = v1 & multiplication(all_0_6_6, all_0_2_2) = v0 & addition(v0, v1) = all_35_2_33)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (20) with all_58_0_41, all_19_0_23, all_77_0_69, all_0_7_7, all_0_8_8 and discharging atoms multiplication(all_0_8_8, all_19_0_23) = all_58_0_41, addition(all_0_7_7, all_77_0_69) = all_19_0_23, yields:
% 48.72/16.49 | (244) ? [v0] : ? [v1] : (multiplication(all_0_8_8, all_77_0_69) = v1 & multiplication(all_0_8_8, all_0_7_7) = v0 & addition(v0, v1) = all_58_0_41)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (20) with all_88_0_80, all_27_0_29, all_73_0_65, all_0_7_7, all_0_8_8 and discharging atoms multiplication(all_0_8_8, all_27_0_29) = all_88_0_80, addition(all_0_7_7, all_73_0_65) = all_27_0_29, yields:
% 48.72/16.49 | (245) ? [v0] : ? [v1] : (multiplication(all_0_8_8, all_73_0_65) = v1 & multiplication(all_0_8_8, all_0_7_7) = v0 & addition(v0, v1) = all_88_0_80)
% 48.72/16.49 |
% 48.72/16.49 | Instantiating formula (20) with all_58_0_41, all_19_0_23, all_63_0_52, all_0_7_7, all_0_8_8 and discharging atoms multiplication(all_0_8_8, all_19_0_23) = all_58_0_41, addition(all_0_7_7, all_63_0_52) = all_19_0_23, yields:
% 48.72/16.49 | (246) ? [v0] : ? [v1] : (multiplication(all_0_8_8, all_63_0_52) = v1 & multiplication(all_0_8_8, all_0_7_7) = v0 & addition(v0, v1) = all_58_0_41)
% 48.72/16.50 |
% 48.72/16.50 | Instantiating formula (20) with all_35_2_33, all_0_1_1, all_88_0_80, all_0_8_8, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_1_1) = all_35_2_33, addition(all_0_8_8, all_88_0_80) = all_0_1_1, yields:
% 48.72/16.50 | (247) ? [v0] : ? [v1] : (multiplication(all_0_9_9, all_88_0_80) = v1 & multiplication(all_0_9_9, all_0_8_8) = v0 & addition(v0, v1) = all_35_2_33)
% 48.72/16.50 |
% 48.72/16.50 | Instantiating formula (25) with all_40_0_34, all_0_1_1, all_0_3_3, all_0_8_8, all_88_0_80 and discharging atoms addition(all_0_3_3, all_0_1_1) = all_40_0_34, addition(all_0_8_8, all_88_0_80) = all_0_1_1, yields:
% 48.72/16.50 | (248) ? [v0] : (addition(v0, all_88_0_80) = all_40_0_34 & addition(all_0_3_3, all_0_8_8) = v0)
% 48.72/16.50 |
% 48.72/16.50 | Instantiating formula (25) with all_104_0_95, all_0_1_1, all_35_1_32, all_0_8_8, all_88_0_80 and discharging atoms addition(all_35_1_32, all_0_1_1) = all_104_0_95, addition(all_0_8_8, all_88_0_80) = all_0_1_1, yields:
% 48.72/16.50 | (249) ? [v0] : (addition(v0, all_88_0_80) = all_104_0_95 & addition(all_35_1_32, all_0_8_8) = v0)
% 48.72/16.50 |
% 48.72/16.50 | Instantiating formula (25) with all_40_0_34, all_0_3_3, all_0_1_1, all_0_8_8, all_86_0_78 and discharging atoms addition(all_0_1_1, all_0_3_3) = all_40_0_34, addition(all_0_8_8, all_86_0_78) = all_0_3_3, yields:
% 48.72/16.50 | (250) ? [v0] : (addition(v0, all_86_0_78) = all_40_0_34 & addition(all_0_1_1, all_0_8_8) = v0)
% 48.72/16.50 |
% 48.72/16.50 | Instantiating formula (25) with all_40_0_34, all_0_3_3, all_0_1_1, all_0_8_8, all_75_0_67 and discharging atoms addition(all_0_1_1, all_0_3_3) = all_40_0_34, addition(all_0_8_8, all_75_0_67) = all_0_3_3, yields:
% 48.72/16.50 | (251) ? [v0] : (addition(v0, all_75_0_67) = all_40_0_34 & addition(all_0_1_1, all_0_8_8) = v0)
% 48.72/16.50 |
% 48.72/16.50 | Instantiating formula (20) with all_35_2_33, all_0_1_1, all_58_0_41, all_0_8_8, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_1_1) = all_35_2_33, addition(all_0_8_8, all_58_0_41) = all_0_1_1, yields:
% 48.72/16.50 | (252) ? [v0] : ? [v1] : (multiplication(all_0_9_9, all_58_0_41) = v1 & multiplication(all_0_9_9, all_0_8_8) = v0 & addition(v0, v1) = all_35_2_33)
% 48.72/16.50 |
% 48.72/16.50 | Instantiating formula (25) with all_40_0_34, all_0_1_1, all_0_3_3, all_0_8_8, all_58_0_41 and discharging atoms addition(all_0_3_3, all_0_1_1) = all_40_0_34, addition(all_0_8_8, all_58_0_41) = all_0_1_1, yields:
% 48.72/16.50 | (253) ? [v0] : (addition(v0, all_58_0_41) = all_40_0_34 & addition(all_0_3_3, all_0_8_8) = v0)
% 48.72/16.50 |
% 48.72/16.50 | Instantiating formula (25) with all_104_0_95, all_0_1_1, all_35_1_32, all_0_8_8, all_58_0_41 and discharging atoms addition(all_35_1_32, all_0_1_1) = all_104_0_95, addition(all_0_8_8, all_58_0_41) = all_0_1_1, yields:
% 48.72/16.50 | (254) ? [v0] : (addition(v0, all_58_0_41) = all_104_0_95 & addition(all_35_1_32, all_0_8_8) = v0)
% 48.72/16.50 |
% 48.72/16.50 | Instantiating formula (32) with all_104_0_95, all_35_1_32, all_0_8_8, all_35_2_33, all_0_1_1 and discharging atoms addition(all_35_1_32, all_0_1_1) = all_104_0_95, addition(all_0_8_8, all_35_2_33) = all_35_1_32, yields:
% 48.72/16.50 | (255) ? [v0] : (addition(all_35_2_33, all_0_1_1) = v0 & addition(all_0_8_8, v0) = all_104_0_95)
% 48.72/16.50 |
% 48.72/16.50 | Instantiating formula (37) with all_86_0_78, all_29_0_30, all_0_8_8, all_96_0_87, all_0_9_9 and discharging atoms multiplication(all_29_0_30, all_0_8_8) = all_86_0_78, addition(all_0_9_9, all_96_0_87) = all_29_0_30, yields:
% 48.72/16.50 | (256) ? [v0] : ? [v1] : (multiplication(all_96_0_87, all_0_8_8) = v1 & multiplication(all_0_9_9, all_0_8_8) = v0 & addition(v0, v1) = all_86_0_78)
% 48.72/16.50 |
% 48.72/16.50 | Instantiating formula (37) with all_75_0_67, all_23_0_26, all_0_8_8, all_92_0_83, all_0_9_9 and discharging atoms multiplication(all_23_0_26, all_0_8_8) = all_75_0_67, addition(all_0_9_9, all_92_0_83) = all_23_0_26, yields:
% 48.72/16.50 | (257) ? [v0] : ? [v1] : (multiplication(all_92_0_83, all_0_8_8) = v1 & multiplication(all_0_9_9, all_0_8_8) = v0 & addition(v0, v1) = all_75_0_67)
% 48.72/16.50 |
% 48.72/16.50 | Instantiating formula (37) with all_86_0_78, all_29_0_30, all_0_8_8, all_79_0_71, all_0_9_9 and discharging atoms multiplication(all_29_0_30, all_0_8_8) = all_86_0_78, addition(all_0_9_9, all_79_0_71) = all_29_0_30, yields:
% 48.72/16.50 | (258) ? [v0] : ? [v1] : (multiplication(all_79_0_71, all_0_8_8) = v1 & multiplication(all_0_9_9, all_0_8_8) = v0 & addition(v0, v1) = all_86_0_78)
% 48.72/16.50 |
% 48.72/16.50 | Instantiating formula (37) with all_75_0_67, all_23_0_26, all_0_8_8, all_71_0_63, all_0_9_9 and discharging atoms multiplication(all_23_0_26, all_0_8_8) = all_75_0_67, addition(all_0_9_9, all_71_0_63) = all_23_0_26, yields:
% 48.72/16.50 | (259) ? [v0] : ? [v1] : (multiplication(all_71_0_63, all_0_8_8) = v1 & multiplication(all_0_9_9, all_0_8_8) = v0 & addition(v0, v1) = all_75_0_67)
% 48.72/16.50 |
% 48.72/16.50 | Instantiating (239) with all_127_0_115, all_127_1_116 yields:
% 48.72/16.50 | (260) multiplication(all_23_0_26, all_0_8_8) = all_127_1_116 & multiplication(one, all_0_8_8) = all_127_0_115 & addition(all_127_1_116, all_127_0_115) = all_0_3_3
% 48.72/16.50 |
% 48.72/16.50 | Applying alpha-rule on (260) yields:
% 48.72/16.50 | (261) multiplication(all_23_0_26, all_0_8_8) = all_127_1_116
% 48.72/16.50 | (262) multiplication(one, all_0_8_8) = all_127_0_115
% 48.72/16.51 | (263) addition(all_127_1_116, all_127_0_115) = all_0_3_3
% 48.72/16.51 |
% 48.72/16.51 | Instantiating (253) with all_131_0_118 yields:
% 48.72/16.51 | (264) addition(all_131_0_118, all_58_0_41) = all_40_0_34 & addition(all_0_3_3, all_0_8_8) = all_131_0_118
% 48.72/16.51 |
% 48.72/16.51 | Applying alpha-rule on (264) yields:
% 48.72/16.51 | (265) addition(all_131_0_118, all_58_0_41) = all_40_0_34
% 48.72/16.51 | (266) addition(all_0_3_3, all_0_8_8) = all_131_0_118
% 48.72/16.51 |
% 48.72/16.51 | Instantiating (252) with all_134_0_122, all_134_1_123 yields:
% 48.72/16.51 | (267) multiplication(all_0_9_9, all_58_0_41) = all_134_0_122 & multiplication(all_0_9_9, all_0_8_8) = all_134_1_123 & addition(all_134_1_123, all_134_0_122) = all_35_2_33
% 48.72/16.51 |
% 48.72/16.51 | Applying alpha-rule on (267) yields:
% 48.72/16.51 | (268) multiplication(all_0_9_9, all_58_0_41) = all_134_0_122
% 48.72/16.51 | (269) multiplication(all_0_9_9, all_0_8_8) = all_134_1_123
% 48.72/16.51 | (270) addition(all_134_1_123, all_134_0_122) = all_35_2_33
% 48.72/16.51 |
% 48.72/16.51 | Instantiating (254) with all_136_0_124 yields:
% 48.72/16.51 | (271) addition(all_136_0_124, all_58_0_41) = all_104_0_95 & addition(all_35_1_32, all_0_8_8) = all_136_0_124
% 48.72/16.51 |
% 48.72/16.51 | Applying alpha-rule on (271) yields:
% 48.72/16.51 | (272) addition(all_136_0_124, all_58_0_41) = all_104_0_95
% 48.72/16.51 | (273) addition(all_35_1_32, all_0_8_8) = all_136_0_124
% 48.72/16.51 |
% 48.72/16.51 | Instantiating (248) with all_140_0_126 yields:
% 48.72/16.51 | (274) addition(all_140_0_126, all_88_0_80) = all_40_0_34 & addition(all_0_3_3, all_0_8_8) = all_140_0_126
% 48.72/16.51 |
% 48.72/16.51 | Applying alpha-rule on (274) yields:
% 48.72/16.51 | (275) addition(all_140_0_126, all_88_0_80) = all_40_0_34
% 48.72/16.51 | (276) addition(all_0_3_3, all_0_8_8) = all_140_0_126
% 48.72/16.51 |
% 48.80/16.51 | Instantiating (249) with all_143_0_130 yields:
% 48.80/16.51 | (277) addition(all_143_0_130, all_88_0_80) = all_104_0_95 & addition(all_35_1_32, all_0_8_8) = all_143_0_130
% 48.80/16.51 |
% 48.80/16.51 | Applying alpha-rule on (277) yields:
% 48.80/16.51 | (278) addition(all_143_0_130, all_88_0_80) = all_104_0_95
% 48.80/16.51 | (279) addition(all_35_1_32, all_0_8_8) = all_143_0_130
% 48.80/16.51 |
% 48.80/16.51 | Instantiating (247) with all_149_0_143, all_149_1_144 yields:
% 48.80/16.51 | (280) multiplication(all_0_9_9, all_88_0_80) = all_149_0_143 & multiplication(all_0_9_9, all_0_8_8) = all_149_1_144 & addition(all_149_1_144, all_149_0_143) = all_35_2_33
% 48.80/16.51 |
% 48.80/16.51 | Applying alpha-rule on (280) yields:
% 48.80/16.51 | (281) multiplication(all_0_9_9, all_88_0_80) = all_149_0_143
% 48.80/16.51 | (282) multiplication(all_0_9_9, all_0_8_8) = all_149_1_144
% 48.80/16.51 | (283) addition(all_149_1_144, all_149_0_143) = all_35_2_33
% 48.80/16.51 |
