TSTP Solution File: LCL452+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : LCL452+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 09:36:36 EDT 2022
% Result : Theorem 3.92s 1.48s
% Output : Proof 5.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL452+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 23:22:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.52/0.59 ____ _
% 0.52/0.59 ___ / __ \_____(_)___ ________ __________
% 0.52/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.52/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.52/0.59
% 0.52/0.59 A Theorem Prover for First-Order Logic
% 0.52/0.59 (ePrincess v.1.0)
% 0.52/0.59
% 0.52/0.59 (c) Philipp Rümmer, 2009-2015
% 0.52/0.59 (c) Peter Backeman, 2014-2015
% 0.52/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.59 Bug reports to peter@backeman.se
% 0.52/0.59
% 0.52/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.59
% 0.52/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.79/0.95 Prover 0: Preprocessing ...
% 3.21/1.34 Prover 0: Constructing countermodel ...
% 3.92/1.48 Prover 0: proved (845ms)
% 3.92/1.48
% 3.92/1.48 No countermodel exists, formula is valid
% 3.92/1.48 % SZS status Theorem for theBenchmark
% 3.92/1.48
% 3.92/1.48 Generating proof ... found it (size 12)
% 5.31/1.81
% 5.31/1.81 % SZS output start Proof for theBenchmark
% 5.31/1.81 Assumed formulas after preprocessing and simplification:
% 5.31/1.81 | (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] : (not(v32) = v34 & implies(v34, v33) = v35 & implies(v32, v35) = v36 & op_implies & op_equiv & op_implies_and & op_or & equivalence_3 & equivalence_2 & equivalence_1 & or_3 & or_2 & or_1 & and_3 & and_2 & and_1 & implies_3 & implies_2 & implies_1 & modus_tollens & substitution_of_equivalents & modus_ponens & ~ cn2 & ~ is_a_theorem(v36) & ! [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] : ( ~ (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(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] : ( ~ (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)) & ( ~ op_implies_or | ( ! [v62] : ! [v63] : ! [v64] : ! [v65] : ( ~ (or(v64, v63) = v65) | ~ (not(v62) = v64) | implies(v62, v63) = v65) & ! [v62] : ! [v63] : ! [v64] : ( ~ (implies(v62, v63) = v64) | ? [v65] : (or(v65, v63) = v64 & not(v62) = v65)))) & ( ~ op_and | ( ! [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] : ( ~ (and(v62, v63) = v64) | ? [v65] : ? [v66] : ? [v67] : (or(v65, v66) = v67 & not(v67) = v64 & not(v63) = v66 & 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(v17, v16) = v19 & or(v16, v17) = v18 & implies(v18, v19) = v20 & ~ r3 & ~ is_a_theorem(v20)) | (r3 & ! [v62] : ! [v63] : ! [v64] : ! [v65] : ! [v66] : ( ~ (or(v63, v62) = v65) | ~ (or(v62, v63) = v64) | ~ (implies(v64, v65) = v66) | is_a_theorem(v66)))) & ((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(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)))))
% 5.58/1.87 | 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:
% 5.58/1.87 | (1) 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 & op_implies & op_equiv & op_implies_and & op_or & equivalence_3 & equivalence_2 & equivalence_1 & or_3 & or_2 & or_1 & and_3 & and_2 & and_1 & implies_3 & implies_2 & implies_1 & modus_tollens & substitution_of_equivalents & modus_ponens & ~ cn2 & ~ is_a_theorem(all_0_25_25) & ! [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] : ( ~ (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(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] : ( ~ (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_36_36, all_0_36_36) = all_0_35_35 & implies(all_0_35_35, all_0_36_36) = all_0_34_34 & ~ r1 & ~ is_a_theorem(all_0_34_34)) | (r1 & ! [v0] : ! [v1] : ! [v2] : ( ~ (or(v0, v0) = v1) | ~ (implies(v1, v0) = v2) | is_a_theorem(v2)))) & ((or(all_0_40_40, all_0_39_39) = all_0_38_38 & implies(all_0_39_39, all_0_38_38) = all_0_37_37 & ~ r2 & ~ is_a_theorem(all_0_37_37)) | (r2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3)))) & ((or(all_0_44_44, all_0_45_45) = all_0_42_42 & or(all_0_45_45, all_0_44_44) = all_0_43_43 & implies(all_0_43_43, all_0_42_42) = all_0_41_41 & ~ r3 & ~ is_a_theorem(all_0_41_41)) | (r3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (or(v1, v0) = v3) | ~ (or(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | is_a_theorem(v4)))) & ((or(all_0_52_52, all_0_48_48) = all_0_47_47 & or(all_0_52_52, all_0_51_51) = all_0_50_50 & or(all_0_53_53, all_0_50_50) = all_0_49_49 & or(all_0_53_53, all_0_51_51) = all_0_48_48 & implies(all_0_49_49, all_0_47_47) = all_0_46_46 & ~ r4 & ~ is_a_theorem(all_0_46_46)) | (r4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (or(v1, v5) = v6) | ~ (or(v1, v2) = v3) | ~ (or(v0, v3) = v4) | ~ (or(v0, v2) = v5) | ~ (implies(v4, v6) = v7) | is_a_theorem(v7)))) & ((or(all_0_61_61, all_0_59_59) = all_0_56_56 & or(all_0_61_61, all_0_60_60) = all_0_57_57 & implies(all_0_57_57, all_0_56_56) = all_0_55_55 & implies(all_0_58_58, all_0_55_55) = all_0_54_54 & implies(all_0_60_60, all_0_59_59) = all_0_58_58 & ~ r5 & ~ is_a_theorem(all_0_54_54)) | (r5 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (or(v0, v2) = v5) | ~ (or(v0, v1) = v4) | ~ (implies(v4, v5) = v6) | ~ (implies(v3, v6) = v7) | ~ (implies(v1, v2) = v3) | is_a_theorem(v7)))) & ((and(all_0_2_2, all_0_2_2) = all_0_1_1 & implies(all_0_2_2, all_0_1_1) = all_0_0_0 & ~ kn1 & ~ is_a_theorem(all_0_0_0)) | (kn1 & ! [v0] : ! [v1] : ! [v2] : ( ~ (and(v0, v0) = v1) | ~ (implies(v0, v1) = v2) | is_a_theorem(v2)))) & ((and(all_0_6_6, all_0_5_5) = all_0_4_4 & implies(all_0_4_4, all_0_6_6) = all_0_3_3 & ~ kn2 & ~ is_a_theorem(all_0_3_3)) | (kn2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | is_a_theorem(v3)))) & ((and(all_0_14_14, all_0_16_16) = all_0_10_10 & and(all_0_15_15, all_0_14_14) = all_0_12_12 & not(all_0_10_10) = all_0_9_9 & not(all_0_12_12) = all_0_11_11 & implies(all_0_11_11, all_0_9_9) = all_0_8_8 & implies(all_0_13_13, all_0_8_8) = all_0_7_7 & implies(all_0_16_16, all_0_15_15) = all_0_13_13 & ~ kn3 & ~ is_a_theorem(all_0_7_7)) | (kn3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (and(v2, v0) = v6) | ~ (and(v1, v2) = v4) | ~ (not(v6) = v7) | ~ (not(v4) = v5) | ~ (implies(v5, v7) = v8) | ~ (implies(v3, v8) = v9) | ~ (implies(v0, v1) = v3) | is_a_theorem(v9)))) & ((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))))
% 5.58/1.89 |
% 5.58/1.89 | Applying alpha-rule on (1) yields:
% 5.58/1.89 | (2) or_2
% 5.58/1.89 | (3) ~ cn2
% 5.58/1.89 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v0) = v3) | is_a_theorem(v3))
% 5.58/1.89 | (5) ! [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))
% 5.58/1.89 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | is_a_theorem(v3))
% 5.58/1.89 | (7) op_implies_and
% 5.58/1.89 | (8) (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)))
% 5.58/1.89 | (9) or_3
% 5.58/1.89 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equiv(v0, v1) = v2) | ~ is_a_theorem(v2))
