%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE129+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n023.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 01:51:29 EDT 2022

% Result   : Theorem 14.88s 6.21s
% Output   : Proof 16.30s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : KLE129+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun 16 10:02:20 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.56/0.59          ____       _                          
% 0.56/0.59    ___  / __ \_____(_)___  ________  __________
% 0.56/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.56/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.56/0.59  
% 0.56/0.59  A Theorem Prover for First-Order Logic
% 0.56/0.59  (ePrincess v.1.0)
% 0.56/0.59  
% 0.56/0.59  (c) Philipp Rümmer, 2009-2015
% 0.56/0.59  (c) Peter Backeman, 2014-2015
% 0.56/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.59  Bug reports to peter@backeman.se
% 0.56/0.59  
% 0.56/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.59  
% 0.56/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.62/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.53/0.92  Prover 0: Preprocessing ...
% 2.73/1.23  Prover 0: Warning: ignoring some quantifiers
% 2.73/1.26  Prover 0: Constructing countermodel ...
% 13.55/5.93  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 13.55/5.97  Prover 1: Preprocessing ...
% 13.95/6.04  Prover 1: Constructing countermodel ...
% 13.95/6.07  Prover 1: gave up
% 13.95/6.07  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 13.95/6.09  Prover 2: Preprocessing ...
% 14.37/6.16  Prover 2: Warning: ignoring some quantifiers
% 14.37/6.16  Prover 2: Constructing countermodel ...
% 14.88/6.21  Prover 2: proved (134ms)
% 14.88/6.21  Prover 0: stopped
% 14.88/6.21  
% 14.88/6.21  No countermodel exists, formula is valid
% 14.88/6.21  % SZS status Theorem for theBenchmark
% 14.88/6.21  
% 14.88/6.21  Generating proof ... Warning: ignoring some quantifiers
% 15.72/6.43  found it (size 18)
% 15.72/6.43  
% 15.72/6.43  % SZS output start Proof for theBenchmark
% 15.72/6.43  Assumed formulas after preprocessing and simplification: 
% 15.72/6.43  | (0)  ? [v0] :  ? [v1] : ( ~ (v1 = zero) & divergence(v0) = v1 &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = v10 |  ~ (star(v3) = v8) |  ~ (divergence(v3) = v7) |  ~ (forward_diamond(v8, v6) = v9) |  ~ (domain(v4) = v6) |  ~ (domain(v2) = v5) |  ~ (addition(v7, v9) = v10) |  ~ (addition(v5, v10) = v11) |  ? [v12] :  ? [v13] :  ? [v14] : ( ~ (v14 = v13) & forward_diamond(v3, v5) = v12 & addition(v12, v6) = v13 & addition(v5, v13) = v14)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (forward_diamond(v3, v5) = v6) |  ~ (domain(v4) = v7) |  ~ (domain(v2) = v5) |  ~ (addition(v6, v7) = v8) |  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] : ((v13 = v12 & star(v3) = v10 & divergence(v3) = v9 & forward_diamond(v10, v7) = v11 & addition(v9, v11) = v12 & addition(v5, v12) = v12) | ( ~ (v9 = v8) & addition(v5, v8) = v9))) &  ! [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 |  ~ (star(v4) = v3) |  ~ (star(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (divergence(v4) = v3) |  ~ (divergence(v4) = v2)) &  ! [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 |  ~ (domain(v2) = v3) |  ? [v4] :  ? [v5] : ( ~ (v5 = v4) & forward_diamond(v0, v3) = v4 & addition(v3, v4) = v5)) &  ! [v2] :  ! [v3] : (v3 = zero |  ~ (multiplication(v2, zero) = v3)) &  ! [v2] :  ! [v3] : (v3 = zero |  ~ (multiplication(zero, v2) = v3)) &  ! [v2] :  ! [v3] : ( ~ (divergence(v2) = v3) | forward_diamond(v2, v3) = 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] : star(v2) = v3 &  ? [v2] :  ? [v3] : divergence(v2) = v3 &  ? [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)