% 48.80/16.51 | Instantiating (236) with all_157_0_159, all_157_1_160 yields:
% 48.80/16.51 | (284) multiplication(all_0_9_9, all_29_0_30) = all_157_1_160 & multiplication(all_0_9_9, one) = all_157_0_159 & addition(all_157_1_160, all_157_0_159) = all_23_0_26
% 48.80/16.51 |
% 48.80/16.51 | Applying alpha-rule on (284) yields:
% 48.80/16.51 | (285) multiplication(all_0_9_9, all_29_0_30) = all_157_1_160
% 48.80/16.51 | (286) multiplication(all_0_9_9, one) = all_157_0_159
% 48.80/16.51 | (287) addition(all_157_1_160, all_157_0_159) = all_23_0_26
% 48.80/16.51 |
% 48.80/16.51 | Instantiating (235) with all_159_0_161, all_159_1_162 yields:
% 48.80/16.51 | (288) multiplication(all_29_0_30, all_0_8_8) = all_159_1_162 & multiplication(one, all_0_8_8) = all_159_0_161 & addition(all_159_1_162, all_159_0_161) = all_0_3_3
% 48.80/16.51 |
% 48.80/16.51 | Applying alpha-rule on (288) yields:
% 48.80/16.51 | (289) multiplication(all_29_0_30, all_0_8_8) = all_159_1_162
% 48.80/16.51 | (290) multiplication(one, all_0_8_8) = all_159_0_161
% 48.80/16.51 | (291) addition(all_159_1_162, all_159_0_161) = all_0_3_3
% 48.80/16.51 |
% 48.80/16.51 | Instantiating (251) with all_171_0_184 yields:
% 48.80/16.51 | (292) addition(all_171_0_184, all_75_0_67) = all_40_0_34 & addition(all_0_1_1, all_0_8_8) = all_171_0_184
% 48.80/16.51 |
% 48.80/16.51 | Applying alpha-rule on (292) yields:
% 48.80/16.51 | (293) addition(all_171_0_184, all_75_0_67) = all_40_0_34
% 48.80/16.52 | (294) addition(all_0_1_1, all_0_8_8) = all_171_0_184
% 48.80/16.52 |
% 48.80/16.52 | Instantiating (258) with all_194_0_219, all_194_1_220 yields:
% 48.80/16.52 | (295) multiplication(all_79_0_71, all_0_8_8) = all_194_0_219 & multiplication(all_0_9_9, all_0_8_8) = all_194_1_220 & addition(all_194_1_220, all_194_0_219) = all_86_0_78
% 48.80/16.52 |
% 48.80/16.52 | Applying alpha-rule on (295) yields:
% 48.80/16.52 | (296) multiplication(all_79_0_71, all_0_8_8) = all_194_0_219
% 48.80/16.52 | (297) multiplication(all_0_9_9, all_0_8_8) = all_194_1_220
% 48.80/16.52 | (298) addition(all_194_1_220, all_194_0_219) = all_86_0_78
% 48.80/16.52 |
% 48.80/16.52 | Instantiating (250) with all_197_0_224 yields:
% 48.80/16.52 | (299) addition(all_197_0_224, all_86_0_78) = all_40_0_34 & addition(all_0_1_1, all_0_8_8) = all_197_0_224
% 48.80/16.52 |
% 48.80/16.52 | Applying alpha-rule on (299) yields:
% 48.80/16.52 | (300) addition(all_197_0_224, all_86_0_78) = all_40_0_34
% 48.80/16.52 | (301) addition(all_0_1_1, all_0_8_8) = all_197_0_224
% 48.80/16.52 |
% 48.80/16.52 | Instantiating (259) with all_224_0_267, all_224_1_268 yields:
% 48.80/16.52 | (302) multiplication(all_71_0_63, all_0_8_8) = all_224_0_267 & multiplication(all_0_9_9, all_0_8_8) = all_224_1_268 & addition(all_224_1_268, all_224_0_267) = all_75_0_67
% 48.80/16.52 |
% 48.80/16.52 | Applying alpha-rule on (302) yields:
% 48.80/16.52 | (303) multiplication(all_71_0_63, all_0_8_8) = all_224_0_267
% 48.80/16.52 | (304) multiplication(all_0_9_9, all_0_8_8) = all_224_1_268
% 48.80/16.52 | (305) addition(all_224_1_268, all_224_0_267) = all_75_0_67
% 48.80/16.52 |
% 48.80/16.52 | Instantiating (257) with all_267_0_335, all_267_1_336 yields:
% 48.80/16.52 | (306) multiplication(all_92_0_83, all_0_8_8) = all_267_0_335 & multiplication(all_0_9_9, all_0_8_8) = all_267_1_336 & addition(all_267_1_336, all_267_0_335) = all_75_0_67
% 48.80/16.52 |
% 48.80/16.52 | Applying alpha-rule on (306) yields:
% 48.80/16.52 | (307) multiplication(all_92_0_83, all_0_8_8) = all_267_0_335
% 48.80/16.52 | (308) multiplication(all_0_9_9, all_0_8_8) = all_267_1_336
% 48.80/16.52 | (309) addition(all_267_1_336, all_267_0_335) = all_75_0_67
% 48.80/16.52 |
% 48.80/16.52 | Instantiating (243) with all_275_0_347, all_275_1_348 yields:
% 48.80/16.52 | (310) multiplication(all_0_6_6, all_0_2_2) = all_275_0_347 & multiplication(all_0_6_6, all_0_2_2) = all_275_1_348 & addition(all_275_1_348, all_275_0_347) = all_35_2_33
% 48.80/16.52 |
% 48.80/16.52 | Applying alpha-rule on (310) yields:
% 48.80/16.52 | (311) multiplication(all_0_6_6, all_0_2_2) = all_275_0_347
% 48.80/16.52 | (312) multiplication(all_0_6_6, all_0_2_2) = all_275_1_348
% 48.80/16.52 | (313) addition(all_275_1_348, all_275_0_347) = all_35_2_33
% 48.80/16.52 |
% 48.80/16.52 | Instantiating (242) with all_287_0_371 yields:
% 48.80/16.52 | (314) multiplication(all_0_9_9, all_287_0_371) = all_0_6_6 & addition(all_0_8_8, all_0_8_8) = all_287_0_371
% 48.80/16.52 |
% 48.80/16.52 | Applying alpha-rule on (314) yields:
% 48.80/16.52 | (315) multiplication(all_0_9_9, all_287_0_371) = all_0_6_6
% 48.80/16.52 | (316) addition(all_0_8_8, all_0_8_8) = all_287_0_371
% 48.80/16.52 |
% 48.80/16.52 | Instantiating (256) with all_320_0_417, all_320_1_418 yields:
% 48.80/16.52 | (317) multiplication(all_96_0_87, all_0_8_8) = all_320_0_417 & multiplication(all_0_9_9, all_0_8_8) = all_320_1_418 & addition(all_320_1_418, all_320_0_417) = all_86_0_78
% 48.80/16.52 |
% 48.80/16.52 | Applying alpha-rule on (317) yields:
% 48.80/16.52 | (318) multiplication(all_96_0_87, all_0_8_8) = all_320_0_417
% 48.80/16.52 | (319) multiplication(all_0_9_9, all_0_8_8) = all_320_1_418
% 48.80/16.52 | (320) addition(all_320_1_418, all_320_0_417) = all_86_0_78
% 48.80/16.52 |
% 48.80/16.52 | Instantiating (255) with all_322_0_419 yields:
% 48.80/16.52 | (321) addition(all_35_2_33, all_0_1_1) = all_322_0_419 & addition(all_0_8_8, all_322_0_419) = all_104_0_95
% 48.80/16.52 |
% 48.80/16.52 | Applying alpha-rule on (321) yields:
% 48.80/16.52 | (322) addition(all_35_2_33, all_0_1_1) = all_322_0_419
% 48.80/16.52 | (323) addition(all_0_8_8, all_322_0_419) = all_104_0_95
% 48.80/16.52 |
% 48.80/16.52 | Instantiating (241) with all_327_0_425, all_327_1_426 yields:
% 48.80/16.52 | (324) multiplication(all_0_6_6, all_19_0_23) = all_327_1_426 & multiplication(all_0_6_6, one) = all_327_0_425 & addition(all_327_1_426, all_327_0_425) = all_35_2_33
% 48.80/16.52 |
% 48.80/16.52 | Applying alpha-rule on (324) yields:
% 48.80/16.52 | (325) multiplication(all_0_6_6, all_19_0_23) = all_327_1_426
% 48.80/16.52 | (326) multiplication(all_0_6_6, one) = all_327_0_425
% 48.80/16.52 | (327) addition(all_327_1_426, all_327_0_425) = all_35_2_33
% 48.80/16.52 |
% 48.80/16.52 | Instantiating (233) with all_351_0_451 yields:
% 48.80/16.52 | (328) addition(all_35_2_33, all_351_0_451) = all_104_0_95 & addition(all_0_8_8, all_0_1_1) = all_351_0_451
% 48.80/16.52 |
% 48.80/16.52 | Applying alpha-rule on (328) yields:
% 48.80/16.52 | (329) addition(all_35_2_33, all_351_0_451) = all_104_0_95
% 48.80/16.52 | (330) addition(all_0_8_8, all_0_1_1) = all_351_0_451
% 48.80/16.52 |
% 48.80/16.52 | Instantiating (230) with all_357_0_459 yields:
% 48.80/16.52 | (331) multiplication(all_0_8_8, all_0_7_7) = all_357_0_459 & multiplication(one, all_357_0_459) = all_0_5_5
% 48.80/16.52 |
% 48.80/16.52 | Applying alpha-rule on (331) yields:
% 48.80/16.52 | (332) multiplication(all_0_8_8, all_0_7_7) = all_357_0_459
% 48.80/16.52 | (333) multiplication(one, all_357_0_459) = all_0_5_5
% 48.80/16.52 |
% 48.80/16.52 | Instantiating (228) with all_363_0_462 yields:
% 48.80/16.52 | (334) multiplication(all_363_0_462, all_0_7_7) = all_19_0_23 & multiplication(all_0_2_2, one) = all_363_0_462
% 48.80/16.52 |
% 48.80/16.52 | Applying alpha-rule on (334) yields:
% 48.80/16.52 | (335) multiplication(all_363_0_462, all_0_7_7) = all_19_0_23
% 48.85/16.52 | (336) multiplication(all_0_2_2, one) = all_363_0_462
% 48.85/16.52 |
% 48.85/16.52 | Instantiating (231) with all_394_0_488 yields:
% 48.85/16.52 | (337) multiplication(all_0_9_9, all_0_8_8) = all_394_0_488 & multiplication(one, all_394_0_488) = all_0_6_6
% 48.85/16.52 |
% 48.85/16.52 | Applying alpha-rule on (337) yields:
% 48.85/16.52 | (338) multiplication(all_0_9_9, all_0_8_8) = all_394_0_488
% 48.85/16.52 | (339) multiplication(one, all_394_0_488) = all_0_6_6
% 48.85/16.52 |
% 48.85/16.52 | Instantiating (219) with all_429_0_508, all_429_1_509 yields:
% 48.85/16.52 | (340) multiplication(all_0_6_6, all_27_0_29) = all_429_0_508 & multiplication(all_0_6_6, one) = all_429_1_509 & addition(all_429_1_509, all_429_0_508) = all_35_2_33
% 48.85/16.52 |
% 48.85/16.52 | Applying alpha-rule on (340) yields:
% 48.85/16.52 | (341) multiplication(all_0_6_6, all_27_0_29) = all_429_0_508
% 48.85/16.52 | (342) multiplication(all_0_6_6, one) = all_429_1_509
% 48.85/16.52 | (343) addition(all_429_1_509, all_429_0_508) = all_35_2_33
% 48.85/16.52 |
% 48.85/16.52 | Instantiating (223) with all_442_0_523 yields:
% 48.85/16.52 | (344) multiplication(all_442_0_523, all_0_2_2) = all_88_0_80 & multiplication(all_0_8_8, all_0_7_7) = all_442_0_523
% 48.85/16.52 |
% 48.85/16.52 | Applying alpha-rule on (344) yields:
% 48.85/16.52 | (345) multiplication(all_442_0_523, all_0_2_2) = all_88_0_80
% 48.85/16.52 | (346) multiplication(all_0_8_8, all_0_7_7) = all_442_0_523
% 48.85/16.52 |
% 48.85/16.52 | Instantiating (227) with all_446_0_525 yields:
% 48.85/16.52 | (347) multiplication(all_0_9_9, all_446_0_525) = all_35_2_33 & multiplication(one, all_0_1_1) = all_446_0_525
% 48.85/16.52 |
% 48.85/16.52 | Applying alpha-rule on (347) yields:
% 48.85/16.52 | (348) multiplication(all_0_9_9, all_446_0_525) = all_35_2_33
% 48.85/16.52 | (349) multiplication(one, all_0_1_1) = all_446_0_525
% 48.85/16.52 |
% 48.85/16.52 | Instantiating (226) with all_448_0_526 yields:
% 48.85/16.52 | (350) multiplication(all_448_0_526, one) = all_29_0_30 & multiplication(all_0_4_4, all_0_9_9) = all_448_0_526
% 48.85/16.52 |
% 48.85/16.52 | Applying alpha-rule on (350) yields:
% 48.85/16.52 | (351) multiplication(all_448_0_526, one) = all_29_0_30
% 48.85/16.52 | (352) multiplication(all_0_4_4, all_0_9_9) = all_448_0_526
% 48.85/16.52 |
