TSTP Solution File: LCL512+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : LCL512+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.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 09:36:53 EDT 2022
% Result : Theorem 3.73s 1.50s
% Output : Proof 5.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL512+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 4 09:37:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.59/0.58 ____ _
% 0.59/0.58 ___ / __ \_____(_)___ ________ __________
% 0.59/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.58
% 0.59/0.58 A Theorem Prover for First-Order Logic
% 0.59/0.58 (ePrincess v.1.0)
% 0.59/0.58
% 0.59/0.58 (c) Philipp Rümmer, 2009-2015
% 0.59/0.58 (c) Peter Backeman, 2014-2015
% 0.59/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.58 Bug reports to peter@backeman.se
% 0.59/0.58
% 0.59/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.58
% 0.59/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.66/0.99 Prover 0: Preprocessing ...
% 2.94/1.38 Prover 0: Constructing countermodel ...
% 3.73/1.50 Prover 0: proved (837ms)
% 3.73/1.50
% 3.73/1.50 No countermodel exists, formula is valid
% 3.73/1.50 % SZS status Theorem for theBenchmark
% 3.73/1.50
% 3.73/1.50 Generating proof ... found it (size 9)
% 5.25/1.83
% 5.25/1.83 % SZS output start Proof for theBenchmark
% 5.25/1.83 Assumed formulas after preprocessing and simplification:
% 5.25/1.83 | (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] : (equiv(v57, v58) = v59 & implies(v59, v60) = v61 & implies(v57, v58) = v60 & op_equiv & op_implies_and & op_or & kn3 & kn2 & kn1 & substitution_of_equivalents & modus_ponens & ~ equivalence_1 & ~ is_a_theorem(v61) & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ! [v120] : ! [v121] : ! [v122] : ! [v123] : ! [v124] : ! [v125] : ( ~ (and(v118, v116) = v122) | ~ (and(v117, v118) = v120) | ~ (not(v122) = v123) | ~ (not(v120) = v121) | ~ (implies(v121, v123) = v124) | ~ (implies(v119, v124) = v125) | ~ (implies(v116, v117) = v119) | is_a_theorem(v125)) & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ! [v120] : ( ~ (and(v118, v119) = v120) | ~ (not(v117) = v119) | ~ (not(v116) = v118) | ? [v121] : (or(v116, v117) = v121 & not(v120) = v121)) & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ! [v120] : ( ~ (and(v118, v119) = v120) | ~ (implies(v117, v116) = v119) | ~ (implies(v116, v117) = v118) | equiv(v116, v117) = v120) & ! [v116] : ! [v117] : ! [v118] : ! [v119] : (v117 = v116 | ~ (or(v119, v118) = v117) | ~ (or(v119, v118) = v116)) & ! [v116] : ! [v117] : ! [v118] : ! [v119] : (v117 = v116 | ~ (and(v119, v118) = v117) | ~ (and(v119, v118) = v116)) & ! [v116] : ! [v117] : ! [v118] : ! [v119] : (v117 = v116 | ~ (equiv(v119, v118) = v117) | ~ (equiv(v119, v118) = v116)) & ! [v116] : ! [v117] : ! [v118] : ! [v119] : (v117 = v116 | ~ (implies(v119, v118) = v117) | ~ (implies(v119, v118) = v116)) & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ( ~ (and(v116, v118) = v119) | ~ (not(v117) = v118) | ? [v120] : (not(v119) = v120 & implies(v116, v117) = v120)) & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ( ~ (and(v116, v117) = v118) | ~ (implies(v118, v116) = v119) | is_a_theorem(v119)) & ! [v116] : ! [v117] : ! [v118] : (v117 = v116 | ~ (not(v118) = v117) | ~ (not(v118) = v116)) & ! [v116] : ! [v117] : ! [v118] : (v117 = v116 | ~ (equiv(v116, v117) = v118) | ~ is_a_theorem(v118)) & ! [v116] : ! [v117] : ! [v118] : ( ~ (or(v116, v117) = v118) | ? [v119] : ? [v120] : ? [v121] : (and(v119, v120) = v121 & not(v121) = v118 & not(v117) = v120 & not(v116) = v119)) & ! [v116] : ! [v117] : ! [v118] : ( ~ (and(v116, v116) = v117) | ~ (implies(v116, v117) = v118) | is_a_theorem(v118)) & ! [v116] : ! [v117] : ! [v118] : ( ~ (equiv(v116, v117) = v118) | ? [v119] : ? [v120] : (and(v119, v120) = v118 & implies(v117, v116) = v120 & implies(v116, v117) = v119)) & ! [v116] : ! [v117] : ! [v118] : ( ~ (implies(v116, v117) = v118) | ~ is_a_theorem(v118) | ~ is_a_theorem(v116) | is_a_theorem(v117)) & ! [v116] : ! [v117] : ! [v118] : ( ~ (implies(v116, v117) = v118) | ? [v119] : ? [v120] : (and(v116, v119) = v120 & not(v120) = v118 & not(v117) = v119)) & ( ~ op_implies_or | ( ! [v116] : ! [v117] : ! [v118] : ! [v119] : ( ~ (or(v118, v117) = v119) | ~ (not(v116) = v118) | implies(v116, v117) = v119) & ! [v116] : ! [v117] : ! [v118] : ( ~ (implies(v116, v117) = v118) | ? [v119] : (or(v119, v117) = v118 & not(v116) = v119)))) & ( ~ op_and | ( ! [v116] : ! [v117] : ! [v118] : ! [v119] : ! [v120] : ( ~ (or(v118, v119) = v120) | ~ (not(v117) = v119) | ~ (not(v116) = v118) | ? [v121] : (and(v116, v117) = v121 & not(v120) = v121)) & ! [v116] : ! [v117] : ! [v118] : ( ~ (and(v116, v117) = v118) | ? [v119] : ? [v120] : ? [v121] : (or(v119, v120) = v121 & not(v121) = v118 & not(v117) = v120 & not(v116) = v119)))) & ((or(v75, v76) = v77 & implies(v75, v77) = v78 & ~ or_1 & ~ is_a_theorem(v78)) | (or_1 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ( ~ (or(v116, v117) = v118) | ~ (implies(v116, v118) = v119) | is_a_theorem(v119)))) & ((or(v71, v72) = v73 & implies(v72, v73) = v74 & ~ or_2 & ~ is_a_theorem(v74)) | (or_2 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ( ~ (or(v116, v117) = v118) | ~ (implies(v117, v118) = v119) | is_a_theorem(v119)))) & ((or(v62, v63) = v67 & implies(v67, v64) = v68 & implies(v66, v68) = v69 & implies(v65, v69) = v70 & implies(v63, v64) = v66 & implies(v62, v64) = v65 & ~ or_3 & ~ is_a_theorem(v70)) | (or_3 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ! [v120] : ! [v121] : ! [v122] : ! [v123] : ! [v124] : ( ~ (or(v116, v117) = v121) | ~ (implies(v121, v118) = v122) | ~ (implies(v120, v122) = v123) | ~ (implies(v119, v123) = v124) | ~ (implies(v117, v118) = v120) | ~ (implies(v116, v118) = v119) | is_a_theorem(v124)))) & ((or(v25, v25) = v26 & implies(v26, v25) = v27 & ~ r1 & ~ is_a_theorem(v27)) | (r1 & ! [v116] : ! [v117] : ! [v118] : ( ~ (or(v116, v116) = v117) | ~ (implies(v117, v116) = v118) | is_a_theorem(v118)))) & ((or(v21, v22) = v23 & implies(v22, v23) = v24 & ~ r2 & ~ is_a_theorem(v24)) | (r2 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ( ~ (or(v116, v117) = v118) | ~ (implies(v117, v118) = v119) | is_a_theorem(v119)))) & ((or(v17, v16) = v19 & or(v16, v17) = v18 & implies(v18, v19) = v20 & ~ r3 & ~ is_a_theorem(v20)) | (r3 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ! [v120] : ( ~ (or(v117, v116) = v119) | ~ (or(v116, v117) = v118) | ~ (implies(v118, v119) = v120) | is_a_theorem(v120)))) & ((or(v9, v13) = v14 & or(v9, v10) = v11 & or(v8, v11) = v12 & or(v8, v10) = v13 & implies(v12, v14) = v15 & ~ r4 & ~ is_a_theorem(v15)) | (r4 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ! [v120] : ! [v121] : ! [v122] : ! [v123] : ( ~ (or(v117, v121) = v122) | ~ (or(v117, v118) = v119) | ~ (or(v116, v119) = v120) | ~ (or(v116, v118) = v121) | ~ (implies(v120, v122) = v123) | is_a_theorem(v123)))) & ((or(v0, v2) = v5 & or(v0, v1) = v4 & implies(v4, v5) = v6 & implies(v3, v6) = v7 & implies(v1, v2) = v3 & ~ r5 & ~ is_a_theorem(v7)) | (r5 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ! [v120] : ! [v121] : ! [v122] : ! [v123] : ( ~ (or(v116, v118) = v121) | ~ (or(v116, v117) = v120) | ~ (implies(v120, v121) = v122) | ~ (implies(v119, v122) = v123) | ~ (implies(v117, v118) = v119) | is_a_theorem(v123)))) & ((and(v88, v89) = v90 & implies(v90, v88) = v91 & ~ and_1 & ~ is_a_theorem(v91)) | (and_1 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ( ~ (and(v116, v117) = v118) | ~ (implies(v118, v116) = v119) | is_a_theorem(v119)))) & ((and(v84, v85) = v86 & implies(v86, v85) = v87 & ~ and_2 & ~ is_a_theorem(v87)) | (and_2 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ( ~ (and(v116, v117) = v118) | ~ (implies(v118, v117) = v119) | is_a_theorem(v119)))) & ((and(v79, v80) = v81 & implies(v80, v81) = v82 & implies(v79, v82) = v83 & ~ and_3 & ~ is_a_theorem(v83)) | (and_3 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ! [v120] : ( ~ (and(v116, v117) = v118) | ~ (implies(v117, v118) = v119) | ~ (implies(v116, v119) = v120) | is_a_theorem(v120)))) & ((not(v110) = v111 & not(v109) = v112 & implies(v113, v114) = v115 & implies(v111, v112) = v113 & implies(v109, v110) = v114 & ~ modus_tollens & ~ is_a_theorem(v115)) | (modus_tollens & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ! [v120] : ! [v121] : ! [v122] : ( ~ (not(v117) = v118) | ~ (not(v116) = v119) | ~ (implies(v120, v121) = v122) | ~ (implies(v118, v119) = v120) | ~ (implies(v116, v117) = v121) | is_a_theorem(v122)))) & ((not(v32) = v34 & implies(v34, v33) = v35 & implies(v32, v35) = v36 & ~ cn2 & ~ is_a_theorem(v36)) | (cn2 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ! [v120] : ( ~ (not(v116) = v118) | ~ (implies(v118, v117) = v119) | ~ (implies(v116, v119) = v120) | is_a_theorem(v120)))) & ((not(v28) = v29 & implies(v30, v28) = v31 & implies(v29, v28) = v30 & ~ cn3 & ~ is_a_theorem(v31)) | (cn3 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ( ~ (not(v116) = v117) | ~ (implies(v118, v116) = v119) | ~ (implies(v117, v116) = v118) | is_a_theorem(v119)))) & ((equiv(v52, v53) = v54 & implies(v54, v55) = v56 & implies(v53, v52) = v55 & ~ equivalence_2 & ~ is_a_theorem(v56)) | (equivalence_2 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ! [v120] : ( ~ (equiv(v116, v117) = v118) | ~ (implies(v118, v119) = v120) | ~ (implies(v117, v116) = v119) | is_a_theorem(v120)))) & ((equiv(v45, v46) = v49 & implies(v48, v49) = v50 & implies(v47, v50) = v51 & implies(v46, v45) = v48 & implies(v45, v46) = v47 & ~ equivalence_3 & ~ is_a_theorem(v51)) | (equivalence_3 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ! [v120] : ! [v121] : ! [v122] : ( ~ (equiv(v116, v117) = v120) | ~ (implies(v119, v120) = v121) | ~ (implies(v118, v121) = v122) | ~ (implies(v117, v116) = v119) | ~ (implies(v116, v117) = v118) | is_a_theorem(v122)))) & ((implies(v106, v105) = v107 & implies(v105, v107) = v108 & ~ implies_1 & ~ is_a_theorem(v108)) | (implies_1 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ( ~ (implies(v117, v116) = v118) | ~ (implies(v116, v118) = v119) | is_a_theorem(v119)))) & ((implies(v103, v102) = v104 & implies(v100, v102) = v103 & implies(v100, v101) = v102 & ~ implies_2 & ~ is_a_theorem(v104)) | (implies_2 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ! [v120] : ( ~ (implies(v119, v118) = v120) | ~ (implies(v116, v118) = v119) | ~ (implies(v116, v117) = v118) | is_a_theorem(v120)))) & ((implies(v96, v97) = v98 & implies(v95, v98) = v99 & implies(v93, v94) = v96 & implies(v92, v94) = v97 & implies(v92, v93) = v95 & ~ implies_3 & ~ is_a_theorem(v99)) | (implies_3 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ! [v120] : ! [v121] : ! [v122] : ! [v123] : ( ~ (implies(v120, v121) = v122) | ~ (implies(v119, v122) = v123) | ~ (implies(v117, v118) = v120) | ~ (implies(v116, v118) = v121) | ~ (implies(v116, v117) = v119) | is_a_theorem(v123)))) & ((implies(v41, v42) = v43 & implies(v40, v43) = v44 & implies(v38, v39) = v41 & implies(v37, v39) = v42 & implies(v37, v38) = v40 & ~ cn1 & ~ is_a_theorem(v44)) | (cn1 & ! [v116] : ! [v117] : ! [v118] : ! [v119] : ! [v120] : ! [v121] : ! [v122] : ! [v123] : ( ~ (implies(v120, v121) = v122) | ~ (implies(v119, v122) = v123) | ~ (implies(v117, v118) = v120) | ~ (implies(v116, v118) = v121) | ~ (implies(v116, v117) = v119) | is_a_theorem(v123)))))
