%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : LCL488+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n018.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 09:36:47 EDT 2022

% Result   : Theorem 27.55s 8.93s
% Output   : Proof 38.66s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : LCL488+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n018.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 04:57:34 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.47/0.62          ____       _                          
% 0.47/0.62    ___  / __ \_____(_)___  ________  __________
% 0.47/0.62   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.47/0.62  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.47/0.62  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.47/0.62  
% 0.47/0.62  A Theorem Prover for First-Order Logic
% 0.47/0.62  (ePrincess v.1.0)
% 0.47/0.62  
% 0.47/0.62  (c) Philipp Rümmer, 2009-2015
% 0.47/0.62  (c) Peter Backeman, 2014-2015
% 0.47/0.62  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.47/0.62  Free software under GNU Lesser General Public License (LGPL).
% 0.47/0.62  Bug reports to peter@backeman.se
% 0.47/0.62  
% 0.47/0.62  For more information, visit http://user.uu.se/~petba168/breu/
% 0.47/0.62  
% 0.47/0.62  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.67  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.87/1.02  Prover 0: Preprocessing ...
% 3.23/1.39  Prover 0: Constructing countermodel ...
% 17.02/5.96  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 17.20/6.02  Prover 1: Preprocessing ...
% 17.80/6.16  Prover 1: Constructing countermodel ...
% 25.92/8.56  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 25.92/8.60  Prover 2: Preprocessing ...
% 26.42/8.71  Prover 2: Warning: ignoring some quantifiers
% 26.42/8.71  Prover 2: Constructing countermodel ...
% 27.55/8.93  Prover 2: proved (368ms)
% 27.55/8.93  Prover 1: stopped
% 27.55/8.93  Prover 0: stopped
% 27.55/8.93  
% 27.55/8.93  No countermodel exists, formula is valid
% 27.55/8.93  % SZS status Theorem for theBenchmark
% 27.55/8.93  
% 27.55/8.93  Generating proof ... Warning: ignoring some quantifiers
% 37.96/12.17  found it (size 167)
% 37.96/12.17  
% 37.96/12.17  % SZS output start Proof for theBenchmark
% 37.96/12.17  Assumed formulas after preprocessing and simplification: 
% 37.96/12.17  | (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] : ( ~ (v90 = 0) & and(v86, v87) = v88 & implies(v88, v87) = v89 & is_a_theorem(v89) = v90 & op_equiv & op_implies_or & op_implies_and & op_and & op_or & r5 & r4 & r3 & r2 & r1 & substitution_of_equivalents & modus_ponens &  ~ and_2 &  ! [v124] :  ! [v125] :  ! [v126] :  ! [v127] :  ! [v128] :  ! [v129] : ( ~ (or(v124, v126) = v128) |  ~ (or(v124, v125) = v127) |  ~ (implies(v127, v128) = v129) |  ? [v130] :  ? [v131] : (implies(v130, v129) = v131 & implies(v125, v126) = v130 & is_a_theorem(v131) = 0)) &  ! [v124] :  ! [v125] :  ! [v126] :  ! [v127] :  ! [v128] : ( ~ (or(v126, v127) = v128) |  ~ (not(v125) = v127) |  ~ (not(v124) = v126) |  ? [v129] : (and(v124, v125) = v129 & not(v128) = v129)) &  ! [v124] :  ! [v125] :  ! [v126] :  ! [v127] :  ! [v128] : ( ~ (or(v125, v127) = v128) |  ~ (or(v124, v126) = v127) |  ? [v129] :  ? [v130] :  ? [v131] : (or(v125, v126) = v129 & or(v124, v129) = v130 & implies(v130, v128) = v131 & is_a_theorem(v131) = 0)) &  ! [v124] :  ! [v125] :  ! [v126] :  ! [v127] :  ! [v128] : ( ~ (or(v125, v126) = v127) |  ~ (or(v124, v127) = v128) |  ? [v129] :  ? [v130] :  ? [v131] : (or(v125, v129) = v130 & or(v124, v126) = v129 & implies(v128, v130) = v131 & is_a_theorem(v131) = 0)) &  ! [v124] :  ! [v125] :  ! [v126] :  ! [v127] :  ! [v128] : ( ~ (and(v126, v127) = v128) |  ~ (not(v125) = v127) |  ~ (not(v124) = v126) |  ? [v129] : (or(v124, v125) = v129 & not(v128) = v129)) &  ! [v124] :  ! [v125] :  ! [v126] :  ! [v127] : (v125 = v124 |  ~ (or(v127, v126) = v125) |  ~ (or(v127, v126) = v124)) &  ! [v124] :  ! [v125] :  ! [v126] :  ! [v127] : (v125 = v124 |  ~ (and(v127, v126) = v125) |  ~ (and(v127, v126) = v124)) &  ! [v124] :  ! [v125] :  ! [v126] :  ! [v127] : (v125 = v124 |  ~ (equiv(v127, v126) = v125) |  ~ (equiv(v127, v126) = v124)) &  ! [v124] :  ! [v125] :  ! [v126] :  ! [v127] : (v125 = v124 |  ~ (implies(v127, v126) = v125) |  ~ (implies(v127, v126) = v124)) &  ! [v124] :  ! [v125] :  ! [v126] :  ! [v127] : ( ~ (or(v126, v125) = v127) |  ~ (not(v124) = v126) | implies(v124, v125) = v127) &  ! [v124] :  ! [v125] :  ! [v126] :  ! [v127] : ( ~ (and(v124, v126) = v127) |  ~ (not(v125) = v126) |  ? [v128] : (not(v127) = v128 & implies(v124, v125) = v128)) &  ! [v124] :  ! [v125] :  ! [v126] : (v125 = v124 |  ~ (not(v126) = v125) |  ~ (not(v126) = v124)) &  ! [v124] :  ! [v125] :  ! [v126] : (v125 = v124 |  ~ (equiv(v124, v125) = v126) |  ? [v127] : ( ~ (v127 = 0) & is_a_theorem(v126) = v127)) &  ! [v124] :  ! [v125] :  ! [v126] : (v125 = v124 |  ~ (is_a_theorem(v126) = v125) |  ~ (is_a_theorem(v126) = v124)) &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (or(v125, v124) = v126) |  ? [v127] :  ? [v128] : (or(v124, v125) = v127 & implies(v127, v126) = v128 & is_a_theorem(v128) = 0)) &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (or(v124, v125) = v126) |  ? [v127] :  ? [v128] :  ? [v129] : (and(v127, v128) = v129 & not(v129) = v126 & not(v125) = v128 & not(v124) = v127)) &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (or(v124, v125) = v126) |  ? [v127] :  ? [v128] : (or(v125, v124) = v127 & implies(v126, v127) = v128 & is_a_theorem(v128) = 0)) &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (or(v124, v125) = v126) |  ? [v127] : (implies(v125, v126) = v127 & is_a_theorem(v127) = 0)) &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (and(v124, v125) = v126) |  ? [v127] :  ? [v128] :  ? [v129] : (or(v127, v128) = v129 & not(v129) = v126 & not(v125) = v128 & not(v124) = v127)) &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (equiv(v124, v125) = v126) |  ? [v127] :  ? [v128] : (and(v127, v128) = v126 & implies(v125, v124) = v128 & implies(v124, v125) = v127)) &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (implies(v125, v124) = v126) |  ? [v127] :  ? [v128] : (and(v128, v126) = v127 & equiv(v124, v125) = v127 & implies(v124, v125) = v128)) &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (implies(v124, v125) = v126) |  ? [v127] :  ? [v128] : (and(v126, v128) = v127 & equiv(v124, v125) = v127 & implies(v125, v124) = v128)) &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (implies(v124, v125) = v126) |  ? [v127] :  ? [v128] : (and(v124, v127) = v128 & not(v128) = v126 & not(v125) = v127)) &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (implies(v124, v125) = v126) |  ? [v127] : (or(v127, v125) = v126 & not(v124) = v127)) &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (implies(v124, v125) = v126) |  ? [v127] : ((v127 = 0 & is_a_theorem(v125) = 0) | ( ~ (v127 = 0) & is_a_theorem(v126) = v127) | ( ~ (v127 = 0) & is_a_theorem(v124) = v127))) &  ! [v124] :  ! [v125] : ( ~ (or(v124, v124) = v125) |  ? [v126] : (implies(v125, v124) = v126 & is_a_theorem(v126) = 0)) &  ? [v124] :  ? [v125] :  ? [v126] : or(v125, v124) = v126 &  ? [v124] :  ? [v125] :  ? [v126] : and(v125, v124) = v126 &  ? [v124] :  ? [v125] :  ? [v126] : equiv(v125, v124) = v126 &  ? [v124] :  ? [v125] :  ? [v126] : implies(v125, v124) = v126 &  ? [v124] :  ? [v125] : not(v124) = v125 &  ? [v124] :  ? [v125] : is_a_theorem(v124) = v125 & (( ~ (v123 = 0) & not(v117) = v118 & not(v116) = v119 & implies(v120, v121) = v122 & implies(v118, v119) = v120 & implies(v116, v117) = v121 & is_a_theorem(v122) = v123 &  ~ modus_tollens) | (modus_tollens &  ! [v124] :  ! [v125] :  ! [v126] :  ! [v127] :  ! [v128] : ( ~ (not(v125) = v126) |  ~ (not(v124) = v127) |  ~ (implies(v126, v127) = v128) |  ? [v129] :  ? [v130] : (implies(v128, v129) = v130 & implies(v124, v125) = v129 & is_a_theorem(v130) = 0)) &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (implies(v124, v125) = v126) |  ? [v127] :  ? [v128] :  ? [v129] :  ? [v130] : (not(v125) = v127 & not(v124) = v128 & implies(v129, v126) = v130 & implies(v127, v128) = v129 & is_a_theorem(v130) = 0)))) & (( ~ (v115 = 0) & implies(v112, v111) = v113 & implies(v111, v113) = v114 & is_a_theorem(v114) = v115 &  ~ implies_1) | (implies_1 &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (implies(v125, v124) = v126) |  ? [v127] : (implies(v124, v126) = v127 & is_a_theorem(v127) = 0)))) & (( ~ (v110 = 0) & implies(v108, v107) = v109 & implies(v105, v107) = v108 & implies(v105, v106) = v107 & is_a_theorem(v109) = v110 &  ~ implies_2) | (implies_2 &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (implies(v124, v125) = v126) |  ? [v127] :  ? [v128] : (implies(v127, v126) = v128 & implies(v124, v126) = v127 & is_a_theorem(v128) = 0)))) & (( ~ (v104 = 0) & implies(v100, v101) = v102 & implies(v99, v102) = v103 & implies(v97, v98) = v100 & implies(v96, v98) = v101 & implies(v96, v97) = v99 & is_a_theorem(v103) = v104 &  ~ implies_3) | (implies_3 &  ! [v124] :  ! [v125] :  ! [v126] :  ! [v127] :  ! [v128] :  ! [v129] : ( ~ (implies(v127, v128) = v129) |  ~ (implies(v125, v126) = v127) |  ~ (implies(v124, v126) = v128) |  ? [v130] :  ? [v131] : (implies(v130, v129) = v131 & implies(v124, v125) = v130 & is_a_theorem(v131) = 0)))) & (( ~ (v95 = 0) & and(v91, v92) = v93 & implies(v93, v91) = v94 & is_a_theorem(v94) = v95 &  ~ and_1) | (and_1 &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (and(v124, v125) = v126) |  ? [v127] : (implies(v126, v124) = v127 & is_a_theorem(v127) = 0)))) & (( ~ (v85 = 0) & and(v80, v81) = v82 & implies(v81, v82) = v83 & implies(v80, v83) = v84 & is_a_theorem(v84) = v85 &  ~ and_3) | (and_3 &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (and(v124, v125) = v126) |  ? [v127] :  ? [v128] : (implies(v125, v126) = v127 & implies(v124, v127) = v128 & is_a_theorem(v128) = 0)))) & (( ~ (v79 = 0) & or(v75, v76) = v77 & implies(v75, v77) = v78 & is_a_theorem(v78) = v79 &  ~ or_1) | (or_1 &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (or(v124, v125) = v126) |  ? [v127] : (implies(v124, v126) = v127 & is_a_theorem(v127) = 0)))) & (( ~ (v74 = 0) & or(v70, v71) = v72 & implies(v71, v72) = v73 & is_a_theorem(v73) = v74 &  ~ or_2) | (or_2 &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (or(v124, v125) = v126) |  ? [v127] : (implies(v125, v126) = v127 & is_a_theorem(v127) = 0)))) & (( ~ (v69 = 0) & or(v60, v61) = v65 & implies(v65, v62) = v66 & implies(v64, v66) = v67 & implies(v63, v67) = v68 & implies(v61, v62) = v64 & implies(v60, v62) = v63 & is_a_theorem(v68) = v69 &  ~ or_3) | (or_3 &  ! [v124] :  ! [v125] :  ! [v126] :  ! [v127] :  ! [v128] : ( ~ (or(v124, v125) = v127) |  ~ (implies(v127, v126) = v128) |  ? [v129] :  ? [v130] :  ? [v131] :  ? [v132] : (implies(v130, v128) = v131 & implies(v129, v131) = v132 & implies(v125, v126) = v130 & implies(v124, v126) = v129 & is_a_theorem(v132) = 0)))) & (( ~ (v59 = 0) & equiv(v54, v55) = v56 & implies(v56, v57) = v58 & implies(v54, v55) = v57 & is_a_theorem(v58) = v59 &  ~ equivalence_1) | (equivalence_1 &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (equiv(v124, v125) = v126) |  ? [v127] :  ? [v128] : (implies(v126, v127) = v128 & implies(v124, v125) = v127 & is_a_theorem(v128) = 0)) &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (implies(v124, v125) = v126) |  ? [v127] :  ? [v128] : (equiv(v124, v125) = v127 & implies(v127, v126) = v128 & is_a_theorem(v128) = 0)))) & (( ~ (v53 = 0) & equiv(v48, v49) = v50 & implies(v50, v51) = v52 & implies(v49, v48) = v51 & is_a_theorem(v52) = v53 &  ~ equivalence_2) | (equivalence_2 &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (equiv(v124, v125) = v126) |  ? [v127] :  ? [v128] : (implies(v126, v127) = v128 & implies(v125, v124) = v127 & is_a_theorem(v128) = 0)) &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (implies(v125, v124) = v126) |  ? [v127] :  ? [v128] : (equiv(v124, v125) = v127 & implies(v127, v126) = v128 & is_a_theorem(v128) = 0)))) & (( ~ (v47 = 0) & equiv(v40, v41) = v44 & implies(v43, v44) = v45 & implies(v42, v45) = v46 & implies(v41, v40) = v43 & implies(v40, v41) = v42 & is_a_theorem(v46) = v47 &  ~ equivalence_3) | (equivalence_3 &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (equiv(v124, v125) = v126) |  ? [v127] :  ? [v128] :  ? [v129] :  ? [v130] : (implies(v128, v126) = v129 & implies(v127, v129) = v130 & implies(v125, v124) = v128 & implies(v124, v125) = v127 & is_a_theorem(v130) = 0)) &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (implies(v125, v124) = v126) |  ? [v127] :  ? [v128] :  ? [v129] :  ? [v130] : (equiv(v124, v125) = v128 & implies(v127, v129) = v130 & implies(v126, v128) = v129 & implies(v124, v125) = v127 & is_a_theorem(v130) = 0)) &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (implies(v124, v125) = v126) |  ? [v127] :  ? [v128] :  ? [v129] :  ? [v130] : (equiv(v124, v125) = v128 & implies(v127, v128) = v129 & implies(v126, v129) = v130 & implies(v125, v124) = v127 & is_a_theorem(v130) = 0)))) & (( ~ (v39 = 0) & and(v36, v36) = v37 & implies(v36, v37) = v38 & is_a_theorem(v38) = v39 &  ~ kn1) | (kn1 &  ! [v124] :  ! [v125] : ( ~ (and(v124, v124) = v125) |  ? [v126] : (implies(v124, v125) = v126 & is_a_theorem(v126) = 0)))) & (( ~ (v35 = 0) & and(v31, v32) = v33 & implies(v33, v31) = v34 & is_a_theorem(v34) = v35 &  ~ kn2) | (kn2 &  ! [v124] :  ! [v125] :  ! [v126] : ( ~ (and(v124, v125) = v126) |  ? [v127] : (implies(v126, v124) = v127 & is_a_theorem(v127) = 0)))) & (( ~ (v30 = 0) & and(v22, v20) = v26 & and(v21, v22) = v24 & not(v26) = v27 & not(v24) = v25 & implies(v25, v27) = v28 & implies(v23, v28) = v29 & implies(v20, v21) = v23 & is_a_theorem(v29) = v30 &  ~ kn3) | (kn3 &  ! [v124] :  ! [v125] :  ! [v126] :  ! [v127] :  ! [v128] :  ! [v129] :  ! [v130] :  ! [v131] : ( ~ (and(v126, v124) = v129) |  ~ (and(v125, v126) = v127) |  ~ (not(v129) = v130) |  ~ (not(v127) = v128) |  ~ (implies(v128, v130) = v131) |  ? [v132] :  ? [v133] : (implies(v132, v131) = v133 & implies(v124, v125) = v132 & is_a_theorem(v133) = 0)))) & (( ~ (v19 = 0) & implies(v15, v16) = v17 & implies(v14, v17) = v18 & implies(v12, v13) = v15 & implies(v11, v13) = v16 & implies(v11, v12) = v14 & is_a_theorem(v18) = v19 &  ~ cn1) | (cn1 &  ! [v124] :  ! [v125] :  ! [v126] :  ! [v127] :  ! [v128] :  ! [v129] : ( ~ (implies(v127, v128) = v129) |  ~ (implies(v125, v126) = v127) |  ~ (implies(v124, v126) = v128) |  ? [v130] :  ? [v131] : (implies(v130, v129) = v131 & implies(v124, v125) = v130 & is_a_theorem(v131) = 0)))) & (( ~ (v10 = 0) & not(v5) = v7 & implies(v7, v6) = v8 & implies(v5, v8) = v9 & is_a_theorem(v9) = v10 &  ~ cn2) | (cn2 &  ! [v124] :  ! [v125] :  ! [v126] :  ! [v127] : ( ~ (not(v124) = v126) |  ~ (implies(v126, v125) = v127) |  ? [v128] : (implies(v124, v127) = v128 & is_a_theorem(v128) = 0)))) & (( ~ (v4 = 0) & not(v0) = v1 & implies(v2, v0) = v3 & implies(v1, v0) = v2 & is_a_theorem(v3) = v4 &  ~ cn3) | (cn3 &  ! [v124] :  ! [v125] : ( ~ (not(v124) = v125) |  ? [v126] :  ? [v127] : (implies(v126, v124) = v127 & implies(v125, v124) = v126 & is_a_theorem(v127) = 0)))))
% 38.38/12.24  | 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 yields:
% 38.38/12.24  | (1)  ~ (all_0_33_33 = 0) & and(all_0_37_37, all_0_36_36) = all_0_35_35 & implies(all_0_35_35, all_0_36_36) = all_0_34_34 & is_a_theorem(all_0_34_34) = all_0_33_33 & op_equiv & op_implies_or & op_implies_and & op_and & op_or & r5 & r4 & r3 & r2 & r1 & substitution_of_equivalents & modus_ponens &  ~ and_2 &  ! [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)) &  ! [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] :  ! [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)) &  ! [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] : (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] : ( ~ (or(v2, v1) = v3) |  ~ (not(v0) = v2) | implies(v0, v1) = v3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (and(v0, v2) = v3) |  ~ (not(v1) = v2) |  ? [v4] : (not(v3) = v4 & implies(v0, v1) = v4)) &  ! [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] : ( ~ (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] :  ? [v5] : (and(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] :  ? [v4] : (or(v1, v0) = v3 & implies(v2, v3) = v4 & is_a_theorem(v4) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] : (implies(v1, v2) = v3 & is_a_theorem(v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (or(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(v1, v0) = v2) |  ? [v3] :  ? [v4] : (and(v4, v2) = v3 & equiv(v0, v1) = v3 & implies(v0, v1) = v4)) &  ! [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] : (or(v3, v1) = v2 & not(v0) = 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] : ( ~ (or(v0, v0) = v1) |  ? [v2] : (implies(v1, v0) = v2 & is_a_theorem(v2) = 0)) &  ? [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] : not(v0) = v1 &  ? [v0] :  ? [v1] : is_a_theorem(v0) = v1 & (( ~ (all_0_0_0 = 0) & not(all_0_6_6) = all_0_5_5 & not(all_0_7_7) = all_0_4_4 & implies(all_0_3_3, all_0_2_2) = all_0_1_1 & implies(all_0_5_5, all_0_4_4) = all_0_3_3 & implies(all_0_7_7, all_0_6_6) = all_0_2_2 & is_a_theorem(all_0_1_1) = all_0_0_0 &  ~ modus_tollens) | (modus_tollens &  ! [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] : ( ~ (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)))) & (( ~ (all_0_8_8 = 0) & implies(all_0_11_11, all_0_12_12) = all_0_10_10 & implies(all_0_12_12, all_0_10_10) = all_0_9_9 & is_a_theorem(all_0_9_9) = all_0_8_8 &  ~ implies_1) | (implies_1 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v1, v0) = v2) |  ? [v3] : (implies(v0, v2) = v3 & is_a_theorem(v3) = 0)))) & (( ~ (all_0_13_13 = 