%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : LCL526+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n010.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 09:36:57 EDT 2022

% Result   : Theorem 26.56s 9.18s
% Output   : Proof 103.85s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : LCL526+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.11/0.33  % Computer : n010.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Sun Jul  3 21:46:48 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.18/0.58          ____       _                          
% 0.18/0.58    ___  / __ \_____(_)___  ________  __________
% 0.18/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.18/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.18/0.58  
% 0.18/0.58  A Theorem Prover for First-Order Logic
% 0.18/0.58  (ePrincess v.1.0)
% 0.18/0.58  
% 0.18/0.58  (c) Philipp Rümmer, 2009-2015
% 0.18/0.58  (c) Peter Backeman, 2014-2015
% 0.18/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58  Bug reports to peter@backeman.se
% 0.18/0.58  
% 0.18/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58  
% 0.18/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.66  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.01/1.02  Prover 0: Preprocessing ...
% 3.70/1.50  Prover 0: Constructing countermodel ...
% 14.94/5.94  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 15.39/6.04  Prover 1: Preprocessing ...
% 16.17/6.24  Prover 1: Constructing countermodel ...
% 24.15/8.55  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 24.51/8.61  Prover 2: Preprocessing ...
% 24.58/8.71  Prover 2: Warning: ignoring some quantifiers
% 24.58/8.71  Prover 2: Constructing countermodel ...
% 26.56/9.17  Prover 2: proved (626ms)
% 26.56/9.18  Prover 0: stopped
% 26.56/9.18  Prover 1: stopped
% 26.56/9.18  
% 26.56/9.18  No countermodel exists, formula is valid
% 26.56/9.18  % SZS status Theorem for theBenchmark
% 26.56/9.18  
% 26.56/9.18  Generating proof ... Warning: ignoring some quantifiers
% 102.74/70.99  found it (size 293)
% 102.74/70.99  
% 102.74/70.99  % SZS output start Proof for theBenchmark
% 102.74/70.99  Assumed formulas after preprocessing and simplification: 
% 102.74/70.99  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] :  ? [v21] :  ? [v22] :  ? [v23] :  ? [v24] :  ? [v25] :  ? [v26] :  ? [v27] :  ? [v28] :  ? [v29] :  ? [v30] :  ? [v31] :  ? [v32] :  ? [v33] :  ? [v34] :  ? [v35] :  ? [v36] :  ? [v37] :  ? [v38] :  ? [v39] :  ? [v40] :  ? [v41] :  ? [v42] :  ? [v43] :  ? [v44] :  ? [v45] :  ? [v46] :  ? [v47] :  ? [v48] :  ? [v49] :  ? [v50] :  ? [v51] :  ? [v52] :  ? [v53] :  ? [v54] :  ? [v55] :  ? [v56] :  ? [v57] :  ? [v58] :  ? [v59] :  ? [v60] :  ? [v61] :  ? [v62] :  ? [v63] :  ? [v64] :  ? [v65] :  ? [v66] :  ? [v67] :  ? [v68] :  ? [v69] :  ? [v70] :  ? [v71] :  ? [v72] :  ? [v73] :  ? [v74] :  ? [v75] :  ? [v76] :  ? [v77] :  ? [v78] :  ? [v79] :  ? [v80] :  ? [v81] :  ? [v82] :  ? [v83] :  ? [v84] :  ? [v85] :  ? [v86] :  ? [v87] :  ? [v88] :  ? [v89] :  ? [v90] :  ? [v91] :  ? [v92] :  ? [v93] :  ? [v94] :  ? [v95] :  ? [v96] :  ? [v97] :  ? [v98] :  ? [v99] :  ? [v100] :  ? [v101] :  ? [v102] :  ? [v103] :  ? [v104] :  ? [v105] :  ? [v106] :  ? [v107] :  ? [v108] :  ? [v109] :  ? [v110] :  ? [v111] :  ? [v112] :  ? [v113] :  ? [v114] :  ? [v115] :  ? [v116] :  ? [v117] :  ? [v118] :  ? [v119] :  ? [v120] :  ? [v121] :  ? [v122] :  ? [v123] :  ? [v124] :  ? [v125] :  ? [v126] :  ? [v127] :  ? [v128] :  ? [v129] :  ? [v130] :  ? [v131] :  ? [v132] :  ? [v133] :  ? [v134] :  ? [v135] :  ? [v136] :  ? [v137] :  ? [v138] :  ? [v139] :  ? [v140] :  ? [v141] :  ? [v142] :  ? [v143] :  ? [v144] :  ? [v145] :  ? [v146] :  ? [v147] :  ? [v148] :  ? [v149] :  ? [v150] :  ? [v151] :  ? [v152] :  ? [v153] :  ? [v154] :  ? [v155] :  ? [v156] :  ? [v157] :  ? [v158] :  ? [v159] :  ? [v160] :  ? [v161] :  ? [v162] :  ? [v163] :  ? [v164] :  ? [v165] :  ? [v166] :  ? [v167] :  ? [v168] :  ? [v169] :  ? [v170] :  ? [v171] :  ? [v172] :  ? [v173] :  ? [v174] :  ? [v175] :  ? [v176] :  ? [v177] :  ? [v178] :  ? [v179] :  ? [v180] :  ? [v181] :  ? [v182] :  ? [v183] :  ? [v184] :  ? [v185] :  ? [v186] :  ? [v187] :  ? [v188] :  ? [v189] :  ? [v190] :  ? [v191] :  ? [v192] :  ? [v193] :  ? [v194] : ( ~ (v108 = v107) & strict_equiv(v107, v108) = v109 & is_a_theorem(v109) = 0 & op_implies & op_strict_equiv & op_strict_implies & op_possibly & axiom_5 & axiom_M & axiom_K & necessitation & op_equiv & op_implies_and & op_or & equivalence_3 & equivalence_2 & equivalence_1 & or_3 & or_2 & or_1 & and_3 & and_2 & and_1 & implies_3 & implies_2 & implies_1 & modus_tollens & substitution_of_equivalents & modus_ponens &  ~ substitution_strict_equiv &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] :  ! [v200] : ( ~ (implies(v198, v199) = v200) |  ~ (implies(v196, v197) = v198) |  ~ (implies(v195, v197) = v199) |  ? [v201] :  ? [v202] : (implies(v201, v200) = v202 & implies(v195, v196) = v201 & is_a_theorem(v202) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] : ( ~ (necessarily(v196) = v198) |  ~ (necessarily(v195) = v197) |  ~ (implies(v197, v198) = v199) |  ? [v200] :  ? [v201] :  ? [v202] : (necessarily(v200) = v201 & implies(v201, v199) = v202 & implies(v195, v196) = v200 & is_a_theorem(v202) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] : ( ~ (or(v195, v196) = v198) |  ~ (implies(v198, v197) = v199) |  ? [v200] :  ? [v201] :  ? [v202] :  ? [v203] : (implies(v201, v199) = v202 & implies(v200, v202) = v203 & implies(v196, v197) = v201 & implies(v195, v197) = v200 & is_a_theorem(v203) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] : ( ~ (and(v197, v198) = v199) |  ~ (not(v196) = v198) |  ~ (not(v195) = v197) |  ? [v200] : (or(v195, v196) = v200 & not(v199) = v200)) &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] : ( ~ (not(v196) = v197) |  ~ (not(v195) = v198) |  ~ (implies(v197, v198) = v199) |  ? [v200] :  ? [v201] : (implies(v199, v200) = v201 & implies(v195, v196) = v200 & is_a_theorem(v201) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] : (v196 = v195 |  ~ (strict_equiv(v198, v197) = v196) |  ~ (strict_equiv(v198, v197) = v195)) &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] : (v196 = v195 |  ~ (strict_implies(v198, v197) = v196) |  ~ (strict_implies(v198, v197) = v195)) &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] : (v196 = v195 |  ~ (or(v198, v197) = v196) |  ~ (or(v198, v197) = v195)) &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] : (v196 = v195 |  ~ (and(v198, v197) = v196) |  ~ (and(v198, v197) = v195)) &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] : (v196 = v195 |  ~ (equiv(v198, v197) = v196) |  ~ (equiv(v198, v197) = v195)) &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] : (v196 = v195 |  ~ (implies(v198, v197) = v196) |  ~ (implies(v198, v197) = v195)) &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] : ( ~ (and(v195, v197) = v198) |  ~ (not(v196) = v197) |  ? [v199] : (not(v198) = v199 & implies(v195, v196) = v199)) &  ! [v195] :  ! [v196] :  ! [v197] : (v196 = v195 |  ~ (possibly(v197) = v196) |  ~ (possibly(v197) = v195)) &  ! [v195] :  ! [v196] :  ! [v197] : (v196 = v195 |  ~ (necessarily(v197) = v196) |  ~ (necessarily(v197) = v195)) &  ! [v195] :  ! [v196] :  ! [v197] : (v196 = v195 |  ~ (not(v197) = v196) |  ~ (not(v197) = v195)) &  ! [v195] :  ! [v196] :  ! [v197] : (v196 = v195 |  ~ (equiv(v195, v196) = v197) |  ? [v198] : ( ~ (v198 = 0) & is_a_theorem(v197) = v198)) &  ! [v195] :  ! [v196] :  ! [v197] : (v196 = v195 |  ~ (is_a_theorem(v197) = v196) |  ~ (is_a_theorem(v197) = v195)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (strict_equiv(v195, v196) = v197) |  ? [v198] :  ? [v199] : (strict_implies(v196, v195) = v199 & strict_implies(v195, v196) = v198 & and(v198, v199) = v197)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (strict_implies(v196, v195) = v197) |  ? [v198] :  ? [v199] : (strict_equiv(v195, v196) = v198 & strict_implies(v195, v196) = v199 & and(v199, v197) = v198)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (strict_implies(v195, v196) = v197) |  ? [v198] :  ? [v199] : (strict_equiv(v195, v196) = v198 & strict_implies(v196, v195) = v199 & and(v197, v199) = v198)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (strict_implies(v195, v196) = v197) |  ? [v198] : (necessarily(v198) = v197 & implies(v195, v196) = v198)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (or(v195, v196) = v197) |  ? [v198] :  ? [v199] :  ? [v200] : (and(v198, v199) = v200 & not(v200) = v197 & not(v196) = v199 & not(v195) = v198)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (or(v195, v196) = v197) |  ? [v198] : (implies(v196, v197) = v198 & is_a_theorem(v198) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (or(v195, v196) = v197) |  ? [v198] : (implies(v195, v197) = v198 & is_a_theorem(v198) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (and(v195, v196) = v197) |  ? [v198] :  ? [v199] : (implies(v196, v197) = v198 & implies(v195, v198) = v199 & is_a_theorem(v199) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (and(v195, v196) = v197) |  ? [v198] : (implies(v197, v196) = v198 & is_a_theorem(v198) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (and(v195, v196) = v197) |  ? [v198] : (implies(v197, v195) = v198 & is_a_theorem(v198) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (equiv(v195, v196) = v197) |  ? [v198] :  ? [v199] :  ? [v200] :  ? [v201] : (implies(v199, v197) = v200 & implies(v198, v200) = v201 & implies(v196, v195) = v199 & implies(v195, v196) = v198 & is_a_theorem(v201) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (equiv(v195, v196) = v197) |  ? [v198] :  ? [v199] : (and(v198, v199) = v197 & implies(v196, v195) = v199 & implies(v195, v196) = v198)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (equiv(v195, v196) = v197) |  ? [v198] :  ? [v199] : (implies(v197, v198) = v199 & implies(v196, v195) = v198 & is_a_theorem(v199) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (equiv(v195, v196) = v197) |  ? [v198] :  ? [v199] : (implies(v197, v198) = v199 & implies(v195, v196) = v198 & is_a_theorem(v199) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (implies(v196, v195) = v197) |  ? [v198] :  ? [v199] :  ? [v200] :  ? [v201] : (equiv(v195, v196) = v199 & implies(v198, v200) = v201 & implies(v197, v199) = v200 & implies(v195, v196) = v198 & is_a_theorem(v201) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (implies(v196, v195) = v197) |  ? [v198] :  ? [v199] : (and(v199, v197) = v198 & equiv(v195, v196) = v198 & implies(v195, v196) = v199)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (implies(v196, v195) = v197) |  ? [v198] :  ? [v199] : (equiv(v195, v196) = v198 & implies(v198, v197) = v199 & is_a_theorem(v199) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (implies(v196, v195) = v197) |  ? [v198] : (implies(v195, v197) = v198 & is_a_theorem(v198) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (implies(v195, v196) = v197) |  ? [v198] :  ? [v199] :  ? [v200] :  ? [v201] :  ? [v202] : (necessarily(v197) = v198 & necessarily(v196) = v200 & necessarily(v195) = v199 & implies(v199, v200) = v201 & implies(v198, v201) = v202 & is_a_theorem(v202) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (implies(v195, v196) = v197) |  ? [v198] :  ? [v199] :  ? [v200] :  ? [v201] : (not(v196) = v198 & not(v195) = v199 & implies(v200, v197) = v201 & implies(v198, v199) = v200 & is_a_theorem(v201) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (implies(v195, v196) = v197) |  ? [v198] :  ? [v199] :  ? [v200] :  ? [v201] : (equiv(v195, v196) = v199 & implies(v198, v199) = v200 & implies(v197, v200) = v201 & implies(v196, v195) = v198 & is_a_theorem(v201) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (implies(v195, v196) = v197) |  ? [v198] :  ? [v199] : (and(v197, v199) = v198 & equiv(v195, v196) = v198 & implies(v196, v195) = v199)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (implies(v195, v196) = v197) |  ? [v198] :  ? [v199] : (and(v195, v198) = v199 & not(v199) = v197 & not(v196) = v198)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (implies(v195, v196) = v197) |  ? [v198] :  ? [v199] : (equiv(v195, v196) = v198 & implies(v198, v197) = v199 & is_a_theorem(v199) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (implies(v195, v196) = v197) |  ? [v198] :  ? [v199] : (implies(v198, v197) = v199 & implies(v195, v197) = v198 & is_a_theorem(v199) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (implies(v195, v196) = v197) |  ? [v198] : (strict_implies(v195, v196) = v198 & necessarily(v197) = v198)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (implies(v195, v196) = v197) |  ? [v198] : ((v198 = 0 & is_a_theorem(v196) = 0) | ( ~ (v198 = 0) & is_a_theorem(v197) = v198) | ( ~ (v198 = 0) & is_a_theorem(v195) = v198))) &  ! [v195] :  ! [v196] : ( ~ (possibly(v195) = v196) |  ? [v197] :  ? [v198] : (necessarily(v197) = v198 & not(v198) = v196 & not(v195) = v197)) &  ! [v195] :  ! [v196] : ( ~ (possibly(v195) = v196) |  ? [v197] :  ? [v198] : (necessarily(v196) = v197 & implies(v196, v197) = v198 & is_a_theorem(v198) = 0)) &  ! [v195] :  ! [v196] : ( ~ (necessarily(v195) = v196) |  ? [v197] : (implies(v196, v195) = v197 & is_a_theorem(v197) = 0)) &  ! [v195] :  ! [v196] : ( ~ (necessarily(v195) = v196) |  ? [v197] : ((v197 = 0 & is_a_theorem(v196) = 0) | ( ~ (v197 = 0) & is_a_theorem(v195) = v197))) &  ! [v195] :  ! [v196] : ( ~ (not(v195) = v196) |  ? [v197] :  ? [v198] : (possibly(v195) = v197 & necessarily(v196) = v198 & not(v198) = v197)) &  ! [v195] : ( ~ (is_a_theorem(v195) = 0) |  ? [v196] : (necessarily(v195) = v196 & is_a_theorem(v196) = 0)) &  ? [v195] :  ? [v196] :  ? [v197] : strict_equiv(v196, v195) = v197 &  ? [v195] :  ? [v196] :  ? [v197] : strict_implies(v196, v195) = v197 &  ? [v195] :  ? [v196] :  ? [v197] : or(v196, v195) = v197 &  ? [v195] :  ? [v196] :  ? [v197] : and(v196, v195) = v197 &  ? [v195] :  ? [v196] :  ? [v197] : equiv(v196, v195) = v197 &  ? [v195] :  ? [v196] :  ? [v197] : implies(v196, v195) = v197 &  ? [v195] :  ? [v196] : possibly(v195) = v196 &  ? [v195] :  ? [v196] : necessarily(v195) = v196 &  ? [v195] :  ? [v196] : not(v195) = v196 &  ? [v195] :  ? [v196] : is_a_theorem(v195) = v196 & ( ~ op_necessarily | ( ! [v195] :  ! [v196] : ( ~ (necessarily(v195) = v196) |  ? [v197] :  ? [v198] : (possibly(v197) = v198 & not(v198) = v196 & not(v195) = v197)) &  ! [v195] :  ! [v196] : ( ~ (not(v195) = v196) |  ? [v197] :  ? [v198] : (possibly(v196) = v198 & necessarily(v195) = v197 & not(v198) = v197)))) & ( ~ op_implies_or | ( ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] : ( ~ (or(v197, v196) = v198) |  ~ (not(v195) = v197) | implies(v195, v196) = v198) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (implies(v195, v196) = v197) |  ? [v198] : (or(v198, v196) = v197 & not(v195) = v198)))) & ( ~ op_and | ( ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] : ( ~ (or(v197, v198) = v199) |  ~ (not(v196) = v198) |  ~ (not(v195) = v197) |  ? [v200] : (and(v195, v196) = v200 & not(v199) = v200)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (and(v195, v196) = v197) |  ? [v198] :  ? [v199] :  ? [v200] : (or(v198, v199) = v200 & not(v200) = v197 & not(v196) = v199 & not(v195) = v198)))) & ((v120 = 0 & v118 = 0 &  ~ (v121 = 0) & strict_implies(v116, v117) = v119 & is_a_theorem(v119) = 0 & is_a_theorem(v117) = v121 & is_a_theorem(v116) = 0 &  ~ modus_ponens_strict_implies) | (modus_ponens_strict_implies &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (strict_implies(v195, v196) = v197) |  ? [v198] : ((v198 = 0 & is_a_theorem(v196) = 0) | ( ~ (v198 = 0) & is_a_theorem(v197) = v198) | ( ~ (v198 = 0) & is_a_theorem(v195) = v198))))) & ((v113 = 0 & v112 = 0 &  ~ (v115 = 0) & and(v110, v111) = v114 & is_a_theorem(v114) = v115 & is_a_theorem(v111) = 0 & is_a_theorem(v110) = 0 &  ~ adjunction) | (adjunction &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (and(v195, v196) = v197) |  ? [v198] : ((v198 = 0 & is_a_theorem(v197) = 0) | ( ~ (v198 = 0) & is_a_theorem(v196) = v198) | ( ~ (v198 = 0) & is_a_theorem(v195) = v198))))) & (( ~ (v194 = 0) & and(v191, v191) = v192 & implies(v191, v192) = v193 & is_a_theorem(v193) = v194 &  ~ kn1) | (kn1 &  ! [v195] :  ! [v196] : ( ~ (and(v195, v195) = v196) |  ? [v197] : (implies(v195, v196) = v197 & is_a_theorem(v197) = 0)))) & (( ~ (v190 = 0) & and(v186, v187) = v188 & implies(v188, v186) = v189 & is_a_theorem(v189) = v190 &  ~ kn2) | (kn2 &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (and(v195, v196) = v197) |  ? [v198] : (implies(v197, v195) = v198 & is_a_theorem(v198) = 0)))) & (( ~ (v185 = 0) & and(v177, v175) = v181 & and(v176, v177) = v179 & not(v181) = v182 & not(v179) = v180 & implies(v180, v182) = v183 & implies(v178, v183) = v184 & implies(v175, v176) = v178 & is_a_theorem(v184) = v185 &  ~ kn3) | (kn3 &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] :  ! [v200] :  ! [v201] :  ! [v202] : ( ~ (and(v197, v195) = v200) |  ~ (and(v196, v197) = v198) |  ~ (not(v200) = v201) |  ~ (not(v198) = v199) |  ~ (implies(v199, v201) = v202) |  ? [v203] :  ? [v204] : (implies(v203, v202) = v204 & implies(v195, v196) = v203 & is_a_theorem(v204) = 0)))) & (( ~ (v174 = 0) & implies(v170, v171) = v172 & implies(v169, v172) = v173 & implies(v167, v168) = v170 & implies(v166, v168) = v171 & implies(v166, v167) = v169 & is_a_theorem(v173) = v174 &  ~ cn1) | (cn1 &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] :  ! [v200] : ( ~ (implies(v198, v199) = v200) |  ~ (implies(v196, v197) = v198) |  ~ (implies(v195, v197) = v199) |  ? [v201] :  ? [v202] : (implies(v201, v200) = v202 & implies(v195, v196) = v201 & is_a_theorem(v202) = 0)))) & (( ~ (v165 = 0) & not(v160) = v162 & implies(v162, v161) = v163 & implies(v160, v163) = v164 & is_a_theorem(v164) = v165 &  ~ cn2) | (cn2 &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] : ( ~ (not(v195) = v197) |  ~ (implies(v197, v196) = v198) |  ? [v199] : (implies(v195, v198) = v199 & is_a_theorem(v199) = 0)))) & (( ~ (v159 = 0) & not(v155) = v156 & implies(v157, v155) = v158 & implies(v156, v155) = v157 & is_a_theorem(v158) = v159 &  ~ cn3) | (cn3 &  ! [v195] :  ! [v196] : ( ~ (not(v195) = v196) |  ? [v197] :  ? [v198] : (implies(v197, v195) = v198 & implies(v196, v195) = v197 & is_a_theorem(v198) = 0)))) & (( ~ (v154 = 0) & or(v151, v151) = v152 & implies(v152, v151) = v153 & is_a_theorem(v153) = v154 &  ~ r1) | (r1 &  ! [v195] :  ! [v196] : ( ~ (or(v195, v195) = v196) |  ? [v197] : (implies(v196, v195) = v197 & is_a_theorem(v197) = 0)))) & (( ~ (v150 = 0) & or(v146, v147) = v148 & implies(v147, v148) = v149 & is_a_theorem(v149) = v150 &  ~ r2) | (r2 &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (or(v195, v196) = v197) |  ? [v198] : (implies(v196, v197) = v198 & is_a_theorem(v198) = 0)))) & (( ~ (v145 = 0) & or(v141, v140) = v143 & or(v140, v141) = v142 & implies(v142, v143) = v144 & is_a_theorem(v144) = v145 &  ~ r3) | (r3 &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (or(v196, v195) = v197) |  ? [v198] :  ? [v199] : (or(v195, v196) = v198 & implies(v198, v197) = v199 & is_a_theorem(v199) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (or(v195, v196) = v197) |  ? [v198] :  ? [v199] : (or(v196, v195) = v198 & implies(v197, v198) = v199 & is_a_theorem(v199) = 0)))) & (( ~ (v139 = 0) & or(v132, v136) = v137 & or(v132, v133) = v134 & or(v131, v134) = v135 & or(v131, v133) = v136 & implies(v135, v137) = v138 & is_a_theorem(v138) = v139 &  ~ r4) | (r4 &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] : ( ~ (or(v196, v198) = v199) |  ~ (or(v195, v197) = v198) |  ? [v200] :  ? [v201] :  ? [v202] : (or(v196, v197) = v200 & or(v195, v200) = v201 & implies(v201, v199) = v202 & is_a_theorem(v202) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] : ( ~ (or(v196, v197) = v198) |  ~ (or(v195, v198) = v199) |  ? [v200] :  ? [v201] :  ? [v202] : (or(v196, v200) = v201 & or(v195, v197) = v200 & implies(v199, v201) = v202 & is_a_theorem(v202) = 0)))) & (( ~ (v130 = 0) & or(v122, v124) = v127 & or(v122, v123) = v126 & implies(v126, v127) = v128 & implies(v125, v128) = v129 & implies(v123, v124) = v125 & is_a_theorem(v129) = v130 &  ~ r5) | (r5 &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] :  ! [v200] : ( ~ (or(v195, v197) = v199) |  ~ (or(v195, v196) = v198) |  ~ (implies(v198, v199) = v200) |  ? [v201] :  ? [v202] : (implies(v201, v200) = v202 & implies(v196, v197) = v201 & is_a_theorem(v202) = 0)))) & (( ~ (v106 = 0) & necessarily(v103) = v104 & necessarily(v102) = v103 & implies(v103, v104) = v105 & is_a_theorem(v105) = v106 &  ~ axiom_4) | (axiom_4 &  ! [v195] :  ! [v196] : ( ~ (necessarily(v195) = v196) |  ? [v197] :  ? [v198] : (necessarily(v196) = v197 & implies(v196, v197) = v198 & is_a_theorem(v198) = 0)))) & (( ~ (v101 = 0) & possibly(v97) = v98 & necessarily(v98) = v99 & implies(v97, v99) = v100 & is_a_theorem(v100) = v101 &  ~ axiom_B) | (axiom_B &  ! [v195] :  ! [v196] : ( ~ (possibly(v195) = v196) |  ? [v197] :  ? [v198] : (necessarily(v196) = v197 & implies(v195, v197) = v198 & is_a_theorem(v198) = 0)))) & (( ~ (v96 = 0) & necessarily(v93) = v94 & necessarily(v90) = v91 & necessarily(v88) = v89 & and(v89, v91) = v92 & implies(v92, v94) = v95 & implies(v86, v87) = v90 & implies(v85, v87) = v93 & implies(v85, v86) = v88 & is_a_theorem(v95) = v96 &  ~ axiom_s1) | (axiom_s1 &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] :  ! [v200] :  ! [v201] :  ! [v202] : ( ~ (necessarily(v200) = v201) |  ~ (necessarily(v198) = v199) |  ~ (and(v199, v201) = v202) |  ~ (implies(v196, v197) = v200) |  ~ (implies(v195, v196) = v198) |  ? [v203] :  ? [v204] :  ? [v205] : (necessarily(v203) = v204 & implies(v202, v204) = v205 & implies(v195, v197) = v203 & is_a_theorem(v205) = 0)))) & (( ~ (v84 = 0) & possibly(v78) = v79 & possibly(v77) = v81 & possibly(v76) = v80 & strict_implies(v79, v82) = v83 & and(v80, v81) = v82 & and(v76, v77) = v78 & is_a_theorem(v83) = v84 &  ~ axiom_s2) | (axiom_s2 &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] : ( ~ (possibly(v196) = v198) |  ~ (possibly(v195) = v197) |  ~ (and(v197, v198) = v199) |  ? [v200] :  ? [v201] :  ? [v202] : (possibly(v200) = v201 & strict_implies(v201, v199) = v202 & and(v195, v196) = v200 & is_a_theorem(v202) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (and(v195, v196) = v197) |  ? [v198] :  ? [v199] :  ? [v200] :  ? [v201] :  ? [v202] : (possibly(v197) = v198 & possibly(v196) = v200 & possibly(v195) = v199 & strict_implies(v198, v201) = v202 & and(v199, v200) = v201 & is_a_theorem(v202) = 0)))) & (( ~ (v75 = 0) & possibly(v67) = v69 & possibly(v66) = v71 & strict_implies(v70, v72) = v73 & strict_implies(v68, v73) = v74 & strict_implies(v66, v67) = v68 & not(v71) = v72 & not(v69) = v70 & is_a_theorem(v74) = v75 &  ~ axiom_s3) | (axiom_s3 &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] :  ! [v200] :  ! [v201] : ( ~ (possibly(v196) = v197) |  ~ (possibly(v195) = v199) |  ~ (strict_implies(v198, v200) = v201) |  ~ (not(v199) = v200) |  ~ (not(v197) = v198) |  ? [v202] :  ? [v203] : (strict_implies(v202, v201) = v203 & strict_implies(v195, v196) = v202 & is_a_theorem(v203) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (strict_implies(v195, v196) = v197) |  ? [v198] :  ? [v199] :  ? [v200] :  ? [v201] :  ? [v202] :  ? [v203] : (possibly(v196) = v198 & possibly(v195) = v200 & strict_implies(v199, v201) = v202 & strict_implies(v197, v202) = v203 & not(v200) = v201 & not(v198) = v199 & is_a_theorem(v203) = 0)))) & (( ~ (v65 = 0) & strict_implies(v62, v63) = v64 & necessarily(v62) = v63 & necessarily(v61) = v62 & is_a_theorem(v64) = v65 &  ~ axiom_s4) | (axiom_s4 &  ! [v195] :  ! [v196] : ( ~ (necessarily(v195) = v196) |  ? [v197] :  ? [v198] : (strict_implies(v196, v197) = v198 & necessarily(v196) = v197 & is_a_theorem(v198) = 0)))) & (( ~ (v60 = 0) & strict_implies(v57, v58) = v59 & and(v56, v55) = v58 & and(v55, v56) = v57 & is_a_theorem(v59) = v60 &  ~ axiom_m1) | (axiom_m1 &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (and(v196, v195) = v197) |  ? [v198] :  ? [v199] : (strict_implies(v198, v197) = v199 & and(v195, v196) = v198 & is_a_theorem(v199) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (and(v195, v196) = v197) |  ? [v198] :  ? [v199] : (strict_implies(v197, v198) = v199 & and(v196, v195) = v198 & is_a_theorem(v199) = 0)))) & (( ~ (v54 = 0) & strict_implies(v52, v50) = v53 & and(v50, v51) = v52 & is_a_theorem(v53) = v54 &  ~ axiom_m2) | (axiom_m2 &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (and(v195, v196) = v197) |  ? [v198] : (strict_implies(v197, v195) = v198 & is_a_theorem(v198) = 0)))) & (( ~ (v49 = 0) & strict_implies(v45, v47) = v48 & and(v44, v43) = v45 & and(v42, v43) = v46 & and(v41, v46) = v47 & and(v41, v42) = v44 & is_a_theorem(v48) = v49 &  ~ axiom_m3) | (axiom_m3 &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] : ( ~ (and(v198, v197) = v199) |  ~ (and(v195, v196) = v198) |  ? [v200] :  ? [v201] :  ? [v202] : (strict_implies(v199, v201) = v202 & and(v196, v197) = v200 & and(v195, v200) = v201 & is_a_theorem(v202) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] : ( ~ (and(v196, v197) = v198) |  ~ (and(v195, v198) = v199) |  ? [v200] :  ? [v201] :  ? [v202] : (strict_implies(v201, v199) = v202 & and(v200, v197) = v201 & and(v195, v196) = v200 & is_a_theorem(v202) = 0)))) & (( ~ (v40 = 0) & strict_implies(v37, v38) = v39 & and(v37, v37) = v38 & is_a_theorem(v39) = v40 &  ~ axiom_m4) | (axiom_m4 &  ! [v195] :  ! [v196] : ( ~ (and(v195, v195) = v196) |  ? [v197] : (strict_implies(v195, v196) = v197 & is_a_theorem(v197) = 0)))) & (( ~ (v36 = 0) & strict_implies(v33, v34) = v35 & strict_implies(v29, v30) = v32 & strict_implies(v28, v30) = v34 & strict_implies(v28, v29) = v31 & and(v31, v32) = v33 & is_a_theorem(v35) = v36 &  ~ axiom_m5) | (axiom_m5 &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] :  ! [v200] : ( ~ (strict_implies(v196, v197) = v199) |  ~ (strict_implies(v195, v196) = v198) |  ~ (and(v198, v199) = v200) |  ? [v201] :  ? [v202] : (strict_implies(v200, v201) = v202 & strict_implies(v195, v197) = v201 & is_a_theorem(v202) = 0)))) & (( ~ (v27 = 0) & possibly(v24) = v25 & strict_implies(v24, v25) = v26 & is_a_theorem(v26) = v27 &  ~ axiom_m6) | (axiom_m6 &  ! [v195] :  ! [v196] : ( ~ (possibly(v195) = v196) |  ? [v197] : (strict_implies(v195, v196) = v197 & is_a_theorem(v197) = 0)))) & (( ~ (v23 = 0) & possibly(v20) = v21 & strict_implies(v21, v18) = v22 & and(v18, v19) = v20 & is_a_theorem(v22) = v23 &  ~ axiom_m7) | (axiom_m7 &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (and(v195, v196) = v197) |  ? [v198] :  ? [v199] : (possibly(v197) = v198 & strict_implies(v198, v195) = v199 & is_a_theorem(v199) = 0)))) & (( ~ (v17 = 0) & possibly(v11) = v14 & possibly(v10) = v13 & strict_implies(v13, v14) = v15 & strict_implies(v12, v15) = v16 & strict_implies(v10, v11) = v12 & is_a_theorem(v16) = v17 &  ~ axiom_m8) | (axiom_m8 &  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] :  ! [v199] : ( ~ (possibly(v196) = v198) |  ~ (possibly(v195) = v197) |  ~ (strict_implies(v197, v198) = v199) |  ? [v200] :  ? [v201] : (strict_implies(v200, v199) = v201 & strict_implies(v195, v196) = v200 & is_a_theorem(v201) = 0)) &  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (strict_implies(v195, v196) = v197) |  ? [v198] :  ? [v199] :  ? [v200] :  ? [v201] : (possibly(v196) = v199 & possibly(v195) = v198 & strict_implies(v198, v199) = v200 & strict_implies(v197, v200) = v201 & is_a_theorem(v201) = 0)))) & (( ~ (v9 = 0) & possibly(v6) = v7 & possibly(v5) = v6 & strict_implies(v7, v6) = v8 & is_a_theorem(v8) = v9 &  ~ axiom_m9) | (axiom_m9 &  ! [v195] :  ! [v196] : ( ~ (possibly(v195) = v196) |  ? [v197] :  ? [v198] : (possibly(v196) = v197 & strict_implies(v197, v196) = v198 & is_a_theorem(v198) = 0)))) & (( ~ (v4 = 0) & possibly(v0) = v1 & strict_implies(v1, v2) = v3 & necessarily(v1) = v2 & is_a_theorem(v3) = v4 &  ~ axiom_m10) | (axiom_m10 &  ! [v195] :  ! [v196] : ( ~ (possibly(v195) = v196) |  ? [v197] :  ? [v198] : (strict_implies(v196, v197) = v198 & necessarily(v196) = v197 & is_a_theorem(v198) = 0)))))
% 102.91/71.07  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19, all_0_20_20, all_0_21_21, all_0_22_22, all_0_23_23, all_0_24_24, all_0_25_25, all_0_26_26, all_0_27_27, all_0_28_28, all_0_29_29, all_0_30_30, all_0_31_31, all_0_32_32, all_0_33_33, all_0_34_34, all_0_35_35, all_0_36_36, all_0_37_37, all_0_38_38, all_0_39_39, all_0_40_40, all_0_41_41, all_0_42_42, all_0_43_43, all_0_44_44, all_0_45_45, all_0_46_46, all_0_47_47, all_0_48_48, all_0_49_49, all_0_50_50, all_0_51_51, all_0_52_52, all_0_53_53, all_0_54_54, all_0_55_55, all_0_56_56, all_0_57_57, all_0_58_58, all_0_59_59, all_0_60_60, all_0_61_61, all_0_62_62, all_0_63_63, all_0_64_64, all_0_65_65, all_0_66_66, all_0_67_67, all_0_68_68, all_0_69_69, all_0_70_70, all_0_71_71, all_0_72_72, all_0_73_73, all_0_74_74, all_0_75_75, all_0_76_76, all_0_77_77, all_0_78_78, all_0_79_79, all_0_80_80, all_0_81_81, all_0_82_82, all_0_83_83, all_0_84_84, all_0_85_85, all_0_86_86, all_0_87_87, all_0_88_88, all_0_89_89, all_0_90_90, all_0_91_91, all_0_92_92, all_0_93_93, all_0_94_94, all_0_95_95, all_0_96_96, all_0_97_97, all_0_98_98, all_0_99_99, all_0_100_100, all_0_101_101, all_0_102_102, all_0_103_103, all_0_104_104, all_0_105_105, all_0_106_106, all_0_107_107, all_0_108_108, all_0_109_109, all_0_110_110, all_0_111_111, all_0_112_112, all_0_113_113, all_0_114_114, all_0_115_115, all_0_116_116, all_0_117_117, all_0_118_118, all_0_119_119, all_0_120_120, all_0_121_121, all_0_122_122, all_0_123_123, all_0_124_124, all_0_125_125, all_0_126_126, all_0_127_127, all_0_128_128, all_0_129_129, all_0_130_130, all_0_131_131, all_0_132_132, all_0_133_133, all_0_134_134, all_0_135_135, all_0_136_136, all_0_137_137, all_0_138_138, all_0_139_139, all_0_140_140, all_0_141_141, all_0_142_142, all_0_143_143, all_0_144_144, all_0_145_145, all_0_146_146, all_0_147_147, all_0_148_148, all_0_149_149, all_0_150_150, all_0_151_151, all_0_152_152, all_0_153_153, all_0_154_154, all_0_155_155, all_0_156_156, all_0_157_157, all_0_158_158, all_0_159_159, all_0_160_160, all_0_161_161, all_0_162_162, all_0_163_163, all_0_164_164, all_0_165_165, all_0_166_166, all_0_167_167, all_0_168_168, all_0_169_169, all_0_170_170, all_0_171_171, all_0_172_172, all_0_173_173, all_0_174_174, all_0_175_175, all_0_176_176, all_0_177_177, all_0_178_178, all_0_179_179, all_0_180_180, all_0_181_181, all_0_182_182, all_0_183_183, all_0_184_184, all_0_185_185, all_0_186_186, all_0_187_187, all_0_188_188, all_0_189_189, all_0_190_190, all_0_191_191, all_0_192_192, all_0_193_193, all_0_194_194 yields:
% 102.91/71.07  | (1)  ~ (all_0_86_86 = all_0_87_87) & strict_equiv(all_0_87_87, all_0_86_86) = all_0_85_85 & is_a_theorem(all_0_85_85) = 0 & op_implies & op_strict_equiv & op_strict_implies & op_possibly & axiom_5 & axiom_M & axiom_K & necessitation & op_equiv & op_implies_and & op_or & equivalence_3 & equivalence_2 & equivalence_1 & or_3 & or_2 & or_1 & and_3 & and_2 & and_1 & implies_3 & implies_2 & implies_1 & modus_tollens & substitution_of_equivalents & modus_ponens &  ~ substitution_strict_equiv &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (implies(v3, v4) = v5) |  ~ (implies(v1, v2) = v3) |  ~ (implies(v0, v2) = v4) |  ? [v6] :  ? [v7] : (implies(v6, v5) = v7 & implies(v0, v1) = v6 & is_a_theorem(v7) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (necessarily(v1) = v3) |  ~ (necessarily(v0) = v2) |  ~ (implies(v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (necessarily(v5) = v6 & implies(v6, v4) = v7 & implies(v0, v1) = v5 & is_a_theorem(v7) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (or(v0, v1) = v3) |  ~ (implies(v3, v2) = v4) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (implies(v6, v4) = v7 & implies(v5, v7) = v8 & implies(v1, v2) = v6 & implies(v0, v2) = v5 & is_a_theorem(v8) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (and(v2, v3) = v4) |  ~ (not(v1) = v3) |  ~ (not(v0) = v2) |  ? [v5] : (or(v0, v1) = v5 & not(v4) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (not(v1) = v2) |  ~ (not(v0) = v3) |  ~ (implies(v2, v3) = v4) |  ? [v5] :  ? [v6] : (implies(v4, v5) = v6 & implies(v0, v1) = v5 & is_a_theorem(v6) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (strict_equiv(v3, v2) = v1) |  ~ (strict_equiv(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (strict_implies(v3, v2) = v1) |  ~ (strict_implies(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (or(v3, v2) = v1) |  ~ (or(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (and(v3, v2) = v1) |  ~ (and(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equiv(v3, v2) = v1) |  ~ (equiv(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (implies(v3, v2) = v1) |  ~ (implies(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (and(v0, v2) = v3) |  ~ (not(v1) = v2) |  ? [v4] : (not(v3) = v4 & implies(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (possibly(v2) = v1) |  ~ (possibly(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (necessarily(v2) = v1) |  ~ (necessarily(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (not(v2) = v1) |  ~ (not(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (equiv(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & is_a_theorem(v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (is_a_theorem(v2) = v1) |  ~ (is_a_theorem(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_equiv(v0, v1) = v2) |  ? [v3] :  ? [v4] : (strict_implies(v1, v0) = v4 & strict_implies(v0, v1) = v3 & and(v3, v4) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_implies(v1, v0) = v2) |  ? [v3] :  ? [v4] : (strict_equiv(v0, v1) = v3 & strict_implies(v0, v1) = v4 & and(v4, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (strict_equiv(v0, v1) = v3 & strict_implies(v1, v0) = v4 & and(v2, v4) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_implies(v0, v1) = v2) |  ? [v3] : (necessarily(v3) = v2 & implies(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (and(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] : (implies(v1, v2) = v3 & is_a_theorem(v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] : (implies(v0, v2) = v3 & is_a_theorem(v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] :  ? [v4] : (implies(v1, v2) = v3 & implies(v0, v3) = v4 & is_a_theorem(v4) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : (implies(v2, v1) = v3 & is_a_theorem(v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : (implies(v2, v0) = v3 & is_a_theorem(v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (equiv(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (implies(v4, v2) = v5 & implies(v3, v5) = v6 & implies(v1, v0) = v4 & implies(v0, v1) = v3 & is_a_theorem(v6) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (equiv(v0, v1) = v2) |  ? [v3] :  ? [v4] : (and(v3, v4) = v2 & implies(v1, v0) = v4 & implies(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (equiv(v0, v1) = v2) |  ? [v3] :  ? [v4] : (implies(v2, v3) = v4 & implies(v1, v0) = v3 & is_a_theorem(v4) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (equiv(v0, v1) = v2) |  ? [v3] :  ? [v4] : (implies(v2, v3) = v4 & implies(v0, v1) = v3 & is_a_theorem(v4) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v1, v0) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (equiv(v0, v1) = v4 & implies(v3, v5) = v6 & implies(v2, v4) = v5 & implies(v0, v1) = v3 & is_a_theorem(v6) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v1, v0) = v2) |  ? [v3] :  ? [v4] : (and(v4, v2) = v3 & equiv(v0, v1) = v3 & implies(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v1, v0) = v2) |  ? [v3] :  ? [v4] : (equiv(v0, v1) = v3 & implies(v3, v2) = v4 & is_a_theorem(v4) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v1, v0) = v2) |  ? [v3] : (implies(v0, v2) = v3 & is_a_theorem(v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (necessarily(v2) = v3 & necessarily(v1) = v5 & necessarily(v0) = v4 & implies(v4, v5) = v6 & implies(v3, v6) = v7 & is_a_theorem(v7) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (not(v1) = v3 & not(v0) = v4 & implies(v5, v2) = v6 & implies(v3, v4) = v5 & is_a_theorem(v6) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (equiv(v0, v1) = v4 & implies(v3, v4) = v5 & implies(v2, v5) = v6 & implies(v1, v0) = v3 & is_a_theorem(v6) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (and(v2, v4) = v3 & equiv(v0, v1) = v3 & implies(v1, v0) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (equiv(v0, v1) = v3 & implies(v3, v2) = v4 & is_a_theorem(v4) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (implies(v3, v2) = v4 & implies(v0, v2) = v3 & is_a_theorem(v4) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] : (strict_implies(v0, v1) = v3 & necessarily(v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & is_a_theorem(v1) = 0) | ( ~ (v3 = 0) & is_a_theorem(v2) = v3) | ( ~ (v3 = 0) & is_a_theorem(v0) = v3))) &  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] :  ? [v3] : (necessarily(v2) = v3 & not(v3) = v1 & not(v0) = v2)) &  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] :  ? [v3] : (necessarily(v1) = v2 & implies(v1, v2) = v3 & is_a_theorem(v3) = 0)) &  ! [v0] :  ! [v1] : ( ~ (necessarily(v0) = v1) |  ? [v2] : (implies(v1, v0) = v2 & is_a_theorem(v2) = 0)) &  ! [v0] :  ! [v1] : ( ~ (necessarily(v0) = v1) |  ? [v2] : ((v2 = 0 & is_a_theorem(v1) = 0) | ( ~ (v2 = 0) & is_a_theorem(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (not(v0) = v1) |  ? [v2] :  ? [v3] : (possibly(v0) = v2 & necessarily(v1) = v3 & not(v3) = v2)) &  ! [v0] : ( ~ (is_a_theorem(v0) = 0) |  ? [v1] : (necessarily(v0) = v1 & is_a_theorem(v1) = 0)) &  ? [v0] :  ? [v1] :  ? [v2] : strict_equiv(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : strict_implies(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : or(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : and(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : equiv(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : implies(v1, v0) = v2 &  ? [v0] :  ? [v1] : possibly(v0) = v1 &  ? [v0] :  ? [v1] : necessarily(v0) = v1 &  ? [v0] :  ? [v1] : not(v0) = v1 &  ? [v0] :  ? [v1] : is_a_theorem(v0) = v1 & ( ~ op_necessarily | ( ! [v0] :  ! [v1] : ( ~ (necessarily(v0) = v1) |  ? [v2] :  ? [v3] : (possibly(v2) = v3 & not(v3) = v1 & not(v0) = v2)) &  ! [v0] :  ! [v1] : ( ~ (not(v0) = v1) |  ? [v2] :  ? [v3] : (possibly(v1) = v3 & necessarily(v0) = v2 & not(v3) = v2)))) & ( ~ op_implies_or | ( ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (or(v2, v1) = v3) |  ~ (not(v0) = v2) | implies(v0, v1) = v3) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] : (or(v3, v1) = v2 & not(v0) = v3)))) & ( ~ op_and | ( ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (or(v2, v3) = v4) |  ~ (not(v1) = v3) |  ~ (not(v0) = v2) |  ? [v5] : (and(v0, v1) = v5 & not(v4) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (or(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3)))) & ((all_0_74_74 = 0 & all_0_76_76 = 0 &  ~ (all_0_73_73 = 0) & strict_implies(all_0_78_78, all_0_77_77) = all_0_75_75 & is_a_theorem(all_0_75_75) = 0 & is_a_theorem(all_0_77_77) = all_0_73_73 & is_a_theorem(all_0_78_78) = 0 &  ~ modus_ponens_strict_implies) | (modus_ponens_strict_implies &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_implies(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & is_a_theorem(v1) = 0) | ( ~ (v3 = 0) & is_a_theorem(v2) = v3) | ( ~ (v3 = 0) & is_a_theorem(v0) = v3))))) & ((all_0_81_81 = 0 & all_0_82_82 = 0 &  ~ (all_0_79_79 = 0) & and(all_0_84_84, all_0_83_83) = all_0_80_80 & is_a_theorem(all_0_80_80) = all_0_79_79 & is_a_theorem(all_0_83_83) = 0 & is_a_theorem(all_0_84_84) = 0 &  ~ adjunction) | (adjunction &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & is_a_theorem(v2) = 0) | ( ~ (v3 = 0) & is_a_theorem(v1) = v3) | ( ~ (v3 = 0) & is_a_theorem(v0) = v3))))) & (( ~ (all_0_0_0 = 0) & and(all_0_3_3, all_0_3_3) = all_0_2_2 & implies(all_0_3_3, all_0_2_2) = all_0_1_1 & is_a_theorem(all_0_1_1) = all_0_0_0 &  ~ kn1) | (kn1 &  ! [v0] :  ! [v1] : ( ~ (and(v0, v0) = v1) |  ? [v2] : (implies(v0, v1) = v2 & is_a_theorem(v2) = 0)))) & (( ~ (all_0_4_4 = 0) & and(all_0_8_8, all_0_7_7) = all_0_6_6 & implies(all_0_6_6, all_0_8_8) = all_0_5_5 & is_a_theorem(all_0_5_5) = all_0_4_4 &  ~ kn2) | (kn2 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : (implies(v2, v0) = v3 & is_a_theorem(v3) = 0)))) & (( ~ (all_0_9_9 = 0) & and(all_0_17_17, all_0_19_19) = all_0_13_13 & and(all_0_18_18, all_0_17_17) = all_0_15_15 & not(all_0_13_13) = all_0_12_12 & not(all_0_15_15) = all_0_14_14 & implies(all_0_14_14, all_0_12_12) = all_0_11_11 & implies(all_0_16_16, all_0_11_11) = all_0_10_10 & implies(all_0_19_19, all_0_18_18) = all_0_16_16 & is_a_theorem(all_0_10_10) = all_0_9_9 &  ~ kn3) | (kn3 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (and(v2, v0) = v5) |  ~ (and(v1, v2) = v3) |  ~ (not(v5) = v6) |  ~ (not(v3) = v4) |  ~ (implies(v4, v6) = v7) |  ? [v8] :  ? [v9] : (implies(v8, v7) = v9 & implies(v0, v1) = v8 & is_a_theorem(v9) = 0)))) & (( ~ (all_0_20_20 = 0) & implies(all_0_24_24, all_0_23_23) = all_0_22_22 & implies(all_0_25_25, all_0_22_22) = all_0_21_21 & implies(all_0_27_27, all_0_26_26) = all_0_24_24 & implies(all_0_28_28, all_0_26_26) = all_0_23_23 & implies(all_0_28_28, all_0_27_27) = all_0_25_25 & is_a_theorem(all_0_21_21) = all_0_20_20 &  ~ cn1) | (cn1 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (implies(v3, v4) = v5) |  ~ (implies(v1, v2) = v3) |  ~ (implies(v0, v2) = v4) |  ? [v6] :  ? [v7] : (implies(v6, v5) = v7 & implies(v0, v1) = v6 & is_a_theorem(v7) = 0)))) & (( ~ (all_0_29_29 = 0) & not(all_0_34_34) = all_0_32_32 & implies(all_0_32_32, all_0_33_33) = all_0_31_31 & implies(all_0_34_34, all_0_31_31) = all_0_30_30 & is_a_theorem(all_0_30_30) = all_0_29_29 &  ~ cn2) | (cn2 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (not(v0) = v2) |  ~ (implies(v2, v1) = v3) |  ? [v4] : (implies(v0, v3) = v4 & is_a_theorem(v4) = 0)))) & (( ~ (all_0_35_35 = 0) & not(all_0_39_39) = all_0_38_38 & implies(all_0_37_37, all_0_39_39) = all_0_36_36 & implies(all_0_38_38, all_0_39_39) = all_0_37_37 & is_a_theorem(all_0_36_36) = all_0_35_35 &  ~ cn3) | (cn3 &  ! [v0] :  ! [v1] : ( ~ (not(v0) = v1) |  ? [v2] :  ? [v3] : (implies(v2, v0) = v3 & implies(v1, v0) = v2 & is_a_theorem(v3) = 0)))) & (( ~ (all_0_40_40 = 0) & or(all_0_43_43, all_0_43_43) = all_0_42_42 & implies(all_0_42_42, all_0_43_43) = all_0_41_41 & is_a_theorem(all_0_41_41) = all_0_40_40 &  ~ r1) | (r1 &  ! [v0] :  ! [v1] : ( ~ (or(v0, v0) = v1) |  ? [v2] : (implies(v1, v0) = v2 & is_a_theorem(v2) = 0)))) & (( ~ (all_0_44_44 = 0) & or(all_0_48_48, all_0_47_47) = all_0_46_46 & implies(all_0_47_47, all_0_46_46) = all_0_45_45 & is_a_theorem(all_0_45_45) = all_0_44_44 &  ~ r2) | (r2 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] : (implies(v1, v2) = v3 & is_a_theorem(v3) = 0)))) & (( ~ (all_0_49_49 = 0) & or(all_0_53_53, all_0_54_54) = all_0_51_51 & or(all_0_54_54, all_0_53_53) = all_0_52_52 & implies(all_0_52_52, all_0_51_51) = all_0_50_50 & is_a_theorem(all_0_50_50) = all_0_49_49 &  ~ r3) | (r3 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v1, v0) = v2) |  ? [v3] :  ? [v4] : (or(v0, v1) = v3 & implies(v3, v2) = v4 & is_a_theorem(v4) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] :  ? [v4] : (or(v1, v0) = v3 & implies(v2, v3) = v4 & is_a_theorem(v4) = 0)))) & (( ~ (all_0_55_55 = 0) & or(all_0_62_62, all_0_58_58) = all_0_57_57 & or(all_0_62_62, all_0_61_61) = all_0_60_60 & or(all_0_63_63, all_0_60_60) = all_0_59_59 & or(all_0_63_63, all_0_61_61) = all_0_58_58 & implies(all_0_59_59, all_0_57_57) = all_0_56_56 & is_a_theorem(all_0_56_56) = all_0_55_55 &  ~ r4) | (r4 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (or(v1, v3) = v4) |  ~ (or(v0, v2) = v3) |  ? [v5] :  ? [v6] :  ? [v7] : (or(v1, v2) = v5 & or(v0, v5) = v6 & implies(v6, v4) = v7 & is_a_theorem(v7) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (or(v1, v2) = v3) |  ~ (or(v0, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (or(v1, v5) = v6 & or(v0, v2) = v5 & implies(v4, v6) = v7 & is_a_theorem(v7) = 0)))) & (( ~ (all_0_64_64 = 0) & or(all_0_72_72, all_0_70_70) = all_0_67_67 & or(all_0_72_72, all_0_71_71) = all_0_68_68 & implies(all_0_68_68, all_0_67_67) = all_0_66_66 & implies(all_0_69_69, all_0_66_66) = all_0_65_65 & implies(all_0_71_71, all_0_70_70) = all_0_69_69 & is_a_theorem(all_0_65_65) = all_0_64_64 &  ~ r5) | (r5 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (or(v0, v2) = v4) |  ~ (or(v0, v1) = v3) |  ~ (implies(v3, v4) = v5) |  ? [v6] :  ? [v7] : (implies(v6, v5) = v7 & implies(v1, v2) = v6 & is_a_theorem(v7) = 0)))) & (( ~ (all_0_88_88 = 0) & necessarily(all_0_91_91) = all_0_90_90 & necessarily(all_0_92_92) = all_0_91_91 & implies(all_0_91_91, all_0_90_90) = all_0_89_89 & is_a_theorem(all_0_89_89) = all_0_88_88 &  ~ axiom_4) | (axiom_4 &  ! [v0] :  ! [v1] : ( ~ (necessarily(v0) = v1) |  ? [v2] :  ? [v3] : (necessarily(v1) = v2 & implies(v1, v2) = v3 & is_a_theorem(v3) = 0)))) & (( ~ (all_0_93_93 = 0) & possibly(all_0_97_97) = all_0_96_96 & necessarily(all_0_96_96) = all_0_95_95 & implies(all_0_97_97, all_0_95_95) = all_0_94_94 & is_a_theorem(all_0_94_94) = all_0_93_93 &  ~ axiom_B) | (axiom_B &  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] :  ? [v3] : (necessarily(v1) = v2 & implies(v0, v2) = v3 & is_a_theorem(v3) = 0)))) & (( ~ (all_0_98_98 = 0) & necessarily(all_0_101_101) = all_0_100_100 & necessarily(all_0_104_104) = all_0_103_103 & necessarily(all_0_106_106) = all_0_105_105 & and(all_0_105_105, all_0_103_103) = all_0_102_102 & implies(all_0_102_102, all_0_100_100) = all_0_99_99 & implies(all_0_108_108, all_0_107_107) = all_0_104_104 & implies(all_0_109_109, all_0_107_107) = all_0_101_101 & implies(all_0_109_109, all_0_108_108) = all_0_106_106 & is_a_theorem(all_0_99_99) = all_0_98_98 &  ~ axiom_s1) | (axiom_s1 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (necessarily(v5) = v6) |  ~ (necessarily(v3) = v4) |  ~ (and(v4, v6) = v7) |  ~ (implies(v1, v2) = v5) |  ~ (implies(v0, v1) = v3) |  ? [v8] :  ? [v9] :  ? [v10] : (necessarily(v8) = v9 & implies(v7, v9) = v10 & implies(v0, v2) = v8 & is_a_theorem(v10) = 0)))) & (( ~ (all_0_110_110 = 0) & possibly(all_0_116_116) = all_0_115_115 & possibly(all_0_117_117) = all_0_113_113 & possibly(all_0_118_118) = all_0_114_114 & strict_implies(all_0_115_115, all_0_112_112) = all_0_111_111 & and(all_0_114_114, all_0_113_113) = all_0_112_112 & and(all_0_118_118, all_0_117_117) = all_0_116_116 & is_a_theorem(all_0_111_111) = all_0_110_110 &  ~ axiom_s2) | (axiom_s2 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (possibly(v1) = v3) |  ~ (possibly(v0) = v2) |  ~ (and(v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (possibly(v5) = v6 & strict_implies(v6, v4) = v7 & and(v0, v1) = v5 & is_a_theorem(v7) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (possibly(v2) = v3 & possibly(v1) = v5 & possibly(v0) = v4 & strict_implies(v3, v6) = v7 & and(v4, v5) = v6 & is_a_theorem(v7) = 0)))) & (( ~ (all_0_119_119 = 0) & possibly(all_0_127_127) = all_0_125_125 & possibly(all_0_128_128) = all_0_123_123 & strict_implies(all_0_124_124, all_0_122_122) = all_0_121_121 & strict_implies(all_0_126_126, all_0_121_121) = all_0_120_120 & strict_implies(all_0_128_128, all_0_127_127) = all_0_126_126 & not(all_0_123_123) = all_0_122_122 & not(all_0_125_125) = all_0_124_124 & is_a_theorem(all_0_120_120) = all_0_119_119 &  ~ axiom_s3) | (axiom_s3 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (possibly(v1) = v2) |  ~ (possibly(v0) = v4) |  ~ (strict_implies(v3, v5) = v6) |  ~ (not(v4) = v5) |  ~ (not(v2) = v3) |  ? [v7] :  ? [v8] : (strict_implies(v7, v6) = v8 & strict_implies(v0, v1) = v7 & is_a_theorem(v8) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_implies(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (possibly(v1) = v3 & possibly(v0) = v5 & strict_implies(v4, v6) = v7 & strict_implies(v2, v7) = v8 & not(v5) = v6 & not(v3) = v4 & is_a_theorem(v8) = 0)))) & (( ~ (all_0_129_129 = 0) & strict_implies(all_0_132_132, all_0_131_131) = all_0_130_130 & necessarily(all_0_132_132) = all_0_131_131 & necessarily(all_0_133_133) = all_0_132_132 & is_a_theorem(all_0_130_130) = all_0_129_129 &  ~ axiom_s4) | (axiom_s4 &  ! [v0] :  ! [v1] : ( ~ (necessarily(v0) = v1) |  ? [v2] :  ? [v3] : (strict_implies(v1, v2) = v3 & necessarily(v1) = v2 & is_a_theorem(v3) = 0)))) & (( ~ (all_0_134_134 = 0) & strict_implies(all_0_137_137, all_0_136_136) = all_0_135_135 & and(all_0_138_138, all_0_139_139) = all_0_136_136 & and(all_0_139_139, all_0_138_138) = all_0_137_137 & is_a_theorem(all_0_135_135) = all_0_134_134 &  ~ axiom_m1) | (axiom_m1 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v1, v0) = v2) |  ? [v3] :  ? [v4] : (strict_implies(v3, v2) = v4 & and(v0, v1) = v3 & is_a_theorem(v4) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] :  ? [v4] : (strict_implies(v2, v3) = v4 & and(v1, v0) = v3 & is_a_theorem(v4) = 0)))) & (( ~ (all_0_140_140 = 0) & strict_implies(all_0_142_142, all_0_144_144) = all_0_141_141 & and(all_0_144_144, all_0_143_143) = all_0_142_142 & is_a_theorem(all_0_141_141) = all_0_140_140 &  ~ axiom_m2) | (axiom_m2 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : (strict_implies(v2, v0) = v3 & is_a_theorem(v3) = 0)))) & (( ~ (all_0_145_145 = 0) & strict_implies(all_0_149_149, all_0_147_147) = all_0_146_146 & and(all_0_150_150, all_0_151_151) = all_0_149_149 & and(all_0_152_152, all_0_151_151) = all_0_148_148 & and(all_0_153_153, all_0_148_148) = all_0_147_147 & and(all_0_153_153, all_0_152_152) = all_0_150_150 & is_a_theorem(all_0_146_146) = all_0_145_145 &  ~ axiom_m3) | (axiom_m3 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (and(v3, v2) = v4) |  ~ (and(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] : (strict_implies(v4, v6) = v7 & and(v1, v2) = v5 & and(v0, v5) = v6 & is_a_theorem(v7) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (and(v1, v2) = v3) |  ~ (and(v0, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (strict_implies(v6, v4) = v7 & and(v5, v2) = v6 & and(v0, v1) = v5 & is_a_theorem(v7) = 0)))) & (( ~ (all_0_154_154 = 0) & strict_implies(all_0_157_157, all_0_156_156) = all_0_155_155 & and(all_0_157_157, all_0_157_157) = all_0_156_156 & is_a_theorem(all_0_155_155) = all_0_154_154 &  ~ axiom_m4) | (axiom_m4 &  ! [v0] :  ! [v1] : ( ~ (and(v0, v0) = v1) |  ? [v2] : (strict_implies(v0, v1) = v2 & is_a_theorem(v2) = 0)))) & (( ~ (all_0_158_158 = 0) & strict_implies(all_0_161_161, all_0_160_160) = all_0_159_159 & strict_implies(all_0_165_165, all_0_164_164) = all_0_162_162 & strict_implies(all_0_166_166, all_0_164_164) = all_0_160_160 & strict_implies(all_0_166_166, all_0_165_165) = all_0_163_163 & and(all_0_163_163, all_0_162_162) = all_0_161_161 & is_a_theorem(all_0_159_159) = all_0_158_158 &  ~ axiom_m5) | (axiom_m5 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (strict_implies(v1, v2) = v4) |  ~ (strict_implies(v0, v1) = v3) |  ~ (and(v3, v4) = v5) |  ? [v6] :  ? [v7] : (strict_implies(v5, v6) = v7 & strict_implies(v0, v2) = v6 & is_a_theorem(v7) = 0)))) & (( ~ (all_0_167_167 = 0) & possibly(all_0_170_170) = all_0_169_169 & strict_implies(all_0_170_170, all_0_169_169) = all_0_168_168 & is_a_theorem(all_0_168_168) = all_0_167_167 &  ~ axiom_m6) | (axiom_m6 &  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] : (strict_implies(v0, v1) = v2 & is_a_theorem(v2) = 0)))) & (( ~ (all_0_171_171 = 0) & possibly(all_0_174_174) = all_0_173_173 & strict_implies(all_0_173_173, all_0_176_176) = all_0_172_172 & and(all_0_176_176, all_0_175_175) = all_0_174_174 & is_a_theorem(all_0_172_172) = all_0_171_171 &  ~ axiom_m7) | (axiom_m7 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] :  ? [v4] : (possibly(v2) = v3 & strict_implies(v3, v0) = v4 & is_a_theorem(v4) = 0)))) & (( ~ (all_0_177_177 = 0) & possibly(all_0_183_183) = all_0_180_180 & possibly(all_0_184_184) = all_0_181_181 & strict_implies(all_0_181_181, all_0_180_180) = all_0_179_179 & strict_implies(all_0_182_182, all_0_179_179) = all_0_178_178 & strict_implies(all_0_184_184, all_0_183_183) = all_0_182_182 & is_a_theorem(all_0_178_178) = all_0_177_177 &  ~ axiom_m8) | (axiom_m8 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (possibly(v1) = v3) |  ~ (possibly(v0) = v2) |  ~ (strict_implies(v2, v3) = v4) |  ? [v5] :  ? [v6] : (strict_implies(v5, v4) = v6 & strict_implies(v0, v1) = v5 & is_a_theorem(v6) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_implies(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (possibly(v1) = v4 & possibly(v0) = v3 & strict_implies(v3, v4) = v5 & strict_implies(v2, v5) = v6 & is_a_theorem(v6) = 0)))) & (( ~ (all_0_185_185 = 0) & possibly(all_0_188_188) = all_0_187_187 & possibly(all_0_189_189) = all_0_188_188 & strict_implies(all_0_187_187, all_0_188_188) = all_0_186_186 & is_a_theorem(all_0_186_186) = all_0_185_185 &  ~ axiom_m9) | (axiom_m9 &  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] :  ? [v3] : (possibly(v1) = v2 & strict_implies(v2, v1) = v3 & is_a_theorem(v3) = 0)))) & (( ~ (all_0_190_190 = 0) & possibly(all_0_194_194) = all_0_193_193 & strict_implies(all_0_193_193, all_0_192_192) = all_0_191_191 & necessarily(all_0_193_193) = all_0_192_192 & is_a_theorem(all_0_191_191) = all_0_190_190 &  ~ axiom_m10) | (axiom_m10 &  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] :  ? [v3] : (strict_implies(v1, v2) = v3 & necessarily(v1) = v2 & is_a_theorem(v3) = 0))))
% 102.91/71.11  |
% 102.91/71.11  | Applying alpha-rule on (1) yields:
% 102.91/71.11  | (2)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (equiv(v0, v1) = v2) |  ? [v3] :  ? [v4] : (implies(v2, v3) = v4 & implies(v1, v0) = v3 & is_a_theorem(v4) = 0))
% 102.91/71.11  | (3)  ? [v0] :  ? [v1] :  ? [v2] : or(v1, v0) = v2
% 102.91/71.11  | (4) or_1
% 102.91/71.11  | (5) ( ~ (all_0_29_29 = 0) & not(all_0_34_34) = all_0_32_32 & implies(all_0_32_32, all_0_33_33) = all_0_31_31 & implies(all_0_34_34, all_0_31_31) = all_0_30_30 & is_a_theorem(all_0_30_30) = all_0_29_29 &  ~ cn2) | (cn2 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (not(v0) = v2) |  ~ (implies(v2, v1) = v3) |  ? [v4] : (implies(v0, v3) = v4 & is_a_theorem(v4) = 0)))
% 103.41/71.11  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) = v3))
% 103.41/71.11  | (7) axiom_5
% 103.41/71.11  | (8) op_implies
% 103.41/71.11  | (9) ( ~ (all_0_119_119 = 0) & possibly(all_0_127_127) = all_0_125_125 & possibly(all_0_128_128) = all_0_123_123 & strict_implies(all_0_124_124, all_0_122_122) = all_0_121_121 & strict_implies(all_0_126_126, all_0_121_121) = all_0_120_120 & strict_implies(all_0_128_128, all_0_127_127) = all_0_126_126 & not(all_0_123_123) = all_0_122_122 & not(all_0_125_125) = all_0_124_124 & is_a_theorem(all_0_120_120) = all_0_119_119 &  ~ axiom_s3) | (axiom_s3 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (possibly(v1) = v2) |  ~ (possibly(v0) = v4) |  ~ (strict_implies(v3, v5) = v6) |  ~ (not(v4) = v5) |  ~ (not(v2) = v3) |  ? [v7] :  ? [v8] : (strict_implies(v7, v6) = v8 & strict_implies(v0, v1) = v7 & is_a_theorem(v8) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_implies(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (possibly(v1) = v3 & possibly(v0) = v5 & strict_implies(v4, v6) = v7 & strict_implies(v2, v7) = v8 & not(v5) = v6 & not(v3) = v4 & is_a_theorem(v8) = 0)))
% 103.41/71.12  | (10) equivalence_1
% 103.41/71.12  | (11) op_equiv
% 103.41/71.12  | (12) ( ~ (all_0_88_88 = 0) & necessarily(all_0_91_91) = all_0_90_90 & necessarily(all_0_92_92) = all_0_91_91 & implies(all_0_91_91, all_0_90_90) = all_0_89_89 & is_a_theorem(all_0_89_89) = all_0_88_88 &  ~ axiom_4) | (axiom_4 &  ! [v0] :  ! [v1] : ( ~ (necessarily(v0) = v1) |  ? [v2] :  ? [v3] : (necessarily(v1) = v2 & implies(v1, v2) = v3 & is_a_theorem(v3) = 0)))
% 103.41/71.12  | (13)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_implies(v1, v0) = v2) |  ? [v3] :  ? [v4] : (strict_equiv(v0, v1) = v3 & strict_implies(v0, v1) = v4 & and(v4, v2) = v3))
% 103.41/71.12  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (not(v1) = v3 & not(v0) = v4 & implies(v5, v2) = v6 & implies(v3, v4) = v5 & is_a_theorem(v6) = 0))
% 103.41/71.12  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (and(v0, v2) = v3) |  ~ (not(v1) = v2) |  ? [v4] : (not(v3) = v4 & implies(v0, v1) = v4))
% 103.41/71.12  | (16) strict_equiv(all_0_87_87, all_0_86_86) = all_0_85_85
% 103.41/71.12  | (17)  ~ op_necessarily | ( ! [v0] :  ! [v1] : ( ~ (necessarily(v0) = v1) |  ? [v2] :  ? [v3] : (possibly(v2) = v3 & not(v3) = v1 & not(v0) = v2)) &  ! [v0] :  ! [v1] : ( ~ (not(v0) = v1) |  ? [v2] :  ? [v3] : (possibly(v1) = v3 & necessarily(v0) = v2 & not(v3) = v2)))
% 103.41/71.12  | (18)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v1, v0) = v2) |  ? [v3] :  ? [v4] : (equiv(v0, v1) = v3 & implies(v3, v2) = v4 & is_a_theorem(v4) = 0))