% 5.25/1.89 | 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 yields:
% 5.25/1.89 | (1) equiv(all_0_58_58, all_0_57_57) = all_0_56_56 & implies(all_0_56_56, all_0_55_55) = all_0_54_54 & implies(all_0_58_58, all_0_57_57) = all_0_55_55 & op_equiv & op_implies_and & op_or & kn3 & kn2 & kn1 & substitution_of_equivalents & modus_ponens & ~ equivalence_1 & ~ is_a_theorem(all_0_54_54) & ! [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)) & ! [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] : (v1 = v0 | ~ (or(v3, v2) = v1) | ~ (or(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v2) = v3) | ~ (not(v1) = v2) | ? [v4] : (not(v3) = v4 & implies(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | is_a_theorem(v3)) & ! [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] : ( ~ (or(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (and(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (and(v0, v0) = v1) | ~ (implies(v0, v1) = v2) | is_a_theorem(v2)) & ! [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)) & ( ~ 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)))) & ((or(all_0_40_40, all_0_39_39) = all_0_38_38 & implies(all_0_40_40, all_0_38_38) = all_0_37_37 & ~ or_1 & ~ is_a_theorem(all_0_37_37)) | (or_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v0, v2) = v3) | is_a_theorem(v3)))) & ((or(all_0_44_44, all_0_43_43) = all_0_42_42 & implies(all_0_43_43, all_0_42_42) = all_0_41_41 & ~ or_2 & ~ is_a_theorem(all_0_41_41)) | (or_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3)))) & ((or(all_0_53_53, all_0_52_52) = all_0_48_48 & implies(all_0_48_48, all_0_51_51) = all_0_47_47 & implies(all_0_49_49, all_0_47_47) = all_0_46_46 & implies(all_0_50_50, all_0_46_46) = all_0_45_45 & implies(all_0_52_52, all_0_51_51) = all_0_49_49 & implies(all_0_53_53, all_0_51_51) = all_0_50_50 & ~ or_3 & ~ is_a_theorem(all_0_45_45)) | (or_3 & ! [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)))) & ((or(all_0_90_90, all_0_90_90) = all_0_89_89 & implies(all_0_89_89, all_0_90_90) = all_0_88_88 & ~ r1 & ~ is_a_theorem(all_0_88_88)) | (r1 & ! [v0] : ! [v1] : ! [v2] : ( ~ (or(v0, v0) = v1) | ~ (implies(v1, v0) = v2) | is_a_theorem(v2)))) & ((or(all_0_94_94, all_0_93_93) = all_0_92_92 & implies(all_0_93_93, all_0_92_92) = all_0_91_91 & ~ r2 & ~ is_a_theorem(all_0_91_91)) | (r2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3)))) & ((or(all_0_98_98, all_0_99_99) = all_0_96_96 & or(all_0_99_99, all_0_98_98) = all_0_97_97 & implies(all_0_97_97, all_0_96_96) = all_0_95_95 & ~ r3 & ~ is_a_theorem(all_0_95_95)) | (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_106_106, all_0_102_102) = all_0_101_101 & or(all_0_106_106, all_0_105_105) = all_0_104_104 & or(all_0_107_107, all_0_104_104) = all_0_103_103 & or(all_0_107_107, all_0_105_105) = all_0_102_102 & implies(all_0_103_103, all_0_101_101) = all_0_100_100 & ~ r4 & ~ is_a_theorem(all_0_100_100)) | (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_115_115, all_0_113_113) = all_0_110_110 & or(all_0_115_115, all_0_114_114) = all_0_111_111 & implies(all_0_111_111, all_0_110_110) = all_0_109_109 & implies(all_0_112_112, all_0_109_109) = all_0_108_108 & implies(all_0_114_114, all_0_113_113) = all_0_112_112 & ~ r5 & ~ is_a_theorem(all_0_108_108)) | (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_27_27, all_0_26_26) = all_0_25_25 & implies(all_0_25_25, all_0_27_27) = all_0_24_24 & ~ and_1 & ~ is_a_theorem(all_0_24_24)) | (and_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | is_a_theorem(v3)))) & ((and(all_0_31_31, all_0_30_30) = all_0_29_29 & implies(all_0_29_29, all_0_30_30) = all_0_28_28 & ~ and_2 & ~ is_a_theorem(all_0_28_28)) | (and_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v1) = v3) | is_a_theorem(v3)))) & ((and(all_0_36_36, all_0_35_35) = all_0_34_34 & implies(all_0_35_35, all_0_34_34) = all_0_33_33 & implies(all_0_36_36, all_0_33_33) = all_0_32_32 & ~ and_3 & ~ is_a_theorem(all_0_32_32)) | (and_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | ~ (implies(v0, v3) = v4) | is_a_theorem(v4)))) & ((not(all_0_5_5) = all_0_4_4 & not(all_0_6_6) = all_0_3_3 & implies(all_0_2_2, all_0_1_1) = all_0_0_0 & implies(all_0_4_4, all_0_3_3) = all_0_2_2 & implies(all_0_6_6, all_0_5_5) = all_0_1_1 & ~ modus_tollens & ~ is_a_theorem(all_0_0_0)) | (modus_tollens & ! [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)))) & ((not(all_0_83_83) = all_0_81_81 & implies(all_0_81_81, all_0_82_82) = all_0_80_80 & implies(all_0_83_83, all_0_80_80) = all_0_79_79 & ~ cn2 & ~ is_a_theorem(all_0_79_79)) | (cn2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (not(v0) = v2) | ~ (implies(v2, v1) = v3) | ~ (implies(v0, v3) = v4) | is_a_theorem(v4)))) & ((not(all_0_87_87) = all_0_86_86 & implies(all_0_85_85, all_0_87_87) = all_0_84_84 & implies(all_0_86_86, all_0_87_87) = all_0_85_85 & ~ cn3 & ~ is_a_theorem(all_0_84_84)) | (cn3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (not(v0) = v1) | ~ (implies(v2, v0) = v3) | ~ (implies(v1, v0) = v2) | is_a_theorem(v3)))) & ((equiv(all_0_63_63, all_0_62_62) = all_0_61_61 & implies(all_0_61_61, all_0_60_60) = all_0_59_59 & implies(all_0_62_62, all_0_63_63) = all_0_60_60 & ~ equivalence_2 & ~ is_a_theorem(all_0_59_59)) | (equivalence_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equiv(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | ~ (implies(v1, v0) = v3) | is_a_theorem(v4)))) & ((equiv(all_0_70_70, all_0_69_69) = all_0_66_66 & implies(all_0_67_67, all_0_66_66) = all_0_65_65 & implies(all_0_68_68, all_0_65_65) = all_0_64_64 & implies(all_0_69_69, all_0_70_70) = all_0_67_67 & implies(all_0_70_70, all_0_69_69) = all_0_68_68 & ~ equivalence_3 & ~ is_a_theorem(all_0_64_64)) | (equivalence_3 & ! [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)))) & ((implies(all_0_9_9, all_0_10_10) = all_0_8_8 & implies(all_0_10_10, all_0_8_8) = all_0_7_7 & ~ implies_1 & ~ is_a_theorem(all_0_7_7)) | (implies_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (implies(v1, v0) = v2) | ~ (implies(v0, v2) = v3) | is_a_theorem(v3)))) & ((implies(all_0_12_12, all_0_13_13) = all_0_11_11 & implies(all_0_15_15, all_0_13_13) = all_0_12_12 & implies(all_0_15_15, all_0_14_14) = all_0_13_13 & ~ implies_2 & ~ is_a_theorem(all_0_11_11)) | (implies_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (implies(v3, v2) = v4) | ~ (implies(v0, v2) = v3) | ~ (implies(v0, v1) = v2) | is_a_theorem(v4)))) & ((implies(all_0_19_19, all_0_18_18) = all_0_17_17 & implies(all_0_20_20, all_0_17_17) = all_0_16_16 & implies(all_0_22_22, all_0_21_21) = all_0_19_19 & implies(all_0_23_23, all_0_21_21) = all_0_18_18 & implies(all_0_23_23, all_0_22_22) = all_0_20_20 & ~ implies_3 & ~ is_a_theorem(all_0_16_16)) | (implies_3 & ! [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)))) & ((implies(all_0_74_74, all_0_73_73) = all_0_72_72 & implies(all_0_75_75, all_0_72_72) = all_0_71_71 & implies(all_0_77_77, all_0_76_76) = all_0_74_74 & implies(all_0_78_78, all_0_76_76) = all_0_73_73 & implies(all_0_78_78, all_0_77_77) = all_0_75_75 & ~ cn1 & ~ is_a_theorem(all_0_71_71)) | (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))))
