%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : LCL544+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n016.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 09:37:02 EDT 2022

% Result   : Theorem 30.35s 9.03s
% Output   : Proof 179.08s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL544+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n016.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul  3 19:47:01 EDT 2022
% 0.12/0.33  % 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 ...
% 0.67/0.65  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.02/1.03  Prover 0: Preprocessing ...
% 4.00/1.55  Prover 0: Constructing countermodel ...
% 18.39/5.94  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 18.80/6.03  Prover 1: Preprocessing ...
% 19.80/6.23  Prover 1: Constructing countermodel ...
% 28.40/8.54  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 28.40/8.61  Prover 2: Preprocessing ...
% 29.10/8.75  Prover 2: Warning: ignoring some quantifiers
% 29.10/8.75  Prover 2: Constructing countermodel ...
% 30.35/9.03  Prover 2: proved (490ms)
% 30.35/9.03  Prover 1: stopped
% 30.35/9.03  Prover 0: stopped
% 30.35/9.03  
% 30.35/9.03  No countermodel exists, formula is valid
% 30.35/9.03  % SZS status Theorem for theBenchmark
% 30.35/9.03  
% 30.35/9.03  Generating proof ... Warning: ignoring some quantifiers
% 178.61/138.13  found it (size 40)
% 178.61/138.13  
% 178.61/138.13  % SZS output start Proof for theBenchmark
% 178.61/138.13  Assumed formulas after preprocessing and simplification: 
% 178.61/138.13  | (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] : ( ~ (v40 = 0) & strict_implies(v37, v38) = v39 & and(v37, v37) = v38 & is_a_theorem(v39) = v40 & op_implies & op_strict_equiv & op_strict_implies & op_possibly & axiom_B & axiom_4 & 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 &  ~ axiom_m4 &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] :  ! [v196] : ( ~ (implies(v194, v195) = v196) |  ~ (implies(v192, v193) = v194) |  ~ (implies(v191, v193) = v195) |  ? [v197] :  ? [v198] : (implies(v197, v196) = v198 & implies(v191, v192) = v197 & is_a_theorem(v198) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] : ( ~ (necessarily(v192) = v194) |  ~ (necessarily(v191) = v193) |  ~ (implies(v193, v194) = v195) |  ? [v196] :  ? [v197] :  ? [v198] : (necessarily(v196) = v197 & implies(v197, v195) = v198 & implies(v191, v192) = v196 & is_a_theorem(v198) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] : ( ~ (or(v191, v192) = v194) |  ~ (implies(v194, v193) = v195) |  ? [v196] :  ? [v197] :  ? [v198] :  ? [v199] : (implies(v197, v195) = v198 & implies(v196, v198) = v199 & implies(v192, v193) = v197 & implies(v191, v193) = v196 & is_a_theorem(v199) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] : ( ~ (and(v193, v194) = v195) |  ~ (not(v192) = v194) |  ~ (not(v191) = v193) |  ? [v196] : (or(v191, v192) = v196 & not(v195) = v196)) &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] : ( ~ (not(v192) = v193) |  ~ (not(v191) = v194) |  ~ (implies(v193, v194) = v195) |  ? [v196] :  ? [v197] : (implies(v195, v196) = v197 & implies(v191, v192) = v196 & is_a_theorem(v197) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] : (v192 = v191 |  ~ (strict_equiv(v194, v193) = v192) |  ~ (strict_equiv(v194, v193) = v191)) &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] : (v192 = v191 |  ~ (strict_implies(v194, v193) = v192) |  ~ (strict_implies(v194, v193) = v191)) &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] : (v192 = v191 |  ~ (or(v194, v193) = v192) |  ~ (or(v194, v193) = v191)) &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] : (v192 = v191 |  ~ (and(v194, v193) = v192) |  ~ (and(v194, v193) = v191)) &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] : (v192 = v191 |  ~ (equiv(v194, v193) = v192) |  ~ (equiv(v194, v193) = v191)) &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] : (v192 = v191 |  ~ (implies(v194, v193) = v192) |  ~ (implies(v194, v193) = v191)) &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] : ( ~ (and(v191, v193) = v194) |  ~ (not(v192) = v193) |  ? [v195] : (not(v194) = v195 & implies(v191, v192) = v195)) &  ! [v191] :  ! [v192] :  ! [v193] : (v192 = v191 |  ~ (possibly(v193) = v192) |  ~ (possibly(v193) = v191)) &  ! [v191] :  ! [v192] :  ! [v193] : (v192 = v191 |  ~ (necessarily(v193) = v192) |  ~ (necessarily(v193) = v191)) &  ! [v191] :  ! [v192] :  ! [v193] : (v192 = v191 |  ~ (not(v193) = v192) |  ~ (not(v193) = v191)) &  ! [v191] :  ! [v192] :  ! [v193] : (v192 = v191 |  ~ (equiv(v191, v192) = v193) |  ? [v194] : ( ~ (v194 = 0) & is_a_theorem(v193) = v194)) &  ! [v191] :  ! [v192] :  ! [v193] : (v192 = v191 |  ~ (is_a_theorem(v193) = v192) |  ~ (is_a_theorem(v193) = v191)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (strict_equiv(v191, v192) = v193) |  ? [v194] :  ? [v195] : (strict_implies(v192, v191) = v195 & strict_implies(v191, v192) = v194 & and(v194, v195) = v193)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (strict_implies(v192, v191) = v193) |  ? [v194] :  ? [v195] : (strict_equiv(v191, v192) = v194 & strict_implies(v191, v192) = v195 & and(v195, v193) = v194)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (strict_implies(v191, v192) = v193) |  ? [v194] :  ? [v195] : (strict_equiv(v191, v192) = v194 & strict_implies(v192, v191) = v195 & and(v193, v195) = v194)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (strict_implies(v191, v192) = v193) |  ? [v194] : (necessarily(v194) = v193 & implies(v191, v192) = v194)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (or(v191, v192) = v193) |  ? [v194] :  ? [v195] :  ? [v196] : (and(v194, v195) = v196 & not(v196) = v193 & not(v192) = v195 & not(v191) = v194)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (or(v191, v192) = v193) |  ? [v194] : (implies(v192, v193) = v194 & is_a_theorem(v194) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (or(v191, v192) = v193) |  ? [v194] : (implies(v191, v193) = v194 & is_a_theorem(v194) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (and(v191, v192) = v193) |  ? [v194] :  ? [v195] : (implies(v192, v193) = v194 & implies(v191, v194) = v195 & is_a_theorem(v195) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (and(v191, v192) = v193) |  ? [v194] : (implies(v193, v192) = v194 & is_a_theorem(v194) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (and(v191, v192) = v193) |  ? [v194] : (implies(v193, v191) = v194 & is_a_theorem(v194) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (equiv(v191, v192) = v193) |  ? [v194] :  ? [v195] :  ? [v196] :  ? [v197] : (implies(v195, v193) = v196 & implies(v194, v196) = v197 & implies(v192, v191) = v195 & implies(v191, v192) = v194 & is_a_theorem(v197) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (equiv(v191, v192) = v193) |  ? [v194] :  ? [v195] : (and(v194, v195) = v193 & implies(v192, v191) = v195 & implies(v191, v192) = v194)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (equiv(v191, v192) = v193) |  ? [v194] :  ? [v195] : (implies(v193, v194) = v195 & implies(v192, v191) = v194 & is_a_theorem(v195) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (equiv(v191, v192) = v193) |  ? [v194] :  ? [v195] : (implies(v193, v194) = v195 & implies(v191, v192) = v194 & is_a_theorem(v195) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (implies(v192, v191) = v193) |  ? [v194] :  ? [v195] :  ? [v196] :  ? [v197] : (equiv(v191, v192) = v195 & implies(v194, v196) = v197 & implies(v193, v195) = v196 & implies(v191, v192) = v194 & is_a_theorem(v197) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (implies(v192, v191) = v193) |  ? [v194] :  ? [v195] : (and(v195, v193) = v194 & equiv(v191, v192) = v194 & implies(v191, v192) = v195)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (implies(v192, v191) = v193) |  ? [v194] :  ? [v195] : (equiv(v191, v192) = v194 & implies(v194, v193) = v195 & is_a_theorem(v195) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (implies(v192, v191) = v193) |  ? [v194] : (implies(v191, v193) = v194 & is_a_theorem(v194) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (implies(v191, v192) = v193) |  ? [v194] :  ? [v195] :  ? [v196] :  ? [v197] :  ? [v198] : (necessarily(v193) = v194 & necessarily(v192) = v196 & necessarily(v191) = v195 & implies(v195, v196) = v197 & implies(v194, v197) = v198 & is_a_theorem(v198) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (implies(v191, v192) = v193) |  ? [v194] :  ? [v195] :  ? [v196] :  ? [v197] : (not(v192) = v194 & not(v191) = v195 & implies(v196, v193) = v197 & implies(v194, v195) = v196 & is_a_theorem(v197) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (implies(v191, v192) = v193) |  ? [v194] :  ? [v195] :  ? [v196] :  ? [v197] : (equiv(v191, v192) = v195 & implies(v194, v195) = v196 & implies(v193, v196) = v197 & implies(v192, v191) = v194 & is_a_theorem(v197) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (implies(v191, v192) = v193) |  ? [v194] :  ? [v195] : (and(v193, v195) = v194 & equiv(v191, v192) = v194 & implies(v192, v191) = v195)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (implies(v191, v192) = v193) |  ? [v194] :  ? [v195] : (and(v191, v194) = v195 & not(v195) = v193 & not(v192) = v194)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (implies(v191, v192) = v193) |  ? [v194] :  ? [v195] : (equiv(v191, v192) = v194 & implies(v194, v193) = v195 & is_a_theorem(v195) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (implies(v191, v192) = v193) |  ? [v194] :  ? [v195] : (implies(v194, v193) = v195 & implies(v191, v193) = v194 & is_a_theorem(v195) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (implies(v191, v192) = v193) |  ? [v194] : (strict_implies(v191, v192) = v194 & necessarily(v193) = v194)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (implies(v191, v192) = v193) |  ? [v194] : ((v194 = 0 & is_a_theorem(v192) = 0) | ( ~ (v194 = 0) & is_a_theorem(v193) = v194) | ( ~ (v194 = 0) & is_a_theorem(v191) = v194))) &  ! [v191] :  ! [v192] : ( ~ (possibly(v191) = v192) |  ? [v193] :  ? [v194] : (necessarily(v193) = v194 & not(v194) = v192 & not(v191) = v193)) &  ! [v191] :  ! [v192] : ( ~ (possibly(v191) = v192) |  ? [v193] :  ? [v194] : (necessarily(v192) = v193 & implies(v191, v193) = v194 & is_a_theorem(v194) = 0)) &  ! [v191] :  ! [v192] : ( ~ (necessarily(v191) = v192) |  ? [v193] :  ? [v194] : (necessarily(v192) = v193 & implies(v192, v193) = v194 & is_a_theorem(v194) = 0)) &  ! [v191] :  ! [v192] : ( ~ (necessarily(v191) = v192) |  ? [v193] : (implies(v192, v191) = v193 & is_a_theorem(v193) = 0)) &  ! [v191] :  ! [v192] : ( ~ (necessarily(v191) = v192) |  ? [v193] : ((v193 = 0 & is_a_theorem(v192) = 0) | ( ~ (v193 = 0) & is_a_theorem(v191) = v193))) &  ! [v191] :  ! [v192] : ( ~ (not(v191) = v192) |  ? [v193] :  ? [v194] : (possibly(v191) = v193 & necessarily(v192) = v194 & not(v194) = v193)) &  ! [v191] : ( ~ (is_a_theorem(v191) = 0) |  ? [v192] : (necessarily(v191) = v192 & is_a_theorem(v192) = 0)) &  ? [v191] :  ? [v192] :  ? [v193] : strict_equiv(v192, v191) = v193 &  ? [v191] :  ? [v192] :  ? [v193] : strict_implies(v192, v191) = v193 &  ? [v191] :  ? [v192] :  ? [v193] : or(v192, v191) = v193 &  ? [v191] :  ? [v192] :  ? [v193] : and(v192, v191) = v193 &  ? [v191] :  ? [v192] :  ? [v193] : equiv(v192, v191) = v193 &  ? [v191] :  ? [v192] :  ? [v193] : implies(v192, v191) = v193 &  ? [v191] :  ? [v192] : possibly(v191) = v192 &  ? [v191] :  ? [v192] : necessarily(v191) = v192 &  ? [v191] :  ? [v192] : not(v191) = v192 &  ? [v191] :  ? [v192] : is_a_theorem(v191) = v192 & ( ~ op_necessarily | ( ! [v191] :  ! [v192] : ( ~ (necessarily(v191) = v192) |  ? [v193] :  ? [v194] : (possibly(v193) = v194 & not(v194) = v192 & not(v191) = v193)) &  ! [v191] :  ! [v192] : ( ~ (not(v191) = v192) |  ? [v193] :  ? [v194] : (possibly(v192) = v194 & necessarily(v191) = v193 & not(v194) = v193)))) & ( ~ op_implies_or | ( ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] : ( ~ (or(v193, v192) = v194) |  ~ (not(v191) = v193) | implies(v191, v192) = v194) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (implies(v191, v192) = v193) |  ? [v194] : (or(v194, v192) = v193 & not(v191) = v194)))) & ( ~ op_and | ( ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] : ( ~ (or(v193, v194) = v195) |  ~ (not(v192) = v194) |  ~ (not(v191) = v193) |  ? [v196] : (and(v191, v192) = v196 & not(v195) = v196)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (and(v191, v192) = v193) |  ? [v194] :  ? [v195] :  ? [v196] : (or(v194, v195) = v196 & not(v196) = v193 & not(v192) = v195 & not(v191) = v194)))) & ((v116 = 0 & v114 = 0 &  ~ (v117 = 0) & strict_implies(v112, v113) = v115 & is_a_theorem(v115) = 0 & is_a_theorem(v113) = v117 & is_a_theorem(v112) = 0 &  ~ modus_ponens_strict_implies) | (modus_ponens_strict_implies &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (strict_implies(v191, v192) = v193) |  ? [v194] : ((v194 = 0 & is_a_theorem(v192) = 0) | ( ~ (v194 = 0) & is_a_theorem(v193) = v194) | ( ~ (v194 = 0) & is_a_theorem(v191) = v194))))) & ((v109 = 0 & v108 = 0 &  ~ (v111 = 0) & and(v106, v107) = v110 & is_a_theorem(v110) = v111 & is_a_theorem(v107) = 0 & is_a_theorem(v106) = 0 &  ~ adjunction) | (adjunction &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (and(v191, v192) = v193) |  ? [v194] : ((v194 = 0 & is_a_theorem(v193) = 0) | ( ~ (v194 = 0) & is_a_theorem(v192) = v194) | ( ~ (v194 = 0) & is_a_theorem(v191) = v194))))) & ((v105 = 0 &  ~ (v103 = v102) & strict_equiv(v102, v103) = v104 & is_a_theorem(v104) = 0 &  ~ substitution_strict_equiv) | (substitution_strict_equiv &  ! [v191] :  ! [v192] :  ! [v193] : (v192 = v191 |  ~ (strict_equiv(v191, v192) = v193) |  ? [v194] : ( ~ (v194 = 0) & is_a_theorem(v193) = v194)))) & (( ~ (v190 = 0) & and(v187, v187) = v188 & implies(v187, v188) = v189 & is_a_theorem(v189) = v190 &  ~ kn1) | (kn1 &  ! [v191] :  ! [v192] : ( ~ (and(v191, v191) = v192) |  ? [v193] : (implies(v191, v192) = v193 & is_a_theorem(v193) = 0)))) & (( ~ (v186 = 0) & and(v182, v183) = v184 & implies(v184, v182) = v185 & is_a_theorem(v185) = v186 &  ~ kn2) | (kn2 &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (and(v191, v192) = v193) |  ? [v194] : (implies(v193, v191) = v194 & is_a_theorem(v194) = 0)))) & (( ~ (v181 = 0) & and(v173, v171) = v177 & and(v172, v173) = v175 & not(v177) = v178 & not(v175) = v176 & implies(v176, v178) = v179 & implies(v174, v179) = v180 & implies(v171, v172) = v174 & is_a_theorem(v180) = v181 &  ~ kn3) | (kn3 &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] : ( ~ (and(v193, v191) = v196) |  ~ (and(v192, v193) = v194) |  ~ (not(v196) = v197) |  ~ (not(v194) = v195) |  ~ (implies(v195, v197) = v198) |  ? [v199] :  ? [v200] : (implies(v199, v198) = v200 & implies(v191, v192) = v199 & is_a_theorem(v200) = 0)))) & (( ~ (v170 = 0) & implies(v166, v167) = v168 & implies(v165, v168) = v169 & implies(v163, v164) = v166 & implies(v162, v164) = v167 & implies(v162, v163) = v165 & is_a_theorem(v169) = v170 &  ~ cn1) | (cn1 &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] :  ! [v196] : ( ~ (implies(v194, v195) = v196) |  ~ (implies(v192, v193) = v194) |  ~ (implies(v191, v193) = v195) |  ? [v197] :  ? [v198] : (implies(v197, v196) = v198 & implies(v191, v192) = v197 & is_a_theorem(v198) = 0)))) & (( ~ (v161 = 0) & not(v156) = v158 & implies(v158, v157) = v159 & implies(v156, v159) = v160 & is_a_theorem(v160) = v161 &  ~ cn2) | (cn2 &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] : ( ~ (not(v191) = v193) |  ~ (implies(v193, v192) = v194) |  ? [v195] : (implies(v191, v194) = v195 & is_a_theorem(v195) = 0)))) & (( ~ (v155 = 0) & not(v151) = v152 & implies(v153, v151) = v154 & implies(v152, v151) = v153 & is_a_theorem(v154) = v155 &  ~ cn3) | (cn3 &  ! [v191] :  ! [v192] : ( ~ (not(v191) = v192) |  ? [v193] :  ? [v194] : (implies(v193, v191) = v194 & implies(v192, v191) = v193 & is_a_theorem(v194) = 0)))) & (( ~ (v150 = 0) & or(v147, v147) = v148 & implies(v148, v147) = v149 & is_a_theorem(v149) = v150 &  ~ r1) | (r1 &  ! [v191] :  ! [v192] : ( ~ (or(v191, v191) = v192) |  ? [v193] : (implies(v192, v191) = v193 & is_a_theorem(v193) = 0)))) & (( ~ (v146 = 0) & or(v142, v143) = v144 & implies(v143, v144) = v145 & is_a_theorem(v145) = v146 &  ~ r2) | (r2 &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (or(v191, v192) = v193) |  ? [v194] : (implies(v192, v193) = v194 & is_a_theorem(v194) = 0)))) & (( ~ (v141 = 0) & or(v137, v136) = v139 & or(v136, v137) = v138 & implies(v138, v139) = v140 & is_a_theorem(v140) = v141 &  ~ r3) | (r3 &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (or(v192, v191) = v193) |  ? [v194] :  ? [v195] : (or(v191, v192) = v194 & implies(v194, v193) = v195 & is_a_theorem(v195) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (or(v191, v192) = v193) |  ? [v194] :  ? [v195] : (or(v192, v191) = v194 & implies(v193, v194) = v195 & is_a_theorem(v195) = 0)))) & (( ~ (v135 = 0) & or(v128, v132) = v133 & or(v128, v129) = v130 & or(v127, v130) = v131 & or(v127, v129) = v132 & implies(v131, v133) = v134 & is_a_theorem(v134) = v135 &  ~ r4) | (r4 &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] : ( ~ (or(v192, v194) = v195) |  ~ (or(v191, v193) = v194) |  ? [v196] :  ? [v197] :  ? [v198] : (or(v192, v193) = v196 & or(v191, v196) = v197 & implies(v197, v195) = v198 & is_a_theorem(v198) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] : ( ~ (or(v192, v193) = v194) |  ~ (or(v191, v194) = v195) |  ? [v196] :  ? [v197] :  ? [v198] : (or(v192, v196) = v197 & or(v191, v193) = v196 & implies(v195, v197) = v198 & is_a_theorem(v198) = 0)))) & (( ~ (v126 = 0) & or(v118, v120) = v123 & or(v118, v119) = v122 & implies(v122, v123) = v124 & implies(v121, v124) = v125 & implies(v119, v120) = v121 & is_a_theorem(v125) = v126 &  ~ r5) | (r5 &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] :  ! [v196] : ( ~ (or(v191, v193) = v195) |  ~ (or(v191, v192) = v194) |  ~ (implies(v194, v195) = v196) |  ? [v197] :  ? [v198] : (implies(v197, v196) = v198 & implies(v192, v193) = v197 & is_a_theorem(v198) = 0)))) & (( ~ (v101 = 0) & possibly(v97) = v98 & necessarily(v98) = v99 & implies(v98, v99) = v100 & is_a_theorem(v100) = v101 &  ~ axiom_5) | (axiom_5 &  ! [v191] :  ! [v192] : ( ~ (possibly(v191) = v192) |  ? [v193] :  ? [v194] : (necessarily(v192) = v193 & implies(v192, v193) = v194 & is_a_theorem(v194) = 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 &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] :  ! [v196] :  ! [v197] :  ! [v198] : ( ~ (necessarily(v196) = v197) |  ~ (necessarily(v194) = v195) |  ~ (and(v195, v197) = v198) |  ~ (implies(v192, v193) = v196) |  ~ (implies(v191, v192) = v194) |  ? [v199] :  ? [v200] :  ? [v201] : (necessarily(v199) = v200 & implies(v198, v200) = v201 & implies(v191, v193) = v199 & is_a_theorem(v201) = 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 &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] : ( ~ (possibly(v192) = v194) |  ~ (possibly(v191) = v193) |  ~ (and(v193, v194) = v195) |  ? [v196] :  ? [v197] :  ? [v198] : (possibly(v196) = v197 & strict_implies(v197, v195) = v198 & and(v191, v192) = v196 & is_a_theorem(v198) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (and(v191, v192) = v193) |  ? [v194] :  ? [v195] :  ? [v196] :  ? [v197] :  ? [v198] : (possibly(v193) = v194 & possibly(v192) = v196 & possibly(v191) = v195 & strict_implies(v194, v197) = v198 & and(v195, v196) = v197 & is_a_theorem(v198) = 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 &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] :  ! [v196] :  ! [v197] : ( ~ (possibly(v192) = v193) |  ~ (possibly(v191) = v195) |  ~ (strict_implies(v194, v196) = v197) |  ~ (not(v195) = v196) |  ~ (not(v193) = v194) |  ? [v198] :  ? [v199] : (strict_implies(v198, v197) = v199 & strict_implies(v191, v192) = v198 & is_a_theorem(v199) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (strict_implies(v191, v192) = v193) |  ? [v194] :  ? [v195] :  ? [v196] :  ? [v197] :  ? [v198] :  ? [v199] : (possibly(v192) = v194 & possibly(v191) = v196 & strict_implies(v195, v197) = v198 & strict_implies(v193, v198) = v199 & not(v196) = v197 & not(v194) = v195 & is_a_theorem(v199) = 0)))) & (( ~ (v65 = 0) & strict_implies(v62, v63) = v64 & necessarily(v62) = v63 & necessarily(v61) = v62 & is_a_theorem(v64) = v65 &  ~ axiom_s4) | (axiom_s4 &  ! [v191] :  ! [v192] : ( ~ (necessarily(v191) = v192) |  ? [v193] :  ? [v194] : (strict_implies(v192, v193) = v194 & necessarily(v192) = v193 & is_a_theorem(v194) = 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 &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (and(v192, v191) = v193) |  ? [v194] :  ? [v195] : (strict_implies(v194, v193) = v195 & and(v191, v192) = v194 & is_a_theorem(v195) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (and(v191, v192) = v193) |  ? [v194] :  ? [v195] : (strict_implies(v193, v194) = v195 & and(v192, v191) = v194 & is_a_theorem(v195) = 0)))) & (( ~ (v54 = 0) & strict_implies(v52, v50) = v53 & and(v50, v51) = v52 & is_a_theorem(v53) = v54 &  ~ axiom_m2) | (axiom_m2 &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (and(v191, v192) = v193) |  ? [v194] : (strict_implies(v193, v191) = v194 & is_a_theorem(v194) = 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 &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] : ( ~ (and(v194, v193) = v195) |  ~ (and(v191, v192) = v194) |  ? [v196] :  ? [v197] :  ? [v198] : (strict_implies(v195, v197) = v198 & and(v192, v193) = v196 & and(v191, v196) = v197 & is_a_theorem(v198) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] : ( ~ (and(v192, v193) = v194) |  ~ (and(v191, v194) = v195) |  ? [v196] :  ? [v197] :  ? [v198] : (strict_implies(v197, v195) = v198 & and(v196, v193) = v197 & and(v191, v192) = v196 & is_a_theorem(v198) = 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 &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] :  ! [v196] : ( ~ (strict_implies(v192, v193) = v195) |  ~ (strict_implies(v191, v192) = v194) |  ~ (and(v194, v195) = v196) |  ? [v197] :  ? [v198] : (strict_implies(v196, v197) = v198 & strict_implies(v191, v193) = v197 & is_a_theorem(v198) = 0)))) & (( ~ (v27 = 0) & possibly(v24) = v25 & strict_implies(v24, v25) = v26 & is_a_theorem(v26) = v27 &  ~ axiom_m6) | (axiom_m6 &  ! [v191] :  ! [v192] : ( ~ (possibly(v191) = v192) |  ? [v193] : (strict_implies(v191, v192) = v193 & is_a_theorem(v193) = 0)))) & (( ~ (v23 = 0) & possibly(v20) = v21 & strict_implies(v21, v18) = v22 & and(v18, v19) = v20 & is_a_theorem(v22) = v23 &  ~ axiom_m7) | (axiom_m7 &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (and(v191, v192) = v193) |  ? [v194] :  ? [v195] : (possibly(v193) = v194 & strict_implies(v194, v191) = v195 & is_a_theorem(v195) = 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 &  ! [v191] :  ! [v192] :  ! [v193] :  ! [v194] :  ! [v195] : ( ~ (possibly(v192) = v194) |  ~ (possibly(v191) = v193) |  ~ (strict_implies(v193, v194) = v195) |  ? [v196] :  ? [v197] : (strict_implies(v196, v195) = v197 & strict_implies(v191, v192) = v196 & is_a_theorem(v197) = 0)) &  ! [v191] :  ! [v192] :  ! [v193] : ( ~ (strict_implies(v191, v192) = v193) |  ? [v194] :  ? [v195] :  ? [v196] :  ? [v197] : (possibly(v192) = v195 & possibly(v191) = v194 & strict_implies(v194, v195) = v196 & strict_implies(v193, v196) = v197 & is_a_theorem(v197) = 0)))) & (( ~ (v9 = 0) & possibly(v6) = v7 & possibly(v5) = v6 & strict_implies(v7, v6) = v8 & is_a_theorem(v8) = v9 &  ~ axiom_m9) | (axiom_m9 &  ! [v191] :  ! [v192] : ( ~ (possibly(v191) = v192) |  ? [v193] :  ? [v194] : (possibly(v192) = v193 & strict_implies(v193, v192) = v194 & is_a_theorem(v194) = 0)))) & (( ~ (v4 = 0) & possibly(v0) = v1 & strict_implies(v1, v2) = v3 & necessarily(v1) = v2 & is_a_theorem(v3) = v4 &  ~ axiom_m10) | (axiom_m10 &  ! [v191] :  ! [v192] : ( ~ (possibly(v191) = v192) |  ? [v193] :  ? [v194] : (strict_implies(v192, v193) = v194 & necessarily(v192) = v193 & is_a_theorem(v194) = 0)))))
% 178.96/138.23  | 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 yields:
% 178.96/138.23  | (1)  ~ (all_0_150_150 = 0) & strict_implies(all_0_153_153, all_0_152_152) = all_0_151_151 & and(all_0_153_153, all_0_153_153) = all_0_152_152 & is_a_theorem(all_0_151_151) = all_0_150_150 & op_implies & op_strict_equiv & op_strict_implies & op_possibly & axiom_B & axiom_4 & 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 &  ~ axiom_m4 &  ! [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(v0, v2) = v3 & is_a_theorem(v3) = 0)) &  ! [v0] :  ! [v1] : ( ~ (necessarily(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_85_85 = 0 &  ~ (all_0_87_87 = all_0_88_88) & strict_equiv(all_0_88_88, all_0_87_87) = all_0_86_86 & is_a_theorem(all_0_86_86) = 0 &  ~ substitution_strict_equiv) | (substitution_strict_equiv &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (strict_equiv(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & is_a_theorem(v2) = 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_89_89 = 0) & possibly(all_0_93_93) = all_0_92_92 & necessarily(all_0_92_92) = all_0_91_91 & implies(all_0_92_92, all_0_91_91) = all_0_90_90 & is_a_theorem(all_0_90_90) = all_0_89_89 &  ~ axiom_5) | (axiom_5 &  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] :  ? [v3] : (necessarily(v1) = v2 & implies(v1, v2) = v3 & is_a_theorem(v3) = 0)))) & (( ~ (all_0_94_94 = 0) & necessarily(all_0_97_97) = all_0_96_96 & necessarily(all_0_100_100) = all_0_99_99 & necessarily(all_0_102_102) = all_0_101_101 & and(all_0_101_101, all_0_99_99) = all_0_98_98 & implies(all_0_98_98, all_0_96_96) = all_0_95_95 & implies(all_0_104_104, all_0_103_103) = all_0_100_100 & implies(all_0_105_105, all_0_103_103) = all_0_97_97 & implies(all_0_105_105, all_0_104_104) = all_0_102_102 & is_a_theorem(all_0_95_95) = all_0_94_94 &  ~ 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_106_106 = 0) & possibly(all_0_112_112) = all_0_111_111 & possibly(all_0_113_113) = all_0_109_109 & possibly(all_0_114_114) = all_0_110_110 & strict_implies(all_0_111_111, all_0_108_108) = all_0_107_107 & and(all_0_110_110, all_0_109_109) = all_0_108_108 & and(all_0_114_114, all_0_113_113) = all_0_112_112 & is_a_theorem(all_0_107_107) = all_0_106_106 &  ~ 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_115_115 = 0) & possibly(all_0_123_123) = all_0_121_121 & possibly(all_0_124_124) = all_0_119_119 & strict_implies(all_0_120_120, all_0_118_118) = all_0_117_117 & strict_implies(all_0_122_122, all_0_117_117) = all_0_116_116 & strict_implies(all_0_124_124, all_0_123_123) = all_0_122_122 & not(all_0_119_119) = all_0_118_118 & not(all_0_121_121) = all_0_120_120 & is_a_theorem(all_0_116_116) = all_0_115_115 &  ~ 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_125_125 = 0) & strict_implies(all_0_128_128, all_0_127_127) = all_0_126_126 & necessarily(all_0_128_128) = all_0_127_127 & necessarily(all_0_129_129) = all_0_128_128 & is_a_theorem(all_0_126_126) = all_0_125_125 &  ~ 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_130_130 = 0) & strict_implies(all_0_133_133, all_0_132_132) = all_0_131_131 & and(all_0_134_134, all_0_135_135) = all_0_132_132 & and(all_0_135_135, all_0_134_134) = all_0_133_133 & is_a_theorem(all_0_131_131) = all_0_130_130 &  ~ 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_136_136 = 0) & strict_implies(all_0_138_138, all_0_140_140) = all_0_137_137 & and(all_0_140_140, all_0_139_139) = all_0_138_138 & is_a_theorem(all_0_137_137) = all_0_136_136 &  ~ axiom_m2) | (axiom_m2 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : (strict_implies(v2, v0) = v3 & is_a_theorem(v3) = 0)))) & (( ~ (all_0_141_141 = 0) & strict_implies(all_0_145_145, all_0_143_143) = all_0_142_142 & and(all_0_146_146, all_0_147_147) = all_0_145_145 & and(all_0_148_148, all_0_147_147) = all_0_144_144 & and(all_0_149_149, all_0_144_144) = all_0_143_143 & and(all_0_149_149, all_0_148_148) = all_0_146_146 & is_a_theorem(all_0_142_142) = all_0_141_141 &  ~ 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 & strict_implies(all_0_161_161, all_0_160_160) = all_0_158_158 & strict_implies(all_0_162_162, all_0_160_160) = all_0_156_156 & strict_implies(all_0_162_162, all_0_161_161) = all_0_159_159 & and(all_0_159_159, all_0_158_158) = all_0_157_157 & is_a_theorem(all_0_155_155) = all_0_154_154 &  ~ 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_163_163 = 0) & possibly(all_0_166_166) = all_0_165_165 & strict_implies(all_0_166_166, all_0_165_165) = all_0_164_164 & is_a_theorem(all_0_164_164) = all_0_163_163 &  ~ axiom_m6) | (axiom_m6 &  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] : (strict_implies(v0, v1) = v2 & is_a_theorem(v2) = 0)))) & (( ~ (all_0_167_167 = 0) & possibly(all_0_170_170) = all_0_169_169 & strict_implies(all_0_169_169, all_0_172_172) = all_0_168_168 & and(all_0_172_172, all_0_171_171) = all_0_170_170 & is_a_theorem(all_0_168_168) = all_0_167_167 &  ~ 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_173_173 = 0) & possibly(all_0_179_179) = all_0_176_176 & possibly(all_0_180_180) = all_0_177_177 & strict_implies(all_0_177_177, all_0_176_176) = all_0_175_175 & strict_implies(all_0_178_178, all_0_175_175) = all_0_174_174 & strict_implies(all_0_180_180, all_0_179_179) = all_0_178_178 & is_a_theorem(all_0_174_174) = all_0_173_173 &  ~ 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_181_181 = 0) & possibly(all_0_184_184) = all_0_183_183 & possibly(all_0_185_185) = all_0_184_184 & strict_implies(all_0_183_183, all_0_184_184) = all_0_182_182 & is_a_theorem(all_0_182_182) = all_0_181_181 &  ~ 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_186_186 = 0) & possibly(all_0_190_190) = all_0_189_189 & strict_implies(all_0_189_189, all_0_188_188) = all_0_187_187 & necessarily(all_0_189_189) = all_0_188_188 & is_a_theorem(all_0_187_187) = all_0_186_186 &  ~ axiom_m10) | (axiom_m10 &  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] :  ? [v3] : (strict_implies(v1, v2) = v3 & necessarily(v1) = v2 & is_a_theorem(v3) = 0))))
% 179.08/138.25  |
% 179.08/138.25  | Applying alpha-rule on (1) yields:
% 179.08/138.25  | (2) or_1
% 179.08/138.25  | (3)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] : (implies(v1, v2) = v3 & is_a_theorem(v3) = 0))
% 179.08/138.25  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (strict_equiv(v3, v2) = v1) |  ~ (strict_equiv(v3, v2) = v0))
% 179.08/138.25  | (5) equivalence_1
% 179.08/138.25  | (6)  ! [v0] :  ! [v1] : ( ~ (necessarily(v0) = v1) |  ? [v2] :  ? [v3] : (necessarily(v1) = v2 & implies(v1, v2) = v3 & is_a_theorem(v3) = 0))
% 179.08/138.26  | (7) op_equiv
% 179.08/138.26  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_equiv(v0, v1) = v2) |  ? [v3] :  ? [v4] : (strict_implies(v1, v0) = v4 & strict_implies(v0, v1) = v3 & and(v3, v4) = v2))
% 179.08/138.26  | (9) (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))))
% 179.08/138.26  | (10)  ? [v0] :  ? [v1] : not(v0) = v1
% 179.08/138.26  | (11)  ! [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)))
% 179.08/138.26  | (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) = v3))
% 179.08/138.26  | (13)  ? [v0] :  ? [v1] :  ? [v2] : strict_equiv(v1, v0) = v2
% 179.08/138.26  | (14) or_2
% 179.08/138.26  | (15)  ! [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))
% 179.08/138.26  | (16)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (and(v2, v4) = v3 & equiv(v0, v1) = v3 & implies(v1, v0) = v4))
% 179.08/138.26  | (17) implies_2
% 179.08/138.26  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (implies(v3, v2) = v1) |  ~ (implies(v3, v2) = v0))
% 179.08/138.26  | (19)  ? [v0] :  ? [v1] :  ? [v2] : or(v1, v0) = v2
% 179.08/138.26  | (20)  ~ axiom_m4
% 179.08/138.26  | (21)  ! [v0] : ( ~ (is_a_theorem(v0) = 0) |  ? [v1] : (necessarily(v0) = v1 & is_a_theorem(v1) = 0))
% 179.08/138.26  | (22) ( ~ (all_0_130_130 = 0) & strict_implies(all_0_133_133, all_0_132_132) = all_0_131_131 & and(all_0_134_134, all_0_135_135) = all_0_132_132 & and(all_0_135_135, all_0_134_134) = all_0_133_133 & is_a_theorem(all_0_131_131) = all_0_130_130 &  ~ 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)))
% 179.08/138.26  | (23)  ? [v0] :  ? [v1] :  ? [v2] : and(v1, v0) = v2
% 179.08/138.26  | (24)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v1, v0) = v2) |  ? [v3] :  ? [v4] : (equiv(v0, v1) = v3 & implies(v3, v2) = v4 & is_a_theorem(v4) = 0))
% 179.08/138.26  | (25) axiom_4
% 179.08/138.26  | (26)  ! [v0] :  ! [v1] : ( ~ (not(v0) = v1) |  ? [v2] :  ? [v3] : (possibly(v0) = v2 & necessarily(v1) = v3 & not(v3) = v2))
% 179.08/138.26  | (27)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (strict_equiv(v0, v1) = v3 & strict_implies(v1, v0) = v4 & and(v2, v4) = v3))
% 179.08/138.26  | (28) modus_ponens
% 179.08/138.26  | (29)  ! [v0] :  ! [v1] : ( ~ (necessarily(v0) = v1) |  ? [v2] : ((v2 = 0 & is_a_theorem(v1) = 0) | ( ~ (v2 = 0) & is_a_theorem(v0) = v2)))
% 179.08/138.26  | (30) ( ~ (all_0_136_136 = 0) & strict_implies(all_0_138_138, all_0_140_140) = all_0_137_137 & and(all_0_140_140, all_0_139_139) = all_0_138_138 & is_a_theorem(all_0_137_137) = all_0_136_136 &  ~ axiom_m2) | (axiom_m2 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : (strict_implies(v2, v0) = v3 & is_a_theorem(v3) = 0)))
% 179.08/138.26  | (31)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (equiv(v0, v1) = v2) |  ? [v3] :  ? [v4] : (and(v3, v4) = v2 & implies(v1, v0) = v4 & implies(v0, v1) = v3))
% 179.08/138.26  | (32)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (equiv(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & is_a_theorem(v2) = v3))
% 179.08/138.26  | (33) op_implies_and
% 179.08/138.26  | (34) ( ~ (all_0_154_154 = 0) & strict_implies(all_0_157_157, all_0_156_156) = all_0_155_155 & strict_implies(all_0_161_161, all_0_160_160) = all_0_158_158 & strict_implies(all_0_162_162, all_0_160_160) = all_0_156_156 & strict_implies(all_0_162_162, all_0_161_161) = all_0_159_159 & and(all_0_159_159, all_0_158_158) = all_0_157_157 & is_a_theorem(all_0_155_155) = all_0_154_154 &  ~ 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)))
% 179.08/138.26  | (35) ( ~ (all_0_181_181 = 0) & possibly(all_0_184_184) = all_0_183_183 & possibly(all_0_185_185) = all_0_184_184 & strict_implies(all_0_183_183, all_0_184_184) = all_0_182_182 & is_a_theorem(all_0_182_182) = all_0_181_181 &  ~ axiom_m9) | (axiom_m9 &  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] :  ? [v3] : (possibly(v1) = v2 & strict_implies(v2, v1) = v3 & is_a_theorem(v3) = 0)))
% 179.08/138.26  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equiv(v3, v2) = v1) |  ~ (equiv(v3, v2) = v0))
% 179.08/138.26  | (37)  ! [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))
% 179.08/138.26  | (38) ( ~ (all_0_173_173 = 0) & possibly(all_0_179_179) = all_0_176_176 & possibly(all_0_180_180) = all_0_177_177 & strict_implies(all_0_177_177, all_0_176_176) = all_0_175_175 & strict_implies(all_0_178_178, all_0_175_175) = all_0_174_174 & strict_implies(all_0_180_180, all_0_179_179) = all_0_178_178 & is_a_theorem(all_0_174_174) = all_0_173_173 &  ~ 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)))
% 179.08/138.27  | (39)  ! [v0] :  ! [v1] : ( ~ (necessarily(v0) = v1) |  ? [v2] : (implies(v1, v0) = v2 & is_a_theorem(v2) = 0))
% 179.08/138.27  | (40) axiom_K
% 179.08/138.27  | (41) op_possibly
% 179.08/138.27  | (42)  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] :  ? [v3] : (necessarily(v2) = v3 & not(v3) = v1 & not(v0) = v2))
% 179.08/138.27  | (43) and_2
% 179.08/138.27  | (44) axiom_B
% 179.08/138.27  | (45)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v1, v0) = v2) |  ? [v3] : (implies(v0, v2) = v3 & is_a_theorem(v3) = 0))
% 179.08/138.27  | (46)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (necessarily(v2) = v1) |  ~ (necessarily(v2) = v0))