% 5.58/1.89 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (or(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (and(v3, v4) = v5 & not(v5) = v2 & not(v1) = v4 & not(v0) = v3))
% 5.58/1.89 | (12) (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)))
% 5.58/1.89 | (13) op_implies
% 5.58/1.89 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equiv(v3, v2) = v1) | ~ (equiv(v3, v2) = v0))
% 5.58/1.89 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (implies(v0, v1) = v2) | ? [v3] : ? [v4] : (and(v0, v3) = v4 & not(v4) = v2 & not(v1) = v3))
% 5.58/1.89 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (and(v3, v2) = v1) | ~ (and(v3, v2) = v0))
% 5.58/1.89 | (17) (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)))
% 5.58/1.89 | (18) ~ 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)))
% 5.58/1.90 | (19) equivalence_2
% 5.58/1.90 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (equiv(v0, v1) = v2) | ? [v3] : ? [v4] : (and(v3, v4) = v2 & implies(v1, v0) = v4 & implies(v0, v1) = v3))
% 5.58/1.90 | (21) implies(all_0_27_27, all_0_28_28) = all_0_26_26
% 5.58/1.90 | (22) op_or
% 5.58/1.90 | (23) modus_ponens
% 5.58/1.90 | (24) and_3
% 5.58/1.90 | (25) (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)))
% 5.58/1.90 | (26) (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)))
% 5.58/1.90 | (27) (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)))
% 5.58/1.90 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equiv(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | ~ (implies(v0, v1) = v3) | is_a_theorem(v4))
% 5.58/1.90 | (29) modus_tollens
% 5.58/1.90 | (30) equivalence_1
% 5.58/1.90 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v2) = v3) | ~ (not(v1) = v2) | ? [v4] : (not(v3) = v4 & implies(v0, v1) = v4))
% 5.58/1.90 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (not(v2) = v1) | ~ (not(v2) = v0))
% 5.58/1.90 | (33) ! [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))
% 5.58/1.90 | (34) (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)))
% 5.58/1.90 | (35) ! [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))
% 5.58/1.90 | (36) implies_1
% 5.58/1.90 | (37) and_1
% 5.58/1.90 | (38) (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)))
% 5.58/1.90 | (39) op_equiv
% 5.58/1.90 | (40) ~ is_a_theorem(all_0_25_25)
% 5.58/1.90 | (41) implies_2
% 5.58/1.90 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (implies(v3, v2) = v4) | ~ (implies(v0, v2) = v3) | ~ (implies(v0, v1) = v2) | is_a_theorem(v4))
% 5.58/1.90 | (43) and_2
% 5.58/1.90 | (44) (or(all_0_44_44, all_0_45_45) = all_0_42_42 & or(all_0_45_45, all_0_44_44) = all_0_43_43 & implies(all_0_43_43, all_0_42_42) = all_0_41_41 & ~ r3 & ~ is_a_theorem(all_0_41_41)) | (r3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (or(v1, v0) = v3) | ~ (or(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | is_a_theorem(v4)))
% 5.58/1.91 | (45) not(all_0_29_29) = all_0_27_27
% 5.58/1.91 | (46) (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)))
% 5.58/1.91 | (47) implies_3
% 5.58/1.91 | (48) ! [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))
% 5.58/1.91 | (49) ~ 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)))
% 5.58/1.91 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v0, v1) = v2) | ~ (implies(v1, v2) = v3) | ~ (implies(v0, v3) = v4) | is_a_theorem(v4))
% 5.58/1.91 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v2, v3) = v4) | ~ (not(v1) = v3) | ~ (not(v0) = v2) | ? [v5] : (or(v0, v1) = v5 & not(v4) = v5))
