TSTP Solution File: LCL536+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : LCL536+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 09:36:59 EDT 2022
% Result : Theorem 4.42s 1.63s
% Output : Proof 6.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL536+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n027.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 : Mon Jul 4 15:47:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.54/0.58 ____ _
% 0.54/0.58 ___ / __ \_____(_)___ ________ __________
% 0.54/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.58
% 0.54/0.58 A Theorem Prover for First-Order Logic
% 0.54/0.58 (ePrincess v.1.0)
% 0.54/0.58
% 0.54/0.58 (c) Philipp Rümmer, 2009-2015
% 0.54/0.58 (c) Peter Backeman, 2014-2015
% 0.54/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.58 Bug reports to peter@backeman.se
% 0.54/0.58
% 0.54/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.58
% 0.54/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.61/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.82/1.01 Prover 0: Preprocessing ...
% 3.77/1.48 Prover 0: Constructing countermodel ...
% 4.42/1.63 Prover 0: proved (1002ms)
% 4.42/1.63
% 4.42/1.63 No countermodel exists, formula is valid
% 4.42/1.63 % SZS status Theorem for theBenchmark
% 4.42/1.63
% 4.42/1.63 Generating proof ... found it (size 8)
% 6.12/2.04
% 6.12/2.04 % SZS output start Proof for theBenchmark
% 6.12/2.04 Assumed formulas after preprocessing and simplification:
% 6.12/2.04 | (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] : (possibly(v0) = v1 & strict_implies(v1, v2) = v3 & necessarily(v1) = v2 & 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 & ~ axiom_m10 & ~ is_a_theorem(v3) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ! [v167] : ! [v168] : ! [v169] : ! [v170] : ( ~ (or(v162, v163) = v167) | ~ (implies(v167, v164) = v168) | ~ (implies(v166, v168) = v169) | ~ (implies(v165, v169) = v170) | ~ (implies(v163, v164) = v166) | ~ (implies(v162, v164) = v165) | is_a_theorem(v170)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ! [v167] : ! [v168] : ! [v169] : ( ~ (necessarily(v164) = v165) | ~ (necessarily(v163) = v167) | ~ (necessarily(v162) = v166) | ~ (implies(v166, v167) = v168) | ~ (implies(v165, v168) = v169) | ~ (implies(v162, v163) = v164) | is_a_theorem(v169)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ! [v167] : ! [v168] : ! [v169] : ( ~ (implies(v166, v167) = v168) | ~ (implies(v165, v168) = v169) | ~ (implies(v163, v164) = v166) | ~ (implies(v162, v164) = v167) | ~ (implies(v162, v163) = v165) | is_a_theorem(v169)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ! [v167] : ! [v168] : ( ~ (not(v163) = v164) | ~ (not(v162) = v165) | ~ (implies(v166, v167) = v168) | ~ (implies(v164, v165) = v166) | ~ (implies(v162, v163) = v167) | is_a_theorem(v168)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ! [v167] : ! [v168] : ( ~ (equiv(v162, v163) = v166) | ~ (implies(v165, v166) = v167) | ~ (implies(v164, v167) = v168) | ~ (implies(v163, v162) = v165) | ~ (implies(v162, v163) = v164) | is_a_theorem(v168)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ( ~ (strict_implies(v163, v162) = v165) | ~ (strict_implies(v162, v163) = v164) | ~ (and(v164, v165) = v166) | strict_equiv(v162, v163) = v166) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ( ~ (and(v164, v165) = v166) | ~ (not(v163) = v165) | ~ (not(v162) = v164) | ? [v167] : (or(v162, v163) = v167 & not(v166) = v167)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ( ~ (and(v164, v165) = v166) | ~ (implies(v163, v162) = v165) | ~ (implies(v162, v163) = v164) | equiv(v162, v163) = v166) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ( ~ (and(v162, v163) = v164) | ~ (implies(v163, v164) = v165) | ~ (implies(v162, v165) = v166) | is_a_theorem(v166)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ( ~ (equiv(v162, v163) = v164) | ~ (implies(v164, v165) = v166) | ~ (implies(v163, v162) = v165) | is_a_theorem(v166)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ( ~ (equiv(v162, v163) = v164) | ~ (implies(v164, v165) = v166) | ~ (implies(v162, v163) = v165) | is_a_theorem(v166)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ( ~ (implies(v165, v164) = v166) | ~ (implies(v162, v164) = v165) | ~ (implies(v162, v163) = v164) | is_a_theorem(v166)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : (v163 = v162 | ~ (strict_equiv(v165, v164) = v163) | ~ (strict_equiv(v165, v164) = v162)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : (v163 = v162 | ~ (strict_implies(v165, v164) = v163) | ~ (strict_implies(v165, v164) = v162)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : (v163 = v162 | ~ (or(v165, v164) = v163) | ~ (or(v165, v164) = v162)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : (v163 = v162 | ~ (and(v165, v164) = v163) | ~ (and(v165, v164) = v162)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : (v163 = v162 | ~ (equiv(v165, v164) = v163) | ~ (equiv(v165, v164) = v162)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : (v163 = v162 | ~ (implies(v165, v164) = v163) | ~ (implies(v165, v164) = v162)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ( ~ (possibly(v162) = v163) | ~ (necessarily(v163) = v164) | ~ (implies(v163, v164) = v165) | is_a_theorem(v165)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ( ~ (or(v162, v163) = v164) | ~ (implies(v163, v164) = v165) | is_a_theorem(v165)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ( ~ (or(v162, v163) = v164) | ~ (implies(v162, v164) = v165) | is_a_theorem(v165)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ( ~ (and(v162, v164) = v165) | ~ (not(v163) = v164) | ? [v166] : (not(v165) = v166 & implies(v162, v163) = v166)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ( ~ (and(v162, v163) = v164) | ~ (implies(v164, v163) = v165) | is_a_theorem(v165)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ( ~ (and(v162, v163) = v164) | ~ (implies(v164, v162) = v165) | is_a_theorem(v165)) & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ( ~ (implies(v163, v162) = v164) | ~ (implies(v162, v164) = v165) | is_a_theorem(v165)) & ! [v162] : ! [v163] : ! [v164] : (v163 = v162 | ~ (possibly(v164) = v163) | ~ (possibly(v164) = v162)) & ! [v162] : ! [v163] : ! [v164] : (v163 = v162 | ~ (necessarily(v164) = v163) | ~ (necessarily(v164) = v162)) & ! [v162] : ! [v163] : ! [v164] : (v163 = v162 | ~ (not(v164) = v163) | ~ (not(v164) = v162)) & ! [v162] : ! [v163] : ! [v164] : (v163 = v162 | ~ (equiv(v162, v163) = v164) | ~ is_a_theorem(v164)) & ! [v162] : ! [v163] : ! [v164] : ( ~ (strict_equiv(v162, v163) = v164) | ? [v165] : ? [v166] : (strict_implies(v163, v162) = v166 & strict_implies(v162, v163) = v165 & and(v165, v166) = v164)) & ! [v162] : ! [v163] : ! [v164] : ( ~ (strict_implies(v162, v163) = v164) | ? [v165] : (necessarily(v165) = v164 & implies(v162, v163) = v165)) & ! [v162] : ! [v163] : ! [v164] : ( ~ (necessarily(v162) = v163) | ~ (implies(v163, v162) = v164) | is_a_theorem(v164)) & ! [v162] : ! [v163] : ! [v164] : ( ~ (or(v162, v163) = v164) | ? [v165] : ? [v166] : ? [v167] : (and(v165, v166) = v167 & not(v167) = v164 & not(v163) = v166 & not(v162) = v165)) & ! [v162] : ! [v163] : ! [v164] : ( ~ (equiv(v162, v163) = v164) | ? [v165] : ? [v166] : (and(v165, v166) = v164 & implies(v163, v162) = v166 & implies(v162, v163) = v165)) & ! [v162] : ! [v163] : ! [v164] : ( ~ (implies(v162, v163) = v164) | ~ is_a_theorem(v164) | ~ is_a_theorem(v162) | is_a_theorem(v163)) & ! [v162] : ! [v163] : ! [v164] : ( ~ (implies(v162, v163) = v164) | ? [v165] : ? [v166] : (and(v162, v165) = v166 & not(v166) = v164 & not(v163) = v165)) & ! [v162] : ! [v163] : ! [v164] : ( ~ (implies(v162, v163) = v164) | ? [v165] : (strict_implies(v162, v163) = v165 & necessarily(v164) = v165)) & ! [v162] : ! [v163] : ( ~ (possibly(v162) = v163) | ? [v164] : ? [v165] : (necessarily(v164) = v165 & not(v165) = v163 & not(v162) = v164)) & ! [v162] : ! [v163] : ( ~ (necessarily(v162) = v163) | ~ is_a_theorem(v162) | is_a_theorem(v163)) & ! [v162] : ! [v163] : ( ~ (not(v162) = v163) | ? [v164] : ? [v165] : (possibly(v162) = v164 & necessarily(v163) = v165 & not(v165) = v164)) & ( ~ op_necessarily | ( ! [v162] : ! [v163] : ( ~ (necessarily(v162) = v163) | ? [v164] : ? [v165] : (possibly(v164) = v165 & not(v165) = v163 & not(v162) = v164)) & ! [v162] : ! [v163] : ( ~ (not(v162) = v163) | ? [v164] : ? [v165] : (possibly(v163) = v165 & necessarily(v162) = v164 & not(v165) = v164)))) & ( ~ op_implies_or | ( ! [v162] : ! [v163] : ! [v164] : ! [v165] : ( ~ (or(v164, v163) = v165) | ~ (not(v162) = v164) | implies(v162, v163) = v165) & ! [v162] : ! [v163] : ! [v164] : ( ~ (implies(v162, v163) = v164) | ? [v165] : (or(v165, v163) = v164 & not(v162) = v165)))) & ( ~ op_and | ( ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ( ~ (or(v164, v165) = v166) | ~ (not(v163) = v165) | ~ (not(v162) = v164) | ? [v167] : (and(v162, v163) = v167 & not(v166) = v167)) & ! [v162] : ! [v163] : ! [v164] : ( ~ (and(v162, v163) = v164) | ? [v165] : ? [v166] : ? [v167] : (or(v165, v166) = v167 & not(v167) = v164 & not(v163) = v166 & not(v162) = v165)))) & (( ~ (v92 = v91) & strict_equiv(v91, v92) = v93 & is_a_theorem(v93) & ~ substitution_strict_equiv) | (substitution_strict_equiv & ! [v162] : ! [v163] : ! [v164] : (v163 = v162 | ~ (strict_equiv(v162, v163) = v164) | ~ is_a_theorem(v164)))) & ((possibly(v83) = v84 & necessarily(v84) = v85 & implies(v83, v85) = v86 & ~ axiom_B & ~ is_a_theorem(v86)) | (axiom_B & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ( ~ (possibly(v162) = v163) | ~ (necessarily(v163) = v164) | ~ (implies(v162, v164) = v165) | is_a_theorem(v165)))) & ((possibly(v66) = v67 & possibly(v65) = v69 & possibly(v64) = v68 & strict_implies(v67, v70) = v71 & and(v68, v69) = v70 & and(v64, v65) = v66 & ~ axiom_s2 & ~ is_a_theorem(v71)) | (axiom_s2 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ! [v167] : ! [v168] : ! [v169] : ( ~ (possibly(v164) = v165) | ~ (possibly(v163) = v167) | ~ (possibly(v162) = v166) | ~ (strict_implies(v165, v168) = v169) | ~ (and(v166, v167) = v168) | ~ (and(v162, v163) = v164) | is_a_theorem(v169)))) & ((possibly(v56) = v58 & possibly(v55) = v60 & strict_implies(v59, v61) = v62 & strict_implies(v57, v62) = v63 & strict_implies(v55, v56) = v57 & not(v60) = v61 & not(v58) = v59 & ~ axiom_s3 & ~ is_a_theorem(v63)) | (axiom_s3 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ! [v167] : ! [v168] : ! [v169] : ! [v170] : ( ~ (possibly(v163) = v165) | ~ (possibly(v162) = v167) | ~ (strict_implies(v166, v168) = v169) | ~ (strict_implies(v164, v169) = v170) | ~ (strict_implies(v162, v163) = v164) | ~ (not(v167) = v168) | ~ (not(v165) = v166) | is_a_theorem(v170)))) & ((possibly(v20) = v21 & strict_implies(v20, v21) = v22 & ~ axiom_m6 & ~ is_a_theorem(v22)) | (axiom_m6 & ! [v162] : ! [v163] : ! [v164] : ( ~ (possibly(v162) = v163) | ~ (strict_implies(v162, v163) = v164) | is_a_theorem(v164)))) & ((possibly(v17) = v18 & strict_implies(v18, v15) = v19 & and(v15, v16) = v17 & ~ axiom_m7 & ~ is_a_theorem(v19)) | (axiom_m7 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ( ~ (possibly(v164) = v165) | ~ (strict_implies(v165, v162) = v166) | ~ (and(v162, v163) = v164) | is_a_theorem(v166)))) & ((possibly(v9) = v12 & possibly(v8) = v11 & strict_implies(v11, v12) = v13 & strict_implies(v10, v13) = v14 & strict_implies(v8, v9) = v10 & ~ axiom_m8 & ~ is_a_theorem(v14)) | (axiom_m8 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ! [v167] : ! [v168] : ( ~ (possibly(v163) = v166) | ~ (possibly(v162) = v165) | ~ (strict_implies(v165, v166) = v167) | ~ (strict_implies(v164, v167) = v168) | ~ (strict_implies(v162, v163) = v164) | is_a_theorem(v168)))) & ((possibly(v5) = v6 & possibly(v4) = v5 & strict_implies(v6, v5) = v7 & ~ axiom_m9 & ~ is_a_theorem(v7)) | (axiom_m9 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ( ~ (possibly(v163) = v164) | ~ (possibly(v162) = v163) | ~ (strict_implies(v164, v163) = v165) | is_a_theorem(v165)))) & ((strict_implies(v97, v98) = v99 & is_a_theorem(v99) & is_a_theorem(v97) & ~ modus_ponens_strict_implies & ~ is_a_theorem(v98)) | (modus_ponens_strict_implies & ! [v162] : ! [v163] : ! [v164] : ( ~ (strict_implies(v162, v163) = v164) | ~ is_a_theorem(v164) | ~ is_a_theorem(v162) | is_a_theorem(v163)))) & ((strict_implies(v52, v53) = v54 & necessarily(v52) = v53 & necessarily(v51) = v52 & ~ axiom_s4 & ~ is_a_theorem(v54)) | (axiom_s4 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ( ~ (strict_implies(v163, v164) = v165) | ~ (necessarily(v163) = v164) | ~ (necessarily(v162) = v163) | is_a_theorem(v165)))) & ((strict_implies(v48, v49) = v50 & and(v47, v46) = v49 & and(v46, v47) = v48 & ~ axiom_m1 & ~ is_a_theorem(v50)) | (axiom_m1 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ( ~ (strict_implies(v164, v165) = v166) | ~ (and(v163, v162) = v165) | ~ (and(v162, v163) = v164) | is_a_theorem(v166)))) & ((strict_implies(v44, v42) = v45 & and(v42, v43) = v44 & ~ axiom_m2 & ~ is_a_theorem(v45)) | (axiom_m2 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ( ~ (strict_implies(v164, v162) = v165) | ~ (and(v162, v163) = v164) | is_a_theorem(v165)))) & ((strict_implies(v38, v40) = v41 & and(v37, v36) = v38 & and(v35, v36) = v39 & and(v34, v39) = v40 & and(v34, v35) = v37 & ~ axiom_m3 & ~ is_a_theorem(v41)) | (axiom_m3 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ! [v167] : ! [v168] : ! [v169] : ( ~ (strict_implies(v166, v168) = v169) | ~ (and(v165, v164) = v166) | ~ (and(v163, v164) = v167) | ~ (and(v162, v167) = v168) | ~ (and(v162, v163) = v165) | is_a_theorem(v169)))) & ((strict_implies(v31, v32) = v33 & and(v31, v31) = v32 & ~ axiom_m4 & ~ is_a_theorem(v33)) | (axiom_m4 & ! [v162] : ! [v163] : ! [v164] : ( ~ (strict_implies(v162, v163) = v164) | ~ (and(v162, v162) = v163) | is_a_theorem(v164)))) & ((strict_implies(v28, v29) = v30 & strict_implies(v24, v25) = v27 & strict_implies(v23, v25) = v29 & strict_implies(v23, v24) = v26 & and(v26, v27) = v28 & ~ axiom_m5 & ~ is_a_theorem(v30)) | (axiom_m5 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ! [v167] : ! [v168] : ! [v169] : ( ~ (strict_implies(v167, v168) = v169) | ~ (strict_implies(v163, v164) = v166) | ~ (strict_implies(v162, v164) = v168) | ~ (strict_implies(v162, v163) = v165) | ~ (and(v165, v166) = v167) | is_a_theorem(v169)))) & ((necessarily(v88) = v89 & necessarily(v87) = v88 & implies(v88, v89) = v90 & ~ axiom_4 & ~ is_a_theorem(v90)) | (axiom_4 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ( ~ (necessarily(v163) = v164) | ~ (necessarily(v162) = v163) | ~ (implies(v163, v164) = v165) | is_a_theorem(v165)))) & ((necessarily(v80) = v81 & necessarily(v77) = v78 & necessarily(v75) = v76 & and(v76, v78) = v79 & implies(v79, v81) = v82 & implies(v73, v74) = v77 & implies(v72, v74) = v80 & implies(v72, v73) = v75 & ~ axiom_s1 & ~ is_a_theorem(v82)) | (axiom_s1 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ! [v167] : ! [v168] : ! [v169] : ! [v170] : ! [v171] : ! [v172] : ( ~ (necessarily(v170) = v171) | ~ (necessarily(v167) = v168) | ~ (necessarily(v165) = v166) | ~ (and(v166, v168) = v169) | ~ (implies(v169, v171) = v172) | ~ (implies(v163, v164) = v167) | ~ (implies(v162, v164) = v170) | ~ (implies(v162, v163) = v165) | is_a_theorem(v172)))) & ((or(v125, v125) = v126 & implies(v126, v125) = v127 & ~ r1 & ~ is_a_theorem(v127)) | (r1 & ! [v162] : ! [v163] : ! [v164] : ( ~ (or(v162, v162) = v163) | ~ (implies(v163, v162) = v164) | is_a_theorem(v164)))) & ((or(v121, v122) = v123 & implies(v122, v123) = v124 & ~ r2 & ~ is_a_theorem(v124)) | (r2 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ( ~ (or(v162, v163) = v164) | ~ (implies(v163, v164) = v165) | is_a_theorem(v165)))) & ((or(v117, v116) = v119 & or(v116, v117) = v118 & implies(v118, v119) = v120 & ~ r3 & ~ is_a_theorem(v120)) | (r3 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ( ~ (or(v163, v162) = v165) | ~ (or(v162, v163) = v164) | ~ (implies(v164, v165) = v166) | is_a_theorem(v166)))) & ((or(v109, v113) = v114 & or(v109, v110) = v111 & or(v108, v111) = v112 & or(v108, v110) = v113 & implies(v112, v114) = v115 & ~ r4 & ~ is_a_theorem(v115)) | (r4 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ! [v167] : ! [v168] : ! [v169] : ( ~ (or(v163, v167) = v168) | ~ (or(v163, v164) = v165) | ~ (or(v162, v165) = v166) | ~ (or(v162, v164) = v167) | ~ (implies(v166, v168) = v169) | is_a_theorem(v169)))) & ((or(v100, v102) = v105 & or(v100, v101) = v104 & implies(v104, v105) = v106 & implies(v103, v106) = v107 & implies(v101, v102) = v103 & ~ r5 & ~ is_a_theorem(v107)) | (r5 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ! [v167] : ! [v168] : ! [v169] : ( ~ (or(v162, v164) = v167) | ~ (or(v162, v163) = v166) | ~ (implies(v166, v167) = v168) | ~ (implies(v165, v168) = v169) | ~ (implies(v163, v164) = v165) | is_a_theorem(v169)))) & ((and(v159, v159) = v160 & implies(v159, v160) = v161 & ~ kn1 & ~ is_a_theorem(v161)) | (kn1 & ! [v162] : ! [v163] : ! [v164] : ( ~ (and(v162, v162) = v163) | ~ (implies(v162, v163) = v164) | is_a_theorem(v164)))) & ((and(v155, v156) = v157 & implies(v157, v155) = v158 & ~ kn2 & ~ is_a_theorem(v158)) | (kn2 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ( ~ (and(v162, v163) = v164) | ~ (implies(v164, v162) = v165) | is_a_theorem(v165)))) & ((and(v147, v145) = v151 & and(v146, v147) = v149 & not(v151) = v152 & not(v149) = v150 & implies(v150, v152) = v153 & implies(v148, v153) = v154 & implies(v145, v146) = v148 & ~ kn3 & ~ is_a_theorem(v154)) | (kn3 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ! [v167] : ! [v168] : ! [v169] : ! [v170] : ! [v171] : ( ~ (and(v164, v162) = v168) | ~ (and(v163, v164) = v166) | ~ (not(v168) = v169) | ~ (not(v166) = v167) | ~ (implies(v167, v169) = v170) | ~ (implies(v165, v170) = v171) | ~ (implies(v162, v163) = v165) | is_a_theorem(v171)))) & ((and(v94, v95) = v96 & is_a_theorem(v95) & is_a_theorem(v94) & ~ adjunction & ~ is_a_theorem(v96)) | (adjunction & ! [v162] : ! [v163] : ! [v164] : ( ~ (and(v162, v163) = v164) | ~ is_a_theorem(v163) | ~ is_a_theorem(v162) | is_a_theorem(v164)))) & ((not(v132) = v134 & implies(v134, v133) = v135 & implies(v132, v135) = v136 & ~ cn2 & ~ is_a_theorem(v136)) | (cn2 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ( ~ (not(v162) = v164) | ~ (implies(v164, v163) = v165) | ~ (implies(v162, v165) = v166) | is_a_theorem(v166)))) & ((not(v128) = v129 & implies(v130, v128) = v131 & implies(v129, v128) = v130 & ~ cn3 & ~ is_a_theorem(v131)) | (cn3 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ( ~ (not(v162) = v163) | ~ (implies(v164, v162) = v165) | ~ (implies(v163, v162) = v164) | is_a_theorem(v165)))) & ((implies(v141, v142) = v143 & implies(v140, v143) = v144 & implies(v138, v139) = v141 & implies(v137, v139) = v142 & implies(v137, v138) = v140 & ~ cn1 & ~ is_a_theorem(v144)) | (cn1 & ! [v162] : ! [v163] : ! [v164] : ! [v165] : ! [v166] : ! [v167] : ! [v168] : ! [v169] : ( ~ (implies(v166, v167) = v168) | ~ (implies(v165, v168) = v169) | ~ (implies(v163, v164) = v166) | ~ (implies(v162, v164) = v167) | ~ (implies(v162, v163) = v165) | is_a_theorem(v169)))))
% 6.61/2.11 | 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 yields:
% 6.61/2.11 | (1) possibly(all_0_161_161) = all_0_160_160 & strict_implies(all_0_160_160, all_0_159_159) = all_0_158_158 & necessarily(all_0_160_160) = all_0_159_159 & 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 & ~ axiom_m10 & ~ is_a_theorem(all_0_158_158) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (or(v0, v1) = v5) | ~ (implies(v5, v2) = v6) | ~ (implies(v4, v6) = v7) | ~ (implies(v3, v7) = v8) | ~ (implies(v1, v2) = v4) | ~ (implies(v0, v2) = v3) | is_a_theorem(v8)) & ! [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) | ~ (implies(v0, v1) = v2) | is_a_theorem(v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (implies(v4, v5) = v6) | ~ (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v4) | ~ (implies(v0, v2) = v5) | ~ (implies(v0, v1) = v3) | is_a_theorem(v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (not(v1) = v2) | ~ (not(v0) = v3) | ~ (implies(v4, v5) = v6) | ~ (implies(v2, v3) = v4) | ~ (implies(v0, v1) = v5) | is_a_theorem(v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (equiv(v0, v1) = v4) | ~ (implies(v3, v4) = v5) | ~ (implies(v2, v5) = v6) | ~ (implies(v1, v0) = v3) | ~ (implies(v0, v1) = v2) | is_a_theorem(v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (strict_implies(v1, v0) = v3) | ~ (strict_implies(v0, v1) = v2) | ~ (and(v2, v3) = v4) | strict_equiv(v0, v1) = v4) & ! [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] : ( ~ (and(v2, v3) = v4) | ~ (implies(v1, v0) = v3) | ~ (implies(v0, v1) = v2) | equiv(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | ~ (implies(v0, v3) = v4) | is_a_theorem(v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equiv(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | ~ (implies(v1, v0) = v3) | is_a_theorem(v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equiv(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | ~ (implies(v0, v1) = v3) | is_a_theorem(v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (implies(v3, v2) = v4) | ~ (implies(v0, v2) = v3) | ~ (implies(v0, v1) = v2) | is_a_theorem(v4)) & ! [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] : ( ~ (possibly(v0) = v1) | ~ (necessarily(v1) = v2) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v0, v2) = v3) | is_a_theorem(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v2) = v3) | ~ (not(v1) = v2) | ? [v4] : (not(v3) = v4 & implies(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v1) = v3) | is_a_theorem(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | is_a_theorem(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (implies(v1, v0) = v2) | ~ (implies(v0, v2) = v3) | is_a_theorem(v3)) & ! [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) | ~ is_a_theorem(v2)) & ! [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(v0, v1) = v2) | ? [v3] : (necessarily(v3) = v2 & implies(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (necessarily(v0) = v1) | ~ (implies(v1, v0) = v2) | is_a_theorem(v2)) & ! [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] : ( ~ (equiv(v0, v1) = v2) | ? [v3] : ? [v4] : (and(v3, v4) = v2 & implies(v1, v0) = v4 & implies(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (implies(v0, v1) = v2) | ~ is_a_theorem(v2) | ~ is_a_theorem(v0) | is_a_theorem(v1)) & ! [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] : (strict_implies(v0, v1) = v3 & necessarily(v2) = v3)) & ! [v0] : ! [v1] : ( ~ (possibly(v0) = v1) | ? [v2] : ? [v3] : (necessarily(v2) = v3 & not(v3) = v1 & not(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (necessarily(v0) = v1) | ~ is_a_theorem(v0) | is_a_theorem(v1)) & ! [v0] : ! [v1] : ( ~ (not(v0) = v1) | ? [v2] : ? [v3] : (possibly(v0) = v2 & necessarily(v1) = v3 & not(v3) = v2)) & ( ~ 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_69_69 = all_0_70_70) & strict_equiv(all_0_70_70, all_0_69_69) = all_0_68_68 & is_a_theorem(all_0_68_68) & ~ substitution_strict_equiv) | (substitution_strict_equiv & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strict_equiv(v0, v1) = v2) | ~ is_a_theorem(v2)))) & ((possibly(all_0_78_78) = all_0_77_77 & necessarily(all_0_77_77) = all_0_76_76 & implies(all_0_78_78, all_0_76_76) = all_0_75_75 & ~ axiom_B & ~ is_a_theorem(all_0_75_75)) | (axiom_B & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (possibly(v0) = v1) | ~ (necessarily(v1) = v2) | ~ (implies(v0, v2) = v3) | is_a_theorem(v3)))) & ((possibly(all_0_95_95) = all_0_94_94 & possibly(all_0_96_96) = all_0_92_92 & possibly(all_0_97_97) = all_0_93_93 & strict_implies(all_0_94_94, all_0_91_91) = all_0_90_90 & and(all_0_93_93, all_0_92_92) = all_0_91_91 & and(all_0_97_97, all_0_96_96) = all_0_95_95 & ~ axiom_s2 & ~ is_a_theorem(all_0_90_90)) | (axiom_s2 & ! [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) | ~ (and(v0, v1) = v2) | is_a_theorem(v7)))) & ((possibly(all_0_105_105) = all_0_103_103 & possibly(all_0_106_106) = all_0_101_101 & strict_implies(all_0_102_102, all_0_100_100) = all_0_99_99 & strict_implies(all_0_104_104, all_0_99_99) = all_0_98_98 & strict_implies(all_0_106_106, all_0_105_105) = all_0_104_104 & not(all_0_101_101) = all_0_100_100 & not(all_0_103_103) = all_0_102_102 & ~ axiom_s3 & ~ is_a_theorem(all_0_98_98)) | (axiom_s3 & ! [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) | ~ (strict_implies(v0, v1) = v2) | ~ (not(v5) = v6) | ~ (not(v3) = v4) | is_a_theorem(v8)))) & ((possibly(all_0_141_141) = all_0_140_140 & strict_implies(all_0_141_141, all_0_140_140) = all_0_139_139 & ~ axiom_m6 & ~ is_a_theorem(all_0_139_139)) | (axiom_m6 & ! [v0] : ! [v1] : ! [v2] : ( ~ (possibly(v0) = v1) | ~ (strict_implies(v0, v1) = v2) | is_a_theorem(v2)))) & ((possibly(all_0_144_144) = all_0_143_143 & strict_implies(all_0_143_143, all_0_146_146) = all_0_142_142 & and(all_0_146_146, all_0_145_145) = all_0_144_144 & ~ axiom_m7 & ~ is_a_theorem(all_0_142_142)) | (axiom_m7 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (possibly(v2) = v3) | ~ (strict_implies(v3, v0) = v4) | ~ (and(v0, v1) = v2) | is_a_theorem(v4)))) & ((possibly(all_0_152_152) = all_0_149_149 & possibly(all_0_153_153) = all_0_150_150 & strict_implies(all_0_150_150, all_0_149_149) = all_0_148_148 & strict_implies(all_0_151_151, all_0_148_148) = all_0_147_147 & strict_implies(all_0_153_153, all_0_152_152) = all_0_151_151 & ~ axiom_m8 & ~ is_a_theorem(all_0_147_147)) | (axiom_m8 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (possibly(v1) = v4) | ~ (possibly(v0) = v3) | ~ (strict_implies(v3, v4) = v5) | ~ (strict_implies(v2, v5) = v6) | ~ (strict_implies(v0, v1) = v2) | is_a_theorem(v6)))) & ((possibly(all_0_156_156) = all_0_155_155 & possibly(all_0_157_157) = all_0_156_156 & strict_implies(all_0_155_155, all_0_156_156) = all_0_154_154 & ~ axiom_m9 & ~ is_a_theorem(all_0_154_154)) | (axiom_m9 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (possibly(v1) = v2) | ~ (possibly(v0) = v1) | ~ (strict_implies(v2, v1) = v3) | is_a_theorem(v3)))) & ((strict_implies(all_0_64_64, all_0_63_63) = all_0_62_62 & is_a_theorem(all_0_62_62) & is_a_theorem(all_0_64_64) & ~ modus_ponens_strict_implies & ~ is_a_theorem(all_0_63_63)) | (modus_ponens_strict_implies & ! [v0] : ! [v1] : ! [v2] : ( ~ (strict_implies(v0, v1) = v2) | ~ is_a_theorem(v2) | ~ is_a_theorem(v0) | is_a_theorem(v1)))) & ((strict_implies(all_0_109_109, all_0_108_108) = all_0_107_107 & necessarily(all_0_109_109) = all_0_108_108 & necessarily(all_0_110_110) = all_0_109_109 & ~ axiom_s4 & ~ is_a_theorem(all_0_107_107)) | (axiom_s4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (strict_implies(v1, v2) = v3) | ~ (necessarily(v1) = v2) | ~ (necessarily(v0) = v1) | is_a_theorem(v3)))) & ((strict_implies(all_0_113_113, all_0_112_112) = all_0_111_111 & and(all_0_114_114, all_0_115_115) = all_0_112_112 & and(all_0_115_115, all_0_114_114) = all_0_113_113 & ~ axiom_m1 & ~ is_a_theorem(all_0_111_111)) | (axiom_m1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (strict_implies(v2, v3) = v4) | ~ (and(v1, v0) = v3) | ~ (and(v0, v1) = v2) | is_a_theorem(v4)))) & ((strict_implies(all_0_117_117, all_0_119_119) = all_0_116_116 & and(all_0_119_119, all_0_118_118) = all_0_117_117 & ~ axiom_m2 & ~ is_a_theorem(all_0_116_116)) | (axiom_m2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (strict_implies(v2, v0) = v3) | ~ (and(v0, v1) = v2) | is_a_theorem(v3)))) & ((strict_implies(all_0_123_123, all_0_121_121) = all_0_120_120 & and(all_0_124_124, all_0_125_125) = all_0_123_123 & and(all_0_126_126, all_0_125_125) = all_0_122_122 & and(all_0_127_127, all_0_122_122) = all_0_121_121 & and(all_0_127_127, all_0_126_126) = all_0_124_124 & ~ axiom_m3 & ~ is_a_theorem(all_0_120_120)) | (axiom_m3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (strict_implies(v4, v6) = v7) | ~ (and(v3, v2) = v4) | ~ (and(v1, v2) = v5) | ~ (and(v0, v5) = v6) | ~ (and(v0, v1) = v3) | is_a_theorem(v7)))) & ((strict_implies(all_0_130_130, all_0_129_129) = all_0_128_128 & and(all_0_130_130, all_0_130_130) = all_0_129_129 & ~ axiom_m4 & ~ is_a_theorem(all_0_128_128)) | (axiom_m4 & ! [v0] : ! [v1] : ! [v2] : ( ~ (strict_implies(v0, v1) = v2) | ~ (and(v0, v0) = v1) | is_a_theorem(v2)))) & ((strict_implies(all_0_133_133, all_0_132_132) = all_0_131_131 & strict_implies(all_0_137_137, all_0_136_136) = all_0_134_134 & strict_implies(all_0_138_138, all_0_136_136) = all_0_132_132 & strict_implies(all_0_138_138, all_0_137_137) = all_0_135_135 & and(all_0_135_135, all_0_134_134) = all_0_133_133 & ~ axiom_m5 & ~ is_a_theorem(all_0_131_131)) | (axiom_m5 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (strict_implies(v5, v6) = v7) | ~ (strict_implies(v1, v2) = v4) | ~ (strict_implies(v0, v2) = v6) | ~ (strict_implies(v0, v1) = v3) | ~ (and(v3, v4) = v5) | is_a_theorem(v7)))) & ((necessarily(all_0_73_73) = all_0_72_72 & necessarily(all_0_74_74) = all_0_73_73 & implies(all_0_73_73, all_0_72_72) = all_0_71_71 & ~ axiom_4 & ~ is_a_theorem(all_0_71_71)) | (axiom_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (necessarily(v1) = v2) | ~ (necessarily(v0) = v1) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3)))) & ((necessarily(all_0_81_81) = all_0_80_80 & necessarily(all_0_84_84) = all_0_83_83 & necessarily(all_0_86_86) = all_0_85_85 & and(all_0_85_85, all_0_83_83) = all_0_82_82 & implies(all_0_82_82, all_0_80_80) = all_0_79_79 & implies(all_0_88_88, all_0_87_87) = all_0_84_84 & implies(all_0_89_89, all_0_87_87) = all_0_81_81 & implies(all_0_89_89, all_0_88_88) = all_0_86_86 & ~ axiom_s1 & ~ is_a_theorem(all_0_79_79)) | (axiom_s1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (necessarily(v8) = v9) | ~ (necessarily(v5) = v6) | ~ (necessarily(v3) = v4) | ~ (and(v4, v6) = v7) | ~ (implies(v7, v9) = v10) | ~ (implies(v1, v2) = v5) | ~ (implies(v0, v2) = v8) | ~ (implies(v0, v1) = v3) | is_a_theorem(v10)))) & ((or(all_0_36_36, all_0_36_36) = all_0_35_35 & implies(all_0_35_35, all_0_36_36) = all_0_34_34 & ~ r1 & ~ is_a_theorem(all_0_34_34)) | (r1 & ! [v0] : ! [v1] : ! [v2] : ( ~ (or(v0, v0) = v1) | ~ (implies(v1, v0) = v2) | is_a_theorem(v2)))) & ((or(all_0_40_40, all_0_39_39) = all_0_38_38 & implies(all_0_39_39, all_0_38_38) = all_0_37_37 & ~ r2 & ~ is_a_theorem(all_0_37_37)) | (r2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3)))) & ((or(all_0_44_44, all_0_45_45) = all_0_42_42 & or(all_0_45_45, all_0_44_44) = all_0_43_43 & implies(all_0_43_43, all_0_42_42) = all_0_41_41 & ~ r3 & ~ is_a_theorem(all_0_41_41)) | (r3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (or(v1, v0) = v3) | ~ (or(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | is_a_theorem(v4)))) & ((or(all_0_52_52, all_0_48_48) = all_0_47_47 & or(all_0_52_52, all_0_51_51) = all_0_50_50 & or(all_0_53_53, all_0_50_50) = all_0_49_49 & or(all_0_53_53, all_0_51_51) = all_0_48_48 & implies(all_0_49_49, all_0_47_47) = all_0_46_46 & ~ r4 & ~ is_a_theorem(all_0_46_46)) | (r4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (or(v1, v5) = v6) | ~ (or(v1, v2) = v3) | ~ (or(v0, v3) = v4) | ~ (or(v0, v2) = v5) | ~ (implies(v4, v6) = v7) | is_a_theorem(v7)))) & ((or(all_0_61_61, all_0_59_59) = all_0_56_56 & or(all_0_61_61, all_0_60_60) = all_0_57_57 & implies(all_0_57_57, all_0_56_56) = all_0_55_55 & implies(all_0_58_58, all_0_55_55) = all_0_54_54 & implies(all_0_60_60, all_0_59_59) = all_0_58_58 & ~ r5 & ~ is_a_theorem(all_0_54_54)) | (r5 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (or(v0, v2) = v5) | ~ (or(v0, v1) = v4) | ~ (implies(v4, v5) = v6) | ~ (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v3) | is_a_theorem(v7)))) & ((and(all_0_2_2, all_0_2_2) = all_0_1_1 & implies(all_0_2_2, all_0_1_1) = all_0_0_0 & ~ kn1 & ~ is_a_theorem(all_0_0_0)) | (kn1 & ! [v0] : ! [v1] : ! [v2] : ( ~ (and(v0, v0) = v1) | ~ (implies(v0, v1) = v2) | is_a_theorem(v2)))) & ((and(all_0_6_6, all_0_5_5) = all_0_4_4 & implies(all_0_4_4, all_0_6_6) = all_0_3_3 & ~ kn2 & ~ is_a_theorem(all_0_3_3)) | (kn2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | is_a_theorem(v3)))) & ((and(all_0_14_14, all_0_16_16) = all_0_10_10 & and(all_0_15_15, all_0_14_14) = all_0_12_12 & not(all_0_10_10) = all_0_9_9 & not(all_0_12_12) = all_0_11_11 & implies(all_0_11_11, all_0_9_9) = all_0_8_8 & implies(all_0_13_13, all_0_8_8) = all_0_7_7 & implies(all_0_16_16, all_0_15_15) = all_0_13_13 & ~ kn3 & ~ is_a_theorem(all_0_7_7)) | (kn3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (and(v2, v0) = v6) | ~ (and(v1, v2) = v4) | ~ (not(v6) = v7) | ~ (not(v4) = v5) | ~ (implies(v5, v7) = v8) | ~ (implies(v3, v8) = v9) | ~ (implies(v0, v1) = v3) | is_a_theorem(v9)))) & ((and(all_0_67_67, all_0_66_66) = all_0_65_65 & is_a_theorem(all_0_66_66) & is_a_theorem(all_0_67_67) & ~ adjunction & ~ is_a_theorem(all_0_65_65)) | (adjunction & ! [v0] : ! [v1] : ! [v2] : ( ~ (and(v0, v1) = v2) | ~ is_a_theorem(v1) | ~ is_a_theorem(v0) | is_a_theorem(v2)))) & ((not(all_0_29_29) = all_0_27_27 & implies(all_0_27_27, all_0_28_28) = all_0_26_26 & implies(all_0_29_29, all_0_26_26) = all_0_25_25 & ~ cn2 & ~ is_a_theorem(all_0_25_25)) | (cn2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (not(v0) = v2) | ~ (implies(v2, v1) = v3) | ~ (implies(v0, v3) = v4) | is_a_theorem(v4)))) & ((not(all_0_33_33) = all_0_32_32 & implies(all_0_31_31, all_0_33_33) = all_0_30_30 & implies(all_0_32_32, all_0_33_33) = all_0_31_31 & ~ cn3 & ~ is_a_theorem(all_0_30_30)) | (cn3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (not(v0) = v1) | ~ (implies(v2, v0) = v3) | ~ (implies(v1, v0) = v2) | is_a_theorem(v3)))) & ((implies(all_0_20_20, all_0_19_19) = all_0_18_18 & implies(all_0_21_21, all_0_18_18) = all_0_17_17 & implies(all_0_23_23, all_0_22_22) = all_0_20_20 & implies(all_0_24_24, all_0_22_22) = all_0_19_19 & implies(all_0_24_24, all_0_23_23) = all_0_21_21 & ~ cn1 & ~ is_a_theorem(all_0_17_17)) | (cn1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (implies(v4, v5) = v6) | ~ (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v4) | ~ (implies(v0, v2) = v5) | ~ (implies(v0, v1) = v3) | is_a_theorem(v7))))
