%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE114+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sun Jul 17 01:51:25 EDT 2022

% Result   : Theorem 14.44s 6.31s
% Output   : Proof 17.12s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : KLE114+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n015.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Thu Jun 16 12:20:26 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.57          ____       _                          
% 0.19/0.57    ___  / __ \_____(_)___  ________  __________
% 0.19/0.57   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.57  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.57  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.57  
% 0.19/0.57  A Theorem Prover for First-Order Logic
% 0.19/0.57  (ePrincess v.1.0)
% 0.19/0.57  
% 0.19/0.57  (c) Philipp Rümmer, 2009-2015
% 0.19/0.57  (c) Peter Backeman, 2014-2015
% 0.19/0.57  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.57  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.57  Bug reports to peter@backeman.se
% 0.19/0.57  
% 0.19/0.57  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.57  
% 0.19/0.57  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.62  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.54/0.91  Prover 0: Preprocessing ...
% 2.65/1.24  Prover 0: Constructing countermodel ...
% 12.53/5.92  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 12.53/5.96  Prover 1: Preprocessing ...
% 13.11/6.05  Prover 1: Constructing countermodel ...
% 13.11/6.08  Prover 1: gave up
% 13.11/6.08  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 13.11/6.10  Prover 2: Preprocessing ...
% 13.54/6.16  Prover 2: Warning: ignoring some quantifiers
% 13.54/6.17  Prover 2: Constructing countermodel ...
% 14.44/6.31  Prover 2: proved (230ms)
% 14.44/6.31  Prover 0: stopped
% 14.44/6.31  
% 14.44/6.31  No countermodel exists, formula is valid
% 14.44/6.31  % SZS status Theorem for theBenchmark
% 14.44/6.31  
% 14.44/6.32  Generating proof ... Warning: ignoring some quantifiers
% 16.27/6.80  found it (size 253)
% 16.27/6.80  
% 16.27/6.80  % SZS output start Proof for theBenchmark
% 16.27/6.80  Assumed formulas after preprocessing and simplification: 
% 16.27/6.80  | (0)  ? [v0] :  ? [v1] : ( ~ (v1 = one) & forward_box(v0, one) = v1 &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (multiplication(v3, v4) = v6) |  ~ (multiplication(v2, v4) = v5) |  ~ (addition(v5, v6) = v7) |  ? [v8] : (multiplication(v8, v4) = v7 & addition(v2, v3) = v8)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (multiplication(v2, v4) = v6) |  ~ (multiplication(v2, v3) = v5) |  ~ (addition(v5, v6) = v7) |  ? [v8] : (multiplication(v2, v8) = v7 & addition(v3, v4) = v8)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (coantidomain(v4) = v5) |  ~ (coantidomain(v2) = v4) |  ~ (multiplication(v5, v3) = v6) |  ? [v7] :  ? [v8] :  ? [v9] : (coantidomain(v7) = v8 & coantidomain(v6) = v9 & multiplication(v2, v3) = v7 & addition(v8, v9) = v9)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (domain(v2) = v4) |  ~ (antidomain(v3) = v5) |  ~ (multiplication(v4, v5) = v6) | domain_difference(v2, v3) = v6) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (antidomain(v4) = v5) |  ~ (antidomain(v3) = v4) |  ~ (multiplication(v2, v5) = v6) |  ? [v7] :  ? [v8] :  ? [v9] : (antidomain(v7) = v8 & antidomain(v6) = v9 & multiplication(v2, v3) = v7 & addition(v8, v9) = v9)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v5, v4) = v6) |  ~ (multiplication(v2, v3) = v5) |  ? [v7] : (multiplication(v3, v4) = v7 & multiplication(v2, v7) = v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v5, v4) = v6) |  ~ (addition(v2, v3) = v5) |  ? [v7] :  ? [v8] : (multiplication(v3, v4) = v8 & multiplication(v2, v4) = v7 & addition(v7, v8) = v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v3, v4) = v5) |  ~ (multiplication(v2, v5) = v6) |  ? [v7] : (multiplication(v7, v4) = v6 & multiplication(v2, v3) = v7)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (multiplication(v2, v5) = v6) |  ~ (addition(v3, v4) = v5) |  ? [v7] :  ? [v8] : (multiplication(v2, v4) = v8 & multiplication(v2, v3) = v7 & addition(v7, v8) = v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (addition(v5, v2) = v6) |  ~ (addition(v4, v3) = v5) |  ? [v7] : (addition(v4, v7) = v6 & addition(v3, v2) = v7)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (addition(v4, v5) = v6) |  ~ (addition(v3, v2) = v5) |  ? [v7] : (addition(v7, v2) = v6 & addition(v4, v3) = v7)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (backward_box(v5, v4) = v3) |  ~ (backward_box(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (forward_box(v5, v4) = v3) |  ~ (forward_box(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (backward_diamond(v5, v4) = v3) |  ~ (backward_diamond(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (forward_diamond(v5, v4) = v3) |  ~ (forward_diamond(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (domain_difference(v5, v4) = v3) |  ~ (domain_difference(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (leq(v5, v4) = v3) |  ~ (leq(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (multiplication(v5, v4) = v3) |  ~ (multiplication(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (addition(v5, v4) = v3) |  ~ (addition(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (backward_diamond(v2, v4) = v5) |  ~ (c(v3) = v4) |  ? [v6] : (backward_box(v2, v3) = v6 & c(v5) = v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (forward_diamond(v2, v4) = v5) |  ~ (c(v3) = v4) |  ? [v6] : (forward_box(v2, v3) = v6 & c(v5) = v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (codomain(v3) = v4) |  ~ (multiplication(v4, v2) = v5) |  ? [v6] : (backward_diamond(v2, v3) = v6 & codomain(v5) = v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (domain(v3) = v4) |  ~ (multiplication(v2, v4) = v5) |  ? [v6] : (forward_diamond(v2, v3) = v6 & domain(v5) = v6)) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (addition(v2, v3) = v4) |  ? [v5] : ( ~ (v5 = 0) & leq(v2, v3) = v5)) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (leq(v2, v3) = v4) |  ? [v5] : ( ~ (v5 = v3) & addition(v2, v3) = v5)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (c(v4) = v3) |  ~ (c(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (codomain(v4) = v3) |  ~ (codomain(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (coantidomain(v4) = v3) |  ~ (coantidomain(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (domain(v4) = v3) |  ~ (domain(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (antidomain(v4) = v3) |  ~ (antidomain(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (backward_box(v2, v3) = v4) |  ? [v5] :  ? [v6] : (backward_diamond(v2, v5) = v6 & c(v6) = v4 & c(v3) = v5)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (forward_box(v2, v3) = v4) |  ? [v5] :  ? [v6] : (forward_diamond(v2, v5) = v6 & c(v6) = v4 & c(v3) = v5)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (backward_diamond(v2, v3) = v4) |  ? [v5] :  ? [v6] : (codomain(v6) = v4 & codomain(v3) = v5 & multiplication(v5, v2) = v6)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (forward_diamond(v2, v3) = v4) |  ? [v5] :  ? [v6] : (domain(v6) = v4 & domain(v3) = v5 & multiplication(v2, v5) = v6)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (domain_difference(v2, v3) = v4) |  ? [v5] :  ? [v6] : (domain(v2) = v5 & antidomain(v3) = v6 & multiplication(v5, v6) = v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (coantidomain(v8) = v9 & coantidomain(v6) = v7 & coantidomain(v4) = v5 & coantidomain(v2) = v6 & multiplication(v7, v3) = v8 & addition(v5, v9) = v9)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (antidomain(v8) = v9 & antidomain(v6) = v7 & antidomain(v4) = v5 & antidomain(v3) = v6 & multiplication(v2, v7) = v8 & addition(v5, v9) = v9)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v2) = v4) | addition(v2, v3) = v4) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) | addition(v3, v2) = v4) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (multiplication(v2, one) = v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (multiplication(one, v2) = v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (addition(v2, v2) = v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (addition(v2, zero) = v3)) &  ! [v2] :  ! [v3] : (v3 = zero |  ~ (multiplication(v2, zero) = v3)) &  ! [v2] :  ! [v3] : (v3 = zero |  ~ (multiplication(zero, v2) = v3)) &  ! [v2] :  ! [v3] : ( ~ (c(v2) = v3) |  ? [v4] : (domain(v2) = v4 & antidomain(v4) = v3)) &  ! [v2] :  ! [v3] : ( ~ (codomain(v2) = v3) |  ? [v4] : (coantidomain(v4) = v3 & coantidomain(v2) = v4)) &  ! [v2] :  ! [v3] : ( ~ (coantidomain(v2) = v3) | multiplication(v2, v3) = zero) &  ! [v2] :  ! [v3] : ( ~ (coantidomain(v2) = v3) |  ? [v4] : (codomain(v2) = v4 & coantidomain(v3) = v4)) &  ! [v2] :  ! [v3] : ( ~ (coantidomain(v2) = v3) |  ? [v4] : (coantidomain(v3) = v4 & addition(v4, v3) = one)) &  ! [v2] :  ! [v3] : ( ~ (domain(v2) = v3) |  ? [v4] : (c(v2) = v4 & antidomain(v3) = v4)) &  ! [v2] :  ! [v3] : ( ~ (domain(v2) = v3) |  ? [v4] : (antidomain(v4) = v3 & antidomain(v2) = v4)) &  ! [v2] :  ! [v3] : ( ~ (antidomain(v2) = v3) | multiplication(v3, v2) = zero) &  ! [v2] :  ! [v3] : ( ~ (antidomain(v2) = v3) |  ? [v4] : (domain(v2) = v4 & antidomain(v3) = v4)) &  ! [v2] :  ! [v3] : ( ~ (antidomain(v2) = v3) |  ? [v4] : (antidomain(v3) = v4 & addition(v4, v3) = one)) &  ! [v2] :  ! [v3] : ( ~ (leq(v2, v3) = 0) | addition(v2, v3) = v3) &  ! [v2] :  ! [v3] : ( ~ (addition(v2, v3) = v3) | leq(v2, v3) = 0) &  ? [v2] :  ? [v3] :  ? [v4] : backward_box(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : forward_box(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : backward_diamond(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : forward_diamond(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : domain_difference(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : leq(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : multiplication(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : addition(v3, v2) = v4 &  ? [v2] :  ? [v3] : c(v2) = v3 &  ? [v2] :  ? [v3] : codomain(v2) = v3 &  ? [v2] :  ? [v3] : coantidomain(v2) = v3 &  ? [v2] :  ? [v3] : domain(v2) = v3 &  ? [v2] :  ? [v3] : antidomain(v2) = v3)