0) & implies(all_0_15_15, all_0_16_16) = all_0_14_14 & implies(all_0_18_18, all_0_16_16) = all_0_15_15 & implies(all_0_18_18, all_0_17_17) = all_0_16_16 & is_a_theorem(all_0_14_14) = all_0_13_13 &  ~ implies_2) | (implies_2 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (implies(v3, v2) = v4 & implies(v0, v2) = v3 & is_a_theorem(v4) = 0)))) & (( ~ (all_0_19_19 = 0) & implies(all_0_23_23, all_0_22_22) = all_0_21_21 & implies(all_0_24_24, all_0_21_21) = all_0_20_20 & implies(all_0_26_26, all_0_25_25) = all_0_23_23 & implies(all_0_27_27, all_0_25_25) = all_0_22_22 & implies(all_0_27_27, all_0_26_26) = all_0_24_24 & is_a_theorem(all_0_20_20) = all_0_19_19 &  ~ implies_3) | (implies_3 &  ! [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_28_28 = 0) & and(all_0_32_32, all_0_31_31) = all_0_30_30 & implies(all_0_30_30, all_0_32_32) = all_0_29_29 & is_a_theorem(all_0_29_29) = all_0_28_28 &  ~ and_1) | (and_1 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : (implies(v2, v0) = v3 & is_a_theorem(v3) = 0)))) & (( ~ (all_0_38_38 = 0) & and(all_0_43_43, all_0_42_42) = all_0_41_41 & implies(all_0_42_42, all_0_41_41) = all_0_40_40 & implies(all_0_43_43, all_0_40_40) = all_0_39_39 & is_a_theorem(all_0_39_39) = all_0_38_38 &  ~ and_3) | (and_3 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] :  ? [v4] : (implies(v1, v2) = v3 & implies(v0, v3) = v4 & is_a_theorem(v4) = 0)))) & (( ~ (all_0_44_44 = 0) & or(all_0_48_48, all_0_47_47) = all_0_46_46 & implies(all_0_48_48, all_0_46_46) = all_0_45_45 & is_a_theorem(all_0_45_45) = all_0_44_44 &  ~ or_1) | (or_1 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] : (implies(v0, v2) = v3 & is_a_theorem(v3) = 0)))) & (( ~ (all_0_49_49 = 0) & or(all_0_53_53, all_0_52_52) = all_0_51_51 & implies(all_0_52_52, all_0_51_51) = all_0_50_50 & is_a_theorem(all_0_50_50) = all_0_49_49 &  ~ or_2) | (or_2 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] : (implies(v1, v2) = v3 & is_a_theorem(v3) = 0)))) & (( ~ (all_0_54_54 = 0) & or(all_0_63_63, all_0_62_62) = all_0_58_58 & implies(all_0_58_58, all_0_61_61) = all_0_57_57 & implies(all_0_59_59, all_0_57_57) = all_0_56_56 & implies(all_0_60_60, all_0_56_56) = all_0_55_55 & implies(all_0_62_62, all_0_61_61) = all_0_59_59 & implies(all_0_63_63, all_0_61_61) = all_0_60_60 & is_a_theorem(all_0_55_55) = all_0_54_54 &  ~ or_3) | (or_3 &  ! [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)))) & (( ~ (all_0_64_64 = 0) & equiv(all_0_69_69, all_0_68_68) = all_0_67_67 & implies(all_0_67_67, all_0_66_66) = all_0_65_65 & implies(all_0_69_69, all_0_68_68) = all_0_66_66 & is_a_theorem(all_0_65_65) = all_0_64_64 &  ~ equivalence_1) | (equivalence_1 &  ! [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(v0, v1) = v2) |  ? [v3] :  ? [v4] : (equiv(v0, v1) = v3 & implies(v3, v2) = v4 & is_a_theorem(v4) = 0)))) & (( ~ (all_0_70_70 = 0) & equiv(all_0_75_75, all_0_74_74) = all_0_73_73 & implies(all_0_73_73, all_0_72_72) = all_0_71_71 & implies(all_0_74_74, all_0_75_75) = all_0_72_72 & is_a_theorem(all_0_71_71) = all_0_70_70 &  ~ equivalence_2) | (equivalence_2 &  ! [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] : ( ~ (implies(v1, v0) = v2) |  ? [v3] :  ? [v4] : (equiv(v0, v1) = v3 & implies(v3, v2) = v4 & is_a_theorem(v4) = 0)))) & (( ~ (all_0_76_76 = 0) & equiv(all_0_83_83, all_0_82_82) = all_0_79_79 & implies(all_0_80_80, all_0_79_79) = all_0_78_78 & implies(all_0_81_81, all_0_78_78) = all_0_77_77 & implies(all_0_82_82, all_0_83_83) = all_0_80_80 & implies(all_0_83_83, all_0_82_82) = all_0_81_81 & is_a_theorem(all_0_77_77) = all_0_76_76 &  ~ equivalence_3) | (equivalence_3 &  ! [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] : ( ~ (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(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)))) & (( ~ (all_0_84_84 = 0) & and(all_0_87_87, all_0_87_87) = all_0_86_86 & implies(all_0_87_87, all_0_86_86) = all_0_85_85 & is_a_theorem(all_0_85_85) = all_0_84_84 &  ~ kn1) | (kn1 &  ! [v0] :  ! [v1] : ( ~ (and(v0, v0) = v1) |  ? [v2] : (implies(v0, v1) = v2 & is_a_theorem(v2) = 0)))) & (( ~ (all_0_88_88 = 0) & and(all_0_92_92, all_0_91_91) = all_0_90_90 & implies(all_0_90_90, all_0_92_92) = all_0_89_89 & is_a_theorem(all_0_89_89) = all_0_88_88 &  ~ kn2) | (kn2 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : (implies(v2, v0) = v3 & is_a_theorem(v3) = 0)))) & (( ~ (all_0_93_93 = 0) & and(all_0_101_101, all_0_103_103) = all_0_97_97 & and(all_0_102_102, all_0_101_101) = all_0_99_99 & not(all_0_97_97) = all_0_96_96 & not(all_0_99_99) = all_0_98_98 & implies(all_0_98_98, all_0_96_96) = all_0_95_95 & implies(all_0_100_100, all_0_95_95) = all_0_94_94 & implies(all_0_103_103, all_0_102_102) = all_0_100_100 & is_a_theorem(all_0_94_94) = all_0_93_93 &  ~ 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_104_104 = 0) & implies(all_0_108_108, all_0_107_107) = all_0_106_106 & implies(all_0_109_109, all_0_106_106) = all_0_105_105 & implies(all_0_111_111, all_0_110_110) = all_0_108_108 & implies(all_0_112_112, all_0_110_110) = all_0_107_107 & implies(all_0_112_112, all_0_111_111) = all_0_109_109 & is_a_theorem(all_0_105_105) = all_0_104_104 &  ~ 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_113_113 = 0) & not(all_0_118_118) = all_0_116_116 & implies(all_0_116_116, all_0_117_117) = all_0_115_115 & implies(all_0_118_118, all_0_115_115) = all_0_114_114 & is_a_theorem(all_0_114_114) = all_0_113_113 &  ~ 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_119_119 = 0) & not(all_0_123_123) = all_0_122_122 & implies(all_0_121_121, all_0_123_123) = all_0_120_120 & implies(all_0_122_122, all_0_123_123) = all_0_121_121 & is_a_theorem(all_0_120_120) = all_0_119_119 &  ~ cn3) | (cn3 &  ! [v0] :  ! [v1] : ( ~ (not(v0) = v1) |  ? [v2] :  ? [v3] : (implies(v2, v0) = v3 & implies(v1, v0) = v2 & is_a_theorem(v3) = 0))))
% 38.38/12.27  |
% 38.38/12.27  | Applying alpha-rule on (1) yields:
% 38.38/12.27  | (2)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (equiv(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & is_a_theorem(v2) = v3))
% 38.38/12.27  | (3) ( ~ (all_0_38_38 = 0) & and(all_0_43_43, all_0_42_42) = all_0_41_41 & implies(all_0_42_42, all_0_41_41) = all_0_40_40 & implies(all_0_43_43, all_0_40_40) = all_0_39_39 & is_a_theorem(all_0_39_39) = all_0_38_38 &  ~ and_3) | (and_3 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] :  ? [v4] : (implies(v1, v2) = v3 & implies(v0, v3) = v4 & is_a_theorem(v4) = 0)))
% 38.38/12.27  | (4)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (or(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3))
% 38.38/12.27  | (5) ( ~ (all_0_119_119 = 0) & not(all_0_123_123) = all_0_122_122 & implies(all_0_121_121, all_0_123_123) = all_0_120_120 & implies(all_0_122_122, all_0_123_123) = all_0_121_121 & is_a_theorem(all_0_120_120) = all_0_119_119 &  ~ cn3) | (cn3 &  ! [v0] :  ! [v1] : ( ~ (not(v0) = v1) |  ? [v2] :  ? [v3] : (implies(v2, v0) = v3 & implies(v1, v0) = v2 & is_a_theorem(v3) = 0)))
% 38.38/12.27  | (6)  ~ and_2
% 38.38/12.27  | (7) op_implies_or
% 38.38/12.27  | (8)  ! [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)))
% 38.38/12.27  | (9)  ? [v0] :  ? [v1] :  ? [v2] : equiv(v1, v0) = v2
% 38.38/12.27  | (10) modus_ponens
% 38.38/12.27  | (11) r3
% 38.38/12.27  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equiv(v3, v2) = v1) |  ~ (equiv(v3, v2) = v0))
% 38.38/12.27  | (13) ( ~ (all_0_113_113 = 0) & not(all_0_118_118) = all_0_116_116 & implies(all_0_116_116, all_0_117_117) = all_0_115_115 & implies(all_0_118_118, all_0_115_115) = all_0_114_114 & is_a_theorem(all_0_114_114) = all_0_113_113 &  ~ cn2) | (cn2 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (not(v0) = v2) |  ~ (implies(v2, v1) = v3) |  ? [v4] : (implies(v0, v3) = v4 & is_a_theorem(v4) = 0)))
% 38.38/12.27  | (14)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (not(v2) = v1) |  ~ (not(v2) = v0))
% 38.38/12.27  | (15) ( ~ (all_0_88_88 = 0) & and(all_0_92_92, all_0_91_91) = all_0_90_90 & implies(all_0_90_90, all_0_92_92) = all_0_89_89 & is_a_theorem(all_0_89_89) = all_0_88_88 &  ~ kn2) | (kn2 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : (implies(v2, v0) = v3 & is_a_theorem(v3) = 0)))
% 38.38/12.27  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (and(v0, v2) = v3) |  ~ (not(v1) = v2) |  ? [v4] : (not(v3) = v4 & implies(v0, v1) = v4))
% 38.38/12.27  | (17) and(all_0_37_37, all_0_36_36) = all_0_35_35
% 38.38/12.27  | (18) ( ~ (all_0_84_84 = 0) & and(all_0_87_87, all_0_87_87) = all_0_86_86 & implies(all_0_87_87, all_0_86_86) = all_0_85_85 & is_a_theorem(all_0_85_85) = all_0_84_84 &  ~ kn1) | (kn1 &  ! [v0] :  ! [v1] : ( ~ (and(v0, v0) = v1) |  ? [v2] : (implies(v0, v1) = v2 & is_a_theorem(v2) = 0)))
% 38.38/12.27  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (implies(v3, v2) = v1) |  ~ (implies(v3, v2) = v0))