% 48.85/16.52 | Instantiating (232) with all_450_0_527 yields:
% 48.85/16.52 | (353) multiplication(all_0_9_9, all_29_0_30) = all_450_0_527 & multiplication(one, all_450_0_527) = all_92_0_83
% 48.85/16.52 |
% 48.85/16.52 | Applying alpha-rule on (353) yields:
% 48.85/16.52 | (354) multiplication(all_0_9_9, all_29_0_30) = all_450_0_527
% 48.85/16.52 | (355) multiplication(one, all_450_0_527) = all_92_0_83
% 48.85/16.52 |
% 48.85/16.52 | Instantiating (229) with all_454_0_529 yields:
% 48.85/16.52 | (356) multiplication(all_0_7_7, all_19_0_23) = all_454_0_529 & multiplication(one, all_454_0_529) = all_73_0_65
% 48.85/16.52 |
% 48.85/16.52 | Applying alpha-rule on (356) yields:
% 48.85/16.52 | (357) multiplication(all_0_7_7, all_19_0_23) = all_454_0_529
% 48.85/16.52 | (358) multiplication(one, all_454_0_529) = all_73_0_65
% 48.85/16.52 |
% 48.85/16.52 | Instantiating (222) with all_466_0_535 yields:
% 48.85/16.52 | (359) multiplication(all_466_0_535, one) = all_0_5_5 & multiplication(all_0_8_8, all_0_7_7) = all_466_0_535
% 48.85/16.52 |
% 48.85/16.52 | Applying alpha-rule on (359) yields:
% 48.85/16.52 | (360) multiplication(all_466_0_535, one) = all_0_5_5
% 48.85/16.52 | (361) multiplication(all_0_8_8, all_0_7_7) = all_466_0_535
% 48.85/16.52 |
% 48.85/16.52 | Instantiating (220) with all_472_0_538, all_472_1_539 yields:
% 48.85/16.52 | (362) multiplication(all_0_6_6, all_19_0_23) = all_472_0_538 & multiplication(all_0_6_6, one) = all_472_1_539 & addition(all_472_1_539, all_472_0_538) = all_35_2_33
% 48.85/16.52 |
% 48.85/16.52 | Applying alpha-rule on (362) yields:
% 48.85/16.52 | (363) multiplication(all_0_6_6, all_19_0_23) = all_472_0_538
% 48.85/16.52 | (364) multiplication(all_0_6_6, one) = all_472_1_539
% 48.85/16.52 | (365) addition(all_472_1_539, all_472_0_538) = all_35_2_33
% 48.85/16.52 |
% 48.85/16.52 | Instantiating (221) with all_478_0_543 yields:
% 48.85/16.52 | (366) multiplication(all_478_0_543, one) = all_19_0_23 & multiplication(all_0_2_2, all_0_7_7) = all_478_0_543
% 48.85/16.52 |
% 48.85/16.52 | Applying alpha-rule on (366) yields:
% 48.85/16.52 | (367) multiplication(all_478_0_543, one) = all_19_0_23
% 48.85/16.52 | (368) multiplication(all_0_2_2, all_0_7_7) = all_478_0_543
% 48.85/16.53 |
% 48.85/16.53 | Instantiating (244) with all_504_0_570, all_504_1_571 yields:
% 48.85/16.53 | (369) multiplication(all_0_8_8, all_77_0_69) = all_504_0_570 & multiplication(all_0_8_8, all_0_7_7) = all_504_1_571 & addition(all_504_1_571, all_504_0_570) = all_58_0_41
% 48.85/16.53 |
% 48.85/16.53 | Applying alpha-rule on (369) yields:
% 48.85/16.53 | (370) multiplication(all_0_8_8, all_77_0_69) = all_504_0_570
% 48.85/16.53 | (371) multiplication(all_0_8_8, all_0_7_7) = all_504_1_571
% 48.85/16.53 | (372) addition(all_504_1_571, all_504_0_570) = all_58_0_41
% 48.85/16.53 |
% 48.85/16.53 | Instantiating (240) with all_513_0_584, all_513_1_585 yields:
% 48.85/16.53 | (373) multiplication(all_0_7_7, all_19_0_23) = all_513_1_585 & multiplication(all_0_7_7, one) = all_513_0_584 & addition(all_513_1_585, all_513_0_584) = all_27_0_29
% 48.85/16.53 |
% 48.85/16.53 | Applying alpha-rule on (373) yields:
% 48.85/16.53 | (374) multiplication(all_0_7_7, all_19_0_23) = all_513_1_585
% 48.85/16.53 | (375) multiplication(all_0_7_7, one) = all_513_0_584
% 48.85/16.53 | (376) addition(all_513_1_585, all_513_0_584) = all_27_0_29
% 48.85/16.53 |
% 48.85/16.53 | Instantiating (238) with all_551_0_641, all_551_1_642 yields:
% 48.85/16.53 | (377) multiplication(all_0_6_6, all_27_0_29) = all_551_1_642 & multiplication(all_0_6_6, one) = all_551_0_641 & addition(all_551_1_642, all_551_0_641) = all_35_2_33
% 48.85/16.53 |
% 48.85/16.53 | Applying alpha-rule on (377) yields:
% 48.85/16.53 | (378) multiplication(all_0_6_6, all_27_0_29) = all_551_1_642
% 48.85/16.53 | (379) multiplication(all_0_6_6, one) = all_551_0_641
% 48.85/16.53 | (380) addition(all_551_1_642, all_551_0_641) = all_35_2_33
% 48.85/16.53 |
% 48.85/16.53 | Instantiating (237) with all_560_0_656, all_560_1_657 yields:
% 48.85/16.53 | (381) multiplication(all_0_8_8, all_27_0_29) = all_560_1_657 & multiplication(all_0_8_8, one) = all_560_0_656 & addition(all_560_1_657, all_560_0_656) = all_0_1_1
% 48.85/16.53 |
% 48.85/16.53 | Applying alpha-rule on (381) yields:
% 48.85/16.53 | (382) multiplication(all_0_8_8, all_27_0_29) = all_560_1_657
% 48.85/16.53 | (383) multiplication(all_0_8_8, one) = all_560_0_656
% 48.85/16.53 | (384) addition(all_560_1_657, all_560_0_656) = all_0_1_1
% 48.85/16.53 |
% 48.85/16.53 | Instantiating (245) with all_565_0_663, all_565_1_664 yields:
% 48.85/16.53 | (385) multiplication(all_0_8_8, all_73_0_65) = all_565_0_663 & multiplication(all_0_8_8, all_0_7_7) = all_565_1_664 & addition(all_565_1_664, all_565_0_663) = all_88_0_80
% 48.85/16.53 |
% 48.85/16.53 | Applying alpha-rule on (385) yields:
% 48.85/16.53 | (386) multiplication(all_0_8_8, all_73_0_65) = all_565_0_663
% 48.85/16.53 | (387) multiplication(all_0_8_8, all_0_7_7) = all_565_1_664
% 48.85/16.53 | (388) addition(all_565_1_664, all_565_0_663) = all_88_0_80
% 48.85/16.53 |
% 48.85/16.53 | Instantiating (246) with all_589_0_709, all_589_1_710 yields:
% 48.85/16.53 | (389) multiplication(all_0_8_8, all_63_0_52) = all_589_0_709 & multiplication(all_0_8_8, all_0_7_7) = all_589_1_710 & addition(all_589_1_710, all_589_0_709) = all_58_0_41
% 48.85/16.53 |
% 48.85/16.53 | Applying alpha-rule on (389) yields:
% 48.85/16.53 | (390) multiplication(all_0_8_8, all_63_0_52) = all_589_0_709
% 48.85/16.53 | (391) multiplication(all_0_8_8, all_0_7_7) = all_589_1_710
% 48.85/16.53 | (392) addition(all_589_1_710, all_589_0_709) = all_58_0_41
% 48.85/16.53 |
% 48.85/16.53 | Instantiating (216) with all_606_0_734 yields:
% 48.85/16.53 | (393) multiplication(all_0_4_4, all_606_0_734) = all_86_0_78 & multiplication(all_0_9_9, all_0_8_8) = all_606_0_734
% 48.85/16.53 |
% 48.85/16.53 | Applying alpha-rule on (393) yields:
% 48.85/16.53 | (394) multiplication(all_0_4_4, all_606_0_734) = all_86_0_78
% 48.85/16.53 | (395) multiplication(all_0_9_9, all_0_8_8) = all_606_0_734
% 48.85/16.53 |
% 48.85/16.53 | Instantiating (217) with all_611_0_739 yields:
% 48.85/16.53 | (396) multiplication(all_0_2_2, all_0_7_7) = all_611_0_739 & multiplication(all_0_7_7, all_611_0_739) = all_63_0_52
% 48.85/16.53 |
% 48.85/16.53 | Applying alpha-rule on (396) yields:
% 48.85/16.53 | (397) multiplication(all_0_2_2, all_0_7_7) = all_611_0_739
% 48.85/16.53 | (398) multiplication(all_0_7_7, all_611_0_739) = all_63_0_52
% 48.85/16.53 |
% 48.85/16.53 | Instantiating (225) with all_615_0_741 yields:
% 48.85/16.53 | (399) multiplication(all_615_0_741, one) = all_86_0_78 & multiplication(all_29_0_30, all_0_8_8) = all_615_0_741
% 48.85/16.53 |
% 48.85/16.53 | Applying alpha-rule on (399) yields:
% 48.85/16.53 | (400) multiplication(all_615_0_741, one) = all_86_0_78
% 48.85/16.53 | (401) multiplication(all_29_0_30, all_0_8_8) = all_615_0_741
% 48.85/16.53 |
% 48.85/16.53 | Instantiating (224) with all_622_0_748 yields:
% 48.85/16.53 | (402) multiplication(all_622_0_748, one) = all_0_6_6 & multiplication(all_0_9_9, all_0_8_8) = all_622_0_748
% 48.85/16.53 |
% 48.85/16.53 | Applying alpha-rule on (402) yields:
% 48.85/16.53 | (403) multiplication(all_622_0_748, one) = all_0_6_6
% 48.85/16.53 | (404) multiplication(all_0_9_9, all_0_8_8) = all_622_0_748
% 48.85/16.53 |
% 48.85/16.53 | Instantiating (218) with all_632_0_755 yields:
% 48.85/16.53 | (405) multiplication(all_0_4_4, all_0_9_9) = all_632_0_755 & multiplication(all_0_9_9, all_632_0_755) = all_79_0_71
% 48.85/16.53 |
% 48.85/16.53 | Applying alpha-rule on (405) yields:
% 48.85/16.53 | (406) multiplication(all_0_4_4, all_0_9_9) = all_632_0_755
% 48.85/16.53 | (407) multiplication(all_0_9_9, all_632_0_755) = all_79_0_71
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_29_0_30, all_0_8_8, all_615_0_741, all_86_0_78 and discharging atoms multiplication(all_29_0_30, all_0_8_8) = all_615_0_741, multiplication(all_29_0_30, all_0_8_8) = all_86_0_78, yields:
% 48.85/16.53 | (408) all_615_0_741 = all_86_0_78
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_29_0_30, all_0_8_8, all_159_1_162, all_615_0_741 and discharging atoms multiplication(all_29_0_30, all_0_8_8) = all_615_0_741, multiplication(all_29_0_30, all_0_8_8) = all_159_1_162, yields:
% 48.85/16.53 | (409) all_615_0_741 = all_159_1_162
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_2_2, all_0_7_7, all_611_0_739, all_19_0_23 and discharging atoms multiplication(all_0_2_2, all_0_7_7) = all_611_0_739, multiplication(all_0_2_2, all_0_7_7) = all_19_0_23, yields:
% 48.85/16.53 | (410) all_611_0_739 = all_19_0_23
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_2_2, all_0_7_7, all_478_0_543, all_611_0_739 and discharging atoms multiplication(all_0_2_2, all_0_7_7) = all_611_0_739, multiplication(all_0_2_2, all_0_7_7) = all_478_0_543, yields:
% 48.85/16.53 | (411) all_611_0_739 = all_478_0_543
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (3) with all_363_0_462, all_0_2_2 and discharging atoms multiplication(all_0_2_2, one) = all_363_0_462, yields:
% 48.85/16.53 | (412) all_363_0_462 = all_0_2_2
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_4_4, all_0_9_9, all_632_0_755, all_29_0_30 and discharging atoms multiplication(all_0_4_4, all_0_9_9) = all_632_0_755, multiplication(all_0_4_4, all_0_9_9) = all_29_0_30, yields:
% 48.85/16.53 | (413) all_632_0_755 = all_29_0_30
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_4_4, all_0_9_9, all_448_0_526, all_632_0_755 and discharging atoms multiplication(all_0_4_4, all_0_9_9) = all_632_0_755, multiplication(all_0_4_4, all_0_9_9) = all_448_0_526, yields:
% 48.85/16.53 | (414) all_632_0_755 = all_448_0_526
