TSTP Solution File: SWV167+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWV167+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n023.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 : Wed Jul 20 17:50:14 EDT 2022
% Result : Theorem 27.38s 7.81s
% Output : Proof 38.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWV167+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.00/0.09 % Command : ePrincess-casc -timeout=%d %s
% 0.09/0.29 % Computer : n023.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Wed Jun 15 13:53:35 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.14/0.46 ____ _
% 0.14/0.46 ___ / __ \_____(_)___ ________ __________
% 0.14/0.46 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.14/0.46 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.14/0.46 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.14/0.46
% 0.14/0.46 A Theorem Prover for First-Order Logic
% 0.14/0.47 (ePrincess v.1.0)
% 0.14/0.47
% 0.14/0.47 (c) Philipp Rümmer, 2009-2015
% 0.14/0.47 (c) Peter Backeman, 2014-2015
% 0.14/0.47 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.14/0.47 Free software under GNU Lesser General Public License (LGPL).
% 0.14/0.47 Bug reports to peter@backeman.se
% 0.14/0.47
% 0.14/0.47 For more information, visit http://user.uu.se/~petba168/breu/
% 0.14/0.47
% 0.14/0.47 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.14/0.51 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.99/0.92 Prover 0: Preprocessing ...
% 3.62/1.38 Prover 0: Warning: ignoring some quantifiers
% 3.96/1.42 Prover 0: Constructing countermodel ...
% 19.08/5.80 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.58/5.94 Prover 1: Preprocessing ...
% 20.46/6.15 Prover 1: Warning: ignoring some quantifiers
% 20.46/6.16 Prover 1: Constructing countermodel ...
% 27.38/7.81 Prover 1: proved (2002ms)
% 27.38/7.81 Prover 0: stopped
% 27.38/7.81
% 27.38/7.81 No countermodel exists, formula is valid
% 27.38/7.81 % SZS status Theorem for theBenchmark
% 27.38/7.81
% 27.38/7.81 Generating proof ... Warning: ignoring some quantifiers
% 36.97/10.07 found it (size 459)
% 36.97/10.07
% 36.97/10.07 % SZS output start Proof for theBenchmark
% 36.97/10.07 Assumed formulas after preprocessing and simplification:
% 36.97/10.07 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = init) & ~ (def = use) & a_select2(sigma_init, pv40) = init & a_select2(mu_init, v2) = v3 & a_select2(mu_init, pv40) = init & succ(n4) = n5 & succ(n3) = n4 & succ(n2) = n3 & succ(n1) = n2 & succ(tptp_minus_1) = n0 & succ(n0) = n1 & pred(pv40) = v0 & leq(v2, pv40) = 0 & leq(pv40, n4) = 0 & leq(n0, v2) = 0 & leq(n0, pv40) = 0 & gt(loopcounter, n1) = v1 & gt(n135299, n5) = 0 & gt(n135299, n4) = 0 & gt(n135299, n3) = 0 & gt(n135299, n2) = 0 & gt(n135299, n1) = 0 & gt(n135299, tptp_minus_1) = 0 & gt(n135299, n0) = 0 & gt(n5, n4) = 0 & gt(n5, n3) = 0 & gt(n5, n2) = 0 & gt(n5, n1) = 0 & gt(n5, tptp_minus_1) = 0 & gt(n5, n0) = 0 & gt(n4, n3) = 0 & gt(n4, n2) = 0 & gt(n4, n1) = 0 & gt(n4, tptp_minus_1) = 0 & gt(n4, n0) = 0 & gt(n3, n2) = 0 & gt(n3, n1) = 0 & gt(n3, tptp_minus_1) = 0 & gt(n3, n0) = 0 & gt(n2, n1) = 0 & gt(n2, tptp_minus_1) = 0 & gt(n2, n0) = 0 & gt(n1, tptp_minus_1) = 0 & gt(n1, n0) = 0 & gt(n0, tptp_minus_1) = 0 & true & ? [v4] : ? [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (tptp_mmul(v18, v19) = v20) | ~ (tptp_mmul(v11, v15) = v16) | ~ (tptp_mmul(v10, v16) = v17) | ~ (tptp_mmul(v9, v12) = v13) | ~ (tptp_mmul(v8, v13) = v14) | ~ (tptp_mmul(v7, v20) = v21) | ~ (tptp_madd(v14, v17) = v18) | ~ (tptp_madd(v6, v21) = v22) | ~ (trans(v10) = v15) | ~ (trans(v8) = v12) | ~ (trans(v7) = v19) | ~ (a_select3(v22, v23, v24) = v25) | ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : ? [v32] : ? [v33] : ((v31 = 0 & v30 = 0 & v29 = 0 & v28 = 0 & ~ (v33 = v32) & a_select3(v11, v27, v26) = v33 & a_select3(v11, v26, v27) = v32 & leq(v27, v4) = 0 & leq(v26, v4) = 0 & leq(n0, v27) = 0 & leq(n0, v26) = 0) | (v31 = 0 & v30 = 