% 179.08/138.27  | (47) ( ~ (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)))
% 179.08/138.27  | (48) op_strict_implies
% 179.08/138.27  | (49) op_implies
% 179.08/138.27  | (50)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (possibly(v2) = v1) |  ~ (possibly(v2) = v0))
% 179.08/138.27  | (51)  ? [v0] :  ? [v1] : is_a_theorem(v0) = v1
% 179.08/138.27  | (52)  ? [v0] :  ? [v1] :  ? [v2] : equiv(v1, v0) = v2
% 179.08/138.27  | (53) substitution_of_equivalents
% 179.08/138.27  | (54)  ~ (all_0_150_150 = 0)
% 179.08/138.27  | (55)  ! [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))
% 179.08/138.27  | (56)  ~ 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)))
% 179.08/138.27  | (57) equivalence_2
% 179.08/138.27  | (58) ( ~ (all_0_94_94 = 0) & necessarily(all_0_97_97) = all_0_96_96 & necessarily(all_0_100_100) = all_0_99_99 & necessarily(all_0_102_102) = all_0_101_101 & and(all_0_101_101, all_0_99_99) = all_0_98_98 & implies(all_0_98_98, all_0_96_96) = all_0_95_95 & implies(all_0_104_104, all_0_103_103) = all_0_100_100 & implies(all_0_105_105, all_0_103_103) = all_0_97_97 & implies(all_0_105_105, all_0_104_104) = all_0_102_102 & is_a_theorem(all_0_95_95) = all_0_94_94 &  ~ 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)))
% 179.08/138.27  | (59)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (and(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3))
% 179.08/138.27  | (60) ( ~ (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)))
% 179.08/138.27  | (61)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (implies(v3, v2) = v4 & implies(v0, v2) = v3 & is_a_theorem(v4) = 0))
% 179.08/138.27  | (62) implies_1
% 179.08/138.27  | (63)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (equiv(v0, v1) = v2) |  ? [v3] :  ? [v4] : (implies(v2, v3) = v4 & implies(v1, v0) = v3 & is_a_theorem(v4) = 0))
% 179.08/138.27  | (64)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] : (strict_implies(v0, v1) = v3 & necessarily(v2) = v3))
% 179.08/138.27  | (65) and(all_0_153_153, all_0_153_153) = all_0_152_152
% 179.08/138.27  | (66) and_3
% 179.08/138.27  | (67)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : (implies(v2, v0) = v3 & is_a_theorem(v3) = 0))
% 179.08/138.27  | (68)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (is_a_theorem(v2) = v1) |  ~ (is_a_theorem(v2) = v0))
% 179.08/138.27  | (69)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (and(v3, v2) = v1) |  ~ (and(v3, v2) = v0))
% 179.08/138.27  | (70)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v1, v0) = v2) |  ? [v3] :  ? [v4] : (and(v4, v2) = v3 & equiv(v0, v1) = v3 & implies(v0, v1) = v4))
% 179.08/138.27  | (71) necessitation
% 179.08/138.27  | (72)  ? [v0] :  ? [v1] :  ? [v2] : implies(v1, v0) = v2
% 179.08/138.27  | (73)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (and(v0, v2) = v3) |  ~ (not(v1) = v2) |  ? [v4] : (not(v3) = v4 & implies(v0, v1) = v4))
% 179.08/138.27  | (74)  ! [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))
% 179.08/138.27  | (75) ( ~ (all_0_167_167 = 0) & possibly(all_0_170_170) = all_0_169_169 & strict_implies(all_0_169_169, all_0_172_172) = all_0_168_168 & and(all_0_172_172, all_0_171_171) = all_0_170_170 & is_a_theorem(all_0_168_168) = all_0_167_167 &  ~ 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)))
% 179.08/138.27  | (76) ( ~ (all_0_115_115 = 0) & possibly(all_0_123_123) = all_0_121_121 & possibly(all_0_124_124) = all_0_119_119 & strict_implies(all_0_120_120, all_0_118_118) = all_0_117_117 & strict_implies(all_0_122_122, all_0_117_117) = all_0_116_116 & strict_implies(all_0_124_124, all_0_123_123) = all_0_122_122 & not(all_0_119_119) = all_0_118_118 & not(all_0_121_121) = all_0_120_120 & is_a_theorem(all_0_116_116) = all_0_115_115 &  ~ 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)))
% 179.08/138.28  | (77) or_3
% 179.08/138.28  | (78) implies_3
% 179.08/138.28  | (79) ( ~ (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)))
% 179.08/138.28  | (80) ( ~ (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)))
% 179.08/138.28  | (81) op_or
% 179.08/138.28  | (82) ( ~ (all_0_106_106 = 0) & possibly(all_0_112_112) = all_0_111_111 & possibly(all_0_113_113) = all_0_109_109 & possibly(all_0_114_114) = all_0_110_110 & strict_implies(all_0_111_111, all_0_108_108) = all_0_107_107 & and(all_0_110_110, all_0_109_109) = all_0_108_108 & and(all_0_114_114, all_0_113_113) = all_0_112_112 & is_a_theorem(all_0_107_107) = all_0_106_106 &  ~ 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)))
% 179.08/138.28  | (83) ( ~ (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)))
% 179.08/138.28  | (84)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (and(v2, v3) = v4) |  ~ (not(v1) = v3) |  ~ (not(v0) = v2) |  ? [v5] : (or(v0, v1) = v5 & not(v4) = v5))
% 179.08/138.28  | (85) and_1
% 179.08/138.28  | (86)  ~ 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)))
% 179.08/138.28  | (87) modus_tollens
% 179.08/138.28  | (88) strict_implies(all_0_153_153, all_0_152_152) = all_0_151_151
% 179.08/138.28  | (89)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] : (implies(v0, v2) = v3 & is_a_theorem(v3) = 0))
% 179.08/138.28  | (90)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_implies(v1, v0) = v2) |  ? [v3] :  ? [v4] : (strict_equiv(v0, v1) = v3 & strict_implies(v0, v1) = v4 & and(v4, v2) = v3))
% 179.08/138.28  | (91) ( ~ (all_0_186_186 = 0) & possibly(all_0_190_190) = all_0_189_189 & strict_implies(all_0_189_189, all_0_188_188) = all_0_187_187 & necessarily(all_0_189_189) = all_0_188_188 & is_a_theorem(all_0_187_187) = all_0_186_186 &  ~ axiom_m10) | (axiom_m10 &  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] :  ? [v3] : (strict_implies(v1, v2) = v3 & necessarily(v1) = v2 & is_a_theorem(v3) = 0)))
% 179.08/138.28  | (92)  ! [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))
% 179.08/138.28  | (93) ( ~ (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)))
% 179.08/138.28  | (94)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (or(v3, v2) = v1) |  ~ (or(v3, v2) = v0))
% 179.08/138.28  | (95) ( ~ (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)))
% 179.08/138.28  | (96) ( ~ (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)))
% 179.08/138.28  | (97)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (equiv(v0, v1) = v3 & implies(v3, v2) = v4 & is_a_theorem(v4) = 0))
% 179.08/138.28  | (98) ( ~ (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)))
% 179.08/138.29  | (99)  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] :  ? [v3] : (necessarily(v1) = v2 & implies(v0, v2) = v3 & is_a_theorem(v3) = 0))
% 179.08/138.29  | (100)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (equiv(v0, v1) = v2) |  ? [v3] :  ? [v4] : (implies(v2, v3) = v4 & implies(v0, v1) = v3 & is_a_theorem(v4) = 0))
% 179.08/138.29  | (101) ( ~ (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)))
% 179.08/138.29  | (102) op_strict_equiv
% 179.08/138.29  | (103)  ~ 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)))
% 179.08/138.29  | (104)  ! [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))