% 38.38/12.27  | (20)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v1, v0) = v2) |  ? [v3] :  ? [v4] : (or(v0, v1) = v3 & implies(v3, v2) = v4 & is_a_theorem(v4) = 0))
% 38.38/12.27  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (equiv(v0, v1) = v2) |  ? [v3] :  ? [v4] : (and(v3, v4) = v2 & implies(v1, v0) = v4 & implies(v0, v1) = v3))
% 38.38/12.27  | (22) is_a_theorem(all_0_34_34) = all_0_33_33
% 38.38/12.27  | (23) substitution_of_equivalents
% 38.38/12.27  | (24)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (is_a_theorem(v2) = v1) |  ~ (is_a_theorem(v2) = v0))
% 38.38/12.28  | (25)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v1, v0) = v2) |  ? [v3] :  ? [v4] : (and(v4, v2) = v3 & equiv(v0, v1) = v3 & implies(v0, v1) = v4))
% 38.38/12.28  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (or(v2, v1) = v3) |  ~ (not(v0) = v2) | implies(v0, v1) = v3)
% 38.38/12.28  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (or(v2, v3) = v4) |  ~ (not(v1) = v3) |  ~ (not(v0) = v2) |  ? [v5] : (and(v0, v1) = v5 & not(v4) = v5))
% 38.38/12.28  | (28) op_equiv
% 38.38/12.28  | (29) op_and
% 38.38/12.28  | (30) r2
% 38.38/12.28  | (31) ( ~ (all_0_19_19 = 0) & implies(all_0_23_23, all_0_22_22) = all_0_21_21 & implies(all_0_24_24, all_0_21_21) = all_0_20_20 & implies(all_0_26_26, all_0_25_25) = all_0_23_23 & implies(all_0_27_27, all_0_25_25) = all_0_22_22 & implies(all_0_27_27, all_0_26_26) = all_0_24_24 & is_a_theorem(all_0_20_20) = all_0_19_19 &  ~ implies_3) | (implies_3 &  ! [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)))
% 38.38/12.28  | (32) ( ~ (all_0_8_8 = 0) & implies(all_0_11_11, all_0_12_12) = all_0_10_10 & implies(all_0_12_12, all_0_10_10) = all_0_9_9 & is_a_theorem(all_0_9_9) = all_0_8_8 &  ~ implies_1) | (implies_1 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v1, v0) = v2) |  ? [v3] : (implies(v0, v2) = v3 & is_a_theorem(v3) = 0)))
% 38.38/12.28  | (33) ( ~ (all_0_104_104 = 0) & implies(all_0_108_108, all_0_107_107) = all_0_106_106 & implies(all_0_109_109, all_0_106_106) = all_0_105_105 & implies(all_0_111_111, all_0_110_110) = all_0_108_108 & implies(all_0_112_112, all_0_110_110) = all_0_107_107 & implies(all_0_112_112, all_0_111_111) = all_0_109_109 & is_a_theorem(all_0_105_105) = all_0_104_104 &  ~ 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)))
% 38.38/12.28  | (34) ( ~ (all_0_0_0 = 0) & not(all_0_6_6) = all_0_5_5 & not(all_0_7_7) = all_0_4_4 & implies(all_0_3_3, all_0_2_2) = all_0_1_1 & implies(all_0_5_5, all_0_4_4) = all_0_3_3 & implies(all_0_7_7, all_0_6_6) = all_0_2_2 & is_a_theorem(all_0_1_1) = all_0_0_0 &  ~ modus_tollens) | (modus_tollens &  ! [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] : ( ~ (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)))
% 38.38/12.28  | (35)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] :  ? [v4] : (or(v1, v0) = v3 & implies(v2, v3) = v4 & is_a_theorem(v4) = 0))
% 38.38/12.28  | (36)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) = v3))
% 38.38/12.28  | (37) ( ~ (all_0_76_76 = 0) & equiv(all_0_83_83, all_0_82_82) = all_0_79_79 & implies(all_0_80_80, all_0_79_79) = all_0_78_78 & implies(all_0_81_81, all_0_78_78) = all_0_77_77 & implies(all_0_82_82, all_0_83_83) = all_0_80_80 & implies(all_0_83_83, all_0_82_82) = all_0_81_81 & is_a_theorem(all_0_77_77) = all_0_76_76 &  ~ equivalence_3) | (equivalence_3 &  ! [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] : ( ~ (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(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)))
% 38.38/12.28  | (38) ( ~ (all_0_28_28 = 0) & and(all_0_32_32, all_0_31_31) = all_0_30_30 & implies(all_0_30_30, all_0_32_32) = all_0_29_29 & is_a_theorem(all_0_29_29) = all_0_28_28 &  ~ and_1) | (and_1 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and(v0, v1) = v2) |  ? [v3] : (implies(v2, v0) = v3 & is_a_theorem(v3) = 0)))
% 38.38/12.28  | (39)  ! [v0] :  ! [v1] : ( ~ (or(v0, v0) = v1) |  ? [v2] : (implies(v1, v0) = v2 & is_a_theorem(v2) = 0))
% 38.38/12.28  | (40)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] : (or(v3, v1) = v2 & not(v0) = v3))
% 38.38/12.28  | (41)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (and(v2, v4) = v3 & equiv(v0, v1) = v3 & implies(v1, v0) = v4))
% 38.38/12.28  | (42)  ? [v0] :  ? [v1] :  ? [v2] : and(v1, v0) = v2
% 38.38/12.28  | (43) ( ~ (all_0_54_54 = 0) & or(all_0_63_63, all_0_62_62) = all_0_58_58 & implies(all_0_58_58, all_0_61_61) = all_0_57_57 & implies(all_0_59_59, all_0_57_57) = all_0_56_56 & implies(all_0_60_60, all_0_56_56) = all_0_55_55 & implies(all_0_62_62, all_0_61_61) = all_0_59_59 & implies(all_0_63_63, all_0_61_61) = all_0_60_60 & is_a_theorem(all_0_55_55) = all_0_54_54 &  ~ or_3) | (or_3 &  ! [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)))
% 38.38/12.29  | (44)  ? [v0] :  ? [v1] :  ? [v2] : or(v1, v0) = v2
% 38.38/12.29  | (45) ( ~ (all_0_13_13 = 0) & implies(all_0_15_15, all_0_16_16) = all_0_14_14 & implies(all_0_18_18, all_0_16_16) = all_0_15_15 & implies(all_0_18_18, all_0_17_17) = all_0_16_16 & is_a_theorem(all_0_14_14) = all_0_13_13 &  ~ implies_2) | (implies_2 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (implies(v0, v1) = v2) |  ? [v3] :  ? [v4] : (implies(v3, v2) = v4 & implies(v0, v2) = v3 & is_a_theorem(v4) = 0)))
% 38.38/12.29  | (46)  ~ (all_0_33_33 = 0)
% 38.38/12.29  | (47)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] : (implies(v1, v2) = v3 & is_a_theorem(v3) = 0))
% 38.38/12.29  | (48) r5
% 38.38/12.29  | (49)  ! [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))
% 38.38/12.29  | (50)  ? [v0] :  ? [v1] : is_a_theorem(v0) = v1
% 38.38/12.29  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (and(v3, v2) = v1) |  ~ (and(v3, v2) = v0))
% 38.38/12.29  | (52) ( ~ (all_0_70_70 = 0) & equiv(all_0_75_75, all_0_74_74) = all_0_73_73 & implies(all_0_73_73, all_0_72_72) = all_0_71_71 & implies(all_0_74_74, all_0_75_75) = all_0_72_72 & is_a_theorem(all_0_71_71) = all_0_70_70 &  ~ equivalence_2) | (equivalence_2 &  ! [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] : ( ~ (implies(v1, v0) = v2) |  ? [v3] :  ? [v4] : (equiv(v0, v1) = v3 & implies(v3, v2) = v4 & is_a_theorem(v4) = 0)))
% 38.38/12.29  | (53) op_or
% 38.38/12.29  | (54) ( ~ (all_0_64_64 = 0) & equiv(all_0_69_69, all_0_68_68) = all_0_67_67 & implies(all_0_67_67, all_0_66_66) = all_0_65_65 & implies(all_0_69_69, all_0_68_68) = all_0_66_66 & is_a_theorem(all_0_65_65) = all_0_64_64 &  ~ equivalence_1) | (equivalence_1 &  ! [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(v0, v1) = v2) |  ? [v3] :  ? [v4] : (equiv(v0, v1) = v3 & implies(v3, v2) = v4 & is_a_theorem(v4) = 0)))
% 38.38/12.29  | (55)  ? [v0] :  ? [v1] :  ? [v2] : implies(v1, v0) = v2
% 38.38/12.29  | (56) r1
% 38.38/12.29  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (or(v3, v2) = v1) |  ~ (or(v3, v2) = v0))
% 38.38/12.29  | (58)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (and(v2, v3) = v4) |  ~ (not(v1) = v3) |  ~ (not(v0) = v2) |  ? [v5] : (or(v0, v1) = v5 & not(v4) = v5))
% 38.38/12.29  | (59)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (and(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3))
% 38.38/12.29  | (60)  ? [v0] :  ? [v1] : not(v0) = v1
% 38.38/12.29  | (61)  ! [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))
% 38.38/12.29  | (62)  ! [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))
% 38.38/12.29  | (63) r4
% 38.38/12.29  | (64) ( ~ (all_0_44_44 = 0) & or(all_0_48_48, all_0_47_47) = all_0_46_46 & implies(all_0_48_48, all_0_46_46) = all_0_45_45 & is_a_theorem(all_0_45_45) = all_0_44_44 &  ~ or_1) | (or_1 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] : (implies(v0, v2) = v3 & is_a_theorem(v3) = 0)))
% 38.38/12.29  | (65) op_implies_and
% 38.38/12.29  | (66) implies(all_0_35_35, all_0_36_36) = all_0_34_34
% 38.38/12.29  | (67) ( ~ (all_0_93_93 = 0) & and(all_0_101_101, all_0_103_103) = all_0_97_97 & and(all_0_102_102, all_0_101_101) = all_0_99_99 & not(all_0_97_97) = all_0_96_96 & not(all_0_99_99) = all_0_98_98 & implies(all_0_98_98, all_0_96_96) = all_0_95_95 & implies(all_0_100_100, all_0_95_95) = all_0_94_94 & implies(all_0_103_103, all_0_102_102) = all_0_100_100 & is_a_theorem(all_0_94_94) = all_0_93_93 &  ~ 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)))
% 38.38/12.30  | (68) ( ~ (all_0_49_49 = 0) & or(all_0_53_53, all_0_52_52) = all_0_51_51 & implies(all_0_52_52, all_0_51_51) = all_0_50_50 & is_a_theorem(all_0_50_50) = all_0_49_49 &  ~ or_2) | (or_2 &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or(v0, v1) = v2) |  ? [v3] : (implies(v1, v2) = v3 & is_a_theorem(v3) = 0)))
% 38.38/12.30  |
% 38.38/12.30  | Instantiating formula (4) with all_0_35_35, all_0_36_36, all_0_37_37 and discharging atoms and(all_0_37_37, all_0_36_36) = all_0_35_35, yields:
% 38.38/12.30  | (69)  ? [v0] :  ? [v1] :  ? [v2] : (or(v0, v1) = v2 & not(v2) = all_0_35_35 & not(all_0_36_36) = v1 & not(all_0_37_37) = v0)