% 16.66/6.85  | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 16.66/6.85  | (1)  ~ (all_0_0_0 = one) & forward_box(all_0_1_1, one) = all_0_0_0 &  ! [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] : ( ~ (coantidomain(v2) = v3) |  ~ (coantidomain(v0) = v2) |  ~ (multiplication(v3, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (coantidomain(v5) = v6 & coantidomain(v4) = v7 & multiplication(v0, v1) = v5 & addition(v6, v7) = v7)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (domain(v0) = v2) |  ~ (antidomain(v1) = v3) |  ~ (multiplication(v2, v3) = v4) | domain_difference(v0, v1) = v4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (antidomain(v2) = v3) |  ~ (antidomain(v1) = v2) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (antidomain(v5) = v6 & antidomain(v4) = v7 & multiplication(v0, v1) = v5 & addition(v6, v7) = v7)) &  ! [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 |  ~ (backward_box(v3, v2) = v1) |  ~ (backward_box(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (forward_box(v3, v2) = v1) |  ~ (forward_box(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (backward_diamond(v3, v2) = v1) |  ~ (backward_diamond(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (forward_diamond(v3, v2) = v1) |  ~ (forward_diamond(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (domain_difference(v3, v2) = v1) |  ~ (domain_difference(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] :  ! [v3] : ( ~ (backward_diamond(v0, v2) = v3) |  ~ (c(v1) = v2) |  ? [v4] : (backward_box(v0, v1) = v4 & c(v3) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (forward_diamond(v0, v2) = v3) |  ~ (c(v1) = v2) |  ? [v4] : (forward_box(v0, v1) = v4 & c(v3) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (codomain(v1) = v2) |  ~ (multiplication(v2, v0) = v3) |  ? [v4] : (backward_diamond(v0, v1) = v4 & codomain(v3) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (domain(v1) = v2) |  ~ (multiplication(v0, v2) = v3) |  ? [v4] : (forward_diamond(v0, v1) = v4 & domain(v3) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (c(v2) = v1) |  ~ (c(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (codomain(v2) = v1) |  ~ (codomain(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (coantidomain(v2) = v1) |  ~ (coantidomain(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (antidomain(v2) = v1) |  ~ (antidomain(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (backward_box(v0, v1) = v2) |  ? [v3] :  ? [v4] : (backward_diamond(v0, v3) = v4 & c(v4) = v2 & c(v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (forward_box(v0, v1) = v2) |  ? [v3] :  ? [v4] : (forward_diamond(v0, v3) = v4 & c(v4) = v2 & c(v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (backward_diamond(v0, v1) = v2) |  ? [v3] :  ? [v4] : (codomain(v4) = v2 & codomain(v1) = v3 & multiplication(v3, v0) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (forward_diamond(v0, v1) = v2) |  ? [v3] :  ? [v4] : (domain(v4) = v2 & domain(v1) = v3 & multiplication(v0, v3) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (domain_difference(v0, v1) = v2) |  ? [v3] :  ? [v4] : (domain(v0) = v3 & antidomain(v1) = v4 & multiplication(v3, v4) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (coantidomain(v6) = v7 & coantidomain(v4) = v5 & coantidomain(v2) = v3 & coantidomain(v0) = v4 & multiplication(v5, v1) = v6 & addition(v3, v7) = v7)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (antidomain(v6) = v7 & antidomain(v4) = v5 & antidomain(v2) = v3 & antidomain(v1) = v4 & multiplication(v0, v5) = v6 & addition(v3, v7) = v7)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1)) &  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1)) &  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (c(v0) = v1) |  ? [v2] : (domain(v0) = v2 & antidomain(v2) = v1)) &  ! [v0] :  ! [v1] : ( ~ (codomain(v0) = v1) |  ? [v2] : (coantidomain(v2) = v1 & coantidomain(v0) = v2)) &  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) | multiplication(v0, v1) = zero) &  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) |  ? [v2] : (codomain(v0) = v2 & coantidomain(v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) |  ? [v2] : (coantidomain(v1) = v2 & addition(v2, v1) = one)) &  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) |  ? [v2] : (c(v0) = v2 & antidomain(v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) |  ? [v2] : (antidomain(v2) = v1 & antidomain(v0) = v2)) &  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) | multiplication(v1, v0) = zero) &  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) |  ? [v2] : (domain(v0) = v2 & antidomain(v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) |  ? [v2] : (antidomain(v1) = v2 & addition(v2, v1) = one)) &  ! [v0] :  ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) &  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) &  ? [v0] :  ? [v1] :  ? [v2] : backward_box(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : forward_box(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : backward_diamond(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : forward_diamond(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : domain_difference(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : leq(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : multiplication(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : addition(v1, v0) = v2 &  ? [v0] :  ? [v1] : c(v0) = v1 &  ? [v0] :  ? [v1] : codomain(v0) = v1 &  ? [v0] :  ? [v1] : coantidomain(v0) = v1 &  ? [v0] :  ? [v1] : domain(v0) = v1 &  ? [v0] :  ? [v1] : antidomain(v0) = v1
% 16.66/6.86  |
% 16.66/6.86  | Applying alpha-rule on (1) yields:
% 16.66/6.86  | (2)  ? [v0] :  ? [v1] :  ? [v2] : forward_diamond(v1, v0) = v2
% 16.66/6.86  | (3)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (domain_difference(v0, v1) = v2) |  ? [v3] :  ? [v4] : (domain(v0) = v3 & antidomain(v1) = v4 & multiplication(v3, v4) = v2))
% 16.66/6.86  | (4)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1))
% 16.66/6.86  | (5)  ? [v0] :  ? [v1] : coantidomain(v0) = v1
% 16.66/6.86  | (6)  ? [v0] :  ? [v1] :  ? [v2] : backward_box(v1, v0) = v2
% 16.66/6.86  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 16.66/6.86  | (8)  ? [v0] :  ? [v1] : c(v0) = v1
% 16.66/6.86  | (9)  ? [v0] :  ? [v1] :  ? [v2] : backward_diamond(v1, v0) = v2
% 16.66/6.86  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (forward_box(v3, v2) = v1) |  ~ (forward_box(v3, v2) = v0))
% 16.66/6.86  | (11)  ! [v0] :  ! [v1] : ( ~ (codomain(v0) = v1) |  ? [v2] : (coantidomain(v2) = v1 & coantidomain(v0) = v2))
% 16.66/6.86  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 16.66/6.86  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (backward_diamond(v0, v2) = v3) |  ~ (c(v1) = v2) |  ? [v4] : (backward_box(v0, v1) = v4 & c(v3) = v4))
% 16.66/6.86  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 16.66/6.86  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 16.66/6.86  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 16.66/6.87  | (17)  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) | multiplication(v1, v0) = zero)
% 16.66/6.87  | (18)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0))
% 16.66/6.87  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (domain_difference(v3, v2) = v1) |  ~ (domain_difference(v3, v2) = v0))
% 16.66/6.87  | (20)  ? [v0] :  ? [v1] : domain(v0) = v1
% 16.66/6.87  | (21)  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) |  ? [v2] : (coantidomain(v1) = v2 & addition(v2, v1) = one))
% 16.66/6.87  | (22)  ~ (all_0_0_0 = one)
% 16.66/6.87  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (backward_box(v3, v2) = v1) |  ~ (backward_box(v3, v2) = v0))
% 16.66/6.87  | (24)  ! [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))
% 16.66/6.87  | (25)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 16.66/6.87  | (26)  ? [v0] :  ? [v1] :  ? [v2] : multiplication(v1, v0) = v2
% 16.66/6.87  | (27)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (antidomain(v6) = v7 & antidomain(v4) = v5 & antidomain(v2) = v3 & antidomain(v1) = v4 & multiplication(v0, v5) = v6 & addition(v3, v7) = v7))
% 16.66/6.87  | (28)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 16.66/6.87  | (29)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 16.66/6.87  | (30)  ? [v0] :  ? [v1] :  ? [v2] : domain_difference(v1, v0) = v2