% 103.41/71.12  | (19) ( ~ (all_0_145_145 = 0) & strict_implies(all_0_149_149, all_0_147_147) = all_0_146_146 & and(all_0_150_150, all_0_151_151) = all_0_149_149 & and(all_0_152_152, all_0_151_151) = all_0_148_148 & and(all_0_153_153, all_0_148_148) = all_0_147_147 & and(all_0_153_153, all_0_152_152) = all_0_150_150 & is_a_theorem(all_0_146_146) = all_0_145_145 &  ~ axiom_m3) | (axiom_m3 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (and(v3, v2) = v4) |  ~ (and(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] : (strict_implies(v4, v6) = v7 & and(v1, v2) = v5 & and(v0, v5) = v6 & is_a_theorem(v7) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (and(v1, v2) = v3) |  ~ (and(v0, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (strict_implies(v6, v4) = v7 & and(v5, v2) = v6 & and(v0, v1) = v5 & is_a_theorem(v7) = 0)))
% 103.41/71.12  | (20) ( ~ (all_0_20_20 = 0) & implies(all_0_24_24, all_0_23_23) = all_0_22_22 & implies(all_0_25_25, all_0_22_22) = all_0_21_21 & implies(all_0_27_27, all_0_26_26) = all_0_24_24 & implies(all_0_28_28, all_0_26_26) = all_0_23_23 & implies(all_0_28_28, all_0_27_27) = all_0_25_25 & is_a_theorem(all_0_21_21) = all_0_20_20 &  ~ cn1) | (cn1 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (implies(v3, v4) = v5) |  ~ (implies(v1, v2) = v3) |  ~ (implies(v0, v2) = v4) |  ? [v6] :  ? [v7] : (implies(v6, v5) = v7 & implies(v0, v1) = v6 & is_a_theorem(v7) = 0)))
% 103.41/71.12  | (21) or_2
% 103.41/71.12  | (22) implies_2
% 103.41/71.12  | (23)  ? [v0] :  ? [v1] :  ? [v2] : strict_implies(v1, v0) = v2
% 103.41/71.12  | (24)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] : (strict_implies(v0, v1) = v3 & necessarily(v2) = v3))
% 103.41/71.12  | (25)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (possibly(v2) = v1) |  ~ (possibly(v2) = v0))
% 103.41/71.12  | (26) ( ~ (all_0_129_129 = 0) & strict_implies(all_0_132_132, all_0_131_131) = all_0_130_130 & necessarily(all_0_132_132) = all_0_131_131 & necessarily(all_0_133_133) = all_0_132_132 & is_a_theorem(all_0_130_130) = all_0_129_129 &  ~ axiom_s4) | (axiom_s4 &  ! [v0] :  ! [v1] : ( ~ (necessarily(v0) = v1) |  ? [v2] :  ? [v3] : (strict_implies(v1, v2) = v3 & necessarily(v1) = v2 & is_a_theorem(v3) = 0)))
% 103.41/71.12  | (27)  ? [v0] :  ? [v1] : is_a_theorem(v0) = v1
% 103.41/71.12  | (28)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_implies(v0, v1) = v2) |  ? [v3] : (necessarily(v3) = v2 & implies(v0, v1) = v3))
% 103.41/71.12  | (29)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : (implies(v2, v0) = v3 & is_a_theorem(v3) = 0))
% 103.41/71.12  | (30) modus_ponens
% 103.41/71.12  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (or(v0, v1) = v3) |  ~ (implies(v3, v2) = v4) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (implies(v6, v4) = v7 & implies(v5, v7) = v8 & implies(v1, v2) = v6 & implies(v0, v2) = v5 & is_a_theorem(v8) = 0))
% 103.41/71.12  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (necessarily(v1) = v3) |  ~ (necessarily(v0) = v2) |  ~ (implies(v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (necessarily(v5) = v6 & implies(v6, v4) = v7 & implies(v0, v1) = v5 & is_a_theorem(v7) = 0))
% 103.41/71.12  | (33) ( ~ (all_0_190_190 = 0) & possibly(all_0_194_194) = all_0_193_193 & strict_implies(all_0_193_193, all_0_192_192) = all_0_191_191 & necessarily(all_0_193_193) = all_0_192_192 & is_a_theorem(all_0_191_191) = all_0_190_190 &  ~ axiom_m10) | (axiom_m10 &  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] :  ? [v3] : (strict_implies(v1, v2) = v3 & necessarily(v1) = v2 & is_a_theorem(v3) = 0)))
% 103.41/71.12  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (or(v3, v2) = v1) |  ~ (or(v3, v2) = v0))
% 103.41/71.12  | (35) op_implies_and
% 103.41/71.12  | (36)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (equiv(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (implies(v4, v2) = v5 & implies(v3, v5) = v6 & implies(v1, v0) = v4 & implies(v0, v1) = v3 & is_a_theorem(v6) = 0))
% 103.41/71.13  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (and(v3, v2) = v1) |  ~ (and(v3, v2) = v0))
% 103.41/71.13  | (38)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v1, v0) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (equiv(v0, v1) = v4 & implies(v3, v5) = v6 & implies(v2, v4) = v5 & implies(v0, v1) = v3 & is_a_theorem(v6) = 0))
% 103.41/71.13  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (implies(v3, v2) = v1) |  ~ (implies(v3, v2) = v0))
% 103.41/71.13  | (40) axiom_K
% 103.41/71.13  | (41) op_possibly
% 103.41/71.13  | (42) and_2
% 103.41/71.13  | (43)  ~ (all_0_86_86 = all_0_87_87)
% 103.41/71.13  | (44)  ? [v0] :  ? [v1] :  ? [v2] : equiv(v1, v0) = v2
% 103.41/71.13  | (45)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] : (implies(v0, v2) = v3 & is_a_theorem(v3) = 0))
% 103.41/71.13  | (46) op_strict_implies
% 103.41/71.13  | (47) ( ~ (all_0_9_9 = 0) & and(all_0_17_17, all_0_19_19) = all_0_13_13 & and(all_0_18_18, all_0_17_17) = all_0_15_15 & not(all_0_13_13) = all_0_12_12 & not(all_0_15_15) = all_0_14_14 & implies(all_0_14_14, all_0_12_12) = all_0_11_11 & implies(all_0_16_16, all_0_11_11) = all_0_10_10 & implies(all_0_19_19, all_0_18_18) = all_0_16_16 & is_a_theorem(all_0_10_10) = all_0_9_9 &  ~ kn3) | (kn3 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (and(v2, v0) = v5) |  ~ (and(v1, v2) = v3) |  ~ (not(v5) = v6) |  ~ (not(v3) = v4) |  ~ (implies(v4, v6) = v7) |  ? [v8] :  ? [v9] : (implies(v8, v7) = v9 & implies(v0, v1) = v8 & is_a_theorem(v9) = 0)))
% 103.41/71.13  | (48)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (strict_equiv(v0, v1) = v3 & strict_implies(v1, v0) = v4 & and(v2, v4) = v3))
% 103.41/71.13  | (49)  ? [v0] :  ? [v1] :  ? [v2] : strict_equiv(v1, v0) = v2
% 103.41/71.13  | (50)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (and(v2, v3) = v4) |  ~ (not(v1) = v3) |  ~ (not(v0) = v2) |  ? [v5] : (or(v0, v1) = v5 & not(v4) = v5))
% 103.41/71.13  | (51)  ? [v0] :  ? [v1] :  ? [v2] : and(v1, v0) = v2
% 103.41/71.13  | (52)  ? [v0] :  ? [v1] : not(v0) = v1
% 103.41/71.13  | (53)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (strict_equiv(v3, v2) = v1) |  ~ (strict_equiv(v3, v2) = v0))
% 103.41/71.13  | (54)  ~ op_and | ( ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (or(v2, v3) = v4) |  ~ (not(v1) = v3) |  ~ (not(v0) = v2) |  ? [v5] : (and(v0, v1) = v5 & not(v4) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (or(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3)))
% 103.41/71.13  | (55) substitution_of_equivalents
% 103.41/71.13  | (56)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (equiv(v0, v1) = v4 & implies(v3, v4) = v5 & implies(v2, v5) = v6 & implies(v1, v0) = v3 & is_a_theorem(v6) = 0))
% 103.41/71.13  | (57) equivalence_2
% 103.41/71.13  | (58) ( ~ (all_0_134_134 = 0) & strict_implies(all_0_137_137, all_0_136_136) = all_0_135_135 & and(all_0_138_138, all_0_139_139) = all_0_136_136 & and(all_0_139_139, all_0_138_138) = all_0_137_137 & is_a_theorem(all_0_135_135) = all_0_134_134 &  ~ axiom_m1) | (axiom_m1 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v1, v0) = v2) |  ? [v3] :  ? [v4] : (strict_implies(v3, v2) = v4 & and(v0, v1) = v3 & is_a_theorem(v4) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] :  ? [v4] : (strict_implies(v2, v3) = v4 & and(v1, v0) = v3 & is_a_theorem(v4) = 0)))
% 103.41/71.13  | (59) (all_0_81_81 = 0 & all_0_82_82 = 0 &  ~ (all_0_79_79 = 0) & and(all_0_84_84, all_0_83_83) = all_0_80_80 & is_a_theorem(all_0_80_80) = all_0_79_79 & is_a_theorem(all_0_83_83) = 0 & is_a_theorem(all_0_84_84) = 0 &  ~ adjunction) | (adjunction &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & is_a_theorem(v2) = 0) | ( ~ (v3 = 0) & is_a_theorem(v1) = v3) | ( ~ (v3 = 0) & is_a_theorem(v0) = v3))))
% 103.41/71.13  | (60) ( ~ (all_0_98_98 = 0) & necessarily(all_0_101_101) = all_0_100_100 & necessarily(all_0_104_104) = all_0_103_103 & necessarily(all_0_106_106) = all_0_105_105 & and(all_0_105_105, all_0_103_103) = all_0_102_102 & implies(all_0_102_102, all_0_100_100) = all_0_99_99 & implies(all_0_108_108, all_0_107_107) = all_0_104_104 & implies(all_0_109_109, all_0_107_107) = all_0_101_101 & implies(all_0_109_109, all_0_108_108) = all_0_106_106 & is_a_theorem(all_0_99_99) = all_0_98_98 &  ~ axiom_s1) | (axiom_s1 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (necessarily(v5) = v6) |  ~ (necessarily(v3) = v4) |  ~ (and(v4, v6) = v7) |  ~ (implies(v1, v2) = v5) |  ~ (implies(v0, v1) = v3) |  ? [v8] :  ? [v9] :  ? [v10] : (necessarily(v8) = v9 & implies(v7, v9) = v10 & implies(v0, v2) = v8 & is_a_theorem(v10) = 0)))
% 103.41/71.13  | (61)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (and(v2, v4) = v3 & equiv(v0, v1) = v3 & implies(v1, v0) = v4))
% 103.41/71.13  | (62) ( ~ (all_0_154_154 = 0) & strict_implies(all_0_157_157, all_0_156_156) = all_0_155_155 & and(all_0_157_157, all_0_157_157) = all_0_156_156 & is_a_theorem(all_0_155_155) = all_0_154_154 &  ~ axiom_m4) | (axiom_m4 &  ! [v0] :  ! [v1] : ( ~ (and(v0, v0) = v1) |  ? [v2] : (strict_implies(v0, v1) = v2 & is_a_theorem(v2) = 0)))
% 103.41/71.13  | (63) ( ~ (all_0_167_167 = 0) & possibly(all_0_170_170) = all_0_169_169 & strict_implies(all_0_170_170, all_0_169_169) = all_0_168_168 & is_a_theorem(all_0_168_168) = all_0_167_167 &  ~ axiom_m6) | (axiom_m6 &  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] : (strict_implies(v0, v1) = v2 & is_a_theorem(v2) = 0)))
% 103.41/71.13  | (64)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (equiv(v0, v1) = v2) |  ? [v3] :  ? [v4] : (and(v3, v4) = v2 & implies(v1, v0) = v4 & implies(v0, v1) = v3))
% 103.41/71.14  | (65)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (not(v2) = v1) |  ~ (not(v2) = v0))
% 103.41/71.14  | (66)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (equiv(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & is_a_theorem(v2) = v3))
% 103.41/71.14  | (67)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v1, v0) = v2) |  ? [v3] :  ? [v4] : (and(v4, v2) = v3 & equiv(v0, v1) = v3 & implies(v0, v1) = v4))
% 103.41/71.14  | (68) implies_1
% 103.41/71.14  | (69) ( ~ (all_0_35_35 = 0) & not(all_0_39_39) = all_0_38_38 & implies(all_0_37_37, all_0_39_39) = all_0_36_36 & implies(all_0_38_38, all_0_39_39) = all_0_37_37 & is_a_theorem(all_0_36_36) = all_0_35_35 &  ~ cn3) | (cn3 &  ! [v0] :  ! [v1] : ( ~ (not(v0) = v1) |  ? [v2] :  ? [v3] : (implies(v2, v0) = v3 & implies(v1, v0) = v2 & is_a_theorem(v3) = 0)))
% 103.41/71.14  | (70)  ! [v0] :  ! [v1] : ( ~ (necessarily(v0) = v1) |  ? [v2] : (implies(v1, v0) = v2 & is_a_theorem(v2) = 0))
% 103.41/71.14  | (71) ( ~ (all_0_64_64 = 0) & or(all_0_72_72, all_0_70_70) = all_0_67_67 & or(all_0_72_72, all_0_71_71) = all_0_68_68 & implies(all_0_68_68, all_0_67_67) = all_0_66_66 & implies(all_0_69_69, all_0_66_66) = all_0_65_65 & implies(all_0_71_71, all_0_70_70) = all_0_69_69 & is_a_theorem(all_0_65_65) = all_0_64_64 &  ~ r5) | (r5 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (or(v0, v2) = v4) |  ~ (or(v0, v1) = v3) |  ~ (implies(v3, v4) = v5) |  ? [v6] :  ? [v7] : (implies(v6, v5) = v7 & implies(v1, v2) = v6 & is_a_theorem(v7) = 0)))
% 103.41/71.14  | (72) ( ~ (all_0_158_158 = 0) & strict_implies(all_0_161_161, all_0_160_160) = all_0_159_159 & strict_implies(all_0_165_165, all_0_164_164) = all_0_162_162 & strict_implies(all_0_166_166, all_0_164_164) = all_0_160_160 & strict_implies(all_0_166_166, all_0_165_165) = all_0_163_163 & and(all_0_163_163, all_0_162_162) = all_0_161_161 & is_a_theorem(all_0_159_159) = all_0_158_158 &  ~ axiom_m5) | (axiom_m5 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (strict_implies(v1, v2) = v4) |  ~ (strict_implies(v0, v1) = v3) |  ~ (and(v3, v4) = v5) |  ? [v6] :  ? [v7] : (strict_implies(v5, v6) = v7 & strict_implies(v0, v2) = v6 & is_a_theorem(v7) = 0)))
% 103.41/71.14  | (73) and_3
% 103.41/71.14  | (74)  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] :  ? [v3] : (necessarily(v1) = v2 & implies(v1, v2) = v3 & is_a_theorem(v3) = 0))
% 103.41/71.14  | (75)  ~ op_implies_or | ( ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (or(v2, v1) = v3) |  ~ (not(v0) = v2) | implies(v0, v1) = v3) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] : (or(v3, v1) = v2 & not(v0) = v3)))
% 103.41/71.14  | (76)  ! [v0] :  ! [v1] : ( ~ (necessarily(v0) = v1) |  ? [v2] : ((v2 = 0 & is_a_theorem(v1) = 0) | ( ~ (v2 = 0) & is_a_theorem(v0) = v2)))
% 103.41/71.14  | (77) necessitation
% 103.41/71.14  | (78)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & is_a_theorem(v1) = 0) | ( ~ (v3 = 0) & is_a_theorem(v2) = v3) | ( ~ (v3 = 0) & is_a_theorem(v0) = v3)))
% 103.41/71.14  | (79) ( ~ (all_0_40_40 = 0) & or(all_0_43_43, all_0_43_43) = all_0_42_42 & implies(all_0_42_42, all_0_43_43) = all_0_41_41 & is_a_theorem(all_0_41_41) = all_0_40_40 &  ~ r1) | (r1 &  ! [v0] :  ! [v1] : ( ~ (or(v0, v0) = v1) |  ? [v2] : (implies(v1, v0) = v2 & is_a_theorem(v2) = 0)))
% 103.41/71.14  | (80) ( ~ (all_0_177_177 = 0) & possibly(all_0_183_183) = all_0_180_180 & possibly(all_0_184_184) = all_0_181_181 & strict_implies(all_0_181_181, all_0_180_180) = all_0_179_179 & strict_implies(all_0_182_182, all_0_179_179) = all_0_178_178 & strict_implies(all_0_184_184, all_0_183_183) = all_0_182_182 & is_a_theorem(all_0_178_178) = all_0_177_177 &  ~ axiom_m8) | (axiom_m8 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (possibly(v1) = v3) |  ~ (possibly(v0) = v2) |  ~ (strict_implies(v2, v3) = v4) |  ? [v5] :  ? [v6] : (strict_implies(v5, v4) = v6 & strict_implies(v0, v1) = v5 & is_a_theorem(v6) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_implies(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (possibly(v1) = v4 & possibly(v0) = v3 & strict_implies(v3, v4) = v5 & strict_implies(v2, v5) = v6 & is_a_theorem(v6) = 0)))
% 103.41/71.14  | (81)  ! [v0] :  ! [v1] : ( ~ (not(v0) = v1) |  ? [v2] :  ? [v3] : (possibly(v0) = v2 & necessarily(v1) = v3 & not(v3) = v2))
% 103.41/71.14  | (82) or_3
% 103.41/71.14  | (83) implies_3
% 103.41/71.14  | (84)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : (implies(v2, v1) = v3 & is_a_theorem(v3) = 0))
% 103.41/71.14  | (85)  ? [v0] :  ? [v1] : possibly(v0) = v1
% 103.41/71.14  | (86)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (necessarily(v2) = v1) |  ~ (necessarily(v2) = v0))
% 103.41/71.14  | (87)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (equiv(v0, v1) = v3 & implies(v3, v2) = v4 & is_a_theorem(v4) = 0))
% 103.41/71.14  | (88) op_or
% 103.41/71.14  | (89) ( ~ (all_0_171_171 = 0) & possibly(all_0_174_174) = all_0_173_173 & strict_implies(all_0_173_173, all_0_176_176) = all_0_172_172 & and(all_0_176_176, all_0_175_175) = all_0_174_174 & is_a_theorem(all_0_172_172) = all_0_171_171 &  ~ axiom_m7) | (axiom_m7 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] :  ? [v4] : (possibly(v2) = v3 & strict_implies(v3, v0) = v4 & is_a_theorem(v4) = 0)))
% 103.41/71.14  | (90) is_a_theorem(all_0_85_85) = 0
% 103.41/71.14  | (91)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equiv(v3, v2) = v1) |  ~ (equiv(v3, v2) = v0))
% 103.41/71.14  | (92)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_equiv(v0, v1) = v2) |  ? [v3] :  ? [v4] : (strict_implies(v1, v0) = v4 & strict_implies(v0, v1) = v3 & and(v3, v4) = v2))
% 103.41/71.14  | (93)  ! [v0] : ( ~ (is_a_theorem(v0) = 0) |  ? [v1] : (necessarily(v0) = v1 & is_a_theorem(v1) = 0))
% 103.41/71.14  | (94)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] : (implies(v1, v2) = v3 & is_a_theorem(v3) = 0))
% 103.41/71.15  | (95) and_1
% 103.41/71.15  | (96) modus_tollens
% 103.41/71.15  | (97)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] :  ? [v4] : (implies(v1, v2) = v3 & implies(v0, v3) = v4 & is_a_theorem(v4) = 0))
% 103.41/71.15  | (98)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (necessarily(v2) = v3 & necessarily(v1) = v5 & necessarily(v0) = v4 & implies(v4, v5) = v6 & implies(v3, v6) = v7 & is_a_theorem(v7) = 0))
% 103.41/71.15  | (99) ( ~ (all_0_44_44 = 0) & or(all_0_48_48, all_0_47_47) = all_0_46_46 & implies(all_0_47_47, all_0_46_46) = all_0_45_45 & is_a_theorem(all_0_45_45) = all_0_44_44 &  ~ r2) | (r2 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] : (implies(v1, v2) = v3 & is_a_theorem(v3) = 0)))
% 103.41/71.15  | (100)  ? [v0] :  ? [v1] : necessarily(v0) = v1
% 103.41/71.15  | (101)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (not(v1) = v2) |  ~ (not(v0) = v3) |  ~ (implies(v2, v3) = v4) |  ? [v5] :  ? [v6] : (implies(v4, v5) = v6 & implies(v0, v1) = v5 & is_a_theorem(v6) = 0))
% 103.41/71.15  | (102)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (strict_implies(v3, v2) = v1) |  ~ (strict_implies(v3, v2) = v0))
% 103.41/71.15  | (103) op_strict_equiv
% 103.41/71.15  | (104)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (implies(v3, v2) = v4 & implies(v0, v2) = v3 & is_a_theorem(v4) = 0))
% 103.41/71.15  | (105) ( ~ (all_0_49_49 = 0) & or(all_0_53_53, all_0_54_54) = all_0_51_51 & or(all_0_54_54, all_0_53_53) = all_0_52_52 & implies(all_0_52_52, all_0_51_51) = all_0_50_50 & is_a_theorem(all_0_50_50) = all_0_49_49 &  ~ r3) | (r3 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v1, v0) = v2) |  ? [v3] :  ? [v4] : (or(v0, v1) = v3 & implies(v3, v2) = v4 & is_a_theorem(v4) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] :  ? [v4] : (or(v1, v0) = v3 & implies(v2, v3) = v4 & is_a_theorem(v4) = 0)))
% 103.41/71.15  | (106)  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] :  ? [v3] : (necessarily(v2) = v3 & not(v3) = v1 & not(v0) = v2))
% 103.41/71.15  | (107) equivalence_3
% 103.41/71.15  | (108) ( ~ (all_0_140_140 = 0) & strict_implies(all_0_142_142, all_0_144_144) = all_0_141_141 & and(all_0_144_144, all_0_143_143) = all_0_142_142 & is_a_theorem(all_0_141_141) = all_0_140_140 &  ~ axiom_m2) | (axiom_m2 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : (strict_implies(v2, v0) = v3 & is_a_theorem(v3) = 0)))
% 103.41/71.15  | (109) ( ~ (all_0_93_93 = 0) & possibly(all_0_97_97) = all_0_96_96 & necessarily(all_0_96_96) = all_0_95_95 & implies(all_0_97_97, all_0_95_95) = all_0_94_94 & is_a_theorem(all_0_94_94) = all_0_93_93 &  ~ axiom_B) | (axiom_B &  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] :  ? [v3] : (necessarily(v1) = v2 & implies(v0, v2) = v3 & is_a_theorem(v3) = 0)))
% 103.41/71.15  | (110) ( ~ (all_0_185_185 = 0) & possibly(all_0_188_188) = all_0_187_187 & possibly(all_0_189_189) = all_0_188_188 & strict_implies(all_0_187_187, all_0_188_188) = all_0_186_186 & is_a_theorem(all_0_186_186) = all_0_185_185 &  ~ axiom_m9) | (axiom_m9 &  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] :  ? [v3] : (possibly(v1) = v2 & strict_implies(v2, v1) = v3 & is_a_theorem(v3) = 0)))
