TSTP Solution File: LCL491+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : LCL491+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 09:36:48 EDT 2022
% Result : Theorem 3.40s 1.42s
% Output : Proof 5.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL491+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jul 2 23:17:05 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.51/0.59 ____ _
% 0.51/0.59 ___ / __ \_____(_)___ ________ __________
% 0.51/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.59
% 0.51/0.59 A Theorem Prover for First-Order Logic
% 0.51/0.59 (ePrincess v.1.0)
% 0.51/0.59
% 0.51/0.59 (c) Philipp Rümmer, 2009-2015
% 0.51/0.59 (c) Peter Backeman, 2014-2015
% 0.51/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.59 Bug reports to peter@backeman.se
% 0.51/0.59
% 0.51/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.59
% 0.51/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.75/0.95 Prover 0: Preprocessing ...
% 2.99/1.33 Prover 0: Constructing countermodel ...
% 3.40/1.42 Prover 0: proved (785ms)
% 3.40/1.42
% 3.40/1.42 No countermodel exists, formula is valid
% 3.40/1.42 % SZS status Theorem for theBenchmark
% 3.40/1.42
% 3.40/1.42 Generating proof ... found it (size 4)
% 4.82/1.71
% 4.82/1.71 % SZS output start Proof for theBenchmark
% 4.82/1.71 Assumed formulas after preprocessing and simplification:
% 4.82/1.71 | (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] : (or(v60, v61) = v62 & implies(v61, v62) = v63 & op_equiv & op_implies_or & op_implies_and & op_and & op_or & r5 & r4 & r3 & r2 & r1 & substitution_of_equivalents & modus_ponens & ~ or_2 & ~ is_a_theorem(v63) & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ! [v109] : ! [v110] : ! [v111] : ! [v112] : ( ~ (or(v106, v110) = v111) | ~ (or(v106, v107) = v108) | ~ (or(v105, v108) = v109) | ~ (or(v105, v107) = v110) | ~ (implies(v109, v111) = v112) | is_a_theorem(v112)) & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ! [v109] : ! [v110] : ! [v111] : ! [v112] : ( ~ (or(v105, v107) = v110) | ~ (or(v105, v106) = v109) | ~ (implies(v109, v110) = v111) | ~ (implies(v108, v111) = v112) | ~ (implies(v106, v107) = v108) | is_a_theorem(v112)) & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ! [v109] : ( ~ (or(v107, v108) = v109) | ~ (not(v106) = v108) | ~ (not(v105) = v107) | ? [v110] : (and(v105, v106) = v110 & not(v109) = v110)) & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ! [v109] : ( ~ (or(v106, v105) = v108) | ~ (or(v105, v106) = v107) | ~ (implies(v107, v108) = v109) | is_a_theorem(v109)) & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ! [v109] : ( ~ (and(v107, v108) = v109) | ~ (not(v106) = v108) | ~ (not(v105) = v107) | ? [v110] : (or(v105, v106) = v110 & not(v109) = v110)) & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ! [v109] : ( ~ (and(v107, v108) = v109) | ~ (implies(v106, v105) = v108) | ~ (implies(v105, v106) = v107) | equiv(v105, v106) = v109) & ! [v105] : ! [v106] : ! [v107] : ! [v108] : (v106 = v105 | ~ (or(v108, v107) = v106) | ~ (or(v108, v107) = v105)) & ! [v105] : ! [v106] : ! [v107] : ! [v108] : (v106 = v105 | ~ (and(v108, v107) = v106) | ~ (and(v108, v107) = v105)) & ! [v105] : ! [v106] : ! [v107] : ! [v108] : (v106 = v105 | ~ (equiv(v108, v107) = v106) | ~ (equiv(v108, v107) = v105)) & ! [v105] : ! [v106] : ! [v107] : ! [v108] : (v106 = v105 | ~ (implies(v108, v107) = v106) | ~ (implies(v108, v107) = v105)) & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ( ~ (or(v107, v106) = v108) | ~ (not(v105) = v107) | implies(v105, v106) = v108) & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ( ~ (or(v105, v106) = v107) | ~ (implies(v106, v107) = v108) | is_a_theorem(v108)) & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ( ~ (and(v105, v107) = v108) | ~ (not(v106) = v107) | ? [v109] : (not(v108) = v109 & implies(v105, v106) = v109)) & ! [v105] : ! [v106] : ! [v107] : (v106 = v105 | ~ (not(v107) = v106) | ~ (not(v107) = v105)) & ! [v105] : ! [v106] : ! [v107] : (v106 = v105 | ~ (equiv(v105, v106) = v107) | ~ is_a_theorem(v107)) & ! [v105] : ! [v106] : ! [v107] : ( ~ (or(v105, v106) = v107) | ? [v108] : ? [v109] : ? [v110] : (and(v108, v109) = v110 & not(v110) = v107 & not(v106) = v109 & not(v105) = v108)) & ! [v105] : ! [v106] : ! [v107] : ( ~ (or(v105, v105) = v106) | ~ (implies(v106, v105) = v107) | is_a_theorem(v107)) & ! [v105] : ! [v106] : ! [v107] : ( ~ (and(v105, v106) = v107) | ? [v108] : ? [v109] : ? [v110] : (or(v108, v109) = v110 & not(v110) = v107 & not(v106) = v109 & not(v105) = v108)) & ! [v105] : ! [v106] : ! [v107] : ( ~ (equiv(v105, v106) = v107) | ? [v108] : ? [v109] : (and(v108, v109) = v107 & implies(v106, v105) = v109 & implies(v105, v106) = v108)) & ! [v105] : ! [v106] : ! [v107] : ( ~ (implies(v105, v106) = v107) | ~ is_a_theorem(v107) | ~ is_a_theorem(v105) | is_a_theorem(v106)) & ! [v105] : ! [v106] : ! [v107] : ( ~ (implies(v105, v106) = v107) | ? [v108] : ? [v109] : (and(v105, v108) = v109 & not(v109) = v107 & not(v106) = v108)) & ! [v105] : ! [v106] : ! [v107] : ( ~ (implies(v105, v106) = v107) | ? [v108] : (or(v108, v106) = v107 & not(v105) = v108)) & ((or(v64, v65) = v66 & implies(v64, v66) = v67 & ~ or_1 & ~ is_a_theorem(v67)) | (or_1 & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ( ~ (or(v105, v106) = v107) | ~ (implies(v105, v107) = v108) | is_a_theorem(v108)))) & ((or(v51, v52) = v56 & implies(v56, v53) = v57 & implies(v55, v57) = v58 & implies(v54, v58) = v59 & implies(v52, v53) = v55 & implies(v51, v53) = v54 & ~ or_3 & ~ is_a_theorem(v59)) | (or_3 & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ! [v109] : ! [v110] : ! [v111] : ! [v112] : ! [v113] : ( ~ (or(v105, v106) = v110) | ~ (implies(v110, v107) = v111) | ~ (implies(v109, v111) = v112) | ~ (implies(v108, v112) = v113) | ~ (implies(v106, v107) = v109) | ~ (implies(v105, v107) = v108) | is_a_theorem(v113)))) & ((and(v77, v78) = v79 & implies(v79, v77) = v80 & ~ and_1 & ~ is_a_theorem(v80)) | (and_1 & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ( ~ (and(v105, v106) = v107) | ~ (implies(v107, v105) = v108) | is_a_theorem(v108)))) & ((and(v73, v74) = v75 & implies(v75, v74) = v76 & ~ and_2 & ~ is_a_theorem(v76)) | (and_2 & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ( ~ (and(v105, v106) = v107) | ~ (implies(v107, v106) = v108) | is_a_theorem(v108)))) & ((and(v68, v69) = v70 & implies(v69, v70) = v71 & implies(v68, v71) = v72 & ~ and_3 & ~ is_a_theorem(v72)) | (and_3 & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ! [v109] : ( ~ (and(v105, v106) = v107) | ~ (implies(v106, v107) = v108) | ~ (implies(v105, v108) = v109) | is_a_theorem(v109)))) & ((and(v31, v31) = v32 & implies(v31, v32) = v33 & ~ kn1 & ~ is_a_theorem(v33)) | (kn1 & ! [v105] : ! [v106] : ! [v107] : ( ~ (and(v105, v105) = v106) | ~ (implies(v105, v106) = v107) | is_a_theorem(v107)))) & ((and(v27, v28) = v29 & implies(v29, v27) = v30 & ~ kn2 & ~ is_a_theorem(v30)) | (kn2 & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ( ~ (and(v105, v106) = v107) | ~ (implies(v107, v105) = v108) | is_a_theorem(v108)))) & ((and(v19, v17) = v23 & and(v18, v19) = v21 & not(v23) = v24 & not(v21) = v22 & implies(v22, v24) = v25 & implies(v20, v25) = v26 & implies(v17, v18) = v20 & ~ kn3 & ~ is_a_theorem(v26)) | (kn3 & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ! [v109] : ! [v110] : ! [v111] : ! [v112] : ! [v113] : ! [v114] : ( ~ (and(v107, v105) = v111) | ~ (and(v106, v107) = v109) | ~ (not(v111) = v112) | ~ (not(v109) = v110) | ~ (implies(v110, v112) = v113) | ~ (implies(v108, v113) = v114) | ~ (implies(v105, v106) = v108) | is_a_theorem(v114)))) & ((not(v99) = v100 & not(v98) = v101 & implies(v102, v103) = v104 & implies(v100, v101) = v102 & implies(v98, v99) = v103 & ~ modus_tollens & ~ is_a_theorem(v104)) | (modus_tollens & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ! [v109] : ! [v110] : ! [v111] : ( ~ (not(v106) = v107) | ~ (not(v105) = v108) | ~ (implies(v109, v110) = v111) | ~ (implies(v107, v108) = v109) | ~ (implies(v105, v106) = v110) | is_a_theorem(v111)))) & ((not(v4) = v6 & implies(v6, v5) = v7 & implies(v4, v7) = v8 & ~ cn2 & ~ is_a_theorem(v8)) | (cn2 & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ! [v109] : ( ~ (not(v105) = v107) | ~ (implies(v107, v106) = v108) | ~ (implies(v105, v108) = v109) | is_a_theorem(v109)))) & ((not(v0) = v1 & implies(v2, v0) = v3 & implies(v1, v0) = v2 & ~ cn3 & ~ is_a_theorem(v3)) | (cn3 & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ( ~ (not(v105) = v106) | ~ (implies(v107, v105) = v108) | ~ (implies(v106, v105) = v107) | is_a_theorem(v108)))) & ((equiv(v46, v47) = v48 & implies(v48, v49) = v50 & implies(v46, v47) = v49 & ~ equivalence_1 & ~ is_a_theorem(v50)) | (equivalence_1 & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ! [v109] : ( ~ (equiv(v105, v106) = v107) | ~ (implies(v107, v108) = v109) | ~ (implies(v105, v106) = v108) | is_a_theorem(v109)))) & ((equiv(v41, v42) = v43 & implies(v43, v44) = v45 & implies(v42, v41) = v44 & ~ equivalence_2 & ~ is_a_theorem(v45)) | (equivalence_2 & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ! [v109] : ( ~ (equiv(v105, v106) = v107) | ~ (implies(v107, v108) = v109) | ~ (implies(v106, v105) = v108) | is_a_theorem(v109)))) & ((equiv(v34, v35) = v38 & implies(v37, v38) = v39 & implies(v36, v39) = v40 & implies(v35, v34) = v37 & implies(v34, v35) = v36 & ~ equivalence_3 & ~ is_a_theorem(v40)) | (equivalence_3 & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ! [v109] : ! [v110] : ! [v111] : ( ~ (equiv(v105, v106) = v109) | ~ (implies(v108, v109) = v110) | ~ (implies(v107, v110) = v111) | ~ (implies(v106, v105) = v108) | ~ (implies(v105, v106) = v107) | is_a_theorem(v111)))) & ((implies(v95, v94) = v96 & implies(v94, v96) = v97 & ~ implies_1 & ~ is_a_theorem(v97)) | (implies_1 & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ( ~ (implies(v106, v105) = v107) | ~ (implies(v105, v107) = v108) | is_a_theorem(v108)))) & ((implies(v92, v91) = v93 & implies(v89, v91) = v92 & implies(v89, v90) = v91 & ~ implies_2 & ~ is_a_theorem(v93)) | (implies_2 & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ! [v109] : ( ~ (implies(v108, v107) = v109) | ~ (implies(v105, v107) = v108) | ~ (implies(v105, v106) = v107) | is_a_theorem(v109)))) & ((implies(v85, v86) = v87 & implies(v84, v87) = v88 & implies(v82, v83) = v85 & implies(v81, v83) = v86 & implies(v81, v82) = v84 & ~ implies_3 & ~ is_a_theorem(v88)) | (implies_3 & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ! [v109] : ! [v110] : ! [v111] : ! [v112] : ( ~ (implies(v109, v110) = v111) | ~ (implies(v108, v111) = v112) | ~ (implies(v106, v107) = v109) | ~ (implies(v105, v107) = v110) | ~ (implies(v105, v106) = v108) | is_a_theorem(v112)))) & ((implies(v13, v14) = v15 & implies(v12, v15) = v16 & implies(v10, v11) = v13 & implies(v9, v11) = v14 & implies(v9, v10) = v12 & ~ cn1 & ~ is_a_theorem(v16)) | (cn1 & ! [v105] : ! [v106] : ! [v107] : ! [v108] : ! [v109] : ! [v110] : ! [v111] : ! [v112] : ( ~ (implies(v109, v110) = v111) | ~ (implies(v108, v111) = v112) | ~ (implies(v106, v107) = v109) | ~ (implies(v105, v107) = v110) | ~ (implies(v105, v106) = v108) | is_a_theorem(v112)))))
% 5.23/1.77 | 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 yields:
% 5.23/1.77 | (1) 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 & op_equiv & op_implies_or & op_implies_and & op_and & op_or & r5 & r4 & r3 & r2 & r1 & substitution_of_equivalents & modus_ponens & ~ or_2 & ~ is_a_theorem(all_0_41_41) & ! [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)) & ! [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)) & ! [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, v0) = v3) | ~ (or(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | is_a_theorem(v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v2, v3) = v4) | ~ (not(v1) = v3) | ~ (not(v0) = v2) | ? [v5] : (or(v0, v1) = v5 & not(v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v2, v3) = v4) | ~ (implies(v1, v0) = v3) | ~ (implies(v0, v1) = v2) | equiv(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (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] : ( ~ (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v2) = v3) | ~ (not(v1) = v2) | ? [v4] : (not(v3) = v4 & implies(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : (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] : ( ~ (or(v0, v0) = v1) | ~ (implies(v1, v0) = v2) | is_a_theorem(v2)) & ! [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(v0, v1) = v2) | ~ is_a_theorem(v2) | ~ is_a_theorem(v0) | is_a_theorem(v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (implies(v0, v1) = v2) | ? [v3] : ? [v4] : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (implies(v0, v1) = v2) | ? [v3] : (or(v3, v1) = v2 & 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_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)))) & ((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)))) & ((and(all_0_73_73, all_0_73_73) = all_0_72_72 & implies(all_0_73_73, all_0_72_72) = all_0_71_71 & ~ kn1 & ~ is_a_theorem(all_0_71_71)) | (kn1 & ! [v0] : ! [v1] : ! [v2] : ( ~ (and(v0, v0) = v1) | ~ (implies(v0, v1) = v2) | is_a_theorem(v2)))) & ((and(all_0_77_77, all_0_76_76) = all_0_75_75 & implies(all_0_75_75, all_0_77_77) = all_0_74_74 & ~ kn2 & ~ is_a_theorem(all_0_74_74)) | (kn2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | is_a_theorem(v3)))) & ((and(all_0_85_85, all_0_87_87) = all_0_81_81 & and(all_0_86_86, all_0_85_85) = all_0_83_83 & not(all_0_81_81) = all_0_80_80 & not(all_0_83_83) = all_0_82_82 & implies(all_0_82_82, all_0_80_80) = all_0_79_79 & implies(all_0_84_84, all_0_79_79) = all_0_78_78 & implies(all_0_87_87, all_0_86_86) = all_0_84_84 & ~ kn3 & ~ is_a_theorem(all_0_78_78)) | (kn3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (and(v2, v0) = v6) | ~ (and(v1, v2) = v4) | ~ (not(v6) = v7) | ~ (not(v4) = v5) | ~ (implies(v5, v7) = v8) | ~ (implies(v3, v8) = v9) | ~ (implies(v0, v1) = v3) | is_a_theorem(v9)))) & ((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_100_100) = all_0_98_98 & implies(all_0_98_98, all_0_99_99) = all_0_97_97 & implies(all_0_100_100, all_0_97_97) = all_0_96_96 & ~ cn2 & ~ is_a_theorem(all_0_96_96)) | (cn2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (not(v0) = v2) | ~ (implies(v2, v1) = v3) | ~ (implies(v0, v3) = v4) | is_a_theorem(v4)))) & ((not(all_0_104_104) = all_0_103_103 & implies(all_0_102_102, all_0_104_104) = all_0_101_101 & implies(all_0_103_103, all_0_104_104) = all_0_102_102 & ~ cn3 & ~ is_a_theorem(all_0_101_101)) | (cn3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (not(v0) = v1) | ~ (implies(v2, v0) = v3) | ~ (implies(v1, v0) = v2) | is_a_theorem(v3)))) & ((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 & ~ equivalence_1 & ~ is_a_theorem(all_0_54_54)) | (equivalence_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equiv(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | ~ (implies(v0, v1) = v3) | is_a_theorem(v4)))) & ((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_91_91, all_0_90_90) = all_0_89_89 & implies(all_0_92_92, all_0_89_89) = all_0_88_88 & implies(all_0_94_94, all_0_93_93) = all_0_91_91 & implies(all_0_95_95, all_0_93_93) = all_0_90_90 & implies(all_0_95_95, all_0_94_94) = all_0_92_92 & ~ cn1 & ~ is_a_theorem(all_0_88_88)) | (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))))
