TSTP Solution File: LCL456+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : LCL456+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n009.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 09:36:37 EDT 2022
% Result : Theorem 4.15s 1.60s
% Output : Proof 6.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LCL456+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.11 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sun Jul 3 19:13:52 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.17/0.56 ____ _
% 0.17/0.56 ___ / __ \_____(_)___ ________ __________
% 0.17/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.17/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.17/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.17/0.56
% 0.17/0.56 A Theorem Prover for First-Order Logic
% 0.17/0.56 (ePrincess v.1.0)
% 0.17/0.56
% 0.17/0.56 (c) Philipp Rümmer, 2009-2015
% 0.17/0.56 (c) Peter Backeman, 2014-2015
% 0.17/0.56 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.17/0.56 Free software under GNU Lesser General Public License (LGPL).
% 0.17/0.56 Bug reports to peter@backeman.se
% 0.17/0.56
% 0.17/0.56 For more information, visit http://user.uu.se/~petba168/breu/
% 0.17/0.56
% 0.17/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.72/0.93 Prover 0: Preprocessing ...
% 2.80/1.29 Prover 0: Constructing countermodel ...
% 4.15/1.59 Prover 0: proved (969ms)
% 4.15/1.60
% 4.15/1.60 No countermodel exists, formula is valid
% 4.15/1.60 % SZS status Theorem for theBenchmark
% 4.15/1.60
% 4.15/1.60 Generating proof ... found it (size 45)
% 6.18/1.98
% 6.18/1.98 % SZS output start Proof for theBenchmark
% 6.18/1.98 Assumed formulas after preprocessing and simplification:
% 6.18/1.98 | (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] : (or(v17, v16) = v19 & or(v16, v17) = v18 & implies(v18, v19) = v20 & op_equiv & op_implies_or & op_implies_and & op_and & op_or & equivalence_3 & equivalence_2 & equivalence_1 & or_3 & or_2 & or_1 & and_3 & and_2 & and_1 & implies_3 & implies_2 & implies_1 & modus_tollens & substitution_of_equivalents & modus_ponens & ~ r3 & ~ is_a_theorem(v20) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ! [v66] : ! [v67] : ! [v68] : ! [v69] : ! [v70] : ( ~ (or(v62, v63) = v67) | ~ (implies(v67, v64) = v68) | ~ (implies(v66, v68) = v69) | ~ (implies(v65, v69) = v70) | ~ (implies(v63, v64) = v66) | ~ (implies(v62, v64) = v65) | is_a_theorem(v70)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ! [v66] : ! [v67] : ! [v68] : ! [v69] : ( ~ (implies(v66, v67) = v68) | ~ (implies(v65, v68) = v69) | ~ (implies(v63, v64) = v66) | ~ (implies(v62, v64) = v67) | ~ (implies(v62, v63) = v65) | is_a_theorem(v69)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ! [v66] : ! [v67] : ! [v68] : ( ~ (not(v63) = v64) | ~ (not(v62) = v65) | ~ (implies(v66, v67) = v68) | ~ (implies(v64, v65) = v66) | ~ (implies(v62, v63) = v67) | is_a_theorem(v68)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ! [v66] : ! [v67] : ! [v68] : ( ~ (equiv(v62, v63) = v66) | ~ (implies(v65, v66) = v67) | ~ (implies(v64, v67) = v68) | ~ (implies(v63, v62) = v65) | ~ (implies(v62, v63) = v64) | is_a_theorem(v68)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ! [v66] : ( ~ (or(v64, v65) = v66) | ~ (not(v63) = v65) | ~ (not(v62) = v64) | ? [v67] : (and(v62, v63) = v67 & not(v66) = v67)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ! [v66] : ( ~ (and(v64, v65) = v66) | ~ (not(v63) = v65) | ~ (not(v62) = v64) | ? [v67] : (or(v62, v63) = v67 & not(v66) = v67)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ! [v66] : ( ~ (and(v64, v65) = v66) | ~ (implies(v63, v62) = v65) | ~ (implies(v62, v63) = v64) | equiv(v62, v63) = v66) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ! [v66] : ( ~ (and(v62, v63) = v64) | ~ (implies(v63, v64) = v65) | ~ (implies(v62, v65) = v66) | is_a_theorem(v66)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ! [v66] : ( ~ (equiv(v62, v63) = v64) | ~ (implies(v64, v65) = v66) | ~ (implies(v63, v62) = v65) | is_a_theorem(v66)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ! [v66] : ( ~ (equiv(v62, v63) = v64) | ~ (implies(v64, v65) = v66) | ~ (implies(v62, v63) = v65) | is_a_theorem(v66)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ! [v66] : ( ~ (implies(v65, v64) = v66) | ~ (implies(v62, v64) = v65) | ~ (implies(v62, v63) = v64) | is_a_theorem(v66)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : (v63 = v62 | ~ (or(v65, v64) = v63) | ~ (or(v65, v64) = v62)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : (v63 = v62 | ~ (and(v65, v64) = v63) | ~ (and(v65, v64) = v62)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : (v63 = v62 | ~ (equiv(v65, v64) = v63) | ~ (equiv(v65, v64) = v62)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : (v63 = v62 | ~ (implies(v65, v64) = v63) | ~ (implies(v65, v64) = v62)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ( ~ (or(v64, v63) = v65) | ~ (not(v62) = v64) | implies(v62, v63) = v65) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ( ~ (or(v62, v63) = v64) | ~ (implies(v63, v64) = v65) | is_a_theorem(v65)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ( ~ (or(v62, v63) = v64) | ~ (implies(v62, v64) = v65) | is_a_theorem(v65)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ( ~ (and(v62, v64) = v65) | ~ (not(v63) = v64) | ? [v66] : (not(v65) = v66 & implies(v62, v63) = v66)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ( ~ (and(v62, v63) = v64) | ~ (implies(v64, v63) = v65) | is_a_theorem(v65)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ( ~ (and(v62, v63) = v64) | ~ (implies(v64, v62) = v65) | is_a_theorem(v65)) & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ( ~ (implies(v63, v62) = v64) | ~ (implies(v62, v64) = v65) | is_a_theorem(v65)) & ! [v62] : ! [v63] : ! [v64] : (v63 = v62 | ~ (not(v64) = v63) | ~ (not(v64) = v62)) & ! [v62] : ! [v63] : ! [v64] : (v63 = v62 | ~ (equiv(v62, v63) = v64) | ~ is_a_theorem(v64)) & ! [v62] : ! [v63] : ! [v64] : ( ~ (or(v62, v63) = v64) | ? [v65] : ? [v66] : ? [v67] : (and(v65, v66) = v67 & not(v67) = v64 & not(v63) = v66 & not(v62) = v65)) & ! [v62] : ! [v63] : ! [v64] : ( ~ (and(v62, v63) = v64) | ? [v65] : ? [v66] : ? [v67] : (or(v65, v66) = v67 & not(v67) = v64 & not(v63) = v66 & not(v62) = v65)) & ! [v62] : ! [v63] : ! [v64] : ( ~ (equiv(v62, v63) = v64) | ? [v65] : ? [v66] : (and(v65, v66) = v64 & implies(v63, v62) = v66 & implies(v62, v63) = v65)) & ! [v62] : ! [v63] : ! [v64] : ( ~ (implies(v62, v63) = v64) | ~ is_a_theorem(v64) | ~ is_a_theorem(v62) | is_a_theorem(v63)) & ! [v62] : ! [v63] : ! [v64] : ( ~ (implies(v62, v63) = v64) | ? [v65] : ? [v66] : (and(v62, v65) = v66 & not(v66) = v64 & not(v63) = v65)) & ! [v62] : ! [v63] : ! [v64] : ( ~ (implies(v62, v63) = v64) | ? [v65] : (or(v65, v63) = v64 & not(v62) = v65)) & ((or(v25, v25) = v26 & implies(v26, v25) = v27 & ~ r1 & ~ is_a_theorem(v27)) | (r1 & ! [v62] : ! [v63] : ! [v64] : ( ~ (or(v62, v62) = v63) | ~ (implies(v63, v62) = v64) | is_a_theorem(v64)))) & ((or(v21, v22) = v23 & implies(v22, v23) = v24 & ~ r2 & ~ is_a_theorem(v24)) | (r2 & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ( ~ (or(v62, v63) = v64) | ~ (implies(v63, v64) = v65) | is_a_theorem(v65)))) & ((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 & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ! [v66] : ! [v67] : ! [v68] : ! [v69] : ( ~ (or(v63, v67) = v68) | ~ (or(v63, v64) = v65) | ~ (or(v62, v65) = v66) | ~ (or(v62, v64) = v67) | ~ (implies(v66, v68) = v69) | is_a_theorem(v69)))) & ((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 & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ! [v66] : ! [v67] : ! [v68] : ! [v69] : ( ~ (or(v62, v64) = v67) | ~ (or(v62, v63) = v66) | ~ (implies(v66, v67) = v68) | ~ (implies(v65, v68) = v69) | ~ (implies(v63, v64) = v65) | is_a_theorem(v69)))) & ((and(v59, v59) = v60 & implies(v59, v60) = v61 & ~ kn1 & ~ is_a_theorem(v61)) | (kn1 & ! [v62] : ! [v63] : ! [v64] : ( ~ (and(v62, v62) = v63) | ~ (implies(v62, v63) = v64) | is_a_theorem(v64)))) & ((and(v55, v56) = v57 & implies(v57, v55) = v58 & ~ kn2 & ~ is_a_theorem(v58)) | (kn2 & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ( ~ (and(v62, v63) = v64) | ~ (implies(v64, v62) = v65) | is_a_theorem(v65)))) & ((and(v47, v45) = v51 & and(v46, v47) = v49 & not(v51) = v52 & not(v49) = v50 & implies(v50, v52) = v53 & implies(v48, v53) = v54 & implies(v45, v46) = v48 & ~ kn3 & ~ is_a_theorem(v54)) | (kn3 & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ! [v66] : ! [v67] : ! [v68] : ! [v69] : ! [v70] : ! [v71] : ( ~ (and(v64, v62) = v68) | ~ (and(v63, v64) = v66) | ~ (not(v68) = v69) | ~ (not(v66) = v67) | ~ (implies(v67, v69) = v70) | ~ (implies(v65, v70) = v71) | ~ (implies(v62, v63) = v65) | is_a_theorem(v71)))) & ((not(v32) = v34 & implies(v34, v33) = v35 & implies(v32, v35) = v36 & ~ cn2 & ~ is_a_theorem(v36)) | (cn2 & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ! [v66] : ( ~ (not(v62) = v64) | ~ (implies(v64, v63) = v65) | ~ (implies(v62, v65) = v66) | is_a_theorem(v66)))) & ((not(v28) = v29 & implies(v30, v28) = v31 & implies(v29, v28) = v30 & ~ cn3 & ~ is_a_theorem(v31)) | (cn3 & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ( ~ (not(v62) = v63) | ~ (implies(v64, v62) = v65) | ~ (implies(v63, v62) = v64) | is_a_theorem(v65)))) & ((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 & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ! [v66] : ! [v67] : ! [v68] : ! [v69] : ( ~ (implies(v66, v67) = v68) | ~ (implies(v65, v68) = v69) | ~ (implies(v63, v64) = v66) | ~ (implies(v62, v64) = v67) | ~ (implies(v62, v63) = v65) | is_a_theorem(v69)))))
% 6.18/2.03 | 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 yields:
% 6.18/2.03 | (1) or(all_0_44_44, all_0_45_45) = all_0_42_42 & or(all_0_45_45, all_0_44_44) = all_0_43_43 & implies(all_0_43_43, all_0_42_42) = all_0_41_41 & op_equiv & op_implies_or & op_implies_and & op_and & op_or & equivalence_3 & equivalence_2 & equivalence_1 & or_3 & or_2 & or_1 & and_3 & and_2 & and_1 & implies_3 & implies_2 & implies_1 & modus_tollens & substitution_of_equivalents & modus_ponens & ~ r3 & ~ is_a_theorem(all_0_41_41) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (or(v0, v1) = v5) | ~ (implies(v5, v2) = v6) | ~ (implies(v4, v6) = v7) | ~ (implies(v3, v7) = v8) | ~ (implies(v1, v2) = v4) | ~ (implies(v0, v2) = v3) | is_a_theorem(v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (implies(v4, v5) = v6) | ~ (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v4) | ~ (implies(v0, v2) = v5) | ~ (implies(v0, v1) = v3) | is_a_theorem(v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (not(v1) = v2) | ~ (not(v0) = v3) | ~ (implies(v4, v5) = v6) | ~ (implies(v2, v3) = v4) | ~ (implies(v0, v1) = v5) | is_a_theorem(v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (equiv(v0, v1) = v4) | ~ (implies(v3, v4) = v5) | ~ (implies(v2, v5) = v6) | ~ (implies(v1, v0) = v3) | ~ (implies(v0, v1) = v2) | is_a_theorem(v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (or(v2, v3) = v4) | ~ (not(v1) = v3) | ~ (not(v0) = v2) | ? [v5] : (and(v0, v1) = v5 & not(v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v2, v3) = v4) | ~ (not(v1) = v3) | ~ (not(v0) = v2) | ? [v5] : (or(v0, v1) = v5 & not(v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v2, v3) = v4) | ~ (implies(v1, v0) = v3) | ~ (implies(v0, v1) = v2) | equiv(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | ~ (implies(v0, v3) = v4) | is_a_theorem(v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equiv(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | ~ (implies(v1, v0) = v3) | is_a_theorem(v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equiv(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | ~ (implies(v0, v1) = v3) | is_a_theorem(v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (implies(v3, v2) = v4) | ~ (implies(v0, v2) = v3) | ~ (implies(v0, v1) = v2) | is_a_theorem(v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (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] : ( ~ (or(v0, v1) = v2) | ~ (implies(v0, v2) = v3) | is_a_theorem(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v2) = v3) | ~ (not(v1) = v2) | ? [v4] : (not(v3) = v4 & implies(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v1) = v3) | is_a_theorem(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | is_a_theorem(v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (implies(v1, v0) = v2) | ~ (implies(v0, v2) = v3) | is_a_theorem(v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (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, 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_36_36, all_0_36_36) = all_0_35_35 & implies(all_0_35_35, all_0_36_36) = all_0_34_34 & ~ r1 & ~ is_a_theorem(all_0_34_34)) | (r1 & ! [v0] : ! [v1] : ! [v2] : ( ~ (or(v0, v0) = v1) | ~ (implies(v1, v0) = v2) | is_a_theorem(v2)))) & ((or(all_0_40_40, all_0_39_39) = all_0_38_38 & implies(all_0_39_39, all_0_38_38) = all_0_37_37 & ~ r2 & ~ is_a_theorem(all_0_37_37)) | (r2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3)))) & ((or(all_0_52_52, all_0_48_48) = all_0_47_47 & or(all_0_52_52, all_0_51_51) = all_0_50_50 & or(all_0_53_53, all_0_50_50) = all_0_49_49 & or(all_0_53_53, all_0_51_51) = all_0_48_48 & implies(all_0_49_49, all_0_47_47) = all_0_46_46 & ~ r4 & ~ is_a_theorem(all_0_46_46)) | (r4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (or(v1, v5) = v6) | ~ (or(v1, v2) = v3) | ~ (or(v0, v3) = v4) | ~ (or(v0, v2) = v5) | ~ (implies(v4, v6) = v7) | is_a_theorem(v7)))) & ((or(all_0_61_61, all_0_59_59) = all_0_56_56 & or(all_0_61_61, all_0_60_60) = all_0_57_57 & implies(all_0_57_57, all_0_56_56) = all_0_55_55 & implies(all_0_58_58, all_0_55_55) = all_0_54_54 & implies(all_0_60_60, all_0_59_59) = all_0_58_58 & ~ r5 & ~ is_a_theorem(all_0_54_54)) | (r5 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (or(v0, v2) = v5) | ~ (or(v0, v1) = v4) | ~ (implies(v4, v5) = v6) | ~ (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v3) | is_a_theorem(v7)))) & ((and(all_0_2_2, all_0_2_2) = all_0_1_1 & implies(all_0_2_2, all_0_1_1) = all_0_0_0 & ~ kn1 & ~ is_a_theorem(all_0_0_0)) | (kn1 & ! [v0] : ! [v1] : ! [v2] : ( ~ (and(v0, v0) = v1) | ~ (implies(v0, v1) = v2) | is_a_theorem(v2)))) & ((and(all_0_6_6, all_0_5_5) = all_0_4_4 & implies(all_0_4_4, all_0_6_6) = all_0_3_3 & ~ kn2 & ~ is_a_theorem(all_0_3_3)) | (kn2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | is_a_theorem(v3)))) & ((and(all_0_14_14, all_0_16_16) = all_0_10_10 & and(all_0_15_15, all_0_14_14) = all_0_12_12 & not(all_0_10_10) = all_0_9_9 & not(all_0_12_12) = all_0_11_11 & implies(all_0_11_11, all_0_9_9) = all_0_8_8 & implies(all_0_13_13, all_0_8_8) = all_0_7_7 & implies(all_0_16_16, all_0_15_15) = all_0_13_13 & ~ kn3 & ~ is_a_theorem(all_0_7_7)) | (kn3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (and(v2, v0) = v6) | ~ (and(v1, v2) = v4) | ~ (not(v6) = v7) | ~ (not(v4) = v5) | ~ (implies(v5, v7) = v8) | ~ (implies(v3, v8) = v9) | ~ (implies(v0, v1) = v3) | is_a_theorem(v9)))) & ((not(all_0_29_29) = all_0_27_27 & implies(all_0_27_27, all_0_28_28) = all_0_26_26 & implies(all_0_29_29, all_0_26_26) = all_0_25_25 & ~ cn2 & ~ is_a_theorem(all_0_25_25)) | (cn2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (not(v0) = v2) | ~ (implies(v2, v1) = v3) | ~ (implies(v0, v3) = v4) | is_a_theorem(v4)))) & ((not(all_0_33_33) = all_0_32_32 & implies(all_0_31_31, all_0_33_33) = all_0_30_30 & implies(all_0_32_32, all_0_33_33) = all_0_31_31 & ~ cn3 & ~ is_a_theorem(all_0_30_30)) | (cn3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (not(v0) = v1) | ~ (implies(v2, v0) = v3) | ~ (implies(v1, v0) = v2) | is_a_theorem(v3)))) & ((implies(all_0_20_20, all_0_19_19) = all_0_18_18 & implies(all_0_21_21, all_0_18_18) = all_0_17_17 & implies(all_0_23_23, all_0_22_22) = all_0_20_20 & implies(all_0_24_24, all_0_22_22) = all_0_19_19 & implies(all_0_24_24, all_0_23_23) = all_0_21_21 & ~ cn1 & ~ is_a_theorem(all_0_17_17)) | (cn1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (implies(v4, v5) = v6) | ~ (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v4) | ~ (implies(v0, v2) = v5) | ~ (implies(v0, v1) = v3) | is_a_theorem(v7))))
% 6.18/2.04 |
% 6.18/2.04 | Applying alpha-rule on (1) yields:
% 6.18/2.04 | (2) implies_2
% 6.18/2.05 | (3) or(all_0_45_45, all_0_44_44) = all_0_43_43
% 6.18/2.05 | (4) equivalence_2
% 6.18/2.05 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equiv(v0, v1) = v2) | ~ is_a_theorem(v2))
% 6.18/2.05 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0))
% 6.18/2.05 | (7) and_1
% 6.18/2.05 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (and(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (or(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3))
% 6.18/2.05 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3))
% 6.18/2.05 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (or(v3, v2) = v1) | ~ (or(v3, v2) = v0))
% 6.18/2.05 | (11) ~ r3
% 6.18/2.05 | (12) modus_ponens
% 6.18/2.05 | (13) ~ is_a_theorem(all_0_41_41)
% 6.18/2.05 | (14) op_equiv
% 6.18/2.05 | (15) equivalence_1
% 6.18/2.05 | (16) or_2
% 6.18/2.05 | (17) op_implies_or
% 6.18/2.05 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0))
% 6.18/2.05 | (19) implies_3
% 6.18/2.05 | (20) (not(all_0_29_29) = all_0_27_27 & implies(all_0_27_27, all_0_28_28) = all_0_26_26 & implies(all_0_29_29, all_0_26_26) = all_0_25_25 & ~ cn2 & ~ is_a_theorem(all_0_25_25)) | (cn2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (not(v0) = v2) | ~ (implies(v2, v1) = v3) | ~ (implies(v0, v3) = v4) | is_a_theorem(v4)))