% 179.08/138.29  | (105) is_a_theorem(all_0_151_151) = all_0_150_150
% 179.08/138.29  | (106)  ! [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))
% 179.08/138.29  | (107) equivalence_3
% 179.08/138.29  | (108)  ? [v0] :  ? [v1] :  ? [v2] : strict_implies(v1, v0) = v2
% 179.08/138.29  | (109)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strict_implies(v0, v1) = v2) |  ? [v3] : (necessarily(v3) = v2 & implies(v0, v1) = v3))
% 179.08/138.29  | (110) (all_0_85_85 = 0 &  ~ (all_0_87_87 = all_0_88_88) & strict_equiv(all_0_88_88, all_0_87_87) = all_0_86_86 & is_a_theorem(all_0_86_86) = 0 &  ~ substitution_strict_equiv) | (substitution_strict_equiv &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (strict_equiv(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & is_a_theorem(v2) = v3)))
% 179.08/138.29  | (111)  ! [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))
% 179.08/138.29  | (112)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : (implies(v2, v1) = v3 & is_a_theorem(v3) = 0))
% 179.08/138.29  | (113) ( ~ (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)))
% 179.08/138.29  | (114)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] :  ? [v4] : (implies(v1, v2) = v3 & implies(v0, v3) = v4 & is_a_theorem(v4) = 0))
% 179.08/138.29  | (115) ( ~ (all_0_141_141 = 0) & strict_implies(all_0_145_145, all_0_143_143) = all_0_142_142 & and(all_0_146_146, all_0_147_147) = all_0_145_145 & and(all_0_148_148, all_0_147_147) = all_0_144_144 & and(all_0_149_149, all_0_144_144) = all_0_143_143 & and(all_0_149_149, all_0_148_148) = all_0_146_146 & is_a_theorem(all_0_142_142) = all_0_141_141 &  ~ 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)))
% 179.08/138.29  | (116)  ? [v0] :  ? [v1] : necessarily(v0) = v1
% 179.08/138.29  | (117) ( ~ (all_0_125_125 = 0) & strict_implies(all_0_128_128, all_0_127_127) = all_0_126_126 & necessarily(all_0_128_128) = all_0_127_127 & necessarily(all_0_129_129) = all_0_128_128 & is_a_theorem(all_0_126_126) = all_0_125_125 &  ~ axiom_s4) | (axiom_s4 &  ! [v0] :  ! [v1] : ( ~ (necessarily(v0) = v1) |  ? [v2] :  ? [v3] : (strict_implies(v1, v2) = v3 & necessarily(v1) = v2 & is_a_theorem(v3) = 0)))
% 179.08/138.29  | (118)  ! [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))
% 179.08/138.29  | (119)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (strict_implies(v3, v2) = v1) |  ~ (strict_implies(v3, v2) = v0))
% 179.08/138.29  | (120) (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))))
% 179.08/138.29  | (121) ( ~ (all_0_163_163 = 0) & possibly(all_0_166_166) = all_0_165_165 & strict_implies(all_0_166_166, all_0_165_165) = all_0_164_164 & is_a_theorem(all_0_164_164) = all_0_163_163 &  ~ axiom_m6) | (axiom_m6 &  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] : (strict_implies(v0, v1) = v2 & is_a_theorem(v2) = 0)))
% 179.08/138.29  | (122)  ? [v0] :  ? [v1] : possibly(v0) = v1
% 179.08/138.29  | (123) axiom_M
% 179.08/138.29  | (124)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (not(v2) = v1) |  ~ (not(v2) = v0))
% 179.08/138.29  | (125) ( ~ (all_0_89_89 = 0) & possibly(all_0_93_93) = all_0_92_92 & necessarily(all_0_92_92) = all_0_91_91 & implies(all_0_92_92, all_0_91_91) = all_0_90_90 & is_a_theorem(all_0_90_90) = all_0_89_89 &  ~ axiom_5) | (axiom_5 &  ! [v0] :  ! [v1] : ( ~ (possibly(v0) = v1) |  ? [v2] :  ? [v3] : (necessarily(v1) = v2 & implies(v1, v2) = v3 & is_a_theorem(v3) = 0)))
% 179.08/138.30  |
% 179.08/138.30  | Instantiating formula (109) with all_0_151_151, all_0_152_152, all_0_153_153 and discharging atoms strict_implies(all_0_153_153, all_0_152_152) = all_0_151_151, yields:
% 179.08/138.30  | (126)  ? [v0] : (necessarily(v0) = all_0_151_151 & implies(all_0_153_153, all_0_152_152) = v0)
% 179.08/138.30  |
% 179.08/138.30  | Instantiating formula (114) with all_0_152_152, all_0_153_153, all_0_153_153 and discharging atoms and(all_0_153_153, all_0_153_153) = all_0_152_152, yields:
% 179.08/138.30  | (127)  ? [v0] :  ? [v1] : (implies(all_0_153_153, v0) = v1 & implies(all_0_153_153, all_0_152_152) = v0 & is_a_theorem(v1) = 0)
% 179.08/138.30  |
% 179.08/138.30  | Instantiating (127) with all_30_0_218, all_30_1_219 yields:
% 179.08/138.30  | (128) implies(all_0_153_153, all_30_1_219) = all_30_0_218 & implies(all_0_153_153, all_0_152_152) = all_30_1_219 & is_a_theorem(all_30_0_218) = 0
% 179.08/138.30  |
% 179.08/138.30  | Applying alpha-rule on (128) yields:
% 179.08/138.30  | (129) implies(all_0_153_153, all_30_1_219) = all_30_0_218
% 179.08/138.30  | (130) implies(all_0_153_153, all_0_152_152) = all_30_1_219
% 179.08/138.30  | (131) is_a_theorem(all_30_0_218) = 0
% 179.08/138.30  |
% 179.08/138.30  | Instantiating (126) with all_36_0_224 yields:
% 179.08/138.30  | (132) necessarily(all_36_0_224) = all_0_151_151 & implies(all_0_153_153, all_0_152_152) = all_36_0_224
% 179.08/138.30  |
% 179.08/138.30  | Applying alpha-rule on (132) yields:
% 179.08/138.30  | (133) necessarily(all_36_0_224) = all_0_151_151
% 179.08/138.30  | (134) implies(all_0_153_153, all_0_152_152) = all_36_0_224
% 179.08/138.30  |
% 179.08/138.30  | Instantiating formula (18) with all_0_153_153, all_0_152_152, all_30_1_219, all_36_0_224 and discharging atoms implies(all_0_153_153, all_0_152_152) = all_36_0_224, implies(all_0_153_153, all_0_152_152) = all_30_1_219, yields:
% 179.08/138.30  | (135) all_36_0_224 = all_30_1_219
% 179.08/138.30  |
% 179.08/138.30  | From (135) and (133) follows:
% 179.08/138.30  | (136) necessarily(all_30_1_219) = all_0_151_151
% 179.08/138.30  |
% 179.08/138.30  | From (135) and (134) follows:
% 179.08/138.30  | (130) implies(all_0_153_153, all_0_152_152) = all_30_1_219
% 179.08/138.30  |
% 179.08/138.30  | Instantiating formula (29) with all_0_151_151, all_30_1_219 and discharging atoms necessarily(all_30_1_219) = all_0_151_151, yields:
% 179.08/138.30  | (138)  ? [v0] : ((v0 = 0 & is_a_theorem(all_0_151_151) = 0) | ( ~ (v0 = 0) & is_a_theorem(all_30_1_219) = v0))
% 179.08/138.30  |
% 179.08/138.30  | Instantiating formula (61) with all_30_1_219, all_0_152_152, all_0_153_153 and discharging atoms implies(all_0_153_153, all_0_152_152) = all_30_1_219, yields:
% 179.08/138.30  | (139)  ? [v0] :  ? [v1] : (implies(v0, all_30_1_219) = v1 & implies(all_0_153_153, all_30_1_219) = v0 & is_a_theorem(v1) = 0)
% 179.08/138.30  |
% 179.08/138.30  | Instantiating (139) with all_69_0_246, all_69_1_247 yields:
% 179.08/138.30  | (140) implies(all_69_1_247, all_30_1_219) = all_69_0_246 & implies(all_0_153_153, all_30_1_219) = all_69_1_247 & is_a_theorem(all_69_0_246) = 0
% 179.08/138.30  |
% 179.08/138.30  | Applying alpha-rule on (140) yields:
% 179.08/138.30  | (141) implies(all_69_1_247, all_30_1_219) = all_69_0_246
% 179.08/138.30  | (142) implies(all_0_153_153, all_30_1_219) = all_69_1_247
% 179.08/138.30  | (143) is_a_theorem(all_69_0_246) = 0
% 179.08/138.30  |
% 179.08/138.30  | Instantiating (138) with all_132_0_325 yields:
% 179.08/138.30  | (144) (all_132_0_325 = 0 & is_a_theorem(all_0_151_151) = 0) | ( ~ (all_132_0_325 = 0) & is_a_theorem(all_30_1_219) = all_132_0_325)
% 179.08/138.30  |
% 179.08/138.30  +-Applying beta-rule and splitting (144), into two cases.
