TSTP Solution File: KLE007+2 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE007+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n022.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 01:50:48 EDT 2022

% Result   : Theorem 39.62s 12.53s
% Output   : Proof 46.86s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : KLE007+2 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.15  % Command  : ePrincess-casc -timeout=%d %s
% 0.15/0.37  % Computer : n022.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 600
% 0.15/0.37  % DateTime : Thu Jun 16 13:32:32 EDT 2022
% 0.15/0.37  % CPUTime  : 
% 0.57/0.61          ____       _                          
% 0.57/0.61    ___  / __ \_____(_)___  ________  __________
% 0.57/0.61   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.61  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.57/0.61  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.57/0.61  
% 0.57/0.61  A Theorem Prover for First-Order Logic
% 0.57/0.61  (ePrincess v.1.0)
% 0.57/0.61  
% 0.57/0.61  (c) Philipp Rümmer, 2009-2015
% 0.57/0.61  (c) Peter Backeman, 2014-2015
% 0.57/0.61  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.61  Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.61  Bug reports to peter@backeman.se
% 0.57/0.61  
% 0.57/0.61  For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.61  
% 0.57/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.66  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.64/0.96  Prover 0: Preprocessing ...
% 2.38/1.23  Prover 0: Constructing countermodel ...
% 18.23/5.95  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 18.23/5.98  Prover 1: Preprocessing ...
% 18.51/6.08  Prover 1: Constructing countermodel ...
% 28.79/8.55  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 28.79/8.57  Prover 2: Preprocessing ...
% 29.27/8.67  Prover 2: Warning: ignoring some quantifiers
% 29.27/8.67  Prover 2: Constructing countermodel ...
% 36.52/11.60  Prover 0: stopped
% 36.65/11.80  Prover 3: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 36.75/11.82  Prover 3: Preprocessing ...
% 36.75/11.86  Prover 3: Constructing countermodel ...
% 37.99/12.13  Prover 3: gave up
% 37.99/12.13  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 37.99/12.14  Prover 4: Preprocessing ...
% 37.99/12.19  Prover 4: Warning: ignoring some quantifiers
% 38.37/12.19  Prover 4: Constructing countermodel ...
% 39.62/12.53  Prover 4: proved (397ms)
% 39.62/12.53  Prover 1: stopped
% 39.62/12.53  Prover 2: stopped
% 39.62/12.53  
% 39.62/12.53  No countermodel exists, formula is valid
% 39.62/12.53  % SZS status Theorem for theBenchmark
% 39.62/12.53  
% 39.62/12.53  Generating proof ... Warning: ignoring some quantifiers
% 45.95/14.11  found it (size 397)
% 45.95/14.11  
% 45.95/14.11  % SZS output start Proof for theBenchmark
% 45.95/14.11  Assumed formulas after preprocessing and simplification: 
% 45.95/14.11  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (c(v1) = v5 & c(v0) = v2 & test(v1) = 0 & test(v0) = 0 & leq(v7, one) = v9 & leq(one, v7) = v8 & multiplication(v3, v5) = v6 & multiplication(v3, v1) = v4 & addition(v4, v6) = v7 & addition(v0, v2) = v3 &  ! [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(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] : ( ~ (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 |  ~ (complement(v13, v12) = v11) |  ~ (complement(v13, v12) = v10)) &  ! [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 |  ~ (complement(v11, v10) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : (multiplication(v11, v10) = v14 & multiplication(v10, v11) = v13 & addition(v10, v11) = v15 & ( ~ (v15 = one) |  ~ (v14 = zero) |  ~ (v13 = zero)))) &  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (leq(v10, v11) = v12) |  ? [v13] : ( ~ (v13 = v11) & addition(v10, v11) = v13)) &  ! [v10] :  ! [v11] :  ! [v12] : (v11 = v10 |  ~ (c(v12) = v11) |  ~ (c(v12) = v10)) &  ! [v10] :  ! [v11] :  ! [v12] : (v11 = v10 |  ~ (test(v12) = v11) |  ~ (test(v12) = v10)) &  ! [v10] :  ! [v11] :  ! [v12] : (v11 = 0 |  ~ (test(v10) = v11) |  ~ (complement(v12, v10) = 0)) &  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (complement(v10, v11) = v12) |  ? [v13] :  ? [v14] : (c(v10) = v14 & test(v10) = v13 & ( ~ (v13 = 0) | (( ~ (v14 = v11) | v12 = 0) & ( ~ (v12 = 0) | v14 = v11))))) &  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (multiplication(v11, v10) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : (complement(v11, v10) = v13 & multiplication(v10, v11) = v14 & addition(v10, v11) = v15 & ( ~ (v13 = 0) | (v15 = one & v14 = zero & v12 = zero)))) &  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (multiplication(v10, v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : (complement(v11, v10) = v13 & multiplication(v11, v10) = v14 & addition(v10, v11) = v15 & ( ~ (v13 = 0) | (v15 = one & v14 = zero & v12 = zero)))) &  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (addition(v11, v10) = v12) | addition(v10, v11) = v12) &  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (addition(v10, v11) = v12) | addition(v11, v10) = v12) &  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (addition(v10, v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : (complement(v11, v10) = v13 & multiplication(v11, v10) = v15 & multiplication(v10, v11) = v14 & ( ~ (v13 = 0) | (v15 = zero & v14 = zero & v12 = one)))) &  ! [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 |  ~ (c(v10) = v11) | test(v10) = 0) &  ! [v10] :  ! [v11] : (v11 = zero |  ~ (multiplication(v10, zero) = v11)) &  ! [v10] :  ! [v11] : (v11 = zero |  ~ (multiplication(zero, v10) = v11)) &  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (test(v10) = v11) | c(v10) = zero) &  ! [v10] :  ! [v11] : ( ~ (complement(v11, v10) = 0) | (multiplication(v11, v10) = zero & multiplication(v10, v11) = zero & addition(v10, v11) = one)) &  ! [v10] :  ! [v11] : ( ~ (leq(v10, v11) = 0) | addition(v10, v11) = v11) &  ! [v10] :  ! [v11] : ( ~ (multiplication(v11, v10) = zero) |  ? [v12] :  ? [v13] :  ? [v14] : (complement(v11, v10) = v14 & multiplication(v10, v11) = v12 & addition(v10, v11) = v13 & ( ~ (v13 = one) |  ~ (v12 = zero) | v14 = 0))) &  ! [v10] :  ! [v11] : ( ~ (multiplication(v10, v11) = zero) |  ? [v12] :  ? [v13] :  ? [v14] : (complement(v11, v10) = v14 & multiplication(v11, v10) = v12 & addition(v10, v11) = v13 & ( ~ (v13 = one) |  ~ (v12 = zero) | v14 = 0))) &  ! [v10] :  ! [v11] : ( ~ (addition(v10, v11) = v11) | leq(v10, v11) = 0) &  ! [v10] :  ! [v11] : ( ~ (addition(v10, v11) = one) |  ? [v12] :  ? [v13] :  ? [v14] : (complement(v11, v10) = v14 & multiplication(v11, v10) = v13 & multiplication(v10, v11) = v12 & ( ~ (v13 = zero) |  ~ (v12 = zero) | v14 = 0))) &  ! [v10] : ( ~ (test(v10) = 0) |  ? [v11] : complement(v11, v10) = 0) &  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] : (complement(v11, v10) = v15 & multiplication(v11, v10) = v13 & multiplication(v10, v11) = v12 & addition(v10, v11) = v14 & ( ~ (v14 = one) |  ~ (v13 = zero) |  ~ (v12 = zero) | v15 = 0)) &  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] : (leq(v10, v11) = v13 & addition(v10, v11) = v12 & ( ~ (v12 = v11) | v13 = 0)) &  ? [v10] :  ? [v11] :  ? [v12] : (c(v10) = v12 & test(v10) = v11 & (v12 = zero | v11 = 0)) & ( ~ (v9 = 0) |  ~ (v8 = 0)))
% 45.98/14.16  | 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:
% 45.98/14.16  | (1) c(all_0_8_8) = all_0_4_4 & c(all_0_9_9) = all_0_7_7 & test(all_0_8_8) = 0 & test(all_0_9_9) = 0 & leq(all_0_2_2, one) = all_0_0_0 & leq(one, all_0_2_2) = all_0_1_1 & multiplication(all_0_6_6, all_0_4_4) = all_0_3_3 & multiplication(all_0_6_6, all_0_8_8) = all_0_5_5 & addition(all_0_5_5, all_0_3_3) = all_0_2_2 & addition(all_0_9_9, all_0_7_7) = all_0_6_6 &  ! [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(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] : ( ~ (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 |  ~ (complement(v3, v2) = v1) |  ~ (complement(v3, v2) = v0)) &  ! [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 |  ~ (complement(v1, v0) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (multiplication(v1, v0) = v4 & multiplication(v0, v1) = v3 & addition(v0, v1) = v5 & ( ~ (v5 = one) |  ~ (v4 = zero) |  ~ (v3 = zero)))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (c(v2) = v1) |  ~ (c(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (test(v2) = v1) |  ~ (test(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = 0 |  ~ (test(v0) = v1) |  ~ (complement(v2, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (complement(v0, v1) = v2) |  ? [v3] :  ? [v4] : (c(v0) = v4 & test(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = v1) | v2 = 0) & ( ~ (v2 = 0) | v4 = v1))))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v1, v0) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (complement(v1, v0) = v3 & multiplication(v0, v1) = v4 & addition(v0, v1) = v5 & ( ~ (v3 = 0) | (v5 = one & v4 = zero & v2 = zero)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (complement(v1, v0) = v3 & multiplication(v1, v0) = v4 & addition(v0, v1) = v5 & ( ~ (v3 = 0) | (v5 = one & v4 = zero & v2 = zero)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (complement(v1, v0) = v3 & multiplication(v1, v0) = v5 & multiplication(v0, v1) = v4 & ( ~ (v3 = 0) | (v5 = zero & v4 = zero & v2 = one)))) &  ! [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 |  ~ (c(v0) = v1) | test(v0) = 0) &  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1)) &  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (test(v0) = v1) | c(v0) = zero) &  ! [v0] :  ! [v1] : ( ~ (complement(v1, v0) = 0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero & addition(v0, v1) = one)) &  ! [v0] :  ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) &  ! [v0] :  ! [v1] : ( ~ (multiplication(v1, v0) = zero) |  ? [v2] :  ? [v3] :  ? [v4] : (complement(v1, v0) = v4 & multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) |  ~ (v2 = zero) | v4 = 0))) &  ! [v0] :  ! [v1] : ( ~ (multiplication(v0, v1) = zero) |  ? [v2] :  ? [v3] :  ? [v4] : (complement(v1, v0) = v4 & multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) |  ~ (v2 = zero) | v4 = 0))) &  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) &  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = one) |  ? [v2] :  ? [v3] :  ? [v4] : (complement(v1, v0) = v4 & multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) |  ~ (v2 = zero) | v4 = 0))) &  ! [v0] : ( ~ (test(v0) = 0) |  ? [v1] : complement(v1, v0) = 0) &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : (complement(v1, v0) = v5 & multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & addition(v0, v1) = v4 & ( ~ (v4 = one) |  ~ (v3 = zero) |  ~ (v2 = zero) | v5 = 0)) &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (leq(v0, v1) = v3 & addition(v0, v1) = v2 & ( ~ (v2 = v1) | v3 = 0)) &  ? [v0] :  ? [v1] :  ? [v2] : (c(v0) = v2 & test(v0) = v1 & (v2 = zero | v1 = 0)) & ( ~ (all_0_0_0 = 0) |  ~ (all_0_1_1 = 0))
% 45.98/14.18  |
% 45.98/14.18  | Applying alpha-rule on (1) yields:
% 45.98/14.18  | (2)  ! [v0] :  ! [v1] : ( ~ (multiplication(v0, v1) = zero) |  ? [v2] :  ? [v3] :  ? [v4] : (complement(v1, v0) = v4 & multiplication(v1, v0) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) |  ~ (v2 = zero) | v4 = 0)))
% 45.98/14.18  | (3)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (c(v2) = v1) |  ~ (c(v2) = v0))
% 45.98/14.18  | (4)  ! [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))
% 45.98/14.18  | (5) test(all_0_9_9) = 0
% 45.98/14.18  | (6) c(all_0_9_9) = all_0_7_7
% 45.98/14.18  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 45.98/14.18  | (8)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (complement(v1, v0) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (multiplication(v1, v0) = v4 & multiplication(v0, v1) = v3 & addition(v0, v1) = v5 & ( ~ (v5 = one) |  ~ (v4 = zero) |  ~ (v3 = zero))))
% 45.98/14.18  | (9)  ! [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))
% 45.98/14.18  | (10) leq(all_0_2_2, one) = all_0_0_0
% 45.98/14.18  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (complement(v1, v0) = v3 & multiplication(v1, v0) = v5 & multiplication(v0, v1) = v4 & ( ~ (v3 = 0) | (v5 = zero & v4 = zero & v2 = one))))
% 45.98/14.18  | (12)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (leq(v0, v1) = v3 & addition(v0, v1) = v2 & ( ~ (v2 = v1) | v3 = 0))
% 45.98/14.18  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (complement(v3, v2) = v1) |  ~ (complement(v3, v2) = v0))
% 45.98/14.18  | (14)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 45.98/14.18  | (15)  ! [v0] :  ! [v1] : ( ~ (complement(v1, v0) = 0) | (multiplication(v1, v0) = zero & multiplication(v0, v1) = zero & addition(v0, v1) = one))
% 45.98/14.18  | (16)  ! [v0] : ( ~ (test(v0) = 0) |  ? [v1] : complement(v1, v0) = 0)
% 45.98/14.18  | (17)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1))
% 45.98/14.18  | (18)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (test(v0) = v1) | c(v0) = zero)
% 45.98/14.18  | (19) multiplication(all_0_6_6, all_0_8_8) = all_0_5_5
% 45.98/14.18  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 45.98/14.18  | (21)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 45.98/14.18  | (22)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v1, v0) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (complement(v1, v0) = v3 & multiplication(v0, v1) = v4 & addition(v0, v1) = v5 & ( ~ (v3 = 0) | (v5 = one & v4 = zero & v2 = zero))))
% 45.98/14.19  | (23) c(all_0_8_8) = all_0_4_4
% 45.98/14.19  | (24)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 45.98/14.19  | (25)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 45.98/14.19  | (26)  ! [v0] :  ! [v1] : ( ~ (multiplication(v1, v0) = zero) |  ? [v2] :  ? [v3] :  ? [v4] : (complement(v1, v0) = v4 & multiplication(v0, v1) = v2 & addition(v0, v1) = v3 & ( ~ (v3 = one) |  ~ (v2 = zero) | v4 = 0)))
% 45.98/14.19  | (27)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (complement(v0, v1) = v2) |  ? [v3] :  ? [v4] : (c(v0) = v4 & test(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = v1) | v2 = 0) & ( ~ (v2 = 0) | v4 = v1)))))
% 45.98/14.19  | (28) multiplication(all_0_6_6, all_0_4_4) = all_0_3_3
% 45.98/14.19  | (29) addition(all_0_5_5, all_0_3_3) = all_0_2_2
% 45.98/14.19  | (30)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 45.98/14.19  | (31)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 45.98/14.19  | (32)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (complement(v1, v0) = v3 & multiplication(v1, v0) = v4 & addition(v0, v1) = v5 & ( ~ (v3 = 0) | (v5 = one & v4 = zero & v2 = zero))))
% 45.98/14.19  | (33)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = 0 |  ~ (test(v0) = v1) |  ~ (complement(v2, v0) = 0))
% 45.98/14.19  | (34)  ? [v0] :  ? [v1] :  ? [v2] : (c(v0) = v2 & test(v0) = v1 & (v2 = zero | v1 = 0))
% 45.98/14.19  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 45.98/14.19  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 45.98/14.19  | (37) test(all_0_8_8) = 0
% 45.98/14.19  | (38)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (test(v2) = v1) |  ~ (test(v2) = v0))