% 5.58/1.91 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (implies(v3, v2) = v1) | ~ (implies(v3, v2) = v0))
% 5.58/1.91 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (or(v0, v1) = v2) | ~ (implies(v0, v2) = v3) | is_a_theorem(v3))
% 5.58/1.91 | (54) substitution_of_equivalents
% 5.58/1.91 | (55) or_1
% 5.58/1.91 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equiv(v0, v1) = v2) | ~ (implies(v2, v3) = v4) | ~ (implies(v1, v0) = v3) | is_a_theorem(v4))
% 5.58/1.91 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (and(v0, v1) = v2) | ~ (implies(v2, v1) = v3) | is_a_theorem(v3))
% 5.58/1.91 | (58) implies(all_0_29_29, all_0_26_26) = all_0_25_25
% 5.58/1.91 | (59) equivalence_3
% 5.58/1.91 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (or(v3, v2) = v1) | ~ (or(v3, v2) = v0))
% 5.58/1.91 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (implies(v1, v0) = v2) | ~ (implies(v0, v2) = v3) | is_a_theorem(v3))
% 5.58/1.91 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (and(v2, v3) = v4) | ~ (implies(v1, v0) = v3) | ~ (implies(v0, v1) = v2) | equiv(v0, v1) = v4)
% 5.58/1.91 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (implies(v0, v1) = v2) | ~ is_a_theorem(v2) | ~ is_a_theorem(v0) | is_a_theorem(v1))
% 5.58/1.91 |
% 5.58/1.91 | Instantiating formula (15) with all_0_26_26, all_0_28_28, all_0_27_27 and discharging atoms implies(all_0_27_27, all_0_28_28) = all_0_26_26, yields:
% 5.58/1.91 | (64) ? [v0] : ? [v1] : (and(all_0_27_27, v0) = v1 & not(v1) = all_0_26_26 & not(all_0_28_28) = v0)
% 5.58/1.92 |
% 5.58/1.92 | Instantiating (64) with all_10_0_64, all_10_1_65 yields:
% 5.58/1.92 | (65) and(all_0_27_27, all_10_1_65) = all_10_0_64 & not(all_10_0_64) = all_0_26_26 & not(all_0_28_28) = all_10_1_65
% 5.58/1.92 |
% 5.58/1.92 | Applying alpha-rule on (65) yields:
% 5.58/1.92 | (66) and(all_0_27_27, all_10_1_65) = all_10_0_64
% 5.58/1.92 | (67) not(all_10_0_64) = all_0_26_26
% 5.58/1.92 | (68) not(all_0_28_28) = all_10_1_65
% 5.58/1.92 |
% 5.58/1.92 | Instantiating formula (51) with all_10_0_64, all_10_1_65, all_0_27_27, all_0_28_28, all_0_29_29 and discharging atoms and(all_0_27_27, all_10_1_65) = all_10_0_64, not(all_0_28_28) = all_10_1_65, not(all_0_29_29) = all_0_27_27, yields:
% 5.58/1.92 | (69) ? [v0] : (or(all_0_29_29, all_0_28_28) = v0 & not(all_10_0_64) = v0)
% 5.58/1.92 |
% 5.58/1.92 | Instantiating (69) with all_17_0_66 yields:
% 5.58/1.92 | (70) or(all_0_29_29, all_0_28_28) = all_17_0_66 & not(all_10_0_64) = all_17_0_66
% 5.58/1.92 |
% 5.58/1.92 | Applying alpha-rule on (70) yields:
% 5.58/1.92 | (71) or(all_0_29_29, all_0_28_28) = all_17_0_66
% 5.58/1.92 | (72) not(all_10_0_64) = all_17_0_66
% 5.58/1.92 |
% 5.58/1.92 | Instantiating formula (32) with all_10_0_64, all_17_0_66, all_0_26_26 and discharging atoms not(all_10_0_64) = all_17_0_66, not(all_10_0_64) = all_0_26_26, yields:
% 5.58/1.92 | (73) all_17_0_66 = all_0_26_26
% 5.58/1.92 |
% 5.58/1.92 | From (73) and (71) follows:
% 5.58/1.92 | (74) or(all_0_29_29, all_0_28_28) = all_0_26_26
% 5.58/1.92 |
% 5.96/1.92 | Instantiating formula (53) with all_0_25_25, all_0_26_26, all_0_28_28, all_0_29_29 and discharging atoms or(all_0_29_29, all_0_28_28) = all_0_26_26, implies(all_0_29_29, all_0_26_26) = all_0_25_25, ~ is_a_theorem(all_0_25_25), yields:
% 5.96/1.92 | (75) $false
% 5.96/1.92 |
% 5.96/1.92 |-The branch is then unsatisfiable
% 5.96/1.92 % SZS output end Proof for theBenchmark
% 5.96/1.92
% 5.96/1.92 1320ms
%------------------------------------------------------------------------------