% 5.62/1.91 |
% 5.62/1.91 | Applying alpha-rule on (1) yields:
% 5.62/1.91 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v2) = v3) | ~ (not(v1) = v2) | ? [v4] : (not(v3) = v4 & implies(v0, v1) = v4))
% 5.62/1.92 | (3) (implies(all_0_74_74, all_0_73_73) = all_0_72_72 & implies(all_0_75_75, all_0_72_72) = all_0_71_71 & implies(all_0_77_77, all_0_76_76) = all_0_74_74 & implies(all_0_78_78, all_0_76_76) = all_0_73_73 & implies(all_0_78_78, all_0_77_77) = all_0_75_75 & ~ cn1 & ~ is_a_theorem(all_0_71_71)) | (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)))
% 5.62/1.92 | (4) op_equiv
% 5.62/1.92 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v2, v3) = v4) | ~ (implies(v1, v0) = v3) | ~ (implies(v0, v1) = v2) | equiv(v0, v1) = v4)
% 5.62/1.92 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0))
% 5.62/1.92 | (7) substitution_of_equivalents
% 5.62/1.92 | (8) equiv(all_0_58_58, all_0_57_57) = all_0_56_56
% 5.62/1.92 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (and(v0, v0) = v1) | ~ (implies(v0, v1) = v2) | is_a_theorem(v2))
% 5.62/1.92 | (10) (or(all_0_115_115, all_0_113_113) = all_0_110_110 & or(all_0_115_115, all_0_114_114) = all_0_111_111 & implies(all_0_111_111, all_0_110_110) = all_0_109_109 & implies(all_0_112_112, all_0_109_109) = all_0_108_108 & implies(all_0_114_114, all_0_113_113) = all_0_112_112 & ~ r5 & ~ is_a_theorem(all_0_108_108)) | (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)))
% 5.62/1.92 | (11) op_implies_and
% 5.62/1.92 | (12) ! [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))
% 5.62/1.92 | (13) (or(all_0_44_44, all_0_43_43) = all_0_42_42 & implies(all_0_43_43, all_0_42_42) = all_0_41_41 & ~ or_2 & ~ is_a_theorem(all_0_41_41)) | (or_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3)))
% 5.62/1.92 | (14) (not(all_0_5_5) = all_0_4_4 & not(all_0_6_6) = all_0_3_3 & implies(all_0_2_2, all_0_1_1) = all_0_0_0 & implies(all_0_4_4, all_0_3_3) = all_0_2_2 & implies(all_0_6_6, all_0_5_5) = all_0_1_1 & ~ modus_tollens & ~ is_a_theorem(all_0_0_0)) | (modus_tollens & ! [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)))
% 5.62/1.92 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (or(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (and(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3))
% 5.62/1.92 | (16) ~ equivalence_1
% 5.62/1.92 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (not(v2) = v1) | ~ (not(v2) = v0))
% 5.62/1.92 | (18) (not(all_0_83_83) = all_0_81_81 & implies(all_0_81_81, all_0_82_82) = all_0_80_80 & implies(all_0_83_83, all_0_80_80) = all_0_79_79 & ~ cn2 & ~ is_a_theorem(all_0_79_79)) | (cn2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (not(v0) = v2) | ~ (implies(v2, v1) = v3) | ~ (implies(v0, v3) = v4) | is_a_theorem(v4)))
% 5.62/1.92 | (19) kn1
% 5.62/1.92 | (20) (equiv(all_0_70_70, all_0_69_69) = all_0_66_66 & implies(all_0_67_67, all_0_66_66) = all_0_65_65 & implies(all_0_68_68, all_0_65_65) = all_0_64_64 & implies(all_0_69_69, all_0_70_70) = all_0_67_67 & implies(all_0_70_70, all_0_69_69) = all_0_68_68 & ~ equivalence_3 & ~ is_a_theorem(all_0_64_64)) | (equivalence_3 & ! [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)))
% 5.62/1.93 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v2, v3) = v4) | ~ (not(v1) = v3) | ~ (not(v0) = v2) | ? [v5] : (or(v0, v1) = v5 & not(v4) = v5))