% 16.66/6.87  | (31)  ! [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))
% 16.66/6.87  | (32)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (antidomain(v2) = v1) |  ~ (antidomain(v2) = v0))
% 16.66/6.87  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 16.66/6.87  | (34)  ? [v0] :  ? [v1] : codomain(v0) = v1
% 16.66/6.87  | (35)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (forward_box(v0, v1) = v2) |  ? [v3] :  ? [v4] : (forward_diamond(v0, v3) = v4 & c(v4) = v2 & c(v1) = v3))
% 16.66/6.87  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (forward_diamond(v0, v2) = v3) |  ~ (c(v1) = v2) |  ? [v4] : (forward_box(v0, v1) = v4 & c(v3) = v4))
% 16.66/6.87  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (codomain(v1) = v2) |  ~ (multiplication(v2, v0) = v3) |  ? [v4] : (backward_diamond(v0, v1) = v4 & codomain(v3) = v4))
% 16.66/6.87  | (38)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (backward_diamond(v3, v2) = v1) |  ~ (backward_diamond(v3, v2) = v0))
% 16.66/6.87  | (39)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0)
% 16.66/6.87  | (40)  ! [v0] :  ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 16.66/6.87  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (forward_diamond(v3, v2) = v1) |  ~ (forward_diamond(v3, v2) = v0))
% 16.66/6.87  | (42)  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) |  ? [v2] : (codomain(v0) = v2 & coantidomain(v1) = v2))
% 16.66/6.87  | (43)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (coantidomain(v2) = v1) |  ~ (coantidomain(v2) = v0))
% 16.66/6.87  | (44)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (backward_box(v0, v1) = v2) |  ? [v3] :  ? [v4] : (backward_diamond(v0, v3) = v4 & c(v4) = v2 & c(v1) = v3))
% 16.66/6.87  | (45)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 16.66/6.87  | (46) forward_box(all_0_1_1, one) = all_0_0_0
% 16.66/6.87  | (47)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 16.66/6.87  | (48)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (forward_diamond(v0, v1) = v2) |  ? [v3] :  ? [v4] : (domain(v4) = v2 & domain(v1) = v3 & multiplication(v0, v3) = v4))
% 16.66/6.87  | (49)  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) |  ? [v2] : (antidomain(v1) = v2 & addition(v2, v1) = one))
% 16.66/6.87  | (50)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (c(v2) = v1) |  ~ (c(v2) = v0))
% 16.66/6.87  | (51)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 16.66/6.87  | (52)  ! [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))
% 16.66/6.87  | (53)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 16.66/6.87  | (54)  ! [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))
% 16.66/6.87  | (55)  ? [v0] :  ? [v1] :  ? [v2] : addition(v1, v0) = v2
% 16.66/6.87  | (56)  ? [v0] :  ? [v1] : antidomain(v0) = v1
% 16.66/6.87  | (57)  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) |  ? [v2] : (domain(v0) = v2 & antidomain(v1) = v2))
% 16.66/6.87  | (58)  ? [v0] :  ? [v1] :  ? [v2] : leq(v1, v0) = v2
% 16.66/6.87  | (59)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 16.66/6.87  | (60)  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) |  ? [v2] : (c(v0) = v2 & antidomain(v1) = v2))
% 16.66/6.87  | (61)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (coantidomain(v2) = v3) |  ~ (coantidomain(v0) = v2) |  ~ (multiplication(v3, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (coantidomain(v5) = v6 & coantidomain(v4) = v7 & multiplication(v0, v1) = v5 & addition(v6, v7) = v7))
% 16.66/6.87  | (62)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (domain(v0) = v2) |  ~ (antidomain(v1) = v3) |  ~ (multiplication(v2, v3) = v4) | domain_difference(v0, v1) = v4)
% 16.66/6.87  | (63)  ? [v0] :  ? [v1] :  ? [v2] : forward_box(v1, v0) = v2
% 16.66/6.87  | (64)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (backward_diamond(v0, v1) = v2) |  ? [v3] :  ? [v4] : (codomain(v4) = v2 & codomain(v1) = v3 & multiplication(v3, v0) = v4))
% 16.66/6.87  | (65)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (multiplication(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (coantidomain(v6) = v7 & coantidomain(v4) = v5 & coantidomain(v2) = v3 & coantidomain(v0) = v4 & multiplication(v5, v1) = v6 & addition(v3, v7) = v7))
% 16.66/6.88  | (66)  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) |  ? [v2] : (antidomain(v2) = v1 & antidomain(v0) = v2))
% 16.66/6.88  | (67)  ! [v0] :  ! [v1] : ( ~ (c(v0) = v1) |  ? [v2] : (domain(v0) = v2 & antidomain(v2) = v1))
% 16.66/6.88  | (68)  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) | multiplication(v0, v1) = zero)
% 16.66/6.88  | (69)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (antidomain(v2) = v3) |  ~ (antidomain(v1) = v2) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (antidomain(v5) = v6 & antidomain(v4) = v7 & multiplication(v0, v1) = v5 & addition(v6, v7) = v7))
% 16.66/6.88  | (70)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 16.66/6.88  | (71)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (domain(v1) = v2) |  ~ (multiplication(v0, v2) = v3) |  ? [v4] : (forward_diamond(v0, v1) = v4 & domain(v3) = v4))
% 16.66/6.88  | (72)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (codomain(v2) = v1) |  ~ (codomain(v2) = v0))
% 16.66/6.88  | (73)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (35) with all_0_0_0, one, all_0_1_1 and discharging atoms forward_box(all_0_1_1, one) = all_0_0_0, yields:
% 16.66/6.88  | (74)  ? [v0] :  ? [v1] : (forward_diamond(all_0_1_1, v0) = v1 & c(v1) = all_0_0_0 & c(one) = v0)
% 16.66/6.88  |
% 16.66/6.88  | Instantiating (74) with all_34_0_36, all_34_1_37 yields:
% 16.66/6.88  | (75) forward_diamond(all_0_1_1, all_34_1_37) = all_34_0_36 & c(all_34_0_36) = all_0_0_0 & c(one) = all_34_1_37
% 16.66/6.88  |
% 16.66/6.88  | Applying alpha-rule on (75) yields:
% 16.66/6.88  | (76) forward_diamond(all_0_1_1, all_34_1_37) = all_34_0_36
% 16.66/6.88  | (77) c(all_34_0_36) = all_0_0_0
% 16.66/6.88  | (78) c(one) = all_34_1_37
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (48) with all_34_0_36, all_34_1_37, all_0_1_1 and discharging atoms forward_diamond(all_0_1_1, all_34_1_37) = all_34_0_36, yields:
% 16.66/6.88  | (79)  ? [v0] :  ? [v1] : (domain(v1) = all_34_0_36 & domain(all_34_1_37) = v0 & multiplication(all_0_1_1, v0) = v1)
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (67) with all_0_0_0, all_34_0_36 and discharging atoms c(all_34_0_36) = all_0_0_0, yields:
% 16.66/6.88  | (80)  ? [v0] : (domain(all_34_0_36) = v0 & antidomain(v0) = all_0_0_0)
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (67) with all_34_1_37, one and discharging atoms c(one) = all_34_1_37, yields:
% 16.66/6.88  | (81)  ? [v0] : (domain(one) = v0 & antidomain(v0) = all_34_1_37)
% 16.66/6.88  |
% 16.66/6.88  | Instantiating (81) with all_41_0_38 yields:
% 16.66/6.88  | (82) domain(one) = all_41_0_38 & antidomain(all_41_0_38) = all_34_1_37
% 16.66/6.88  |
% 16.66/6.88  | Applying alpha-rule on (82) yields:
% 16.66/6.88  | (83) domain(one) = all_41_0_38
% 16.66/6.88  | (84) antidomain(all_41_0_38) = all_34_1_37
% 16.66/6.88  |
% 16.66/6.88  | Instantiating (80) with all_43_0_39 yields:
% 16.66/6.88  | (85) domain(all_34_0_36) = all_43_0_39 & antidomain(all_43_0_39) = all_0_0_0
% 16.66/6.88  |
% 16.66/6.88  | Applying alpha-rule on (85) yields:
% 16.66/6.88  | (86) domain(all_34_0_36) = all_43_0_39
% 16.66/6.88  | (87) antidomain(all_43_0_39) = all_0_0_0
% 16.66/6.88  |
% 16.66/6.88  | Instantiating (79) with all_45_0_40, all_45_1_41 yields:
% 16.66/6.88  | (88) domain(all_45_0_40) = all_34_0_36 & domain(all_34_1_37) = all_45_1_41 & multiplication(all_0_1_1, all_45_1_41) = all_45_0_40
% 16.66/6.88  |
% 16.66/6.88  | Applying alpha-rule on (88) yields:
% 16.66/6.88  | (89) domain(all_45_0_40) = all_34_0_36
% 16.66/6.88  | (90) domain(all_34_1_37) = all_45_1_41
% 16.66/6.88  | (91) multiplication(all_0_1_1, all_45_1_41) = all_45_0_40
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (60) with all_34_0_36, all_45_0_40 and discharging atoms domain(all_45_0_40) = all_34_0_36, yields:
% 16.66/6.88  | (92)  ? [v0] : (c(all_45_0_40) = v0 & antidomain(all_34_0_36) = v0)
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (66) with all_34_0_36, all_45_0_40 and discharging atoms domain(all_45_0_40) = all_34_0_36, yields:
% 16.66/6.88  | (93)  ? [v0] : (antidomain(v0) = all_34_0_36 & antidomain(all_45_0_40) = v0)
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (66) with all_43_0_39, all_34_0_36 and discharging atoms domain(all_34_0_36) = all_43_0_39, yields:
% 16.66/6.88  | (94)  ? [v0] : (antidomain(v0) = all_43_0_39 & antidomain(all_34_0_36) = v0)
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (60) with all_45_1_41, all_34_1_37 and discharging atoms domain(all_34_1_37) = all_45_1_41, yields:
% 16.66/6.88  | (95)  ? [v0] : (c(all_34_1_37) = v0 & antidomain(all_45_1_41) = v0)
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (66) with all_45_1_41, all_34_1_37 and discharging atoms domain(all_34_1_37) = all_45_1_41, yields:
% 16.66/6.88  | (96)  ? [v0] : (antidomain(v0) = all_45_1_41 & antidomain(all_34_1_37) = v0)
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (66) with all_41_0_38, one and discharging atoms domain(one) = all_41_0_38, yields:
% 16.66/6.88  | (97)  ? [v0] : (antidomain(v0) = all_41_0_38 & antidomain(one) = v0)