% 45.98/14.19  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 45.98/14.19  | (40)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 45.98/14.19  | (41) addition(all_0_9_9, all_0_7_7) = all_0_6_6
% 45.98/14.19  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 45.98/14.19  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 45.98/14.19  | (44)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (c(v0) = v1) | test(v0) = 0)
% 45.98/14.19  | (45)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : (complement(v1, v0) = v5 & multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & addition(v0, v1) = v4 & ( ~ (v4 = one) |  ~ (v3 = zero) |  ~ (v2 = zero) | v5 = 0))
% 45.98/14.19  | (46)  ~ (all_0_0_0 = 0) |  ~ (all_0_1_1 = 0)
% 45.98/14.19  | (47)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0)
% 45.98/14.19  | (48)  ! [v0] :  ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 45.98/14.19  | (49)  ! [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))
% 45.98/14.19  | (50)  ! [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))
% 45.98/14.19  | (51)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 45.98/14.19  | (52) leq(one, all_0_2_2) = all_0_1_1
% 45.98/14.19  | (53)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = one) |  ? [v2] :  ? [v3] :  ? [v4] : (complement(v1, v0) = v4 & multiplication(v1, v0) = v3 & multiplication(v0, v1) = v2 & ( ~ (v3 = zero) |  ~ (v2 = zero) | v4 = 0)))
% 45.98/14.20  | (54)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 45.98/14.20  |
% 45.98/14.20  | Instantiating formula (16) with all_0_8_8 and discharging atoms test(all_0_8_8) = 0, yields:
% 45.98/14.20  | (55)  ? [v0] : complement(v0, all_0_8_8) = 0
% 45.98/14.20  |
% 45.98/14.20  | Instantiating formula (16) with all_0_9_9 and discharging atoms test(all_0_9_9) = 0, yields:
% 45.98/14.20  | (56)  ? [v0] : complement(v0, all_0_9_9) = 0
% 45.98/14.20  |
% 45.98/14.20  | Instantiating formula (54) with all_0_0_0, one, all_0_2_2 and discharging atoms leq(all_0_2_2, one) = all_0_0_0, yields:
% 45.98/14.20  | (57) all_0_0_0 = 0 |  ? [v0] : ( ~ (v0 = one) & addition(all_0_2_2, one) = v0)
% 45.98/14.20  |
% 45.98/14.20  | Instantiating formula (22) with all_0_3_3, all_0_6_6, all_0_4_4 and discharging atoms multiplication(all_0_6_6, all_0_4_4) = all_0_3_3, yields:
% 45.98/14.20  | (58)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_6_6, all_0_4_4) = v0 & multiplication(all_0_4_4, all_0_6_6) = v1 & addition(all_0_4_4, all_0_6_6) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_0_3_3 = zero)))
% 45.98/14.20  |
% 45.98/14.20  | Instantiating formula (32) with all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms multiplication(all_0_6_6, all_0_4_4) = all_0_3_3, yields:
% 45.98/14.20  | (59)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_4_4, all_0_6_6) = v0 & multiplication(all_0_4_4, all_0_6_6) = v1 & addition(all_0_6_6, all_0_4_4) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_0_3_3 = zero)))
% 45.98/14.20  |
% 45.98/14.20  | Instantiating formula (22) with all_0_5_5, all_0_6_6, all_0_8_8 and discharging atoms multiplication(all_0_6_6, all_0_8_8) = all_0_5_5, yields:
% 45.98/14.20  | (60)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_6_6, all_0_8_8) = v0 & multiplication(all_0_8_8, all_0_6_6) = v1 & addition(all_0_8_8, all_0_6_6) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_0_5_5 = zero)))
% 45.98/14.20  |
% 45.98/14.20  | Instantiating formula (32) with all_0_5_5, all_0_8_8, all_0_6_6 and discharging atoms multiplication(all_0_6_6, all_0_8_8) = all_0_5_5, yields:
% 45.98/14.20  | (61)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_8_8, all_0_6_6) = v0 & multiplication(all_0_8_8, all_0_6_6) = v1 & addition(all_0_6_6, all_0_8_8) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_0_5_5 = zero)))
% 45.98/14.20  |
% 45.98/14.20  | Instantiating formula (4) with all_0_2_2, all_0_3_3, all_0_5_5, all_0_4_4, all_0_8_8, all_0_6_6 and discharging atoms multiplication(all_0_6_6, all_0_4_4) = all_0_3_3, multiplication(all_0_6_6, all_0_8_8) = all_0_5_5, addition(all_0_5_5, all_0_3_3) = all_0_2_2, yields:
% 45.98/14.20  | (62)  ? [v0] : (multiplication(all_0_6_6, v0) = all_0_2_2 & addition(all_0_8_8, all_0_4_4) = v0)
% 45.98/14.20  |
% 45.98/14.20  | Instantiating formula (31) with all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms addition(all_0_5_5, all_0_3_3) = all_0_2_2, yields:
% 45.98/14.20  | (63) addition(all_0_3_3, all_0_5_5) = all_0_2_2
% 45.98/14.20  |
% 45.98/14.20  | Instantiating formula (11) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms addition(all_0_5_5, all_0_3_3) = all_0_2_2, yields:
% 45.98/14.20  | (64)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_3_3, all_0_5_5) = v0 & multiplication(all_0_3_3, all_0_5_5) = v2 & multiplication(all_0_5_5, all_0_3_3) = v1 & ( ~ (v0 = 0) | (v2 = zero & v1 = zero & all_0_2_2 = one)))
% 45.98/14.20  |
% 45.98/14.20  | Instantiating formula (49) with all_0_3_3, all_0_6_6, all_0_4_4, all_0_7_7, all_0_9_9 and discharging atoms multiplication(all_0_6_6, all_0_4_4) = all_0_3_3, addition(all_0_9_9, all_0_7_7) = all_0_6_6, yields:
% 45.98/14.20  | (65)  ? [v0] :  ? [v1] : (multiplication(all_0_7_7, all_0_4_4) = v1 & multiplication(all_0_9_9, all_0_4_4) = v0 & addition(v0, v1) = all_0_3_3)
% 45.98/14.20  |
% 45.98/14.20  | Instantiating formula (49) with all_0_5_5, all_0_6_6, all_0_8_8, all_0_7_7, all_0_9_9 and discharging atoms multiplication(all_0_6_6, all_0_8_8) = all_0_5_5, addition(all_0_9_9, all_0_7_7) = all_0_6_6, yields:
% 45.98/14.20  | (66)  ? [v0] :  ? [v1] : (multiplication(all_0_7_7, all_0_8_8) = v1 & multiplication(all_0_9_9, all_0_8_8) = v0 & addition(v0, v1) = all_0_5_5)
% 45.98/14.20  |
% 45.98/14.20  | Instantiating formula (31) with all_0_6_6, all_0_9_9, all_0_7_7 and discharging atoms addition(all_0_9_9, all_0_7_7) = all_0_6_6, yields:
% 45.98/14.20  | (67) addition(all_0_7_7, all_0_9_9) = all_0_6_6
% 45.98/14.20  |
% 45.98/14.20  | Instantiating formula (11) with all_0_6_6, all_0_7_7, all_0_9_9 and discharging atoms addition(all_0_9_9, all_0_7_7) = all_0_6_6, yields:
% 45.98/14.20  | (68)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_7_7, all_0_9_9) = v0 & multiplication(all_0_7_7, all_0_9_9) = v2 & multiplication(all_0_9_9, all_0_7_7) = v1 & ( ~ (v0 = 0) | (v2 = zero & v1 = zero & all_0_6_6 = one)))
% 45.98/14.20  |
% 45.98/14.20  | Instantiating (65) with all_15_0_23, all_15_1_24 yields:
% 45.98/14.20  | (69) multiplication(all_0_7_7, all_0_4_4) = all_15_0_23 & multiplication(all_0_9_9, all_0_4_4) = all_15_1_24 & addition(all_15_1_24, all_15_0_23) = all_0_3_3
% 45.98/14.20  |
% 45.98/14.20  | Applying alpha-rule on (69) yields:
% 45.98/14.20  | (70) multiplication(all_0_7_7, all_0_4_4) = all_15_0_23
% 46.44/14.20  | (71) multiplication(all_0_9_9, all_0_4_4) = all_15_1_24
% 46.44/14.20  | (72) addition(all_15_1_24, all_15_0_23) = all_0_3_3
% 46.44/14.20  |
% 46.44/14.20  | Instantiating (64) with all_17_0_25, all_17_1_26, all_17_2_27 yields:
% 46.44/14.20  | (73) complement(all_0_3_3, all_0_5_5) = all_17_2_27 & multiplication(all_0_3_3, all_0_5_5) = all_17_0_25 & multiplication(all_0_5_5, all_0_3_3) = all_17_1_26 & ( ~ (all_17_2_27 = 0) | (all_17_0_25 = zero & all_17_1_26 = zero & all_0_2_2 = one))
% 46.44/14.20  |
% 46.44/14.20  | Applying alpha-rule on (73) yields:
% 46.44/14.20  | (74) complement(all_0_3_3, all_0_5_5) = all_17_2_27
% 46.44/14.20  | (75) multiplication(all_0_3_3, all_0_5_5) = all_17_0_25
% 46.44/14.21  | (76) multiplication(all_0_5_5, all_0_3_3) = all_17_1_26
% 46.44/14.21  | (77)  ~ (all_17_2_27 = 0) | (all_17_0_25 = zero & all_17_1_26 = zero & all_0_2_2 = one)
% 46.44/14.21  |
% 46.44/14.21  | Instantiating (61) with all_19_0_28, all_19_1_29, all_19_2_30 yields:
% 46.44/14.21  | (78) complement(all_0_8_8, all_0_6_6) = all_19_2_30 & multiplication(all_0_8_8, all_0_6_6) = all_19_1_29 & addition(all_0_6_6, all_0_8_8) = all_19_0_28 & ( ~ (all_19_2_30 = 0) | (all_19_0_28 = one & all_19_1_29 = zero & all_0_5_5 = zero))
% 46.44/14.21  |
% 46.44/14.21  | Applying alpha-rule on (78) yields:
% 46.44/14.21  | (79) complement(all_0_8_8, all_0_6_6) = all_19_2_30
% 46.44/14.21  | (80) multiplication(all_0_8_8, all_0_6_6) = all_19_1_29
% 46.44/14.21  | (81) addition(all_0_6_6, all_0_8_8) = all_19_0_28
% 46.44/14.21  | (82)  ~ (all_19_2_30 = 0) | (all_19_0_28 = one & all_19_1_29 = zero & all_0_5_5 = zero)
% 46.44/14.21  |
% 46.44/14.21  | Instantiating (62) with all_21_0_31 yields:
% 46.44/14.21  | (83) multiplication(all_0_6_6, all_21_0_31) = all_0_2_2 & addition(all_0_8_8, all_0_4_4) = all_21_0_31
% 46.44/14.21  |
% 46.44/14.21  | Applying alpha-rule on (83) yields:
% 46.44/14.21  | (84) multiplication(all_0_6_6, all_21_0_31) = all_0_2_2
% 46.44/14.21  | (85) addition(all_0_8_8, all_0_4_4) = all_21_0_31
% 46.44/14.21  |
% 46.44/14.21  | Instantiating (68) with all_29_0_41, all_29_1_42, all_29_2_43 yields:
% 46.44/14.21  | (86) complement(all_0_7_7, all_0_9_9) = all_29_2_43 & multiplication(all_0_7_7, all_0_9_9) = all_29_0_41 & multiplication(all_0_9_9, all_0_7_7) = all_29_1_42 & ( ~ (all_29_2_43 = 0) | (all_29_0_41 = zero & all_29_1_42 = zero & all_0_6_6 = one))
% 46.44/14.21  |
% 46.44/14.21  | Applying alpha-rule on (86) yields:
% 46.44/14.21  | (87) complement(all_0_7_7, all_0_9_9) = all_29_2_43
% 46.44/14.21  | (88) multiplication(all_0_7_7, all_0_9_9) = all_29_0_41
% 46.44/14.21  | (89) multiplication(all_0_9_9, all_0_7_7) = all_29_1_42
% 46.44/14.21  | (90)  ~ (all_29_2_43 = 0) | (all_29_0_41 = zero & all_29_1_42 = zero & all_0_6_6 = one)
% 46.44/14.21  |
% 46.44/14.21  | Instantiating (56) with all_33_0_47 yields:
% 46.44/14.21  | (91) complement(all_33_0_47, all_0_9_9) = 0
% 46.44/14.21  |
% 46.44/14.21  | Instantiating (55) with all_39_0_53 yields:
% 46.44/14.21  | (92) complement(all_39_0_53, all_0_8_8) = 0
% 46.44/14.21  |
% 46.44/14.21  | Instantiating (60) with all_41_0_54, all_41_1_55, all_41_2_56 yields:
% 46.44/14.21  | (93) complement(all_0_6_6, all_0_8_8) = all_41_2_56 & multiplication(all_0_8_8, all_0_6_6) = all_41_1_55 & addition(all_0_8_8, all_0_6_6) = all_41_0_54 & ( ~ (all_41_2_56 = 0) | (all_41_0_54 = one & all_41_1_55 = zero & all_0_5_5 = zero))
% 46.44/14.21  |
% 46.44/14.21  | Applying alpha-rule on (93) yields:
% 46.44/14.21  | (94) complement(all_0_6_6, all_0_8_8) = all_41_2_56
% 46.44/14.21  | (95) multiplication(all_0_8_8, all_0_6_6) = all_41_1_55
% 46.44/14.21  | (96) addition(all_0_8_8, all_0_6_6) = all_41_0_54
% 46.44/14.21  | (97)  ~ (all_41_2_56 = 0) | (all_41_0_54 = one & all_41_1_55 = zero & all_0_5_5 = zero)
% 46.44/14.21  |
% 46.44/14.21  | Instantiating (59) with all_43_0_57, all_43_1_58, all_43_2_59 yields:
% 46.44/14.21  | (98) complement(all_0_4_4, all_0_6_6) = all_43_2_59 & multiplication(all_0_4_4, all_0_6_6) = all_43_1_58 & addition(all_0_6_6, all_0_4_4) = all_43_0_57 & ( ~ (all_43_2_59 = 0) | (all_43_0_57 = one & all_43_1_58 = zero & all_0_3_3 = zero))
% 46.44/14.21  |
% 46.44/14.21  | Applying alpha-rule on (98) yields:
% 46.44/14.21  | (99) complement(all_0_4_4, all_0_6_6) = all_43_2_59
% 46.44/14.21  | (100) multiplication(all_0_4_4, all_0_6_6) = all_43_1_58
% 46.44/14.21  | (101) addition(all_0_6_6, all_0_4_4) = all_43_0_57
% 46.44/14.21  | (102)  ~ (all_43_2_59 = 0) | (all_43_0_57 = one & all_43_1_58 = zero & all_0_3_3 = zero)
% 46.44/14.21  |
% 46.44/14.21  | Instantiating (58) with all_45_0_60, all_45_1_61, all_45_2_62 yields:
% 46.44/14.21  | (103) complement(all_0_6_6, all_0_4_4) = all_45_2_62 & multiplication(all_0_4_4, all_0_6_6) = all_45_1_61 & addition(all_0_4_4, all_0_6_6) = all_45_0_60 & ( ~ (all_45_2_62 = 0) | (all_45_0_60 = one & all_45_1_61 = zero & all_0_3_3 = zero))
% 46.44/14.21  |
% 46.44/14.21  | Applying alpha-rule on (103) yields:
% 46.44/14.21  | (104) complement(all_0_6_6, all_0_4_4) = all_45_2_62
% 46.44/14.21  | (105) multiplication(all_0_4_4, all_0_6_6) = all_45_1_61
% 46.44/14.21  | (106) addition(all_0_4_4, all_0_6_6) = all_45_0_60
% 46.44/14.21  | (107)  ~ (all_45_2_62 = 0) | (all_45_0_60 = one & all_45_1_61 = zero & all_0_3_3 = zero)
% 46.44/14.21  |
% 46.44/14.21  | Instantiating (66) with all_49_0_66, all_49_1_67 yields:
% 46.44/14.21  | (108) multiplication(all_0_7_7, all_0_8_8) = all_49_0_66 & multiplication(all_0_9_9, all_0_8_8) = all_49_1_67 & addition(all_49_1_67, all_49_0_66) = all_0_5_5
% 46.44/14.21  |
% 46.44/14.21  | Applying alpha-rule on (108) yields:
% 46.44/14.21  | (109) multiplication(all_0_7_7, all_0_8_8) = all_49_0_66
% 46.44/14.21  | (110) multiplication(all_0_9_9, all_0_8_8) = all_49_1_67
% 46.44/14.21  | (111) addition(all_49_1_67, all_49_0_66) = all_0_5_5
% 46.44/14.21  |
% 46.44/14.21  | Instantiating formula (42) with all_0_4_4, all_0_6_6, all_43_1_58, all_45_1_61 and discharging atoms multiplication(all_0_4_4, all_0_6_6) = all_45_1_61, multiplication(all_0_4_4, all_0_6_6) = all_43_1_58, yields:
% 46.44/14.21  | (112) all_45_1_61 = all_43_1_58
% 46.44/14.21  |
% 46.44/14.21  | Instantiating formula (42) with all_0_8_8, all_0_6_6, all_19_1_29, all_41_1_55 and discharging atoms multiplication(all_0_8_8, all_0_6_6) = all_41_1_55, multiplication(all_0_8_8, all_0_6_6) = all_19_1_29, yields:
% 46.44/14.22  | (113) all_41_1_55 = all_19_1_29
% 46.44/14.22  |
% 46.44/14.22  | From (112) and (105) follows:
% 46.44/14.22  | (100) multiplication(all_0_4_4, all_0_6_6) = all_43_1_58
% 46.44/14.22  |
% 46.44/14.22  | From (113) and (95) follows:
% 46.44/14.22  | (80) multiplication(all_0_8_8, all_0_6_6) = all_19_1_29
% 46.44/14.22  |
% 46.44/14.22  | Instantiating formula (27) with all_19_2_30, all_0_6_6, all_0_8_8 and discharging atoms complement(all_0_8_8, all_0_6_6) = all_19_2_30, yields:
% 46.44/14.22  | (116)  ? [v0] :  ? [v1] : (c(all_0_8_8) = v1 & test(all_0_8_8) = v0 & ( ~ (v0 = 0) | (( ~ (v1 = all_0_6_6) | all_19_2_30 = 0) & ( ~ (all_19_2_30 = 0) | v1 = all_0_6_6))))
% 46.44/14.22  |
% 46.44/14.22  | Instantiating formula (35) with all_17_0_25, all_0_3_3, all_0_5_5, all_0_4_4, all_0_6_6 and discharging atoms multiplication(all_0_3_3, all_0_5_5) = all_17_0_25, multiplication(all_0_6_6, all_0_4_4) = all_0_3_3, yields:
% 46.44/14.22  | (117)  ? [v0] : (multiplication(all_0_4_4, all_0_5_5) = v0 & multiplication(all_0_6_6, v0) = all_17_0_25)
% 46.44/14.22  |
% 46.44/14.22  | Instantiating formula (36) with all_17_0_25, all_0_5_5, all_0_8_8, all_0_6_6, all_0_3_3 and discharging atoms multiplication(all_0_3_3, all_0_5_5) = all_17_0_25, multiplication(all_0_6_6, all_0_8_8) = all_0_5_5, yields:
% 46.44/14.22  | (118)  ? [v0] : (multiplication(v0, all_0_8_8) = all_17_0_25 & multiplication(all_0_3_3, all_0_6_6) = v0)
% 46.44/14.22  |
% 46.44/14.22  | Instantiating formula (32) with all_17_0_25, all_0_5_5, all_0_3_3 and discharging atoms multiplication(all_0_3_3, all_0_5_5) = all_17_0_25, yields:
% 46.44/14.22  | (119)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_5_5, all_0_3_3) = v0 & multiplication(all_0_5_5, all_0_3_3) = v1 & addition(all_0_3_3, all_0_5_5) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_17_0_25 = zero)))
% 46.44/14.22  |
% 46.44/14.22  | Instantiating formula (22) with all_43_1_58, all_0_4_4, all_0_6_6 and discharging atoms multiplication(all_0_4_4, all_0_6_6) = all_43_1_58, yields:
% 46.44/14.22  | (120)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_4_4, all_0_6_6) = v0 & multiplication(all_0_6_6, all_0_4_4) = v1 & addition(all_0_6_6, all_0_4_4) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_43_1_58 = zero)))
% 46.44/14.22  |
% 46.44/14.22  | Instantiating formula (32) with all_43_1_58, all_0_6_6, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_6_6) = all_43_1_58, yields:
% 46.44/14.22  | (121)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_6_6, all_0_4_4) = v0 & multiplication(all_0_6_6, all_0_4_4) = v1 & addition(all_0_4_4, all_0_6_6) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_43_1_58 = zero)))
% 46.44/14.22  |
% 46.44/14.22  | Instantiating formula (36) with all_17_1_26, all_0_3_3, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms multiplication(all_0_5_5, all_0_3_3) = all_17_1_26, multiplication(all_0_6_6, all_0_4_4) = all_0_3_3, yields:
% 46.44/14.22  | (122)  ? [v0] : (multiplication(v0, all_0_4_4) = all_17_1_26 & multiplication(all_0_5_5, all_0_6_6) = v0)
% 46.44/14.22  |
% 46.44/14.22  | Instantiating formula (35) with all_17_1_26, all_0_5_5, all_0_3_3, all_0_8_8, all_0_6_6 and discharging atoms multiplication(all_0_5_5, all_0_3_3) = all_17_1_26, multiplication(all_0_6_6, all_0_8_8) = all_0_5_5, yields:
% 46.44/14.22  | (123)  ? [v0] : (multiplication(all_0_6_6, v0) = all_17_1_26 & multiplication(all_0_8_8, all_0_3_3) = v0)
% 46.44/14.22  |
% 46.44/14.22  | Instantiating formula (22) with all_17_1_26, all_0_5_5, all_0_3_3 and discharging atoms multiplication(all_0_5_5, all_0_3_3) = all_17_1_26, yields:
% 46.44/14.22  | (124)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_5_5, all_0_3_3) = v0 & multiplication(all_0_3_3, all_0_5_5) = v1 & addition(all_0_3_3, all_0_5_5) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_17_1_26 = zero)))
% 46.44/14.22  |
% 46.44/14.22  | Instantiating formula (22) with all_0_2_2, all_0_6_6, all_21_0_31 and discharging atoms multiplication(all_0_6_6, all_21_0_31) = all_0_2_2, yields:
% 46.44/14.22  | (125)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_6_6, all_21_0_31) = v0 & multiplication(all_21_0_31, all_0_6_6) = v1 & addition(all_21_0_31, all_0_6_6) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_0_2_2 = zero)))
% 46.44/14.22  |
% 46.44/14.22  | Instantiating formula (32) with all_0_2_2, all_21_0_31, all_0_6_6 and discharging atoms multiplication(all_0_6_6, all_21_0_31) = all_0_2_2, yields:
% 46.44/14.22  | (126)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_21_0_31, all_0_6_6) = v0 & multiplication(all_21_0_31, all_0_6_6) = v1 & addition(all_0_6_6, all_21_0_31) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_0_2_2 = zero)))
% 46.44/14.22  |
% 46.44/14.22  | Instantiating formula (32) with all_49_0_66, all_0_8_8, all_0_7_7 and discharging atoms multiplication(all_0_7_7, all_0_8_8) = all_49_0_66, yields:
% 46.44/14.22  | (127)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_8_8, all_0_7_7) = v0 & multiplication(all_0_8_8, all_0_7_7) = v1 & addition(all_0_7_7, all_0_8_8) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_49_0_66 = zero)))
% 46.44/14.22  |
% 46.44/14.22  | Instantiating formula (32) with all_29_0_41, all_0_9_9, all_0_7_7 and discharging atoms multiplication(all_0_7_7, all_0_9_9) = all_29_0_41, yields:
% 46.44/14.22  | (128)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_9_9, all_0_7_7) = v0 & multiplication(all_0_9_9, all_0_7_7) = v1 & addition(all_0_7_7, all_0_9_9) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_29_0_41 = zero)))
% 46.44/14.22  |
% 46.44/14.22  | Instantiating formula (22) with all_19_1_29, all_0_8_8, all_0_6_6 and discharging atoms multiplication(all_0_8_8, all_0_6_6) = all_19_1_29, yields:
% 46.44/14.22  | (129)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_8_8, all_0_6_6) = v0 & multiplication(all_0_6_6, all_0_8_8) = v1 & addition(all_0_6_6, all_0_8_8) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_19_1_29 = zero)))
% 46.44/14.22  |
% 46.44/14.22  | Instantiating formula (32) with all_19_1_29, all_0_6_6, all_0_8_8 and discharging atoms multiplication(all_0_8_8, all_0_6_6) = all_19_1_29, yields:
% 46.44/14.22  | (130)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_6_6, all_0_8_8) = v0 & multiplication(all_0_6_6, all_0_8_8) = v1 & addition(all_0_8_8, all_0_6_6) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_19_1_29 = zero)))
% 46.44/14.23  |
% 46.44/14.23  | Instantiating formula (22) with all_15_1_24, all_0_9_9, all_0_4_4 and discharging atoms multiplication(all_0_9_9, all_0_4_4) = all_15_1_24, yields:
% 46.44/14.23  | (131)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_9_9, all_0_4_4) = v0 & multiplication(all_0_4_4, all_0_9_9) = v1 & addition(all_0_4_4, all_0_9_9) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_15_1_24 = zero)))
% 46.44/14.23  |
% 46.44/14.23  | Instantiating formula (22) with all_29_1_42, all_0_9_9, all_0_7_7 and discharging atoms multiplication(all_0_9_9, all_0_7_7) = all_29_1_42, yields:
% 46.44/14.23  | (132)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_9_9, all_0_7_7) = v0 & multiplication(all_0_7_7, all_0_9_9) = v1 & addition(all_0_7_7, all_0_9_9) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_29_1_42 = zero)))
% 46.44/14.23  |
% 46.44/14.23  | Instantiating formula (22) with all_49_1_67, all_0_9_9, all_0_8_8 and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_49_1_67, yields:
% 46.44/14.23  | (133)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_9_9, all_0_8_8) = v0 & multiplication(all_0_8_8, all_0_9_9) = v1 & addition(all_0_8_8, all_0_9_9) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_49_1_67 = zero)))
% 46.44/14.23  |
% 46.44/14.23  | Instantiating formula (32) with all_49_1_67, all_0_8_8, all_0_9_9 and discharging atoms multiplication(all_0_9_9, all_0_8_8) = all_49_1_67, yields:
% 46.44/14.23  | (134)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_8_8, all_0_9_9) = v0 & multiplication(all_0_8_8, all_0_9_9) = v1 & addition(all_0_9_9, all_0_8_8) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_49_1_67 = zero)))
% 46.44/14.23  |
% 46.44/14.23  | Instantiating formula (4) with all_0_2_2, all_0_5_5, all_0_3_3, all_0_8_8, all_0_4_4, all_0_6_6 and discharging atoms multiplication(all_0_6_6, all_0_4_4) = all_0_3_3, multiplication(all_0_6_6, all_0_8_8) = all_0_5_5, addition(all_0_3_3, all_0_5_5) = all_0_2_2, yields:
% 46.44/14.23  | (135)  ? [v0] : (multiplication(all_0_6_6, v0) = all_0_2_2 & addition(all_0_4_4, all_0_8_8) = v0)
% 46.44/14.23  |
% 46.44/14.23  | Instantiating formula (11) with all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms addition(all_0_3_3, all_0_5_5) = all_0_2_2, yields:
% 46.44/14.23  | (136)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_5_5, all_0_3_3) = v0 & multiplication(all_0_3_3, all_0_5_5) = v1 & multiplication(all_0_5_5, all_0_3_3) = v2 & ( ~ (v0 = 0) | (v2 = zero & v1 = zero & all_0_2_2 = one)))
% 46.44/14.23  |
% 46.44/14.23  | Instantiating formula (11) with all_45_0_60, all_0_6_6, all_0_4_4 and discharging atoms addition(all_0_4_4, all_0_6_6) = all_45_0_60, yields:
% 46.44/14.23  | (137)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_6_6, all_0_4_4) = v0 & multiplication(all_0_4_4, all_0_6_6) = v1 & multiplication(all_0_6_6, all_0_4_4) = v2 & ( ~ (v0 = 0) | (v2 = zero & v1 = zero & all_45_0_60 = one)))
% 46.44/14.23  |
% 46.44/14.23  | Instantiating formula (11) with all_43_0_57, all_0_4_4, all_0_6_6 and discharging atoms addition(all_0_6_6, all_0_4_4) = all_43_0_57, yields:
% 46.44/14.23  | (138)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_4_4, all_0_6_6) = v0 & multiplication(all_0_4_4, all_0_6_6) = v2 & multiplication(all_0_6_6, all_0_4_4) = v1 & ( ~ (v0 = 0) | (v2 = zero & v1 = zero & all_43_0_57 = one)))
% 46.44/14.23  |
% 46.44/14.23  | Instantiating formula (11) with all_19_0_28, all_0_8_8, all_0_6_6 and discharging atoms addition(all_0_6_6, all_0_8_8) = all_19_0_28, yields:
% 46.44/14.23  | (139)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_8_8, all_0_6_6) = v0 & multiplication(all_0_6_6, all_0_8_8) = v1 & multiplication(all_0_8_8, all_0_6_6) = v2 & ( ~ (v0 = 0) | (v2 = zero & v1 = zero & all_19_0_28 = one)))
% 46.44/14.23  |
% 46.44/14.23  | Instantiating formula (11) with all_0_6_6, all_0_9_9, all_0_7_7 and discharging atoms addition(all_0_7_7, all_0_9_9) = all_0_6_6, yields:
% 46.44/14.23  | (140)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_9_9, all_0_7_7) = v0 & multiplication(all_0_7_7, all_0_9_9) = v1 & multiplication(all_0_9_9, all_0_7_7) = v2 & ( ~ (v0 = 0) | (v2 = zero & v1 = zero & all_0_6_6 = one)))
% 46.44/14.23  |
% 46.44/14.23  | Instantiating formula (31) with all_21_0_31, all_0_8_8, all_0_4_4 and discharging atoms addition(all_0_8_8, all_0_4_4) = all_21_0_31, yields:
% 46.44/14.23  | (141) addition(all_0_4_4, all_0_8_8) = all_21_0_31
% 46.44/14.23  |
% 46.44/14.23  | Instantiating formula (11) with all_21_0_31, all_0_4_4, all_0_8_8 and discharging atoms addition(all_0_8_8, all_0_4_4) = all_21_0_31, yields:
% 46.44/14.23  | (142)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_4_4, all_0_8_8) = v0 & multiplication(all_0_4_4, all_0_8_8) = v2 & multiplication(all_0_8_8, all_0_4_4) = v1 & ( ~ (v0 = 0) | (v2 = zero & v1 = zero & all_21_0_31 = one)))
% 46.44/14.23  |
% 46.44/14.23  | Instantiating formula (11) with all_41_0_54, all_0_6_6, all_0_8_8 and discharging atoms addition(all_0_8_8, all_0_6_6) = all_41_0_54, yields:
% 46.44/14.23  | (143)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_6_6, all_0_8_8) = v0 & multiplication(all_0_6_6, all_0_8_8) = v2 & multiplication(all_0_8_8, all_0_6_6) = v1 & ( ~ (v0 = 0) | (v2 = zero & v1 = zero & all_41_0_54 = one)))
% 46.44/14.23  |
% 46.44/14.23  | Instantiating (120) with all_63_0_70, all_63_1_71, all_63_2_72 yields:
% 46.44/14.23  | (144) complement(all_0_4_4, all_0_6_6) = all_63_2_72 & multiplication(all_0_6_6, all_0_4_4) = all_63_1_71 & addition(all_0_6_6, all_0_4_4) = all_63_0_70 & ( ~ (all_63_2_72 = 0) | (all_63_0_70 = one & all_63_1_71 = zero & all_43_1_58 = zero))
% 46.44/14.23  |
% 46.44/14.23  | Applying alpha-rule on (144) yields:
% 46.44/14.23  | (145) complement(all_0_4_4, all_0_6_6) = all_63_2_72
% 46.44/14.23  | (146) multiplication(all_0_6_6, all_0_4_4) = all_63_1_71
% 46.44/14.23  | (147) addition(all_0_6_6, all_0_4_4) = all_63_0_70
% 46.44/14.23  | (148)  ~ (all_63_2_72 = 0) | (all_63_0_70 = one & all_63_1_71 = zero & all_43_1_58 = zero)
% 46.44/14.23  |
% 46.44/14.23  | Instantiating (119) with all_65_0_73, all_65_1_74, all_65_2_75 yields:
% 46.44/14.23  | (149) complement(all_0_5_5, all_0_3_3) = all_65_2_75 & multiplication(all_0_5_5, all_0_3_3) = all_65_1_74 & addition(all_0_3_3, all_0_5_5) = all_65_0_73 & ( ~ (all_65_2_75 = 0) | (all_65_0_73 = one & all_65_1_74 = zero & all_17_0_25 = zero))
% 46.44/14.23  |
% 46.44/14.23  | Applying alpha-rule on (149) yields:
% 46.44/14.23  | (150) complement(all_0_5_5, all_0_3_3) = all_65_2_75
% 46.44/14.24  | (151) multiplication(all_0_5_5, all_0_3_3) = all_65_1_74
% 46.44/14.24  | (152) addition(all_0_3_3, all_0_5_5) = all_65_0_73
% 46.44/14.24  | (153)  ~ (all_65_2_75 = 0) | (all_65_0_73 = one & all_65_1_74 = zero & all_17_0_25 = zero)
% 46.44/14.24  |
% 46.44/14.24  | Instantiating (143) with all_69_0_79, all_69_1_80, all_69_2_81 yields:
% 46.44/14.24  | (154) complement(all_0_6_6, all_0_8_8) = all_69_2_81 & multiplication(all_0_6_6, all_0_8_8) = all_69_0_79 & multiplication(all_0_8_8, all_0_6_6) = all_69_1_80 & ( ~ (all_69_2_81 = 0) | (all_69_0_79 = zero & all_69_1_80 = zero & all_41_0_54 = one))
% 46.44/14.24  |
% 46.44/14.24  | Applying alpha-rule on (154) yields:
% 46.44/14.24  | (155) complement(all_0_6_6, all_0_8_8) = all_69_2_81
% 46.44/14.24  | (156) multiplication(all_0_6_6, all_0_8_8) = all_69_0_79
% 46.44/14.24  | (157) multiplication(all_0_8_8, all_0_6_6) = all_69_1_80
% 46.44/14.24  | (158)  ~ (all_69_2_81 = 0) | (all_69_0_79 = zero & all_69_1_80 = zero & all_41_0_54 = one)
% 46.44/14.24  |
% 46.44/14.24  | Instantiating (129) with all_77_0_87, all_77_1_88, all_77_2_89 yields:
% 46.44/14.24  | (159) complement(all_0_8_8, all_0_6_6) = all_77_2_89 & multiplication(all_0_6_6, all_0_8_8) = all_77_1_88 & addition(all_0_6_6, all_0_8_8) = all_77_0_87 & ( ~ (all_77_2_89 = 0) | (all_77_0_87 = one & all_77_1_88 = zero & all_19_1_29 = zero))
% 46.44/14.24  |
% 46.44/14.24  | Applying alpha-rule on (159) yields:
% 46.44/14.24  | (160) complement(all_0_8_8, all_0_6_6) = all_77_2_89
% 46.44/14.24  | (161) multiplication(all_0_6_6, all_0_8_8) = all_77_1_88
% 46.44/14.24  | (162) addition(all_0_6_6, all_0_8_8) = all_77_0_87
% 46.44/14.24  | (163)  ~ (all_77_2_89 = 0) | (all_77_0_87 = one & all_77_1_88 = zero & all_19_1_29 = zero)
% 46.44/14.24  |
% 46.44/14.24  | Instantiating (128) with all_79_0_90, all_79_1_91, all_79_2_92 yields:
% 46.44/14.24  | (164) complement(all_0_9_9, all_0_7_7) = all_79_2_92 & multiplication(all_0_9_9, all_0_7_7) = all_79_1_91 & addition(all_0_7_7, all_0_9_9) = all_79_0_90 & ( ~ (all_79_2_92 = 0) | (all_79_0_90 = one & all_79_1_91 = zero & all_29_0_41 = zero))
% 46.44/14.24  |
% 46.44/14.24  | Applying alpha-rule on (164) yields:
% 46.44/14.24  | (165) complement(all_0_9_9, all_0_7_7) = all_79_2_92
% 46.44/14.24  | (166) multiplication(all_0_9_9, all_0_7_7) = all_79_1_91
% 46.44/14.24  | (167) addition(all_0_7_7, all_0_9_9) = all_79_0_90
% 46.44/14.24  | (168)  ~ (all_79_2_92 = 0) | (all_79_0_90 = one & all_79_1_91 = zero & all_29_0_41 = zero)
% 46.44/14.24  |
% 46.44/14.24  | Instantiating (127) with all_85_0_98, all_85_1_99, all_85_2_100 yields:
% 46.44/14.24  | (169) complement(all_0_8_8, all_0_7_7) = all_85_2_100 & multiplication(all_0_8_8, all_0_7_7) = all_85_1_99 & addition(all_0_7_7, all_0_8_8) = all_85_0_98 & ( ~ (all_85_2_100 = 0) | (all_85_0_98 = one & all_85_1_99 = zero & all_49_0_66 = zero))
% 46.44/14.24  |
% 46.44/14.24  | Applying alpha-rule on (169) yields:
% 46.44/14.24  | (170) complement(all_0_8_8, all_0_7_7) = all_85_2_100
% 46.44/14.24  | (171) multiplication(all_0_8_8, all_0_7_7) = all_85_1_99
% 46.44/14.24  | (172) addition(all_0_7_7, all_0_8_8) = all_85_0_98
% 46.44/14.24  | (173)  ~ (all_85_2_100 = 0) | (all_85_0_98 = one & all_85_1_99 = zero & all_49_0_66 = zero)
% 46.44/14.24  |
% 46.44/14.24  | Instantiating (126) with all_95_0_113, all_95_1_114, all_95_2_115 yields:
% 46.44/14.24  | (174) complement(all_21_0_31, all_0_6_6) = all_95_2_115 & multiplication(all_21_0_31, all_0_6_6) = all_95_1_114 & addition(all_0_6_6, all_21_0_31) = all_95_0_113 & ( ~ (all_95_2_115 = 0) | (all_95_0_113 = one & all_95_1_114 = zero & all_0_2_2 = zero))
% 46.44/14.24  |
% 46.44/14.24  | Applying alpha-rule on (174) yields:
% 46.44/14.24  | (175) complement(all_21_0_31, all_0_6_6) = all_95_2_115
% 46.44/14.24  | (176) multiplication(all_21_0_31, all_0_6_6) = all_95_1_114
% 46.44/14.24  | (177) addition(all_0_6_6, all_21_0_31) = all_95_0_113
% 46.44/14.24  | (178)  ~ (all_95_2_115 = 0) | (all_95_0_113 = one & all_95_1_114 = zero & all_0_2_2 = zero)
% 46.44/14.24  |
% 46.44/14.24  | Instantiating (125) with all_97_0_116, all_97_1_117, all_97_2_118 yields:
% 46.44/14.24  | (179) complement(all_0_6_6, all_21_0_31) = all_97_2_118 & multiplication(all_21_0_31, all_0_6_6) = all_97_1_117 & addition(all_21_0_31, all_0_6_6) = all_97_0_116 & ( ~ (all_97_2_118 = 0) | (all_97_0_116 = one & all_97_1_117 = zero & all_0_2_2 = zero))
% 46.44/14.24  |
% 46.44/14.24  | Applying alpha-rule on (179) yields:
% 46.44/14.24  | (180) complement(all_0_6_6, all_21_0_31) = all_97_2_118
% 46.44/14.24  | (181) multiplication(all_21_0_31, all_0_6_6) = all_97_1_117
% 46.44/14.24  | (182) addition(all_21_0_31, all_0_6_6) = all_97_0_116
% 46.44/14.24  | (183)  ~ (all_97_2_118 = 0) | (all_97_0_116 = one & all_97_1_117 = zero & all_0_2_2 = zero)
% 46.44/14.24  |
% 46.44/14.24  | Instantiating (140) with all_99_0_119, all_99_1_120, all_99_2_121 yields:
% 46.44/14.24  | (184) complement(all_0_9_9, all_0_7_7) = all_99_2_121 & multiplication(all_0_7_7, all_0_9_9) = all_99_1_120 & multiplication(all_0_9_9, all_0_7_7) = all_99_0_119 & ( ~ (all_99_2_121 = 0) | (all_99_0_119 = zero & all_99_1_120 = zero & all_0_6_6 = one))
% 46.44/14.25  |
% 46.44/14.25  | Applying alpha-rule on (184) yields:
% 46.44/14.25  | (185) complement(all_0_9_9, all_0_7_7) = all_99_2_121
% 46.44/14.25  | (186) multiplication(all_0_7_7, all_0_9_9) = all_99_1_120
% 46.44/14.25  | (187) multiplication(all_0_9_9, all_0_7_7) = all_99_0_119
% 46.44/14.25  | (188)  ~ (all_99_2_121 = 0) | (all_99_0_119 = zero & all_99_1_120 = zero & all_0_6_6 = one)
% 46.44/14.25  |
% 46.44/14.25  | Instantiating (116) with all_103_0_125, all_103_1_126 yields:
% 46.44/14.25  | (189) c(all_0_8_8) = all_103_0_125 & test(all_0_8_8) = all_103_1_126 & ( ~ (all_103_1_126 = 0) | (( ~ (all_103_0_125 = all_0_6_6) | all_19_2_30 = 0) & ( ~ (all_19_2_30 = 0) | all_103_0_125 = all_0_6_6)))
% 46.44/14.25  |
% 46.44/14.25  | Applying alpha-rule on (189) yields:
% 46.44/14.25  | (190) c(all_0_8_8) = all_103_0_125
% 46.44/14.25  | (191) test(all_0_8_8) = all_103_1_126
% 46.44/14.25  | (192)  ~ (all_103_1_126 = 0) | (( ~ (all_103_0_125 = all_0_6_6) | all_19_2_30 = 0) & ( ~ (all_19_2_30 = 0) | all_103_0_125 = all_0_6_6))
% 46.44/14.25  |
% 46.44/14.25  | Instantiating (124) with all_109_0_132, all_109_1_133, all_109_2_134 yields:
% 46.44/14.25  | (193) complement(all_0_5_5, all_0_3_3) = all_109_2_134 & multiplication(all_0_3_3, all_0_5_5) = all_109_1_133 & addition(all_0_3_3, all_0_5_5) = all_109_0_132 & ( ~ (all_109_2_134 = 0) | (all_109_0_132 = one & all_109_1_133 = zero & all_17_1_26 = zero))
% 46.44/14.25  |
% 46.44/14.25  | Applying alpha-rule on (193) yields:
% 46.44/14.25  | (194) complement(all_0_5_5, all_0_3_3) = all_109_2_134
% 46.44/14.25  | (195) multiplication(all_0_3_3, all_0_5_5) = all_109_1_133
% 46.44/14.25  | (196) addition(all_0_3_3, all_0_5_5) = all_109_0_132
% 46.44/14.25  | (197)  ~ (all_109_2_134 = 0) | (all_109_0_132 = one & all_109_1_133 = zero & all_17_1_26 = zero)
% 46.44/14.25  |
% 46.44/14.25  | Instantiating (122) with all_111_0_135 yields:
% 46.44/14.25  | (198) multiplication(all_111_0_135, all_0_4_4) = all_17_1_26 & multiplication(all_0_5_5, all_0_6_6) = all_111_0_135
% 46.44/14.25  |
% 46.44/14.25  | Applying alpha-rule on (198) yields:
% 46.44/14.25  | (199) multiplication(all_111_0_135, all_0_4_4) = all_17_1_26
% 46.44/14.25  | (200) multiplication(all_0_5_5, all_0_6_6) = all_111_0_135
% 46.44/14.25  |
% 46.44/14.25  | Instantiating (121) with all_113_0_136, all_113_1_137, all_113_2_138 yields:
% 46.44/14.25  | (201) complement(all_0_6_6, all_0_4_4) = all_113_2_138 & multiplication(all_0_6_6, all_0_4_4) = all_113_1_137 & addition(all_0_4_4, all_0_6_6) = all_113_0_136 & ( ~ (all_113_2_138 = 0) | (all_113_0_136 = one & all_113_1_137 = zero & all_43_1_58 = zero))
% 46.44/14.25  |
% 46.44/14.25  | Applying alpha-rule on (201) yields:
% 46.44/14.25  | (202) complement(all_0_6_6, all_0_4_4) = all_113_2_138
% 46.44/14.25  | (203) multiplication(all_0_6_6, all_0_4_4) = all_113_1_137
% 46.44/14.25  | (204) addition(all_0_4_4, all_0_6_6) = all_113_0_136
% 46.44/14.25  | (205)  ~ (all_113_2_138 = 0) | (all_113_0_136 = one & all_113_1_137 = zero & all_43_1_58 = zero)
% 46.44/14.25  |
% 46.44/14.25  | Instantiating (118) with all_119_0_143 yields:
% 46.44/14.25  | (206) multiplication(all_119_0_143, all_0_8_8) = all_17_0_25 & multiplication(all_0_3_3, all_0_6_6) = all_119_0_143
% 46.44/14.25  |
% 46.44/14.25  | Applying alpha-rule on (206) yields:
% 46.44/14.25  | (207) multiplication(all_119_0_143, all_0_8_8) = all_17_0_25
% 46.44/14.25  | (208) multiplication(all_0_3_3, all_0_6_6) = all_119_0_143
% 46.44/14.25  |
% 46.44/14.25  | Instantiating (117) with all_121_0_144 yields:
% 46.44/14.25  | (209) multiplication(all_0_4_4, all_0_5_5) = all_121_0_144 & multiplication(all_0_6_6, all_121_0_144) = all_17_0_25
% 46.44/14.25  |
% 46.44/14.25  | Applying alpha-rule on (209) yields:
% 46.44/14.25  | (210) multiplication(all_0_4_4, all_0_5_5) = all_121_0_144
% 46.44/14.25  | (211) multiplication(all_0_6_6, all_121_0_144) = all_17_0_25
% 46.44/14.25  |
% 46.44/14.25  | Instantiating (139) with all_131_0_150, all_131_1_151, all_131_2_152 yields:
% 46.44/14.25  | (212) complement(all_0_8_8, all_0_6_6) = all_131_2_152 & multiplication(all_0_6_6, all_0_8_8) = all_131_1_151 & multiplication(all_0_8_8, all_0_6_6) = all_131_0_150 & ( ~ (all_131_2_152 = 0) | (all_131_0_150 = zero & all_131_1_151 = zero & all_19_0_28 = one))
% 46.44/14.26  |
% 46.44/14.26  | Applying alpha-rule on (212) yields:
% 46.44/14.26  | (213) complement(all_0_8_8, all_0_6_6) = all_131_2_152
% 46.44/14.26  | (214) multiplication(all_0_6_6, all_0_8_8) = all_131_1_151
% 46.44/14.26  | (215) multiplication(all_0_8_8, all_0_6_6) = all_131_0_150
% 46.44/14.26  | (216)  ~ (all_131_2_152 = 0) | (all_131_0_150 = zero & all_131_1_151 = zero & all_19_0_28 = one)
% 46.44/14.26  |
% 46.44/14.26  | Instantiating (135) with all_149_0_168 yields:
% 46.44/14.26  | (217) multiplication(all_0_6_6, all_149_0_168) = all_0_2_2 & addition(all_0_4_4, all_0_8_8) = all_149_0_168
% 46.44/14.26  |
% 46.44/14.26  | Applying alpha-rule on (217) yields:
% 46.44/14.26  | (218) multiplication(all_0_6_6, all_149_0_168) = all_0_2_2
% 46.44/14.26  | (219) addition(all_0_4_4, all_0_8_8) = all_149_0_168
% 46.44/14.26  |
% 46.44/14.26  | Instantiating (134) with all_157_0_175, all_157_1_176, all_157_2_177 yields:
% 46.44/14.26  | (220) complement(all_0_8_8, all_0_9_9) = all_157_2_177 & multiplication(all_0_8_8, all_0_9_9) = all_157_1_176 & addition(all_0_9_9, all_0_8_8) = all_157_0_175 & ( ~ (all_157_2_177 = 0) | (all_157_0_175 = one & all_157_1_176 = zero & all_49_1_67 = zero))
% 46.44/14.26  |
% 46.44/14.26  | Applying alpha-rule on (220) yields:
% 46.44/14.26  | (221) complement(all_0_8_8, all_0_9_9) = all_157_2_177
% 46.44/14.26  | (222) multiplication(all_0_8_8, all_0_9_9) = all_157_1_176
% 46.44/14.26  | (223) addition(all_0_9_9, all_0_8_8) = all_157_0_175
% 46.44/14.26  | (224)  ~ (all_157_2_177 = 0) | (all_157_0_175 = one & all_157_1_176 = zero & all_49_1_67 = zero)
% 46.44/14.26  |
% 46.44/14.26  | Instantiating (132) with all_159_0_178, all_159_1_179, all_159_2_180 yields:
% 46.44/14.26  | (225) complement(all_0_9_9, all_0_7_7) = all_159_2_180 & multiplication(all_0_7_7, all_0_9_9) = all_159_1_179 & addition(all_0_7_7, all_0_9_9) = all_159_0_178 & ( ~ (all_159_2_180 = 0) | (all_159_0_178 = one & all_159_1_179 = zero & all_29_1_42 = zero))
% 46.44/14.26  |
% 46.44/14.26  | Applying alpha-rule on (225) yields:
% 46.44/14.26  | (226) complement(all_0_9_9, all_0_7_7) = all_159_2_180
% 46.44/14.26  | (227) multiplication(all_0_7_7, all_0_9_9) = all_159_1_179
% 46.44/14.26  | (228) addition(all_0_7_7, all_0_9_9) = all_159_0_178
% 46.44/14.26  | (229)  ~ (all_159_2_180 = 0) | (all_159_0_178 = one & all_159_1_179 = zero & all_29_1_42 = zero)
% 46.44/14.26  |
% 46.44/14.26  | Instantiating (133) with all_163_0_184, all_163_1_185, all_163_2_186 yields:
% 46.44/14.26  | (230) complement(all_0_9_9, all_0_8_8) = all_163_2_186 & multiplication(all_0_8_8, all_0_9_9) = all_163_1_185 & addition(all_0_8_8, all_0_9_9) = all_163_0_184 & ( ~ (all_163_2_186 = 0) | (all_163_0_184 = one & all_163_1_185 = zero & all_49_1_67 = zero))
% 46.44/14.26  |
% 46.44/14.26  | Applying alpha-rule on (230) yields:
% 46.44/14.26  | (231) complement(all_0_9_9, all_0_8_8) = all_163_2_186
% 46.44/14.26  | (232) multiplication(all_0_8_8, all_0_9_9) = all_163_1_185
% 46.44/14.26  | (233) addition(all_0_8_8, all_0_9_9) = all_163_0_184
% 46.44/14.26  | (234)  ~ (all_163_2_186 = 0) | (all_163_0_184 = one & all_163_1_185 = zero & all_49_1_67 = zero)
% 46.44/14.26  |
% 46.44/14.26  | Instantiating (138) with all_165_0_187, all_165_1_188, all_165_2_189 yields:
% 46.44/14.26  | (235) complement(all_0_4_4, all_0_6_6) = all_165_2_189 & multiplication(all_0_4_4, all_0_6_6) = all_165_0_187 & multiplication(all_0_6_6, all_0_4_4) = all_165_1_188 & ( ~ (all_165_2_189 = 0) | (all_165_0_187 = zero & all_165_1_188 = zero & all_43_0_57 = one))
% 46.44/14.26  |
% 46.44/14.26  | Applying alpha-rule on (235) yields:
% 46.44/14.26  | (236) complement(all_0_4_4, all_0_6_6) = all_165_2_189
% 46.44/14.26  | (237) multiplication(all_0_4_4, all_0_6_6) = all_165_0_187
% 46.44/14.26  | (238) multiplication(all_0_6_6, all_0_4_4) = all_165_1_188
% 46.44/14.26  | (239)  ~ (all_165_2_189 = 0) | (all_165_0_187 = zero & all_165_1_188 = zero & all_43_0_57 = one)
% 46.44/14.26  |
% 46.44/14.26  | Instantiating (142) with all_177_0_198, all_177_1_199, all_177_2_200 yields:
% 46.44/14.26  | (240) complement(all_0_4_4, all_0_8_8) = all_177_2_200 & multiplication(all_0_4_4, all_0_8_8) = all_177_0_198 & multiplication(all_0_8_8, all_0_4_4) = all_177_1_199 & ( ~ (all_177_2_200 = 0) | (all_177_0_198 = zero & all_177_1_199 = zero & all_21_0_31 = one))
% 46.44/14.26  |
% 46.44/14.26  | Applying alpha-rule on (240) yields:
% 46.44/14.26  | (241) complement(all_0_4_4, all_0_8_8) = all_177_2_200
% 46.44/14.26  | (242) multiplication(all_0_4_4, all_0_8_8) = all_177_0_198
% 46.44/14.26  | (243) multiplication(all_0_8_8, all_0_4_4) = all_177_1_199
% 46.44/14.26  | (244)  ~ (all_177_2_200 = 0) | (all_177_0_198 = zero & all_177_1_199 = zero & all_21_0_31 = one)
% 46.44/14.26  |
% 46.44/14.26  | Instantiating (123) with all_179_0_201 yields:
% 46.44/14.26  | (245) multiplication(all_0_6_6, all_179_0_201) = all_17_1_26 & multiplication(all_0_8_8, all_0_3_3) = all_179_0_201
% 46.44/14.26  |
% 46.44/14.26  | Applying alpha-rule on (245) yields:
% 46.44/14.26  | (246) multiplication(all_0_6_6, all_179_0_201) = all_17_1_26
% 46.44/14.26  | (247) multiplication(all_0_8_8, all_0_3_3) = all_179_0_201
% 46.44/14.26  |
% 46.44/14.26  | Instantiating (137) with all_189_0_211, all_189_1_212, all_189_2_213 yields:
% 46.44/14.26  | (248) complement(all_0_6_6, all_0_4_4) = all_189_2_213 & multiplication(all_0_4_4, all_0_6_6) = all_189_1_212 & multiplication(all_0_6_6, all_0_4_4) = all_189_0_211 & ( ~ (all_189_2_213 = 0) | (all_189_0_211 = zero & all_189_1_212 = zero & all_45_0_60 = one))
% 46.44/14.26  |
% 46.44/14.26  | Applying alpha-rule on (248) yields:
% 46.44/14.26  | (249) complement(all_0_6_6, all_0_4_4) = all_189_2_213
% 46.44/14.26  | (250) multiplication(all_0_4_4, all_0_6_6) = all_189_1_212
% 46.44/14.26  | (251) multiplication(all_0_6_6, all_0_4_4) = all_189_0_211
% 46.44/14.26  | (252)  ~ (all_189_2_213 = 0) | (all_189_0_211 = zero & all_189_1_212 = zero & all_45_0_60 = one)
% 46.44/14.26  |
% 46.44/14.26  | Instantiating (136) with all_191_0_214, all_191_1_215, all_191_2_216 yields:
% 46.44/14.26  | (253) complement(all_0_5_5, all_0_3_3) = all_191_2_216 & multiplication(all_0_3_3, all_0_5_5) = all_191_1_215 & multiplication(all_0_5_5, all_0_3_3) = all_191_0_214 & ( ~ (all_191_2_216 = 0) | (all_191_0_214 = zero & all_191_1_215 = zero & all_0_2_2 = one))
% 46.44/14.26  |
% 46.44/14.26  | Applying alpha-rule on (253) yields:
% 46.44/14.26  | (254) complement(all_0_5_5, all_0_3_3) = all_191_2_216
% 46.44/14.26  | (255) multiplication(all_0_3_3, all_0_5_5) = all_191_1_215
% 46.44/14.26  | (256) multiplication(all_0_5_5, all_0_3_3) = all_191_0_214
% 46.44/14.26  | (257)  ~ (all_191_2_216 = 0) | (all_191_0_214 = zero & all_191_1_215 = zero & all_0_2_2 = one)
% 46.44/14.26  |
% 46.44/14.26  | Instantiating (131) with all_193_0_217, all_193_1_218, all_193_2_219 yields:
% 46.44/14.26  | (258) complement(all_0_9_9, all_0_4_4) = all_193_2_219 & multiplication(all_0_4_4, all_0_9_9) = all_193_1_218 & addition(all_0_4_4, all_0_9_9) = all_193_0_217 & ( ~ (all_193_2_219 = 0) | (all_193_0_217 = one & all_193_1_218 = zero & all_15_1_24 = zero))
% 46.44/14.26  |
% 46.44/14.26  | Applying alpha-rule on (258) yields:
% 46.44/14.26  | (259) complement(all_0_9_9, all_0_4_4) = all_193_2_219
% 46.44/14.26  | (260) multiplication(all_0_4_4, all_0_9_9) = all_193_1_218
% 46.44/14.26  | (261) addition(all_0_4_4, all_0_9_9) = all_193_0_217
% 46.44/14.26  | (262)  ~ (all_193_2_219 = 0) | (all_193_0_217 = one & all_193_1_218 = zero & all_15_1_24 = zero)
% 46.44/14.26  |
% 46.44/14.26  | Instantiating (130) with all_195_0_220, all_195_1_221, all_195_2_222 yields:
% 46.44/14.26  | (263) complement(all_0_6_6, all_0_8_8) = all_195_2_222 & multiplication(all_0_6_6, all_0_8_8) = all_195_1_221 & addition(all_0_8_8, all_0_6_6) = all_195_0_220 & ( ~ (all_195_2_222 = 0) | (all_195_0_220 = one & all_195_1_221 = zero & all_19_1_29 = zero))
% 46.44/14.26  |
% 46.44/14.26  | Applying alpha-rule on (263) yields:
% 46.44/14.26  | (264) complement(all_0_6_6, all_0_8_8) = all_195_2_222
% 46.44/14.26  | (265) multiplication(all_0_6_6, all_0_8_8) = all_195_1_221
% 46.44/14.26  | (266) addition(all_0_8_8, all_0_6_6) = all_195_0_220
% 46.44/14.27  | (267)  ~ (all_195_2_222 = 0) | (all_195_0_220 = one & all_195_1_221 = zero & all_19_1_29 = zero)
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (3) with all_0_8_8, all_103_0_125, all_0_4_4 and discharging atoms c(all_0_8_8) = all_103_0_125, c(all_0_8_8) = all_0_4_4, yields:
% 46.44/14.27  | (268) all_103_0_125 = all_0_4_4
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (13) with all_0_5_5, all_0_3_3, all_109_2_134, all_191_2_216 and discharging atoms complement(all_0_5_5, all_0_3_3) = all_191_2_216, complement(all_0_5_5, all_0_3_3) = all_109_2_134, yields:
% 46.44/14.27  | (269) all_191_2_216 = all_109_2_134
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (13) with all_0_5_5, all_0_3_3, all_65_2_75, all_191_2_216 and discharging atoms complement(all_0_5_5, all_0_3_3) = all_191_2_216, complement(all_0_5_5, all_0_3_3) = all_65_2_75, yields:
% 46.44/14.27  | (270) all_191_2_216 = all_65_2_75
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (13) with all_0_9_9, all_0_7_7, all_99_2_121, all_159_2_180 and discharging atoms complement(all_0_9_9, all_0_7_7) = all_159_2_180, complement(all_0_9_9, all_0_7_7) = all_99_2_121, yields:
% 46.44/14.27  | (271) all_159_2_180 = all_99_2_121
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (13) with all_0_9_9, all_0_7_7, all_79_2_92, all_159_2_180 and discharging atoms complement(all_0_9_9, all_0_7_7) = all_159_2_180, complement(all_0_9_9, all_0_7_7) = all_79_2_92, yields:
% 46.44/14.27  | (272) all_159_2_180 = all_79_2_92
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (42) with all_21_0_31, all_0_6_6, all_95_1_114, all_97_1_117 and discharging atoms multiplication(all_21_0_31, all_0_6_6) = all_97_1_117, multiplication(all_21_0_31, all_0_6_6) = all_95_1_114, yields:
% 46.44/14.27  | (273) all_97_1_117 = all_95_1_114
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (42) with all_0_4_4, all_0_6_6, all_189_1_212, all_43_1_58 and discharging atoms multiplication(all_0_4_4, all_0_6_6) = all_189_1_212, multiplication(all_0_4_4, all_0_6_6) = all_43_1_58, yields:
% 46.44/14.27  | (274) all_189_1_212 = all_43_1_58
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (42) with all_0_4_4, all_0_6_6, all_165_0_187, all_189_1_212 and discharging atoms multiplication(all_0_4_4, all_0_6_6) = all_189_1_212, multiplication(all_0_4_4, all_0_6_6) = all_165_0_187, yields:
% 46.44/14.27  | (275) all_189_1_212 = all_165_0_187
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (42) with all_0_6_6, all_0_4_4, all_189_0_211, all_0_3_3 and discharging atoms multiplication(all_0_6_6, all_0_4_4) = all_189_0_211, multiplication(all_0_6_6, all_0_4_4) = all_0_3_3, yields:
% 46.44/14.27  | (276) all_189_0_211 = all_0_3_3
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (42) with all_0_6_6, all_0_4_4, all_165_1_188, all_189_0_211 and discharging atoms multiplication(all_0_6_6, all_0_4_4) = all_189_0_211, multiplication(all_0_6_6, all_0_4_4) = all_165_1_188, yields:
% 46.44/14.27  | (277) all_189_0_211 = all_165_1_188
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (42) with all_0_6_6, all_0_4_4, all_113_1_137, all_189_0_211 and discharging atoms multiplication(all_0_6_6, all_0_4_4) = all_189_0_211, multiplication(all_0_6_6, all_0_4_4) = all_113_1_137, yields:
% 46.44/14.27  | (278) all_189_0_211 = all_113_1_137
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (42) with all_0_6_6, all_0_4_4, all_63_1_71, all_165_1_188 and discharging atoms multiplication(all_0_6_6, all_0_4_4) = all_165_1_188, multiplication(all_0_6_6, all_0_4_4) = all_63_1_71, yields:
% 46.44/14.27  | (279) all_165_1_188 = all_63_1_71
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (42) with all_0_6_6, all_0_8_8, all_195_1_221, all_0_5_5 and discharging atoms multiplication(all_0_6_6, all_0_8_8) = all_195_1_221, multiplication(all_0_6_6, all_0_8_8) = all_0_5_5, yields:
% 46.44/14.27  | (280) all_195_1_221 = all_0_5_5
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (42) with all_0_6_6, all_0_8_8, all_77_1_88, all_195_1_221 and discharging atoms multiplication(all_0_6_6, all_0_8_8) = all_195_1_221, multiplication(all_0_6_6, all_0_8_8) = all_77_1_88, yields:
% 46.44/14.27  | (281) all_195_1_221 = all_77_1_88
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (42) with all_0_6_6, all_0_8_8, all_77_1_88, all_131_1_151 and discharging atoms multiplication(all_0_6_6, all_0_8_8) = all_131_1_151, multiplication(all_0_6_6, all_0_8_8) = all_77_1_88, yields:
% 46.44/14.27  | (282) all_131_1_151 = all_77_1_88
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (42) with all_0_6_6, all_0_8_8, all_69_0_79, all_131_1_151 and discharging atoms multiplication(all_0_6_6, all_0_8_8) = all_131_1_151, multiplication(all_0_6_6, all_0_8_8) = all_69_0_79, yields:
% 46.44/14.27  | (283) all_131_1_151 = all_69_0_79
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (42) with all_0_8_8, all_0_6_6, all_131_0_150, all_19_1_29 and discharging atoms multiplication(all_0_8_8, all_0_6_6) = all_131_0_150, multiplication(all_0_8_8, all_0_6_6) = all_19_1_29, yields:
% 46.44/14.27  | (284) all_131_0_150 = all_19_1_29
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (42) with all_0_8_8, all_0_6_6, all_69_1_80, all_131_0_150 and discharging atoms multiplication(all_0_8_8, all_0_6_6) = all_131_0_150, multiplication(all_0_8_8, all_0_6_6) = all_69_1_80, yields:
% 46.44/14.27  | (285) all_131_0_150 = all_69_1_80
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (43) with all_0_4_4, all_0_8_8, all_21_0_31, all_149_0_168 and discharging atoms addition(all_0_4_4, all_0_8_8) = all_149_0_168, addition(all_0_4_4, all_0_8_8) = all_21_0_31, yields:
% 46.44/14.27  | (286) all_149_0_168 = all_21_0_31
% 46.44/14.27  |
% 46.44/14.27  | Combining equations (281,280) yields a new equation:
% 46.44/14.27  | (287) all_77_1_88 = all_0_5_5
% 46.44/14.27  |
% 46.44/14.27  | Simplifying 287 yields:
% 46.44/14.27  | (288) all_77_1_88 = all_0_5_5
% 46.44/14.27  |
% 46.44/14.27  | Combining equations (269,270) yields a new equation:
% 46.44/14.27  | (289) all_109_2_134 = all_65_2_75
% 46.44/14.27  |
% 46.44/14.27  | Simplifying 289 yields:
% 46.44/14.27  | (290) all_109_2_134 = all_65_2_75
% 46.44/14.27  |
% 46.44/14.27  | Combining equations (277,278) yields a new equation:
% 46.44/14.27  | (291) all_165_1_188 = all_113_1_137
% 46.44/14.27  |
% 46.44/14.27  | Simplifying 291 yields:
% 46.44/14.27  | (292) all_165_1_188 = all_113_1_137
% 46.44/14.27  |
% 46.44/14.27  | Combining equations (276,278) yields a new equation:
% 46.44/14.27  | (293) all_113_1_137 = all_0_3_3
% 46.44/14.27  |
% 46.44/14.27  | Combining equations (274,275) yields a new equation:
% 46.44/14.27  | (294) all_165_0_187 = all_43_1_58
% 46.44/14.27  |
% 46.44/14.27  | Combining equations (292,279) yields a new equation:
% 46.44/14.27  | (295) all_113_1_137 = all_63_1_71
% 46.44/14.27  |
% 46.44/14.27  | Simplifying 295 yields:
% 46.44/14.27  | (296) all_113_1_137 = all_63_1_71
% 46.44/14.27  |
% 46.44/14.27  | Combining equations (271,272) yields a new equation:
% 46.44/14.27  | (297) all_99_2_121 = all_79_2_92
% 46.44/14.27  |
% 46.44/14.27  | Simplifying 297 yields:
% 46.44/14.27  | (298) all_99_2_121 = all_79_2_92
% 46.44/14.27  |
% 46.44/14.27  | Combining equations (285,284) yields a new equation:
% 46.44/14.27  | (299) all_69_1_80 = all_19_1_29
% 46.44/14.27  |
% 46.44/14.27  | Simplifying 299 yields:
% 46.44/14.27  | (300) all_69_1_80 = all_19_1_29
% 46.44/14.27  |
% 46.44/14.27  | Combining equations (282,283) yields a new equation:
% 46.44/14.27  | (301) all_77_1_88 = all_69_0_79
% 46.44/14.27  |
% 46.44/14.27  | Simplifying 301 yields:
% 46.44/14.27  | (302) all_77_1_88 = all_69_0_79
% 46.44/14.27  |
% 46.44/14.27  | Combining equations (293,296) yields a new equation:
% 46.44/14.27  | (303) all_63_1_71 = all_0_3_3
% 46.44/14.27  |
% 46.44/14.27  | Combining equations (302,288) yields a new equation:
% 46.44/14.27  | (304) all_69_0_79 = all_0_5_5
% 46.44/14.27  |
% 46.44/14.27  | Simplifying 304 yields:
% 46.44/14.27  | (305) all_69_0_79 = all_0_5_5
% 46.44/14.27  |
% 46.44/14.27  | From (268) and (190) follows:
% 46.44/14.27  | (23) c(all_0_8_8) = all_0_4_4
% 46.44/14.27  |
% 46.44/14.27  | From (290) and (194) follows:
% 46.44/14.27  | (150) complement(all_0_5_5, all_0_3_3) = all_65_2_75
% 46.44/14.27  |
% 46.44/14.27  | From (298) and (185) follows:
% 46.44/14.27  | (165) complement(all_0_9_9, all_0_7_7) = all_79_2_92
% 46.44/14.27  |
% 46.44/14.27  | From (273) and (181) follows:
% 46.44/14.27  | (176) multiplication(all_21_0_31, all_0_6_6) = all_95_1_114
% 46.44/14.27  |
% 46.44/14.27  | From (294) and (237) follows:
% 46.44/14.27  | (100) multiplication(all_0_4_4, all_0_6_6) = all_43_1_58
% 46.44/14.27  |
% 46.44/14.27  | From (286) and (218) follows:
% 46.44/14.27  | (84) multiplication(all_0_6_6, all_21_0_31) = all_0_2_2
% 46.44/14.27  |
% 46.44/14.27  | From (303) and (146) follows:
% 46.44/14.27  | (28) multiplication(all_0_6_6, all_0_4_4) = all_0_3_3
% 46.44/14.27  |
% 46.44/14.27  | From (305) and (156) follows:
% 46.44/14.27  | (19) multiplication(all_0_6_6, all_0_8_8) = all_0_5_5
% 46.44/14.27  |
% 46.44/14.27  | From (300) and (157) follows:
% 46.44/14.27  | (80) multiplication(all_0_8_8, all_0_6_6) = all_19_1_29
% 46.44/14.27  |
% 46.44/14.27  | From (286) and (219) follows:
% 46.44/14.27  | (141) addition(all_0_4_4, all_0_8_8) = all_21_0_31
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (27) with all_65_2_75, all_0_3_3, all_0_5_5 and discharging atoms complement(all_0_5_5, all_0_3_3) = all_65_2_75, yields:
% 46.44/14.27  | (316)  ? [v0] :  ? [v1] : (c(all_0_5_5) = v1 & test(all_0_5_5) = v0 & ( ~ (v0 = 0) | (( ~ (v1 = all_0_3_3) | all_65_2_75 = 0) & ( ~ (all_65_2_75 = 0) | v1 = all_0_3_3))))
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (27) with all_85_2_100, all_0_7_7, all_0_8_8 and discharging atoms complement(all_0_8_8, all_0_7_7) = all_85_2_100, yields:
% 46.44/14.27  | (317)  ? [v0] :  ? [v1] : (c(all_0_8_8) = v1 & test(all_0_8_8) = v0 & ( ~ (v0 = 0) | (( ~ (v1 = all_0_7_7) | all_85_2_100 = 0) & ( ~ (all_85_2_100 = 0) | v1 = all_0_7_7))))
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (27) with all_157_2_177, all_0_9_9, all_0_8_8 and discharging atoms complement(all_0_8_8, all_0_9_9) = all_157_2_177, yields:
% 46.44/14.27  | (318)  ? [v0] :  ? [v1] : (c(all_0_8_8) = v1 & test(all_0_8_8) = v0 & ( ~ (v0 = 0) | (( ~ (v1 = all_0_9_9) | all_157_2_177 = 0) & ( ~ (all_157_2_177 = 0) | v1 = all_0_9_9))))
% 46.44/14.27  |
% 46.44/14.27  | Instantiating formula (27) with all_193_2_219, all_0_4_4, all_0_9_9 and discharging atoms complement(all_0_9_9, all_0_4_4) = all_193_2_219, yields:
% 46.44/14.27  | (319)  ? [v0] :  ? [v1] : (c(all_0_9_9) = v1 & test(all_0_9_9) = v0 & ( ~ (v0 = 0) | (( ~ (v1 = all_0_4_4) | all_193_2_219 = 0) & ( ~ (all_193_2_219 = 0) | v1 = all_0_4_4))))
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (27) with all_79_2_92, all_0_7_7, all_0_9_9 and discharging atoms complement(all_0_9_9, all_0_7_7) = all_79_2_92, yields:
% 46.44/14.28  | (320)  ? [v0] :  ? [v1] : (c(all_0_9_9) = v1 & test(all_0_9_9) = v0 & ( ~ (v0 = 0) | (( ~ (v1 = all_0_7_7) | all_79_2_92 = 0) & ( ~ (all_79_2_92 = 0) | v1 = all_0_7_7))))
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (27) with all_163_2_186, all_0_8_8, all_0_9_9 and discharging atoms complement(all_0_9_9, all_0_8_8) = all_163_2_186, yields:
% 46.44/14.28  | (321)  ? [v0] :  ? [v1] : (c(all_0_9_9) = v1 & test(all_0_9_9) = v0 & ( ~ (v0 = 0) | (( ~ (v1 = all_0_8_8) | all_163_2_186 = 0) & ( ~ (all_163_2_186 = 0) | v1 = all_0_8_8))))
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (32) with all_17_0_25, all_0_8_8, all_119_0_143 and discharging atoms multiplication(all_119_0_143, all_0_8_8) = all_17_0_25, yields:
% 46.44/14.28  | (322)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_8_8, all_119_0_143) = v0 & multiplication(all_0_8_8, all_119_0_143) = v1 & addition(all_119_0_143, all_0_8_8) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_17_0_25 = zero)))
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (22) with all_17_1_26, all_111_0_135, all_0_4_4 and discharging atoms multiplication(all_111_0_135, all_0_4_4) = all_17_1_26, yields:
% 46.44/14.28  | (323)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_111_0_135, all_0_4_4) = v0 & multiplication(all_0_4_4, all_111_0_135) = v1 & addition(all_0_4_4, all_111_0_135) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_17_1_26 = zero)))
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (49) with all_95_1_114, all_21_0_31, all_0_6_6, all_0_4_4, all_0_8_8 and discharging atoms multiplication(all_21_0_31, all_0_6_6) = all_95_1_114, addition(all_0_8_8, all_0_4_4) = all_21_0_31, yields:
% 46.44/14.28  | (324)  ? [v0] :  ? [v1] : (multiplication(all_0_4_4, all_0_6_6) = v1 & multiplication(all_0_8_8, all_0_6_6) = v0 & addition(v0, v1) = all_95_1_114)
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (22) with all_95_1_114, all_21_0_31, all_0_6_6 and discharging atoms multiplication(all_21_0_31, all_0_6_6) = all_95_1_114, yields:
% 46.44/14.28  | (325)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_21_0_31, all_0_6_6) = v0 & multiplication(all_0_6_6, all_21_0_31) = v1 & addition(all_0_6_6, all_21_0_31) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_95_1_114 = zero)))
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (32) with all_95_1_114, all_0_6_6, all_21_0_31 and discharging atoms multiplication(all_21_0_31, all_0_6_6) = all_95_1_114, yields:
% 46.44/14.28  | (326)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_6_6, all_21_0_31) = v0 & multiplication(all_0_6_6, all_21_0_31) = v1 & addition(all_21_0_31, all_0_6_6) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_95_1_114 = zero)))
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (35) with all_119_0_143, all_0_3_3, all_0_6_6, all_0_4_4, all_0_6_6 and discharging atoms multiplication(all_0_3_3, all_0_6_6) = all_119_0_143, multiplication(all_0_6_6, all_0_4_4) = all_0_3_3, yields:
% 46.44/14.28  | (327)  ? [v0] : (multiplication(all_0_4_4, all_0_6_6) = v0 & multiplication(all_0_6_6, v0) = all_119_0_143)
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (36) with all_121_0_144, all_0_5_5, all_0_8_8, all_0_6_6, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_5_5) = all_121_0_144, multiplication(all_0_6_6, all_0_8_8) = all_0_5_5, yields:
% 46.44/14.28  | (328)  ? [v0] : (multiplication(v0, all_0_8_8) = all_121_0_144 & multiplication(all_0_4_4, all_0_6_6) = v0)
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (32) with all_121_0_144, all_0_5_5, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_5_5) = all_121_0_144, yields:
% 46.44/14.28  | (329)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_5_5, all_0_4_4) = v0 & multiplication(all_0_5_5, all_0_4_4) = v1 & addition(all_0_4_4, all_0_5_5) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_121_0_144 = zero)))
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (32) with all_177_0_198, all_0_8_8, all_0_4_4 and discharging atoms multiplication(all_0_4_4, all_0_8_8) = all_177_0_198, yields:
% 46.44/14.28  | (330)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_8_8, all_0_4_4) = v0 & multiplication(all_0_8_8, all_0_4_4) = v1 & addition(all_0_4_4, all_0_8_8) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_177_0_198 = zero)))
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (35) with all_111_0_135, all_0_5_5, all_0_6_6, all_0_8_8, all_0_6_6 and discharging atoms multiplication(all_0_5_5, all_0_6_6) = all_111_0_135, multiplication(all_0_6_6, all_0_8_8) = all_0_5_5, yields:
% 46.44/14.28  | (331)  ? [v0] : (multiplication(all_0_6_6, v0) = all_111_0_135 & multiplication(all_0_8_8, all_0_6_6) = v0)
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (36) with all_179_0_201, all_0_3_3, all_0_4_4, all_0_6_6, all_0_8_8 and discharging atoms multiplication(all_0_6_6, all_0_4_4) = all_0_3_3, multiplication(all_0_8_8, all_0_3_3) = all_179_0_201, yields:
% 46.44/14.28  | (332)  ? [v0] : (multiplication(v0, all_0_4_4) = all_179_0_201 & multiplication(all_0_8_8, all_0_6_6) = v0)
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (22) with all_179_0_201, all_0_8_8, all_0_3_3 and discharging atoms multiplication(all_0_8_8, all_0_3_3) = all_179_0_201, yields:
% 46.44/14.28  | (333)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_8_8, all_0_3_3) = v0 & multiplication(all_0_3_3, all_0_8_8) = v1 & addition(all_0_3_3, all_0_8_8) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_179_0_201 = zero)))
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (22) with all_177_1_199, all_0_8_8, all_0_4_4 and discharging atoms multiplication(all_0_8_8, all_0_4_4) = all_177_1_199, yields:
% 46.44/14.28  | (334)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_8_8, all_0_4_4) = v0 & multiplication(all_0_4_4, all_0_8_8) = v1 & addition(all_0_4_4, all_0_8_8) = v2 & ( ~ (v0 = 0) | (v2 = one & v1 = zero & all_177_1_199 = zero)))