% 103.41/71.15  | (111) ( ~ (all_0_110_110 = 0) & possibly(all_0_116_116) = all_0_115_115 & possibly(all_0_117_117) = all_0_113_113 & possibly(all_0_118_118) = all_0_114_114 & strict_implies(all_0_115_115, all_0_112_112) = all_0_111_111 & and(all_0_114_114, all_0_113_113) = all_0_112_112 & and(all_0_118_118, all_0_117_117) = all_0_116_116 & is_a_theorem(all_0_111_111) = all_0_110_110 &  ~ axiom_s2) | (axiom_s2 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (possibly(v1) = v3) |  ~ (possibly(v0) = v2) |  ~ (and(v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (possibly(v5) = v6 & strict_implies(v6, v4) = v7 & and(v0, v1) = v5 & is_a_theorem(v7) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (possibly(v2) = v3 & possibly(v1) = v5 & possibly(v0) = v4 & strict_implies(v3, v6) = v7 & and(v4, v5) = v6 & is_a_theorem(v7) = 0)))
% 103.41/71.15  | (112)  ? [v0] :  ? [v1] :  ? [v2] : implies(v1, v0) = v2
% 103.41/71.15  | (113) (all_0_74_74 = 0 & all_0_76_76 = 0 &  ~ (all_0_73_73 = 0) & strict_implies(all_0_78_78, all_0_77_77) = all_0_75_75 & is_a_theorem(all_0_75_75) = 0 & is_a_theorem(all_0_77_77) = all_0_73_73 & is_a_theorem(all_0_78_78) = 0 &  ~ modus_ponens_strict_implies) | (modus_ponens_strict_implies &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_implies(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & is_a_theorem(v1) = 0) | ( ~ (v3 = 0) & is_a_theorem(v2) = v3) | ( ~ (v3 = 0) & is_a_theorem(v0) = v3))))
% 103.41/71.15  | (114)  ~ substitution_strict_equiv
% 103.41/71.15  | (115) ( ~ (all_0_55_55 = 0) & or(all_0_62_62, all_0_58_58) = all_0_57_57 & or(all_0_62_62, all_0_61_61) = all_0_60_60 & or(all_0_63_63, all_0_60_60) = all_0_59_59 & or(all_0_63_63, all_0_61_61) = all_0_58_58 & implies(all_0_59_59, all_0_57_57) = all_0_56_56 & is_a_theorem(all_0_56_56) = all_0_55_55 &  ~ r4) | (r4 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (or(v1, v3) = v4) |  ~ (or(v0, v2) = v3) |  ? [v5] :  ? [v6] :  ? [v7] : (or(v1, v2) = v5 & or(v0, v5) = v6 & implies(v6, v4) = v7 & is_a_theorem(v7) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (or(v1, v2) = v3) |  ~ (or(v0, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (or(v1, v5) = v6 & or(v0, v2) = v5 & implies(v4, v6) = v7 & is_a_theorem(v7) = 0)))
% 103.41/71.15  | (116)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (and(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3))
% 103.41/71.15  | (117)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (implies(v3, v4) = v5) |  ~ (implies(v1, v2) = v3) |  ~ (implies(v0, v2) = v4) |  ? [v6] :  ? [v7] : (implies(v6, v5) = v7 & implies(v0, v1) = v6 & is_a_theorem(v7) = 0))
% 103.41/71.15  | (118)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v1, v0) = v2) |  ? [v3] : (implies(v0, v2) = v3 & is_a_theorem(v3) = 0))
% 103.41/71.15  | (119) axiom_M
% 103.41/71.15  | (120) ( ~ (all_0_0_0 = 0) & and(all_0_3_3, all_0_3_3) = all_0_2_2 & implies(all_0_3_3, all_0_2_2) = all_0_1_1 & is_a_theorem(all_0_1_1) = all_0_0_0 &  ~ kn1) | (kn1 &  ! [v0] :  ! [v1] : ( ~ (and(v0, v0) = v1) |  ? [v2] : (implies(v0, v1) = v2 & is_a_theorem(v2) = 0)))
% 103.41/71.16  | (121) ( ~ (all_0_4_4 = 0) & and(all_0_8_8, all_0_7_7) = all_0_6_6 & implies(all_0_6_6, all_0_8_8) = all_0_5_5 & is_a_theorem(all_0_5_5) = all_0_4_4 &  ~ kn2) | (kn2 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : (implies(v2, v0) = v3 & is_a_theorem(v3) = 0)))
% 103.41/71.16  | (122)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (is_a_theorem(v2) = v1) |  ~ (is_a_theorem(v2) = v0))
% 103.41/71.16  | (123)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (equiv(v0, v1) = v2) |  ? [v3] :  ? [v4] : (implies(v2, v3) = v4 & implies(v0, v1) = v3 & is_a_theorem(v4) = 0))
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (92) with all_0_85_85, all_0_86_86, all_0_87_87 and discharging atoms strict_equiv(all_0_87_87, all_0_86_86) = all_0_85_85, yields:
% 103.41/71.16  | (124)  ? [v0] :  ? [v1] : (strict_implies(all_0_86_86, all_0_87_87) = v1 & strict_implies(all_0_87_87, all_0_86_86) = v0 & and(v0, v1) = all_0_85_85)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating (124) with all_30_0_222, all_30_1_223 yields:
% 103.41/71.16  | (125) strict_implies(all_0_86_86, all_0_87_87) = all_30_0_222 & strict_implies(all_0_87_87, all_0_86_86) = all_30_1_223 & and(all_30_1_223, all_30_0_222) = all_0_85_85
% 103.41/71.16  |
% 103.41/71.16  | Applying alpha-rule on (125) yields:
% 103.41/71.16  | (126) strict_implies(all_0_86_86, all_0_87_87) = all_30_0_222
% 103.41/71.16  | (127) strict_implies(all_0_87_87, all_0_86_86) = all_30_1_223
% 103.41/71.16  | (128) and(all_30_1_223, all_30_0_222) = all_0_85_85
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (28) with all_30_0_222, all_0_87_87, all_0_86_86 and discharging atoms strict_implies(all_0_86_86, all_0_87_87) = all_30_0_222, yields:
% 103.41/71.16  | (129)  ? [v0] : (necessarily(v0) = all_30_0_222 & implies(all_0_86_86, all_0_87_87) = v0)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (28) with all_30_1_223, all_0_86_86, all_0_87_87 and discharging atoms strict_implies(all_0_87_87, all_0_86_86) = all_30_1_223, yields:
% 103.41/71.16  | (130)  ? [v0] : (necessarily(v0) = all_30_1_223 & implies(all_0_87_87, all_0_86_86) = v0)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (97) with all_0_85_85, all_30_0_222, all_30_1_223 and discharging atoms and(all_30_1_223, all_30_0_222) = all_0_85_85, yields:
% 103.41/71.16  | (131)  ? [v0] :  ? [v1] : (implies(all_30_0_222, all_0_85_85) = v0 & implies(all_30_1_223, v0) = v1 & is_a_theorem(v1) = 0)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (84) with all_0_85_85, all_30_0_222, all_30_1_223 and discharging atoms and(all_30_1_223, all_30_0_222) = all_0_85_85, yields:
% 103.41/71.16  | (132)  ? [v0] : (implies(all_0_85_85, all_30_0_222) = v0 & is_a_theorem(v0) = 0)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (29) with all_0_85_85, all_30_0_222, all_30_1_223 and discharging atoms and(all_30_1_223, all_30_0_222) = all_0_85_85, yields:
% 103.41/71.16  | (133)  ? [v0] : (implies(all_0_85_85, all_30_1_223) = v0 & is_a_theorem(v0) = 0)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating (133) with all_39_0_225 yields:
% 103.41/71.16  | (134) implies(all_0_85_85, all_30_1_223) = all_39_0_225 & is_a_theorem(all_39_0_225) = 0
% 103.41/71.16  |
% 103.41/71.16  | Applying alpha-rule on (134) yields:
% 103.41/71.16  | (135) implies(all_0_85_85, all_30_1_223) = all_39_0_225
% 103.41/71.16  | (136) is_a_theorem(all_39_0_225) = 0
% 103.41/71.16  |
% 103.41/71.16  | Instantiating (132) with all_41_0_226 yields:
% 103.41/71.16  | (137) implies(all_0_85_85, all_30_0_222) = all_41_0_226 & is_a_theorem(all_41_0_226) = 0
% 103.41/71.16  |
% 103.41/71.16  | Applying alpha-rule on (137) yields:
% 103.41/71.16  | (138) implies(all_0_85_85, all_30_0_222) = all_41_0_226
% 103.41/71.16  | (139) is_a_theorem(all_41_0_226) = 0
% 103.41/71.16  |
% 103.41/71.16  | Instantiating (131) with all_43_0_227, all_43_1_228 yields:
% 103.41/71.16  | (140) implies(all_30_0_222, all_0_85_85) = all_43_1_228 & implies(all_30_1_223, all_43_1_228) = all_43_0_227 & is_a_theorem(all_43_0_227) = 0
% 103.41/71.16  |
% 103.41/71.16  | Applying alpha-rule on (140) yields:
% 103.41/71.16  | (141) implies(all_30_0_222, all_0_85_85) = all_43_1_228
% 103.41/71.16  | (142) implies(all_30_1_223, all_43_1_228) = all_43_0_227
% 103.41/71.16  | (143) is_a_theorem(all_43_0_227) = 0
% 103.41/71.16  |
% 103.41/71.16  | Instantiating (130) with all_47_0_230 yields:
% 103.41/71.16  | (144) necessarily(all_47_0_230) = all_30_1_223 & implies(all_0_87_87, all_0_86_86) = all_47_0_230
% 103.41/71.16  |
% 103.41/71.16  | Applying alpha-rule on (144) yields:
% 103.41/71.16  | (145) necessarily(all_47_0_230) = all_30_1_223
% 103.41/71.16  | (146) implies(all_0_87_87, all_0_86_86) = all_47_0_230
% 103.41/71.16  |
% 103.41/71.16  | Instantiating (129) with all_51_0_233 yields:
% 103.41/71.16  | (147) necessarily(all_51_0_233) = all_30_0_222 & implies(all_0_86_86, all_0_87_87) = all_51_0_233
% 103.41/71.16  |
% 103.41/71.16  | Applying alpha-rule on (147) yields:
% 103.41/71.16  | (148) necessarily(all_51_0_233) = all_30_0_222
% 103.41/71.16  | (149) implies(all_0_86_86, all_0_87_87) = all_51_0_233
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (70) with all_30_0_222, all_51_0_233 and discharging atoms necessarily(all_51_0_233) = all_30_0_222, yields:
% 103.41/71.16  | (150)  ? [v0] : (implies(all_30_0_222, all_51_0_233) = v0 & is_a_theorem(v0) = 0)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (70) with all_30_1_223, all_47_0_230 and discharging atoms necessarily(all_47_0_230) = all_30_1_223, yields:
% 103.41/71.16  | (151)  ? [v0] : (implies(all_30_1_223, all_47_0_230) = v0 & is_a_theorem(v0) = 0)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (38) with all_43_1_228, all_30_0_222, all_0_85_85 and discharging atoms implies(all_30_0_222, all_0_85_85) = all_43_1_228, yields:
% 103.41/71.16  | (152)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (equiv(all_0_85_85, all_30_0_222) = v1 & implies(v0, v2) = v3 & implies(all_43_1_228, v1) = v2 & implies(all_0_85_85, all_30_0_222) = v0 & is_a_theorem(v3) = 0)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (67) with all_43_1_228, all_30_0_222, all_0_85_85 and discharging atoms implies(all_30_0_222, all_0_85_85) = all_43_1_228, yields:
% 103.41/71.16  | (153)  ? [v0] :  ? [v1] : (and(v1, all_43_1_228) = v0 & equiv(all_0_85_85, all_30_0_222) = v0 & implies(all_0_85_85, all_30_0_222) = v1)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (18) with all_43_1_228, all_30_0_222, all_0_85_85 and discharging atoms implies(all_30_0_222, all_0_85_85) = all_43_1_228, yields:
% 103.41/71.16  | (154)  ? [v0] :  ? [v1] : (equiv(all_0_85_85, all_30_0_222) = v0 & implies(v0, all_43_1_228) = v1 & is_a_theorem(v1) = 0)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (56) with all_43_1_228, all_0_85_85, all_30_0_222 and discharging atoms implies(all_30_0_222, all_0_85_85) = all_43_1_228, yields:
% 103.41/71.16  | (155)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (equiv(all_30_0_222, all_0_85_85) = v1 & implies(v0, v1) = v2 & implies(all_43_1_228, v2) = v3 & implies(all_0_85_85, all_30_0_222) = v0 & is_a_theorem(v3) = 0)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (61) with all_43_1_228, all_0_85_85, all_30_0_222 and discharging atoms implies(all_30_0_222, all_0_85_85) = all_43_1_228, yields:
% 103.41/71.16  | (156)  ? [v0] :  ? [v1] : (and(all_43_1_228, v1) = v0 & equiv(all_30_0_222, all_0_85_85) = v0 & implies(all_0_85_85, all_30_0_222) = v1)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (78) with all_43_0_227, all_43_1_228, all_30_1_223 and discharging atoms implies(all_30_1_223, all_43_1_228) = all_43_0_227, yields:
% 103.41/71.16  | (157)  ? [v0] : ((v0 = 0 & is_a_theorem(all_43_1_228) = 0) | ( ~ (v0 = 0) & is_a_theorem(all_43_0_227) = v0) | ( ~ (v0 = 0) & is_a_theorem(all_30_1_223) = v0))
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (38) with all_41_0_226, all_0_85_85, all_30_0_222 and discharging atoms implies(all_0_85_85, all_30_0_222) = all_41_0_226, yields:
% 103.41/71.16  | (158)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (equiv(all_30_0_222, all_0_85_85) = v1 & implies(v0, v2) = v3 & implies(all_41_0_226, v1) = v2 & implies(all_30_0_222, all_0_85_85) = v0 & is_a_theorem(v3) = 0)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (67) with all_41_0_226, all_0_85_85, all_30_0_222 and discharging atoms implies(all_0_85_85, all_30_0_222) = all_41_0_226, yields:
% 103.41/71.16  | (159)  ? [v0] :  ? [v1] : (and(v1, all_41_0_226) = v0 & equiv(all_30_0_222, all_0_85_85) = v0 & implies(all_30_0_222, all_0_85_85) = v1)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (56) with all_41_0_226, all_30_0_222, all_0_85_85 and discharging atoms implies(all_0_85_85, all_30_0_222) = all_41_0_226, yields:
% 103.41/71.16  | (160)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (equiv(all_0_85_85, all_30_0_222) = v1 & implies(v0, v1) = v2 & implies(all_41_0_226, v2) = v3 & implies(all_30_0_222, all_0_85_85) = v0 & is_a_theorem(v3) = 0)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (61) with all_41_0_226, all_30_0_222, all_0_85_85 and discharging atoms implies(all_0_85_85, all_30_0_222) = all_41_0_226, yields:
% 103.41/71.16  | (161)  ? [v0] :  ? [v1] : (and(all_41_0_226, v1) = v0 & equiv(all_0_85_85, all_30_0_222) = v0 & implies(all_30_0_222, all_0_85_85) = v1)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (87) with all_41_0_226, all_30_0_222, all_0_85_85 and discharging atoms implies(all_0_85_85, all_30_0_222) = all_41_0_226, yields:
% 103.41/71.16  | (162)  ? [v0] :  ? [v1] : (equiv(all_0_85_85, all_30_0_222) = v0 & implies(v0, all_41_0_226) = v1 & is_a_theorem(v1) = 0)
% 103.41/71.16  |
% 103.41/71.16  | Instantiating formula (78) with all_41_0_226, all_30_0_222, all_0_85_85 and discharging atoms implies(all_0_85_85, all_30_0_222) = all_41_0_226, yields:
% 103.41/71.16  | (163)  ? [v0] : ((v0 = 0 & is_a_theorem(all_30_0_222) = 0) | ( ~ (v0 = 0) & is_a_theorem(all_41_0_226) = v0) | ( ~ (v0 = 0) & is_a_theorem(all_0_85_85) = v0))
% 103.41/71.17  |
% 103.41/71.17  | Instantiating formula (78) with all_39_0_225, all_30_1_223, all_0_85_85 and discharging atoms implies(all_0_85_85, all_30_1_223) = all_39_0_225, yields:
% 103.41/71.17  | (164)  ? [v0] : ((v0 = 0 & is_a_theorem(all_30_1_223) = 0) | ( ~ (v0 = 0) & is_a_theorem(all_39_0_225) = v0) | ( ~ (v0 = 0) & is_a_theorem(all_0_85_85) = v0))
% 103.41/71.17  |
% 103.41/71.17  | Instantiating formula (56) with all_51_0_233, all_0_87_87, all_0_86_86 and discharging atoms implies(all_0_86_86, all_0_87_87) = all_51_0_233, yields:
% 103.41/71.17  | (165)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (equiv(all_0_86_86, all_0_87_87) = v1 & implies(v0, v1) = v2 & implies(all_51_0_233, v2) = v3 & implies(all_0_87_87, all_0_86_86) = v0 & is_a_theorem(v3) = 0)
% 103.41/71.17  |
% 103.41/71.17  | Instantiating formula (61) with all_51_0_233, all_0_87_87, all_0_86_86 and discharging atoms implies(all_0_86_86, all_0_87_87) = all_51_0_233, yields:
% 103.41/71.17  | (166)  ? [v0] :  ? [v1] : (and(all_51_0_233, v1) = v0 & equiv(all_0_86_86, all_0_87_87) = v0 & implies(all_0_87_87, all_0_86_86) = v1)
% 103.41/71.17  |
% 103.41/71.17  | Instantiating formula (87) with all_51_0_233, all_0_87_87, all_0_86_86 and discharging atoms implies(all_0_86_86, all_0_87_87) = all_51_0_233, yields:
% 103.41/71.17  | (167)  ? [v0] :  ? [v1] : (equiv(all_0_86_86, all_0_87_87) = v0 & implies(v0, all_51_0_233) = v1 & is_a_theorem(v1) = 0)
% 103.41/71.17  |
% 103.41/71.17  | Instantiating formula (38) with all_47_0_230, all_0_87_87, all_0_86_86 and discharging atoms implies(all_0_87_87, all_0_86_86) = all_47_0_230, yields:
% 103.41/71.17  | (168)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (equiv(all_0_86_86, all_0_87_87) = v1 & implies(v0, v2) = v3 & implies(all_47_0_230, v1) = v2 & implies(all_0_86_86, all_0_87_87) = v0 & is_a_theorem(v3) = 0)
% 103.41/71.17  |
% 103.41/71.17  | Instantiating formula (67) with all_47_0_230, all_0_87_87, all_0_86_86 and discharging atoms implies(all_0_87_87, all_0_86_86) = all_47_0_230, yields:
% 103.41/71.17  | (169)  ? [v0] :  ? [v1] : (and(v1, all_47_0_230) = v0 & equiv(all_0_86_86, all_0_87_87) = v0 & implies(all_0_86_86, all_0_87_87) = v1)
% 103.41/71.17  |
% 103.41/71.17  | Instantiating formula (18) with all_47_0_230, all_0_87_87, all_0_86_86 and discharging atoms implies(all_0_87_87, all_0_86_86) = all_47_0_230, yields:
% 103.41/71.17  | (170)  ? [v0] :  ? [v1] : (equiv(all_0_86_86, all_0_87_87) = v0 & implies(v0, all_47_0_230) = v1 & is_a_theorem(v1) = 0)
% 103.41/71.17  |
% 103.41/71.17  | Instantiating formula (56) with all_47_0_230, all_0_86_86, all_0_87_87 and discharging atoms implies(all_0_87_87, all_0_86_86) = all_47_0_230, yields:
% 103.41/71.17  | (171)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (equiv(all_0_87_87, all_0_86_86) = v1 & implies(v0, v1) = v2 & implies(all_47_0_230, v2) = v3 & implies(all_0_86_86, all_0_87_87) = v0 & is_a_theorem(v3) = 0)
% 103.41/71.17  |
% 103.41/71.17  | Instantiating formula (61) with all_47_0_230, all_0_86_86, all_0_87_87 and discharging atoms implies(all_0_87_87, all_0_86_86) = all_47_0_230, yields:
% 103.41/71.17  | (172)  ? [v0] :  ? [v1] : (and(all_47_0_230, v1) = v0 & equiv(all_0_87_87, all_0_86_86) = v0 & implies(all_0_86_86, all_0_87_87) = v1)
% 103.41/71.17  |
% 103.41/71.17  | Instantiating (169) with all_79_0_252, all_79_1_253 yields:
% 103.41/71.17  | (173) and(all_79_0_252, all_47_0_230) = all_79_1_253 & equiv(all_0_86_86, all_0_87_87) = all_79_1_253 & implies(all_0_86_86, all_0_87_87) = all_79_0_252
% 103.41/71.17  |
% 103.41/71.17  | Applying alpha-rule on (173) yields:
% 103.41/71.17  | (174) and(all_79_0_252, all_47_0_230) = all_79_1_253
% 103.41/71.17  | (175) equiv(all_0_86_86, all_0_87_87) = all_79_1_253
% 103.41/71.17  | (176) implies(all_0_86_86, all_0_87_87) = all_79_0_252
% 103.41/71.17  |
% 103.41/71.17  | Instantiating (168) with all_81_0_254, all_81_1_255, all_81_2_256, all_81_3_257 yields:
% 103.41/71.17  | (177) equiv(all_0_86_86, all_0_87_87) = all_81_2_256 & implies(all_81_3_257, all_81_1_255) = all_81_0_254 & implies(all_47_0_230, all_81_2_256) = all_81_1_255 & implies(all_0_86_86, all_0_87_87) = all_81_3_257 & is_a_theorem(all_81_0_254) = 0
% 103.41/71.17  |
% 103.41/71.17  | Applying alpha-rule on (177) yields:
% 103.41/71.17  | (178) implies(all_0_86_86, all_0_87_87) = all_81_3_257
% 103.41/71.17  | (179) implies(all_81_3_257, all_81_1_255) = all_81_0_254
% 103.41/71.17  | (180) equiv(all_0_86_86, all_0_87_87) = all_81_2_256
% 103.41/71.17  | (181) implies(all_47_0_230, all_81_2_256) = all_81_1_255
% 103.41/71.17  | (182) is_a_theorem(all_81_0_254) = 0
% 103.41/71.17  |
% 103.41/71.17  | Instantiating (156) with all_87_0_262, all_87_1_263 yields:
% 103.41/71.17  | (183) and(all_43_1_228, all_87_0_262) = all_87_1_263 & equiv(all_30_0_222, all_0_85_85) = all_87_1_263 & implies(all_0_85_85, all_30_0_222) = all_87_0_262
% 103.41/71.17  |
% 103.41/71.17  | Applying alpha-rule on (183) yields:
% 103.41/71.17  | (184) and(all_43_1_228, all_87_0_262) = all_87_1_263
% 103.41/71.17  | (185) equiv(all_30_0_222, all_0_85_85) = all_87_1_263
% 103.41/71.17  | (186) implies(all_0_85_85, all_30_0_222) = all_87_0_262
% 103.41/71.17  |
% 103.41/71.17  | Instantiating (155) with all_89_0_264, all_89_1_265, all_89_2_266, all_89_3_267 yields:
% 103.41/71.17  | (187) equiv(all_30_0_222, all_0_85_85) = all_89_2_266 & implies(all_89_3_267, all_89_2_266) = all_89_1_265 & implies(all_43_1_228, all_89_1_265) = all_89_0_264 & implies(all_0_85_85, all_30_0_222) = all_89_3_267 & is_a_theorem(all_89_0_264) = 0
% 103.41/71.17  |
% 103.41/71.17  | Applying alpha-rule on (187) yields:
% 103.41/71.17  | (188) implies(all_89_3_267, all_89_2_266) = all_89_1_265
% 103.41/71.17  | (189) is_a_theorem(all_89_0_264) = 0
% 103.41/71.17  | (190) implies(all_0_85_85, all_30_0_222) = all_89_3_267
% 103.41/71.17  | (191) equiv(all_30_0_222, all_0_85_85) = all_89_2_266
% 103.41/71.17  | (192) implies(all_43_1_228, all_89_1_265) = all_89_0_264
% 103.41/71.17  |
% 103.41/71.17  | Instantiating (162) with all_110_0_288, all_110_1_289 yields:
% 103.41/71.17  | (193) equiv(all_0_85_85, all_30_0_222) = all_110_1_289 & implies(all_110_1_289, all_41_0_226) = all_110_0_288 & is_a_theorem(all_110_0_288) = 0