% 6.18/2.05 | (21) and_2
% 6.18/2.05 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v2, v1) = v3) | ~ (not(v0) = v2) | implies(v0, v1) = v3)
% 6.18/2.05 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (implies(v4, v5) = v6) | ~ (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v4) | ~ (implies(v0, v2) = v5) | ~ (implies(v0, v1) = v3) | is_a_theorem(v7))
% 6.18/2.05 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v1) = v3) | is_a_theorem(v3))
% 6.18/2.05 | (25) op_implies_and
% 6.18/2.05 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (equiv(v0, v1) = v2) | ? [v3] : ? [v4] : (and(v3, v4) = v2 & implies(v1, v0) = v4 & implies(v0, v1) = v3))
% 6.18/2.05 | (27) substitution_of_equivalents
% 6.18/2.05 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | ~ (implies(v0, v3) = v4) | is_a_theorem(v4))
% 6.18/2.05 | (29) (or(all_0_52_52, all_0_48_48) = all_0_47_47 & or(all_0_52_52, all_0_51_51) = all_0_50_50 & or(all_0_53_53, all_0_50_50) = all_0_49_49 & or(all_0_53_53, all_0_51_51) = all_0_48_48 & implies(all_0_49_49, all_0_47_47) = all_0_46_46 & ~ r4 & ~ is_a_theorem(all_0_46_46)) | (r4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (or(v1, v5) = v6) | ~ (or(v1, v2) = v3) | ~ (or(v0, v3) = v4) | ~ (or(v0, v2) = v5) | ~ (implies(v4, v6) = v7) | is_a_theorem(v7)))
% 6.18/2.05 | (30) or_3
% 6.18/2.05 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (implies(v1, v0) = v2) | ~ (implies(v0, v2) = v3) | is_a_theorem(v3))
% 6.18/2.05 | (32) equivalence_3
% 6.18/2.05 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v2) = v3) | ~ (not(v1) = v2) | ? [v4] : (not(v3) = v4 & implies(v0, v1) = v4))
% 6.18/2.05 | (34) (or(all_0_40_40, all_0_39_39) = all_0_38_38 & implies(all_0_39_39, all_0_38_38) = all_0_37_37 & ~ r2 & ~ is_a_theorem(all_0_37_37)) | (r2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3)))
% 6.18/2.05 | (35) or_1
% 6.18/2.05 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (or(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (and(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3))
% 6.18/2.05 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (not(v1) = v2) | ~ (not(v0) = v3) | ~ (implies(v4, v5) = v6) | ~ (implies(v2, v3) = v4) | ~ (implies(v0, v1) = v5) | is_a_theorem(v6))
% 6.18/2.05 | (38) and_3
% 6.18/2.05 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (equiv(v0, v1) = v4) | ~ (implies(v3, v4) = v5) | ~ (implies(v2, v5) = v6) | ~ (implies(v1, v0) = v3) | ~ (implies(v0, v1) = v2) | is_a_theorem(v6))
% 6.18/2.05 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (implies(v3, v2) = v4) | ~ (implies(v0, v2) = v3) | ~ (implies(v0, v1) = v2) | is_a_theorem(v4))
% 6.18/2.06 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equiv(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | ~ (implies(v0, v1) = v3) | is_a_theorem(v4))
% 6.18/2.06 | (42) modus_tollens
% 6.18/2.06 | (43) op_and
% 6.18/2.06 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (implies(v0, v1) = v2) | ? [v3] : ? [v4] : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) = v3))
% 6.18/2.06 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (or(v2, v3) = v4) | ~ (not(v1) = v3) | ~ (not(v0) = v2) | ? [v5] : (and(v0, v1) = v5 & not(v4) = v5))
% 6.18/2.06 | (46) (implies(all_0_20_20, all_0_19_19) = all_0_18_18 & implies(all_0_21_21, all_0_18_18) = all_0_17_17 & implies(all_0_23_23, all_0_22_22) = all_0_20_20 & implies(all_0_24_24, all_0_22_22) = all_0_19_19 & implies(all_0_24_24, all_0_23_23) = all_0_21_21 & ~ cn1 & ~ is_a_theorem(all_0_17_17)) | (cn1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (implies(v4, v5) = v6) | ~ (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v4) | ~ (implies(v0, v2) = v5) | ~ (implies(v0, v1) = v3) | is_a_theorem(v7)))
% 6.18/2.06 | (47) (or(all_0_61_61, all_0_59_59) = all_0_56_56 & or(all_0_61_61, all_0_60_60) = all_0_57_57 & implies(all_0_57_57, all_0_56_56) = all_0_55_55 & implies(all_0_58_58, all_0_55_55) = all_0_54_54 & implies(all_0_60_60, all_0_59_59) = all_0_58_58 & ~ r5 & ~ is_a_theorem(all_0_54_54)) | (r5 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (or(v0, v2) = v5) | ~ (or(v0, v1) = v4) | ~ (implies(v4, v5) = v6) | ~ (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v3) | is_a_theorem(v7)))