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (17) with all_0_0_0, all_43_0_39 and discharging atoms antidomain(all_43_0_39) = all_0_0_0, yields:
% 16.66/6.88  | (98) multiplication(all_0_0_0, all_43_0_39) = zero
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (57) with all_0_0_0, all_43_0_39 and discharging atoms antidomain(all_43_0_39) = all_0_0_0, yields:
% 16.66/6.88  | (99)  ? [v0] : (domain(all_43_0_39) = v0 & antidomain(all_0_0_0) = v0)
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (49) with all_0_0_0, all_43_0_39 and discharging atoms antidomain(all_43_0_39) = all_0_0_0, yields:
% 16.66/6.88  | (100)  ? [v0] : (antidomain(all_0_0_0) = v0 & addition(v0, all_0_0_0) = one)
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (17) with all_34_1_37, all_41_0_38 and discharging atoms antidomain(all_41_0_38) = all_34_1_37, yields:
% 16.66/6.88  | (101) multiplication(all_34_1_37, all_41_0_38) = zero
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (57) with all_34_1_37, all_41_0_38 and discharging atoms antidomain(all_41_0_38) = all_34_1_37, yields:
% 16.66/6.88  | (102)  ? [v0] : (domain(all_41_0_38) = v0 & antidomain(all_34_1_37) = v0)
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (49) with all_34_1_37, all_41_0_38 and discharging atoms antidomain(all_41_0_38) = all_34_1_37, yields:
% 16.66/6.88  | (103)  ? [v0] : (antidomain(all_34_1_37) = v0 & addition(v0, all_34_1_37) = one)
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (65) with all_45_0_40, all_45_1_41, all_0_1_1 and discharging atoms multiplication(all_0_1_1, all_45_1_41) = all_45_0_40, yields:
% 16.66/6.88  | (104)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (coantidomain(v3) = v4 & coantidomain(v1) = v2 & coantidomain(all_45_0_40) = v0 & coantidomain(all_0_1_1) = v1 & multiplication(v2, all_45_1_41) = v3 & addition(v0, v4) = v4)
% 16.66/6.88  |
% 16.66/6.88  | Instantiating formula (27) with all_45_0_40, all_45_1_41, all_0_1_1 and discharging atoms multiplication(all_0_1_1, all_45_1_41) = all_45_0_40, yields:
% 16.66/6.88  | (105)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (antidomain(v3) = v4 & antidomain(v1) = v2 & antidomain(all_45_0_40) = v0 & antidomain(all_45_1_41) = v1 & multiplication(all_0_1_1, v2) = v3 & addition(v0, v4) = v4)
% 16.66/6.88  |
% 16.66/6.89  | Instantiating (99) with all_53_0_42 yields:
% 16.66/6.89  | (106) domain(all_43_0_39) = all_53_0_42 & antidomain(all_0_0_0) = all_53_0_42
% 16.66/6.89  |
% 16.66/6.89  | Applying alpha-rule on (106) yields:
% 16.66/6.89  | (107) domain(all_43_0_39) = all_53_0_42
% 16.66/6.89  | (108) antidomain(all_0_0_0) = all_53_0_42
% 16.66/6.89  |
% 16.66/6.89  | Instantiating (105) with all_55_0_43, all_55_1_44, all_55_2_45, all_55_3_46, all_55_4_47 yields:
% 16.66/6.89  | (109) antidomain(all_55_1_44) = all_55_0_43 & antidomain(all_55_3_46) = all_55_2_45 & antidomain(all_45_0_40) = all_55_4_47 & antidomain(all_45_1_41) = all_55_3_46 & multiplication(all_0_1_1, all_55_2_45) = all_55_1_44 & addition(all_55_4_47, all_55_0_43) = all_55_0_43
% 16.66/6.89  |
% 16.66/6.89  | Applying alpha-rule on (109) yields:
% 16.66/6.89  | (110) multiplication(all_0_1_1, all_55_2_45) = all_55_1_44
% 16.66/6.89  | (111) antidomain(all_45_0_40) = all_55_4_47
% 16.66/6.89  | (112) addition(all_55_4_47, all_55_0_43) = all_55_0_43
% 16.66/6.89  | (113) antidomain(all_45_1_41) = all_55_3_46
% 16.66/6.89  | (114) antidomain(all_55_3_46) = all_55_2_45
% 16.66/6.89  | (115) antidomain(all_55_1_44) = all_55_0_43
% 16.66/6.89  |
% 16.66/6.89  | Instantiating (100) with all_57_0_48 yields:
% 16.66/6.89  | (116) antidomain(all_0_0_0) = all_57_0_48 & addition(all_57_0_48, all_0_0_0) = one
% 16.66/6.89  |
% 16.66/6.89  | Applying alpha-rule on (116) yields:
% 16.66/6.89  | (117) antidomain(all_0_0_0) = all_57_0_48
% 16.66/6.89  | (118) addition(all_57_0_48, all_0_0_0) = one
% 16.66/6.89  |
% 16.66/6.89  | Instantiating (95) with all_59_0_49 yields:
% 16.66/6.89  | (119) c(all_34_1_37) = all_59_0_49 & antidomain(all_45_1_41) = all_59_0_49
% 16.66/6.89  |
% 16.66/6.89  | Applying alpha-rule on (119) yields:
% 16.66/6.89  | (120) c(all_34_1_37) = all_59_0_49
% 16.66/6.89  | (121) antidomain(all_45_1_41) = all_59_0_49
% 16.66/6.89  |
% 16.66/6.89  | Instantiating (93) with all_61_0_50 yields:
% 16.66/6.89  | (122) antidomain(all_61_0_50) = all_34_0_36 & antidomain(all_45_0_40) = all_61_0_50
% 16.66/6.89  |
% 16.66/6.89  | Applying alpha-rule on (122) yields:
% 16.66/6.89  | (123) antidomain(all_61_0_50) = all_34_0_36
% 16.66/6.89  | (124) antidomain(all_45_0_40) = all_61_0_50
% 16.66/6.89  |
% 16.66/6.89  | Instantiating (92) with all_63_0_51 yields:
% 16.66/6.89  | (125) c(all_45_0_40) = all_63_0_51 & antidomain(all_34_0_36) = all_63_0_51
% 16.66/6.89  |
% 16.66/6.89  | Applying alpha-rule on (125) yields:
% 16.66/6.89  | (126) c(all_45_0_40) = all_63_0_51
% 16.66/6.89  | (127) antidomain(all_34_0_36) = all_63_0_51
% 16.66/6.89  |
% 16.66/6.89  | Instantiating (104) with all_65_0_52, all_65_1_53, all_65_2_54, all_65_3_55, all_65_4_56 yields:
% 16.66/6.89  | (128) coantidomain(all_65_1_53) = all_65_0_52 & coantidomain(all_65_3_55) = all_65_2_54 & coantidomain(all_45_0_40) = all_65_4_56 & coantidomain(all_0_1_1) = all_65_3_55 & multiplication(all_65_2_54, all_45_1_41) = all_65_1_53 & addition(all_65_4_56, all_65_0_52) = all_65_0_52
% 16.66/6.89  |
% 16.66/6.89  | Applying alpha-rule on (128) yields:
% 16.66/6.89  | (129) addition(all_65_4_56, all_65_0_52) = all_65_0_52
% 16.66/6.89  | (130) coantidomain(all_65_3_55) = all_65_2_54
% 16.66/6.89  | (131) coantidomain(all_45_0_40) = all_65_4_56
% 16.66/6.89  | (132) multiplication(all_65_2_54, all_45_1_41) = all_65_1_53
% 16.66/6.89  | (133) coantidomain(all_0_1_1) = all_65_3_55
% 16.66/6.89  | (134) coantidomain(all_65_1_53) = all_65_0_52
% 16.66/6.89  |
% 16.66/6.89  | Instantiating (94) with all_67_0_57 yields:
% 16.66/6.89  | (135) antidomain(all_67_0_57) = all_43_0_39 & antidomain(all_34_0_36) = all_67_0_57
% 16.66/6.89  |
% 16.66/6.89  | Applying alpha-rule on (135) yields:
% 16.66/6.89  | (136) antidomain(all_67_0_57) = all_43_0_39
% 16.66/6.89  | (137) antidomain(all_34_0_36) = all_67_0_57
% 16.66/6.89  |
% 16.66/6.89  | Instantiating (103) with all_69_0_58 yields:
% 16.66/6.89  | (138) antidomain(all_34_1_37) = all_69_0_58 & addition(all_69_0_58, all_34_1_37) = one
% 16.66/6.89  |
% 16.66/6.89  | Applying alpha-rule on (138) yields:
% 16.66/6.89  | (139) antidomain(all_34_1_37) = all_69_0_58
% 16.66/6.89  | (140) addition(all_69_0_58, all_34_1_37) = one
% 16.66/6.89  |
% 16.66/6.89  | Instantiating (102) with all_71_0_59 yields:
% 16.66/6.89  | (141) domain(all_41_0_38) = all_71_0_59 & antidomain(all_34_1_37) = all_71_0_59
% 16.66/6.89  |
% 16.66/6.89  | Applying alpha-rule on (141) yields:
% 16.66/6.89  | (142) domain(all_41_0_38) = all_71_0_59
% 16.66/6.89  | (143) antidomain(all_34_1_37) = all_71_0_59
% 16.66/6.89  |
% 16.66/6.89  | Instantiating (97) with all_73_0_60 yields:
% 16.66/6.89  | (144) antidomain(all_73_0_60) = all_41_0_38 & antidomain(one) = all_73_0_60
% 16.66/6.89  |
% 16.66/6.89  | Applying alpha-rule on (144) yields:
% 16.66/6.89  | (145) antidomain(all_73_0_60) = all_41_0_38
% 16.66/6.89  | (146) antidomain(one) = all_73_0_60
% 16.66/6.89  |
% 16.66/6.89  | Instantiating (96) with all_75_0_61 yields:
% 16.66/6.89  | (147) antidomain(all_75_0_61) = all_45_1_41 & antidomain(all_34_1_37) = all_75_0_61
% 16.66/6.89  |
% 16.66/6.89  | Applying alpha-rule on (147) yields:
% 16.66/6.89  | (148) antidomain(all_75_0_61) = all_45_1_41
% 16.66/6.89  | (149) antidomain(all_34_1_37) = all_75_0_61
% 16.66/6.89  |
% 16.66/6.89  | Instantiating formula (32) with all_45_0_40, all_55_4_47, all_61_0_50 and discharging atoms antidomain(all_45_0_40) = all_61_0_50, antidomain(all_45_0_40) = all_55_4_47, yields:
% 16.66/6.89  | (150) all_61_0_50 = all_55_4_47
% 16.66/6.89  |
% 16.66/6.89  | Instantiating formula (32) with all_45_1_41, all_55_3_46, all_59_0_49 and discharging atoms antidomain(all_45_1_41) = all_59_0_49, antidomain(all_45_1_41) = all_55_3_46, yields:
% 16.66/6.89  | (151) all_59_0_49 = all_55_3_46
% 16.66/6.89  |
% 16.66/6.89  | Instantiating formula (32) with all_34_0_36, all_63_0_51, all_67_0_57 and discharging atoms antidomain(all_34_0_36) = all_67_0_57, antidomain(all_34_0_36) = all_63_0_51, yields:
% 16.66/6.89  | (152) all_67_0_57 = all_63_0_51
% 16.66/6.89  |
% 16.66/6.89  | Instantiating formula (32) with all_34_1_37, all_71_0_59, all_75_0_61 and discharging atoms antidomain(all_34_1_37) = all_75_0_61, antidomain(all_34_1_37) = all_71_0_59, yields:
% 16.66/6.89  | (153) all_75_0_61 = all_71_0_59
% 16.66/6.89  |
% 16.66/6.89  | Instantiating formula (32) with all_34_1_37, all_69_0_58, all_75_0_61 and discharging atoms antidomain(all_34_1_37) = all_75_0_61, antidomain(all_34_1_37) = all_69_0_58, yields:
% 16.66/6.89  | (154) all_75_0_61 = all_69_0_58
% 16.66/6.89  |
% 16.66/6.89  | Instantiating formula (32) with all_0_0_0, all_53_0_42, all_57_0_48 and discharging atoms antidomain(all_0_0_0) = all_57_0_48, antidomain(all_0_0_0) = all_53_0_42, yields:
% 16.66/6.89  | (155) all_57_0_48 = all_53_0_42
% 16.66/6.89  |
% 16.66/6.89  | Combining equations (153,154) yields a new equation:
% 16.66/6.89  | (156) all_71_0_59 = all_69_0_58
% 16.66/6.89  |
% 16.66/6.89  | Simplifying 156 yields:
% 16.66/6.89  | (157) all_71_0_59 = all_69_0_58
% 16.66/6.89  |