% 38.38/12.30  |
% 38.38/12.30  | Instantiating formula (25) with all_0_34_34, all_0_35_35, all_0_36_36 and discharging atoms implies(all_0_35_35, all_0_36_36) = all_0_34_34, yields:
% 38.38/12.30  | (70)  ? [v0] :  ? [v1] : (and(v1, all_0_34_34) = v0 & equiv(all_0_36_36, all_0_35_35) = v0 & implies(all_0_36_36, all_0_35_35) = v1)
% 38.38/12.30  |
% 38.38/12.30  | Instantiating formula (41) with all_0_34_34, all_0_36_36, all_0_35_35 and discharging atoms implies(all_0_35_35, all_0_36_36) = all_0_34_34, yields:
% 38.38/12.30  | (71)  ? [v0] :  ? [v1] : (and(all_0_34_34, v1) = v0 & equiv(all_0_35_35, all_0_36_36) = v0 & implies(all_0_36_36, all_0_35_35) = v1)
% 38.38/12.30  |
% 38.38/12.30  | Instantiating formula (36) with all_0_34_34, all_0_36_36, all_0_35_35 and discharging atoms implies(all_0_35_35, all_0_36_36) = all_0_34_34, yields:
% 38.38/12.30  | (72)  ? [v0] :  ? [v1] : (and(all_0_35_35, v0) = v1 & not(v1) = all_0_34_34 & not(all_0_36_36) = v0)
% 38.38/12.30  |
% 38.38/12.30  | Instantiating formula (40) with all_0_34_34, all_0_36_36, all_0_35_35 and discharging atoms implies(all_0_35_35, all_0_36_36) = all_0_34_34, yields:
% 38.38/12.30  | (73)  ? [v0] : (or(v0, all_0_36_36) = all_0_34_34 & not(all_0_35_35) = v0)
% 38.38/12.30  |
% 38.38/12.30  | Instantiating (72) with all_21_0_141, all_21_1_142 yields:
% 38.38/12.30  | (74) and(all_0_35_35, all_21_1_142) = all_21_0_141 & not(all_21_0_141) = all_0_34_34 & not(all_0_36_36) = all_21_1_142
% 38.66/12.30  |
% 38.66/12.30  | Applying alpha-rule on (74) yields:
% 38.66/12.30  | (75) and(all_0_35_35, all_21_1_142) = all_21_0_141
% 38.66/12.30  | (76) not(all_21_0_141) = all_0_34_34
% 38.66/12.30  | (77) not(all_0_36_36) = all_21_1_142
% 38.66/12.30  |
% 38.66/12.30  | Instantiating (70) with all_23_0_143, all_23_1_144 yields:
% 38.66/12.30  | (78) and(all_23_0_143, all_0_34_34) = all_23_1_144 & equiv(all_0_36_36, all_0_35_35) = all_23_1_144 & implies(all_0_36_36, all_0_35_35) = all_23_0_143
% 38.66/12.30  |
% 38.66/12.30  | Applying alpha-rule on (78) yields:
% 38.66/12.30  | (79) and(all_23_0_143, all_0_34_34) = all_23_1_144
% 38.66/12.30  | (80) equiv(all_0_36_36, all_0_35_35) = all_23_1_144
% 38.66/12.30  | (81) implies(all_0_36_36, all_0_35_35) = all_23_0_143
% 38.66/12.30  |
% 38.66/12.30  | Instantiating (69) with all_25_0_145, all_25_1_146, all_25_2_147 yields:
% 38.66/12.30  | (82) or(all_25_2_147, all_25_1_146) = all_25_0_145 & not(all_25_0_145) = all_0_35_35 & not(all_0_36_36) = all_25_1_146 & not(all_0_37_37) = all_25_2_147
% 38.66/12.30  |
% 38.66/12.30  | Applying alpha-rule on (82) yields:
% 38.66/12.30  | (83) or(all_25_2_147, all_25_1_146) = all_25_0_145
% 38.66/12.30  | (84) not(all_25_0_145) = all_0_35_35
% 38.66/12.30  | (85) not(all_0_36_36) = all_25_1_146
% 38.66/12.30  | (86) not(all_0_37_37) = all_25_2_147
% 38.66/12.30  |
% 38.66/12.30  | Instantiating (71) with all_27_0_148, all_27_1_149 yields:
% 38.66/12.30  | (87) and(all_0_34_34, all_27_0_148) = all_27_1_149 & equiv(all_0_35_35, all_0_36_36) = all_27_1_149 & implies(all_0_36_36, all_0_35_35) = all_27_0_148
% 38.66/12.30  |
% 38.66/12.30  | Applying alpha-rule on (87) yields:
% 38.66/12.30  | (88) and(all_0_34_34, all_27_0_148) = all_27_1_149
% 38.66/12.30  | (89) equiv(all_0_35_35, all_0_36_36) = all_27_1_149
% 38.66/12.30  | (90) implies(all_0_36_36, all_0_35_35) = all_27_0_148
% 38.66/12.30  |
% 38.66/12.30  | Instantiating (73) with all_29_0_150 yields:
% 38.66/12.30  | (91) or(all_29_0_150, all_0_36_36) = all_0_34_34 & not(all_0_35_35) = all_29_0_150
% 38.66/12.30  |
% 38.66/12.30  | Applying alpha-rule on (91) yields:
% 38.66/12.30  | (92) or(all_29_0_150, all_0_36_36) = all_0_34_34
% 38.66/12.30  | (93) not(all_0_35_35) = all_29_0_150
% 38.66/12.30  |
% 38.66/12.30  | Instantiating formula (14) with all_0_36_36, all_21_1_142, all_25_1_146 and discharging atoms not(all_0_36_36) = all_25_1_146, not(all_0_36_36) = all_21_1_142, yields:
% 38.66/12.30  | (94) all_25_1_146 = all_21_1_142
% 38.66/12.30  |
% 38.66/12.30  | Instantiating formula (19) with all_0_36_36, all_0_35_35, all_23_0_143, all_27_0_148 and discharging atoms implies(all_0_36_36, all_0_35_35) = all_27_0_148, implies(all_0_36_36, all_0_35_35) = all_23_0_143, yields:
% 38.66/12.30  | (95) all_27_0_148 = all_23_0_143
% 38.66/12.30  |
% 38.66/12.30  | From (94) and (83) follows:
% 38.66/12.31  | (96) or(all_25_2_147, all_21_1_142) = all_25_0_145
% 38.66/12.31  |
% 38.66/12.31  | From (94) and (85) follows:
% 38.66/12.31  | (77) not(all_0_36_36) = all_21_1_142
% 38.66/12.31  |
% 38.66/12.31  | From (95) and (90) follows:
% 38.66/12.31  | (81) implies(all_0_36_36, all_0_35_35) = all_23_0_143
% 38.66/12.31  |
% 38.66/12.31  | Instantiating formula (20) with all_0_34_34, all_29_0_150, all_0_36_36 and discharging atoms or(all_29_0_150, all_0_36_36) = all_0_34_34, yields:
% 38.66/12.31  | (99)  ? [v0] :  ? [v1] : (or(all_0_36_36, all_29_0_150) = v0 & implies(v0, all_0_34_34) = v1 & is_a_theorem(v1) = 0)
% 38.66/12.31  |
% 38.66/12.31  | Instantiating formula (59) with all_0_34_34, all_0_36_36, all_29_0_150 and discharging atoms or(all_29_0_150, all_0_36_36) = all_0_34_34, yields:
% 38.66/12.31  | (100)  ? [v0] :  ? [v1] :  ? [v2] : (and(v0, v1) = v2 & not(v2) = all_0_34_34 & not(all_29_0_150) = v0 & not(all_0_36_36) = v1)
% 38.66/12.31  |
% 38.66/12.31  | Instantiating formula (35) with all_0_34_34, all_0_36_36, all_29_0_150 and discharging atoms or(all_29_0_150, all_0_36_36) = all_0_34_34, yields:
% 38.66/12.31  | (101)  ? [v0] :  ? [v1] : (or(all_0_36_36, all_29_0_150) = v0 & implies(all_0_34_34, v0) = v1 & is_a_theorem(v1) = 0)
% 38.66/12.31  |
% 38.66/12.31  | Instantiating formula (47) with all_0_34_34, all_0_36_36, all_29_0_150 and discharging atoms or(all_29_0_150, all_0_36_36) = all_0_34_34, yields:
% 38.66/12.31  | (102)  ? [v0] : (implies(all_0_36_36, all_0_34_34) = v0 & is_a_theorem(v0) = 0)
% 38.66/12.31  |
% 38.66/12.31  | Instantiating formula (20) with all_25_0_145, all_25_2_147, all_21_1_142 and discharging atoms or(all_25_2_147, all_21_1_142) = all_25_0_145, yields:
% 38.66/12.31  | (103)  ? [v0] :  ? [v1] : (or(all_21_1_142, all_25_2_147) = v0 & implies(v0, all_25_0_145) = v1 & is_a_theorem(v1) = 0)
% 38.66/12.31  |
% 38.66/12.31  | Instantiating formula (35) with all_25_0_145, all_21_1_142, all_25_2_147 and discharging atoms or(all_25_2_147, all_21_1_142) = all_25_0_145, yields:
% 38.66/12.31  | (104)  ? [v0] :  ? [v1] : (or(all_21_1_142, all_25_2_147) = v0 & implies(all_25_0_145, v0) = v1 & is_a_theorem(v1) = 0)
% 38.66/12.31  |
% 38.66/12.31  | Instantiating formula (47) with all_25_0_145, all_21_1_142, all_25_2_147 and discharging atoms or(all_25_2_147, all_21_1_142) = all_25_0_145, yields:
% 38.66/12.31  | (105)  ? [v0] : (implies(all_21_1_142, all_25_0_145) = v0 & is_a_theorem(v0) = 0)
% 38.66/12.31  |
% 38.66/12.31  | Instantiating formula (4) with all_21_0_141, all_21_1_142, all_0_35_35 and discharging atoms and(all_0_35_35, all_21_1_142) = all_21_0_141, yields:
% 38.66/12.31  | (106)  ? [v0] :  ? [v1] :  ? [v2] : (or(v0, v1) = v2 & not(v2) = all_21_0_141 & not(all_21_1_142) = v1 & not(all_0_35_35) = v0)
% 38.66/12.31  |
% 38.66/12.31  | Instantiating formula (58) with all_21_0_141, all_21_1_142, all_0_35_35, all_0_36_36, all_25_0_145 and discharging atoms and(all_0_35_35, all_21_1_142) = all_21_0_141, not(all_25_0_145) = all_0_35_35, not(all_0_36_36) = all_21_1_142, yields:
% 38.66/12.31  | (107)  ? [v0] : (or(all_25_0_145, all_0_36_36) = v0 & not(all_21_0_141) = v0)
% 38.66/12.31  |
% 38.66/12.31  | Instantiating formula (36) with all_23_0_143, all_0_35_35, all_0_36_36 and discharging atoms implies(all_0_36_36, all_0_35_35) = all_23_0_143, yields:
% 38.66/12.31  | (108)  ? [v0] :  ? [v1] : (and(all_0_36_36, v0) = v1 & not(v1) = all_23_0_143 & not(all_0_35_35) = v0)
% 38.66/12.31  |
% 38.66/12.31  | Instantiating formula (40) with all_23_0_143, all_0_35_35, all_0_36_36 and discharging atoms implies(all_0_36_36, all_0_35_35) = all_23_0_143, yields:
% 38.66/12.31  | (109)  ? [v0] : (or(v0, all_0_35_35) = all_23_0_143 & not(all_0_36_36) = v0)
% 38.66/12.31  |
% 38.66/12.31  | Instantiating (105) with all_41_0_151 yields:
% 38.66/12.31  | (110) implies(all_21_1_142, all_25_0_145) = all_41_0_151 & is_a_theorem(all_41_0_151) = 0
% 38.66/12.31  |
% 38.66/12.31  | Applying alpha-rule on (110) yields:
% 38.66/12.31  | (111) implies(all_21_1_142, all_25_0_145) = all_41_0_151
% 38.66/12.31  | (112) is_a_theorem(all_41_0_151) = 0
% 38.66/12.31  |
% 38.66/12.31  | Instantiating (104) with all_43_0_152, all_43_1_153 yields:
% 38.66/12.31  | (113) or(all_21_1_142, all_25_2_147) = all_43_1_153 & implies(all_25_0_145, all_43_1_153) = all_43_0_152 & is_a_theorem(all_43_0_152) = 0
% 38.66/12.31  |
% 38.66/12.31  | Applying alpha-rule on (113) yields:
% 38.66/12.31  | (114) or(all_21_1_142, all_25_2_147) = all_43_1_153