% 6.18/2.06 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (implies(v0, v1) = v2) | ~ is_a_theorem(v2) | ~ is_a_theorem(v0) | is_a_theorem(v1))
% 6.18/2.06 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | is_a_theorem(v3))
% 6.18/2.06 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) = v0))
% 6.18/2.06 | (51) implies(all_0_43_43, all_0_42_42) = all_0_41_41
% 6.18/2.06 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equiv(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | ~ (implies(v1, v0) = v3) | is_a_theorem(v4))
% 6.18/2.06 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v2, v3) = v4) | ~ (not(v1) = v3) | ~ (not(v0) = v2) | ? [v5] : (or(v0, v1) = v5 & not(v4) = v5))
% 6.18/2.06 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (implies(v0, v1) = v2) | ? [v3] : (or(v3, v1) = v2 & not(v0) = v3))
% 6.18/2.06 | (55) implies_1
% 6.18/2.06 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v0, v2) = v3) | is_a_theorem(v3))
% 6.18/2.06 | (57) (or(all_0_36_36, all_0_36_36) = all_0_35_35 & implies(all_0_35_35, all_0_36_36) = all_0_34_34 & ~ r1 & ~ is_a_theorem(all_0_34_34)) | (r1 & ! [v0] : ! [v1] : ! [v2] : ( ~ (or(v0, v0) = v1) | ~ (implies(v1, v0) = v2) | is_a_theorem(v2)))
% 6.18/2.06 | (58) op_or
% 6.18/2.06 | (59) (not(all_0_33_33) = all_0_32_32 & implies(all_0_31_31, all_0_33_33) = all_0_30_30 & implies(all_0_32_32, all_0_33_33) = all_0_31_31 & ~ cn3 & ~ is_a_theorem(all_0_30_30)) | (cn3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (not(v0) = v1) | ~ (implies(v2, v0) = v3) | ~ (implies(v1, v0) = v2) | is_a_theorem(v3)))
% 6.18/2.06 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (or(v0, v1) = v5) | ~ (implies(v5, v2) = v6) | ~ (implies(v4, v6) = v7) | ~ (implies(v3, v7) = v8) | ~ (implies(v1, v2) = v4) | ~ (implies(v0, v2) = v3) | is_a_theorem(v8))
% 6.18/2.06 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v2, v3) = v4) | ~ (implies(v1, v0) = v3) | ~ (implies(v0, v1) = v2) | equiv(v0, v1) = v4)
% 6.18/2.06 | (62) (and(all_0_6_6, all_0_5_5) = all_0_4_4 & implies(all_0_4_4, all_0_6_6) = all_0_3_3 & ~ kn2 & ~ is_a_theorem(all_0_3_3)) | (kn2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | is_a_theorem(v3)))
% 6.18/2.06 | (63) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (not(v2) = v1) | ~ (not(v2) = v0))
% 6.18/2.07 | (64) (and(all_0_2_2, all_0_2_2) = all_0_1_1 & implies(all_0_2_2, all_0_1_1) = all_0_0_0 & ~ kn1 & ~ is_a_theorem(all_0_0_0)) | (kn1 & ! [v0] : ! [v1] : ! [v2] : ( ~ (and(v0, v0) = v1) | ~ (implies(v0, v1) = v2) | is_a_theorem(v2)))
% 6.18/2.07 | (65) or(all_0_44_44, all_0_45_45) = all_0_42_42
% 6.18/2.07 | (66) (and(all_0_14_14, all_0_16_16) = all_0_10_10 & and(all_0_15_15, all_0_14_14) = all_0_12_12 & not(all_0_10_10) = all_0_9_9 & not(all_0_12_12) = all_0_11_11 & implies(all_0_11_11, all_0_9_9) = all_0_8_8 & implies(all_0_13_13, all_0_8_8) = all_0_7_7 & implies(all_0_16_16, all_0_15_15) = all_0_13_13 & ~ kn3 & ~ is_a_theorem(all_0_7_7)) | (kn3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (and(v2, v0) = v6) | ~ (and(v1, v2) = v4) | ~ (not(v6) = v7) | ~ (not(v4) = v5) | ~ (implies(v5, v7) = v8) | ~ (implies(v3, v8) = v9) | ~ (implies(v0, v1) = v3) | is_a_theorem(v9)))
% 6.61/2.07 |
% 6.61/2.07 | Instantiating formula (36) with all_0_42_42, all_0_45_45, all_0_44_44 and discharging atoms or(all_0_44_44, all_0_45_45) = all_0_42_42, yields:
% 6.61/2.07 | (67) ? [v0] : ? [v1] : ? [v2] : (and(v0, v1) = v2 & not(v2) = all_0_42_42 & not(all_0_44_44) = v0 & not(all_0_45_45) = v1)
% 6.61/2.07 |
% 6.61/2.07 | Instantiating formula (36) with all_0_43_43, all_0_44_44, all_0_45_45 and discharging atoms or(all_0_45_45, all_0_44_44) = all_0_43_43, yields:
% 6.61/2.07 | (68) ? [v0] : ? [v1] : ? [v2] : (and(v0, v1) = v2 & not(v2) = all_0_43_43 & not(all_0_44_44) = v1 & not(all_0_45_45) = v0)
% 6.61/2.07 |
% 6.61/2.07 | Instantiating formula (44) with all_0_41_41, all_0_42_42, all_0_43_43 and discharging atoms implies(all_0_43_43, all_0_42_42) = all_0_41_41, yields:
% 6.61/2.07 | (69) ? [v0] : ? [v1] : (and(all_0_43_43, v0) = v1 & not(v1) = all_0_41_41 & not(all_0_42_42) = v0)
% 6.61/2.07 |
% 6.61/2.07 | Instantiating (69) with all_10_0_63, all_10_1_64 yields:
% 6.61/2.07 | (70) and(all_0_43_43, all_10_1_64) = all_10_0_63 & not(all_10_0_63) = all_0_41_41 & not(all_0_42_42) = all_10_1_64
% 6.61/2.07 |