% 16.66/6.89  | From (151) and (120) follows:
% 16.66/6.89  | (158) c(all_34_1_37) = all_55_3_46
% 16.66/6.89  |
% 16.66/6.89  | From (157) and (142) follows:
% 16.66/6.89  | (159) domain(all_41_0_38) = all_69_0_58
% 16.66/6.89  |
% 16.66/6.89  | From (154) and (148) follows:
% 16.66/6.89  | (160) antidomain(all_69_0_58) = all_45_1_41
% 16.66/6.89  |
% 16.66/6.89  | From (152) and (136) follows:
% 16.66/6.89  | (161) antidomain(all_63_0_51) = all_43_0_39
% 16.66/6.89  |
% 16.66/6.89  | From (150) and (124) follows:
% 16.66/6.89  | (111) antidomain(all_45_0_40) = all_55_4_47
% 16.66/6.89  |
% 16.66/6.89  | From (151) and (121) follows:
% 16.66/6.89  | (113) antidomain(all_45_1_41) = all_55_3_46
% 16.66/6.89  |
% 16.66/6.89  | From (157) and (143) follows:
% 16.66/6.89  | (139) antidomain(all_34_1_37) = all_69_0_58
% 16.66/6.89  |
% 16.66/6.89  | From (155) and (118) follows:
% 16.66/6.89  | (165) addition(all_53_0_42, all_0_0_0) = one
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (60) with all_69_0_58, all_41_0_38 and discharging atoms domain(all_41_0_38) = all_69_0_58, yields:
% 16.66/6.90  | (166)  ? [v0] : (c(all_41_0_38) = v0 & antidomain(all_69_0_58) = v0)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (57) with all_41_0_38, all_73_0_60 and discharging atoms antidomain(all_73_0_60) = all_41_0_38, yields:
% 16.66/6.90  | (167)  ? [v0] : (domain(all_73_0_60) = v0 & antidomain(all_41_0_38) = v0)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (49) with all_41_0_38, all_73_0_60 and discharging atoms antidomain(all_73_0_60) = all_41_0_38, yields:
% 16.66/6.90  | (168)  ? [v0] : (antidomain(all_41_0_38) = v0 & addition(v0, all_41_0_38) = one)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (57) with all_45_1_41, all_69_0_58 and discharging atoms antidomain(all_69_0_58) = all_45_1_41, yields:
% 16.66/6.90  | (169)  ? [v0] : (domain(all_69_0_58) = v0 & antidomain(all_45_1_41) = v0)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (49) with all_45_1_41, all_69_0_58 and discharging atoms antidomain(all_69_0_58) = all_45_1_41, yields:
% 16.66/6.90  | (170)  ? [v0] : (antidomain(all_45_1_41) = v0 & addition(v0, all_45_1_41) = one)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (57) with all_43_0_39, all_63_0_51 and discharging atoms antidomain(all_63_0_51) = all_43_0_39, yields:
% 16.66/6.90  | (171)  ? [v0] : (domain(all_63_0_51) = v0 & antidomain(all_43_0_39) = v0)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (49) with all_43_0_39, all_63_0_51 and discharging atoms antidomain(all_63_0_51) = all_43_0_39, yields:
% 16.66/6.90  | (172)  ? [v0] : (antidomain(all_43_0_39) = v0 & addition(v0, all_43_0_39) = one)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (57) with all_55_2_45, all_55_3_46 and discharging atoms antidomain(all_55_3_46) = all_55_2_45, yields:
% 16.66/6.90  | (173)  ? [v0] : (domain(all_55_3_46) = v0 & antidomain(all_55_2_45) = v0)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (49) with all_55_2_45, all_55_3_46 and discharging atoms antidomain(all_55_3_46) = all_55_2_45, yields:
% 16.66/6.90  | (174)  ? [v0] : (antidomain(all_55_2_45) = v0 & addition(v0, all_55_2_45) = one)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (57) with all_55_3_46, all_45_1_41 and discharging atoms antidomain(all_45_1_41) = all_55_3_46, yields:
% 16.66/6.90  | (175)  ? [v0] : (domain(all_45_1_41) = v0 & antidomain(all_55_3_46) = v0)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (69) with all_45_0_40, all_45_1_41, all_69_0_58, all_34_1_37, all_0_1_1 and discharging atoms antidomain(all_69_0_58) = all_45_1_41, antidomain(all_34_1_37) = all_69_0_58, multiplication(all_0_1_1, all_45_1_41) = all_45_0_40, yields:
% 16.66/6.90  | (176)  ? [v0] :  ? [v1] :  ? [v2] : (antidomain(v0) = v1 & antidomain(all_45_0_40) = v2 & multiplication(all_0_1_1, all_34_1_37) = v0 & addition(v1, v2) = v2)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (49) with all_69_0_58, all_34_1_37 and discharging atoms antidomain(all_34_1_37) = all_69_0_58, yields:
% 16.66/6.90  | (177)  ? [v0] : (antidomain(all_69_0_58) = v0 & addition(v0, all_69_0_58) = one)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (17) with all_73_0_60, one and discharging atoms antidomain(one) = all_73_0_60, yields:
% 16.66/6.90  | (178) multiplication(all_73_0_60, one) = zero
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (49) with all_73_0_60, one and discharging atoms antidomain(one) = all_73_0_60, yields:
% 16.66/6.90  | (179)  ? [v0] : (antidomain(all_73_0_60) = v0 & addition(v0, all_73_0_60) = one)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (69) with all_65_1_53, all_45_1_41, all_69_0_58, all_34_1_37, all_65_2_54 and discharging atoms antidomain(all_69_0_58) = all_45_1_41, antidomain(all_34_1_37) = all_69_0_58, multiplication(all_65_2_54, all_45_1_41) = all_65_1_53, yields:
% 16.66/6.90  | (180)  ? [v0] :  ? [v1] :  ? [v2] : (antidomain(v0) = v1 & antidomain(all_65_1_53) = v2 & multiplication(all_65_2_54, all_34_1_37) = v0 & addition(v1, v2) = v2)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (27) with all_65_1_53, all_45_1_41, all_65_2_54 and discharging atoms multiplication(all_65_2_54, all_45_1_41) = all_65_1_53, yields:
% 16.66/6.90  | (181)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (antidomain(v3) = v4 & antidomain(v1) = v2 & antidomain(all_65_1_53) = v0 & antidomain(all_45_1_41) = v1 & multiplication(all_65_2_54, v2) = v3 & addition(v0, v4) = v4)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (71) with zero, all_41_0_38, one, all_34_1_37 and discharging atoms domain(one) = all_41_0_38, multiplication(all_34_1_37, all_41_0_38) = zero, yields:
% 16.66/6.90  | (182)  ? [v0] : (forward_diamond(all_34_1_37, one) = v0 & domain(zero) = v0)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (69) with zero, all_41_0_38, all_73_0_60, one, all_34_1_37 and discharging atoms antidomain(all_73_0_60) = all_41_0_38, antidomain(one) = all_73_0_60, multiplication(all_34_1_37, all_41_0_38) = zero, yields:
% 16.66/6.90  | (183)  ? [v0] :  ? [v1] :  ? [v2] : (antidomain(v0) = v1 & antidomain(zero) = v2 & multiplication(all_34_1_37, one) = v0 & addition(v1, v2) = v2)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (27) with zero, all_41_0_38, all_34_1_37 and discharging atoms multiplication(all_34_1_37, all_41_0_38) = zero, yields:
% 16.66/6.90  | (184)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (antidomain(v3) = v4 & antidomain(v1) = v2 & antidomain(all_41_0_38) = v1 & antidomain(zero) = v0 & multiplication(all_34_1_37, v2) = v3 & addition(v0, v4) = v4)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (71) with zero, all_43_0_39, all_34_0_36, all_0_0_0 and discharging atoms domain(all_34_0_36) = all_43_0_39, multiplication(all_0_0_0, all_43_0_39) = zero, yields:
% 16.66/6.90  | (185)  ? [v0] : (forward_diamond(all_0_0_0, all_34_0_36) = v0 & domain(zero) = v0)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (27) with zero, all_43_0_39, all_0_0_0 and discharging atoms multiplication(all_0_0_0, all_43_0_39) = zero, yields:
% 16.66/6.90  | (186)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (antidomain(v3) = v4 & antidomain(v1) = v2 & antidomain(all_43_0_39) = v1 & antidomain(zero) = v0 & multiplication(all_0_0_0, v2) = v3 & addition(v0, v4) = v4)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (27) with all_55_1_44, all_55_2_45, all_0_1_1 and discharging atoms multiplication(all_0_1_1, all_55_2_45) = all_55_1_44, yields:
% 16.66/6.90  | (187)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (antidomain(v3) = v4 & antidomain(v1) = v2 & antidomain(all_55_1_44) = v0 & antidomain(all_55_2_45) = v1 & multiplication(all_0_1_1, v2) = v3 & addition(v0, v4) = v4)
% 16.66/6.90  |
% 16.66/6.90  | Instantiating formula (47) with one, all_0_0_0, all_53_0_42 and discharging atoms addition(all_53_0_42, all_0_0_0) = one, yields:
% 16.66/6.90  | (188) all_0_0_0 = one |  ? [v0] : ( ~ (v0 = 0) & leq(all_53_0_42, all_0_0_0) = v0)
% 17.12/6.90  |
% 17.12/6.90  | Instantiating (170) with all_89_0_63 yields:
% 17.12/6.90  | (189) antidomain(all_45_1_41) = all_89_0_63 & addition(all_89_0_63, all_45_1_41) = one
% 17.12/6.90  |
% 17.12/6.90  | Applying alpha-rule on (189) yields:
% 17.12/6.90  | (190) antidomain(all_45_1_41) = all_89_0_63
% 17.12/6.90  | (191) addition(all_89_0_63, all_45_1_41) = one
% 17.12/6.90  |
% 17.12/6.90  | Instantiating (169) with all_91_0_64 yields:
% 17.12/6.90  | (192) domain(all_69_0_58) = all_91_0_64 & antidomain(all_45_1_41) = all_91_0_64
% 17.12/6.90  |
% 17.12/6.90  | Applying alpha-rule on (192) yields:
% 17.12/6.90  | (193) domain(all_69_0_58) = all_91_0_64
% 17.12/6.90  | (194) antidomain(all_45_1_41) = all_91_0_64
% 17.12/6.90  |
% 17.12/6.90  | Instantiating (167) with all_93_0_65 yields:
% 17.12/6.90  | (195) domain(all_73_0_60) = all_93_0_65 & antidomain(all_41_0_38) = all_93_0_65
% 17.12/6.90  |
% 17.12/6.90  | Applying alpha-rule on (195) yields:
% 17.12/6.90  | (196) domain(all_73_0_60) = all_93_0_65
% 17.12/6.90  | (197) antidomain(all_41_0_38) = all_93_0_65
% 17.12/6.90  |
% 17.12/6.90  | Instantiating (171) with all_95_0_66 yields:
% 17.12/6.90  | (198) domain(all_63_0_51) = all_95_0_66 & antidomain(all_43_0_39) = all_95_0_66
% 17.12/6.90  |
% 17.12/6.90  | Applying alpha-rule on (198) yields:
% 17.12/6.90  | (199) domain(all_63_0_51) = all_95_0_66