% 6.67/2.14 |
% 6.67/2.14 | Applying alpha-rule on (1) yields:
% 6.67/2.14 | (2) or_2
% 6.67/2.14 | (3) (and(all_0_67_67, all_0_66_66) = all_0_65_65 & is_a_theorem(all_0_66_66) & is_a_theorem(all_0_67_67) & ~ adjunction & ~ is_a_theorem(all_0_65_65)) | (adjunction & ! [v0] : ! [v1] : ! [v2] : ( ~ (and(v0, v1) = v2) | ~ is_a_theorem(v1) | ~ is_a_theorem(v0) | is_a_theorem(v2)))
% 6.67/2.14 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (implies(v0, v1) = v2) | ? [v3] : ? [v4] : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) = v3))
% 6.67/2.14 | (5) op_implies_and
% 6.67/2.14 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (necessarily(v0) = v1) | ~ (implies(v1, v0) = v2) | is_a_theorem(v2))
% 6.67/2.14 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v0, v2) = v3) | is_a_theorem(v3))
% 6.67/2.14 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (not(v1) = v2) | ~ (not(v0) = v3) | ~ (implies(v4, v5) = v6) | ~ (implies(v2, v3) = v4) | ~ (implies(v0, v1) = v5) | is_a_theorem(v6))
% 6.67/2.14 | (9) (and(all_0_6_6, all_0_5_5) = all_0_4_4 & implies(all_0_4_4, all_0_6_6) = all_0_3_3 & ~ kn2 & ~ is_a_theorem(all_0_3_3)) | (kn2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | is_a_theorem(v3)))
% 6.67/2.14 | (10) op_strict_equiv
% 6.67/2.14 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v2, v3) = v4) | ~ (implies(v1, v0) = v3) | ~ (implies(v0, v1) = v2) | equiv(v0, v1) = v4)
% 6.67/2.14 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (implies(v0, v1) = v2) | ? [v3] : (strict_implies(v0, v1) = v3 & necessarily(v2) = v3))
% 6.67/2.14 | (13) ~ is_a_theorem(all_0_158_158)
% 6.67/2.14 | (14) axiom_K
% 6.67/2.14 | (15) or_3
% 6.67/2.14 | (16) (or(all_0_52_52, all_0_48_48) = all_0_47_47 & or(all_0_52_52, all_0_51_51) = all_0_50_50 & or(all_0_53_53, all_0_50_50) = all_0_49_49 & or(all_0_53_53, all_0_51_51) = all_0_48_48 & implies(all_0_49_49, all_0_47_47) = all_0_46_46 & ~ r4 & ~ is_a_theorem(all_0_46_46)) | (r4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (or(v1, v5) = v6) | ~ (or(v1, v2) = v3) | ~ (or(v0, v3) = v4) | ~ (or(v0, v2) = v5) | ~ (implies(v4, v6) = v7) | is_a_theorem(v7)))
% 6.67/2.14 | (17) (strict_implies(all_0_117_117, all_0_119_119) = all_0_116_116 & and(all_0_119_119, all_0_118_118) = all_0_117_117 & ~ axiom_m2 & ~ is_a_theorem(all_0_116_116)) | (axiom_m2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (strict_implies(v2, v0) = v3) | ~ (and(v0, v1) = v2) | is_a_theorem(v3)))
% 6.67/2.14 | (18) possibly(all_0_161_161) = all_0_160_160
% 6.67/2.14 | (19) (possibly(all_0_95_95) = all_0_94_94 & possibly(all_0_96_96) = all_0_92_92 & possibly(all_0_97_97) = all_0_93_93 & strict_implies(all_0_94_94, all_0_91_91) = all_0_90_90 & and(all_0_93_93, all_0_92_92) = all_0_91_91 & and(all_0_97_97, all_0_96_96) = all_0_95_95 & ~ axiom_s2 & ~ is_a_theorem(all_0_90_90)) | (axiom_s2 & ! [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) | ~ (and(v0, v1) = v2) | is_a_theorem(v7)))
% 6.67/2.14 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equiv(v0, v1) = v2) | ~ is_a_theorem(v2))
% 6.67/2.14 | (21) (or(all_0_40_40, all_0_39_39) = all_0_38_38 & implies(all_0_39_39, all_0_38_38) = all_0_37_37 & ~ r2 & ~ is_a_theorem(all_0_37_37)) | (r2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3)))
% 6.67/2.14 | (22) necessitation
% 6.67/2.14 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0))
% 6.67/2.14 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (or(v3, v2) = v1) | ~ (or(v3, v2) = v0))
% 6.67/2.14 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strict_equiv(v3, v2) = v1) | ~ (strict_equiv(v3, v2) = v0))
% 6.67/2.14 | (26) equivalence_2
% 6.67/2.14 | (27) (strict_implies(all_0_123_123, all_0_121_121) = all_0_120_120 & and(all_0_124_124, all_0_125_125) = all_0_123_123 & and(all_0_126_126, all_0_125_125) = all_0_122_122 & and(all_0_127_127, all_0_122_122) = all_0_121_121 & and(all_0_127_127, all_0_126_126) = all_0_124_124 & ~ axiom_m3 & ~ is_a_theorem(all_0_120_120)) | (axiom_m3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (strict_implies(v4, v6) = v7) | ~ (and(v3, v2) = v4) | ~ (and(v1, v2) = v5) | ~ (and(v0, v5) = v6) | ~ (and(v0, v1) = v3) | is_a_theorem(v7)))
% 6.67/2.14 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v2) = v3) | ~ (not(v1) = v2) | ? [v4] : (not(v3) = v4 & implies(v0, v1) = v4))
% 6.67/2.14 | (29) (or(all_0_36_36, all_0_36_36) = all_0_35_35 & implies(all_0_35_35, all_0_36_36) = all_0_34_34 & ~ r1 & ~ is_a_theorem(all_0_34_34)) | (r1 & ! [v0] : ! [v1] : ! [v2] : ( ~ (or(v0, v0) = v1) | ~ (implies(v1, v0) = v2) | is_a_theorem(v2)))
% 6.67/2.15 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equiv(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | ~ (implies(v0, v1) = v3) | is_a_theorem(v4))
% 6.67/2.15 | (31) op_strict_implies
% 6.67/2.15 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (or(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (and(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3))
% 6.67/2.15 | (33) necessarily(all_0_160_160) = all_0_159_159
% 6.67/2.15 | (34) (possibly(all_0_105_105) = all_0_103_103 & possibly(all_0_106_106) = all_0_101_101 & strict_implies(all_0_102_102, all_0_100_100) = all_0_99_99 & strict_implies(all_0_104_104, all_0_99_99) = all_0_98_98 & strict_implies(all_0_106_106, all_0_105_105) = all_0_104_104 & not(all_0_101_101) = all_0_100_100 & not(all_0_103_103) = all_0_102_102 & ~ axiom_s3 & ~ is_a_theorem(all_0_98_98)) | (axiom_s3 & ! [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) | ~ (strict_implies(v0, v1) = v2) | ~ (not(v5) = v6) | ~ (not(v3) = v4) | is_a_theorem(v8)))
% 6.67/2.15 | (35) op_or
% 6.67/2.15 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (equiv(v0, v1) = v4) | ~ (implies(v3, v4) = v5) | ~ (implies(v2, v5) = v6) | ~ (implies(v1, v0) = v3) | ~ (implies(v0, v1) = v2) | is_a_theorem(v6))
% 6.67/2.15 | (37) modus_ponens
% 6.67/2.15 | (38) and_3
% 6.67/2.15 | (39) (strict_implies(all_0_133_133, all_0_132_132) = all_0_131_131 & strict_implies(all_0_137_137, all_0_136_136) = all_0_134_134 & strict_implies(all_0_138_138, all_0_136_136) = all_0_132_132 & strict_implies(all_0_138_138, all_0_137_137) = all_0_135_135 & and(all_0_135_135, all_0_134_134) = all_0_133_133 & ~ axiom_m5 & ~ is_a_theorem(all_0_131_131)) | (axiom_m5 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (strict_implies(v5, v6) = v7) | ~ (strict_implies(v1, v2) = v4) | ~ (strict_implies(v0, v2) = v6) | ~ (strict_implies(v0, v1) = v3) | ~ (and(v3, v4) = v5) | is_a_theorem(v7)))