% 6.61/2.07 | Applying alpha-rule on (70) yields:
% 6.61/2.07 | (71) and(all_0_43_43, all_10_1_64) = all_10_0_63
% 6.61/2.07 | (72) not(all_10_0_63) = all_0_41_41
% 6.61/2.07 | (73) not(all_0_42_42) = all_10_1_64
% 6.61/2.07 |
% 6.61/2.07 | Instantiating (68) with all_12_0_65, all_12_1_66, all_12_2_67 yields:
% 6.61/2.07 | (74) and(all_12_2_67, all_12_1_66) = all_12_0_65 & not(all_12_0_65) = all_0_43_43 & not(all_0_44_44) = all_12_1_66 & not(all_0_45_45) = all_12_2_67
% 6.61/2.07 |
% 6.61/2.07 | Applying alpha-rule on (74) yields:
% 6.61/2.07 | (75) and(all_12_2_67, all_12_1_66) = all_12_0_65
% 6.61/2.07 | (76) not(all_12_0_65) = all_0_43_43
% 6.61/2.07 | (77) not(all_0_44_44) = all_12_1_66
% 6.61/2.07 | (78) not(all_0_45_45) = all_12_2_67
% 6.61/2.07 |
% 6.61/2.07 | Instantiating (67) with all_14_0_68, all_14_1_69, all_14_2_70 yields:
% 6.61/2.07 | (79) and(all_14_2_70, all_14_1_69) = all_14_0_68 & not(all_14_0_68) = all_0_42_42 & not(all_0_44_44) = all_14_2_70 & not(all_0_45_45) = all_14_1_69
% 6.61/2.07 |
% 6.61/2.07 | Applying alpha-rule on (79) yields:
% 6.61/2.07 | (80) and(all_14_2_70, all_14_1_69) = all_14_0_68
% 6.61/2.07 | (81) not(all_14_0_68) = all_0_42_42
% 6.61/2.07 | (82) not(all_0_44_44) = all_14_2_70
% 6.61/2.07 | (83) not(all_0_45_45) = all_14_1_69
% 6.61/2.07 |
% 6.61/2.07 | Instantiating formula (63) with all_0_44_44, all_12_1_66, all_14_2_70 and discharging atoms not(all_0_44_44) = all_14_2_70, not(all_0_44_44) = all_12_1_66, yields:
% 6.61/2.07 | (84) all_14_2_70 = all_12_1_66
% 6.61/2.08 |
% 6.61/2.08 | Instantiating formula (63) with all_0_45_45, all_12_2_67, all_14_1_69 and discharging atoms not(all_0_45_45) = all_14_1_69, not(all_0_45_45) = all_12_2_67, yields:
% 6.61/2.08 | (85) all_14_1_69 = all_12_2_67
% 6.61/2.08 |
% 6.61/2.08 | From (84)(85) and (80) follows:
% 6.61/2.08 | (86) and(all_12_1_66, all_12_2_67) = all_14_0_68
% 6.61/2.08 |
% 6.61/2.08 | From (85) and (83) follows:
% 6.61/2.08 | (78) not(all_0_45_45) = all_12_2_67
% 6.61/2.08 |
% 6.61/2.08 | Instantiating formula (8) with all_14_0_68, all_12_2_67, all_12_1_66 and discharging atoms and(all_12_1_66, all_12_2_67) = all_14_0_68, yields:
% 6.61/2.08 | (88) ? [v0] : ? [v1] : ? [v2] : (or(v0, v1) = v2 & not(v2) = all_14_0_68 & not(all_12_1_66) = v0 & not(all_12_2_67) = v1)
% 6.61/2.08 |
% 6.61/2.08 | Instantiating formula (8) with all_12_0_65, all_12_1_66, all_12_2_67 and discharging atoms and(all_12_2_67, all_12_1_66) = all_12_0_65, yields:
% 6.61/2.08 | (89) ? [v0] : ? [v1] : ? [v2] : (or(v0, v1) = v2 & not(v2) = all_12_0_65 & not(all_12_1_66) = v1 & not(all_12_2_67) = v0)
% 6.61/2.08 |
% 6.61/2.08 | Instantiating formula (53) with all_10_0_63, all_10_1_64, all_0_43_43, all_0_42_42, all_12_0_65 and discharging atoms and(all_0_43_43, all_10_1_64) = all_10_0_63, not(all_12_0_65) = all_0_43_43, not(all_0_42_42) = all_10_1_64, yields:
% 6.61/2.08 | (90) ? [v0] : (or(all_12_0_65, all_0_42_42) = v0 & not(all_10_0_63) = v0)
% 6.61/2.08 |
% 6.61/2.08 | Instantiating formula (33) with all_14_0_68, all_12_2_67, all_0_45_45, all_12_1_66 and discharging atoms and(all_12_1_66, all_12_2_67) = all_14_0_68, not(all_0_45_45) = all_12_2_67, yields:
% 6.61/2.08 | (91) ? [v0] : (not(all_14_0_68) = v0 & implies(all_12_1_66, all_0_45_45) = v0)
% 6.61/2.08 |
% 6.61/2.08 | Instantiating (91) with all_25_0_71 yields:
% 6.61/2.08 | (92) not(all_14_0_68) = all_25_0_71 & implies(all_12_1_66, all_0_45_45) = all_25_0_71
% 6.61/2.08 |
% 6.61/2.08 | Applying alpha-rule on (92) yields:
% 6.61/2.08 | (93) not(all_14_0_68) = all_25_0_71
% 6.61/2.08 | (94) implies(all_12_1_66, all_0_45_45) = all_25_0_71
% 6.61/2.08 |
% 6.61/2.08 | Instantiating (90) with all_29_0_73 yields:
% 6.61/2.08 | (95) or(all_12_0_65, all_0_42_42) = all_29_0_73 & not(all_10_0_63) = all_29_0_73
% 6.61/2.08 |
% 6.61/2.08 | Applying alpha-rule on (95) yields:
% 6.61/2.08 | (96) or(all_12_0_65, all_0_42_42) = all_29_0_73
% 6.61/2.08 | (97) not(all_10_0_63) = all_29_0_73
% 6.61/2.08 |
% 6.61/2.08 | Instantiating (88) with all_35_0_78, all_35_1_79, all_35_2_80 yields:
% 6.61/2.08 | (98) or(all_35_2_80, all_35_1_79) = all_35_0_78 & not(all_35_0_78) = all_14_0_68 & not(all_12_1_66) = all_35_2_80 & not(all_12_2_67) = all_35_1_79
% 6.61/2.08 |
% 6.61/2.08 | Applying alpha-rule on (98) yields:
% 6.61/2.08 | (99) or(all_35_2_80, all_35_1_79) = all_35_0_78
% 6.61/2.08 | (100) not(all_35_0_78) = all_14_0_68