% 38.66/12.31  | (115) implies(all_25_0_145, all_43_1_153) = all_43_0_152
% 38.66/12.31  | (116) is_a_theorem(all_43_0_152) = 0
% 38.66/12.31  |
% 38.66/12.31  | Instantiating (102) with all_45_0_154 yields:
% 38.66/12.31  | (117) implies(all_0_36_36, all_0_34_34) = all_45_0_154 & is_a_theorem(all_45_0_154) = 0
% 38.66/12.31  |
% 38.66/12.31  | Applying alpha-rule on (117) yields:
% 38.66/12.31  | (118) implies(all_0_36_36, all_0_34_34) = all_45_0_154
% 38.66/12.31  | (119) is_a_theorem(all_45_0_154) = 0
% 38.66/12.31  |
% 38.66/12.31  | Instantiating (100) with all_47_0_155, all_47_1_156, all_47_2_157 yields:
% 38.66/12.31  | (120) and(all_47_2_157, all_47_1_156) = all_47_0_155 & not(all_47_0_155) = all_0_34_34 & not(all_29_0_150) = all_47_2_157 & not(all_0_36_36) = all_47_1_156
% 38.66/12.31  |
% 38.66/12.31  | Applying alpha-rule on (120) yields:
% 38.66/12.31  | (121) and(all_47_2_157, all_47_1_156) = all_47_0_155
% 38.66/12.31  | (122) not(all_47_0_155) = all_0_34_34
% 38.66/12.31  | (123) not(all_29_0_150) = all_47_2_157
% 38.66/12.32  | (124) not(all_0_36_36) = all_47_1_156
% 38.66/12.32  |
% 38.66/12.32  | Instantiating (99) with all_49_0_158, all_49_1_159 yields:
% 38.66/12.32  | (125) or(all_0_36_36, all_29_0_150) = all_49_1_159 & implies(all_49_1_159, all_0_34_34) = all_49_0_158 & is_a_theorem(all_49_0_158) = 0
% 38.66/12.32  |
% 38.66/12.32  | Applying alpha-rule on (125) yields:
% 38.66/12.32  | (126) or(all_0_36_36, all_29_0_150) = all_49_1_159
% 38.66/12.32  | (127) implies(all_49_1_159, all_0_34_34) = all_49_0_158
% 38.66/12.32  | (128) is_a_theorem(all_49_0_158) = 0
% 38.66/12.32  |
% 38.66/12.32  | Instantiating (101) with all_51_0_160, all_51_1_161 yields:
% 38.66/12.32  | (129) or(all_0_36_36, all_29_0_150) = all_51_1_161 & implies(all_0_34_34, all_51_1_161) = all_51_0_160 & is_a_theorem(all_51_0_160) = 0
% 38.66/12.32  |
% 38.66/12.32  | Applying alpha-rule on (129) yields:
% 38.66/12.32  | (130) or(all_0_36_36, all_29_0_150) = all_51_1_161
% 38.66/12.32  | (131) implies(all_0_34_34, all_51_1_161) = all_51_0_160
% 38.66/12.32  | (132) is_a_theorem(all_51_0_160) = 0
% 38.66/12.32  |
% 38.66/12.32  | Instantiating (103) with all_55_0_165, all_55_1_166 yields:
% 38.66/12.32  | (133) or(all_21_1_142, all_25_2_147) = all_55_1_166 & implies(all_55_1_166, all_25_0_145) = all_55_0_165 & is_a_theorem(all_55_0_165) = 0
% 38.66/12.32  |
% 38.66/12.32  | Applying alpha-rule on (133) yields:
% 38.66/12.32  | (134) or(all_21_1_142, all_25_2_147) = all_55_1_166
% 38.66/12.32  | (135) implies(all_55_1_166, all_25_0_145) = all_55_0_165
% 38.66/12.32  | (136) is_a_theorem(all_55_0_165) = 0
% 38.66/12.32  |
% 38.66/12.32  | Instantiating (107) with all_58_0_168 yields:
% 38.66/12.32  | (137) or(all_25_0_145, all_0_36_36) = all_58_0_168 & not(all_21_0_141) = all_58_0_168
% 38.66/12.32  |
% 38.66/12.32  | Applying alpha-rule on (137) yields:
% 38.66/12.32  | (138) or(all_25_0_145, all_0_36_36) = all_58_0_168
% 38.66/12.32  | (139) not(all_21_0_141) = all_58_0_168
% 38.66/12.32  |
% 38.66/12.32  | Instantiating (106) with all_66_0_176, all_66_1_177, all_66_2_178 yields:
% 38.66/12.32  | (140) or(all_66_2_178, all_66_1_177) = all_66_0_176 & not(all_66_0_176) = all_21_0_141 & not(all_21_1_142) = all_66_1_177 & not(all_0_35_35) = all_66_2_178
% 38.66/12.32  |
% 38.66/12.32  | Applying alpha-rule on (140) yields:
% 38.66/12.32  | (141) or(all_66_2_178, all_66_1_177) = all_66_0_176
% 38.66/12.32  | (142) not(all_66_0_176) = all_21_0_141
% 38.66/12.32  | (143) not(all_21_1_142) = all_66_1_177
% 38.66/12.32  | (144) not(all_0_35_35) = all_66_2_178
% 38.66/12.32  |
% 38.66/12.32  | Instantiating (109) with all_68_0_179 yields:
% 38.66/12.32  | (145) or(all_68_0_179, all_0_35_35) = all_23_0_143 & not(all_0_36_36) = all_68_0_179
% 38.66/12.32  |
% 38.66/12.32  | Applying alpha-rule on (145) yields:
% 38.66/12.32  | (146) or(all_68_0_179, all_0_35_35) = all_23_0_143
% 38.66/12.32  | (147) not(all_0_36_36) = all_68_0_179
% 38.66/12.32  |
% 38.66/12.32  | Instantiating (108) with all_70_0_180, all_70_1_181 yields:
% 38.66/12.32  | (148) and(all_0_36_36, all_70_1_181) = all_70_0_180 & not(all_70_0_180) = all_23_0_143 & not(all_0_35_35) = all_70_1_181
% 38.66/12.32  |
% 38.66/12.32  | Applying alpha-rule on (148) yields:
% 38.66/12.32  | (149) and(all_0_36_36, all_70_1_181) = all_70_0_180
% 38.66/12.32  | (150) not(all_70_0_180) = all_23_0_143
% 38.66/12.32  | (151) not(all_0_35_35) = all_70_1_181
% 38.66/12.32  |
% 38.66/12.32  | Instantiating formula (57) with all_21_1_142, all_25_2_147, all_43_1_153, all_55_1_166 and discharging atoms or(all_21_1_142, all_25_2_147) = all_55_1_166, or(all_21_1_142, all_25_2_147) = all_43_1_153, yields:
% 38.66/12.32  | (152) all_55_1_166 = all_43_1_153
% 38.66/12.32  |
% 38.66/12.32  | Instantiating formula (57) with all_0_36_36, all_29_0_150, all_49_1_159, all_51_1_161 and discharging atoms or(all_0_36_36, all_29_0_150) = all_51_1_161, or(all_0_36_36, all_29_0_150) = all_49_1_159, yields:
% 38.66/12.32  | (153) all_51_1_161 = all_49_1_159
% 38.66/12.32  |
% 38.66/12.32  | Instantiating formula (14) with all_21_0_141, all_58_0_168, all_0_34_34 and discharging atoms not(all_21_0_141) = all_58_0_168, not(all_21_0_141) = all_0_34_34, yields:
% 38.66/12.32  | (154) all_58_0_168 = all_0_34_34
% 38.66/12.32  |
% 38.66/12.32  | Instantiating formula (14) with all_0_35_35, all_70_1_181, all_29_0_150 and discharging atoms not(all_0_35_35) = all_70_1_181, not(all_0_35_35) = all_29_0_150, yields:
% 38.66/12.32  | (155) all_70_1_181 = all_29_0_150
% 38.66/12.32  |
% 38.66/12.32  | Instantiating formula (14) with all_0_35_35, all_66_2_178, all_70_1_181 and discharging atoms not(all_0_35_35) = all_70_1_181, not(all_0_35_35) = all_66_2_178, yields:
% 38.66/12.32  | (156) all_70_1_181 = all_66_2_178
% 38.66/12.32  |
% 38.66/12.32  | Instantiating formula (14) with all_0_36_36, all_68_0_179, all_21_1_142 and discharging atoms not(all_0_36_36) = all_68_0_179, not(all_0_36_36) = all_21_1_142, yields:
% 38.66/12.32  | (157) all_68_0_179 = all_21_1_142
% 38.66/12.32  |
% 38.66/12.32  | Instantiating formula (14) with all_0_36_36, all_47_1_156, all_68_0_179 and discharging atoms not(all_0_36_36) = all_68_0_179, not(all_0_36_36) = all_47_1_156, yields:
% 38.66/12.32  | (158) all_68_0_179 = all_47_1_156
% 38.66/12.32  |
% 38.66/12.32  | Combining equations (155,156) yields a new equation:
% 38.66/12.32  | (159) all_66_2_178 = all_29_0_150
% 38.66/12.32  |
% 38.66/12.32  | Combining equations (158,157) yields a new equation:
% 38.66/12.32  | (160) all_47_1_156 = all_21_1_142
% 38.66/12.32  |
% 38.66/12.32  | Simplifying 160 yields:
% 38.66/12.32  | (161) all_47_1_156 = all_21_1_142
% 38.66/12.32  |
% 38.66/12.32  | Combining equations (159,156) yields a new equation:
% 38.66/12.32  | (155) all_70_1_181 = all_29_0_150
% 38.66/12.32  |
% 38.66/12.32  | From (154) and (138) follows:
% 38.66/12.32  | (163) or(all_25_0_145, all_0_36_36) = all_0_34_34
% 38.66/12.32  |
% 38.66/12.32  | From (153) and (130) follows:
% 38.66/12.32  | (126) or(all_0_36_36, all_29_0_150) = all_49_1_159
% 38.66/12.32  |
% 38.66/12.32  | From (155) and (149) follows:
% 38.66/12.32  | (165) and(all_0_36_36, all_29_0_150) = all_70_0_180
% 38.66/12.32  |
% 38.66/12.32  | From (161) and (124) follows:
% 38.66/12.32  | (77) not(all_0_36_36) = all_21_1_142
% 38.66/12.32  |
% 38.66/12.32  | From (152) and (135) follows:
% 38.66/12.32  | (167) implies(all_43_1_153, all_25_0_145) = all_55_0_165
% 38.66/12.32  |
% 38.66/12.32  | From (153) and (131) follows:
% 38.66/12.32  | (168) implies(all_0_34_34, all_49_1_159) = all_51_0_160
% 38.66/12.32  |
% 38.66/12.32  | Instantiating formula (20) with all_0_34_34, all_25_0_145, all_0_36_36 and discharging atoms or(all_25_0_145, all_0_36_36) = all_0_34_34, yields:
% 38.66/12.32  | (169)  ? [v0] :  ? [v1] : (or(all_0_36_36, all_25_0_145) = v0 & implies(v0, all_0_34_34) = v1 & is_a_theorem(v1) = 0)
% 38.66/12.32  |
% 38.66/12.32  | Instantiating formula (35) with all_0_34_34, all_0_36_36, all_25_0_145 and discharging atoms or(all_25_0_145, all_0_36_36) = all_0_34_34, yields:
% 38.66/12.32  | (170)  ? [v0] :  ? [v1] : (or(all_0_36_36, all_25_0_145) = v0 & implies(all_0_34_34, v0) = v1 & is_a_theorem(v1) = 0)
% 38.66/12.32  |
% 38.66/12.32  | Instantiating formula (59) with all_49_1_159, all_29_0_150, all_0_36_36 and discharging atoms or(all_0_36_36, all_29_0_150) = all_49_1_159, yields:
% 38.66/12.33  | (171)  ? [v0] :  ? [v1] :  ? [v2] : (and(v0, v1) = v2 & not(v2) = all_49_1_159 & not(all_29_0_150) = v1 & not(all_0_36_36) = v0)
% 38.66/12.33  |
% 38.66/12.33  | Instantiating formula (4) with all_70_0_180, all_29_0_150, all_0_36_36 and discharging atoms and(all_0_36_36, all_29_0_150) = all_70_0_180, yields:
% 38.66/12.33  | (172)  ? [v0] :  ? [v1] :  ? [v2] : (or(v0, v1) = v2 & not(v2) = all_70_0_180 & not(all_29_0_150) = v1 & not(all_0_36_36) = v0)
% 38.66/12.33  |