% 6.67/2.15 | (40) ! [v0] : ! [v1] : ( ~ (necessarily(v0) = v1) | ~ is_a_theorem(v0) | is_a_theorem(v1))
% 6.67/2.15 | (41) modus_tollens
% 6.67/2.15 | (42) equivalence_1
% 6.67/2.15 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (equiv(v0, v1) = v2) | ? [v3] : ? [v4] : (and(v3, v4) = v2 & implies(v1, v0) = v4 & implies(v0, v1) = v3))
% 6.67/2.15 | (44) (possibly(all_0_152_152) = all_0_149_149 & possibly(all_0_153_153) = all_0_150_150 & strict_implies(all_0_150_150, all_0_149_149) = all_0_148_148 & strict_implies(all_0_151_151, all_0_148_148) = all_0_147_147 & strict_implies(all_0_153_153, all_0_152_152) = all_0_151_151 & ~ axiom_m8 & ~ is_a_theorem(all_0_147_147)) | (axiom_m8 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (possibly(v1) = v4) | ~ (possibly(v0) = v3) | ~ (strict_implies(v3, v4) = v5) | ~ (strict_implies(v2, v5) = v6) | ~ (strict_implies(v0, v1) = v2) | is_a_theorem(v6)))
% 6.67/2.15 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v2, v3) = v4) | ~ (not(v1) = v3) | ~ (not(v0) = v2) | ? [v5] : (or(v0, v1) = v5 & not(v4) = v5))
% 6.67/2.15 | (46) ! [v0] : ! [v1] : ( ~ (not(v0) = v1) | ? [v2] : ? [v3] : (possibly(v0) = v2 & necessarily(v1) = v3 & not(v3) = v2))
% 6.67/2.15 | (47) ~ 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)))
% 6.67/2.15 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (necessarily(v2) = v1) | ~ (necessarily(v2) = v0))
% 6.67/2.15 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (strict_equiv(v0, v1) = v2) | ? [v3] : ? [v4] : (strict_implies(v1, v0) = v4 & strict_implies(v0, v1) = v3 & and(v3, v4) = v2))
% 6.67/2.15 | (50) implies_1
% 6.67/2.15 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strict_implies(v3, v2) = v1) | ~ (strict_implies(v3, v2) = v0))
% 6.67/2.15 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (not(v2) = v1) | ~ (not(v2) = v0))
% 6.67/2.15 | (53) (possibly(all_0_141_141) = all_0_140_140 & strict_implies(all_0_141_141, all_0_140_140) = all_0_139_139 & ~ axiom_m6 & ~ is_a_theorem(all_0_139_139)) | (axiom_m6 & ! [v0] : ! [v1] : ! [v2] : ( ~ (possibly(v0) = v1) | ~ (strict_implies(v0, v1) = v2) | is_a_theorem(v2)))
% 6.67/2.15 | (54) and_1
% 6.67/2.16 | (55) (and(all_0_2_2, all_0_2_2) = all_0_1_1 & implies(all_0_2_2, all_0_1_1) = all_0_0_0 & ~ kn1 & ~ is_a_theorem(all_0_0_0)) | (kn1 & ! [v0] : ! [v1] : ! [v2] : ( ~ (and(v0, v0) = v1) | ~ (implies(v0, v1) = v2) | is_a_theorem(v2)))
% 6.67/2.16 | (56) (strict_implies(all_0_64_64, all_0_63_63) = all_0_62_62 & is_a_theorem(all_0_62_62) & is_a_theorem(all_0_64_64) & ~ modus_ponens_strict_implies & ~ is_a_theorem(all_0_63_63)) | (modus_ponens_strict_implies & ! [v0] : ! [v1] : ! [v2] : ( ~ (strict_implies(v0, v1) = v2) | ~ is_a_theorem(v2) | ~ is_a_theorem(v0) | is_a_theorem(v1)))
% 6.67/2.16 | (57) (not(all_0_29_29) = all_0_27_27 & implies(all_0_27_27, all_0_28_28) = all_0_26_26 & implies(all_0_29_29, all_0_26_26) = all_0_25_25 & ~ cn2 & ~ is_a_theorem(all_0_25_25)) | (cn2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (not(v0) = v2) | ~ (implies(v2, v1) = v3) | ~ (implies(v0, v3) = v4) | is_a_theorem(v4)))
% 6.67/2.16 | (58) op_equiv
% 6.67/2.16 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (or(v0, v1) = v5) | ~ (implies(v5, v2) = v6) | ~ (implies(v4, v6) = v7) | ~ (implies(v3, v7) = v8) | ~ (implies(v1, v2) = v4) | ~ (implies(v0, v2) = v3) | is_a_theorem(v8))
% 6.67/2.16 | (60) ~ axiom_m10
% 6.67/2.16 | (61) axiom_5
% 6.67/2.16 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equiv(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | ~ (implies(v1, v0) = v3) | is_a_theorem(v4))
% 6.67/2.16 | (63) (possibly(all_0_156_156) = all_0_155_155 & possibly(all_0_157_157) = all_0_156_156 & strict_implies(all_0_155_155, all_0_156_156) = all_0_154_154 & ~ axiom_m9 & ~ is_a_theorem(all_0_154_154)) | (axiom_m9 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (possibly(v1) = v2) | ~ (possibly(v0) = v1) | ~ (strict_implies(v2, v1) = v3) | is_a_theorem(v3)))
% 6.67/2.16 | (64) (possibly(all_0_144_144) = all_0_143_143 & strict_implies(all_0_143_143, all_0_146_146) = all_0_142_142 & and(all_0_146_146, all_0_145_145) = all_0_144_144 & ~ axiom_m7 & ~ is_a_theorem(all_0_142_142)) | (axiom_m7 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (possibly(v2) = v3) | ~ (strict_implies(v3, v0) = v4) | ~ (and(v0, v1) = v2) | is_a_theorem(v4)))
% 6.67/2.16 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (implies(v1, v0) = v2) | ~ (implies(v0, v2) = v3) | is_a_theorem(v3))
% 6.67/2.16 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (strict_implies(v1, v0) = v3) | ~ (strict_implies(v0, v1) = v2) | ~ (and(v2, v3) = v4) | strict_equiv(v0, v1) = v4)
% 6.67/2.16 | (67) ~ 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)))
% 6.67/2.16 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (strict_implies(v0, v1) = v2) | ? [v3] : (necessarily(v3) = v2 & implies(v0, v1) = v3))
% 6.67/2.16 | (69) implies_2
% 6.67/2.16 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (implies(v4, v5) = v6) | ~ (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v4) | ~ (implies(v0, v2) = v5) | ~ (implies(v0, v1) = v3) | is_a_theorem(v7))
% 6.67/2.16 | (71) axiom_M
% 6.67/2.16 | (72) ! [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) | ~ (implies(v0, v1) = v2) | is_a_theorem(v7))
% 6.67/2.16 | (73) and_2
% 6.67/2.16 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (possibly(v0) = v1) | ~ (necessarily(v1) = v2) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3))
% 6.67/2.16 | (75) (and(all_0_14_14, all_0_16_16) = all_0_10_10 & and(all_0_15_15, all_0_14_14) = all_0_12_12 & not(all_0_10_10) = all_0_9_9 & not(all_0_12_12) = all_0_11_11 & implies(all_0_11_11, all_0_9_9) = all_0_8_8 & implies(all_0_13_13, all_0_8_8) = all_0_7_7 & implies(all_0_16_16, all_0_15_15) = all_0_13_13 & ~ kn3 & ~ is_a_theorem(all_0_7_7)) | (kn3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (and(v2, v0) = v6) | ~ (and(v1, v2) = v4) | ~ (not(v6) = v7) | ~ (not(v4) = v5) | ~ (implies(v5, v7) = v8) | ~ (implies(v3, v8) = v9) | ~ (implies(v0, v1) = v3) | is_a_theorem(v9)))
% 6.67/2.16 | (76) (possibly(all_0_78_78) = all_0_77_77 & necessarily(all_0_77_77) = all_0_76_76 & implies(all_0_78_78, all_0_76_76) = all_0_75_75 & ~ axiom_B & ~ is_a_theorem(all_0_75_75)) | (axiom_B & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (possibly(v0) = v1) | ~ (necessarily(v1) = v2) | ~ (implies(v0, v2) = v3) | is_a_theorem(v3)))
% 6.67/2.16 | (77) (strict_implies(all_0_109_109, all_0_108_108) = all_0_107_107 & necessarily(all_0_109_109) = all_0_108_108 & necessarily(all_0_110_110) = all_0_109_109 & ~ axiom_s4 & ~ is_a_theorem(all_0_107_107)) | (axiom_s4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (strict_implies(v1, v2) = v3) | ~ (necessarily(v1) = v2) | ~ (necessarily(v0) = v1) | is_a_theorem(v3)))