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_6_6, all_27_0_29, all_429_0_508, all_551_1_642 and discharging atoms multiplication(all_0_6_6, all_27_0_29) = all_551_1_642, multiplication(all_0_6_6, all_27_0_29) = all_429_0_508, yields:
% 48.85/16.53 | (415) all_551_1_642 = all_429_0_508
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_6_6, all_19_0_23, all_327_1_426, all_472_0_538 and discharging atoms multiplication(all_0_6_6, all_19_0_23) = all_472_0_538, multiplication(all_0_6_6, all_19_0_23) = all_327_1_426, yields:
% 48.85/16.53 | (416) all_472_0_538 = all_327_1_426
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_6_6, all_0_2_2, all_275_0_347, all_35_2_33 and discharging atoms multiplication(all_0_6_6, all_0_2_2) = all_275_0_347, multiplication(all_0_6_6, all_0_2_2) = all_35_2_33, yields:
% 48.85/16.53 | (417) all_275_0_347 = all_35_2_33
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_6_6, all_0_2_2, all_275_1_348, all_275_0_347 and discharging atoms multiplication(all_0_6_6, all_0_2_2) = all_275_0_347, multiplication(all_0_6_6, all_0_2_2) = all_275_1_348, yields:
% 48.85/16.53 | (418) all_275_0_347 = all_275_1_348
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_7_7, all_19_0_23, all_513_1_585, all_73_0_65 and discharging atoms multiplication(all_0_7_7, all_19_0_23) = all_513_1_585, multiplication(all_0_7_7, all_19_0_23) = all_73_0_65, yields:
% 48.85/16.53 | (419) all_513_1_585 = all_73_0_65
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_7_7, all_19_0_23, all_454_0_529, all_513_1_585 and discharging atoms multiplication(all_0_7_7, all_19_0_23) = all_513_1_585, multiplication(all_0_7_7, all_19_0_23) = all_454_0_529, yields:
% 48.85/16.53 | (420) all_513_1_585 = all_454_0_529
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_8_8, all_27_0_29, all_560_1_657, all_88_0_80 and discharging atoms multiplication(all_0_8_8, all_27_0_29) = all_560_1_657, multiplication(all_0_8_8, all_27_0_29) = all_88_0_80, yields:
% 48.85/16.53 | (421) all_560_1_657 = all_88_0_80
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_8_8, all_0_7_7, all_565_1_664, all_0_5_5 and discharging atoms multiplication(all_0_8_8, all_0_7_7) = all_565_1_664, multiplication(all_0_8_8, all_0_7_7) = all_0_5_5, yields:
% 48.85/16.53 | (422) all_565_1_664 = all_0_5_5
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_8_8, all_0_7_7, all_565_1_664, all_589_1_710 and discharging atoms multiplication(all_0_8_8, all_0_7_7) = all_589_1_710, multiplication(all_0_8_8, all_0_7_7) = all_565_1_664, yields:
% 48.85/16.53 | (423) all_589_1_710 = all_565_1_664
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_8_8, all_0_7_7, all_504_1_571, all_589_1_710 and discharging atoms multiplication(all_0_8_8, all_0_7_7) = all_589_1_710, multiplication(all_0_8_8, all_0_7_7) = all_504_1_571, yields:
% 48.85/16.53 | (424) all_589_1_710 = all_504_1_571
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_8_8, all_0_7_7, all_466_0_535, all_565_1_664 and discharging atoms multiplication(all_0_8_8, all_0_7_7) = all_565_1_664, multiplication(all_0_8_8, all_0_7_7) = all_466_0_535, yields:
% 48.85/16.53 | (425) all_565_1_664 = all_466_0_535
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_8_8, all_0_7_7, all_442_0_523, all_589_1_710 and discharging atoms multiplication(all_0_8_8, all_0_7_7) = all_589_1_710, multiplication(all_0_8_8, all_0_7_7) = all_442_0_523, yields:
% 48.85/16.53 | (426) all_589_1_710 = all_442_0_523
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_8_8, all_0_7_7, all_357_0_459, all_565_1_664 and discharging atoms multiplication(all_0_8_8, all_0_7_7) = all_565_1_664, multiplication(all_0_8_8, all_0_7_7) = all_357_0_459, yields:
% 48.85/16.53 | (427) all_565_1_664 = all_357_0_459
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (3) with all_560_0_656, all_0_8_8 and discharging atoms multiplication(all_0_8_8, one) = all_560_0_656, yields:
% 48.85/16.53 | (428) all_560_0_656 = all_0_8_8
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_9_9, all_29_0_30, all_157_1_160, all_450_0_527 and discharging atoms multiplication(all_0_9_9, all_29_0_30) = all_450_0_527, multiplication(all_0_9_9, all_29_0_30) = all_157_1_160, yields:
% 48.85/16.53 | (429) all_450_0_527 = all_157_1_160
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_9_9, all_0_8_8, all_622_0_748, all_0_6_6 and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_622_0_748, multiplication(all_0_9_9, all_0_8_8) = all_0_6_6, yields:
% 48.85/16.53 | (430) all_622_0_748 = all_0_6_6
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_9_9, all_0_8_8, all_394_0_488, all_606_0_734 and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_606_0_734, multiplication(all_0_9_9, all_0_8_8) = all_394_0_488, yields:
% 48.85/16.53 | (431) all_606_0_734 = all_394_0_488
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_9_9, all_0_8_8, all_320_1_418, all_394_0_488 and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_394_0_488, multiplication(all_0_9_9, all_0_8_8) = all_320_1_418, yields:
% 48.85/16.53 | (432) all_394_0_488 = all_320_1_418
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_9_9, all_0_8_8, all_267_1_336, all_622_0_748 and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_622_0_748, multiplication(all_0_9_9, all_0_8_8) = all_267_1_336, yields:
% 48.85/16.53 | (433) all_622_0_748 = all_267_1_336
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_9_9, all_0_8_8, all_267_1_336, all_320_1_418 and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_320_1_418, multiplication(all_0_9_9, all_0_8_8) = all_267_1_336, yields:
% 48.85/16.53 | (434) all_320_1_418 = all_267_1_336
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_9_9, all_0_8_8, all_224_1_268, all_622_0_748 and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_622_0_748, multiplication(all_0_9_9, all_0_8_8) = all_224_1_268, yields:
% 48.85/16.53 | (435) all_622_0_748 = all_224_1_268
% 48.85/16.53 |
% 48.85/16.53 | Instantiating formula (42) with all_0_9_9, all_0_8_8, all_194_1_220, all_622_0_748 and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_622_0_748, multiplication(all_0_9_9, all_0_8_8) = all_194_1_220, yields:
% 48.85/16.54 | (436) all_622_0_748 = all_194_1_220
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (42) with all_0_9_9, all_0_8_8, all_149_1_144, all_606_0_734 and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_606_0_734, multiplication(all_0_9_9, all_0_8_8) = all_149_1_144, yields:
% 48.85/16.54 | (437) all_606_0_734 = all_149_1_144
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (42) with all_0_9_9, all_0_8_8, all_134_1_123, all_224_1_268 and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_224_1_268, multiplication(all_0_9_9, all_0_8_8) = all_134_1_123, yields:
% 48.85/16.54 | (438) all_224_1_268 = all_134_1_123
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (30) with all_92_0_83, all_450_0_527 and discharging atoms multiplication(one, all_450_0_527) = all_92_0_83, yields:
% 48.85/16.54 | (439) all_450_0_527 = all_92_0_83
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (30) with all_446_0_525, all_0_1_1 and discharging atoms multiplication(one, all_0_1_1) = all_446_0_525, yields:
% 48.85/16.54 | (440) all_446_0_525 = all_0_1_1
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (30) with all_159_0_161, all_0_8_8 and discharging atoms multiplication(one, all_0_8_8) = all_159_0_161, yields:
% 48.85/16.54 | (441) all_159_0_161 = all_0_8_8
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (42) with one, all_0_8_8, all_127_0_115, all_159_0_161 and discharging atoms multiplication(one, all_0_8_8) = all_159_0_161, multiplication(one, all_0_8_8) = all_127_0_115, yields:
% 48.85/16.54 | (442) all_159_0_161 = all_127_0_115
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (23) with all_35_1_32, all_0_8_8, all_136_0_124, all_143_0_130 and discharging atoms addition(all_35_1_32, all_0_8_8) = all_143_0_130, addition(all_35_1_32, all_0_8_8) = all_136_0_124, yields:
% 48.85/16.54 | (443) all_143_0_130 = all_136_0_124
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (23) with all_0_1_1, all_0_8_8, all_171_0_184, all_197_0_224 and discharging atoms addition(all_0_1_1, all_0_8_8) = all_197_0_224, addition(all_0_1_1, all_0_8_8) = all_171_0_184, yields:
% 48.85/16.54 | (444) all_197_0_224 = all_171_0_184
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (23) with all_0_3_3, all_0_8_8, all_131_0_118, all_140_0_126 and discharging atoms addition(all_0_3_3, all_0_8_8) = all_140_0_126, addition(all_0_3_3, all_0_8_8) = all_131_0_118, yields:
% 48.85/16.54 | (445) all_140_0_126 = all_131_0_118
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (44) with all_287_0_371, all_0_8_8 and discharging atoms addition(all_0_8_8, all_0_8_8) = all_287_0_371, yields:
% 48.85/16.54 | (446) all_287_0_371 = all_0_8_8
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (413,414) yields a new equation:
% 48.85/16.54 | (447) all_448_0_526 = all_29_0_30
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (435,436) yields a new equation:
% 48.85/16.54 | (448) all_224_1_268 = all_194_1_220
% 48.85/16.54 |
% 48.85/16.54 | Simplifying 448 yields:
% 48.85/16.54 | (449) all_224_1_268 = all_194_1_220
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (433,436) yields a new equation:
% 48.85/16.54 | (450) all_267_1_336 = all_194_1_220
% 48.85/16.54 |
% 48.85/16.54 | Simplifying 450 yields:
% 48.85/16.54 | (451) all_267_1_336 = all_194_1_220
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (430,436) yields a new equation:
% 48.85/16.54 | (452) all_194_1_220 = all_0_6_6
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (408,409) yields a new equation:
% 48.85/16.54 | (453) all_159_1_162 = all_86_0_78
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (410,411) yields a new equation:
% 48.85/16.54 | (454) all_478_0_543 = all_19_0_23
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (431,437) yields a new equation:
% 48.85/16.54 | (455) all_394_0_488 = all_149_1_144
% 48.85/16.54 |
% 48.85/16.54 | Simplifying 455 yields:
% 48.85/16.54 | (456) all_394_0_488 = all_149_1_144
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (423,424) yields a new equation:
% 48.85/16.54 | (457) all_565_1_664 = all_504_1_571
% 48.85/16.54 |
% 48.85/16.54 | Simplifying 457 yields:
% 48.85/16.54 | (458) all_565_1_664 = all_504_1_571
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (426,424) yields a new equation:
% 48.85/16.54 | (459) all_504_1_571 = all_442_0_523
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (422,425) yields a new equation:
% 48.85/16.54 | (460) all_466_0_535 = all_0_5_5
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (458,425) yields a new equation:
% 48.85/16.54 | (461) all_504_1_571 = all_466_0_535
% 48.85/16.54 |
% 48.85/16.54 | Simplifying 461 yields:
% 48.85/16.54 | (462) all_504_1_571 = all_466_0_535
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (427,425) yields a new equation:
% 48.85/16.54 | (463) all_466_0_535 = all_357_0_459
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (420,419) yields a new equation:
% 48.85/16.54 | (464) all_454_0_529 = all_73_0_65
% 48.85/16.54 |
% 48.85/16.54 | Simplifying 464 yields:
% 48.85/16.54 | (465) all_454_0_529 = all_73_0_65
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (462,459) yields a new equation:
% 48.85/16.54 | (466) all_466_0_535 = all_442_0_523
% 48.85/16.54 |
% 48.85/16.54 | Simplifying 466 yields:
% 48.85/16.54 | (467) all_466_0_535 = all_442_0_523
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (460,467) yields a new equation:
% 48.85/16.54 | (468) all_442_0_523 = all_0_5_5
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (463,467) yields a new equation:
% 48.85/16.54 | (469) all_442_0_523 = all_357_0_459
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (439,429) yields a new equation:
% 48.85/16.54 | (470) all_157_1_160 = all_92_0_83
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (468,469) yields a new equation:
% 48.85/16.54 | (471) all_357_0_459 = all_0_5_5
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (432,456) yields a new equation:
% 48.85/16.54 | (472) all_320_1_418 = all_149_1_144
% 48.85/16.54 |
% 48.85/16.54 | Simplifying 472 yields:
% 48.85/16.54 | (473) all_320_1_418 = all_149_1_144
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (434,473) yields a new equation:
% 48.85/16.54 | (474) all_267_1_336 = all_149_1_144
% 48.85/16.54 |
% 48.85/16.54 | Simplifying 474 yields:
% 48.85/16.54 | (475) all_267_1_336 = all_149_1_144
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (418,417) yields a new equation:
% 48.85/16.54 | (476) all_275_1_348 = all_35_2_33
% 48.85/16.54 |
% 48.85/16.54 | Simplifying 476 yields:
% 48.85/16.54 | (477) all_275_1_348 = all_35_2_33
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (451,475) yields a new equation:
% 48.85/16.54 | (478) all_194_1_220 = all_149_1_144
% 48.85/16.54 |
% 48.85/16.54 | Simplifying 478 yields:
% 48.85/16.54 | (479) all_194_1_220 = all_149_1_144
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (449,438) yields a new equation:
% 48.85/16.54 | (480) all_194_1_220 = all_134_1_123
% 48.85/16.54 |
% 48.85/16.54 | Simplifying 480 yields:
% 48.85/16.54 | (481) all_194_1_220 = all_134_1_123
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (452,479) yields a new equation:
% 48.85/16.54 | (482) all_149_1_144 = all_0_6_6
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (481,479) yields a new equation:
% 48.85/16.54 | (483) all_149_1_144 = all_134_1_123
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (441,442) yields a new equation:
% 48.85/16.54 | (484) all_127_0_115 = all_0_8_8
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (482,483) yields a new equation:
% 48.85/16.54 | (485) all_134_1_123 = all_0_6_6
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (485,483) yields a new equation:
% 48.85/16.54 | (482) all_149_1_144 = all_0_6_6
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (484,442) yields a new equation:
% 48.85/16.54 | (441) all_159_0_161 = all_0_8_8
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (482,479) yields a new equation:
% 48.85/16.54 | (452) all_194_1_220 = all_0_6_6
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (482,475) yields a new equation:
% 48.85/16.54 | (489) all_267_1_336 = all_0_6_6
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (471,469) yields a new equation:
% 48.85/16.54 | (468) all_442_0_523 = all_0_5_5
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (468,467) yields a new equation:
% 48.85/16.54 | (460) all_466_0_535 = all_0_5_5
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (468,459) yields a new equation:
% 48.85/16.54 | (492) all_504_1_571 = all_0_5_5
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (460,425) yields a new equation:
% 48.85/16.54 | (422) all_565_1_664 = all_0_5_5
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (492,424) yields a new equation:
% 48.85/16.54 | (494) all_589_1_710 = all_0_5_5
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (454,411) yields a new equation:
% 48.85/16.54 | (410) all_611_0_739 = all_19_0_23
% 48.85/16.54 |
% 48.85/16.54 | Combining equations (447,414) yields a new equation:
% 48.85/16.54 | (413) all_632_0_755 = all_29_0_30
% 48.85/16.54 |
% 48.85/16.54 | From (468) and (345) follows:
% 48.85/16.54 | (497) multiplication(all_0_5_5, all_0_2_2) = all_88_0_80
% 48.85/16.54 |
% 48.85/16.54 | From (454) and (368) follows:
% 48.85/16.54 | (59) multiplication(all_0_2_2, all_0_7_7) = all_19_0_23
% 48.85/16.54 |
% 48.85/16.54 | From (412) and (336) follows:
% 48.85/16.54 | (499) multiplication(all_0_2_2, one) = all_0_2_2
% 48.85/16.54 |
% 48.85/16.54 | From (415) and (378) follows:
% 48.85/16.54 | (341) multiplication(all_0_6_6, all_27_0_29) = all_429_0_508
% 48.85/16.54 |
% 48.85/16.54 | From (416) and (363) follows:
% 48.85/16.54 | (325) multiplication(all_0_6_6, all_19_0_23) = all_327_1_426
% 48.85/16.54 |
% 48.85/16.54 | From (477) and (312) follows:
% 48.85/16.54 | (195) multiplication(all_0_6_6, all_0_2_2) = all_35_2_33
% 48.85/16.54 |
% 48.85/16.54 | From (410) and (398) follows:
% 48.85/16.54 | (503) multiplication(all_0_7_7, all_19_0_23) = all_63_0_52
% 48.85/16.54 |
% 48.85/16.54 | From (465) and (357) follows:
% 48.85/16.54 | (131) multiplication(all_0_7_7, all_19_0_23) = all_73_0_65
% 48.85/16.54 |
% 48.85/16.54 | From (413) and (407) follows:
% 48.85/16.54 | (505) multiplication(all_0_9_9, all_29_0_30) = all_79_0_71
% 48.85/16.54 |
% 48.85/16.54 | From (470) and (285) follows:
% 48.85/16.54 | (155) multiplication(all_0_9_9, all_29_0_30) = all_92_0_83
% 48.85/16.54 |
% 48.85/16.54 | From (440) and (349) follows:
% 48.85/16.54 | (507) multiplication(one, all_0_1_1) = all_0_1_1
% 48.85/16.54 |
% 48.85/16.54 | From (484) and (262) follows:
% 48.85/16.54 | (201) multiplication(one, all_0_8_8) = all_0_8_8
% 48.85/16.54 |
% 48.85/16.54 | From (494) and (392) follows:
% 48.85/16.54 | (509) addition(all_0_5_5, all_589_0_709) = all_58_0_41
% 48.85/16.54 |
% 48.85/16.54 | From (422) and (388) follows:
% 48.85/16.54 | (510) addition(all_0_5_5, all_565_0_663) = all_88_0_80
% 48.85/16.54 |
% 48.85/16.54 | From (421)(428) and (384) follows:
% 48.85/16.54 | (511) addition(all_88_0_80, all_0_8_8) = all_0_1_1
% 48.85/16.54 |
% 48.85/16.54 | From (489) and (309) follows:
% 48.85/16.54 | (512) addition(all_0_6_6, all_267_0_335) = all_75_0_67
% 48.85/16.54 |
% 48.85/16.54 | From (452) and (298) follows:
% 48.85/16.54 | (513) addition(all_0_6_6, all_194_0_219) = all_86_0_78
% 48.85/16.54 |
% 48.85/16.54 | From (453)(441) and (291) follows:
% 48.85/16.54 | (514) addition(all_86_0_78, all_0_8_8) = all_0_3_3
% 48.85/16.54 |
% 48.85/16.54 | From (443) and (279) follows:
% 48.85/16.54 | (273) addition(all_35_1_32, all_0_8_8) = all_136_0_124
% 48.85/16.54 |
% 48.85/16.54 | From (444) and (301) follows:
% 48.85/16.54 | (294) addition(all_0_1_1, all_0_8_8) = all_171_0_184
% 48.85/16.54 |
% 48.85/16.54 | From (445) and (276) follows:
% 48.85/16.54 | (266) addition(all_0_3_3, all_0_8_8) = all_131_0_118
% 48.85/16.54 |
% 48.85/16.54 | From (446) and (316) follows:
% 48.85/16.54 | (518) addition(all_0_8_8, all_0_8_8) = all_0_8_8
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (42) with all_0_7_7, all_19_0_23, all_63_0_52, all_73_0_65 and discharging atoms multiplication(all_0_7_7, all_19_0_23) = all_73_0_65, multiplication(all_0_7_7, all_19_0_23) = all_63_0_52, yields:
% 48.85/16.54 | (519) all_73_0_65 = all_63_0_52
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (42) with all_0_9_9, all_29_0_30, all_79_0_71, all_92_0_83 and discharging atoms multiplication(all_0_9_9, all_29_0_30) = all_92_0_83, multiplication(all_0_9_9, all_29_0_30) = all_79_0_71, yields:
% 48.85/16.54 | (520) all_92_0_83 = all_79_0_71
% 48.85/16.54 |
% 48.85/16.54 | From (520) and (307) follows:
% 48.85/16.54 | (521) multiplication(all_79_0_71, all_0_8_8) = all_267_0_335
% 48.85/16.54 |
% 48.85/16.54 | From (519) and (386) follows:
% 48.85/16.54 | (522) multiplication(all_0_8_8, all_63_0_52) = all_565_0_663
% 48.85/16.54 |
% 48.85/16.54 | From (519) and (210) follows:
% 48.85/16.54 | (523) addition(all_0_7_7, all_63_0_52) = all_27_0_29
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (42) with all_79_0_71, all_0_8_8, all_267_0_335, all_194_0_219 and discharging atoms multiplication(all_79_0_71, all_0_8_8) = all_267_0_335, multiplication(all_79_0_71, all_0_8_8) = all_194_0_219, yields:
% 48.85/16.54 | (524) all_267_0_335 = all_194_0_219
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (42) with all_0_8_8, all_63_0_52, all_565_0_663, all_589_0_709 and discharging atoms multiplication(all_0_8_8, all_63_0_52) = all_589_0_709, multiplication(all_0_8_8, all_63_0_52) = all_565_0_663, yields:
% 48.85/16.54 | (525) all_589_0_709 = all_565_0_663
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (23) with all_0_7_7, all_63_0_52, all_27_0_29, all_19_0_23 and discharging atoms addition(all_0_7_7, all_63_0_52) = all_27_0_29, addition(all_0_7_7, all_63_0_52) = all_19_0_23, yields:
% 48.85/16.54 | (526) all_27_0_29 = all_19_0_23
% 48.85/16.54 |
% 48.85/16.54 | From (526) and (341) follows:
% 48.85/16.54 | (527) multiplication(all_0_6_6, all_19_0_23) = all_429_0_508
% 48.85/16.54 |
% 48.85/16.54 | From (525) and (509) follows:
% 48.85/16.54 | (528) addition(all_0_5_5, all_565_0_663) = all_58_0_41
% 48.85/16.54 |
% 48.85/16.54 | From (524) and (512) follows:
% 48.85/16.54 | (529) addition(all_0_6_6, all_194_0_219) = all_75_0_67
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (42) with all_0_6_6, all_19_0_23, all_429_0_508, all_327_1_426 and discharging atoms multiplication(all_0_6_6, all_19_0_23) = all_429_0_508, multiplication(all_0_6_6, all_19_0_23) = all_327_1_426, yields:
% 48.85/16.54 | (530) all_429_0_508 = all_327_1_426
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (23) with all_0_5_5, all_565_0_663, all_58_0_41, all_88_0_80 and discharging atoms addition(all_0_5_5, all_565_0_663) = all_88_0_80, addition(all_0_5_5, all_565_0_663) = all_58_0_41, yields:
% 48.85/16.54 | (531) all_88_0_80 = all_58_0_41
% 48.85/16.54 |
% 48.85/16.54 | Instantiating formula (23) with all_0_6_6, all_194_0_219, all_75_0_67, all_86_0_78 and discharging atoms addition(all_0_6_6, all_194_0_219) = all_86_0_78, addition(all_0_6_6, all_194_0_219) = all_75_0_67, yields:
% 48.85/16.54 | (532) all_86_0_78 = all_75_0_67
% 48.85/16.54 |
% 48.85/16.54 | From (531) and (497) follows:
% 48.85/16.54 | (533) multiplication(all_0_5_5, all_0_2_2) = all_58_0_41
% 48.85/16.54 |
% 48.85/16.54 | From (530) and (527) follows:
% 48.85/16.55 | (325) multiplication(all_0_6_6, all_19_0_23) = all_327_1_426
% 48.85/16.55 |
% 48.85/16.55 | From (531) and (511) follows:
% 48.85/16.55 | (535) addition(all_58_0_41, all_0_8_8) = all_0_1_1
% 48.85/16.55 |
% 48.85/16.55 | From (532) and (514) follows:
% 48.85/16.55 | (536) addition(all_75_0_67, all_0_8_8) = all_0_3_3
% 48.85/16.55 |
% 48.85/16.55 | From (531) and (205) follows:
% 48.85/16.55 | (213) addition(all_0_8_8, all_58_0_41) = all_0_1_1
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (40) with all_35_2_33, all_0_2_2, one, all_0_2_2, all_0_6_6 and discharging atoms multiplication(all_0_2_2, one) = all_0_2_2, multiplication(all_0_6_6, all_0_2_2) = all_35_2_33, yields:
% 48.85/16.55 | (538) ? [v0] : (multiplication(v0, one) = all_35_2_33 & multiplication(all_0_6_6, all_0_2_2) = v0)
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (40) with all_58_0_41, all_0_2_2, one, all_0_2_2, all_0_5_5 and discharging atoms multiplication(all_0_2_2, one) = all_0_2_2, multiplication(all_0_5_5, all_0_2_2) = all_58_0_41, yields:
% 48.85/16.55 | (539) ? [v0] : (multiplication(v0, one) = all_58_0_41 & multiplication(all_0_5_5, all_0_2_2) = v0)
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (37) with all_58_0_41, all_0_5_5, all_0_2_2, all_0_6_6, all_0_5_5 and discharging atoms multiplication(all_0_5_5, all_0_2_2) = all_58_0_41, addition(all_0_5_5, all_0_6_6) = all_0_5_5, yields:
% 48.85/16.55 | (540) ? [v0] : ? [v1] : (multiplication(all_0_5_5, all_0_2_2) = v0 & multiplication(all_0_6_6, all_0_2_2) = v1 & addition(v0, v1) = all_58_0_41)
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (37) with all_58_0_41, all_0_5_5, all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms multiplication(all_0_5_5, all_0_2_2) = all_58_0_41, addition(all_0_6_6, all_0_5_5) = all_0_5_5, yields:
% 48.85/16.55 | (541) ? [v0] : ? [v1] : (multiplication(all_0_5_5, all_0_2_2) = v1 & multiplication(all_0_6_6, all_0_2_2) = v0 & addition(v0, v1) = all_58_0_41)
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (40) with all_327_1_426, all_19_0_23, all_0_7_7, all_0_2_2, all_0_6_6 and discharging atoms multiplication(all_0_2_2, all_0_7_7) = all_19_0_23, multiplication(all_0_6_6, all_19_0_23) = all_327_1_426, yields:
% 48.85/16.55 | (542) ? [v0] : (multiplication(v0, all_0_7_7) = all_327_1_426 & multiplication(all_0_6_6, all_0_2_2) = v0)
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (32) with all_40_0_34, all_0_3_3, all_75_0_67, all_0_8_8, all_0_1_1 and discharging atoms addition(all_75_0_67, all_0_8_8) = all_0_3_3, addition(all_0_3_3, all_0_1_1) = all_40_0_34, yields:
% 48.85/16.55 | (543) ? [v0] : (addition(all_75_0_67, v0) = all_40_0_34 & addition(all_0_8_8, all_0_1_1) = v0)
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (32) with all_136_0_124, all_35_1_32, all_35_2_33, all_0_8_8, all_0_8_8 and discharging atoms addition(all_35_1_32, all_0_8_8) = all_136_0_124, addition(all_35_2_33, all_0_8_8) = all_35_1_32, yields:
% 48.85/16.55 | (544) ? [v0] : (addition(all_35_2_33, v0) = all_136_0_124 & addition(all_0_8_8, all_0_8_8) = v0)
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (19) with all_104_0_95, all_351_0_451, all_35_2_33 and discharging atoms addition(all_35_2_33, all_351_0_451) = all_104_0_95, yields:
% 48.85/16.55 | (545) all_351_0_451 = all_104_0_95 | ? [v0] : ( ~ (v0 = 0) & leq(all_35_2_33, all_351_0_451) = v0)
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (15) with all_104_0_95, all_35_2_33, all_351_0_451 and discharging atoms addition(all_35_2_33, all_351_0_451) = all_104_0_95, yields:
% 48.85/16.55 | (546) addition(all_351_0_451, all_35_2_33) = all_104_0_95
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (25) with all_322_0_419, all_0_1_1, all_35_2_33, all_58_0_41, all_0_8_8 and discharging atoms addition(all_58_0_41, all_0_8_8) = all_0_1_1, addition(all_35_2_33, all_0_1_1) = all_322_0_419, yields:
% 48.85/16.55 | (547) ? [v0] : (addition(v0, all_0_8_8) = all_322_0_419 & addition(all_35_2_33, all_58_0_41) = v0)
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (15) with all_322_0_419, all_35_2_33, all_0_1_1 and discharging atoms addition(all_35_2_33, all_0_1_1) = all_322_0_419, yields:
% 48.85/16.55 | (548) addition(all_0_1_1, all_35_2_33) = all_322_0_419
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (25) with all_104_0_95, all_35_1_32, all_0_1_1, all_35_2_33, all_0_8_8 and discharging atoms addition(all_35_2_33, all_0_8_8) = all_35_1_32, addition(all_0_1_1, all_35_1_32) = all_104_0_95, yields:
% 48.85/16.55 | (549) ? [v0] : (addition(v0, all_0_8_8) = all_104_0_95 & addition(all_0_1_1, all_35_2_33) = v0)
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (32) with all_171_0_184, all_0_1_1, all_58_0_41, all_0_8_8, all_0_8_8 and discharging atoms addition(all_58_0_41, all_0_8_8) = all_0_1_1, addition(all_0_1_1, all_0_8_8) = all_171_0_184, yields:
% 48.85/16.55 | (550) ? [v0] : (addition(all_58_0_41, v0) = all_171_0_184 & addition(all_0_8_8, all_0_8_8) = v0)
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (15) with all_171_0_184, all_0_1_1, all_0_8_8 and discharging atoms addition(all_0_1_1, all_0_8_8) = all_171_0_184, yields:
% 48.85/16.55 | (551) addition(all_0_8_8, all_0_1_1) = all_171_0_184
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (32) with all_131_0_118, all_0_3_3, all_75_0_67, all_0_8_8, all_0_8_8 and discharging atoms addition(all_75_0_67, all_0_8_8) = all_0_3_3, addition(all_0_3_3, all_0_8_8) = all_131_0_118, yields:
% 48.85/16.55 | (552) ? [v0] : (addition(all_75_0_67, v0) = all_131_0_118 & addition(all_0_8_8, all_0_8_8) = v0)
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (48) with all_351_0_451, all_0_1_1, all_0_8_8, all_0_1_1, all_0_8_8, one and discharging atoms multiplication(one, all_0_1_1) = all_0_1_1, multiplication(one, all_0_8_8) = all_0_8_8, addition(all_0_8_8, all_0_1_1) = all_351_0_451, yields:
% 48.85/16.55 | (553) ? [v0] : (multiplication(one, v0) = all_351_0_451 & addition(all_0_8_8, all_0_1_1) = v0)
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (25) with all_351_0_451, all_0_1_1, all_0_8_8, all_0_8_8, all_58_0_41 and discharging atoms addition(all_0_8_8, all_58_0_41) = all_0_1_1, addition(all_0_8_8, all_0_1_1) = all_351_0_451, yields:
% 48.85/16.55 | (554) ? [v0] : (addition(v0, all_58_0_41) = all_351_0_451 & addition(all_0_8_8, all_0_8_8) = v0)
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (25) with all_351_0_451, all_0_1_1, all_0_8_8, all_58_0_41, all_0_8_8 and discharging atoms addition(all_58_0_41, all_0_8_8) = all_0_1_1, addition(all_0_8_8, all_0_1_1) = all_351_0_451, yields:
% 48.85/16.55 | (555) ? [v0] : (addition(v0, all_0_8_8) = all_351_0_451 & addition(all_0_8_8, all_58_0_41) = v0)
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (32) with all_0_1_1, all_0_8_8, all_0_8_8, all_0_8_8, all_58_0_41 and discharging atoms addition(all_0_8_8, all_58_0_41) = all_0_1_1, addition(all_0_8_8, all_0_8_8) = all_0_8_8, yields:
% 48.85/16.55 | (556) ? [v0] : (addition(all_0_8_8, v0) = all_0_1_1 & addition(all_0_8_8, all_58_0_41) = v0)
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (32) with all_351_0_451, all_0_8_8, all_0_8_8, all_0_8_8, all_0_1_1 and discharging atoms addition(all_0_8_8, all_0_1_1) = all_351_0_451, addition(all_0_8_8, all_0_8_8) = all_0_8_8, yields:
% 48.85/16.55 | (557) ? [v0] : (addition(all_0_8_8, v0) = all_351_0_451 & addition(all_0_8_8, all_0_1_1) = v0)
% 48.85/16.55 |
% 48.85/16.55 | Instantiating (544) with all_876_0_1059 yields:
% 48.85/16.55 | (558) addition(all_35_2_33, all_876_0_1059) = all_136_0_124 & addition(all_0_8_8, all_0_8_8) = all_876_0_1059
% 48.85/16.55 |
% 48.85/16.55 | Applying alpha-rule on (558) yields:
% 48.85/16.55 | (559) addition(all_35_2_33, all_876_0_1059) = all_136_0_124
% 48.85/16.55 | (560) addition(all_0_8_8, all_0_8_8) = all_876_0_1059
% 48.85/16.55 |
% 48.85/16.55 | Instantiating (538) with all_1091_0_1368 yields:
% 48.85/16.55 | (561) multiplication(all_1091_0_1368, one) = all_35_2_33 & multiplication(all_0_6_6, all_0_2_2) = all_1091_0_1368
% 48.85/16.55 |
% 48.85/16.55 | Applying alpha-rule on (561) yields:
% 48.85/16.55 | (562) multiplication(all_1091_0_1368, one) = all_35_2_33
% 48.85/16.55 | (563) multiplication(all_0_6_6, all_0_2_2) = all_1091_0_1368
% 48.85/16.55 |
% 48.85/16.55 | Instantiating (541) with all_1123_0_1396, all_1123_1_1397 yields:
% 48.85/16.55 | (564) multiplication(all_0_5_5, all_0_2_2) = all_1123_0_1396 & multiplication(all_0_6_6, all_0_2_2) = all_1123_1_1397 & addition(all_1123_1_1397, all_1123_0_1396) = all_58_0_41
% 48.85/16.55 |
% 48.85/16.55 | Applying alpha-rule on (564) yields:
% 48.85/16.55 | (565) multiplication(all_0_5_5, all_0_2_2) = all_1123_0_1396
% 48.85/16.55 | (566) multiplication(all_0_6_6, all_0_2_2) = all_1123_1_1397
% 48.85/16.55 | (567) addition(all_1123_1_1397, all_1123_0_1396) = all_58_0_41
% 48.85/16.55 |
% 48.85/16.55 | Instantiating (540) with all_1125_0_1398, all_1125_1_1399 yields:
% 48.85/16.55 | (568) multiplication(all_0_5_5, all_0_2_2) = all_1125_1_1399 & multiplication(all_0_6_6, all_0_2_2) = all_1125_0_1398 & addition(all_1125_1_1399, all_1125_0_1398) = all_58_0_41
% 48.85/16.55 |
% 48.85/16.55 | Applying alpha-rule on (568) yields:
% 48.85/16.55 | (569) multiplication(all_0_5_5, all_0_2_2) = all_1125_1_1399
% 48.85/16.55 | (570) multiplication(all_0_6_6, all_0_2_2) = all_1125_0_1398
% 48.85/16.55 | (571) addition(all_1125_1_1399, all_1125_0_1398) = all_58_0_41
% 48.85/16.55 |
% 48.85/16.55 | Instantiating (539) with all_1129_0_1402 yields:
% 48.85/16.55 | (572) multiplication(all_1129_0_1402, one) = all_58_0_41 & multiplication(all_0_5_5, all_0_2_2) = all_1129_0_1402
% 48.85/16.55 |
% 48.85/16.55 | Applying alpha-rule on (572) yields:
% 48.85/16.55 | (573) multiplication(all_1129_0_1402, one) = all_58_0_41
% 48.85/16.55 | (574) multiplication(all_0_5_5, all_0_2_2) = all_1129_0_1402
% 48.85/16.55 |
% 48.85/16.55 | Instantiating (542) with all_1249_0_1540 yields:
% 48.85/16.55 | (575) multiplication(all_1249_0_1540, all_0_7_7) = all_327_1_426 & multiplication(all_0_6_6, all_0_2_2) = all_1249_0_1540
% 48.85/16.55 |
% 48.85/16.55 | Applying alpha-rule on (575) yields:
% 48.85/16.55 | (576) multiplication(all_1249_0_1540, all_0_7_7) = all_327_1_426
% 48.85/16.55 | (577) multiplication(all_0_6_6, all_0_2_2) = all_1249_0_1540
% 48.85/16.55 |
% 48.85/16.55 | Instantiating (547) with all_1311_0_1640 yields:
% 48.85/16.55 | (578) addition(all_1311_0_1640, all_0_8_8) = all_322_0_419 & addition(all_35_2_33, all_58_0_41) = all_1311_0_1640
% 48.85/16.55 |
% 48.85/16.55 | Applying alpha-rule on (578) yields:
% 48.85/16.55 | (579) addition(all_1311_0_1640, all_0_8_8) = all_322_0_419
% 48.85/16.55 | (580) addition(all_35_2_33, all_58_0_41) = all_1311_0_1640
% 48.85/16.55 |
% 48.85/16.55 | Instantiating (543) with all_1421_0_1741 yields:
% 48.85/16.55 | (581) addition(all_75_0_67, all_1421_0_1741) = all_40_0_34 & addition(all_0_8_8, all_0_1_1) = all_1421_0_1741
% 48.85/16.55 |
% 48.85/16.55 | Applying alpha-rule on (581) yields:
% 48.85/16.55 | (582) addition(all_75_0_67, all_1421_0_1741) = all_40_0_34
% 48.85/16.55 | (583) addition(all_0_8_8, all_0_1_1) = all_1421_0_1741
% 48.85/16.55 |
% 48.85/16.55 | Instantiating (557) with all_1821_0_2280 yields:
% 48.85/16.55 | (584) addition(all_0_8_8, all_1821_0_2280) = all_351_0_451 & addition(all_0_8_8, all_0_1_1) = all_1821_0_2280
% 48.85/16.55 |
% 48.85/16.55 | Applying alpha-rule on (584) yields:
% 48.85/16.55 | (585) addition(all_0_8_8, all_1821_0_2280) = all_351_0_451
% 48.85/16.55 | (586) addition(all_0_8_8, all_0_1_1) = all_1821_0_2280
% 48.85/16.55 |
% 48.85/16.55 | Instantiating (556) with all_2126_0_2702 yields:
% 48.85/16.55 | (587) addition(all_0_8_8, all_2126_0_2702) = all_0_1_1 & addition(all_0_8_8, all_58_0_41) = all_2126_0_2702
% 48.85/16.55 |
% 48.85/16.55 | Applying alpha-rule on (587) yields:
% 48.85/16.55 | (588) addition(all_0_8_8, all_2126_0_2702) = all_0_1_1
% 48.85/16.55 | (589) addition(all_0_8_8, all_58_0_41) = all_2126_0_2702
% 48.85/16.55 |
% 48.85/16.55 | Instantiating (552) with all_2346_0_3048 yields:
% 48.85/16.55 | (590) addition(all_75_0_67, all_2346_0_3048) = all_131_0_118 & addition(all_0_8_8, all_0_8_8) = all_2346_0_3048
% 48.85/16.55 |
% 48.85/16.55 | Applying alpha-rule on (590) yields:
% 48.85/16.55 | (591) addition(all_75_0_67, all_2346_0_3048) = all_131_0_118
% 48.85/16.55 | (592) addition(all_0_8_8, all_0_8_8) = all_2346_0_3048
% 48.85/16.55 |
% 48.85/16.55 | Instantiating (550) with all_2571_0_3413 yields:
% 48.85/16.55 | (593) addition(all_58_0_41, all_2571_0_3413) = all_171_0_184 & addition(all_0_8_8, all_0_8_8) = all_2571_0_3413
% 48.85/16.55 |
% 48.85/16.55 | Applying alpha-rule on (593) yields:
% 48.85/16.55 | (594) addition(all_58_0_41, all_2571_0_3413) = all_171_0_184
% 48.85/16.55 | (595) addition(all_0_8_8, all_0_8_8) = all_2571_0_3413
% 48.85/16.55 |
% 48.85/16.55 | Instantiating (549) with all_2603_0_3455 yields:
% 48.85/16.55 | (596) addition(all_2603_0_3455, all_0_8_8) = all_104_0_95 & addition(all_0_1_1, all_35_2_33) = all_2603_0_3455
% 48.85/16.55 |
% 48.85/16.55 | Applying alpha-rule on (596) yields:
% 48.85/16.55 | (597) addition(all_2603_0_3455, all_0_8_8) = all_104_0_95
% 48.85/16.55 | (598) addition(all_0_1_1, all_35_2_33) = all_2603_0_3455
% 48.85/16.55 |
% 48.85/16.55 | Instantiating (555) with all_2629_0_3491 yields:
% 48.85/16.55 | (599) addition(all_2629_0_3491, all_0_8_8) = all_351_0_451 & addition(all_0_8_8, all_58_0_41) = all_2629_0_3491
% 48.85/16.55 |
% 48.85/16.55 | Applying alpha-rule on (599) yields:
% 48.85/16.55 | (600) addition(all_2629_0_3491, all_0_8_8) = all_351_0_451
% 48.85/16.55 | (601) addition(all_0_8_8, all_58_0_41) = all_2629_0_3491
% 48.85/16.55 |
% 48.85/16.55 | Instantiating (554) with all_2661_0_3528 yields:
% 48.85/16.55 | (602) addition(all_2661_0_3528, all_58_0_41) = all_351_0_451 & addition(all_0_8_8, all_0_8_8) = all_2661_0_3528
% 48.85/16.55 |
% 48.85/16.55 | Applying alpha-rule on (602) yields:
% 48.85/16.55 | (603) addition(all_2661_0_3528, all_58_0_41) = all_351_0_451
% 48.85/16.55 | (604) addition(all_0_8_8, all_0_8_8) = all_2661_0_3528
% 48.85/16.55 |
% 48.85/16.55 | Instantiating (553) with all_2663_0_3529 yields:
% 48.85/16.55 | (605) multiplication(one, all_2663_0_3529) = all_351_0_451 & addition(all_0_8_8, all_0_1_1) = all_2663_0_3529
% 48.85/16.55 |
% 48.85/16.55 | Applying alpha-rule on (605) yields:
% 48.85/16.55 | (606) multiplication(one, all_2663_0_3529) = all_351_0_451
% 48.85/16.55 | (607) addition(all_0_8_8, all_0_1_1) = all_2663_0_3529
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (42) with all_0_5_5, all_0_2_2, all_1129_0_1402, all_58_0_41 and discharging atoms multiplication(all_0_5_5, all_0_2_2) = all_1129_0_1402, multiplication(all_0_5_5, all_0_2_2) = all_58_0_41, yields:
% 48.85/16.55 | (608) all_1129_0_1402 = all_58_0_41
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (42) with all_0_5_5, all_0_2_2, all_1125_1_1399, all_1129_0_1402 and discharging atoms multiplication(all_0_5_5, all_0_2_2) = all_1129_0_1402, multiplication(all_0_5_5, all_0_2_2) = all_1125_1_1399, yields:
% 48.85/16.55 | (609) all_1129_0_1402 = all_1125_1_1399
% 48.85/16.55 |
% 48.85/16.55 | Instantiating formula (42) with all_0_5_5, all_0_2_2, all_1123_0_1396, all_1129_0_1402 and discharging atoms multiplication(all_0_5_5, all_0_2_2) = all_1129_0_1402, multiplication(all_0_5_5, all_0_2_2) = all_1123_0_1396, yields:
% 48.85/16.55 | (610) all_1129_0_1402 = all_1123_0_1396
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (42) with all_0_6_6, all_0_2_2, all_1125_0_1398, all_35_2_33 and discharging atoms multiplication(all_0_6_6, all_0_2_2) = all_1125_0_1398, multiplication(all_0_6_6, all_0_2_2) = all_35_2_33, yields:
% 48.85/16.56 | (611) all_1125_0_1398 = all_35_2_33
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (42) with all_0_6_6, all_0_2_2, all_1123_1_1397, all_1249_0_1540 and discharging atoms multiplication(all_0_6_6, all_0_2_2) = all_1249_0_1540, multiplication(all_0_6_6, all_0_2_2) = all_1123_1_1397, yields:
% 48.85/16.56 | (612) all_1249_0_1540 = all_1123_1_1397
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (42) with all_0_6_6, all_0_2_2, all_1123_1_1397, all_1125_0_1398 and discharging atoms multiplication(all_0_6_6, all_0_2_2) = all_1125_0_1398, multiplication(all_0_6_6, all_0_2_2) = all_1123_1_1397, yields:
% 48.85/16.56 | (613) all_1125_0_1398 = all_1123_1_1397
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (42) with all_0_6_6, all_0_2_2, all_1091_0_1368, all_1249_0_1540 and discharging atoms multiplication(all_0_6_6, all_0_2_2) = all_1249_0_1540, multiplication(all_0_6_6, all_0_2_2) = all_1091_0_1368, yields:
% 48.85/16.56 | (614) all_1249_0_1540 = all_1091_0_1368
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (23) with all_0_1_1, all_35_2_33, all_322_0_419, all_2603_0_3455 and discharging atoms addition(all_0_1_1, all_35_2_33) = all_2603_0_3455, addition(all_0_1_1, all_35_2_33) = all_322_0_419, yields:
% 48.85/16.56 | (615) all_2603_0_3455 = all_322_0_419
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (23) with all_0_8_8, all_58_0_41, all_2629_0_3491, all_0_1_1 and discharging atoms addition(all_0_8_8, all_58_0_41) = all_2629_0_3491, addition(all_0_8_8, all_58_0_41) = all_0_1_1, yields:
% 48.85/16.56 | (616) all_2629_0_3491 = all_0_1_1
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (23) with all_0_8_8, all_58_0_41, all_2126_0_2702, all_2629_0_3491 and discharging atoms addition(all_0_8_8, all_58_0_41) = all_2629_0_3491, addition(all_0_8_8, all_58_0_41) = all_2126_0_2702, yields:
% 48.85/16.56 | (617) all_2629_0_3491 = all_2126_0_2702
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (23) with all_0_8_8, all_0_1_1, all_2663_0_3529, all_351_0_451 and discharging atoms addition(all_0_8_8, all_0_1_1) = all_2663_0_3529, addition(all_0_8_8, all_0_1_1) = all_351_0_451, yields:
% 48.85/16.56 | (618) all_2663_0_3529 = all_351_0_451
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (23) with all_0_8_8, all_0_1_1, all_1821_0_2280, all_2663_0_3529 and discharging atoms addition(all_0_8_8, all_0_1_1) = all_2663_0_3529, addition(all_0_8_8, all_0_1_1) = all_1821_0_2280, yields:
% 48.85/16.56 | (619) all_2663_0_3529 = all_1821_0_2280
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (23) with all_0_8_8, all_0_1_1, all_1421_0_1741, all_1821_0_2280 and discharging atoms addition(all_0_8_8, all_0_1_1) = all_1821_0_2280, addition(all_0_8_8, all_0_1_1) = all_1421_0_1741, yields:
% 48.85/16.56 | (620) all_1821_0_2280 = all_1421_0_1741
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (23) with all_0_8_8, all_0_1_1, all_171_0_184, all_1421_0_1741 and discharging atoms addition(all_0_8_8, all_0_1_1) = all_1421_0_1741, addition(all_0_8_8, all_0_1_1) = all_171_0_184, yields:
% 48.85/16.56 | (621) all_1421_0_1741 = all_171_0_184
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (23) with all_0_8_8, all_0_8_8, all_2571_0_3413, all_2661_0_3528 and discharging atoms addition(all_0_8_8, all_0_8_8) = all_2661_0_3528, addition(all_0_8_8, all_0_8_8) = all_2571_0_3413, yields:
% 48.85/16.56 | (622) all_2661_0_3528 = all_2571_0_3413
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (44) with all_2571_0_3413, all_0_8_8 and discharging atoms addition(all_0_8_8, all_0_8_8) = all_2571_0_3413, yields:
% 48.85/16.56 | (623) all_2571_0_3413 = all_0_8_8
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (23) with all_0_8_8, all_0_8_8, all_2346_0_3048, all_2661_0_3528 and discharging atoms addition(all_0_8_8, all_0_8_8) = all_2661_0_3528, addition(all_0_8_8, all_0_8_8) = all_2346_0_3048, yields:
% 48.85/16.56 | (624) all_2661_0_3528 = all_2346_0_3048
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (23) with all_0_8_8, all_0_8_8, all_876_0_1059, all_2571_0_3413 and discharging atoms addition(all_0_8_8, all_0_8_8) = all_2571_0_3413, addition(all_0_8_8, all_0_8_8) = all_876_0_1059, yields:
% 48.85/16.56 | (625) all_2571_0_3413 = all_876_0_1059
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (619,618) yields a new equation:
% 48.85/16.56 | (626) all_1821_0_2280 = all_351_0_451
% 48.85/16.56 |
% 48.85/16.56 | Simplifying 626 yields:
% 48.85/16.56 | (627) all_1821_0_2280 = all_351_0_451
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (622,624) yields a new equation:
% 48.85/16.56 | (628) all_2571_0_3413 = all_2346_0_3048
% 48.85/16.56 |
% 48.85/16.56 | Simplifying 628 yields:
% 48.85/16.56 | (629) all_2571_0_3413 = all_2346_0_3048
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (616,617) yields a new equation:
% 48.85/16.56 | (630) all_2126_0_2702 = all_0_1_1
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (623,629) yields a new equation:
% 48.85/16.56 | (631) all_2346_0_3048 = all_0_8_8
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (625,629) yields a new equation:
% 48.85/16.56 | (632) all_2346_0_3048 = all_876_0_1059
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (631,632) yields a new equation:
% 48.85/16.56 | (633) all_876_0_1059 = all_0_8_8
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (620,627) yields a new equation:
% 48.85/16.56 | (634) all_1421_0_1741 = all_351_0_451
% 48.85/16.56 |
% 48.85/16.56 | Simplifying 634 yields:
% 48.85/16.56 | (635) all_1421_0_1741 = all_351_0_451
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (635,621) yields a new equation:
% 48.85/16.56 | (636) all_351_0_451 = all_171_0_184
% 48.85/16.56 |
% 48.85/16.56 | Simplifying 636 yields:
% 48.85/16.56 | (637) all_351_0_451 = all_171_0_184
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (612,614) yields a new equation:
% 48.85/16.56 | (638) all_1123_1_1397 = all_1091_0_1368
% 48.85/16.56 |
% 48.85/16.56 | Simplifying 638 yields:
% 48.85/16.56 | (639) all_1123_1_1397 = all_1091_0_1368
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (610,609) yields a new equation:
% 48.85/16.56 | (640) all_1125_1_1399 = all_1123_0_1396
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (608,609) yields a new equation:
% 48.85/16.56 | (641) all_1125_1_1399 = all_58_0_41
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (613,611) yields a new equation:
% 48.85/16.56 | (642) all_1123_1_1397 = all_35_2_33
% 48.85/16.56 |
% 48.85/16.56 | Simplifying 642 yields:
% 48.85/16.56 | (643) all_1123_1_1397 = all_35_2_33
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (641,640) yields a new equation:
% 48.85/16.56 | (644) all_1123_0_1396 = all_58_0_41
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (643,639) yields a new equation:
% 48.85/16.56 | (645) all_1091_0_1368 = all_35_2_33
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (645,639) yields a new equation:
% 48.85/16.56 | (643) all_1123_1_1397 = all_35_2_33
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (633,632) yields a new equation:
% 48.85/16.56 | (631) all_2346_0_3048 = all_0_8_8
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (631,629) yields a new equation:
% 48.85/16.56 | (623) all_2571_0_3413 = all_0_8_8
% 48.85/16.56 |
% 48.85/16.56 | From (643)(644) and (567) follows:
% 48.85/16.56 | (649) addition(all_35_2_33, all_58_0_41) = all_58_0_41
% 48.85/16.56 |
% 48.85/16.56 | From (637) and (546) follows:
% 48.85/16.56 | (650) addition(all_171_0_184, all_35_2_33) = all_104_0_95
% 48.85/16.56 |
% 48.85/16.56 | From (623) and (594) follows:
% 48.85/16.56 | (651) addition(all_58_0_41, all_0_8_8) = all_171_0_184
% 48.85/16.56 |
% 48.85/16.56 | From (615) and (598) follows:
% 48.85/16.56 | (548) addition(all_0_1_1, all_35_2_33) = all_322_0_419
% 48.85/16.56 |
% 48.85/16.56 | From (630) and (588) follows:
% 48.85/16.56 | (653) addition(all_0_8_8, all_0_1_1) = all_0_1_1
% 48.85/16.56 |
% 48.85/16.56 | From (637) and (330) follows:
% 48.85/16.56 | (551) addition(all_0_8_8, all_0_1_1) = all_171_0_184
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (23) with all_35_2_33, all_58_0_41, all_58_0_41, all_1311_0_1640 and discharging atoms addition(all_35_2_33, all_58_0_41) = all_1311_0_1640, addition(all_35_2_33, all_58_0_41) = all_58_0_41, yields:
% 48.85/16.56 | (655) all_1311_0_1640 = all_58_0_41
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (23) with all_0_8_8, all_0_1_1, all_0_1_1, all_171_0_184 and discharging atoms addition(all_0_8_8, all_0_1_1) = all_171_0_184, addition(all_0_8_8, all_0_1_1) = all_0_1_1, yields:
% 48.85/16.56 | (656) all_171_0_184 = all_0_1_1
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (656,637) yields a new equation:
% 48.85/16.56 | (657) all_351_0_451 = all_0_1_1
% 48.85/16.56 |
% 48.85/16.56 | From (655) and (579) follows:
% 48.85/16.56 | (658) addition(all_58_0_41, all_0_8_8) = all_322_0_419
% 48.85/16.56 |
% 48.85/16.56 | From (656) and (650) follows:
% 48.85/16.56 | (659) addition(all_0_1_1, all_35_2_33) = all_104_0_95
% 48.85/16.56 |
% 48.85/16.56 | From (656) and (651) follows:
% 48.85/16.56 | (535) addition(all_58_0_41, all_0_8_8) = all_0_1_1
% 48.85/16.56 |
% 48.85/16.56 +-Applying beta-rule and splitting (545), into two cases.
% 48.85/16.56 |-Branch one:
% 48.85/16.56 | (661) all_351_0_451 = all_104_0_95
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (657,661) yields a new equation:
% 48.85/16.56 | (662) all_104_0_95 = all_0_1_1
% 48.85/16.56 |
% 48.85/16.56 | Equations (662) can reduce 167 to:
% 48.85/16.56 | (71) $false
% 48.85/16.56 |
% 48.85/16.56 |-The branch is then unsatisfiable
% 48.85/16.56 |-Branch two:
% 48.85/16.56 | (664) ~ (all_351_0_451 = all_104_0_95)
% 48.85/16.56 | (665) ? [v0] : ( ~ (v0 = 0) & leq(all_35_2_33, all_351_0_451) = v0)
% 48.85/16.56 |
% 48.85/16.56 | Equations (657) can reduce 664 to:
% 48.85/16.56 | (666) ~ (all_104_0_95 = all_0_1_1)
% 48.85/16.56 |
% 48.85/16.56 | Simplifying 666 yields:
% 48.85/16.56 | (167) ~ (all_104_0_95 = all_0_1_1)
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (23) with all_58_0_41, all_0_8_8, all_322_0_419, all_0_1_1 and discharging atoms addition(all_58_0_41, all_0_8_8) = all_322_0_419, addition(all_58_0_41, all_0_8_8) = all_0_1_1, yields:
% 48.85/16.56 | (668) all_322_0_419 = all_0_1_1
% 48.85/16.56 |
% 48.85/16.56 | Instantiating formula (23) with all_0_1_1, all_35_2_33, all_104_0_95, all_322_0_419 and discharging atoms addition(all_0_1_1, all_35_2_33) = all_322_0_419, addition(all_0_1_1, all_35_2_33) = all_104_0_95, yields:
% 48.85/16.56 | (669) all_322_0_419 = all_104_0_95
% 48.85/16.56 |
% 48.85/16.56 | Combining equations (669,668) yields a new equation:
% 48.85/16.56 | (670) all_104_0_95 = all_0_1_1
% 48.85/16.56 |
% 48.85/16.56 | Simplifying 670 yields:
% 48.85/16.56 | (662) all_104_0_95 = all_0_1_1
% 48.85/16.56 |
% 48.85/16.56 | Equations (662) can reduce 167 to:
% 48.85/16.56 | (71) $false
% 48.85/16.56 |
% 48.85/16.56 |-The branch is then unsatisfiable
% 48.85/16.56 % SZS output end Proof for theBenchmark
% 48.85/16.56
% 48.85/16.56 15964ms
%------------------------------------------------------------------------------