% 38.66/12.33  | Instantiating formula (8) with all_49_0_158, all_0_34_34, all_49_1_159 and discharging atoms implies(all_49_1_159, all_0_34_34) = all_49_0_158, yields:
% 38.66/12.33  | (173)  ? [v0] : ((v0 = 0 & is_a_theorem(all_0_34_34) = 0) | ( ~ (v0 = 0) & is_a_theorem(all_49_0_158) = v0) | ( ~ (v0 = 0) & is_a_theorem(all_49_1_159) = v0))
% 38.66/12.33  |
% 38.66/12.33  | Instantiating formula (36) with all_55_0_165, all_25_0_145, all_43_1_153 and discharging atoms implies(all_43_1_153, all_25_0_145) = all_55_0_165, yields:
% 38.66/12.33  | (174)  ? [v0] :  ? [v1] : (and(all_43_1_153, v0) = v1 & not(v1) = all_55_0_165 & not(all_25_0_145) = v0)
% 38.66/12.33  |
% 38.66/12.33  | Instantiating formula (40) with all_43_0_152, all_43_1_153, all_25_0_145 and discharging atoms implies(all_25_0_145, all_43_1_153) = all_43_0_152, yields:
% 38.66/12.33  | (175)  ? [v0] : (or(v0, all_43_1_153) = all_43_0_152 & not(all_25_0_145) = v0)
% 38.66/12.33  |
% 38.66/12.33  | Instantiating formula (36) with all_41_0_151, all_25_0_145, all_21_1_142 and discharging atoms implies(all_21_1_142, all_25_0_145) = all_41_0_151, yields:
% 38.66/12.33  | (176)  ? [v0] :  ? [v1] : (and(all_21_1_142, v0) = v1 & not(v1) = all_41_0_151 & not(all_25_0_145) = v0)
% 38.66/12.33  |
% 38.66/12.33  | Instantiating formula (8) with all_51_0_160, all_49_1_159, all_0_34_34 and discharging atoms implies(all_0_34_34, all_49_1_159) = all_51_0_160, yields:
% 38.66/12.33  | (177)  ? [v0] : ((v0 = 0 & is_a_theorem(all_49_1_159) = 0) | ( ~ (v0 = 0) & is_a_theorem(all_51_0_160) = v0) | ( ~ (v0 = 0) & is_a_theorem(all_0_34_34) = v0))
% 38.66/12.33  |
% 38.66/12.33  | Instantiating formula (40) with all_45_0_154, all_0_34_34, all_0_36_36 and discharging atoms implies(all_0_36_36, all_0_34_34) = all_45_0_154, yields:
% 38.66/12.33  | (178)  ? [v0] : (or(v0, all_0_34_34) = all_45_0_154 & not(all_0_36_36) = v0)
% 38.66/12.33  |
% 38.66/12.33  | Instantiating (171) with all_94_0_191, all_94_1_192, all_94_2_193 yields:
% 38.66/12.33  | (179) and(all_94_2_193, all_94_1_192) = all_94_0_191 & not(all_94_0_191) = all_49_1_159 & not(all_29_0_150) = all_94_1_192 & not(all_0_36_36) = all_94_2_193
% 38.66/12.33  |
% 38.66/12.33  | Applying alpha-rule on (179) yields:
% 38.66/12.33  | (180) and(all_94_2_193, all_94_1_192) = all_94_0_191
% 38.66/12.33  | (181) not(all_94_0_191) = all_49_1_159
% 38.66/12.33  | (182) not(all_29_0_150) = all_94_1_192
% 38.66/12.33  | (183) not(all_0_36_36) = all_94_2_193
% 38.66/12.33  |
% 38.66/12.33  | Instantiating (172) with all_98_0_197, all_98_1_198, all_98_2_199 yields:
% 38.66/12.33  | (184) or(all_98_2_199, all_98_1_198) = all_98_0_197 & not(all_98_0_197) = all_70_0_180 & not(all_29_0_150) = all_98_1_198 & not(all_0_36_36) = all_98_2_199
% 38.66/12.33  |
% 38.66/12.33  | Applying alpha-rule on (184) yields:
% 38.66/12.33  | (185) or(all_98_2_199, all_98_1_198) = all_98_0_197
% 38.66/12.33  | (186) not(all_98_0_197) = all_70_0_180
% 38.66/12.33  | (187) not(all_29_0_150) = all_98_1_198
% 38.66/12.33  | (188) not(all_0_36_36) = all_98_2_199
% 38.66/12.33  |
% 38.66/12.33  | Instantiating (170) with all_123_0_217, all_123_1_218 yields:
% 38.66/12.33  | (189) or(all_0_36_36, all_25_0_145) = all_123_1_218 & implies(all_0_34_34, all_123_1_218) = all_123_0_217 & is_a_theorem(all_123_0_217) = 0
% 38.66/12.33  |
% 38.66/12.33  | Applying alpha-rule on (189) yields:
% 38.66/12.33  | (190) or(all_0_36_36, all_25_0_145) = all_123_1_218
% 38.66/12.33  | (191) implies(all_0_34_34, all_123_1_218) = all_123_0_217
% 38.66/12.33  | (192) is_a_theorem(all_123_0_217) = 0
% 38.66/12.33  |
% 38.66/12.33  | Instantiating (176) with all_130_0_224, all_130_1_225 yields:
% 38.66/12.33  | (193) and(all_21_1_142, all_130_1_225) = all_130_0_224 & not(all_130_0_224) = all_41_0_151 & not(all_25_0_145) = all_130_1_225
% 38.66/12.33  |
% 38.66/12.33  | Applying alpha-rule on (193) yields:
% 38.66/12.33  | (194) and(all_21_1_142, all_130_1_225) = all_130_0_224
% 38.66/12.33  | (195) not(all_130_0_224) = all_41_0_151
% 38.66/12.33  | (196) not(all_25_0_145) = all_130_1_225
% 38.66/12.33  |
% 38.66/12.33  | Instantiating (175) with all_134_0_228 yields:
% 38.66/12.33  | (197) or(all_134_0_228, all_43_1_153) = all_43_0_152 & not(all_25_0_145) = all_134_0_228
% 38.66/12.33  |
% 38.66/12.33  | Applying alpha-rule on (197) yields:
% 38.66/12.33  | (198) or(all_134_0_228, all_43_1_153) = all_43_0_152
% 38.66/12.33  | (199) not(all_25_0_145) = all_134_0_228
% 38.66/12.33  |
% 38.66/12.33  | Instantiating (174) with all_145_0_238, all_145_1_239 yields:
% 38.66/12.33  | (200) and(all_43_1_153, all_145_1_239) = all_145_0_238 & not(all_145_0_238) = all_55_0_165 & not(all_25_0_145) = all_145_1_239
% 38.66/12.33  |
% 38.66/12.33  | Applying alpha-rule on (200) yields:
% 38.66/12.33  | (201) and(all_43_1_153, all_145_1_239) = all_145_0_238
% 38.66/12.33  | (202) not(all_145_0_238) = all_55_0_165
% 38.66/12.33  | (203) not(all_25_0_145) = all_145_1_239
% 38.66/12.33  |
% 38.66/12.33  | Instantiating (173) with all_182_0_271 yields:
% 38.66/12.33  | (204) (all_182_0_271 = 0 & is_a_theorem(all_0_34_34) = 0) | ( ~ (all_182_0_271 = 0) & is_a_theorem(all_49_0_158) = all_182_0_271) | ( ~ (all_182_0_271 = 0) & is_a_theorem(all_49_1_159) = all_182_0_271)
% 38.66/12.33  |
% 38.66/12.33  | Instantiating (177) with all_186_0_274 yields:
% 38.66/12.33  | (205) (all_186_0_274 = 0 & is_a_theorem(all_49_1_159) = 0) | ( ~ (all_186_0_274 = 0) & is_a_theorem(all_51_0_160) = all_186_0_274) | ( ~ (all_186_0_274 = 0) & is_a_theorem(all_0_34_34) = all_186_0_274)
% 38.66/12.33  |
% 38.66/12.33  | Instantiating (169) with all_191_0_279, all_191_1_280 yields:
% 38.66/12.33  | (206) or(all_0_36_36, all_25_0_145) = all_191_1_280 & implies(all_191_1_280, all_0_34_34) = all_191_0_279 & is_a_theorem(all_191_0_279) = 0
% 38.66/12.33  |
% 38.66/12.33  | Applying alpha-rule on (206) yields:
% 38.66/12.33  | (207) or(all_0_36_36, all_25_0_145) = all_191_1_280
% 38.66/12.33  | (208) implies(all_191_1_280, all_0_34_34) = all_191_0_279
% 38.66/12.33  | (209) is_a_theorem(all_191_0_279) = 0
% 38.66/12.33  |
% 38.66/12.33  | Instantiating (178) with all_202_0_289 yields:
% 38.66/12.33  | (210) or(all_202_0_289, all_0_34_34) = all_45_0_154 & not(all_0_36_36) = all_202_0_289
% 38.66/12.33  |
% 38.66/12.33  | Applying alpha-rule on (210) yields:
% 38.66/12.33  | (211) or(all_202_0_289, all_0_34_34) = all_45_0_154
% 38.66/12.33  | (212) not(all_0_36_36) = all_202_0_289
% 38.66/12.33  |
% 38.66/12.33  +-Applying beta-rule and splitting (204), into two cases.
% 38.66/12.33  |-Branch one:
% 38.66/12.33  | (213) (all_182_0_271 = 0 & is_a_theorem(all_0_34_34) = 0) | ( ~ (all_182_0_271 = 0) & is_a_theorem(all_49_0_158) = all_182_0_271)
% 38.66/12.33  |
% 38.66/12.33  	+-Applying beta-rule and splitting (213), into two cases.
% 38.66/12.33  	|-Branch one:
% 38.66/12.33  	| (214) all_182_0_271 = 0 & is_a_theorem(all_0_34_34) = 0
% 38.66/12.33  	|
% 38.66/12.33  		| Applying alpha-rule on (214) yields:
% 38.66/12.33  		| (215) all_182_0_271 = 0
% 38.66/12.33  		| (216) is_a_theorem(all_0_34_34) = 0
% 38.66/12.33  		|
% 38.66/12.33  		| Instantiating formula (24) with all_0_34_34, 0, all_0_33_33 and discharging atoms is_a_theorem(all_0_34_34) = all_0_33_33, is_a_theorem(all_0_34_34) = 0, yields:
% 38.66/12.33  		| (217) all_0_33_33 = 0
% 38.66/12.33  		|
% 38.66/12.34  		| Equations (217) can reduce 46 to:
% 38.66/12.34  		| (218) $false
% 38.66/12.34  		|
% 38.66/12.34  		|-The branch is then unsatisfiable
% 38.66/12.34  	|-Branch two:
% 38.66/12.34  	| (219)  ~ (all_182_0_271 = 0) & is_a_theorem(all_49_0_158) = all_182_0_271
% 38.66/12.34  	|
% 38.66/12.34  		| Applying alpha-rule on (219) yields:
% 38.66/12.34  		| (220)  ~ (all_182_0_271 = 0)
% 38.66/12.34  		| (221) is_a_theorem(all_49_0_158) = all_182_0_271
% 38.66/12.34  		|
% 38.66/12.34  		| Instantiating formula (24) with all_49_0_158, all_182_0_271, 0 and discharging atoms is_a_theorem(all_49_0_158) = all_182_0_271, is_a_theorem(all_49_0_158) = 0, yields:
% 38.66/12.34  		| (215) all_182_0_271 = 0
% 38.66/12.34  		|
% 38.66/12.34  		| Equations (215) can reduce 220 to:
% 38.66/12.34  		| (218) $false
% 38.66/12.34  		|
% 38.66/12.34  		|-The branch is then unsatisfiable
% 38.66/12.34  |-Branch two:
% 38.66/12.34  | (224)  ~ (all_182_0_271 = 0) & is_a_theorem(all_49_1_159) = all_182_0_271
% 38.66/12.34  |
% 38.66/12.34  	| Applying alpha-rule on (224) yields:
% 38.66/12.34  	| (220)  ~ (all_182_0_271 = 0)
% 38.66/12.34  	| (226) is_a_theorem(all_49_1_159) = all_182_0_271
% 38.66/12.34  	|
% 38.66/12.34  	+-Applying beta-rule and splitting (205), into two cases.
% 38.66/12.34  	|-Branch one:
% 38.66/12.34  	| (227) (all_186_0_274 = 0 & is_a_theorem(all_49_1_159) = 0) | ( ~ (all_186_0_274 = 0) & is_a_theorem(all_51_0_160) = all_186_0_274)
% 38.66/12.34  	|
% 38.66/12.34  		+-Applying beta-rule and splitting (227), into two cases.