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (31) with all_97_0_116, all_21_0_31, all_0_6_6 and discharging atoms addition(all_21_0_31, all_0_6_6) = all_97_0_116, yields:
% 46.44/14.28  | (335) addition(all_0_6_6, all_21_0_31) = all_97_0_116
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (11) with all_97_0_116, all_0_6_6, all_21_0_31 and discharging atoms addition(all_21_0_31, all_0_6_6) = all_97_0_116, yields:
% 46.44/14.28  | (336)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_6_6, all_21_0_31) = v0 & multiplication(all_21_0_31, all_0_6_6) = v1 & multiplication(all_0_6_6, all_21_0_31) = v2 & ( ~ (v0 = 0) | (v2 = zero & v1 = zero & all_97_0_116 = one)))
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (49) with all_95_1_114, all_21_0_31, all_0_6_6, all_0_8_8, all_0_4_4 and discharging atoms multiplication(all_21_0_31, all_0_6_6) = all_95_1_114, addition(all_0_4_4, all_0_8_8) = all_21_0_31, yields:
% 46.44/14.28  | (337)  ? [v0] :  ? [v1] : (multiplication(all_0_4_4, all_0_6_6) = v0 & multiplication(all_0_8_8, all_0_6_6) = v1 & addition(v0, v1) = all_95_1_114)
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (11) with all_21_0_31, all_0_8_8, all_0_4_4 and discharging atoms addition(all_0_4_4, all_0_8_8) = all_21_0_31, yields:
% 46.44/14.28  | (338)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_0_8_8, all_0_4_4) = v0 & multiplication(all_0_4_4, all_0_8_8) = v1 & multiplication(all_0_8_8, all_0_4_4) = v2 & ( ~ (v0 = 0) | (v2 = zero & v1 = zero & all_21_0_31 = one)))
% 46.44/14.28  |
% 46.44/14.28  | Instantiating formula (11) with all_95_0_113, all_21_0_31, all_0_6_6 and discharging atoms addition(all_0_6_6, all_21_0_31) = all_95_0_113, yields:
% 46.44/14.28  | (339)  ? [v0] :  ? [v1] :  ? [v2] : (complement(all_21_0_31, all_0_6_6) = v0 & multiplication(all_21_0_31, all_0_6_6) = v2 & multiplication(all_0_6_6, all_21_0_31) = v1 & ( ~ (v0 = 0) | (v2 = zero & v1 = zero & all_95_0_113 = one)))
% 46.44/14.28  |
% 46.44/14.28  | Instantiating (334) with all_259_0_285, all_259_1_286, all_259_2_287 yields:
% 46.44/14.28  | (340) complement(all_0_8_8, all_0_4_4) = all_259_2_287 & multiplication(all_0_4_4, all_0_8_8) = all_259_1_286 & addition(all_0_4_4, all_0_8_8) = all_259_0_285 & ( ~ (all_259_2_287 = 0) | (all_259_0_285 = one & all_259_1_286 = zero & all_177_1_199 = zero))
% 46.44/14.28  |
% 46.44/14.28  | Applying alpha-rule on (340) yields:
% 46.44/14.28  | (341) complement(all_0_8_8, all_0_4_4) = all_259_2_287
% 46.44/14.28  | (342) multiplication(all_0_4_4, all_0_8_8) = all_259_1_286
% 46.44/14.28  | (343) addition(all_0_4_4, all_0_8_8) = all_259_0_285
% 46.44/14.28  | (344)  ~ (all_259_2_287 = 0) | (all_259_0_285 = one & all_259_1_286 = zero & all_177_1_199 = zero)
% 46.44/14.28  |
% 46.44/14.28  | Instantiating (333) with all_265_0_294, all_265_1_295, all_265_2_296 yields:
% 46.44/14.28  | (345) complement(all_0_8_8, all_0_3_3) = all_265_2_296 & multiplication(all_0_3_3, all_0_8_8) = all_265_1_295 & addition(all_0_3_3, all_0_8_8) = all_265_0_294 & ( ~ (all_265_2_296 = 0) | (all_265_0_294 = one & all_265_1_295 = zero & all_179_0_201 = zero))
% 46.44/14.28  |
% 46.44/14.28  | Applying alpha-rule on (345) yields:
% 46.44/14.28  | (346) complement(all_0_8_8, all_0_3_3) = all_265_2_296
% 46.44/14.28  | (347) multiplication(all_0_3_3, all_0_8_8) = all_265_1_295
% 46.44/14.28  | (348) addition(all_0_3_3, all_0_8_8) = all_265_0_294
% 46.44/14.28  | (349)  ~ (all_265_2_296 = 0) | (all_265_0_294 = one & all_265_1_295 = zero & all_179_0_201 = zero)
% 46.44/14.28  |
% 46.44/14.28  | Instantiating (338) with all_299_0_334, all_299_1_335, all_299_2_336 yields:
% 46.44/14.28  | (350) complement(all_0_8_8, all_0_4_4) = all_299_2_336 & multiplication(all_0_4_4, all_0_8_8) = all_299_1_335 & multiplication(all_0_8_8, all_0_4_4) = all_299_0_334 & ( ~ (all_299_2_336 = 0) | (all_299_0_334 = zero & all_299_1_335 = zero & all_21_0_31 = one))
% 46.44/14.28  |
% 46.44/14.28  | Applying alpha-rule on (350) yields:
% 46.44/14.28  | (351) complement(all_0_8_8, all_0_4_4) = all_299_2_336
% 46.44/14.28  | (352) multiplication(all_0_4_4, all_0_8_8) = all_299_1_335
% 46.44/14.28  | (353) multiplication(all_0_8_8, all_0_4_4) = all_299_0_334
% 46.44/14.28  | (354)  ~ (all_299_2_336 = 0) | (all_299_0_334 = zero & all_299_1_335 = zero & all_21_0_31 = one)
% 46.44/14.28  |
% 46.44/14.28  | Instantiating (337) with all_319_0_358, all_319_1_359 yields:
% 46.44/14.28  | (355) multiplication(all_0_4_4, all_0_6_6) = all_319_1_359 & multiplication(all_0_8_8, all_0_6_6) = all_319_0_358 & addition(all_319_1_359, all_319_0_358) = all_95_1_114
% 46.44/14.28  |
% 46.44/14.28  | Applying alpha-rule on (355) yields:
% 46.44/14.28  | (356) multiplication(all_0_4_4, all_0_6_6) = all_319_1_359
% 46.44/14.28  | (357) multiplication(all_0_8_8, all_0_6_6) = all_319_0_358
% 46.44/14.28  | (358) addition(all_319_1_359, all_319_0_358) = all_95_1_114
% 46.44/14.28  |
% 46.44/14.28  | Instantiating (316) with all_357_0_402, all_357_1_403 yields:
% 46.44/14.28  | (359) c(all_0_5_5) = all_357_0_402 & test(all_0_5_5) = all_357_1_403 & ( ~ (all_357_1_403 = 0) | (( ~ (all_357_0_402 = all_0_3_3) | all_65_2_75 = 0) & ( ~ (all_65_2_75 = 0) | all_357_0_402 = all_0_3_3)))
% 46.44/14.28  |
% 46.44/14.28  | Applying alpha-rule on (359) yields:
% 46.44/14.28  | (360) c(all_0_5_5) = all_357_0_402
% 46.44/14.28  | (361) test(all_0_5_5) = all_357_1_403
% 46.44/14.28  | (362)  ~ (all_357_1_403 = 0) | (( ~ (all_357_0_402 = all_0_3_3) | all_65_2_75 = 0) & ( ~ (all_65_2_75 = 0) | all_357_0_402 = all_0_3_3))
% 46.44/14.28  |
% 46.44/14.28  | Instantiating (322) with all_383_0_429, all_383_1_430, all_383_2_431 yields:
% 46.44/14.28  | (363) complement(all_0_8_8, all_119_0_143) = all_383_2_431 & multiplication(all_0_8_8, all_119_0_143) = all_383_1_430 & addition(all_119_0_143, all_0_8_8) = all_383_0_429 & ( ~ (all_383_2_431 = 0) | (all_383_0_429 = one & all_383_1_430 = zero & all_17_0_25 = zero))
% 46.44/14.29  |
% 46.44/14.29  | Applying alpha-rule on (363) yields:
% 46.44/14.29  | (364) complement(all_0_8_8, all_119_0_143) = all_383_2_431
% 46.44/14.29  | (365) multiplication(all_0_8_8, all_119_0_143) = all_383_1_430
% 46.44/14.29  | (366) addition(all_119_0_143, all_0_8_8) = all_383_0_429
% 46.44/14.29  | (367)  ~ (all_383_2_431 = 0) | (all_383_0_429 = one & all_383_1_430 = zero & all_17_0_25 = zero)
% 46.44/14.29  |
% 46.44/14.29  | Instantiating (321) with all_393_0_441, all_393_1_442 yields:
% 46.44/14.29  | (368) c(all_0_9_9) = all_393_0_441 & test(all_0_9_9) = all_393_1_442 & ( ~ (all_393_1_442 = 0) | (( ~ (all_393_0_441 = all_0_8_8) | all_163_2_186 = 0) & ( ~ (all_163_2_186 = 0) | all_393_0_441 = all_0_8_8)))
% 46.44/14.29  |
% 46.44/14.29  | Applying alpha-rule on (368) yields:
% 46.44/14.29  | (369) c(all_0_9_9) = all_393_0_441
% 46.44/14.29  | (370) test(all_0_9_9) = all_393_1_442
% 46.44/14.29  | (371)  ~ (all_393_1_442 = 0) | (( ~ (all_393_0_441 = all_0_8_8) | all_163_2_186 = 0) & ( ~ (all_163_2_186 = 0) | all_393_0_441 = all_0_8_8))
% 46.44/14.29  |
% 46.44/14.29  | Instantiating (320) with all_395_0_443, all_395_1_444 yields:
% 46.44/14.29  | (372) c(all_0_9_9) = all_395_0_443 & test(all_0_9_9) = all_395_1_444 & ( ~ (all_395_1_444 = 0) | (( ~ (all_395_0_443 = all_0_7_7) | all_79_2_92 = 0) & ( ~ (all_79_2_92 = 0) | all_395_0_443 = all_0_7_7)))
% 46.44/14.29  |
% 46.44/14.29  | Applying alpha-rule on (372) yields:
% 46.44/14.29  | (373) c(all_0_9_9) = all_395_0_443
% 46.44/14.29  | (374) test(all_0_9_9) = all_395_1_444
% 46.44/14.29  | (375)  ~ (all_395_1_444 = 0) | (( ~ (all_395_0_443 = all_0_7_7) | all_79_2_92 = 0) & ( ~ (all_79_2_92 = 0) | all_395_0_443 = all_0_7_7))
% 46.44/14.29  |
% 46.44/14.29  | Instantiating (317) with all_397_0_445, all_397_1_446 yields:
% 46.44/14.29  | (376) c(all_0_8_8) = all_397_0_445 & test(all_0_8_8) = all_397_1_446 & ( ~ (all_397_1_446 = 0) | (( ~ (all_397_0_445 = all_0_7_7) | all_85_2_100 = 0) & ( ~ (all_85_2_100 = 0) | all_397_0_445 = all_0_7_7)))
% 46.44/14.29  |
% 46.44/14.29  | Applying alpha-rule on (376) yields:
% 46.44/14.29  | (377) c(all_0_8_8) = all_397_0_445
% 46.44/14.29  | (378) test(all_0_8_8) = all_397_1_446
% 46.44/14.29  | (379)  ~ (all_397_1_446 = 0) | (( ~ (all_397_0_445 = all_0_7_7) | all_85_2_100 = 0) & ( ~ (all_85_2_100 = 0) | all_397_0_445 = all_0_7_7))
% 46.44/14.29  |
% 46.44/14.29  | Instantiating (328) with all_407_0_456 yields:
% 46.44/14.29  | (380) multiplication(all_407_0_456, all_0_8_8) = all_121_0_144 & multiplication(all_0_4_4, all_0_6_6) = all_407_0_456
% 46.44/14.29  |
% 46.44/14.29  | Applying alpha-rule on (380) yields:
% 46.44/14.29  | (381) multiplication(all_407_0_456, all_0_8_8) = all_121_0_144
% 46.44/14.29  | (382) multiplication(all_0_4_4, all_0_6_6) = all_407_0_456
% 46.44/14.29  |
% 46.44/14.29  | Instantiating (319) with all_409_0_457, all_409_1_458 yields:
% 46.44/14.29  | (383) c(all_0_9_9) = all_409_0_457 & test(all_0_9_9) = all_409_1_458 & ( ~ (all_409_1_458 = 0) | (( ~ (all_409_0_457 = all_0_4_4) | all_193_2_219 = 0) & ( ~ (all_193_2_219 = 0) | all_409_0_457 = all_0_4_4)))
% 46.44/14.29  |
% 46.44/14.29  | Applying alpha-rule on (383) yields:
% 46.44/14.29  | (384) c(all_0_9_9) = all_409_0_457
% 46.44/14.29  | (385) test(all_0_9_9) = all_409_1_458
% 46.44/14.29  | (386)  ~ (all_409_1_458 = 0) | (( ~ (all_409_0_457 = all_0_4_4) | all_193_2_219 = 0) & ( ~ (all_193_2_219 = 0) | all_409_0_457 = all_0_4_4))
% 46.44/14.29  |
% 46.44/14.29  | Instantiating (318) with all_411_0_459, all_411_1_460 yields:
% 46.44/14.29  | (387) c(all_0_8_8) = all_411_0_459 & test(all_0_8_8) = all_411_1_460 & ( ~ (all_411_1_460 = 0) | (( ~ (all_411_0_459 = all_0_9_9) | all_157_2_177 = 0) & ( ~ (all_157_2_177 = 0) | all_411_0_459 = all_0_9_9)))
% 46.86/14.29  |
% 46.86/14.29  | Applying alpha-rule on (387) yields:
% 46.86/14.29  | (388) c(all_0_8_8) = all_411_0_459
% 46.86/14.29  | (389) test(all_0_8_8) = all_411_1_460
% 46.86/14.29  | (390)  ~ (all_411_1_460 = 0) | (( ~ (all_411_0_459 = all_0_9_9) | all_157_2_177 = 0) & ( ~ (all_157_2_177 = 0) | all_411_0_459 = all_0_9_9))
% 46.86/14.29  |
% 46.86/14.29  | Instantiating (323) with all_413_0_461, all_413_1_462, all_413_2_463 yields:
% 46.86/14.29  | (391) complement(all_111_0_135, all_0_4_4) = all_413_2_463 & multiplication(all_0_4_4, all_111_0_135) = all_413_1_462 & addition(all_0_4_4, all_111_0_135) = all_413_0_461 & ( ~ (all_413_2_463 = 0) | (all_413_0_461 = one & all_413_1_462 = zero & all_17_1_26 = zero))
% 46.86/14.29  |
% 46.86/14.29  | Applying alpha-rule on (391) yields:
% 46.86/14.29  | (392) complement(all_111_0_135, all_0_4_4) = all_413_2_463
% 46.86/14.29  | (393) multiplication(all_0_4_4, all_111_0_135) = all_413_1_462
% 46.86/14.29  | (394) addition(all_0_4_4, all_111_0_135) = all_413_0_461
% 46.86/14.29  | (395)  ~ (all_413_2_463 = 0) | (all_413_0_461 = one & all_413_1_462 = zero & all_17_1_26 = zero)
% 46.86/14.29  |
% 46.86/14.29  | Instantiating (329) with all_421_0_472, all_421_1_473, all_421_2_474 yields:
% 46.86/14.29  | (396) complement(all_0_5_5, all_0_4_4) = all_421_2_474 & multiplication(all_0_5_5, all_0_4_4) = all_421_1_473 & addition(all_0_4_4, all_0_5_5) = all_421_0_472 & ( ~ (all_421_2_474 = 0) | (all_421_0_472 = one & all_421_1_473 = zero & all_121_0_144 = zero))
% 46.86/14.29  |
% 46.86/14.29  | Applying alpha-rule on (396) yields:
% 46.86/14.29  | (397) complement(all_0_5_5, all_0_4_4) = all_421_2_474
% 46.86/14.29  | (398) multiplication(all_0_5_5, all_0_4_4) = all_421_1_473
% 46.86/14.29  | (399) addition(all_0_4_4, all_0_5_5) = all_421_0_472
% 46.86/14.29  | (400)  ~ (all_421_2_474 = 0) | (all_421_0_472 = one & all_421_1_473 = zero & all_121_0_144 = zero)
% 46.86/14.29  |
% 46.86/14.29  | Instantiating (339) with all_441_0_495, all_441_1_496, all_441_2_497 yields:
% 46.86/14.29  | (401) complement(all_21_0_31, all_0_6_6) = all_441_2_497 & multiplication(all_21_0_31, all_0_6_6) = all_441_0_495 & multiplication(all_0_6_6, all_21_0_31) = all_441_1_496 & ( ~ (all_441_2_497 = 0) | (all_441_0_495 = zero & all_441_1_496 = zero & all_95_0_113 = one))
% 46.86/14.29  |
% 46.86/14.29  | Applying alpha-rule on (401) yields:
% 46.86/14.29  | (402) complement(all_21_0_31, all_0_6_6) = all_441_2_497
% 46.86/14.29  | (403) multiplication(all_21_0_31, all_0_6_6) = all_441_0_495
% 46.86/14.29  | (404) multiplication(all_0_6_6, all_21_0_31) = all_441_1_496
% 46.86/14.29  | (405)  ~ (all_441_2_497 = 0) | (all_441_0_495 = zero & all_441_1_496 = zero & all_95_0_113 = one)
% 46.86/14.29  |
% 46.86/14.29  | Instantiating (336) with all_451_0_509, all_451_1_510, all_451_2_511 yields:
% 46.86/14.29  | (406) complement(all_0_6_6, all_21_0_31) = all_451_2_511 & multiplication(all_21_0_31, all_0_6_6) = all_451_1_510 & multiplication(all_0_6_6, all_21_0_31) = all_451_0_509 & ( ~ (all_451_2_511 = 0) | (all_451_0_509 = zero & all_451_1_510 = zero & all_97_0_116 = one))
% 46.86/14.29  |
% 46.86/14.29  | Applying alpha-rule on (406) yields:
% 46.86/14.29  | (407) complement(all_0_6_6, all_21_0_31) = all_451_2_511
% 46.86/14.29  | (408) multiplication(all_21_0_31, all_0_6_6) = all_451_1_510
% 46.86/14.29  | (409) multiplication(all_0_6_6, all_21_0_31) = all_451_0_509
% 46.86/14.29  | (410)  ~ (all_451_2_511 = 0) | (all_451_0_509 = zero & all_451_1_510 = zero & all_97_0_116 = one)
% 46.86/14.29  |
% 46.86/14.29  | Instantiating (327) with all_459_0_515 yields:
% 46.86/14.29  | (411) multiplication(all_0_4_4, all_0_6_6) = all_459_0_515 & multiplication(all_0_6_6, all_459_0_515) = all_119_0_143
% 46.86/14.29  |
% 46.86/14.29  | Applying alpha-rule on (411) yields:
% 46.86/14.29  | (412) multiplication(all_0_4_4, all_0_6_6) = all_459_0_515
% 46.86/14.29  | (413) multiplication(all_0_6_6, all_459_0_515) = all_119_0_143
% 46.86/14.29  |
% 46.86/14.29  | Instantiating (330) with all_473_0_530, all_473_1_531, all_473_2_532 yields:
% 46.86/14.29  | (414) complement(all_0_8_8, all_0_4_4) = all_473_2_532 & multiplication(all_0_8_8, all_0_4_4) = all_473_1_531 & addition(all_0_4_4, all_0_8_8) = all_473_0_530 & ( ~ (all_473_2_532 = 0) | (all_473_0_530 = one & all_473_1_531 = zero & all_177_0_198 = zero))
% 46.86/14.29  |
% 46.86/14.29  | Applying alpha-rule on (414) yields:
% 46.86/14.29  | (415) complement(all_0_8_8, all_0_4_4) = all_473_2_532
% 46.86/14.29  | (416) multiplication(all_0_8_8, all_0_4_4) = all_473_1_531
% 46.86/14.29  | (417) addition(all_0_4_4, all_0_8_8) = all_473_0_530
% 46.86/14.29  | (418)  ~ (all_473_2_532 = 0) | (all_473_0_530 = one & all_473_1_531 = zero & all_177_0_198 = zero)
% 46.86/14.29  |
% 46.86/14.29  | Instantiating (332) with all_547_0_608 yields:
% 46.86/14.29  | (419) multiplication(all_547_0_608, all_0_4_4) = all_179_0_201 & multiplication(all_0_8_8, all_0_6_6) = all_547_0_608
% 46.86/14.29  |
% 46.86/14.29  | Applying alpha-rule on (419) yields:
% 46.86/14.29  | (420) multiplication(all_547_0_608, all_0_4_4) = all_179_0_201
% 46.86/14.29  | (421) multiplication(all_0_8_8, all_0_6_6) = all_547_0_608
% 46.86/14.29  |
% 46.86/14.29  | Instantiating (325) with all_575_0_639, all_575_1_640, all_575_2_641 yields:
% 46.86/14.29  | (422) complement(all_21_0_31, all_0_6_6) = all_575_2_641 & multiplication(all_0_6_6, all_21_0_31) = all_575_1_640 & addition(all_0_6_6, all_21_0_31) = all_575_0_639 & ( ~ (all_575_2_641 = 0) | (all_575_0_639 = one & all_575_1_640 = zero & all_95_1_114 = zero))
% 46.86/14.29  |
% 46.86/14.29  | Applying alpha-rule on (422) yields:
% 46.86/14.29  | (423) complement(all_21_0_31, all_0_6_6) = all_575_2_641
% 46.86/14.29  | (424) multiplication(all_0_6_6, all_21_0_31) = all_575_1_640
% 46.86/14.29  | (425) addition(all_0_6_6, all_21_0_31) = all_575_0_639
% 46.86/14.29  | (426)  ~ (all_575_2_641 = 0) | (all_575_0_639 = one & all_575_1_640 = zero & all_95_1_114 = zero)
% 46.86/14.29  |
% 46.86/14.29  | Instantiating (326) with all_593_0_660, all_593_1_661, all_593_2_662 yields:
% 46.86/14.29  | (427) complement(all_0_6_6, all_21_0_31) = all_593_2_662 & multiplication(all_0_6_6, all_21_0_31) = all_593_1_661 & addition(all_21_0_31, all_0_6_6) = all_593_0_660 & ( ~ (all_593_2_662 = 0) | (all_593_0_660 = one & all_593_1_661 = zero & all_95_1_114 = zero))
% 46.86/14.29  |
% 46.86/14.29  | Applying alpha-rule on (427) yields:
% 46.86/14.29  | (428) complement(all_0_6_6, all_21_0_31) = all_593_2_662
% 46.86/14.29  | (429) multiplication(all_0_6_6, all_21_0_31) = all_593_1_661
% 46.86/14.29  | (430) addition(all_21_0_31, all_0_6_6) = all_593_0_660
% 46.86/14.29  | (431)  ~ (all_593_2_662 = 0) | (all_593_0_660 = one & all_593_1_661 = zero & all_95_1_114 = zero)
% 46.86/14.30  |
% 46.86/14.30  | Instantiating (331) with all_599_0_668 yields:
% 46.86/14.30  | (432) multiplication(all_0_6_6, all_599_0_668) = all_111_0_135 & multiplication(all_0_8_8, all_0_6_6) = all_599_0_668
% 46.86/14.30  |
% 46.86/14.30  | Applying alpha-rule on (432) yields:
% 46.86/14.30  | (433) multiplication(all_0_6_6, all_599_0_668) = all_111_0_135
% 46.86/14.30  | (434) multiplication(all_0_8_8, all_0_6_6) = all_599_0_668
% 46.86/14.30  |
% 46.86/14.30  | Instantiating (324) with all_601_0_669, all_601_1_670 yields:
% 46.86/14.30  | (435) multiplication(all_0_4_4, all_0_6_6) = all_601_0_669 & multiplication(all_0_8_8, all_0_6_6) = all_601_1_670 & addition(all_601_1_670, all_601_0_669) = all_95_1_114
% 46.86/14.30  |
% 46.86/14.30  | Applying alpha-rule on (435) yields:
% 46.86/14.30  | (436) multiplication(all_0_4_4, all_0_6_6) = all_601_0_669
% 46.86/14.30  | (437) multiplication(all_0_8_8, all_0_6_6) = all_601_1_670
% 46.86/14.30  | (438) addition(all_601_1_670, all_601_0_669) = all_95_1_114
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (3) with all_0_8_8, all_411_0_459, all_0_4_4 and discharging atoms c(all_0_8_8) = all_411_0_459, c(all_0_8_8) = all_0_4_4, yields:
% 46.86/14.30  | (439) all_411_0_459 = all_0_4_4
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (3) with all_0_8_8, all_397_0_445, all_411_0_459 and discharging atoms c(all_0_8_8) = all_411_0_459, c(all_0_8_8) = all_397_0_445, yields:
% 46.86/14.30  | (440) all_411_0_459 = all_397_0_445
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (3) with all_0_9_9, all_395_0_443, all_0_7_7 and discharging atoms c(all_0_9_9) = all_395_0_443, c(all_0_9_9) = all_0_7_7, yields:
% 46.86/14.30  | (441) all_395_0_443 = all_0_7_7
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (33) with all_33_0_47, all_409_1_458, all_0_9_9 and discharging atoms test(all_0_9_9) = all_409_1_458, complement(all_33_0_47, all_0_9_9) = 0, yields:
% 46.86/14.30  | (442) all_409_1_458 = 0
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (38) with all_0_9_9, all_395_1_444, all_409_1_458 and discharging atoms test(all_0_9_9) = all_409_1_458, test(all_0_9_9) = all_395_1_444, yields:
% 46.86/14.30  | (443) all_409_1_458 = all_395_1_444
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (38) with all_0_9_9, all_393_1_442, all_395_1_444 and discharging atoms test(all_0_9_9) = all_395_1_444, test(all_0_9_9) = all_393_1_442, yields:
% 46.86/14.30  | (444) all_395_1_444 = all_393_1_442
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (13) with all_0_8_8, all_0_4_4, all_299_2_336, all_473_2_532 and discharging atoms complement(all_0_8_8, all_0_4_4) = all_473_2_532, complement(all_0_8_8, all_0_4_4) = all_299_2_336, yields:
% 46.86/14.30  | (445) all_473_2_532 = all_299_2_336
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (13) with all_0_8_8, all_0_4_4, all_259_2_287, all_473_2_532 and discharging atoms complement(all_0_8_8, all_0_4_4) = all_473_2_532, complement(all_0_8_8, all_0_4_4) = all_259_2_287, yields:
% 46.86/14.30  | (446) all_473_2_532 = all_259_2_287
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (42) with all_0_4_4, all_0_6_6, all_601_0_669, all_43_1_58 and discharging atoms multiplication(all_0_4_4, all_0_6_6) = all_601_0_669, multiplication(all_0_4_4, all_0_6_6) = all_43_1_58, yields:
% 46.86/14.30  | (447) all_601_0_669 = all_43_1_58
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (42) with all_0_4_4, all_0_6_6, all_459_0_515, all_601_0_669 and discharging atoms multiplication(all_0_4_4, all_0_6_6) = all_601_0_669, multiplication(all_0_4_4, all_0_6_6) = all_459_0_515, yields:
% 46.86/14.30  | (448) all_601_0_669 = all_459_0_515
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (42) with all_0_4_4, all_0_6_6, all_407_0_456, all_601_0_669 and discharging atoms multiplication(all_0_4_4, all_0_6_6) = all_601_0_669, multiplication(all_0_4_4, all_0_6_6) = all_407_0_456, yields:
% 46.86/14.30  | (449) all_601_0_669 = all_407_0_456
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (42) with all_0_4_4, all_0_6_6, all_319_1_359, all_601_0_669 and discharging atoms multiplication(all_0_4_4, all_0_6_6) = all_601_0_669, multiplication(all_0_4_4, all_0_6_6) = all_319_1_359, yields:
% 46.86/14.30  | (450) all_601_0_669 = all_319_1_359
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (42) with all_0_6_6, all_21_0_31, all_593_1_661, all_0_2_2 and discharging atoms multiplication(all_0_6_6, all_21_0_31) = all_593_1_661, multiplication(all_0_6_6, all_21_0_31) = all_0_2_2, yields:
% 46.86/14.30  | (451) all_593_1_661 = all_0_2_2
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (42) with all_0_6_6, all_21_0_31, all_575_1_640, all_593_1_661 and discharging atoms multiplication(all_0_6_6, all_21_0_31) = all_593_1_661, multiplication(all_0_6_6, all_21_0_31) = all_575_1_640, yields:
% 46.86/14.30  | (452) all_593_1_661 = all_575_1_640
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (42) with all_0_6_6, all_21_0_31, all_451_0_509, all_593_1_661 and discharging atoms multiplication(all_0_6_6, all_21_0_31) = all_593_1_661, multiplication(all_0_6_6, all_21_0_31) = all_451_0_509, yields:
% 46.86/14.30  | (453) all_593_1_661 = all_451_0_509
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (42) with all_0_6_6, all_21_0_31, all_441_1_496, all_451_0_509 and discharging atoms multiplication(all_0_6_6, all_21_0_31) = all_451_0_509, multiplication(all_0_6_6, all_21_0_31) = all_441_1_496, yields:
% 46.86/14.30  | (454) all_451_0_509 = all_441_1_496
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (42) with all_0_8_8, all_0_6_6, all_601_1_670, all_19_1_29 and discharging atoms multiplication(all_0_8_8, all_0_6_6) = all_601_1_670, multiplication(all_0_8_8, all_0_6_6) = all_19_1_29, yields:
% 46.86/14.30  | (455) all_601_1_670 = all_19_1_29
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (42) with all_0_8_8, all_0_6_6, all_599_0_668, all_601_1_670 and discharging atoms multiplication(all_0_8_8, all_0_6_6) = all_601_1_670, multiplication(all_0_8_8, all_0_6_6) = all_599_0_668, yields:
% 46.86/14.30  | (456) all_601_1_670 = all_599_0_668
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (42) with all_0_8_8, all_0_6_6, all_547_0_608, all_599_0_668 and discharging atoms multiplication(all_0_8_8, all_0_6_6) = all_599_0_668, multiplication(all_0_8_8, all_0_6_6) = all_547_0_608, yields:
% 46.86/14.30  | (457) all_599_0_668 = all_547_0_608
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (42) with all_0_8_8, all_0_6_6, all_319_0_358, all_547_0_608 and discharging atoms multiplication(all_0_8_8, all_0_6_6) = all_547_0_608, multiplication(all_0_8_8, all_0_6_6) = all_319_0_358, yields:
% 46.86/14.30  | (458) all_547_0_608 = all_319_0_358
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (43) with all_0_4_4, all_0_8_8, all_473_0_530, all_21_0_31 and discharging atoms addition(all_0_4_4, all_0_8_8) = all_473_0_530, addition(all_0_4_4, all_0_8_8) = all_21_0_31, yields:
% 46.86/14.30  | (459) all_473_0_530 = all_21_0_31
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (43) with all_0_6_6, all_21_0_31, all_575_0_639, all_95_0_113 and discharging atoms addition(all_0_6_6, all_21_0_31) = all_575_0_639, addition(all_0_6_6, all_21_0_31) = all_95_0_113, yields:
% 46.86/14.30  | (460) all_575_0_639 = all_95_0_113
% 46.86/14.30  |
% 46.86/14.30  | Instantiating formula (43) with all_0_6_6, all_21_0_31, all_97_0_116, all_575_0_639 and discharging atoms addition(all_0_6_6, all_21_0_31) = all_575_0_639, addition(all_0_6_6, all_21_0_31) = all_97_0_116, yields:
% 46.86/14.30  | (461) all_575_0_639 = all_97_0_116
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (449,448) yields a new equation:
% 46.86/14.30  | (462) all_459_0_515 = all_407_0_456
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (450,448) yields a new equation:
% 46.86/14.30  | (463) all_459_0_515 = all_319_1_359
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (447,448) yields a new equation:
% 46.86/14.30  | (464) all_459_0_515 = all_43_1_58
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (456,455) yields a new equation:
% 46.86/14.30  | (465) all_599_0_668 = all_19_1_29
% 46.86/14.30  |
% 46.86/14.30  | Simplifying 465 yields:
% 46.86/14.30  | (466) all_599_0_668 = all_19_1_29
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (457,466) yields a new equation:
% 46.86/14.30  | (467) all_547_0_608 = all_19_1_29
% 46.86/14.30  |
% 46.86/14.30  | Simplifying 467 yields:
% 46.86/14.30  | (468) all_547_0_608 = all_19_1_29
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (451,452) yields a new equation:
% 46.86/14.30  | (469) all_575_1_640 = all_0_2_2
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (453,452) yields a new equation:
% 46.86/14.30  | (470) all_575_1_640 = all_451_0_509
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (460,461) yields a new equation:
% 46.86/14.30  | (471) all_97_0_116 = all_95_0_113
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (470,469) yields a new equation:
% 46.86/14.30  | (472) all_451_0_509 = all_0_2_2
% 46.86/14.30  |
% 46.86/14.30  | Simplifying 472 yields:
% 46.86/14.30  | (473) all_451_0_509 = all_0_2_2
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (458,468) yields a new equation:
% 46.86/14.30  | (474) all_319_0_358 = all_19_1_29
% 46.86/14.30  |
% 46.86/14.30  | Simplifying 474 yields:
% 46.86/14.30  | (475) all_319_0_358 = all_19_1_29
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (446,445) yields a new equation:
% 46.86/14.30  | (476) all_299_2_336 = all_259_2_287
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (463,462) yields a new equation:
% 46.86/14.30  | (477) all_407_0_456 = all_319_1_359
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (464,462) yields a new equation:
% 46.86/14.30  | (478) all_407_0_456 = all_43_1_58
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (454,473) yields a new equation:
% 46.86/14.30  | (479) all_441_1_496 = all_0_2_2
% 46.86/14.30  |
% 46.86/14.30  | Simplifying 479 yields:
% 46.86/14.30  | (480) all_441_1_496 = all_0_2_2
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (440,439) yields a new equation:
% 46.86/14.30  | (481) all_397_0_445 = all_0_4_4
% 46.86/14.30  |
% 46.86/14.30  | Simplifying 481 yields:
% 46.86/14.30  | (482) all_397_0_445 = all_0_4_4
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (443,442) yields a new equation:
% 46.86/14.30  | (483) all_395_1_444 = 0
% 46.86/14.30  |
% 46.86/14.30  | Simplifying 483 yields:
% 46.86/14.30  | (484) all_395_1_444 = 0
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (477,478) yields a new equation:
% 46.86/14.30  | (485) all_319_1_359 = all_43_1_58
% 46.86/14.30  |
% 46.86/14.30  | Simplifying 485 yields:
% 46.86/14.30  | (486) all_319_1_359 = all_43_1_58
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (484,444) yields a new equation:
% 46.86/14.30  | (487) all_393_1_442 = 0
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (487,444) yields a new equation:
% 46.86/14.30  | (484) all_395_1_444 = 0
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (478,462) yields a new equation:
% 46.86/14.30  | (464) all_459_0_515 = all_43_1_58
% 46.86/14.30  |
% 46.86/14.30  | Combining equations (476,445) yields a new equation:
% 46.86/14.30  | (446) all_473_2_532 = all_259_2_287
% 46.86/14.30  |
% 46.86/14.30  | From (482) and (377) follows:
% 46.86/14.30  | (23) c(all_0_8_8) = all_0_4_4
% 46.86/14.30  |
% 46.86/14.30  | From (476) and (351) follows:
% 46.86/14.30  | (341) complement(all_0_8_8, all_0_4_4) = all_259_2_287
% 46.86/14.30  |
% 46.86/14.30  | From (486) and (356) follows:
% 46.86/14.30  | (100) multiplication(all_0_4_4, all_0_6_6) = all_43_1_58
% 46.86/14.30  |
% 46.86/14.30  | From (466) and (433) follows:
% 46.86/14.30  | (494) multiplication(all_0_6_6, all_19_1_29) = all_111_0_135
% 46.86/14.30  |
% 46.86/14.30  | From (464) and (413) follows:
% 46.86/14.30  | (495) multiplication(all_0_6_6, all_43_1_58) = all_119_0_143
% 46.86/14.30  |
% 46.86/14.30  | From (480) and (404) follows:
% 46.86/14.30  | (84) multiplication(all_0_6_6, all_21_0_31) = all_0_2_2
% 46.86/14.30  |
% 46.86/14.30  | From (475) and (357) follows:
% 46.86/14.30  | (80) multiplication(all_0_8_8, all_0_6_6) = all_19_1_29
% 46.86/14.30  |
% 46.86/14.30  | From (471) and (335) follows:
% 46.86/14.30  | (177) addition(all_0_6_6, all_21_0_31) = all_95_0_113
% 46.86/14.30  |
% 46.86/14.30  +-Applying beta-rule and splitting (375), into two cases.
% 46.86/14.30  |-Branch one:
% 46.86/14.30  | (499)  ~ (all_395_1_444 = 0)
% 46.86/14.31  |
% 46.86/14.31  	| Equations (484) can reduce 499 to:
% 46.86/14.31  	| (500) $false
% 46.86/14.31  	|
% 46.86/14.31  	|-The branch is then unsatisfiable
% 46.86/14.31  |-Branch two:
% 46.86/14.31  | (484) all_395_1_444 = 0
% 46.86/14.31  | (502) ( ~ (all_395_0_443 = all_0_7_7) | all_79_2_92 = 0) & ( ~ (all_79_2_92 = 0) | all_395_0_443 = all_0_7_7)
% 46.86/14.31  |
% 46.86/14.31  	| Applying alpha-rule on (502) yields:
% 46.86/14.31  	| (503)  ~ (all_395_0_443 = all_0_7_7) | all_79_2_92 = 0
% 46.86/14.31  	| (504)  ~ (all_79_2_92 = 0) | all_395_0_443 = all_0_7_7
% 46.86/14.31  	|
% 46.86/14.31  	+-Applying beta-rule and splitting (503), into two cases.
% 46.86/14.31  	|-Branch one:
% 46.86/14.31  	| (505)  ~ (all_395_0_443 = all_0_7_7)
% 46.86/14.31  	|
% 46.86/14.31  		| Equations (441) can reduce 505 to:
% 46.86/14.31  		| (500) $false
% 46.86/14.31  		|
% 46.86/14.31  		|-The branch is then unsatisfiable
% 46.86/14.31  	|-Branch two:
% 46.86/14.31  	| (441) all_395_0_443 = all_0_7_7
% 46.86/14.31  	| (508) all_79_2_92 = 0
% 46.86/14.31  	|
% 46.86/14.31  		| Combining equations (508,298) yields a new equation:
% 46.86/14.31  		| (509) all_99_2_121 = 0
% 46.86/14.31  		|
% 46.86/14.31  		+-Applying beta-rule and splitting (188), into two cases.