% 6.61/2.08 | (101) not(all_12_1_66) = all_35_2_80
% 6.61/2.08 | (102) not(all_12_2_67) = all_35_1_79
% 6.61/2.08 |
% 6.61/2.08 | Instantiating (89) with all_39_0_84, all_39_1_85, all_39_2_86 yields:
% 6.61/2.08 | (103) or(all_39_2_86, all_39_1_85) = all_39_0_84 & not(all_39_0_84) = all_12_0_65 & not(all_12_1_66) = all_39_1_85 & not(all_12_2_67) = all_39_2_86
% 6.61/2.08 |
% 6.61/2.08 | Applying alpha-rule on (103) yields:
% 6.61/2.08 | (104) or(all_39_2_86, all_39_1_85) = all_39_0_84
% 6.61/2.08 | (105) not(all_39_0_84) = all_12_0_65
% 6.61/2.08 | (106) not(all_12_1_66) = all_39_1_85
% 6.61/2.08 | (107) not(all_12_2_67) = all_39_2_86
% 6.61/2.08 |
% 6.61/2.08 | Instantiating formula (63) with all_14_0_68, all_25_0_71, all_0_42_42 and discharging atoms not(all_14_0_68) = all_25_0_71, not(all_14_0_68) = all_0_42_42, yields:
% 6.61/2.08 | (108) all_25_0_71 = all_0_42_42
% 6.61/2.08 |
% 6.61/2.08 | Instantiating formula (63) with all_12_1_66, all_35_2_80, all_39_1_85 and discharging atoms not(all_12_1_66) = all_39_1_85, not(all_12_1_66) = all_35_2_80, yields:
% 6.61/2.08 | (109) all_39_1_85 = all_35_2_80
% 6.61/2.08 |
% 6.61/2.08 | Instantiating formula (63) with all_12_2_67, all_35_1_79, all_39_2_86 and discharging atoms not(all_12_2_67) = all_39_2_86, not(all_12_2_67) = all_35_1_79, yields:
% 6.61/2.08 | (110) all_39_2_86 = all_35_1_79
% 6.61/2.08 |
% 6.61/2.08 | Instantiating formula (63) with all_10_0_63, all_29_0_73, all_0_41_41 and discharging atoms not(all_10_0_63) = all_29_0_73, not(all_10_0_63) = all_0_41_41, yields:
% 6.61/2.08 | (111) all_29_0_73 = all_0_41_41
% 6.61/2.08 |
% 6.61/2.08 | From (110)(109) and (104) follows:
% 6.61/2.08 | (112) or(all_35_1_79, all_35_2_80) = all_39_0_84
% 6.61/2.08 |
% 6.61/2.08 | From (111) and (96) follows:
% 6.61/2.08 | (113) or(all_12_0_65, all_0_42_42) = all_0_41_41
% 6.61/2.08 |
% 6.61/2.08 | From (109) and (106) follows:
% 6.61/2.08 | (101) not(all_12_1_66) = all_35_2_80
% 6.61/2.08 |
% 6.61/2.08 | From (110) and (107) follows:
% 6.61/2.08 | (102) not(all_12_2_67) = all_35_1_79
% 6.61/2.08 |
% 6.61/2.08 | From (108) and (94) follows:
% 6.61/2.08 | (116) implies(all_12_1_66, all_0_45_45) = all_0_42_42
% 6.61/2.08 |
% 6.61/2.08 | Instantiating formula (22) with all_0_41_41, all_12_0_65, all_0_42_42, all_39_0_84 and discharging atoms or(all_12_0_65, all_0_42_42) = all_0_41_41, not(all_39_0_84) = all_12_0_65, yields:
% 6.61/2.08 | (117) implies(all_39_0_84, all_0_42_42) = all_0_41_41
% 6.61/2.08 |
% 6.61/2.08 | Instantiating formula (22) with all_39_0_84, all_35_1_79, all_35_2_80, all_12_2_67 and discharging atoms or(all_35_1_79, all_35_2_80) = all_39_0_84, not(all_12_2_67) = all_35_1_79, yields:
% 6.61/2.08 | (118) implies(all_12_2_67, all_35_2_80) = all_39_0_84
% 6.61/2.08 |
% 6.61/2.09 | Instantiating formula (54) with all_0_42_42, all_0_45_45, all_12_1_66 and discharging atoms implies(all_12_1_66, all_0_45_45) = all_0_42_42, yields:
% 6.61/2.09 | (119) ? [v0] : (or(v0, all_0_45_45) = all_0_42_42 & not(all_12_1_66) = v0)
% 6.61/2.09 |
% 6.61/2.09 | Instantiating (119) with all_69_0_104 yields:
% 6.61/2.09 | (120) or(all_69_0_104, all_0_45_45) = all_0_42_42 & not(all_12_1_66) = all_69_0_104
% 6.61/2.09 |
% 6.61/2.09 | Applying alpha-rule on (120) yields:
% 6.61/2.09 | (121) or(all_69_0_104, all_0_45_45) = all_0_42_42
% 6.61/2.09 | (122) not(all_12_1_66) = all_69_0_104
% 6.71/2.09 |
% 6.71/2.09 | Instantiating formula (63) with all_12_1_66, all_69_0_104, all_35_2_80 and discharging atoms not(all_12_1_66) = all_69_0_104, not(all_12_1_66) = all_35_2_80, yields:
% 6.71/2.09 | (123) all_69_0_104 = all_35_2_80
% 6.71/2.09 |
% 6.71/2.09 | From (123) and (122) follows:
% 6.71/2.09 | (101) not(all_12_1_66) = all_35_2_80
% 6.71/2.09 |
% 6.71/2.09 | Instantiating formula (37) with all_0_41_41, all_0_42_42, all_39_0_84, all_35_2_80, all_12_2_67, all_0_45_45, all_12_1_66 and discharging atoms not(all_12_1_66) = all_35_2_80, not(all_0_45_45) = all_12_2_67, implies(all_39_0_84, all_0_42_42) = all_0_41_41, implies(all_12_1_66, all_0_45_45) = all_0_42_42, implies(all_12_2_67, all_35_2_80) = all_39_0_84, ~ is_a_theorem(all_0_41_41), yields:
% 6.71/2.09 | (125) $false
% 6.71/2.09 |
% 6.71/2.09 |-The branch is then unsatisfiable
% 6.71/2.09 % SZS output end Proof for theBenchmark
% 6.71/2.09
% 6.71/2.09 1513ms
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