% 5.62/1.93 | (22) (or(all_0_53_53, all_0_52_52) = all_0_48_48 & implies(all_0_48_48, all_0_51_51) = all_0_47_47 & implies(all_0_49_49, all_0_47_47) = all_0_46_46 & implies(all_0_50_50, all_0_46_46) = all_0_45_45 & implies(all_0_52_52, all_0_51_51) = all_0_49_49 & implies(all_0_53_53, all_0_51_51) = all_0_50_50 & ~ or_3 & ~ is_a_theorem(all_0_45_45)) | (or_3 & ! [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)))
% 5.62/1.93 | (23) kn3
% 5.62/1.93 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | is_a_theorem(v3))
% 5.62/1.93 | (25) implies(all_0_56_56, all_0_55_55) = all_0_54_54
% 5.62/1.93 | (26) modus_ponens
% 5.62/1.93 | (27) op_or
% 5.62/1.93 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (implies(v0, v1) = v2) | ~ is_a_theorem(v2) | ~ is_a_theorem(v0) | is_a_theorem(v1))
% 5.62/1.93 | (29) kn2
% 5.62/1.93 | (30) (and(all_0_31_31, all_0_30_30) = all_0_29_29 & implies(all_0_29_29, all_0_30_30) = all_0_28_28 & ~ and_2 & ~ is_a_theorem(all_0_28_28)) | (and_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v1) = v3) | is_a_theorem(v3)))
% 5.62/1.93 | (31) (or(all_0_106_106, all_0_102_102) = all_0_101_101 & or(all_0_106_106, all_0_105_105) = all_0_104_104 & or(all_0_107_107, all_0_104_104) = all_0_103_103 & or(all_0_107_107, all_0_105_105) = all_0_102_102 & implies(all_0_103_103, all_0_101_101) = all_0_100_100 & ~ r4 & ~ is_a_theorem(all_0_100_100)) | (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)))
% 5.62/1.93 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (or(v3, v2) = v1) | ~ (or(v3, v2) = v0))
% 5.62/1.93 | (33) ~ 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)))
% 5.62/1.93 | (34) (or(all_0_90_90, all_0_90_90) = all_0_89_89 & implies(all_0_89_89, all_0_90_90) = all_0_88_88 & ~ r1 & ~ is_a_theorem(all_0_88_88)) | (r1 & ! [v0] : ! [v1] : ! [v2] : ( ~ (or(v0, v0) = v1) | ~ (implies(v1, v0) = v2) | is_a_theorem(v2)))
% 5.62/1.93 | (35) (implies(all_0_19_19, all_0_18_18) = all_0_17_17 & implies(all_0_20_20, all_0_17_17) = all_0_16_16 & implies(all_0_22_22, all_0_21_21) = all_0_19_19 & implies(all_0_23_23, all_0_21_21) = all_0_18_18 & implies(all_0_23_23, all_0_22_22) = all_0_20_20 & ~ implies_3 & ~ is_a_theorem(all_0_16_16)) | (implies_3 & ! [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)))
% 5.62/1.93 | (36) ~ is_a_theorem(all_0_54_54)
% 5.62/1.93 | (37) (or(all_0_98_98, all_0_99_99) = all_0_96_96 & or(all_0_99_99, all_0_98_98) = all_0_97_97 & implies(all_0_97_97, all_0_96_96) = all_0_95_95 & ~ r3 & ~ is_a_theorem(all_0_95_95)) | (r3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (or(v1, v0) = v3) | ~ (or(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | is_a_theorem(v4)))
% 5.62/1.94 | (38) (and(all_0_27_27, all_0_26_26) = all_0_25_25 & implies(all_0_25_25, all_0_27_27) = all_0_24_24 & ~ and_1 & ~ is_a_theorem(all_0_24_24)) | (and_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | is_a_theorem(v3)))
% 5.62/1.94 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) = v0))
% 5.62/1.94 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (implies(v0, v1) = v2) | ? [v3] : ? [v4] : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) = v3))
% 5.62/1.94 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0))
% 5.62/1.94 | (42) ~ 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)))
% 5.62/1.94 | (43) (equiv(all_0_63_63, all_0_62_62) = all_0_61_61 & implies(all_0_61_61, all_0_60_60) = all_0_59_59 & implies(all_0_62_62, all_0_63_63) = all_0_60_60 & ~ equivalence_2 & ~ is_a_theorem(all_0_59_59)) | (equivalence_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equiv(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | ~ (implies(v1, v0) = v3) | is_a_theorem(v4)))
% 5.62/1.94 | (44) (implies(all_0_12_12, all_0_13_13) = all_0_11_11 & implies(all_0_15_15, all_0_13_13) = all_0_12_12 & implies(all_0_15_15, all_0_14_14) = all_0_13_13 & ~ implies_2 & ~ is_a_theorem(all_0_11_11)) | (implies_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (implies(v3, v2) = v4) | ~ (implies(v0, v2) = v3) | ~ (implies(v0, v1) = v2) | is_a_theorem(v4)))