% 103.41/71.17  |
% 103.41/71.17  | Applying alpha-rule on (193) yields:
% 103.41/71.17  | (194) equiv(all_0_85_85, all_30_0_222) = all_110_1_289
% 103.41/71.17  | (195) implies(all_110_1_289, all_41_0_226) = all_110_0_288
% 103.41/71.17  | (196) is_a_theorem(all_110_0_288) = 0
% 103.41/71.17  |
% 103.41/71.17  | Instantiating (161) with all_112_0_290, all_112_1_291 yields:
% 103.41/71.17  | (197) and(all_41_0_226, all_112_0_290) = all_112_1_291 & equiv(all_0_85_85, all_30_0_222) = all_112_1_291 & implies(all_30_0_222, all_0_85_85) = all_112_0_290
% 103.41/71.17  |
% 103.41/71.17  | Applying alpha-rule on (197) yields:
% 103.41/71.17  | (198) and(all_41_0_226, all_112_0_290) = all_112_1_291
% 103.41/71.17  | (199) equiv(all_0_85_85, all_30_0_222) = all_112_1_291
% 103.41/71.17  | (200) implies(all_30_0_222, all_0_85_85) = all_112_0_290
% 103.41/71.17  |
% 103.41/71.17  | Instantiating (160) with all_114_0_292, all_114_1_293, all_114_2_294, all_114_3_295 yields:
% 103.41/71.17  | (201) equiv(all_0_85_85, all_30_0_222) = all_114_2_294 & implies(all_114_3_295, all_114_2_294) = all_114_1_293 & implies(all_41_0_226, all_114_1_293) = all_114_0_292 & implies(all_30_0_222, all_0_85_85) = all_114_3_295 & is_a_theorem(all_114_0_292) = 0
% 103.41/71.17  |
% 103.41/71.17  | Applying alpha-rule on (201) yields:
% 103.41/71.17  | (202) implies(all_30_0_222, all_0_85_85) = all_114_3_295
% 103.41/71.17  | (203) is_a_theorem(all_114_0_292) = 0
% 103.41/71.17  | (204) equiv(all_0_85_85, all_30_0_222) = all_114_2_294
% 103.41/71.17  | (205) implies(all_41_0_226, all_114_1_293) = all_114_0_292
% 103.41/71.17  | (206) implies(all_114_3_295, all_114_2_294) = all_114_1_293
% 103.41/71.17  |
% 103.41/71.17  | Instantiating (154) with all_128_0_311, all_128_1_312 yields:
% 103.41/71.17  | (207) equiv(all_0_85_85, all_30_0_222) = all_128_1_312 & implies(all_128_1_312, all_43_1_228) = all_128_0_311 & is_a_theorem(all_128_0_311) = 0
% 103.41/71.17  |
% 103.41/71.17  | Applying alpha-rule on (207) yields:
% 103.41/71.17  | (208) equiv(all_0_85_85, all_30_0_222) = all_128_1_312
% 103.41/71.17  | (209) implies(all_128_1_312, all_43_1_228) = all_128_0_311
% 103.41/71.17  | (210) is_a_theorem(all_128_0_311) = 0
% 103.41/71.17  |
% 103.41/71.17  | Instantiating (170) with all_138_0_330, all_138_1_331 yields:
% 103.41/71.17  | (211) equiv(all_0_86_86, all_0_87_87) = all_138_1_331 & implies(all_138_1_331, all_47_0_230) = all_138_0_330 & is_a_theorem(all_138_0_330) = 0
% 103.41/71.17  |
% 103.41/71.17  | Applying alpha-rule on (211) yields:
% 103.41/71.17  | (212) equiv(all_0_86_86, all_0_87_87) = all_138_1_331
% 103.41/71.17  | (213) implies(all_138_1_331, all_47_0_230) = all_138_0_330
% 103.41/71.17  | (214) is_a_theorem(all_138_0_330) = 0
% 103.41/71.17  |
% 103.41/71.17  | Instantiating (166) with all_142_0_334, all_142_1_335 yields:
% 103.41/71.17  | (215) and(all_51_0_233, all_142_0_334) = all_142_1_335 & equiv(all_0_86_86, all_0_87_87) = all_142_1_335 & implies(all_0_87_87, all_0_86_86) = all_142_0_334
% 103.41/71.17  |
% 103.41/71.17  | Applying alpha-rule on (215) yields:
% 103.41/71.17  | (216) and(all_51_0_233, all_142_0_334) = all_142_1_335
% 103.41/71.17  | (217) equiv(all_0_86_86, all_0_87_87) = all_142_1_335
% 103.41/71.17  | (218) implies(all_0_87_87, all_0_86_86) = all_142_0_334
% 103.41/71.17  |
% 103.41/71.17  | Instantiating (165) with all_144_0_336, all_144_1_337, all_144_2_338, all_144_3_339 yields:
% 103.41/71.17  | (219) equiv(all_0_86_86, all_0_87_87) = all_144_2_338 & implies(all_144_3_339, all_144_2_338) = all_144_1_337 & implies(all_51_0_233, all_144_1_337) = all_144_0_336 & implies(all_0_87_87, all_0_86_86) = all_144_3_339 & is_a_theorem(all_144_0_336) = 0
% 103.41/71.17  |
% 103.41/71.17  | Applying alpha-rule on (219) yields:
% 103.41/71.17  | (220) equiv(all_0_86_86, all_0_87_87) = all_144_2_338
% 103.41/71.17  | (221) implies(all_51_0_233, all_144_1_337) = all_144_0_336
% 103.41/71.17  | (222) implies(all_144_3_339, all_144_2_338) = all_144_1_337
% 103.41/71.18  | (223) is_a_theorem(all_144_0_336) = 0
% 103.41/71.18  | (224) implies(all_0_87_87, all_0_86_86) = all_144_3_339
% 103.41/71.18  |
% 103.41/71.18  | Instantiating (164) with all_159_0_356 yields:
% 103.41/71.18  | (225) (all_159_0_356 = 0 & is_a_theorem(all_30_1_223) = 0) | ( ~ (all_159_0_356 = 0) & is_a_theorem(all_39_0_225) = all_159_0_356) | ( ~ (all_159_0_356 = 0) & is_a_theorem(all_0_85_85) = all_159_0_356)
% 103.41/71.18  |
% 103.41/71.18  | Instantiating (172) with all_174_0_375, all_174_1_376 yields:
% 103.41/71.18  | (226) and(all_47_0_230, all_174_0_375) = all_174_1_376 & equiv(all_0_87_87, all_0_86_86) = all_174_1_376 & implies(all_0_86_86, all_0_87_87) = all_174_0_375
% 103.41/71.18  |
% 103.41/71.18  | Applying alpha-rule on (226) yields:
% 103.41/71.18  | (227) and(all_47_0_230, all_174_0_375) = all_174_1_376
% 103.41/71.18  | (228) equiv(all_0_87_87, all_0_86_86) = all_174_1_376
% 103.41/71.18  | (229) implies(all_0_86_86, all_0_87_87) = all_174_0_375
% 103.41/71.18  |
% 103.41/71.18  | Instantiating (171) with all_176_0_377, all_176_1_378, all_176_2_379, all_176_3_380 yields:
% 103.41/71.18  | (230) equiv(all_0_87_87, all_0_86_86) = all_176_2_379 & implies(all_176_3_380, all_176_2_379) = all_176_1_378 & implies(all_47_0_230, all_176_1_378) = all_176_0_377 & implies(all_0_86_86, all_0_87_87) = all_176_3_380 & is_a_theorem(all_176_0_377) = 0
% 103.41/71.18  |
% 103.41/71.18  | Applying alpha-rule on (230) yields:
% 103.41/71.18  | (231) implies(all_47_0_230, all_176_1_378) = all_176_0_377
% 103.41/71.18  | (232) equiv(all_0_87_87, all_0_86_86) = all_176_2_379
% 103.41/71.18  | (233) implies(all_0_86_86, all_0_87_87) = all_176_3_380
% 103.41/71.18  | (234) implies(all_176_3_380, all_176_2_379) = all_176_1_378
% 103.41/71.18  | (235) is_a_theorem(all_176_0_377) = 0
% 103.41/71.18  |
% 103.41/71.18  | Instantiating (167) with all_180_0_385, all_180_1_386 yields:
% 103.41/71.18  | (236) equiv(all_0_86_86, all_0_87_87) = all_180_1_386 & implies(all_180_1_386, all_51_0_233) = all_180_0_385 & is_a_theorem(all_180_0_385) = 0
% 103.41/71.18  |
% 103.41/71.18  | Applying alpha-rule on (236) yields:
% 103.41/71.18  | (237) equiv(all_0_86_86, all_0_87_87) = all_180_1_386
% 103.41/71.18  | (238) implies(all_180_1_386, all_51_0_233) = all_180_0_385
% 103.41/71.18  | (239) is_a_theorem(all_180_0_385) = 0
% 103.41/71.18  |
% 103.41/71.18  | Instantiating (153) with all_182_0_387, all_182_1_388 yields:
% 103.41/71.18  | (240) and(all_182_0_387, all_43_1_228) = all_182_1_388 & equiv(all_0_85_85, all_30_0_222) = all_182_1_388 & implies(all_0_85_85, all_30_0_222) = all_182_0_387
% 103.41/71.18  |
% 103.41/71.18  | Applying alpha-rule on (240) yields:
% 103.41/71.18  | (241) and(all_182_0_387, all_43_1_228) = all_182_1_388
% 103.41/71.18  | (242) equiv(all_0_85_85, all_30_0_222) = all_182_1_388
% 103.41/71.18  | (243) implies(all_0_85_85, all_30_0_222) = all_182_0_387
% 103.41/71.18  |
% 103.41/71.18  | Instantiating (159) with all_186_0_390, all_186_1_391 yields:
% 103.41/71.18  | (244) and(all_186_0_390, all_41_0_226) = all_186_1_391 & equiv(all_30_0_222, all_0_85_85) = all_186_1_391 & implies(all_30_0_222, all_0_85_85) = all_186_0_390
% 103.41/71.18  |
% 103.41/71.18  | Applying alpha-rule on (244) yields:
% 103.41/71.18  | (245) and(all_186_0_390, all_41_0_226) = all_186_1_391
% 103.41/71.18  | (246) equiv(all_30_0_222, all_0_85_85) = all_186_1_391
% 103.41/71.18  | (247) implies(all_30_0_222, all_0_85_85) = all_186_0_390
% 103.41/71.18  |
% 103.41/71.18  | Instantiating (158) with all_188_0_392, all_188_1_393, all_188_2_394, all_188_3_395 yields:
% 103.41/71.18  | (248) equiv(all_30_0_222, all_0_85_85) = all_188_2_394 & implies(all_188_3_395, all_188_1_393) = all_188_0_392 & implies(all_41_0_226, all_188_2_394) = all_188_1_393 & implies(all_30_0_222, all_0_85_85) = all_188_3_395 & is_a_theorem(all_188_0_392) = 0
% 103.41/71.18  |
% 103.41/71.18  | Applying alpha-rule on (248) yields:
% 103.41/71.18  | (249) implies(all_30_0_222, all_0_85_85) = all_188_3_395
% 103.41/71.18  | (250) equiv(all_30_0_222, all_0_85_85) = all_188_2_394
% 103.41/71.18  | (251) implies(all_41_0_226, all_188_2_394) = all_188_1_393
% 103.41/71.18  | (252) implies(all_188_3_395, all_188_1_393) = all_188_0_392
% 103.41/71.18  | (253) is_a_theorem(all_188_0_392) = 0
% 103.41/71.18  |
% 103.41/71.18  | Instantiating (152) with all_190_0_396, all_190_1_397, all_190_2_398, all_190_3_399 yields:
% 103.41/71.18  | (254) equiv(all_0_85_85, all_30_0_222) = all_190_2_398 & implies(all_190_3_399, all_190_1_397) = all_190_0_396 & implies(all_43_1_228, all_190_2_398) = all_190_1_397 & implies(all_0_85_85, all_30_0_222) = all_190_3_399 & is_a_theorem(all_190_0_396) = 0
% 103.41/71.18  |
% 103.41/71.18  | Applying alpha-rule on (254) yields:
% 103.41/71.18  | (255) is_a_theorem(all_190_0_396) = 0
% 103.41/71.18  | (256) equiv(all_0_85_85, all_30_0_222) = all_190_2_398
% 103.41/71.18  | (257) implies(all_0_85_85, all_30_0_222) = all_190_3_399
% 103.41/71.18  | (258) implies(all_190_3_399, all_190_1_397) = all_190_0_396
% 103.41/71.18  | (259) implies(all_43_1_228, all_190_2_398) = all_190_1_397
% 103.41/71.18  |
% 103.41/71.18  | Instantiating (163) with all_206_0_417 yields:
% 103.41/71.18  | (260) (all_206_0_417 = 0 & is_a_theorem(all_30_0_222) = 0) | ( ~ (all_206_0_417 = 0) & is_a_theorem(all_41_0_226) = all_206_0_417) | ( ~ (all_206_0_417 = 0) & is_a_theorem(all_0_85_85) = all_206_0_417)
% 103.41/71.18  |
% 103.41/71.18  | Instantiating (157) with all_217_0_432 yields:
% 103.41/71.18  | (261) (all_217_0_432 = 0 & is_a_theorem(all_43_1_228) = 0) | ( ~ (all_217_0_432 = 0) & is_a_theorem(all_43_0_227) = all_217_0_432) | ( ~ (all_217_0_432 = 0) & is_a_theorem(all_30_1_223) = all_217_0_432)
% 103.41/71.18  |
% 103.41/71.18  | Instantiating (150) with all_250_0_466 yields:
% 103.41/71.18  | (262) implies(all_30_0_222, all_51_0_233) = all_250_0_466 & is_a_theorem(all_250_0_466) = 0
% 103.41/71.18  |
% 103.41/71.18  | Applying alpha-rule on (262) yields:
% 103.41/71.18  | (263) implies(all_30_0_222, all_51_0_233) = all_250_0_466
% 103.41/71.18  | (264) is_a_theorem(all_250_0_466) = 0
% 103.41/71.18  |
% 103.41/71.18  | Instantiating (151) with all_252_0_467 yields:
% 103.41/71.18  | (265) implies(all_30_1_223, all_47_0_230) = all_252_0_467 & is_a_theorem(all_252_0_467) = 0
% 103.41/71.18  |
% 103.41/71.18  | Applying alpha-rule on (265) yields:
% 103.41/71.18  | (266) implies(all_30_1_223, all_47_0_230) = all_252_0_467
% 103.41/71.18  | (267) is_a_theorem(all_252_0_467) = 0
% 103.41/71.18  |
% 103.41/71.18  +-Applying beta-rule and splitting (225), into two cases.
% 103.41/71.18  |-Branch one:
% 103.41/71.18  | (268) (all_159_0_356 = 0 & is_a_theorem(all_30_1_223) = 0) | ( ~ (all_159_0_356 = 0) & is_a_theorem(all_39_0_225) = all_159_0_356)
% 103.41/71.18  |
% 103.41/71.18  	+-Applying beta-rule and splitting (268), into two cases.
% 103.41/71.18  	|-Branch one:
% 103.41/71.18  	| (269) all_159_0_356 = 0 & is_a_theorem(all_30_1_223) = 0
% 103.41/71.18  	|
% 103.41/71.18  		| Applying alpha-rule on (269) yields:
% 103.41/71.18  		| (270) all_159_0_356 = 0
% 103.41/71.18  		| (271) is_a_theorem(all_30_1_223) = 0
% 103.41/71.18  		|
% 103.41/71.18  		+-Applying beta-rule and splitting (261), into two cases.
% 103.41/71.18  		|-Branch one:
% 103.41/71.18  		| (272) (all_217_0_432 = 0 & is_a_theorem(all_43_1_228) = 0) | ( ~ (all_217_0_432 = 0) & is_a_theorem(all_43_0_227) = all_217_0_432)
% 103.41/71.18  		|
% 103.41/71.18  			+-Applying beta-rule and splitting (272), into two cases.
% 103.41/71.18  			|-Branch one:
% 103.41/71.18  			| (273) all_217_0_432 = 0 & is_a_theorem(all_43_1_228) = 0
% 103.41/71.18  			|
% 103.41/71.18  				| Applying alpha-rule on (273) yields:
% 103.41/71.18  				| (274) all_217_0_432 = 0
% 103.41/71.18  				| (275) is_a_theorem(all_43_1_228) = 0
% 103.41/71.18  				|
% 103.41/71.18  				+-Applying beta-rule and splitting (260), into two cases.
% 103.41/71.18  				|-Branch one:
% 103.41/71.18  				| (276) (all_206_0_417 = 0 & is_a_theorem(all_30_0_222) = 0) | ( ~ (all_206_0_417 = 0) & is_a_theorem(all_41_0_226) = all_206_0_417)
% 103.41/71.18  				|
% 103.41/71.18  					+-Applying beta-rule and splitting (276), into two cases.
% 103.41/71.18  					|-Branch one:
% 103.41/71.18  					| (277) all_206_0_417 = 0 & is_a_theorem(all_30_0_222) = 0
% 103.41/71.18  					|
% 103.41/71.18  						| Applying alpha-rule on (277) yields:
% 103.41/71.18  						| (278) all_206_0_417 = 0
% 103.41/71.18  						| (279) is_a_theorem(all_30_0_222) = 0
% 103.41/71.18  						|
% 103.41/71.18  						| Instantiating formula (91) with all_0_85_85, all_30_0_222, all_182_1_388, all_190_2_398 and discharging atoms equiv(all_0_85_85, all_30_0_222) = all_190_2_398, equiv(all_0_85_85, all_30_0_222) = all_182_1_388, yields:
% 103.41/71.18  						| (280) all_190_2_398 = all_182_1_388
% 103.41/71.18  						|
% 103.41/71.18  						| Instantiating formula (91) with all_0_85_85, all_30_0_222, all_128_1_312, all_190_2_398 and discharging atoms equiv(all_0_85_85, all_30_0_222) = all_190_2_398, equiv(all_0_85_85, all_30_0_222) = all_128_1_312, yields:
% 103.41/71.18  						| (281) all_190_2_398 = all_128_1_312
% 103.41/71.18  						|
% 103.41/71.18  						| Instantiating formula (91) with all_0_85_85, all_30_0_222, all_114_2_294, all_182_1_388 and discharging atoms equiv(all_0_85_85, all_30_0_222) = all_182_1_388, equiv(all_0_85_85, all_30_0_222) = all_114_2_294, yields:
% 103.41/71.18  						| (282) all_182_1_388 = all_114_2_294
% 103.41/71.18  						|
% 103.41/71.18  						| Instantiating formula (91) with all_0_85_85, all_30_0_222, all_112_1_291, all_114_2_294 and discharging atoms equiv(all_0_85_85, all_30_0_222) = all_114_2_294, equiv(all_0_85_85, all_30_0_222) = all_112_1_291, yields:
% 103.41/71.18  						| (283) all_114_2_294 = all_112_1_291
% 103.41/71.18  						|
% 103.41/71.18  						| Instantiating formula (91) with all_0_85_85, all_30_0_222, all_110_1_289, all_182_1_388 and discharging atoms equiv(all_0_85_85, all_30_0_222) = all_182_1_388, equiv(all_0_85_85, all_30_0_222) = all_110_1_289, yields:
% 103.41/71.18  						| (284) all_182_1_388 = all_110_1_289
% 103.41/71.18  						|
% 103.41/71.18  						| Instantiating formula (91) with all_0_86_86, all_0_87_87, all_144_2_338, all_180_1_386 and discharging atoms equiv(all_0_86_86, all_0_87_87) = all_180_1_386, equiv(all_0_86_86, all_0_87_87) = all_144_2_338, yields:
% 103.41/71.18  						| (285) all_180_1_386 = all_144_2_338
% 103.41/71.18  						|
% 103.41/71.18  						| Instantiating formula (91) with all_0_86_86, all_0_87_87, all_142_1_335, all_180_1_386 and discharging atoms equiv(all_0_86_86, all_0_87_87) = all_180_1_386, equiv(all_0_86_86, all_0_87_87) = all_142_1_335, yields:
% 103.41/71.18  						| (286) all_180_1_386 = all_142_1_335
% 103.41/71.18  						|
% 103.41/71.18  						| Instantiating formula (91) with all_0_86_86, all_0_87_87, all_138_1_331, all_142_1_335 and discharging atoms equiv(all_0_86_86, all_0_87_87) = all_142_1_335, equiv(all_0_86_86, all_0_87_87) = all_138_1_331, yields:
% 103.41/71.18  						| (287) all_142_1_335 = all_138_1_331
% 103.41/71.18  						|
% 103.41/71.18  						| Instantiating formula (91) with all_0_86_86, all_0_87_87, all_81_2_256, all_180_1_386 and discharging atoms equiv(all_0_86_86, all_0_87_87) = all_180_1_386, equiv(all_0_86_86, all_0_87_87) = all_81_2_256, yields:
% 103.41/71.18  						| (288) all_180_1_386 = all_81_2_256
% 103.41/71.18  						|
% 103.41/71.18  						| Instantiating formula (91) with all_0_86_86, all_0_87_87, all_79_1_253, all_138_1_331 and discharging atoms equiv(all_0_86_86, all_0_87_87) = all_138_1_331, equiv(all_0_86_86, all_0_87_87) = all_79_1_253, yields:
% 103.41/71.18  						| (289) all_138_1_331 = all_79_1_253
% 103.41/71.18  						|
% 103.41/71.18  						| Instantiating formula (39) with all_30_0_222, all_0_85_85, all_186_0_390, all_43_1_228 and discharging atoms implies(all_30_0_222, all_0_85_85) = all_186_0_390, implies(all_30_0_222, all_0_85_85) = all_43_1_228, yields:
% 103.41/71.18  						| (290) all_186_0_390 = all_43_1_228
% 103.41/71.18  						|
% 103.41/71.18  						| Instantiating formula (39) with all_30_0_222, all_0_85_85, all_186_0_390, all_188_3_395 and discharging atoms implies(all_30_0_222, all_0_85_85) = all_188_3_395, implies(all_30_0_222, all_0_85_85) = all_186_0_390, yields:
% 103.41/71.18  						| (291) all_188_3_395 = all_186_0_390
% 103.41/71.18  						|
% 103.41/71.18  						| Instantiating formula (39) with all_30_0_222, all_0_85_85, all_114_3_295, all_186_0_390 and discharging atoms implies(all_30_0_222, all_0_85_85) = all_186_0_390, implies(all_30_0_222, all_0_85_85) = all_114_3_295, yields:
% 103.41/71.18  						| (292) all_186_0_390 = all_114_3_295
% 103.41/71.18  						|
% 103.41/71.18  						| Instantiating formula (39) with all_30_0_222, all_0_85_85, all_112_0_290, all_188_3_395 and discharging atoms implies(all_30_0_222, all_0_85_85) = all_188_3_395, implies(all_30_0_222, all_0_85_85) = all_112_0_290, yields:
% 103.41/71.18  						| (293) all_188_3_395 = all_112_0_290
% 103.41/71.18  						|
% 103.41/71.18  						| Instantiating formula (39) with all_0_85_85, all_30_0_222, all_182_0_387, all_190_3_399 and discharging atoms implies(all_0_85_85, all_30_0_222) = all_190_3_399, implies(all_0_85_85, all_30_0_222) = all_182_0_387, yields:
% 103.41/71.18  						| (294) all_190_3_399 = all_182_0_387
% 103.41/71.18  						|
% 103.41/71.18  						| Instantiating formula (39) with all_0_85_85, all_30_0_222, all_89_3_267, all_41_0_226 and discharging atoms implies(all_0_85_85, all_30_0_222) = all_89_3_267, implies(all_0_85_85, all_30_0_222) = all_41_0_226, yields:
% 103.41/71.18  						| (295) all_89_3_267 = all_41_0_226
% 103.41/71.18  						|
% 103.41/71.19  						| Instantiating formula (39) with all_0_85_85, all_30_0_222, all_89_3_267, all_182_0_387 and discharging atoms implies(all_0_85_85, all_30_0_222) = all_182_0_387, implies(all_0_85_85, all_30_0_222) = all_89_3_267, yields:
% 103.41/71.19  						| (296) all_182_0_387 = all_89_3_267
% 103.41/71.19  						|
% 103.41/71.19  						| Instantiating formula (39) with all_0_85_85, all_30_0_222, all_87_0_262, all_190_3_399 and discharging atoms implies(all_0_85_85, all_30_0_222) = all_190_3_399, implies(all_0_85_85, all_30_0_222) = all_87_0_262, yields:
% 103.41/71.19  						| (297) all_190_3_399 = all_87_0_262
% 103.41/71.19  						|
% 103.41/71.19  						| Instantiating formula (39) with all_0_86_86, all_0_87_87, all_174_0_375, all_51_0_233 and discharging atoms implies(all_0_86_86, all_0_87_87) = all_174_0_375, implies(all_0_86_86, all_0_87_87) = all_51_0_233, yields:
% 103.41/71.19  						| (298) all_174_0_375 = all_51_0_233
% 103.41/71.19  						|
% 103.41/71.19  						| Instantiating formula (39) with all_0_86_86, all_0_87_87, all_174_0_375, all_176_3_380 and discharging atoms implies(all_0_86_86, all_0_87_87) = all_176_3_380, implies(all_0_86_86, all_0_87_87) = all_174_0_375, yields:
% 103.41/71.19  						| (299) all_176_3_380 = all_174_0_375
% 103.41/71.19  						|
% 103.41/71.19  						| Instantiating formula (39) with all_0_86_86, all_0_87_87, all_81_3_257, all_174_0_375 and discharging atoms implies(all_0_86_86, all_0_87_87) = all_174_0_375, implies(all_0_86_86, all_0_87_87) = all_81_3_257, yields:
% 103.41/71.19  						| (300) all_174_0_375 = all_81_3_257
% 103.41/71.19  						|
% 103.41/71.19  						| Instantiating formula (39) with all_0_86_86, all_0_87_87, all_79_0_252, all_176_3_380 and discharging atoms implies(all_0_86_86, all_0_87_87) = all_176_3_380, implies(all_0_86_86, all_0_87_87) = all_79_0_252, yields:
% 103.41/71.19  						| (301) all_176_3_380 = all_79_0_252
% 103.41/71.19  						|
% 103.41/71.19  						| Instantiating formula (39) with all_0_87_87, all_0_86_86, all_144_3_339, all_47_0_230 and discharging atoms implies(all_0_87_87, all_0_86_86) = all_144_3_339, implies(all_0_87_87, all_0_86_86) = all_47_0_230, yields:
% 103.41/71.19  						| (302) all_144_3_339 = all_47_0_230
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (280,281) yields a new equation:
% 103.41/71.19  						| (303) all_182_1_388 = all_128_1_312
% 103.41/71.19  						|
% 103.41/71.19  						| Simplifying 303 yields:
% 103.41/71.19  						| (304) all_182_1_388 = all_128_1_312
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (294,297) yields a new equation:
% 103.41/71.19  						| (305) all_182_0_387 = all_87_0_262
% 103.41/71.19  						|
% 103.41/71.19  						| Simplifying 305 yields:
% 103.41/71.19  						| (306) all_182_0_387 = all_87_0_262
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (291,293) yields a new equation:
% 103.41/71.19  						| (307) all_186_0_390 = all_112_0_290
% 103.41/71.19  						|
% 103.41/71.19  						| Simplifying 307 yields:
% 103.41/71.19  						| (308) all_186_0_390 = all_112_0_290
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (308,292) yields a new equation:
% 103.41/71.19  						| (309) all_114_3_295 = all_112_0_290
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (290,292) yields a new equation:
% 103.41/71.19  						| (310) all_114_3_295 = all_43_1_228
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (296,306) yields a new equation:
% 103.41/71.19  						| (311) all_89_3_267 = all_87_0_262
% 103.41/71.19  						|
% 103.41/71.19  						| Simplifying 311 yields:
% 103.41/71.19  						| (312) all_89_3_267 = all_87_0_262
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (282,304) yields a new equation:
% 103.41/71.19  						| (313) all_128_1_312 = all_114_2_294
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (284,304) yields a new equation:
% 103.41/71.19  						| (314) all_128_1_312 = all_110_1_289
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (286,285) yields a new equation:
% 103.41/71.19  						| (315) all_144_2_338 = all_142_1_335
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (288,285) yields a new equation:
% 103.41/71.19  						| (316) all_144_2_338 = all_81_2_256
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (299,301) yields a new equation:
% 103.41/71.19  						| (317) all_174_0_375 = all_79_0_252
% 103.41/71.19  						|
% 103.41/71.19  						| Simplifying 317 yields:
% 103.41/71.19  						| (318) all_174_0_375 = all_79_0_252
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (318,300) yields a new equation:
% 103.41/71.19  						| (319) all_81_3_257 = all_79_0_252
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (298,300) yields a new equation:
% 103.41/71.19  						| (320) all_81_3_257 = all_51_0_233
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (315,316) yields a new equation:
% 103.41/71.19  						| (321) all_142_1_335 = all_81_2_256
% 103.41/71.19  						|
% 103.41/71.19  						| Simplifying 321 yields:
% 103.41/71.19  						| (322) all_142_1_335 = all_81_2_256
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (287,322) yields a new equation:
% 103.41/71.19  						| (323) all_138_1_331 = all_81_2_256
% 103.41/71.19  						|
% 103.41/71.19  						| Simplifying 323 yields:
% 103.41/71.19  						| (324) all_138_1_331 = all_81_2_256
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (289,324) yields a new equation:
% 103.41/71.19  						| (325) all_81_2_256 = all_79_1_253
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (313,314) yields a new equation:
% 103.41/71.19  						| (326) all_114_2_294 = all_110_1_289
% 103.41/71.19  						|
% 103.41/71.19  						| Simplifying 326 yields:
% 103.41/71.19  						| (327) all_114_2_294 = all_110_1_289
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (327,283) yields a new equation:
% 103.41/71.19  						| (328) all_112_1_291 = all_110_1_289
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (310,309) yields a new equation:
% 103.41/71.19  						| (329) all_112_0_290 = all_43_1_228
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (295,312) yields a new equation:
% 103.41/71.19  						| (330) all_87_0_262 = all_41_0_226
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (320,319) yields a new equation:
% 103.41/71.19  						| (331) all_79_0_252 = all_51_0_233
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (331,319) yields a new equation:
% 103.41/71.19  						| (320) all_81_3_257 = all_51_0_233
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (329,309) yields a new equation:
% 103.41/71.19  						| (310) all_114_3_295 = all_43_1_228
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (328,283) yields a new equation:
% 103.41/71.19  						| (327) all_114_2_294 = all_110_1_289
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (325,316) yields a new equation:
% 103.41/71.19  						| (335) all_144_2_338 = all_79_1_253
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (330,297) yields a new equation:
% 103.41/71.19  						| (336) all_190_3_399 = all_41_0_226
% 103.41/71.19  						|
% 103.41/71.19  						| Combining equations (314,281) yields a new equation:
% 103.41/71.19  						| (337) all_190_2_398 = all_110_1_289
% 103.41/71.19  						|
% 103.41/71.19  						| From (328) and (199) follows:
% 103.41/71.19  						| (194) equiv(all_0_85_85, all_30_0_222) = all_110_1_289
% 103.41/71.19  						|
% 103.41/71.19  						| From (325) and (180) follows:
% 103.41/71.19  						| (175) equiv(all_0_86_86, all_0_87_87) = all_79_1_253
% 103.41/71.19  						|
% 103.41/71.19  						| From (336) and (258) follows:
% 103.41/71.19  						| (340) implies(all_41_0_226, all_190_1_397) = all_190_0_396
% 103.41/71.19  						|
% 103.41/71.19  						| From (302)(335) and (222) follows:
% 103.41/71.19  						| (341) implies(all_47_0_230, all_79_1_253) = all_144_1_337
% 103.41/71.19  						|
% 103.41/71.19  						| From (310)(327) and (206) follows:
% 103.41/71.19  						| (342) implies(all_43_1_228, all_110_1_289) = all_114_1_293
% 103.41/71.19  						|
% 103.41/71.19  						| From (320) and (179) follows:
% 103.41/71.19  						| (343) implies(all_51_0_233, all_81_1_255) = all_81_0_254
% 103.41/71.19  						|
% 103.41/71.19  						| From (325) and (181) follows:
% 103.41/71.19  						| (344) implies(all_47_0_230, all_79_1_253) = all_81_1_255
% 103.41/71.19  						|
% 103.41/71.19  						| From (337) and (259) follows:
% 103.41/71.19  						| (345) implies(all_43_1_228, all_110_1_289) = all_190_1_397
% 103.41/71.19  						|
% 103.41/71.19  						| Instantiating formula (39) with all_47_0_230, all_79_1_253, all_81_1_255, all_144_1_337 and discharging atoms implies(all_47_0_230, all_79_1_253) = all_144_1_337, implies(all_47_0_230, all_79_1_253) = all_81_1_255, yields:
% 103.41/71.19  						| (346) all_144_1_337 = all_81_1_255
% 103.41/71.19  						|
% 103.41/71.19  						| Instantiating formula (39) with all_43_1_228, all_110_1_289, all_114_1_293, all_190_1_397 and discharging atoms implies(all_43_1_228, all_110_1_289) = all_190_1_397, implies(all_43_1_228, all_110_1_289) = all_114_1_293, yields:
% 103.41/71.19  						| (347) all_190_1_397 = all_114_1_293
% 103.41/71.19  						|
% 103.41/71.19  						| From (346) and (221) follows:
% 103.41/71.19  						| (348) implies(all_51_0_233, all_81_1_255) = all_144_0_336
% 103.41/71.19  						|
% 103.41/71.19  						| From (346) and (341) follows:
% 103.41/71.19  						| (344) implies(all_47_0_230, all_79_1_253) = all_81_1_255
% 103.41/71.19  						|
% 103.41/71.19  						| From (347) and (345) follows:
% 103.41/71.19  						| (342) implies(all_43_1_228, all_110_1_289) = all_114_1_293
% 103.41/71.19  						|
% 103.41/71.19  						| From (347) and (340) follows:
% 103.41/71.19  						| (351) implies(all_41_0_226, all_114_1_293) = all_190_0_396
% 103.41/71.19  						|
% 103.41/71.19  						| Instantiating formula (39) with all_51_0_233, all_81_1_255, all_144_0_336, all_81_0_254 and discharging atoms implies(all_51_0_233, all_81_1_255) = all_144_0_336, implies(all_51_0_233, all_81_1_255) = all_81_0_254, yields:
% 103.41/71.19  						| (352) all_144_0_336 = all_81_0_254
% 103.41/71.19  						|
% 103.41/71.19  						| Instantiating formula (39) with all_41_0_226, all_114_1_293, all_190_0_396, all_114_0_292 and discharging atoms implies(all_41_0_226, all_114_1_293) = all_190_0_396, implies(all_41_0_226, all_114_1_293) = all_114_0_292, yields:
% 103.41/71.19  						| (353) all_190_0_396 = all_114_0_292
% 103.41/71.19  						|
% 103.41/71.19  						| From (352) and (348) follows:
% 103.41/71.19  						| (343) implies(all_51_0_233, all_81_1_255) = all_81_0_254
% 103.41/71.19  						|
% 103.41/71.19  						| From (353) and (351) follows:
% 103.41/71.19  						| (205) implies(all_41_0_226, all_114_1_293) = all_114_0_292
% 103.41/71.19  						|
% 103.41/71.19  						| From (353) and (255) follows:
% 103.41/71.19  						| (203) is_a_theorem(all_114_0_292) = 0
% 103.41/71.19  						|
% 103.41/71.19  						| From (352) and (223) follows:
% 103.41/71.19  						| (182) is_a_theorem(all_81_0_254) = 0
% 103.41/71.19  						|
% 103.41/71.19  						| Instantiating formula (66) with all_110_1_289, all_30_0_222, all_0_85_85 and discharging atoms equiv(all_0_85_85, all_30_0_222) = all_110_1_289, yields:
% 103.41/71.19  						| (358) all_30_0_222 = all_0_85_85 |  ? [v0] : ( ~ (v0 = 0) & is_a_theorem(all_110_1_289) = v0)
% 103.41/71.19  						|
% 103.41/71.19  						| Instantiating formula (66) with all_79_1_253, all_0_87_87, all_0_86_86 and discharging atoms equiv(all_0_86_86, all_0_87_87) = all_79_1_253, yields:
% 103.41/71.19  						| (359) all_0_86_86 = all_0_87_87 |  ? [v0] : ( ~ (v0 = 0) & is_a_theorem(all_79_1_253) = v0)
% 103.41/71.19  						|
% 103.41/71.19  						| Instantiating formula (78) with all_81_0_254, all_81_1_255, all_51_0_233 and discharging atoms implies(all_51_0_233, all_81_1_255) = all_81_0_254, yields:
% 103.41/71.19  						| (360)  ? [v0] : ((v0 = 0 & is_a_theorem(all_81_1_255) = 0) | ( ~ (v0 = 0) & is_a_theorem(all_81_0_254) = v0) | ( ~ (v0 = 0) & is_a_theorem(all_51_0_233) = v0))
% 103.41/71.19  						|
% 103.41/71.19  						| Instantiating formula (78) with all_81_1_255, all_79_1_253, all_47_0_230 and discharging atoms implies(all_47_0_230, all_79_1_253) = all_81_1_255, yields:
% 103.41/71.19  						| (361)  ? [v0] : ((v0 = 0 & is_a_theorem(all_79_1_253) = 0) | ( ~ (v0 = 0) & is_a_theorem(all_81_1_255) = v0) | ( ~ (v0 = 0) & is_a_theorem(all_47_0_230) = v0))
% 103.41/71.20  						|
% 103.41/71.20  						| Instantiating formula (78) with all_114_1_293, all_110_1_289, all_43_1_228 and discharging atoms implies(all_43_1_228, all_110_1_289) = all_114_1_293, yields:
% 103.41/71.20  						| (362)  ? [v0] : ((v0 = 0 & is_a_theorem(all_110_1_289) = 0) | ( ~ (v0 = 0) & is_a_theorem(all_114_1_293) = v0) | ( ~ (v0 = 0) & is_a_theorem(all_43_1_228) = v0))
% 103.41/71.20  						|
% 103.41/71.20  						| Instantiating formula (78) with all_114_0_292, all_114_1_293, all_41_0_226 and discharging atoms implies(all_41_0_226, all_114_1_293) = all_114_0_292, yields:
% 103.41/71.20  						| (363)  ? [v0] : ((v0 = 0 & is_a_theorem(all_114_1_293) = 0) | ( ~ (v0 = 0) & is_a_theorem(all_114_0_292) = v0) | ( ~ (v0 = 0) & is_a_theorem(all_41_0_226) = v0))
% 103.41/71.20  						|
% 103.41/71.20  						| Instantiating formula (78) with all_250_0_466, all_51_0_233, all_30_0_222 and discharging atoms implies(all_30_0_222, all_51_0_233) = all_250_0_466, yields:
% 103.41/71.20  						| (364)  ? [v0] : ((v0 = 0 & is_a_theorem(all_51_0_233) = 0) | ( ~ (v0 = 0) & is_a_theorem(all_250_0_466) = v0) | ( ~ (v0 = 0) & is_a_theorem(all_30_0_222) = v0))
% 103.41/71.20  						|
% 103.41/71.20  						| Instantiating formula (78) with all_252_0_467, all_47_0_230, all_30_1_223 and discharging atoms implies(all_30_1_223, all_47_0_230) = all_252_0_467, yields:
% 103.41/71.20  						| (365)  ? [v0] : ((v0 = 0 & is_a_theorem(all_47_0_230) = 0) | ( ~ (v0 = 0) & is_a_theorem(all_252_0_467) = v0) | ( ~ (v0 = 0) & is_a_theorem(all_30_1_223) = v0))
% 103.41/71.20  						|
% 103.41/71.20  						| Instantiating (361) with all_436_0_625 yields:
% 103.41/71.20  						| (366) (all_436_0_625 = 0 & is_a_theorem(all_79_1_253) = 0) | ( ~ (all_436_0_625 = 0) & is_a_theorem(all_81_1_255) = all_436_0_625) | ( ~ (all_436_0_625 = 0) & is_a_theorem(all_47_0_230) = all_436_0_625)
% 103.41/71.20  						|
% 103.41/71.20  						| Instantiating (362) with all_949_0_1219 yields:
% 103.41/71.20  						| (367) (all_949_0_1219 = 0 & is_a_theorem(all_110_1_289) = 0) | ( ~ (all_949_0_1219 = 0) & is_a_theorem(all_114_1_293) = all_949_0_1219) | ( ~ (all_949_0_1219 = 0) & is_a_theorem(all_43_1_228) = all_949_0_1219)
% 103.41/71.20  						|
% 103.41/71.20  						| Instantiating (363) with all_956_0_1227 yields:
% 103.41/71.20  						| (368) (all_956_0_1227 = 0 & is_a_theorem(all_114_1_293) = 0) | ( ~ (all_956_0_1227 = 0) & is_a_theorem(all_114_0_292) = all_956_0_1227) | ( ~ (all_956_0_1227 = 0) & is_a_theorem(all_41_0_226) = all_956_0_1227)
% 103.41/71.20  						|
% 103.41/71.20  						| Instantiating (364) with all_1931_0_2368 yields:
% 103.41/71.20  						| (369) (all_1931_0_2368 = 0 & is_a_theorem(all_51_0_233) = 0) | ( ~ (all_1931_0_2368 = 0) & is_a_theorem(all_250_0_466) = all_1931_0_2368) | ( ~ (all_1931_0_2368 = 0) & is_a_theorem(all_30_0_222) = all_1931_0_2368)
% 103.41/71.20  						|
% 103.41/71.20  						| Instantiating (365) with all_2088_0_2571 yields:
% 103.41/71.20  						| (370) (all_2088_0_2571 = 0 & is_a_theorem(all_47_0_230) = 0) | ( ~ (all_2088_0_2571 = 0) & is_a_theorem(all_252_0_467) = all_2088_0_2571) | ( ~ (all_2088_0_2571 = 0) & is_a_theorem(all_30_1_223) = all_2088_0_2571)
% 103.41/71.20  						|
% 103.41/71.20  						| Instantiating (360) with all_2547_0_3170 yields:
% 103.41/71.20  						| (371) (all_2547_0_3170 = 0 & is_a_theorem(all_81_1_255) = 0) | ( ~ (all_2547_0_3170 = 0) & is_a_theorem(all_81_0_254) = all_2547_0_3170) | ( ~ (all_2547_0_3170 = 0) & is_a_theorem(all_51_0_233) = all_2547_0_3170)
% 103.41/71.20  						|
% 103.41/71.20  						+-Applying beta-rule and splitting (370), into two cases.
% 103.41/71.20  						|-Branch one:
% 103.41/71.20  						| (372) (all_2088_0_2571 = 0 & is_a_theorem(all_47_0_230) = 0) | ( ~ (all_2088_0_2571 = 0) & is_a_theorem(all_252_0_467) = all_2088_0_2571)
% 103.41/71.20  						|
% 103.41/71.20  							+-Applying beta-rule and splitting (372), into two cases.
% 103.41/71.20  							|-Branch one:
% 103.41/71.20  							| (373) all_2088_0_2571 = 0 & is_a_theorem(all_47_0_230) = 0
% 103.41/71.20  							|
% 103.41/71.20  								| Applying alpha-rule on (373) yields:
% 103.41/71.20  								| (374) all_2088_0_2571 = 0
% 103.41/71.20  								| (375) is_a_theorem(all_47_0_230) = 0
% 103.41/71.20  								|
% 103.41/71.20  								+-Applying beta-rule and splitting (368), into two cases.
% 103.41/71.20  								|-Branch one:
% 103.41/71.20  								| (376) (all_956_0_1227 = 0 & is_a_theorem(all_114_1_293) = 0) | ( ~ (all_956_0_1227 = 0) & is_a_theorem(all_114_0_292) = all_956_0_1227)
% 103.41/71.20  								|
% 103.41/71.20  									+-Applying beta-rule and splitting (376), into two cases.
% 103.41/71.20  									|-Branch one:
% 103.41/71.20  									| (377) all_956_0_1227 = 0 & is_a_theorem(all_114_1_293) = 0
% 103.41/71.20  									|
% 103.41/71.20  										| Applying alpha-rule on (377) yields:
% 103.41/71.20  										| (378) all_956_0_1227 = 0
% 103.41/71.20  										| (379) is_a_theorem(all_114_1_293) = 0
% 103.41/71.20  										|
% 103.41/71.20  										+-Applying beta-rule and splitting (367), into two cases.
% 103.41/71.20  										|-Branch one:
% 103.41/71.20  										| (380) (all_949_0_1219 = 0 & is_a_theorem(all_110_1_289) = 0) | ( ~ (all_949_0_1219 = 0) & is_a_theorem(all_114_1_293) = all_949_0_1219)
% 103.41/71.20  										|
% 103.41/71.20  											+-Applying beta-rule and splitting (380), into two cases.
% 103.41/71.20  											|-Branch one:
% 103.41/71.20  											| (381) all_949_0_1219 = 0 & is_a_theorem(all_110_1_289) = 0
% 103.41/71.20  											|
% 103.41/71.20  												| Applying alpha-rule on (381) yields:
% 103.41/71.20  												| (382) all_949_0_1219 = 0
% 103.41/71.20  												| (383) is_a_theorem(all_110_1_289) = 0
% 103.41/71.20  												|
% 103.41/71.20  												+-Applying beta-rule and splitting (358), into two cases.
% 103.41/71.20  												|-Branch one:
% 103.41/71.20  												| (384) all_30_0_222 = all_0_85_85
% 103.41/71.20  												|
% 103.41/71.20  													| From (384) and (279) follows:
% 103.41/71.20  													| (90) is_a_theorem(all_0_85_85) = 0
% 103.41/71.20  													|
% 103.41/71.20  													+-Applying beta-rule and splitting (359), into two cases.
% 103.41/71.20  													|-Branch one:
% 103.41/71.20  													| (386) all_0_86_86 = all_0_87_87
% 103.41/71.20  													|
% 103.41/71.20  														| Equations (386) can reduce 43 to:
% 103.41/71.20  														| (387) $false
% 103.41/71.20  														|
% 103.41/71.20  														|-The branch is then unsatisfiable
% 103.41/71.20  													|-Branch two:
% 103.41/71.20  													| (43)  ~ (all_0_86_86 = all_0_87_87)
% 103.41/71.20  													| (389)  ? [v0] : ( ~ (v0 = 0) & is_a_theorem(all_79_1_253) = v0)
% 103.41/71.20  													|
% 103.41/71.20  														| Instantiating (389) with all_2902_0_3560 yields:
% 103.41/71.20  														| (390)  ~ (all_2902_0_3560 = 0) & is_a_theorem(all_79_1_253) = all_2902_0_3560
% 103.41/71.20  														|
% 103.41/71.20  														| Applying alpha-rule on (390) yields:
% 103.41/71.20  														| (391)  ~ (all_2902_0_3560 = 0)
% 103.41/71.20  														| (392) is_a_theorem(all_79_1_253) = all_2902_0_3560
% 103.41/71.20  														|
% 103.41/71.20  														+-Applying beta-rule and splitting (366), into two cases.
% 103.41/71.20  														|-Branch one:
% 103.41/71.20  														| (393) (all_436_0_625 = 0 & is_a_theorem(all_79_1_253) = 0) | ( ~ (all_436_0_625 = 0) & is_a_theorem(all_81_1_255) = all_436_0_625)
% 103.41/71.20  														|
% 103.41/71.20  															+-Applying beta-rule and splitting (393), into two cases.