% 38.66/12.34  		|-Branch one:
% 38.66/12.34  		| (228) all_186_0_274 = 0 & is_a_theorem(all_49_1_159) = 0
% 38.66/12.34  		|
% 38.66/12.34  			| Applying alpha-rule on (228) yields:
% 38.66/12.34  			| (229) all_186_0_274 = 0
% 38.66/12.34  			| (230) is_a_theorem(all_49_1_159) = 0
% 38.66/12.34  			|
% 38.66/12.34  			| Instantiating formula (24) with all_49_1_159, 0, all_182_0_271 and discharging atoms is_a_theorem(all_49_1_159) = all_182_0_271, is_a_theorem(all_49_1_159) = 0, yields:
% 38.66/12.34  			| (215) all_182_0_271 = 0
% 38.66/12.34  			|
% 38.66/12.34  			| Equations (215) can reduce 220 to:
% 38.66/12.34  			| (218) $false
% 38.66/12.34  			|
% 38.66/12.34  			|-The branch is then unsatisfiable
% 38.66/12.34  		|-Branch two:
% 38.66/12.34  		| (233)  ~ (all_186_0_274 = 0) & is_a_theorem(all_51_0_160) = all_186_0_274
% 38.66/12.34  		|
% 38.66/12.34  			| Applying alpha-rule on (233) yields:
% 38.66/12.34  			| (234)  ~ (all_186_0_274 = 0)
% 38.66/12.34  			| (235) is_a_theorem(all_51_0_160) = all_186_0_274
% 38.66/12.34  			|
% 38.66/12.34  			| Instantiating formula (24) with all_51_0_160, all_186_0_274, 0 and discharging atoms is_a_theorem(all_51_0_160) = all_186_0_274, is_a_theorem(all_51_0_160) = 0, yields:
% 38.66/12.34  			| (229) all_186_0_274 = 0
% 38.66/12.34  			|
% 38.66/12.34  			| Equations (229) can reduce 234 to:
% 38.66/12.34  			| (218) $false
% 38.66/12.34  			|
% 38.66/12.34  			|-The branch is then unsatisfiable
% 38.66/12.34  	|-Branch two:
% 38.66/12.34  	| (238)  ~ (all_186_0_274 = 0) & is_a_theorem(all_0_34_34) = all_186_0_274
% 38.66/12.34  	|
% 38.66/12.34  		| Applying alpha-rule on (238) yields:
% 38.66/12.34  		| (234)  ~ (all_186_0_274 = 0)
% 38.66/12.34  		| (240) is_a_theorem(all_0_34_34) = all_186_0_274
% 38.66/12.34  		|
% 38.66/12.34  		| Instantiating formula (57) with all_0_36_36, all_25_0_145, all_123_1_218, all_191_1_280 and discharging atoms or(all_0_36_36, all_25_0_145) = all_191_1_280, or(all_0_36_36, all_25_0_145) = all_123_1_218, yields:
% 38.66/12.34  		| (241) all_191_1_280 = all_123_1_218
% 38.66/12.34  		|
% 38.66/12.34  		| Instantiating formula (14) with all_25_0_145, all_134_0_228, all_0_35_35 and discharging atoms not(all_25_0_145) = all_134_0_228, not(all_25_0_145) = all_0_35_35, yields:
% 38.66/12.34  		| (242) all_134_0_228 = all_0_35_35
% 38.66/12.34  		|
% 38.66/12.34  		| Instantiating formula (14) with all_25_0_145, all_134_0_228, all_145_1_239 and discharging atoms not(all_25_0_145) = all_145_1_239, not(all_25_0_145) = all_134_0_228, yields:
% 38.66/12.34  		| (243) all_145_1_239 = all_134_0_228
% 38.66/12.34  		|
% 38.66/12.34  		| Instantiating formula (14) with all_25_0_145, all_130_1_225, all_145_1_239 and discharging atoms not(all_25_0_145) = all_145_1_239, not(all_25_0_145) = all_130_1_225, yields:
% 38.66/12.34  		| (244) all_145_1_239 = all_130_1_225
% 38.66/12.34  		|
% 38.66/12.34  		| Instantiating formula (14) with all_0_36_36, all_202_0_289, all_21_1_142 and discharging atoms not(all_0_36_36) = all_202_0_289, not(all_0_36_36) = all_21_1_142, yields:
% 38.66/12.34  		| (245) all_202_0_289 = all_21_1_142
% 38.66/12.34  		|
% 38.66/12.34  		| Instantiating formula (14) with all_0_36_36, all_98_2_199, all_202_0_289 and discharging atoms not(all_0_36_36) = all_202_0_289, not(all_0_36_36) = all_98_2_199, yields:
% 38.66/12.34  		| (246) all_202_0_289 = all_98_2_199
% 38.66/12.34  		|
% 38.66/12.34  		| Instantiating formula (14) with all_0_36_36, all_94_2_193, all_202_0_289 and discharging atoms not(all_0_36_36) = all_202_0_289, not(all_0_36_36) = all_94_2_193, yields:
% 38.66/12.34  		| (247) all_202_0_289 = all_94_2_193
% 38.66/12.34  		|
% 38.66/12.34  		| Instantiating formula (24) with all_0_34_34, all_186_0_274, all_0_33_33 and discharging atoms is_a_theorem(all_0_34_34) = all_186_0_274, is_a_theorem(all_0_34_34) = all_0_33_33, yields:
% 38.66/12.34  		| (248) all_186_0_274 = all_0_33_33
% 38.66/12.34  		|
% 38.66/12.34  		| Combining equations (245,246) yields a new equation:
% 38.66/12.34  		| (249) all_98_2_199 = all_21_1_142
% 38.66/12.34  		|
% 38.66/12.34  		| Combining equations (247,246) yields a new equation:
% 38.66/12.34  		| (250) all_98_2_199 = all_94_2_193
% 38.66/12.34  		|
% 38.66/12.34  		| Combining equations (243,244) yields a new equation:
% 38.66/12.34  		| (251) all_134_0_228 = all_130_1_225
% 38.66/12.34  		|
% 38.66/12.34  		| Simplifying 251 yields:
% 38.66/12.34  		| (252) all_134_0_228 = all_130_1_225
% 38.66/12.34  		|
% 38.66/12.34  		| Combining equations (242,252) yields a new equation:
% 38.66/12.34  		| (253) all_130_1_225 = all_0_35_35
% 38.66/12.34  		|
% 38.66/12.34  		| Combining equations (249,250) yields a new equation:
% 38.66/12.34  		| (254) all_94_2_193 = all_21_1_142
% 38.66/12.34  		|
% 38.66/12.34  		| Equations (248) can reduce 234 to:
% 38.66/12.34  		| (46)  ~ (all_0_33_33 = 0)
% 38.66/12.34  		|
% 38.66/12.34  		| From (241) and (207) follows:
% 38.66/12.34  		| (190) or(all_0_36_36, all_25_0_145) = all_123_1_218
% 38.66/12.34  		|
% 38.66/12.34  		| From (253) and (194) follows:
% 38.66/12.34  		| (257) and(all_21_1_142, all_0_35_35) = all_130_0_224
% 38.66/12.34  		|
% 38.66/12.34  		| From (253) and (196) follows:
% 38.66/12.34  		| (84) not(all_25_0_145) = all_0_35_35
% 38.66/12.34  		|
% 38.66/12.34  		| From (254) and (183) follows:
% 38.66/12.34  		| (77) not(all_0_36_36) = all_21_1_142
% 38.66/12.34  		|
% 38.66/12.34  		| From (241) and (208) follows:
% 38.66/12.34  		| (260) implies(all_123_1_218, all_0_34_34) = all_191_0_279
% 38.66/12.34  		|
% 38.66/12.34  		| From (248) and (240) follows:
% 38.66/12.34  		| (22) is_a_theorem(all_0_34_34) = all_0_33_33
% 38.66/12.34  		|
% 38.66/12.34  		| Instantiating formula (58) with all_130_0_224, all_0_35_35, all_21_1_142, all_25_0_145, all_0_36_36 and discharging atoms and(all_21_1_142, all_0_35_35) = all_130_0_224, not(all_25_0_145) = all_0_35_35, not(all_0_36_36) = all_21_1_142, yields:
% 38.66/12.34  		| (262)  ? [v0] : (or(all_0_36_36, all_25_0_145) = v0 & not(all_130_0_224) = v0)
% 38.66/12.34  		|
% 38.66/12.34  		| Instantiating formula (8) with all_191_0_279, all_0_34_34, all_123_1_218 and discharging atoms implies(all_123_1_218, all_0_34_34) = all_191_0_279, yields:
% 38.66/12.34  		| (263)  ? [v0] : ((v0 = 0 & is_a_theorem(all_0_34_34) = 0) | ( ~ (v0 = 0) & is_a_theorem(all_191_0_279) = v0) | ( ~ (v0 = 0) & is_a_theorem(all_123_1_218) = v0))
% 38.66/12.34  		|
% 38.66/12.34  		| Instantiating (262) with all_268_0_322 yields:
% 38.66/12.34  		| (264) or(all_0_36_36, all_25_0_145) = all_268_0_322 & not(all_130_0_224) = all_268_0_322
% 38.66/12.34  		|
% 38.66/12.34  		| Applying alpha-rule on (264) yields:
% 38.66/12.34  		| (265) or(all_0_36_36, all_25_0_145) = all_268_0_322
% 38.66/12.34  		| (266) not(all_130_0_224) = all_268_0_322
% 38.66/12.34  		|
% 38.66/12.34  		| Instantiating (263) with all_453_0_501 yields:
% 38.66/12.34  		| (267) (all_453_0_501 = 0 & is_a_theorem(all_0_34_34) = 0) | ( ~ (all_453_0_501 = 0) & is_a_theorem(all_191_0_279) = all_453_0_501) | ( ~ (all_453_0_501 = 0) & is_a_theorem(all_123_1_218) = all_453_0_501)
% 38.66/12.34  		|
% 38.66/12.34  		+-Applying beta-rule and splitting (267), into two cases.
% 38.66/12.34  		|-Branch one:
% 38.66/12.34  		| (268) (all_453_0_501 = 0 & is_a_theorem(all_0_34_34) = 0) | ( ~ (all_453_0_501 = 0) & is_a_theorem(all_191_0_279) = all_453_0_501)
% 38.66/12.34  		|
% 38.66/12.34  			+-Applying beta-rule and splitting (268), into two cases.
% 38.66/12.34  			|-Branch one:
% 38.66/12.34  			| (269) all_453_0_501 = 0 & is_a_theorem(all_0_34_34) = 0
% 38.66/12.34  			|
% 38.66/12.34  				| Applying alpha-rule on (269) yields:
% 38.66/12.34  				| (270) all_453_0_501 = 0
% 38.66/12.34  				| (216) is_a_theorem(all_0_34_34) = 0
% 38.66/12.34  				|
% 38.66/12.34  				| Instantiating formula (24) with all_0_34_34, 0, all_0_33_33 and discharging atoms is_a_theorem(all_0_34_34) = all_0_33_33, is_a_theorem(all_0_34_34) = 0, yields:
% 38.66/12.34  				| (217) all_0_33_33 = 0
% 38.66/12.34  				|
% 38.66/12.34  				| Equations (217) can reduce 46 to:
% 38.66/12.35  				| (218) $false
% 38.66/12.35  				|
% 38.66/12.35  				|-The branch is then unsatisfiable
% 38.66/12.35  			|-Branch two:
% 38.66/12.35  			| (274)  ~ (all_453_0_501 = 0) & is_a_theorem(all_191_0_279) = all_453_0_501
% 38.66/12.35  			|
% 38.66/12.35  				| Applying alpha-rule on (274) yields:
% 38.66/12.35  				| (275)  ~ (all_453_0_501 = 0)
% 38.66/12.35  				| (276) is_a_theorem(all_191_0_279) = all_453_0_501
% 38.66/12.35  				|
% 38.66/12.35  				| Instantiating formula (24) with all_191_0_279, all_453_0_501, 0 and discharging atoms is_a_theorem(all_191_0_279) = all_453_0_501, is_a_theorem(all_191_0_279) = 0, yields:
% 38.66/12.35  				| (270) all_453_0_501 = 0
% 38.66/12.35  				|
% 38.66/12.35  				| Equations (270) can reduce 275 to:
% 38.66/12.35  				| (218) $false
% 38.66/12.35  				|
% 38.66/12.35  				|-The branch is then unsatisfiable
% 38.66/12.35  		|-Branch two:
% 38.66/12.35  		| (279)  ~ (all_453_0_501 = 0) & is_a_theorem(all_123_1_218) = all_453_0_501
% 38.66/12.35  		|
% 38.66/12.35  			| Applying alpha-rule on (279) yields:
% 38.66/12.35  			| (275)  ~ (all_453_0_501 = 0)
% 38.66/12.35  			| (281) is_a_theorem(all_123_1_218) = all_453_0_501
% 38.66/12.35  			|
% 38.66/12.35  			| Instantiating formula (57) with all_0_36_36, all_25_0_145, all_268_0_322, all_123_1_218 and discharging atoms or(all_0_36_36, all_25_0_145) = all_268_0_322, or(all_0_36_36, all_25_0_145) = all_123_1_218, yields:
% 38.66/12.35  			| (282) all_268_0_322 = all_123_1_218
% 38.66/12.35  			|
% 38.66/12.35  			| Instantiating formula (14) with all_130_0_224, all_268_0_322, all_41_0_151 and discharging atoms not(all_130_0_224) = all_268_0_322, not(all_130_0_224) = all_41_0_151, yields:
% 38.66/12.35  			| (283) all_268_0_322 = all_41_0_151
% 38.66/12.35  			|
% 38.66/12.35  			| Combining equations (282,283) yields a new equation:
% 38.66/12.35  			| (284) all_123_1_218 = all_41_0_151
% 38.66/12.35  			|
% 38.66/12.35  			| Simplifying 284 yields:
% 38.66/12.35  			| (285) all_123_1_218 = all_41_0_151
% 38.66/12.35  			|
% 38.66/12.35  			| From (285) and (281) follows:
% 38.66/12.35  			| (286) is_a_theorem(all_41_0_151) = all_453_0_501
% 38.66/12.35  			|
% 38.66/12.35  			| Instantiating formula (24) with all_41_0_151, all_453_0_501, 0 and discharging atoms is_a_theorem(all_41_0_151) = all_453_0_501, is_a_theorem(all_41_0_151) = 0, yields:
% 38.66/12.35  			| (270) all_453_0_501 = 0
% 38.66/12.35  			|
% 38.66/12.35  			| Equations (270) can reduce 275 to:
% 38.66/12.35  			| (218) $false
% 38.66/12.35  			|
% 38.66/12.35  			|-The branch is then unsatisfiable
% 38.66/12.35  % SZS output end Proof for theBenchmark
% 38.66/12.35  
% 38.66/12.35  11715ms
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