% 5.23/1.79 |
% 5.23/1.79 | Applying alpha-rule on (1) yields:
% 5.23/1.79 | (2) (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)))
% 5.23/1.79 | (3) ! [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))
% 5.23/1.79 | (4) (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)))
% 5.23/1.79 | (5) r4
% 5.23/1.79 | (6) op_implies_and
% 5.23/1.79 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v2) = v3) | ~ (not(v1) = v2) | ? [v4] : (not(v3) = v4 & implies(v0, v1) = v4))
% 5.23/1.80 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (implies(v0, v1) = v2) | ? [v3] : ? [v4] : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) = v3))
% 5.23/1.80 | (9) (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)))
% 5.23/1.80 | (10) r2
% 5.23/1.80 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (or(v3, v2) = v1) | ~ (or(v3, v2) = v0))
% 5.23/1.80 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (equiv(v0, v1) = v2) | ? [v3] : ? [v4] : (and(v3, v4) = v2 & implies(v1, v0) = v4 & implies(v0, v1) = v3))
% 5.23/1.80 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (and(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (or(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3))
% 5.23/1.80 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3))
% 5.23/1.80 | (15) (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)))
% 5.23/1.80 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (or(v1, v0) = v3) | ~ (or(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | is_a_theorem(v4))
% 5.23/1.80 | (17) op_or
% 5.23/1.80 | (18) (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)))
% 5.23/1.80 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (implies(v0, v1) = v2) | ? [v3] : (or(v3, v1) = v2 & not(v0) = v3))
% 5.23/1.80 | (20) modus_ponens
% 5.23/1.80 | (21) r5
% 5.23/1.80 | (22) r1
% 5.23/1.80 | (23) (and(all_0_77_77, all_0_76_76) = all_0_75_75 & implies(all_0_75_75, all_0_77_77) = all_0_74_74 & ~ kn2 & ~ is_a_theorem(all_0_74_74)) | (kn2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | is_a_theorem(v3)))
% 5.23/1.80 | (24) op_and
% 5.23/1.80 | (25) (not(all_0_104_104) = all_0_103_103 & implies(all_0_102_102, all_0_104_104) = all_0_101_101 & implies(all_0_103_103, all_0_104_104) = all_0_102_102 & ~ cn3 & ~ is_a_theorem(all_0_101_101)) | (cn3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (not(v0) = v1) | ~ (implies(v2, v0) = v3) | ~ (implies(v1, v0) = v2) | is_a_theorem(v3)))
% 5.23/1.80 | (26) ~ or_2
% 5.23/1.80 | (27) op_implies_or
% 5.23/1.80 | (28) (and(all_0_85_85, all_0_87_87) = all_0_81_81 & and(all_0_86_86, all_0_85_85) = all_0_83_83 & not(all_0_81_81) = all_0_80_80 & not(all_0_83_83) = all_0_82_82 & implies(all_0_82_82, all_0_80_80) = all_0_79_79 & implies(all_0_84_84, all_0_79_79) = all_0_78_78 & implies(all_0_87_87, all_0_86_86) = all_0_84_84 & ~ kn3 & ~ is_a_theorem(all_0_78_78)) | (kn3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (and(v2, v0) = v6) | ~ (and(v1, v2) = v4) | ~ (not(v6) = v7) | ~ (not(v4) = v5) | ~ (implies(v5, v7) = v8) | ~ (implies(v3, v8) = v9) | ~ (implies(v0, v1) = v3) | is_a_theorem(v9)))
% 5.23/1.80 | (29) (implies(all_0_91_91, all_0_90_90) = all_0_89_89 & implies(all_0_92_92, all_0_89_89) = all_0_88_88 & implies(all_0_94_94, all_0_93_93) = all_0_91_91 & implies(all_0_95_95, all_0_93_93) = all_0_90_90 & implies(all_0_95_95, all_0_94_94) = all_0_92_92 & ~ cn1 & ~ is_a_theorem(all_0_88_88)) | (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)))