% 16.14/6.48  | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 16.14/6.48  | (1)  ~ (all_0_0_0 = zero) & divergence(all_0_1_1) = all_0_0_0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (star(v1) = v6) |  ~ (divergence(v1) = v5) |  ~ (forward_diamond(v6, v4) = v7) |  ~ (domain(v2) = v4) |  ~ (domain(v0) = v3) |  ~ (addition(v5, v7) = v8) |  ~ (addition(v3, v8) = v9) |  ? [v10] :  ? [v11] :  ? [v12] : ( ~ (v12 = v11) & forward_diamond(v1, v3) = v10 & addition(v10, v4) = v11 & addition(v3, v11) = v12)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (forward_diamond(v1, v3) = v4) |  ~ (domain(v2) = v5) |  ~ (domain(v0) = v3) |  ~ (addition(v4, v5) = v6) |  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] : ((v11 = v10 & star(v1) = v8 & divergence(v1) = v7 & forward_diamond(v8, v5) = v9 & addition(v7, v9) = v10 & addition(v3, v10) = v10) | ( ~ (v7 = v6) & addition(v3, v6) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v1, v2) = v4) |  ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v4) = v5) |  ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v0, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ~ (addition(v3, v4) = v5) |  ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (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 |  ~ (star(v2) = v1) |  ~ (star(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (divergence(v2) = v1) |  ~ (divergence(v2) = v0)) &  ! [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 |  ~ (domain(v0) = v1) |  ? [v2] :  ? [v3] : ( ~ (v3 = v2) & forward_diamond(all_0_1_1, v1) = v2 & addition(v1, v2) = v3)) &  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1)) &  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (divergence(v0) = v1) | forward_diamond(v0, v1) = 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] : star(v0) = v1 &  ? [v0] :  ? [v1] : divergence(v0) = v1 &  ? [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
% 16.20/6.50  |
% 16.20/6.50  | Applying alpha-rule on (1) yields:
% 16.20/6.50  | (2)  ? [v0] :  ? [v1] : star(v0) = v1
% 16.20/6.50  | (3)  ? [v0] :  ? [v1] :  ? [v2] : backward_diamond(v1, v0) = v2
% 16.20/6.50  | (4)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (backward_diamond(v0, v1) = v2) |  ? [v3] :  ? [v4] : (codomain(v4) = v2 & codomain(v1) = v3 & multiplication(v3, v0) = v4))
% 16.20/6.50  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (star(v1) = v6) |  ~ (divergence(v1) = v5) |  ~ (forward_diamond(v6, v4) = v7) |  ~ (domain(v2) = v4) |  ~ (domain(v0) = v3) |  ~ (addition(v5, v7) = v8) |  ~ (addition(v3, v8) = v9) |  ? [v10] :  ? [v11] :  ? [v12] : ( ~ (v12 = v11) & forward_diamond(v1, v3) = v10 & addition(v10, v4) = v11 & addition(v3, v11) = v12))
% 16.20/6.51  | (6)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 16.20/6.51  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 16.20/6.51  | (8)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (leq(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3))
% 16.20/6.51  | (9)  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) |  ? [v2] : (domain(v0) = v2 & antidomain(v1) = v2))
% 16.27/6.51  | (10)  ? [v0] :  ? [v1] :  ? [v2] : forward_diamond(v1, v0) = v2
% 16.27/6.51  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (forward_diamond(v1, v3) = v4) |  ~ (domain(v2) = v5) |  ~ (domain(v0) = v3) |  ~ (addition(v4, v5) = v6) |  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] : ((v11 = v10 & star(v1) = v8 & divergence(v1) = v7 & forward_diamond(v8, v5) = v9 & addition(v7, v9) = v10 & addition(v3, v10) = v10) | ( ~ (v7 = v6) & addition(v3, v6) = v7)))
% 16.27/6.51  | (12)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 16.27/6.51  | (13)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (forward_diamond(v0, v1) = v2) |  ? [v3] :  ? [v4] : (domain(v4) = v2 & domain(v1) = v3 & multiplication(v0, v3) = v4))
% 16.27/6.51  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (forward_diamond(v0, v2) = v3) |  ~ (c(v1) = v2) |  ? [v4] : (forward_box(v0, v1) = v4 & c(v3) = v4))
% 16.27/6.51  | (15)  ? [v0] :  ? [v1] : c(v0) = v1
% 16.27/6.51  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (backward_diamond(v3, v2) = v1) |  ~ (backward_diamond(v3, v2) = v0))