% 5.62/1.94 | (45) implies(all_0_58_58, all_0_57_57) = all_0_55_55
% 5.62/1.94 | (46) (and(all_0_36_36, all_0_35_35) = all_0_34_34 & implies(all_0_35_35, all_0_34_34) = all_0_33_33 & implies(all_0_36_36, all_0_33_33) = all_0_32_32 & ~ and_3 & ~ is_a_theorem(all_0_32_32)) | (and_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | ~ (implies(v0, v3) = v4) | is_a_theorem(v4)))
% 5.62/1.94 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equiv(v0, v1) = v2) | ~ is_a_theorem(v2))
% 5.62/1.94 | (48) (or(all_0_94_94, all_0_93_93) = all_0_92_92 & implies(all_0_93_93, all_0_92_92) = all_0_91_91 & ~ r2 & ~ is_a_theorem(all_0_91_91)) | (r2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3)))
% 5.62/1.94 | (49) (implies(all_0_9_9, all_0_10_10) = all_0_8_8 & implies(all_0_10_10, all_0_8_8) = all_0_7_7 & ~ implies_1 & ~ is_a_theorem(all_0_7_7)) | (implies_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (implies(v1, v0) = v2) | ~ (implies(v0, v2) = v3) | is_a_theorem(v3)))
% 5.62/1.94 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (equiv(v0, v1) = v2) | ? [v3] : ? [v4] : (and(v3, v4) = v2 & implies(v1, v0) = v4 & implies(v0, v1) = v3))
% 5.62/1.94 | (51) (not(all_0_87_87) = all_0_86_86 & implies(all_0_85_85, all_0_87_87) = all_0_84_84 & implies(all_0_86_86, all_0_87_87) = all_0_85_85 & ~ cn3 & ~ is_a_theorem(all_0_84_84)) | (cn3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (not(v0) = v1) | ~ (implies(v2, v0) = v3) | ~ (implies(v1, v0) = v2) | is_a_theorem(v3)))
% 5.62/1.94 | (52) (or(all_0_40_40, all_0_39_39) = all_0_38_38 & implies(all_0_40_40, all_0_38_38) = all_0_37_37 & ~ or_1 & ~ is_a_theorem(all_0_37_37)) | (or_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v0, v2) = v3) | is_a_theorem(v3)))
% 5.62/1.94 |
% 5.62/1.94 | Instantiating formula (50) with all_0_56_56, all_0_57_57, all_0_58_58 and discharging atoms equiv(all_0_58_58, all_0_57_57) = all_0_56_56, yields:
% 5.62/1.94 | (53) ? [v0] : ? [v1] : (and(v0, v1) = all_0_56_56 & implies(all_0_57_57, all_0_58_58) = v1 & implies(all_0_58_58, all_0_57_57) = v0)
% 5.62/1.94 |
% 5.62/1.94 | Instantiating (53) with all_12_0_120, all_12_1_121 yields:
% 5.62/1.94 | (54) and(all_12_1_121, all_12_0_120) = all_0_56_56 & implies(all_0_57_57, all_0_58_58) = all_12_0_120 & implies(all_0_58_58, all_0_57_57) = all_12_1_121
% 5.62/1.94 |
% 5.62/1.94 | Applying alpha-rule on (54) yields:
% 5.62/1.94 | (55) and(all_12_1_121, all_12_0_120) = all_0_56_56
% 5.62/1.94 | (56) implies(all_0_57_57, all_0_58_58) = all_12_0_120
% 5.62/1.95 | (57) implies(all_0_58_58, all_0_57_57) = all_12_1_121
% 5.62/1.95 |
% 5.62/1.95 | Instantiating formula (41) with all_0_58_58, all_0_57_57, all_12_1_121, all_0_55_55 and discharging atoms implies(all_0_58_58, all_0_57_57) = all_12_1_121, implies(all_0_58_58, all_0_57_57) = all_0_55_55, yields:
% 5.62/1.95 | (58) all_12_1_121 = all_0_55_55
% 5.62/1.95 |
% 5.62/1.95 | From (58) and (55) follows:
% 5.62/1.95 | (59) and(all_0_55_55, all_12_0_120) = all_0_56_56
% 5.62/1.95 |
% 5.62/1.95 | Instantiating formula (24) with all_0_54_54, all_0_56_56, all_12_0_120, all_0_55_55 and discharging atoms and(all_0_55_55, all_12_0_120) = all_0_56_56, implies(all_0_56_56, all_0_55_55) = all_0_54_54, ~ is_a_theorem(all_0_54_54), yields:
% 5.62/1.95 | (60) $false
% 5.62/1.95 |
% 5.62/1.95 |-The branch is then unsatisfiable
% 5.62/1.95 % SZS output end Proof for theBenchmark
% 5.62/1.95
% 5.62/1.95 1348ms
%------------------------------------------------------------------------------