% 5.23/1.81 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v2, v1) = v3) | ~ (not(v0) = v2) | implies(v0, v1) = v3)
% 5.23/1.81 | (31) or(all_0_44_44, all_0_43_43) = all_0_42_42
% 5.23/1.81 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (or(v0, v0) = v1) | ~ (implies(v1, v0) = v2) | is_a_theorem(v2))
% 5.23/1.81 | (33) (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)))
% 5.23/1.81 | (34) r3
% 5.23/1.81 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (not(v2) = v1) | ~ (not(v2) = v0))
% 5.23/1.81 | (36) (not(all_0_100_100) = all_0_98_98 & implies(all_0_98_98, all_0_99_99) = all_0_97_97 & implies(all_0_100_100, all_0_97_97) = all_0_96_96 & ~ cn2 & ~ is_a_theorem(all_0_96_96)) | (cn2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (not(v0) = v2) | ~ (implies(v2, v1) = v3) | ~ (implies(v0, v3) = v4) | is_a_theorem(v4)))
% 5.23/1.81 | (37) op_equiv
% 5.23/1.81 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) = v0))
% 5.23/1.81 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equiv(v0, v1) = v2) | ~ is_a_theorem(v2))
% 5.23/1.81 | (40) ! [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))
% 5.23/1.81 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (implies(v0, v1) = v2) | ~ is_a_theorem(v2) | ~ is_a_theorem(v0) | is_a_theorem(v1))
% 5.23/1.81 | (42) implies(all_0_43_43, all_0_42_42) = all_0_41_41
% 5.23/1.81 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0))
% 5.23/1.81 | (44) (and(all_0_73_73, all_0_73_73) = all_0_72_72 & implies(all_0_73_73, all_0_72_72) = all_0_71_71 & ~ kn1 & ~ is_a_theorem(all_0_71_71)) | (kn1 & ! [v0] : ! [v1] : ! [v2] : ( ~ (and(v0, v0) = v1) | ~ (implies(v0, v1) = v2) | is_a_theorem(v2)))
% 5.23/1.81 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v2, v3) = v4) | ~ (implies(v1, v0) = v3) | ~ (implies(v0, v1) = v2) | equiv(v0, v1) = v4)
% 5.23/1.81 | (46) substitution_of_equivalents
% 5.23/1.81 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v2, v3) = v4) | ~ (not(v1) = v3) | ~ (not(v0) = v2) | ? [v5] : (or(v0, v1) = v5 & not(v4) = v5))
% 5.23/1.81 | (48) (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)))
% 5.23/1.81 | (49) (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)))
% 5.23/1.81 | (50) (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)))
% 5.23/1.81 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0))
% 5.23/1.81 | (52) (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 & ~ equivalence_1 & ~ is_a_theorem(all_0_54_54)) | (equivalence_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equiv(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | ~ (implies(v0, v1) = v3) | is_a_theorem(v4)))
% 5.23/1.81 | (53) (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)))
% 5.23/1.82 | (54) (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)))
% 5.23/1.82 | (55) ~ is_a_theorem(all_0_41_41)
% 5.23/1.82 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (or(v2, v3) = v4) | ~ (not(v1) = v3) | ~ (not(v0) = v2) | ? [v5] : (and(v0, v1) = v5 & not(v4) = v5))
% 5.23/1.82 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (or(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (and(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3))
% 5.23/1.82 |
% 5.23/1.82 | Instantiating formula (14) with all_0_41_41, all_0_42_42, all_0_43_43, all_0_44_44 and discharging atoms 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, ~ is_a_theorem(all_0_41_41), yields:
% 5.47/1.82 | (58) $false
% 5.47/1.82 |
% 5.47/1.82 |-The branch is then unsatisfiable
% 5.47/1.82 % SZS output end Proof for theBenchmark
% 5.47/1.82
% 5.47/1.82 1225ms
%------------------------------------------------------------------------------