% 16.27/6.51  | (17)  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) | multiplication(v1, v0) = zero)
% 16.27/6.51  | (18)  ! [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))
% 16.27/6.51  | (19)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0)
% 16.27/6.51  | (20)  ! [v0] :  ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1)
% 16.27/6.51  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 16.27/6.51  | (22) divergence(all_0_1_1) = all_0_0_0
% 16.27/6.51  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (domain(v1) = v2) |  ~ (multiplication(v0, v2) = v3) |  ? [v4] : (forward_diamond(v0, v1) = v4 & domain(v3) = v4))
% 16.27/6.51  | (24)  ! [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))
% 16.27/6.51  | (25)  ! [v0] :  ! [v1] : ( ~ (antidomain(v0) = v1) |  ? [v2] : (antidomain(v1) = v2 & addition(v2, v1) = one))
% 16.30/6.51  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (forward_box(v3, v2) = v1) |  ~ (forward_box(v3, v2) = v0))
% 16.30/6.51  | (27)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (antidomain(v2) = v1) |  ~ (antidomain(v2) = v0))
% 16.30/6.51  | (28)  ? [v0] :  ? [v1] : domain(v0) = v1
% 16.30/6.51  | (29)  ~ (all_0_0_0 = zero)
% 16.30/6.51  | (30)  ! [v0] :  ! [v1] : ( ~ (codomain(v0) = v1) |  ? [v2] : (coantidomain(v2) = v1 & coantidomain(v0) = v2))
% 16.30/6.51  | (31)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (star(v2) = v1) |  ~ (star(v2) = v0))
% 16.30/6.51  | (32)  ? [v0] :  ? [v1] :  ? [v2] : multiplication(v1, v0) = v2
% 16.30/6.51  | (33)  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) | multiplication(v0, v1) = zero)
% 16.30/6.52  | (34)  ? [v0] :  ? [v1] : divergence(v0) = v1
% 16.30/6.52  | (35)  ? [v0] :  ? [v1] :  ? [v2] : backward_box(v1, v0) = v2
% 16.30/6.52  | (36)  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) |  ? [v2] : (antidomain(v2) = v1 & antidomain(v0) = v2))
% 16.30/6.52  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 16.30/6.52  | (38)  ? [v0] :  ? [v1] :  ? [v2] : addition(v1, v0) = v2
% 16.30/6.52  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (codomain(v1) = v2) |  ~ (multiplication(v2, v0) = v3) |  ? [v4] : (backward_diamond(v0, v1) = v4 & codomain(v3) = v4))
% 16.30/6.52  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (forward_diamond(v3, v2) = v1) |  ~ (forward_diamond(v3, v2) = v0))
% 16.30/6.52  | (41)  ? [v0] :  ? [v1] : codomain(v0) = v1
% 16.30/6.52  | (42)  ! [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))
% 16.30/6.52  | (43)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (divergence(v2) = v1) |  ~ (divergence(v2) = v0))
% 16.30/6.52  | (44)  ? [v0] :  ? [v1] :  ? [v2] : forward_box(v1, v0) = v2
% 16.30/6.52  | (45)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 16.30/6.52  | (46)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(v0, zero) = v1))
% 16.30/6.52  | (47)  ! [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))
% 16.30/6.52  | (48)  ? [v0] :  ? [v1] : antidomain(v0) = v1
% 16.30/6.52  | (49)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 16.30/6.52  | (50)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (coantidomain(v2) = v1) |  ~ (coantidomain(v2) = v0))
% 16.30/6.52  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 16.30/6.52  | (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))
% 16.30/6.52  | (53)  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) |  ? [v2] : (coantidomain(v1) = v2 & addition(v2, v1) = one))
% 16.30/6.52  | (54)  ! [v0] :  ! [v1] : ( ~ (divergence(v0) = v1) | forward_diamond(v0, v1) = v1)
% 16.30/6.52  | (55)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (domain(v0) = v1) |  ? [v2] :  ? [v3] : ( ~ (v3 = v2) & forward_diamond(all_0_1_1, v1) = v2 & addition(v1, v2) = v3))
% 16.30/6.52  | (56)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 16.30/6.52  | (57)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 16.30/6.52  | (58)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (c(v2) = v1) |  ~ (c(v2) = v0))