% 103.41/71.20  															|-Branch one:
% 103.41/71.20  															| (394) all_436_0_625 = 0 & is_a_theorem(all_79_1_253) = 0
% 103.41/71.20  															|
% 103.41/71.20  																| Applying alpha-rule on (394) yields:
% 103.41/71.20  																| (395) all_436_0_625 = 0
% 103.41/71.20  																| (396) is_a_theorem(all_79_1_253) = 0
% 103.41/71.20  																|
% 103.41/71.20  																| Instantiating formula (122) with all_79_1_253, 0, all_2902_0_3560 and discharging atoms is_a_theorem(all_79_1_253) = all_2902_0_3560, is_a_theorem(all_79_1_253) = 0, yields:
% 103.41/71.20  																| (397) all_2902_0_3560 = 0
% 103.41/71.20  																|
% 103.41/71.20  																| Equations (397) can reduce 391 to:
% 103.41/71.20  																| (387) $false
% 103.41/71.20  																|
% 103.41/71.20  																|-The branch is then unsatisfiable
% 103.41/71.20  															|-Branch two:
% 103.41/71.20  															| (399)  ~ (all_436_0_625 = 0) & is_a_theorem(all_81_1_255) = all_436_0_625
% 103.41/71.20  															|
% 103.41/71.20  																| Applying alpha-rule on (399) yields:
% 103.41/71.20  																| (400)  ~ (all_436_0_625 = 0)
% 103.41/71.20  																| (401) is_a_theorem(all_81_1_255) = all_436_0_625
% 103.41/71.20  																|
% 103.41/71.20  																+-Applying beta-rule and splitting (371), into two cases.
% 103.41/71.20  																|-Branch one:
% 103.41/71.20  																| (402) (all_2547_0_3170 = 0 & is_a_theorem(all_81_1_255) = 0) | ( ~ (all_2547_0_3170 = 0) & is_a_theorem(all_81_0_254) = all_2547_0_3170)
% 103.41/71.20  																|
% 103.41/71.20  																	+-Applying beta-rule and splitting (402), into two cases.
% 103.41/71.20  																	|-Branch one:
% 103.41/71.20  																	| (403) all_2547_0_3170 = 0 & is_a_theorem(all_81_1_255) = 0
% 103.41/71.20  																	|
% 103.41/71.20  																		| Applying alpha-rule on (403) yields:
% 103.41/71.20  																		| (404) all_2547_0_3170 = 0
% 103.41/71.20  																		| (405) is_a_theorem(all_81_1_255) = 0
% 103.41/71.20  																		|
% 103.41/71.20  																		| Instantiating formula (122) with all_81_1_255, 0, all_436_0_625 and discharging atoms is_a_theorem(all_81_1_255) = all_436_0_625, is_a_theorem(all_81_1_255) = 0, yields:
% 103.41/71.20  																		| (395) all_436_0_625 = 0
% 103.41/71.20  																		|
% 103.41/71.20  																		| Equations (395) can reduce 400 to:
% 103.41/71.20  																		| (387) $false
% 103.41/71.20  																		|
% 103.41/71.20  																		|-The branch is then unsatisfiable
% 103.41/71.20  																	|-Branch two:
% 103.41/71.20  																	| (408)  ~ (all_2547_0_3170 = 0) & is_a_theorem(all_81_0_254) = all_2547_0_3170
% 103.41/71.20  																	|
% 103.41/71.20  																		| Applying alpha-rule on (408) yields:
% 103.41/71.20  																		| (409)  ~ (all_2547_0_3170 = 0)
% 103.41/71.20  																		| (410) is_a_theorem(all_81_0_254) = all_2547_0_3170
% 103.41/71.20  																		|
% 103.41/71.20  																		| Instantiating formula (122) with all_81_0_254, all_2547_0_3170, 0 and discharging atoms is_a_theorem(all_81_0_254) = all_2547_0_3170, is_a_theorem(all_81_0_254) = 0, yields:
% 103.41/71.20  																		| (404) all_2547_0_3170 = 0
% 103.41/71.20  																		|
% 103.41/71.20  																		| Equations (404) can reduce 409 to:
% 103.85/71.20  																		| (387) $false
% 103.85/71.20  																		|
% 103.85/71.20  																		|-The branch is then unsatisfiable
% 103.85/71.20  																|-Branch two:
% 103.85/71.20  																| (413)  ~ (all_2547_0_3170 = 0) & is_a_theorem(all_51_0_233) = all_2547_0_3170
% 103.85/71.20  																|
% 103.85/71.20  																	| Applying alpha-rule on (413) yields:
% 103.85/71.20  																	| (409)  ~ (all_2547_0_3170 = 0)
% 103.85/71.20  																	| (415) is_a_theorem(all_51_0_233) = all_2547_0_3170
% 103.85/71.20  																	|
% 103.85/71.20  																	+-Applying beta-rule and splitting (369), into two cases.
% 103.85/71.20  																	|-Branch one:
% 103.85/71.20  																	| (416) (all_1931_0_2368 = 0 & is_a_theorem(all_51_0_233) = 0) | ( ~ (all_1931_0_2368 = 0) & is_a_theorem(all_250_0_466) = all_1931_0_2368)
% 103.85/71.20  																	|
% 103.85/71.20  																		+-Applying beta-rule and splitting (416), into two cases.
% 103.85/71.20  																		|-Branch one:
% 103.85/71.20  																		| (417) all_1931_0_2368 = 0 & is_a_theorem(all_51_0_233) = 0
% 103.85/71.20  																		|
% 103.85/71.20  																			| Applying alpha-rule on (417) yields:
% 103.85/71.20  																			| (418) all_1931_0_2368 = 0
% 103.85/71.20  																			| (419) is_a_theorem(all_51_0_233) = 0
% 103.85/71.20  																			|
% 103.85/71.20  																			| Instantiating formula (122) with all_51_0_233, 0, all_2547_0_3170 and discharging atoms is_a_theorem(all_51_0_233) = all_2547_0_3170, is_a_theorem(all_51_0_233) = 0, yields:
% 103.85/71.20  																			| (404) all_2547_0_3170 = 0
% 103.85/71.20  																			|
% 103.85/71.20  																			| Equations (404) can reduce 409 to:
% 103.85/71.20  																			| (387) $false
% 103.85/71.20  																			|
% 103.85/71.20  																			|-The branch is then unsatisfiable
% 103.85/71.20  																		|-Branch two:
% 103.85/71.20  																		| (422)  ~ (all_1931_0_2368 = 0) & is_a_theorem(all_250_0_466) = all_1931_0_2368
% 103.85/71.20  																		|
% 103.85/71.20  																			| Applying alpha-rule on (422) yields:
% 103.85/71.20  																			| (423)  ~ (all_1931_0_2368 = 0)
% 103.85/71.21  																			| (424) is_a_theorem(all_250_0_466) = all_1931_0_2368
% 103.85/71.21  																			|
% 103.85/71.21  																			| Instantiating formula (122) with all_250_0_466, all_1931_0_2368, 0 and discharging atoms is_a_theorem(all_250_0_466) = all_1931_0_2368, is_a_theorem(all_250_0_466) = 0, yields:
% 103.85/71.21  																			| (418) all_1931_0_2368 = 0
% 103.85/71.21  																			|
% 103.85/71.21  																			| Equations (418) can reduce 423 to:
% 103.85/71.21  																			| (387) $false
% 103.85/71.21  																			|
% 103.85/71.21  																			|-The branch is then unsatisfiable
% 103.85/71.21  																	|-Branch two:
% 103.85/71.21  																	| (427)  ~ (all_1931_0_2368 = 0) & is_a_theorem(all_30_0_222) = all_1931_0_2368
% 103.85/71.21  																	|
% 103.85/71.21  																		| Applying alpha-rule on (427) yields:
% 103.85/71.21  																		| (423)  ~ (all_1931_0_2368 = 0)
% 103.85/71.21  																		| (429) is_a_theorem(all_30_0_222) = all_1931_0_2368
% 103.85/71.21  																		|
% 103.85/71.21  																		| From (384) and (429) follows:
% 103.85/71.21  																		| (430) is_a_theorem(all_0_85_85) = all_1931_0_2368
% 103.85/71.21  																		|
% 103.85/71.21  																		| Instantiating formula (122) with all_0_85_85, all_1931_0_2368, 0 and discharging atoms is_a_theorem(all_0_85_85) = all_1931_0_2368, is_a_theorem(all_0_85_85) = 0, yields:
% 103.85/71.21  																		| (418) all_1931_0_2368 = 0
% 103.85/71.21  																		|
% 103.85/71.21  																		| Equations (418) can reduce 423 to:
% 103.85/71.21  																		| (387) $false
% 103.85/71.21  																		|
% 103.85/71.21  																		|-The branch is then unsatisfiable
% 103.85/71.21  														|-Branch two:
% 103.85/71.21  														| (433)  ~ (all_436_0_625 = 0) & is_a_theorem(all_47_0_230) = all_436_0_625
% 103.85/71.21  														|
% 103.85/71.21  															| Applying alpha-rule on (433) yields:
% 103.85/71.21  															| (400)  ~ (all_436_0_625 = 0)
% 103.85/71.21  															| (435) is_a_theorem(all_47_0_230) = all_436_0_625
% 103.85/71.21  															|
% 103.85/71.21  															| Instantiating formula (122) with all_47_0_230, 0, all_436_0_625 and discharging atoms is_a_theorem(all_47_0_230) = all_436_0_625, is_a_theorem(all_47_0_230) = 0, yields:
% 103.85/71.21  															| (395) all_436_0_625 = 0
% 103.85/71.21  															|
% 103.85/71.21  															| Equations (395) can reduce 400 to:
% 103.85/71.21  															| (387) $false
% 103.85/71.21  															|
% 103.85/71.21  															|-The branch is then unsatisfiable
% 103.85/71.21  												|-Branch two:
% 103.85/71.21  												| (438)  ~ (all_30_0_222 = all_0_85_85)
% 103.85/71.21  												| (439)  ? [v0] : ( ~ (v0 = 0) & is_a_theorem(all_110_1_289) = v0)
% 103.85/71.21  												|
% 103.85/71.21  													| Instantiating (439) with all_2887_0_3564 yields:
% 103.85/71.21  													| (440)  ~ (all_2887_0_3564 = 0) & is_a_theorem(all_110_1_289) = all_2887_0_3564
% 103.85/71.21  													|
% 103.85/71.21  													| Applying alpha-rule on (440) yields:
% 103.85/71.21  													| (441)  ~ (all_2887_0_3564 = 0)
% 103.85/71.21  													| (442) is_a_theorem(all_110_1_289) = all_2887_0_3564
% 103.85/71.21  													|
% 103.85/71.21  													| Instantiating formula (122) with all_110_1_289, 0, all_2887_0_3564 and discharging atoms is_a_theorem(all_110_1_289) = all_2887_0_3564, is_a_theorem(all_110_1_289) = 0, yields:
% 103.85/71.21  													| (443) all_2887_0_3564 = 0
% 103.85/71.21  													|
% 103.85/71.21  													| Equations (443) can reduce 441 to:
% 103.85/71.21  													| (387) $false
% 103.85/71.21  													|
% 103.85/71.21  													|-The branch is then unsatisfiable
% 103.85/71.21  											|-Branch two:
% 103.85/71.21  											| (445)  ~ (all_949_0_1219 = 0) & is_a_theorem(all_114_1_293) = all_949_0_1219
% 103.85/71.21  											|
% 103.85/71.21  												| Applying alpha-rule on (445) yields:
% 103.85/71.21  												| (446)  ~ (all_949_0_1219 = 0)
% 103.85/71.21  												| (447) is_a_theorem(all_114_1_293) = all_949_0_1219
% 103.85/71.21  												|
% 103.85/71.21  												| Instantiating formula (122) with all_114_1_293, 0, all_949_0_1219 and discharging atoms is_a_theorem(all_114_1_293) = all_949_0_1219, is_a_theorem(all_114_1_293) = 0, yields:
% 103.85/71.21  												| (382) all_949_0_1219 = 0
% 103.85/71.21  												|
% 103.85/71.21  												| Equations (382) can reduce 446 to:
% 103.85/71.21  												| (387) $false
% 103.85/71.21  												|
% 103.85/71.21  												|-The branch is then unsatisfiable
% 103.85/71.21  										|-Branch two:
% 103.85/71.21  										| (450)  ~ (all_949_0_1219 = 0) & is_a_theorem(all_43_1_228) = all_949_0_1219
% 103.85/71.21  										|
% 103.85/71.21  											| Applying alpha-rule on (450) yields:
% 103.85/71.21  											| (446)  ~ (all_949_0_1219 = 0)
% 103.85/71.21  											| (452) is_a_theorem(all_43_1_228) = all_949_0_1219
% 103.85/71.21  											|
% 103.85/71.21  											| Instantiating formula (122) with all_43_1_228, all_949_0_1219, 0 and discharging atoms is_a_theorem(all_43_1_228) = all_949_0_1219, is_a_theorem(all_43_1_228) = 0, yields:
% 103.85/71.21  											| (382) all_949_0_1219 = 0
% 103.85/71.21  											|
% 103.85/71.21  											| Equations (382) can reduce 446 to:
% 103.85/71.21  											| (387) $false
% 103.85/71.21  											|
% 103.85/71.21  											|-The branch is then unsatisfiable
% 103.85/71.21  									|-Branch two:
% 103.85/71.21  									| (455)  ~ (all_956_0_1227 = 0) & is_a_theorem(all_114_0_292) = all_956_0_1227
% 103.85/71.21  									|
% 103.85/71.21  										| Applying alpha-rule on (455) yields:
% 103.85/71.21  										| (456)  ~ (all_956_0_1227 = 0)
% 103.85/71.21  										| (457) is_a_theorem(all_114_0_292) = all_956_0_1227
% 103.85/71.21  										|
% 103.85/71.21  										| Instantiating formula (122) with all_114_0_292, all_956_0_1227, 0 and discharging atoms is_a_theorem(all_114_0_292) = all_956_0_1227, is_a_theorem(all_114_0_292) = 0, yields:
% 103.85/71.21  										| (378) all_956_0_1227 = 0
% 103.85/71.21  										|
% 103.85/71.21  										| Equations (378) can reduce 456 to:
% 103.85/71.21  										| (387) $false
% 103.85/71.21  										|
% 103.85/71.21  										|-The branch is then unsatisfiable
% 103.85/71.21  								|-Branch two:
% 103.85/71.21  								| (460)  ~ (all_956_0_1227 = 0) & is_a_theorem(all_41_0_226) = all_956_0_1227
% 103.85/71.21  								|
% 103.85/71.21  									| Applying alpha-rule on (460) yields:
% 103.85/71.21  									| (456)  ~ (all_956_0_1227 = 0)
% 103.85/71.21  									| (462) is_a_theorem(all_41_0_226) = all_956_0_1227
% 103.85/71.21  									|
% 103.85/71.21  									| Instantiating formula (122) with all_41_0_226, all_956_0_1227, 0 and discharging atoms is_a_theorem(all_41_0_226) = all_956_0_1227, is_a_theorem(all_41_0_226) = 0, yields:
% 103.85/71.21  									| (378) all_956_0_1227 = 0
% 103.85/71.21  									|
% 103.85/71.21  									| Equations (378) can reduce 456 to:
% 103.85/71.21  									| (387) $false
% 103.85/71.21  									|
% 103.85/71.21  									|-The branch is then unsatisfiable
% 103.85/71.21  							|-Branch two:
% 103.85/71.21  							| (465)  ~ (all_2088_0_2571 = 0) & is_a_theorem(all_252_0_467) = all_2088_0_2571
% 103.85/71.21  							|
% 103.85/71.21  								| Applying alpha-rule on (465) yields:
% 103.85/71.21  								| (466)  ~ (all_2088_0_2571 = 0)
% 103.85/71.21  								| (467) is_a_theorem(all_252_0_467) = all_2088_0_2571
% 103.85/71.21  								|
% 103.85/71.21  								| Instantiating formula (122) with all_252_0_467, all_2088_0_2571, 0 and discharging atoms is_a_theorem(all_252_0_467) = all_2088_0_2571, is_a_theorem(all_252_0_467) = 0, yields:
% 103.85/71.21  								| (374) all_2088_0_2571 = 0
% 103.85/71.21  								|
% 103.85/71.21  								| Equations (374) can reduce 466 to:
% 103.85/71.21  								| (387) $false
% 103.85/71.21  								|
% 103.85/71.21  								|-The branch is then unsatisfiable
% 103.85/71.21  						|-Branch two:
% 103.85/71.21  						| (470)  ~ (all_2088_0_2571 = 0) & is_a_theorem(all_30_1_223) = all_2088_0_2571
% 103.85/71.21  						|
% 103.85/71.21  							| Applying alpha-rule on (470) yields:
% 103.85/71.21  							| (466)  ~ (all_2088_0_2571 = 0)
% 103.85/71.21  							| (472) is_a_theorem(all_30_1_223) = all_2088_0_2571
% 103.85/71.21  							|
% 103.85/71.21  							| Instantiating formula (122) with all_30_1_223, all_2088_0_2571, 0 and discharging atoms is_a_theorem(all_30_1_223) = all_2088_0_2571, is_a_theorem(all_30_1_223) = 0, yields:
% 103.85/71.21  							| (374) all_2088_0_2571 = 0
% 103.85/71.21  							|
% 103.85/71.21  							| Equations (374) can reduce 466 to:
% 103.85/71.21  							| (387) $false
% 103.85/71.21  							|
% 103.85/71.21  							|-The branch is then unsatisfiable
% 103.85/71.21  					|-Branch two:
% 103.85/71.21  					| (475)  ~ (all_206_0_417 = 0) & is_a_theorem(all_41_0_226) = all_206_0_417
% 103.85/71.21  					|
% 103.85/71.21  						| Applying alpha-rule on (475) yields:
% 103.85/71.21  						| (476)  ~ (all_206_0_417 = 0)
% 103.85/71.21  						| (477) is_a_theorem(all_41_0_226) = all_206_0_417
% 103.85/71.21  						|
% 103.85/71.21  						| Instantiating formula (122) with all_41_0_226, all_206_0_417, 0 and discharging atoms is_a_theorem(all_41_0_226) = all_206_0_417, is_a_theorem(all_41_0_226) = 0, yields:
% 103.85/71.21  						| (278) all_206_0_417 = 0
% 103.85/71.21  						|
% 103.85/71.21  						| Equations (278) can reduce 476 to:
% 103.85/71.21  						| (387) $false
% 103.85/71.21  						|
% 103.85/71.21  						|-The branch is then unsatisfiable
% 103.85/71.21  				|-Branch two:
% 103.85/71.21  				| (480)  ~ (all_206_0_417 = 0) & is_a_theorem(all_0_85_85) = all_206_0_417
% 103.85/71.21  				|
% 103.85/71.21  					| Applying alpha-rule on (480) yields:
% 103.85/71.21  					| (476)  ~ (all_206_0_417 = 0)
% 103.85/71.21  					| (482) is_a_theorem(all_0_85_85) = all_206_0_417
% 103.85/71.21  					|
% 103.85/71.21  					| Instantiating formula (122) with all_0_85_85, all_206_0_417, 0 and discharging atoms is_a_theorem(all_0_85_85) = all_206_0_417, is_a_theorem(all_0_85_85) = 0, yields:
% 103.85/71.21  					| (278) all_206_0_417 = 0
% 103.85/71.21  					|
% 103.85/71.21  					| Equations (278) can reduce 476 to:
% 103.85/71.21  					| (387) $false
% 103.85/71.21  					|
% 103.85/71.21  					|-The branch is then unsatisfiable
% 103.85/71.21  			|-Branch two:
% 103.85/71.21  			| (485)  ~ (all_217_0_432 = 0) & is_a_theorem(all_43_0_227) = all_217_0_432
% 103.85/71.21  			|
% 103.85/71.21  				| Applying alpha-rule on (485) yields:
% 103.85/71.21  				| (486)  ~ (all_217_0_432 = 0)
% 103.85/71.21  				| (487) is_a_theorem(all_43_0_227) = all_217_0_432
% 103.85/71.21  				|
% 103.85/71.21  				| Instantiating formula (122) with all_43_0_227, all_217_0_432, 0 and discharging atoms is_a_theorem(all_43_0_227) = all_217_0_432, is_a_theorem(all_43_0_227) = 0, yields:
% 103.85/71.21  				| (274) all_217_0_432 = 0
% 103.85/71.21  				|
% 103.85/71.21  				| Equations (274) can reduce 486 to:
% 103.85/71.21  				| (387) $false
% 103.85/71.21  				|
% 103.85/71.21  				|-The branch is then unsatisfiable
% 103.85/71.21  		|-Branch two:
% 103.85/71.21  		| (490)  ~ (all_217_0_432 = 0) & is_a_theorem(all_30_1_223) = all_217_0_432
% 103.85/71.21  		|
% 103.85/71.21  			| Applying alpha-rule on (490) yields:
% 103.85/71.21  			| (486)  ~ (all_217_0_432 = 0)
% 103.85/71.21  			| (492) is_a_theorem(all_30_1_223) = all_217_0_432
% 103.85/71.21  			|
% 103.85/71.21  			| Instantiating formula (122) with all_30_1_223, 0, all_217_0_432 and discharging atoms is_a_theorem(all_30_1_223) = all_217_0_432, is_a_theorem(all_30_1_223) = 0, yields:
% 103.85/71.21  			| (274) all_217_0_432 = 0
% 103.85/71.22  			|
% 103.85/71.22  			| Equations (274) can reduce 486 to:
% 103.85/71.22  			| (387) $false
% 103.85/71.22  			|
% 103.85/71.22  			|-The branch is then unsatisfiable
% 103.85/71.22  	|-Branch two:
% 103.85/71.22  	| (495)  ~ (all_159_0_356 = 0) & is_a_theorem(all_39_0_225) = all_159_0_356
% 103.85/71.22  	|
% 103.85/71.22  		| Applying alpha-rule on (495) yields:
% 103.85/71.22  		| (496)  ~ (all_159_0_356 = 0)
% 103.85/71.22  		| (497) is_a_theorem(all_39_0_225) = all_159_0_356
% 103.85/71.22  		|
% 103.85/71.22  		| Instantiating formula (122) with all_39_0_225, all_159_0_356, 0 and discharging atoms is_a_theorem(all_39_0_225) = all_159_0_356, is_a_theorem(all_39_0_225) = 0, yields:
% 103.85/71.22  		| (270) all_159_0_356 = 0
% 103.85/71.22  		|
% 103.85/71.22  		| Equations (270) can reduce 496 to:
% 103.85/71.22  		| (387) $false
% 103.85/71.22  		|
% 103.85/71.22  		|-The branch is then unsatisfiable
% 103.85/71.22  |-Branch two:
% 103.85/71.22  | (500)  ~ (all_159_0_356 = 0) & is_a_theorem(all_0_85_85) = all_159_0_356
% 103.85/71.22  |
% 103.85/71.22  	| Applying alpha-rule on (500) yields:
% 103.85/71.22  	| (496)  ~ (all_159_0_356 = 0)
% 103.85/71.22  	| (502) is_a_theorem(all_0_85_85) = all_159_0_356
% 103.85/71.22  	|
% 103.85/71.22  	| Instantiating formula (122) with all_0_85_85, all_159_0_356, 0 and discharging atoms is_a_theorem(all_0_85_85) = all_159_0_356, is_a_theorem(all_0_85_85) = 0, yields:
% 103.85/71.22  	| (270) all_159_0_356 = 0
% 103.85/71.22  	|
% 103.85/71.22  	| Equations (270) can reduce 496 to:
% 103.85/71.22  	| (387) $false
% 103.85/71.22  	|
% 103.85/71.22  	|-The branch is then unsatisfiable
% 103.85/71.22  % SZS output end Proof for theBenchmark
% 103.85/71.22  
% 103.85/71.22  70622ms
%------------------------------------------------------------------------------