% 46.86/14.31  		|-Branch one:
% 46.86/14.31  		| (510)  ~ (all_99_2_121 = 0)
% 46.86/14.31  		|
% 46.86/14.31  			| Equations (509) can reduce 510 to:
% 46.86/14.31  			| (500) $false
% 46.86/14.31  			|
% 46.86/14.31  			|-The branch is then unsatisfiable
% 46.86/14.31  		|-Branch two:
% 46.86/14.31  		| (509) all_99_2_121 = 0
% 46.86/14.31  		| (513) all_99_0_119 = zero & all_99_1_120 = zero & all_0_6_6 = one
% 46.86/14.31  		|
% 46.86/14.31  			| Applying alpha-rule on (513) yields:
% 46.86/14.31  			| (514) all_99_0_119 = zero
% 46.86/14.31  			| (515) all_99_1_120 = zero
% 46.86/14.31  			| (516) all_0_6_6 = one
% 46.86/14.31  			|
% 46.86/14.31  			| From (516) and (208) follows:
% 46.86/14.31  			| (517) multiplication(all_0_3_3, one) = all_119_0_143
% 46.86/14.31  			|
% 46.86/14.31  			| From (516) and (100) follows:
% 46.86/14.31  			| (518) multiplication(all_0_4_4, one) = all_43_1_58
% 46.86/14.31  			|
% 46.86/14.31  			| From (516) and (200) follows:
% 46.86/14.31  			| (519) multiplication(all_0_5_5, one) = all_111_0_135
% 46.86/14.31  			|
% 46.86/14.31  			| From (516) and (495) follows:
% 46.86/14.31  			| (520) multiplication(one, all_43_1_58) = all_119_0_143
% 46.86/14.31  			|
% 46.86/14.31  			| From (516) and (84) follows:
% 46.86/14.31  			| (521) multiplication(one, all_21_0_31) = all_0_2_2
% 46.86/14.31  			|
% 46.86/14.31  			| From (516) and (494) follows:
% 46.86/14.31  			| (522) multiplication(one, all_19_1_29) = all_111_0_135
% 46.86/14.31  			|
% 46.86/14.31  			| From (516) and (80) follows:
% 46.86/14.31  			| (523) multiplication(all_0_8_8, one) = all_19_1_29
% 46.86/14.31  			|
% 46.86/14.31  			| From (516) and (177) follows:
% 46.86/14.31  			| (524) addition(one, all_21_0_31) = all_95_0_113
% 46.86/14.31  			|
% 46.86/14.31  			| Instantiating formula (51) with all_119_0_143, all_0_3_3 and discharging atoms multiplication(all_0_3_3, one) = all_119_0_143, yields:
% 46.86/14.31  			| (525) all_119_0_143 = all_0_3_3
% 46.86/14.31  			|
% 46.86/14.31  			| Instantiating formula (51) with all_43_1_58, all_0_4_4 and discharging atoms multiplication(all_0_4_4, one) = all_43_1_58, yields:
% 46.86/14.31  			| (526) all_43_1_58 = all_0_4_4
% 46.86/14.31  			|
% 46.86/14.31  			| Instantiating formula (51) with all_111_0_135, all_0_5_5 and discharging atoms multiplication(all_0_5_5, one) = all_111_0_135, yields:
% 46.86/14.31  			| (527) all_111_0_135 = all_0_5_5
% 46.86/14.31  			|
% 46.86/14.31  			| Instantiating formula (51) with all_19_1_29, all_0_8_8 and discharging atoms multiplication(all_0_8_8, one) = all_19_1_29, yields:
% 46.86/14.31  			| (528) all_19_1_29 = all_0_8_8
% 46.86/14.31  			|
% 46.86/14.31  			| Instantiating formula (24) with all_119_0_143, all_43_1_58 and discharging atoms multiplication(one, all_43_1_58) = all_119_0_143, yields:
% 46.86/14.31  			| (529) all_119_0_143 = all_43_1_58
% 46.86/14.31  			|
% 46.86/14.31  			| Instantiating formula (24) with all_0_2_2, all_21_0_31 and discharging atoms multiplication(one, all_21_0_31) = all_0_2_2, yields:
% 46.86/14.31  			| (530) all_21_0_31 = all_0_2_2
% 46.86/14.31  			|
% 46.86/14.31  			| Instantiating formula (24) with all_111_0_135, all_19_1_29 and discharging atoms multiplication(one, all_19_1_29) = all_111_0_135, yields:
% 46.86/14.31  			| (531) all_111_0_135 = all_19_1_29
% 46.86/14.31  			|
% 46.86/14.31  			| Combining equations (525,529) yields a new equation:
% 46.86/14.31  			| (532) all_43_1_58 = all_0_3_3
% 46.86/14.31  			|
% 46.86/14.31  			| Combining equations (527,531) yields a new equation:
% 46.86/14.31  			| (533) all_19_1_29 = all_0_5_5
% 46.86/14.31  			|
% 46.86/14.31  			| Combining equations (532,526) yields a new equation:
% 46.86/14.31  			| (534) all_0_3_3 = all_0_4_4
% 46.86/14.31  			|
% 46.86/14.31  			| Simplifying 534 yields:
% 46.86/14.31  			| (535) all_0_3_3 = all_0_4_4
% 46.86/14.31  			|
% 46.86/14.31  			| Combining equations (533,528) yields a new equation:
% 46.86/14.31  			| (536) all_0_5_5 = all_0_8_8
% 46.86/14.31  			|
% 46.86/14.31  			| Simplifying 536 yields:
% 46.86/14.31  			| (537) all_0_5_5 = all_0_8_8
% 46.86/14.31  			|
% 46.86/14.31  			| Combining equations (528,531) yields a new equation:
% 46.86/14.31  			| (538) all_111_0_135 = all_0_8_8
% 46.86/14.31  			|
% 46.86/14.31  			| Combining equations (526,529) yields a new equation:
% 46.86/14.31  			| (539) all_119_0_143 = all_0_4_4
% 46.86/14.31  			|
% 46.86/14.31  			| Combining equations (530,459) yields a new equation:
% 46.86/14.31  			| (540) all_473_0_530 = all_0_2_2
% 46.86/14.31  			|
% 46.86/14.31  			| From (537) and (360) follows:
% 46.86/14.31  			| (541) c(all_0_8_8) = all_357_0_402
% 46.86/14.31  			|
% 46.86/14.31  			| From (537) and (361) follows:
% 46.86/14.31  			| (542) test(all_0_8_8) = all_357_1_403
% 46.86/14.31  			|
% 46.86/14.31  			| From (538) and (392) follows:
% 46.86/14.31  			| (543) complement(all_0_8_8, all_0_4_4) = all_413_2_463
% 46.86/14.31  			|
% 46.86/14.31  			| From (537)(535) and (150) follows:
% 46.86/14.31  			| (544) complement(all_0_8_8, all_0_4_4) = all_65_2_75
% 46.86/14.31  			|
% 46.86/14.31  			| From (537) and (397) follows:
% 46.86/14.31  			| (545) complement(all_0_8_8, all_0_4_4) = all_421_2_474
% 46.86/14.31  			|
% 46.86/14.31  			| From (539) and (364) follows:
% 46.86/14.31  			| (546) complement(all_0_8_8, all_0_4_4) = all_383_2_431
% 46.86/14.31  			|
% 46.86/14.31  			| From (535) and (346) follows:
% 46.86/14.31  			| (547) complement(all_0_8_8, all_0_4_4) = all_265_2_296
% 46.86/14.31  			|
% 46.86/14.31  			| From (530) and (524) follows:
% 46.86/14.31  			| (548) addition(one, all_0_2_2) = all_95_0_113
% 46.86/14.31  			|
% 46.86/14.31  			| Instantiating formula (3) with all_0_8_8, all_357_0_402, all_0_4_4 and discharging atoms c(all_0_8_8) = all_357_0_402, c(all_0_8_8) = all_0_4_4, yields:
% 46.86/14.31  			| (549) all_357_0_402 = all_0_4_4
% 46.86/14.31  			|
% 46.86/14.31  			| Instantiating formula (33) with all_39_0_53, all_357_1_403, all_0_8_8 and discharging atoms test(all_0_8_8) = all_357_1_403, complement(all_39_0_53, all_0_8_8) = 0, yields:
% 46.86/14.31  			| (550) all_357_1_403 = 0
% 46.86/14.31  			|
% 46.86/14.31  			| Instantiating formula (13) with all_0_8_8, all_0_4_4, all_421_2_474, all_259_2_287 and discharging atoms complement(all_0_8_8, all_0_4_4) = all_421_2_474, complement(all_0_8_8, all_0_4_4) = all_259_2_287, yields:
% 46.86/14.31  			| (551) all_421_2_474 = all_259_2_287
% 46.86/14.31  			|
% 46.86/14.31  			| Instantiating formula (13) with all_0_8_8, all_0_4_4, all_413_2_463, all_421_2_474 and discharging atoms complement(all_0_8_8, all_0_4_4) = all_421_2_474, complement(all_0_8_8, all_0_4_4) = all_413_2_463, yields:
% 46.86/14.31  			| (552) all_421_2_474 = all_413_2_463
% 46.86/14.31  			|
% 46.86/14.31  			| Instantiating formula (13) with all_0_8_8, all_0_4_4, all_265_2_296, all_413_2_463 and discharging atoms complement(all_0_8_8, all_0_4_4) = all_413_2_463, complement(all_0_8_8, all_0_4_4) = all_265_2_296, yields:
% 46.86/14.31  			| (553) all_413_2_463 = all_265_2_296
% 46.86/14.31  			|
% 46.86/14.31  			| Instantiating formula (13) with all_0_8_8, all_0_4_4, all_265_2_296, all_383_2_431 and discharging atoms complement(all_0_8_8, all_0_4_4) = all_383_2_431, complement(all_0_8_8, all_0_4_4) = all_265_2_296, yields:
% 46.86/14.31  			| (554) all_383_2_431 = all_265_2_296
% 46.86/14.31  			|
% 46.86/14.31  			| Instantiating formula (13) with all_0_8_8, all_0_4_4, all_65_2_75, all_383_2_431 and discharging atoms complement(all_0_8_8, all_0_4_4) = all_383_2_431, complement(all_0_8_8, all_0_4_4) = all_65_2_75, yields:
% 46.86/14.31  			| (555) all_383_2_431 = all_65_2_75
% 46.86/14.31  			|
% 46.86/14.31  			| Combining equations (552,551) yields a new equation:
% 46.86/14.31  			| (556) all_413_2_463 = all_259_2_287
% 46.86/14.31  			|
% 46.86/14.31  			| Simplifying 556 yields:
% 46.86/14.31  			| (557) all_413_2_463 = all_259_2_287
% 46.86/14.31  			|
% 46.86/14.31  			| Combining equations (553,557) yields a new equation:
% 46.86/14.31  			| (558) all_265_2_296 = all_259_2_287
% 46.86/14.31  			|
% 46.86/14.31  			| Simplifying 558 yields:
% 46.86/14.31  			| (559) all_265_2_296 = all_259_2_287
% 46.86/14.31  			|
% 46.86/14.31  			| Combining equations (554,555) yields a new equation:
% 46.86/14.31  			| (560) all_265_2_296 = all_65_2_75
% 46.86/14.31  			|
% 46.86/14.31  			| Simplifying 560 yields:
% 46.86/14.31  			| (561) all_265_2_296 = all_65_2_75
% 46.86/14.31  			|
% 46.86/14.31  			| Combining equations (559,561) yields a new equation:
% 46.86/14.31  			| (562) all_259_2_287 = all_65_2_75
% 46.86/14.31  			|
% 46.86/14.31  			| Simplifying 562 yields:
% 46.86/14.31  			| (563) all_259_2_287 = all_65_2_75
% 46.86/14.31  			|
% 46.86/14.31  			| Combining equations (563,446) yields a new equation:
% 46.86/14.31  			| (564) all_473_2_532 = all_65_2_75
% 46.86/14.31  			|
% 46.86/14.31  			+-Applying beta-rule and splitting (362), into two cases.
% 46.86/14.31  			|-Branch one:
% 46.86/14.31  			| (565)  ~ (all_357_1_403 = 0)
% 46.86/14.31  			|
% 46.86/14.31  				| Equations (550) can reduce 565 to:
% 46.86/14.31  				| (500) $false
% 46.86/14.31  				|
% 46.86/14.31  				|-The branch is then unsatisfiable
% 46.86/14.31  			|-Branch two:
% 46.86/14.31  			| (550) all_357_1_403 = 0
% 46.86/14.31  			| (568) ( ~ (all_357_0_402 = all_0_3_3) | all_65_2_75 = 0) & ( ~ (all_65_2_75 = 0) | all_357_0_402 = all_0_3_3)
% 46.86/14.31  			|
% 46.86/14.31  				| Applying alpha-rule on (568) yields:
% 46.86/14.31  				| (569)  ~ (all_357_0_402 = all_0_3_3) | all_65_2_75 = 0
% 46.86/14.31  				| (570)  ~ (all_65_2_75 = 0) | all_357_0_402 = all_0_3_3
% 46.86/14.31  				|
% 46.86/14.31  				+-Applying beta-rule and splitting (569), into two cases.
% 46.86/14.31  				|-Branch one:
% 46.86/14.31  				| (571)  ~ (all_357_0_402 = all_0_3_3)
% 46.86/14.31  				|
% 46.86/14.31  					| Equations (549,535) can reduce 571 to:
% 46.86/14.31  					| (500) $false
% 46.86/14.31  					|
% 46.86/14.31  					|-The branch is then unsatisfiable
% 46.86/14.31  				|-Branch two:
% 46.86/14.31  				| (573) all_357_0_402 = all_0_3_3
% 46.86/14.31  				| (574) all_65_2_75 = 0
% 46.86/14.31  				|
% 46.86/14.31  					| Combining equations (574,564) yields a new equation:
% 46.86/14.31  					| (575) all_473_2_532 = 0
% 46.86/14.31  					|
% 46.86/14.31  					+-Applying beta-rule and splitting (418), into two cases.
% 46.86/14.31  					|-Branch one:
% 46.86/14.31  					| (576)  ~ (all_473_2_532 = 0)
% 46.86/14.31  					|
% 46.86/14.31  						| Equations (575) can reduce 576 to:
% 46.86/14.31  						| (500) $false
% 46.86/14.31  						|
% 46.86/14.31  						|-The branch is then unsatisfiable
% 46.86/14.31  					|-Branch two:
% 46.86/14.31  					| (575) all_473_2_532 = 0
% 46.86/14.31  					| (579) all_473_0_530 = one & all_473_1_531 = zero & all_177_0_198 = zero
% 46.86/14.31  					|
% 46.86/14.31  						| Applying alpha-rule on (579) yields:
% 46.86/14.31  						| (580) all_473_0_530 = one
% 46.86/14.31  						| (581) all_473_1_531 = zero
% 46.86/14.31  						| (582) all_177_0_198 = zero
% 46.86/14.31  						|
% 46.86/14.31  						| Combining equations (540,580) yields a new equation:
% 46.86/14.31  						| (583) all_0_2_2 = one
% 46.86/14.31  						|
% 46.86/14.31  						| Simplifying 583 yields:
% 46.86/14.31  						| (584) all_0_2_2 = one
% 46.86/14.31  						|
% 46.86/14.31  						| From (584) and (10) follows:
% 46.86/14.31  						| (585) leq(one, one) = all_0_0_0
% 46.86/14.31  						|
% 46.86/14.31  						| From (584) and (52) follows:
% 46.86/14.31  						| (586) leq(one, one) = all_0_1_1
% 46.86/14.31  						|
% 46.86/14.31  						| From (584) and (548) follows:
% 46.86/14.31  						| (587) addition(one, one) = all_95_0_113
% 46.86/14.31  						|
% 46.86/14.31  						| Instantiating formula (20) with one, one, all_0_1_1, all_0_0_0 and discharging atoms leq(one, one) = all_0_0_0, leq(one, one) = all_0_1_1, yields:
% 46.86/14.31  						| (588) all_0_0_0 = all_0_1_1
% 46.86/14.31  						|
% 46.86/14.31  						| Instantiating formula (21) with all_95_0_113, one and discharging atoms addition(one, one) = all_95_0_113, yields:
% 46.86/14.31  						| (589) all_95_0_113 = one
% 46.86/14.31  						|
% 46.86/14.31  						| From (589) and (587) follows:
% 46.86/14.31  						| (590) addition(one, one) = one
% 46.86/14.31  						|
% 46.86/14.31  						+-Applying beta-rule and splitting (46), into two cases.
% 46.86/14.31  						|-Branch one:
% 46.86/14.31  						| (591)  ~ (all_0_0_0 = 0)
% 46.86/14.31  						|
% 46.86/14.31  							| Equations (588) can reduce 591 to:
% 46.86/14.31  							| (592)  ~ (all_0_1_1 = 0)
% 46.86/14.31  							|
% 46.86/14.31  							+-Applying beta-rule and splitting (57), into two cases.
% 46.86/14.31  							|-Branch one:
% 46.86/14.31  							| (593) all_0_0_0 = 0
% 46.86/14.31  							|
% 46.86/14.31  								| Combining equations (588,593) yields a new equation:
% 46.86/14.31  								| (594) all_0_1_1 = 0
% 46.86/14.31  								|
% 46.86/14.31  								| Simplifying 594 yields:
% 46.86/14.31  								| (595) all_0_1_1 = 0
% 46.86/14.31  								|
% 46.86/14.31  								| Equations (595) can reduce 592 to:
% 46.86/14.31  								| (500) $false
% 46.86/14.31  								|
% 46.86/14.31  								|-The branch is then unsatisfiable
% 46.86/14.31  							|-Branch two:
% 46.86/14.31  							| (591)  ~ (all_0_0_0 = 0)
% 46.86/14.31  							| (598)  ? [v0] : ( ~ (v0 = one) & addition(all_0_2_2, one) = v0)
% 46.86/14.32  							|
% 46.86/14.32  								| Instantiating (598) with all_741_0_723 yields:
% 46.86/14.32  								| (599)  ~ (all_741_0_723 = one) & addition(all_0_2_2, one) = all_741_0_723
% 46.86/14.32  								|
% 46.86/14.32  								| Applying alpha-rule on (599) yields:
% 46.86/14.32  								| (600)  ~ (all_741_0_723 = one)
% 46.86/14.32  								| (601) addition(all_0_2_2, one) = all_741_0_723
% 46.86/14.32  								|
% 46.86/14.32  								| From (584) and (601) follows:
% 46.86/14.32  								| (602) addition(one, one) = all_741_0_723
% 46.86/14.32  								|
% 46.86/14.32  								| Instantiating formula (43) with one, one, one, all_741_0_723 and discharging atoms addition(one, one) = all_741_0_723, addition(one, one) = one, yields:
% 46.86/14.32  								| (603) all_741_0_723 = one
% 46.86/14.32  								|
% 46.86/14.32  								| Equations (603) can reduce 600 to:
% 46.86/14.32  								| (500) $false
% 46.86/14.32  								|
% 46.86/14.32  								|-The branch is then unsatisfiable
% 46.86/14.32  						|-Branch two:
% 46.86/14.32  						| (593) all_0_0_0 = 0
% 46.86/14.32  						| (592)  ~ (all_0_1_1 = 0)
% 46.86/14.32  						|
% 46.86/14.32  							| Combining equations (588,593) yields a new equation:
% 46.86/14.32  							| (594) all_0_1_1 = 0
% 46.86/14.32  							|
% 46.86/14.32  							| Simplifying 594 yields:
% 46.86/14.32  							| (595) all_0_1_1 = 0
% 46.86/14.32  							|
% 46.86/14.32  							| Equations (595) can reduce 592 to:
% 46.86/14.32  							| (500) $false
% 46.86/14.32  							|
% 46.86/14.32  							|-The branch is then unsatisfiable
% 46.86/14.32  % SZS output end Proof for theBenchmark
% 46.86/14.32  
% 46.86/14.32  13696ms
%------------------------------------------------------------------------------