% 16.30/6.52  | (59)  ! [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))
% 16.30/6.52  | (60)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (domain(v0) = v2) |  ~ (antidomain(v1) = v3) |  ~ (multiplication(v2, v3) = v4) | domain_difference(v0, v1) = v4)
% 16.30/6.52  | (61)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0))
% 16.30/6.52  | (62)  ! [v0] :  ! [v1] : ( ~ (domain(v0) = v1) |  ? [v2] : (c(v0) = v2 & antidomain(v1) = v2))
% 16.30/6.52  | (63)  ? [v0] :  ? [v1] :  ? [v2] : leq(v1, v0) = v2
% 16.30/6.52  | (64)  ! [v0] :  ! [v1] : ( ~ (coantidomain(v0) = v1) |  ? [v2] : (codomain(v0) = v2 & coantidomain(v1) = v2))
% 16.30/6.52  | (65)  ! [v0] :  ! [v1] : ( ~ (c(v0) = v1) |  ? [v2] : (domain(v0) = v2 & antidomain(v2) = v1))
% 16.30/6.52  | (66)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (forward_box(v0, v1) = v2) |  ? [v3] :  ? [v4] : (forward_diamond(v0, v3) = v4 & c(v4) = v2 & c(v1) = v3))
% 16.30/6.52  | (67)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 16.30/6.52  | (68)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 16.30/6.52  | (69)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 16.30/6.52  | (70)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (domain_difference(v0, v1) = v2) |  ? [v3] :  ? [v4] : (domain(v0) = v3 & antidomain(v1) = v4 & multiplication(v3, v4) = v2))
% 16.30/6.52  | (71)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (codomain(v2) = v1) |  ~ (codomain(v2) = v0))
% 16.30/6.52  | (72)  ? [v0] :  ? [v1] :  ? [v2] : domain_difference(v1, v0) = v2
% 16.30/6.52  | (73)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (backward_diamond(v0, v2) = v3) |  ~ (c(v1) = v2) |  ? [v4] : (backward_box(v0, v1) = v4 & c(v3) = v4))
% 16.30/6.53  | (74)  ! [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))
% 16.30/6.53  | (75)  ! [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))
% 16.30/6.53  | (76)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 16.30/6.53  | (77)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 16.30/6.53  | (78)  ? [v0] :  ? [v1] : coantidomain(v0) = v1
% 16.30/6.53  | (79)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (domain_difference(v3, v2) = v1) |  ~ (domain_difference(v3, v2) = v0))
% 16.30/6.53  | (80)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (backward_box(v0, v1) = v2) |  ? [v3] :  ? [v4] : (backward_diamond(v0, v3) = v4 & c(v4) = v2 & c(v1) = v3))
% 16.30/6.53  | (81)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (backward_box(v3, v2) = v1) |  ~ (backward_box(v3, v2) = v0))
% 16.30/6.53  |
% 16.30/6.53  | Instantiating formula (54) with all_0_0_0, all_0_1_1 and discharging atoms divergence(all_0_1_1) = all_0_0_0, yields:
% 16.30/6.53  | (82) forward_diamond(all_0_1_1, all_0_0_0) = all_0_0_0
% 16.30/6.53  |
% 16.30/6.53  | Instantiating formula (13) with all_0_0_0, all_0_0_0, all_0_1_1 and discharging atoms forward_diamond(all_0_1_1, all_0_0_0) = all_0_0_0, yields:
% 16.30/6.53  | (83)  ? [v0] :  ? [v1] : (domain(v1) = all_0_0_0 & domain(all_0_0_0) = v0 & multiplication(all_0_1_1, v0) = v1)
% 16.30/6.53  |
% 16.30/6.53  | Instantiating (83) with all_44_0_40, all_44_1_41 yields:
% 16.30/6.53  | (84) domain(all_44_0_40) = all_0_0_0 & domain(all_0_0_0) = all_44_1_41 & multiplication(all_0_1_1, all_44_1_41) = all_44_0_40
% 16.30/6.53  |
% 16.30/6.53  | Applying alpha-rule on (84) yields:
% 16.30/6.53  | (85) domain(all_44_0_40) = all_0_0_0
% 16.30/6.53  | (86) domain(all_0_0_0) = all_44_1_41
% 16.30/6.53  | (87) multiplication(all_0_1_1, all_44_1_41) = all_44_0_40
% 16.30/6.53  |
% 16.30/6.53  | Instantiating formula (55) with all_0_0_0, all_44_0_40 and discharging atoms domain(all_44_0_40) = all_0_0_0, yields:
% 16.30/6.53  | (88) all_0_0_0 = zero |  ? [v0] :  ? [v1] : ( ~ (v1 = v0) & forward_diamond(all_0_1_1, all_0_0_0) = v0 & addition(all_0_0_0, v0) = v1)
% 16.30/6.53  |
% 16.30/6.53  +-Applying beta-rule and splitting (88), into two cases.