% 179.08/138.30  |-Branch one:
% 179.08/138.30  | (145) all_132_0_325 = 0 & is_a_theorem(all_0_151_151) = 0
% 179.08/138.30  |
% 179.08/138.30  	| Applying alpha-rule on (145) yields:
% 179.08/138.30  	| (146) all_132_0_325 = 0
% 179.08/138.30  	| (147) is_a_theorem(all_0_151_151) = 0
% 179.08/138.30  	|
% 179.08/138.30  	| Instantiating formula (68) with all_0_151_151, 0, all_0_150_150 and discharging atoms is_a_theorem(all_0_151_151) = all_0_150_150, is_a_theorem(all_0_151_151) = 0, yields:
% 179.08/138.30  	| (148) all_0_150_150 = 0
% 179.08/138.30  	|
% 179.08/138.30  	| Equations (148) can reduce 54 to:
% 179.08/138.30  	| (149) $false
% 179.08/138.30  	|
% 179.08/138.30  	|-The branch is then unsatisfiable
% 179.08/138.30  |-Branch two:
% 179.08/138.30  | (150)  ~ (all_132_0_325 = 0) & is_a_theorem(all_30_1_219) = all_132_0_325
% 179.08/138.30  |
% 179.08/138.30  	| Applying alpha-rule on (150) yields:
% 179.08/138.30  	| (151)  ~ (all_132_0_325 = 0)
% 179.08/138.30  	| (152) is_a_theorem(all_30_1_219) = all_132_0_325
% 179.08/138.30  	|
% 179.08/138.30  	| Instantiating formula (18) with all_0_153_153, all_30_1_219, all_69_1_247, all_30_0_218 and discharging atoms implies(all_0_153_153, all_30_1_219) = all_69_1_247, implies(all_0_153_153, all_30_1_219) = all_30_0_218, yields:
% 179.08/138.30  	| (153) all_69_1_247 = all_30_0_218
% 179.08/138.30  	|
% 179.08/138.30  	| From (153) and (141) follows:
% 179.08/138.30  	| (154) implies(all_30_0_218, all_30_1_219) = all_69_0_246
% 179.08/138.30  	|
% 179.08/138.30  	| Instantiating formula (11) with all_69_0_246, all_30_1_219, all_30_0_218 and discharging atoms implies(all_30_0_218, all_30_1_219) = all_69_0_246, yields:
% 179.08/138.30  	| (155)  ? [v0] : ((v0 = 0 & is_a_theorem(all_30_1_219) = 0) | ( ~ (v0 = 0) & is_a_theorem(all_69_0_246) = v0) | ( ~ (v0 = 0) & is_a_theorem(all_30_0_218) = v0))
% 179.08/138.30  	|
% 179.08/138.30  	| Instantiating (155) with all_817_0_1130 yields:
% 179.08/138.30  	| (156) (all_817_0_1130 = 0 & is_a_theorem(all_30_1_219) = 0) | ( ~ (all_817_0_1130 = 0) & is_a_theorem(all_69_0_246) = all_817_0_1130) | ( ~ (all_817_0_1130 = 0) & is_a_theorem(all_30_0_218) = all_817_0_1130)
% 179.08/138.30  	|
% 179.08/138.30  	+-Applying beta-rule and splitting (156), into two cases.
% 179.08/138.30  	|-Branch one:
% 179.08/138.30  	| (157) (all_817_0_1130 = 0 & is_a_theorem(all_30_1_219) = 0) | ( ~ (all_817_0_1130 = 0) & is_a_theorem(all_69_0_246) = all_817_0_1130)
% 179.08/138.30  	|
% 179.08/138.30  		+-Applying beta-rule and splitting (157), into two cases.
% 179.08/138.30  		|-Branch one:
% 179.08/138.30  		| (158) all_817_0_1130 = 0 & is_a_theorem(all_30_1_219) = 0
% 179.08/138.30  		|
% 179.08/138.30  			| Applying alpha-rule on (158) yields:
% 179.08/138.30  			| (159) all_817_0_1130 = 0
% 179.08/138.30  			| (160) is_a_theorem(all_30_1_219) = 0
% 179.08/138.31  			|
% 179.08/138.31  			| Instantiating formula (68) with all_30_1_219, 0, all_132_0_325 and discharging atoms is_a_theorem(all_30_1_219) = all_132_0_325, is_a_theorem(all_30_1_219) = 0, yields:
% 179.08/138.31  			| (146) all_132_0_325 = 0
% 179.08/138.31  			|
% 179.08/138.31  			| Equations (146) can reduce 151 to:
% 179.08/138.31  			| (149) $false
% 179.08/138.31  			|
% 179.08/138.31  			|-The branch is then unsatisfiable
% 179.08/138.31  		|-Branch two:
% 179.08/138.31  		| (163)  ~ (all_817_0_1130 = 0) & is_a_theorem(all_69_0_246) = all_817_0_1130
% 179.08/138.31  		|
% 179.08/138.31  			| Applying alpha-rule on (163) yields:
% 179.08/138.31  			| (164)  ~ (all_817_0_1130 = 0)
% 179.08/138.31  			| (165) is_a_theorem(all_69_0_246) = all_817_0_1130
% 179.08/138.31  			|
% 179.08/138.31  			| Instantiating formula (68) with all_69_0_246, all_817_0_1130, 0 and discharging atoms is_a_theorem(all_69_0_246) = all_817_0_1130, is_a_theorem(all_69_0_246) = 0, yields:
% 179.08/138.31  			| (159) all_817_0_1130 = 0
% 179.08/138.31  			|
% 179.08/138.31  			| Equations (159) can reduce 164 to:
% 179.08/138.31  			| (149) $false
% 179.08/138.31  			|
% 179.08/138.31  			|-The branch is then unsatisfiable
% 179.08/138.31  	|-Branch two:
% 179.08/138.31  	| (168)  ~ (all_817_0_1130 = 0) & is_a_theorem(all_30_0_218) = all_817_0_1130
% 179.08/138.31  	|
% 179.08/138.31  		| Applying alpha-rule on (168) yields:
% 179.08/138.31  		| (164)  ~ (all_817_0_1130 = 0)
% 179.08/138.31  		| (170) is_a_theorem(all_30_0_218) = all_817_0_1130
% 179.08/138.31  		|
% 179.08/138.31  		| Instantiating formula (68) with all_30_0_218, all_817_0_1130, 0 and discharging atoms is_a_theorem(all_30_0_218) = all_817_0_1130, is_a_theorem(all_30_0_218) = 0, yields:
% 179.08/138.31  		| (159) all_817_0_1130 = 0
% 179.08/138.31  		|
% 179.08/138.31  		| Equations (159) can reduce 164 to:
% 179.08/138.31  		| (149) $false
% 179.08/138.31  		|
% 179.08/138.31  		|-The branch is then unsatisfiable
% 179.08/138.31  % SZS output end Proof for theBenchmark
% 179.08/138.31  
% 179.08/138.31  137719ms
%------------------------------------------------------------------------------