% 17.12/6.90  | (200) antidomain(all_43_0_39) = all_95_0_66
% 17.12/6.90  |
% 17.12/6.90  | Instantiating (187) with all_97_0_67, all_97_1_68, all_97_2_69, all_97_3_70, all_97_4_71 yields:
% 17.12/6.90  | (201) antidomain(all_97_1_68) = all_97_0_67 & antidomain(all_97_3_70) = all_97_2_69 & antidomain(all_55_1_44) = all_97_4_71 & antidomain(all_55_2_45) = all_97_3_70 & multiplication(all_0_1_1, all_97_2_69) = all_97_1_68 & addition(all_97_4_71, all_97_0_67) = all_97_0_67
% 17.12/6.90  |
% 17.12/6.90  | Applying alpha-rule on (201) yields:
% 17.12/6.90  | (202) multiplication(all_0_1_1, all_97_2_69) = all_97_1_68
% 17.12/6.90  | (203) antidomain(all_97_1_68) = all_97_0_67
% 17.12/6.90  | (204) antidomain(all_55_2_45) = all_97_3_70
% 17.12/6.90  | (205) antidomain(all_55_1_44) = all_97_4_71
% 17.12/6.90  | (206) addition(all_97_4_71, all_97_0_67) = all_97_0_67
% 17.12/6.90  | (207) antidomain(all_97_3_70) = all_97_2_69
% 17.12/6.90  |
% 17.12/6.90  | Instantiating (185) with all_99_0_72 yields:
% 17.12/6.90  | (208) forward_diamond(all_0_0_0, all_34_0_36) = all_99_0_72 & domain(zero) = all_99_0_72
% 17.12/6.90  |
% 17.12/6.90  | Applying alpha-rule on (208) yields:
% 17.12/6.90  | (209) forward_diamond(all_0_0_0, all_34_0_36) = all_99_0_72
% 17.12/6.90  | (210) domain(zero) = all_99_0_72
% 17.12/6.90  |
% 17.12/6.90  | Instantiating (184) with all_101_0_73, all_101_1_74, all_101_2_75, all_101_3_76, all_101_4_77 yields:
% 17.12/6.90  | (211) antidomain(all_101_1_74) = all_101_0_73 & antidomain(all_101_3_76) = all_101_2_75 & antidomain(all_41_0_38) = all_101_3_76 & antidomain(zero) = all_101_4_77 & multiplication(all_34_1_37, all_101_2_75) = all_101_1_74 & addition(all_101_4_77, all_101_0_73) = all_101_0_73
% 17.12/6.90  |
% 17.12/6.90  | Applying alpha-rule on (211) yields:
% 17.12/6.90  | (212) antidomain(all_101_1_74) = all_101_0_73
% 17.12/6.90  | (213) antidomain(zero) = all_101_4_77
% 17.12/6.90  | (214) addition(all_101_4_77, all_101_0_73) = all_101_0_73
% 17.12/6.90  | (215) antidomain(all_41_0_38) = all_101_3_76
% 17.12/6.90  | (216) multiplication(all_34_1_37, all_101_2_75) = all_101_1_74
% 17.12/6.90  | (217) antidomain(all_101_3_76) = all_101_2_75
% 17.12/6.90  |
% 17.12/6.90  | Instantiating (182) with all_103_0_78 yields:
% 17.12/6.90  | (218) forward_diamond(all_34_1_37, one) = all_103_0_78 & domain(zero) = all_103_0_78
% 17.12/6.90  |
% 17.12/6.90  | Applying alpha-rule on (218) yields:
% 17.12/6.90  | (219) forward_diamond(all_34_1_37, one) = all_103_0_78
% 17.12/6.90  | (220) domain(zero) = all_103_0_78
% 17.12/6.90  |
% 17.12/6.90  | Instantiating (186) with all_109_0_89, all_109_1_90, all_109_2_91, all_109_3_92, all_109_4_93 yields:
% 17.12/6.90  | (221) antidomain(all_109_1_90) = all_109_0_89 & antidomain(all_109_3_92) = all_109_2_91 & antidomain(all_43_0_39) = all_109_3_92 & antidomain(zero) = all_109_4_93 & multiplication(all_0_0_0, all_109_2_91) = all_109_1_90 & addition(all_109_4_93, all_109_0_89) = all_109_0_89
% 17.12/6.90  |
% 17.12/6.90  | Applying alpha-rule on (221) yields:
% 17.12/6.90  | (222) antidomain(all_109_3_92) = all_109_2_91
% 17.12/6.90  | (223) antidomain(all_43_0_39) = all_109_3_92
% 17.12/6.90  | (224) antidomain(zero) = all_109_4_93
% 17.12/6.90  | (225) antidomain(all_109_1_90) = all_109_0_89
% 17.12/6.90  | (226) multiplication(all_0_0_0, all_109_2_91) = all_109_1_90
% 17.12/6.90  | (227) addition(all_109_4_93, all_109_0_89) = all_109_0_89
% 17.12/6.90  |
% 17.12/6.90  | Instantiating (180) with all_111_0_94, all_111_1_95, all_111_2_96 yields:
% 17.12/6.90  | (228) antidomain(all_111_2_96) = all_111_1_95 & antidomain(all_65_1_53) = all_111_0_94 & multiplication(all_65_2_54, all_34_1_37) = all_111_2_96 & addition(all_111_1_95, all_111_0_94) = all_111_0_94
% 17.12/6.91  |
% 17.12/6.91  | Applying alpha-rule on (228) yields:
% 17.12/6.91  | (229) antidomain(all_111_2_96) = all_111_1_95
% 17.12/6.91  | (230) antidomain(all_65_1_53) = all_111_0_94
% 17.12/6.91  | (231) multiplication(all_65_2_54, all_34_1_37) = all_111_2_96
% 17.12/6.91  | (232) addition(all_111_1_95, all_111_0_94) = all_111_0_94
% 17.12/6.91  |
% 17.12/6.91  | Instantiating (181) with all_113_0_97, all_113_1_98, all_113_2_99, all_113_3_100, all_113_4_101 yields:
% 17.12/6.91  | (233) antidomain(all_113_1_98) = all_113_0_97 & antidomain(all_113_3_100) = all_113_2_99 & antidomain(all_65_1_53) = all_113_4_101 & antidomain(all_45_1_41) = all_113_3_100 & multiplication(all_65_2_54, all_113_2_99) = all_113_1_98 & addition(all_113_4_101, all_113_0_97) = all_113_0_97
% 17.12/6.91  |
% 17.12/6.91  | Applying alpha-rule on (233) yields:
% 17.12/6.91  | (234) addition(all_113_4_101, all_113_0_97) = all_113_0_97
% 17.12/6.91  | (235) antidomain(all_113_1_98) = all_113_0_97
% 17.12/6.91  | (236) antidomain(all_113_3_100) = all_113_2_99
% 17.12/6.91  | (237) antidomain(all_45_1_41) = all_113_3_100
% 17.12/6.91  | (238) antidomain(all_65_1_53) = all_113_4_101
% 17.12/6.91  | (239) multiplication(all_65_2_54, all_113_2_99) = all_113_1_98
% 17.12/6.91  |
% 17.12/6.91  | Instantiating (166) with all_117_0_107 yields:
% 17.12/6.91  | (240) c(all_41_0_38) = all_117_0_107 & antidomain(all_69_0_58) = all_117_0_107
% 17.12/6.91  |
% 17.12/6.91  | Applying alpha-rule on (240) yields:
% 17.12/6.91  | (241) c(all_41_0_38) = all_117_0_107
% 17.12/6.91  | (242) antidomain(all_69_0_58) = all_117_0_107
% 17.12/6.91  |
% 17.12/6.91  | Instantiating (179) with all_127_0_112 yields:
% 17.12/6.91  | (243) antidomain(all_73_0_60) = all_127_0_112 & addition(all_127_0_112, all_73_0_60) = one
% 17.12/6.91  |
% 17.12/6.91  | Applying alpha-rule on (243) yields:
% 17.12/6.91  | (244) antidomain(all_73_0_60) = all_127_0_112
% 17.12/6.91  | (245) addition(all_127_0_112, all_73_0_60) = one
% 17.12/6.91  |
% 17.12/6.91  | Instantiating (177) with all_129_0_113 yields:
% 17.12/6.91  | (246) antidomain(all_69_0_58) = all_129_0_113 & addition(all_129_0_113, all_69_0_58) = one
% 17.12/6.91  |
% 17.12/6.91  | Applying alpha-rule on (246) yields:
% 17.12/6.91  | (247) antidomain(all_69_0_58) = all_129_0_113
% 17.12/6.91  | (248) addition(all_129_0_113, all_69_0_58) = one
% 17.12/6.91  |
% 17.12/6.91  | Instantiating (176) with all_131_0_114, all_131_1_115, all_131_2_116 yields:
% 17.12/6.91  | (249) antidomain(all_131_2_116) = all_131_1_115 & antidomain(all_45_0_40) = all_131_0_114 & multiplication(all_0_1_1, all_34_1_37) = all_131_2_116 & addition(all_131_1_115, all_131_0_114) = all_131_0_114
% 17.12/6.91  |
% 17.12/6.91  | Applying alpha-rule on (249) yields:
% 17.12/6.91  | (250) antidomain(all_131_2_116) = all_131_1_115
% 17.12/6.91  | (251) antidomain(all_45_0_40) = all_131_0_114
% 17.12/6.91  | (252) multiplication(all_0_1_1, all_34_1_37) = all_131_2_116
% 17.12/6.91  | (253) addition(all_131_1_115, all_131_0_114) = all_131_0_114
% 17.12/6.91  |
% 17.12/6.91  | Instantiating (175) with all_143_0_122 yields:
% 17.12/6.91  | (254) domain(all_45_1_41) = all_143_0_122 & antidomain(all_55_3_46) = all_143_0_122
% 17.12/6.91  |
% 17.12/6.91  | Applying alpha-rule on (254) yields:
% 17.12/6.91  | (255) domain(all_45_1_41) = all_143_0_122
% 17.12/6.91  | (256) antidomain(all_55_3_46) = all_143_0_122
% 17.12/6.91  |
% 17.12/6.91  | Instantiating (183) with all_153_0_127, all_153_1_128, all_153_2_129 yields:
% 17.12/6.91  | (257) antidomain(all_153_2_129) = all_153_1_128 & antidomain(zero) = all_153_0_127 & multiplication(all_34_1_37, one) = all_153_2_129 & addition(all_153_1_128, all_153_0_127) = all_153_0_127
% 17.12/6.91  |
% 17.12/6.91  | Applying alpha-rule on (257) yields:
% 17.12/6.91  | (258) antidomain(all_153_2_129) = all_153_1_128
% 17.12/6.91  | (259) antidomain(zero) = all_153_0_127
% 17.12/6.91  | (260) multiplication(all_34_1_37, one) = all_153_2_129
% 17.12/6.91  | (261) addition(all_153_1_128, all_153_0_127) = all_153_0_127
% 17.12/6.91  |
% 17.12/6.91  | Instantiating (174) with all_155_0_130 yields:
% 17.12/6.91  | (262) antidomain(all_55_2_45) = all_155_0_130 & addition(all_155_0_130, all_55_2_45) = one
% 17.12/6.91  |
% 17.12/6.91  | Applying alpha-rule on (262) yields:
% 17.12/6.91  | (263) antidomain(all_55_2_45) = all_155_0_130
% 17.12/6.91  | (264) addition(all_155_0_130, all_55_2_45) = one
% 17.12/6.91  |
% 17.12/6.91  | Instantiating (173) with all_157_0_131 yields:
% 17.12/6.91  | (265) domain(all_55_3_46) = all_157_0_131 & antidomain(all_55_2_45) = all_157_0_131
% 17.12/6.91  |
% 17.12/6.91  | Applying alpha-rule on (265) yields:
% 17.12/6.91  | (266) domain(all_55_3_46) = all_157_0_131
% 17.12/6.91  | (267) antidomain(all_55_2_45) = all_157_0_131
% 17.12/6.91  |
% 17.12/6.91  | Instantiating (172) with all_169_0_141 yields:
% 17.12/6.91  | (268) antidomain(all_43_0_39) = all_169_0_141 & addition(all_169_0_141, all_43_0_39) = one
% 17.12/6.91  |
% 17.12/6.91  | Applying alpha-rule on (268) yields:
% 17.12/6.91  | (269) antidomain(all_43_0_39) = all_169_0_141
% 17.12/6.91  | (270) addition(all_169_0_141, all_43_0_39) = one
% 17.12/6.91  |
% 17.12/6.91  | Instantiating (168) with all_177_0_145 yields:
% 17.12/6.91  | (271) antidomain(all_41_0_38) = all_177_0_145 & addition(all_177_0_145, all_41_0_38) = one
% 17.12/6.91  |
% 17.12/6.91  | Applying alpha-rule on (271) yields:
% 17.12/6.91  | (272) antidomain(all_41_0_38) = all_177_0_145
% 17.12/6.91  | (273) addition(all_177_0_145, all_41_0_38) = one
% 17.12/6.91  |
% 17.12/6.91  +-Applying beta-rule and splitting (188), into two cases.