% 16.30/6.53  |-Branch one:
% 16.30/6.53  | (89) all_0_0_0 = zero
% 16.30/6.53  |
% 16.30/6.53  	| Equations (89) can reduce 29 to:
% 16.30/6.53  	| (90) $false
% 16.30/6.53  	|
% 16.30/6.53  	|-The branch is then unsatisfiable
% 16.30/6.53  |-Branch two:
% 16.30/6.53  | (29)  ~ (all_0_0_0 = zero)
% 16.30/6.53  | (92)  ? [v0] :  ? [v1] : ( ~ (v1 = v0) & forward_diamond(all_0_1_1, all_0_0_0) = v0 & addition(all_0_0_0, v0) = v1)
% 16.30/6.53  |
% 16.30/6.53  	| Instantiating (92) with all_67_0_56, all_67_1_57 yields:
% 16.30/6.53  	| (93)  ~ (all_67_0_56 = all_67_1_57) & forward_diamond(all_0_1_1, all_0_0_0) = all_67_1_57 & addition(all_0_0_0, all_67_1_57) = all_67_0_56
% 16.30/6.53  	|
% 16.30/6.53  	| Applying alpha-rule on (93) yields:
% 16.30/6.53  	| (94)  ~ (all_67_0_56 = all_67_1_57)
% 16.30/6.53  	| (95) forward_diamond(all_0_1_1, all_0_0_0) = all_67_1_57
% 16.30/6.53  	| (96) addition(all_0_0_0, all_67_1_57) = all_67_0_56
% 16.30/6.53  	|
% 16.30/6.53  	| Instantiating formula (40) with all_0_1_1, all_0_0_0, all_67_1_57, all_0_0_0 and discharging atoms forward_diamond(all_0_1_1, all_0_0_0) = all_67_1_57, forward_diamond(all_0_1_1, all_0_0_0) = all_0_0_0, yields:
% 16.30/6.53  	| (97) all_67_1_57 = all_0_0_0
% 16.30/6.53  	|
% 16.30/6.53  	| Equations (97) can reduce 94 to:
% 16.30/6.53  	| (98)  ~ (all_67_0_56 = all_0_0_0)
% 16.30/6.53  	|
% 16.30/6.53  	| From (97) and (96) follows:
% 16.30/6.53  	| (99) addition(all_0_0_0, all_0_0_0) = all_67_0_56
% 16.30/6.53  	|
% 16.30/6.53  	| Instantiating formula (57) with all_67_0_56, all_0_0_0 and discharging atoms addition(all_0_0_0, all_0_0_0) = all_67_0_56, yields:
% 16.30/6.53  	| (100) all_67_0_56 = all_0_0_0
% 16.30/6.53  	|
% 16.30/6.53  	| Equations (100) can reduce 98 to:
% 16.30/6.53  	| (90) $false
% 16.30/6.53  	|
% 16.30/6.53  	|-The branch is then unsatisfiable
% 16.30/6.53  % SZS output end Proof for theBenchmark
% 16.30/6.53  
% 16.30/6.53  5935ms
%------------------------------------------------------------------------------