% 6.67/2.16 | (78) (not(all_0_33_33) = all_0_32_32 & implies(all_0_31_31, all_0_33_33) = all_0_30_30 & implies(all_0_32_32, all_0_33_33) = all_0_31_31 & ~ cn3 & ~ is_a_theorem(all_0_30_30)) | (cn3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (not(v0) = v1) | ~ (implies(v2, v0) = v3) | ~ (implies(v1, v0) = v2) | is_a_theorem(v3)))
% 6.67/2.16 | (79) implies_3
% 6.67/2.16 | (80) (necessarily(all_0_81_81) = all_0_80_80 & necessarily(all_0_84_84) = all_0_83_83 & necessarily(all_0_86_86) = all_0_85_85 & and(all_0_85_85, all_0_83_83) = all_0_82_82 & implies(all_0_82_82, all_0_80_80) = all_0_79_79 & implies(all_0_88_88, all_0_87_87) = all_0_84_84 & implies(all_0_89_89, all_0_87_87) = all_0_81_81 & implies(all_0_89_89, all_0_88_88) = all_0_86_86 & ~ axiom_s1 & ~ is_a_theorem(all_0_79_79)) | (axiom_s1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (necessarily(v8) = v9) | ~ (necessarily(v5) = v6) | ~ (necessarily(v3) = v4) | ~ (and(v4, v6) = v7) | ~ (implies(v7, v9) = v10) | ~ (implies(v1, v2) = v5) | ~ (implies(v0, v2) = v8) | ~ (implies(v0, v1) = v3) | is_a_theorem(v10)))
% 6.67/2.16 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3))
% 6.67/2.16 | (82) strict_implies(all_0_160_160, all_0_159_159) = all_0_158_158
% 6.67/2.16 | (83) ( ~ (all_0_69_69 = all_0_70_70) & strict_equiv(all_0_70_70, all_0_69_69) = all_0_68_68 & is_a_theorem(all_0_68_68) & ~ substitution_strict_equiv) | (substitution_strict_equiv & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strict_equiv(v0, v1) = v2) | ~ is_a_theorem(v2)))
% 6.67/2.16 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) = v0))
% 6.67/2.16 | (85) ~ 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)))
% 6.67/2.16 | (86) (implies(all_0_20_20, all_0_19_19) = all_0_18_18 & implies(all_0_21_21, all_0_18_18) = all_0_17_17 & implies(all_0_23_23, all_0_22_22) = all_0_20_20 & implies(all_0_24_24, all_0_22_22) = all_0_19_19 & implies(all_0_24_24, all_0_23_23) = all_0_21_21 & ~ cn1 & ~ is_a_theorem(all_0_17_17)) | (cn1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (implies(v4, v5) = v6) | ~ (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v4) | ~ (implies(v0, v2) = v5) | ~ (implies(v0, v1) = v3) | is_a_theorem(v7)))
% 6.67/2.17 | (87) (or(all_0_44_44, all_0_45_45) = all_0_42_42 & or(all_0_45_45, all_0_44_44) = all_0_43_43 & implies(all_0_43_43, all_0_42_42) = all_0_41_41 & ~ r3 & ~ is_a_theorem(all_0_41_41)) | (r3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (or(v1, v0) = v3) | ~ (or(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | is_a_theorem(v4)))
% 6.67/2.17 | (88) op_possibly
% 6.67/2.17 | (89) (necessarily(all_0_73_73) = all_0_72_72 & necessarily(all_0_74_74) = all_0_73_73 & implies(all_0_73_73, all_0_72_72) = all_0_71_71 & ~ axiom_4 & ~ is_a_theorem(all_0_71_71)) | (axiom_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (necessarily(v1) = v2) | ~ (necessarily(v0) = v1) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3)))
% 6.67/2.17 | (90) substitution_of_equivalents
% 6.67/2.17 | (91) or_1
% 6.67/2.17 | (92) equivalence_3
% 6.67/2.17 | (93) (strict_implies(all_0_113_113, all_0_112_112) = all_0_111_111 & and(all_0_114_114, all_0_115_115) = all_0_112_112 & and(all_0_115_115, all_0_114_114) = all_0_113_113 & ~ axiom_m1 & ~ is_a_theorem(all_0_111_111)) | (axiom_m1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (strict_implies(v2, v3) = v4) | ~ (and(v1, v0) = v3) | ~ (and(v0, v1) = v2) | is_a_theorem(v4)))
% 6.67/2.17 | (94) (or(all_0_61_61, all_0_59_59) = all_0_56_56 & or(all_0_61_61, all_0_60_60) = all_0_57_57 & implies(all_0_57_57, all_0_56_56) = all_0_55_55 & implies(all_0_58_58, all_0_55_55) = all_0_54_54 & implies(all_0_60_60, all_0_59_59) = all_0_58_58 & ~ r5 & ~ is_a_theorem(all_0_54_54)) | (r5 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (or(v0, v2) = v5) | ~ (or(v0, v1) = v4) | ~ (implies(v4, v5) = v6) | ~ (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v3) | is_a_theorem(v7)))
% 6.67/2.17 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | is_a_theorem(v3))
% 6.67/2.17 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v1) = v3) | is_a_theorem(v3))
% 6.67/2.17 | (97) ! [v0] : ! [v1] : ( ~ (possibly(v0) = v1) | ? [v2] : ? [v3] : (necessarily(v2) = v3 & not(v3) = v1 & not(v0) = v2))
% 6.67/2.17 | (98) (strict_implies(all_0_130_130, all_0_129_129) = all_0_128_128 & and(all_0_130_130, all_0_130_130) = all_0_129_129 & ~ axiom_m4 & ~ is_a_theorem(all_0_128_128)) | (axiom_m4 & ! [v0] : ! [v1] : ! [v2] : ( ~ (strict_implies(v0, v1) = v2) | ~ (and(v0, v0) = v1) | is_a_theorem(v2)))
% 6.67/2.17 | (99) op_implies
% 6.67/2.17 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0))
% 6.67/2.17 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | ~ (implies(v0, v3) = v4) | is_a_theorem(v4))
% 6.67/2.17 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (implies(v3, v2) = v4) | ~ (implies(v0, v2) = v3) | ~ (implies(v0, v1) = v2) | is_a_theorem(v4))
% 6.67/2.17 | (103) ! [v0] : ! [v1] : ! [v2] : ( ~ (implies(v0, v1) = v2) | ~ is_a_theorem(v2) | ~ is_a_theorem(v0) | is_a_theorem(v1))
% 6.67/2.17 | (104) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (possibly(v2) = v1) | ~ (possibly(v2) = v0))
% 6.67/2.17 |
% 6.67/2.17 | Instantiating formula (68) with all_0_158_158, all_0_159_159, all_0_160_160 and discharging atoms strict_implies(all_0_160_160, all_0_159_159) = all_0_158_158, yields:
% 6.67/2.17 | (105) ? [v0] : (necessarily(v0) = all_0_158_158 & implies(all_0_160_160, all_0_159_159) = v0)
% 6.67/2.17 |
% 6.67/2.17 | Instantiating (105) with all_8_0_162 yields:
% 6.67/2.17 | (106) necessarily(all_8_0_162) = all_0_158_158 & implies(all_0_160_160, all_0_159_159) = all_8_0_162
% 6.67/2.17 |
% 6.67/2.17 | Applying alpha-rule on (106) yields:
% 6.67/2.17 | (107) necessarily(all_8_0_162) = all_0_158_158
% 6.67/2.17 | (108) implies(all_0_160_160, all_0_159_159) = all_8_0_162
% 6.67/2.17 |
% 6.67/2.17 | Instantiating formula (74) with all_8_0_162, all_0_159_159, all_0_160_160, all_0_161_161 and discharging atoms possibly(all_0_161_161) = all_0_160_160, necessarily(all_0_160_160) = all_0_159_159, implies(all_0_160_160, all_0_159_159) = all_8_0_162, yields:
% 6.67/2.17 | (109) is_a_theorem(all_8_0_162)
% 6.67/2.17 |
% 6.67/2.17 | Instantiating formula (40) with all_0_158_158, all_8_0_162 and discharging atoms necessarily(all_8_0_162) = all_0_158_158, is_a_theorem(all_8_0_162), ~ is_a_theorem(all_0_158_158), yields:
% 6.67/2.17 | (110) $false
% 6.67/2.17 |
% 6.67/2.17 |-The branch is then unsatisfiable
% 6.67/2.17 % SZS output end Proof for theBenchmark
% 6.67/2.17
% 6.67/2.17 1583ms
%------------------------------------------------------------------------------