% 17.12/6.91  |-Branch one:
% 17.12/6.91  | (274) all_0_0_0 = one
% 17.12/6.91  |
% 17.12/6.91  	| Equations (274) can reduce 22 to:
% 17.12/6.91  	| (275) $false
% 17.12/6.91  	|
% 17.12/6.91  	|-The branch is then unsatisfiable
% 17.12/6.91  |-Branch two:
% 17.12/6.91  | (22)  ~ (all_0_0_0 = one)
% 17.12/6.91  | (277)  ? [v0] : ( ~ (v0 = 0) & leq(all_53_0_42, all_0_0_0) = v0)
% 17.12/6.91  |
% 17.12/6.91  	| Instantiating formula (18) with zero, all_99_0_72, all_103_0_78 and discharging atoms domain(zero) = all_103_0_78, domain(zero) = all_99_0_72, yields:
% 17.12/6.91  	| (278) all_103_0_78 = all_99_0_72
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (32) with all_73_0_60, all_127_0_112, all_41_0_38 and discharging atoms antidomain(all_73_0_60) = all_127_0_112, antidomain(all_73_0_60) = all_41_0_38, yields:
% 17.12/6.91  	| (279) all_127_0_112 = all_41_0_38
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (32) with all_69_0_58, all_129_0_113, all_45_1_41 and discharging atoms antidomain(all_69_0_58) = all_129_0_113, antidomain(all_69_0_58) = all_45_1_41, yields:
% 17.12/6.91  	| (280) all_129_0_113 = all_45_1_41
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (32) with all_69_0_58, all_117_0_107, all_129_0_113 and discharging atoms antidomain(all_69_0_58) = all_129_0_113, antidomain(all_69_0_58) = all_117_0_107, yields:
% 17.12/6.91  	| (281) all_129_0_113 = all_117_0_107
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (32) with all_65_1_53, all_111_0_94, all_113_4_101 and discharging atoms antidomain(all_65_1_53) = all_113_4_101, antidomain(all_65_1_53) = all_111_0_94, yields:
% 17.12/6.91  	| (282) all_113_4_101 = all_111_0_94
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (32) with all_55_2_45, all_155_0_130, all_157_0_131 and discharging atoms antidomain(all_55_2_45) = all_157_0_131, antidomain(all_55_2_45) = all_155_0_130, yields:
% 17.12/6.91  	| (283) all_157_0_131 = all_155_0_130
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (32) with all_55_2_45, all_97_3_70, all_157_0_131 and discharging atoms antidomain(all_55_2_45) = all_157_0_131, antidomain(all_55_2_45) = all_97_3_70, yields:
% 17.12/6.91  	| (284) all_157_0_131 = all_97_3_70
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (32) with all_55_3_46, all_143_0_122, all_55_2_45 and discharging atoms antidomain(all_55_3_46) = all_143_0_122, antidomain(all_55_3_46) = all_55_2_45, yields:
% 17.12/6.91  	| (285) all_143_0_122 = all_55_2_45
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (32) with all_45_0_40, all_131_0_114, all_55_4_47 and discharging atoms antidomain(all_45_0_40) = all_131_0_114, antidomain(all_45_0_40) = all_55_4_47, yields:
% 17.12/6.91  	| (286) all_131_0_114 = all_55_4_47
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (32) with all_45_1_41, all_113_3_100, all_55_3_46 and discharging atoms antidomain(all_45_1_41) = all_113_3_100, antidomain(all_45_1_41) = all_55_3_46, yields:
% 17.12/6.91  	| (287) all_113_3_100 = all_55_3_46
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (32) with all_45_1_41, all_91_0_64, all_113_3_100 and discharging atoms antidomain(all_45_1_41) = all_113_3_100, antidomain(all_45_1_41) = all_91_0_64, yields:
% 17.12/6.91  	| (288) all_113_3_100 = all_91_0_64
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (32) with all_45_1_41, all_89_0_63, all_113_3_100 and discharging atoms antidomain(all_45_1_41) = all_113_3_100, antidomain(all_45_1_41) = all_89_0_63, yields:
% 17.12/6.91  	| (289) all_113_3_100 = all_89_0_63
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (32) with all_43_0_39, all_109_3_92, all_0_0_0 and discharging atoms antidomain(all_43_0_39) = all_109_3_92, antidomain(all_43_0_39) = all_0_0_0, yields:
% 17.12/6.91  	| (290) all_109_3_92 = all_0_0_0
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (32) with all_43_0_39, all_109_3_92, all_169_0_141 and discharging atoms antidomain(all_43_0_39) = all_169_0_141, antidomain(all_43_0_39) = all_109_3_92, yields:
% 17.12/6.91  	| (291) all_169_0_141 = all_109_3_92
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (32) with all_43_0_39, all_95_0_66, all_169_0_141 and discharging atoms antidomain(all_43_0_39) = all_169_0_141, antidomain(all_43_0_39) = all_95_0_66, yields:
% 17.12/6.91  	| (292) all_169_0_141 = all_95_0_66
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (32) with all_41_0_38, all_177_0_145, all_34_1_37 and discharging atoms antidomain(all_41_0_38) = all_177_0_145, antidomain(all_41_0_38) = all_34_1_37, yields:
% 17.12/6.91  	| (293) all_177_0_145 = all_34_1_37
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (32) with all_41_0_38, all_101_3_76, all_177_0_145 and discharging atoms antidomain(all_41_0_38) = all_177_0_145, antidomain(all_41_0_38) = all_101_3_76, yields:
% 17.12/6.91  	| (294) all_177_0_145 = all_101_3_76
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (32) with all_41_0_38, all_93_0_65, all_177_0_145 and discharging atoms antidomain(all_41_0_38) = all_177_0_145, antidomain(all_41_0_38) = all_93_0_65, yields:
% 17.12/6.91  	| (295) all_177_0_145 = all_93_0_65
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (53) with zero, all_73_0_60 and discharging atoms multiplication(all_73_0_60, one) = zero, yields:
% 17.12/6.91  	| (296) all_73_0_60 = zero
% 17.12/6.91  	|
% 17.12/6.91  	| Instantiating formula (53) with all_153_2_129, all_34_1_37 and discharging atoms multiplication(all_34_1_37, one) = all_153_2_129, yields:
% 17.12/6.91  	| (297) all_153_2_129 = all_34_1_37
% 17.12/6.91  	|
% 17.12/6.91  	| Combining equations (293,294) yields a new equation:
% 17.12/6.91  	| (298) all_101_3_76 = all_34_1_37
% 17.12/6.91  	|
% 17.12/6.91  	| Combining equations (295,294) yields a new equation:
% 17.12/6.91  	| (299) all_101_3_76 = all_93_0_65
% 17.12/6.91  	|
% 17.12/6.91  	| Combining equations (291,292) yields a new equation:
% 17.12/6.91  	| (300) all_109_3_92 = all_95_0_66
% 17.12/6.91  	|
% 17.12/6.91  	| Simplifying 300 yields:
% 17.12/6.91  	| (301) all_109_3_92 = all_95_0_66
% 17.12/6.91  	|
% 17.12/6.91  	| Combining equations (283,284) yields a new equation:
% 17.12/6.91  	| (302) all_155_0_130 = all_97_3_70
% 17.12/6.91  	|
% 17.12/6.91  	| Simplifying 302 yields:
% 17.12/6.91  	| (303) all_155_0_130 = all_97_3_70
% 17.12/6.91  	|
% 17.12/6.91  	| Combining equations (280,281) yields a new equation:
% 17.12/6.91  	| (304) all_117_0_107 = all_45_1_41
% 17.12/6.91  	|
% 17.12/6.91  	| Combining equations (287,288) yields a new equation:
% 17.12/6.91  	| (305) all_91_0_64 = all_55_3_46
% 17.12/6.91  	|
% 17.12/6.91  	| Combining equations (289,288) yields a new equation:
% 17.12/6.91  	| (306) all_91_0_64 = all_89_0_63
% 17.12/6.91  	|
% 17.12/6.92  	| Combining equations (290,301) yields a new equation:
% 17.12/6.92  	| (307) all_95_0_66 = all_0_0_0
% 17.12/6.92  	|
% 17.12/6.92  	| Combining equations (299,298) yields a new equation:
% 17.12/6.92  	| (308) all_93_0_65 = all_34_1_37
% 17.12/6.92  	|
% 17.12/6.92  	| Simplifying 308 yields:
% 17.12/6.92  	| (309) all_93_0_65 = all_34_1_37
% 17.12/6.92  	|
% 17.12/6.92  	| Combining equations (306,305) yields a new equation:
% 17.12/6.92  	| (310) all_89_0_63 = all_55_3_46
% 17.12/6.92  	|
% 17.12/6.92  	| Simplifying 310 yields:
% 17.12/6.92  	| (311) all_89_0_63 = all_55_3_46
% 17.12/6.92  	|
% 17.12/6.92  	| From (304) and (241) follows:
% 17.12/6.92  	| (312) c(all_41_0_38) = all_45_1_41
% 17.12/6.92  	|
% 17.12/6.92  	| From (296)(309) and (196) follows:
% 17.12/6.92  	| (313) domain(zero) = all_34_1_37
% 17.12/6.92  	|
% 17.12/6.92  	| From (307) and (199) follows:
% 17.12/6.92  	| (314) domain(all_63_0_51) = all_0_0_0
% 17.12/6.92  	|
% 17.12/6.92  	| From (284) and (266) follows:
% 17.12/6.92  	| (315) domain(all_55_3_46) = all_97_3_70
% 17.12/6.92  	|
% 17.12/6.92  	| From (285) and (255) follows:
% 17.12/6.92  	| (316) domain(all_45_1_41) = all_55_2_45
% 17.12/6.92  	|
% 17.12/6.92  	| From (278) and (220) follows:
% 17.12/6.92  	| (210) domain(zero) = all_99_0_72
% 17.12/6.92  	|
% 17.12/6.92  	| From (297) and (258) follows:
% 17.12/6.92  	| (318) antidomain(all_34_1_37) = all_153_1_128
% 17.12/6.92  	|
% 17.12/6.92  	| From (298) and (217) follows:
% 17.12/6.92  	| (319) antidomain(all_34_1_37) = all_101_2_75
% 17.12/6.92  	|
% 17.12/6.92  	| From (282) and (238) follows:
% 17.12/6.92  	| (230) antidomain(all_65_1_53) = all_111_0_94
% 17.12/6.92  	|
% 17.12/6.92  	| From (303) and (263) follows:
% 17.12/6.92  	| (204) antidomain(all_55_2_45) = all_97_3_70
% 17.12/6.92  	|
% 17.12/6.92  	| From (286) and (251) follows:
% 17.12/6.92  	| (111) antidomain(all_45_0_40) = all_55_4_47
% 17.12/6.92  	|
% 17.12/6.92  	| From (311) and (190) follows:
% 17.12/6.92  	| (113) antidomain(all_45_1_41) = all_55_3_46
% 17.12/6.92  	|
% 17.12/6.92  	| From (279)(296) and (245) follows:
% 17.12/6.92  	| (324) addition(all_41_0_38, zero) = one
% 17.12/6.92  	|
% 17.12/6.92  	| From (311) and (191) follows:
% 17.12/6.92  	| (325) addition(all_55_3_46, all_45_1_41) = one
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (18) with zero, all_34_1_37, all_99_0_72 and discharging atoms domain(zero) = all_99_0_72, domain(zero) = all_34_1_37, yields:
% 17.12/6.92  	| (326) all_99_0_72 = all_34_1_37
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (32) with all_34_1_37, all_153_1_128, all_69_0_58 and discharging atoms antidomain(all_34_1_37) = all_153_1_128, antidomain(all_34_1_37) = all_69_0_58, yields:
% 17.12/6.92  	| (327) all_153_1_128 = all_69_0_58
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (32) with all_34_1_37, all_101_2_75, all_153_1_128 and discharging atoms antidomain(all_34_1_37) = all_153_1_128, antidomain(all_34_1_37) = all_101_2_75, yields:
% 17.12/6.92  	| (328) all_153_1_128 = all_101_2_75
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (70) with one, all_41_0_38 and discharging atoms addition(all_41_0_38, zero) = one, yields:
% 17.12/6.92  	| (329) all_41_0_38 = one
% 17.12/6.92  	|
% 17.12/6.92  	| Combining equations (327,328) yields a new equation:
% 17.12/6.92  	| (330) all_101_2_75 = all_69_0_58
% 17.12/6.92  	|
% 17.12/6.92  	| From (329) and (312) follows:
% 17.12/6.92  	| (331) c(one) = all_45_1_41
% 17.12/6.92  	|
% 17.12/6.92  	| From (329) and (159) follows:
% 17.12/6.92  	| (332) domain(one) = all_69_0_58
% 17.12/6.92  	|
% 17.12/6.92  	| From (329) and (83) follows:
% 17.12/6.92  	| (333) domain(one) = one
% 17.12/6.92  	|
% 17.12/6.92  	| From (326) and (210) follows:
% 17.12/6.92  	| (313) domain(zero) = all_34_1_37
% 17.12/6.92  	|
% 17.12/6.92  	| From (330) and (216) follows:
% 17.12/6.92  	| (335) multiplication(all_34_1_37, all_69_0_58) = all_101_1_74
% 17.12/6.92  	|
% 17.12/6.92  	| From (329) and (101) follows:
% 17.12/6.92  	| (336) multiplication(all_34_1_37, one) = zero
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (50) with one, all_45_1_41, all_34_1_37 and discharging atoms c(one) = all_45_1_41, c(one) = all_34_1_37, yields:
% 17.12/6.92  	| (337) all_45_1_41 = all_34_1_37
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (18) with one, one, all_69_0_58 and discharging atoms domain(one) = all_69_0_58, domain(one) = one, yields:
% 17.12/6.92  	| (338) all_69_0_58 = one
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (53) with zero, all_34_1_37 and discharging atoms multiplication(all_34_1_37, one) = zero, yields:
% 17.12/6.92  	| (339) all_34_1_37 = zero
% 17.12/6.92  	|
% 17.12/6.92  	| Combining equations (339,337) yields a new equation:
% 17.12/6.92  	| (340) all_45_1_41 = zero
% 17.12/6.92  	|
% 17.12/6.92  	| From (339) and (158) follows:
% 17.12/6.92  	| (341) c(zero) = all_55_3_46
% 17.12/6.92  	|
% 17.12/6.92  	| From (340) and (316) follows:
% 17.12/6.92  	| (342) domain(zero) = all_55_2_45
% 17.12/6.92  	|
% 17.12/6.92  	| From (339) and (313) follows:
% 17.12/6.92  	| (343) domain(zero) = zero
% 17.12/6.92  	|
% 17.12/6.92  	| From (340) and (113) follows:
% 17.12/6.92  	| (344) antidomain(zero) = all_55_3_46
% 17.12/6.92  	|
% 17.12/6.92  	| From (340) and (132) follows:
% 17.12/6.92  	| (345) multiplication(all_65_2_54, zero) = all_65_1_53
% 17.12/6.92  	|
% 17.12/6.92  	| From (339) and (231) follows:
% 17.12/6.92  	| (346) multiplication(all_65_2_54, zero) = all_111_2_96
% 17.12/6.92  	|
% 17.12/6.92  	| From (339)(338) and (335) follows:
% 17.12/6.92  	| (347) multiplication(zero, one) = all_101_1_74
% 17.12/6.92  	|
% 17.12/6.92  	| From (340) and (91) follows:
% 17.12/6.92  	| (348) multiplication(all_0_1_1, zero) = all_45_0_40
% 17.12/6.92  	|
% 17.12/6.92  	| From (339) and (252) follows:
% 17.12/6.92  	| (349) multiplication(all_0_1_1, zero) = all_131_2_116
% 17.12/6.92  	|
% 17.12/6.92  	| From (340) and (325) follows:
% 17.12/6.92  	| (350) addition(all_55_3_46, zero) = one
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (18) with zero, zero, all_55_2_45 and discharging atoms domain(zero) = all_55_2_45, domain(zero) = zero, yields:
% 17.12/6.92  	| (351) all_55_2_45 = zero
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (4) with all_111_2_96, all_65_2_54 and discharging atoms multiplication(all_65_2_54, zero) = all_111_2_96, yields:
% 17.12/6.92  	| (352) all_111_2_96 = zero
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (7) with all_65_2_54, zero, all_65_1_53, all_111_2_96 and discharging atoms multiplication(all_65_2_54, zero) = all_111_2_96, multiplication(all_65_2_54, zero) = all_65_1_53, yields:
% 17.12/6.92  	| (353) all_111_2_96 = all_65_1_53
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (4) with all_131_2_116, all_0_1_1 and discharging atoms multiplication(all_0_1_1, zero) = all_131_2_116, yields:
% 17.12/6.92  	| (354) all_131_2_116 = zero
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (7) with all_0_1_1, zero, all_45_0_40, all_131_2_116 and discharging atoms multiplication(all_0_1_1, zero) = all_131_2_116, multiplication(all_0_1_1, zero) = all_45_0_40, yields:
% 17.12/6.92  	| (355) all_131_2_116 = all_45_0_40
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (53) with all_101_1_74, zero and discharging atoms multiplication(zero, one) = all_101_1_74, yields:
% 17.12/6.92  	| (356) all_101_1_74 = zero
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (70) with one, all_55_3_46 and discharging atoms addition(all_55_3_46, zero) = one, yields:
% 17.12/6.92  	| (357) all_55_3_46 = one
% 17.12/6.92  	|
% 17.12/6.92  	| Combining equations (354,355) yields a new equation:
% 17.12/6.92  	| (358) all_45_0_40 = zero
% 17.12/6.92  	|
% 17.12/6.92  	| Combining equations (352,353) yields a new equation:
% 17.12/6.92  	| (359) all_65_1_53 = zero
% 17.12/6.92  	|
% 17.12/6.92  	| Combining equations (359,353) yields a new equation:
% 17.12/6.92  	| (352) all_111_2_96 = zero
% 17.12/6.92  	|
% 17.12/6.92  	| Combining equations (358,355) yields a new equation:
% 17.12/6.92  	| (354) all_131_2_116 = zero
% 17.12/6.92  	|
% 17.12/6.92  	| From (358) and (126) follows:
% 17.12/6.92  	| (362) c(zero) = all_63_0_51
% 17.12/6.92  	|
% 17.12/6.92  	| From (357) and (341) follows:
% 17.12/6.92  	| (363) c(zero) = one
% 17.12/6.92  	|
% 17.12/6.92  	| From (357) and (315) follows:
% 17.12/6.92  	| (364) domain(one) = all_97_3_70
% 17.12/6.92  	|
% 17.12/6.92  	| From (354) and (250) follows:
% 17.12/6.92  	| (365) antidomain(zero) = all_131_1_115
% 17.12/6.92  	|
% 17.12/6.92  	| From (352) and (229) follows:
% 17.12/6.92  	| (366) antidomain(zero) = all_111_1_95
% 17.12/6.92  	|
% 17.12/6.92  	| From (356) and (212) follows:
% 17.12/6.92  	| (367) antidomain(zero) = all_101_0_73
% 17.12/6.92  	|
% 17.12/6.92  	| From (359) and (230) follows:
% 17.12/6.92  	| (368) antidomain(zero) = all_111_0_94
% 17.12/6.92  	|
% 17.12/6.92  	| From (351) and (204) follows:
% 17.12/6.92  	| (369) antidomain(zero) = all_97_3_70
% 17.12/6.92  	|
% 17.12/6.92  	| From (358) and (111) follows:
% 17.12/6.92  	| (370) antidomain(zero) = all_55_4_47
% 17.12/6.92  	|
% 17.12/6.92  	| From (357) and (344) follows:
% 17.12/6.92  	| (371) antidomain(zero) = one
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (50) with zero, one, all_63_0_51 and discharging atoms c(zero) = all_63_0_51, c(zero) = one, yields:
% 17.12/6.92  	| (372) all_63_0_51 = one
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (32) with zero, all_131_1_115, one and discharging atoms antidomain(zero) = all_131_1_115, antidomain(zero) = one, yields:
% 17.12/6.92  	| (373) all_131_1_115 = one
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (32) with zero, all_111_1_95, all_131_1_115 and discharging atoms antidomain(zero) = all_131_1_115, antidomain(zero) = all_111_1_95, yields:
% 17.12/6.92  	| (374) all_131_1_115 = all_111_1_95
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (32) with zero, all_101_0_73, all_131_1_115 and discharging atoms antidomain(zero) = all_131_1_115, antidomain(zero) = all_101_0_73, yields:
% 17.12/6.92  	| (375) all_131_1_115 = all_101_0_73
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (32) with zero, all_97_3_70, all_131_1_115 and discharging atoms antidomain(zero) = all_131_1_115, antidomain(zero) = all_97_3_70, yields:
% 17.12/6.92  	| (376) all_131_1_115 = all_97_3_70
% 17.12/6.92  	|
% 17.12/6.92  	| Instantiating formula (32) with zero, all_97_3_70, all_111_0_94 and discharging atoms antidomain(zero) = all_111_0_94, antidomain(zero) = all_97_3_70, yields:
% 17.12/6.93  	| (377) all_111_0_94 = all_97_3_70
% 17.12/6.93  	|
% 17.12/6.93  	| Instantiating formula (32) with zero, all_55_4_47, all_111_0_94 and discharging atoms antidomain(zero) = all_111_0_94, antidomain(zero) = all_55_4_47, yields:
% 17.12/6.93  	| (378) all_111_0_94 = all_55_4_47
% 17.12/6.93  	|
% 17.12/6.93  	| Combining equations (373,374) yields a new equation:
% 17.12/6.93  	| (379) all_111_1_95 = one
% 17.12/6.93  	|
% 17.12/6.93  	| Combining equations (376,374) yields a new equation:
% 17.12/6.93  	| (380) all_111_1_95 = all_97_3_70
% 17.12/6.93  	|
% 17.12/6.93  	| Combining equations (375,374) yields a new equation:
% 17.12/6.93  	| (381) all_111_1_95 = all_101_0_73
% 17.12/6.93  	|
% 17.12/6.93  	| Combining equations (377,378) yields a new equation:
% 17.12/6.93  	| (382) all_97_3_70 = all_55_4_47
% 17.12/6.93  	|
% 17.12/6.93  	| Simplifying 382 yields:
% 17.12/6.93  	| (383) all_97_3_70 = all_55_4_47
% 17.12/6.93  	|
% 17.12/6.93  	| Combining equations (379,381) yields a new equation:
% 17.12/6.93  	| (384) all_101_0_73 = one
% 17.12/6.93  	|
% 17.12/6.93  	| Combining equations (380,381) yields a new equation:
% 17.12/6.93  	| (385) all_101_0_73 = all_97_3_70
% 17.12/6.93  	|
% 17.12/6.93  	| Combining equations (385,384) yields a new equation:
% 17.12/6.93  	| (386) all_97_3_70 = one
% 17.12/6.93  	|
% 17.12/6.93  	| Simplifying 386 yields:
% 17.12/6.93  	| (387) all_97_3_70 = one
% 17.12/6.93  	|
% 17.12/6.93  	| Combining equations (387,383) yields a new equation:
% 17.12/6.93  	| (388) all_55_4_47 = one
% 17.12/6.93  	|
% 17.12/6.93  	| Combining equations (388,383) yields a new equation:
% 17.12/6.93  	| (387) all_97_3_70 = one
% 17.12/6.93  	|
% 17.12/6.93  	| From (372) and (314) follows:
% 17.12/6.93  	| (390) domain(one) = all_0_0_0
% 17.12/6.93  	|
% 17.12/6.93  	| From (387) and (364) follows:
% 17.12/6.93  	| (333) domain(one) = one
% 17.12/6.93  	|
% 17.12/6.93  	| Instantiating formula (18) with one, all_0_0_0, one and discharging atoms domain(one) = all_0_0_0, domain(one) = one, yields:
% 17.12/6.93  	| (274) all_0_0_0 = one
% 17.12/6.93  	|
% 17.12/6.93  	| Equations (274) can reduce 22 to:
% 17.12/6.93  	| (275) $false
% 17.12/6.93  	|
% 17.12/6.93  	|-The branch is then unsatisfiable
% 17.12/6.93  % SZS output end Proof for theBenchmark
% 17.12/6.93  
% 17.12/6.93  6344ms
%------------------------------------------------------------------------------