0 & v29 = 0 & v28 = 0 & ~ (v33 = v32) & a_select3(v9, v27, v26) = v33 & a_select3(v9, v26, v27) = v32 & leq(v27, v5) = 0 & leq(v26, v5) = 0 & leq(n0, v27) = 0 & leq(n0, v26) = 0) | (v31 = 0 & v30 = 0 & v29 = 0 & v28 = 0 & ~ (v33 = v32) & a_select3(v6, v27, v26) = v33 & a_select3(v6, v26, v27) = v32 & leq(v27, v4) = 0 & leq(v26, v4) = 0 & leq(n0, v27) = 0 & leq(n0, v26) = 0) | (a_select3(v22, v24, v23) = v30 & leq(v24, v4) = v29 & leq(v23, v4) = v27 & leq(n0, v24) = v28 & leq(n0, v23) = v26 & ( ~ (v29 = 0) | ~ (v28 = 0) | ~ (v27 = 0) | ~ (v26 = 0) | v30 = v25)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v10 | ~ (tptp_const_array2(v11, v12, v10) = v13) | ~ (a_select3(v13, v4, v7) = v14) | ~ (dim(v8, v9) = v12) | ~ (dim(v5, v6) = v11) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (leq(v8, v7) = v17 & leq(v7, v9) = v18 & leq(v5, v4) = v15 & leq(v4, v6) = v16 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0)))) & ? [v4] : ? [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (tptp_mmul(v7, v8) = v9) | ~ (tptp_mmul(v6, v9) = v10) | ~ (trans(v6) = v8) | ~ (a_select3(v10, v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ((v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & ~ (v21 = v20) & a_select3(v7, v15, v14) = v21 & a_select3(v7, v14, v15) = v20 & leq(v15, v5) = 0 & leq(v14, v5) = 0 & leq(n0, v15) = 0 & leq(n0, v14) = 0) | (a_select3(v10, v12, v11) = v18 & leq(v12, v4) = v17 & leq(v11, v4) = v15 & leq(n0, v12) = v16 & leq(n0, v11) = v14 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | v18 = v13)))) & ? [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (tptp_mmul(v6, v7) = v8) | ~ (tptp_mmul(v5, v8) = v9) | ~ (trans(v5) = v7) | ~ (a_select3(v9, v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & ~ (v20 = v19) & a_select3(v6, v14, v13) = v20 & a_select3(v6, v13, v14) = v19 & leq(v14, v4) = 0 & leq(v13, v4) = 0 & leq(n0, v14) = 0 & leq(n0, v13) = 0) | (a_select3(v9, v11, v10) = v17 & leq(v11, v4) = v16 & leq(v10, v4) = v14 & leq(n0, v11) = v15 & leq(n0, v10) = v13 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | v17 = v12)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (tptp_update3(v8, v6, v7, v9) = v10) | ~ (a_select3(v10, v4, v5) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & ~ (v18 = v9) & a_select3(v8, v12, v13) = v18 & leq(v13, v7) = 0 & leq(v12, v6) = 0 & leq(n0, v13) = 0 & leq(n0, v12) = 0) | (leq(v5, v7) = v15 & leq(v4, v6) = v13 & leq(n0, v5) = v14 & leq(n0, v4) = v12 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0))))) & ? [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v4 | v7 = v5 | ~ (tptp_update3(v8, v5, v6, v9) = v10) | ~ (a_select3(v10, v7, v6) = v11) | ? [v12] : ( ~ (v12 = v4) & a_select3(v8, v7, v6) = v12)) & ? [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (tptp_update3(v5, v8, v8, v9) = v10) | ~ (a_select3(v10, v6, v7) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & ~ (v19 = v18) & a_select3(v5, v13, v12) = v19 & a_select3(v5, v12, v13) = v18 & leq(v13, v4) = 0 & leq(v12, v4) = 0 & leq(n0, v13) = 0 & leq(n0, v12) = 0) | (a_select3(v10, v7, v6) = v18 & leq(v8, v4) = v17 & leq(v7, v4) = v15 & leq(v6, v4) = v13 & leq(n0, v8) = v16 & leq(n0, v7) = v14 & leq(n0, v6) = v12 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | v18 = v11)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (dim(v5, v6) = v8) | ~ (tptp_const_array1(v8, v7) = v9) | ~ (a_select2(v9, v4) = v10) | ? [v11] : ? [v12] : (leq(v5, v4) = v11 & leq(v4, v6) = v12 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ? [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v4 | v6 = v5 | ~ (tptp_update2(v7, v5, v8) = v9) | ~ (a_select2(v9, v6) = v10) | ? [v11] : ( ~ (v11 = v4) & a_select2(v7, v6) = v11)) & ? [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (tptp_msub(v5, v6) = v7) | ~ (a_select3(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & ~ (v18 = v17) & a_select3(v6, v12, v11) = v18 & a_select3(v6, v11, v12) = v17 & leq(v12, v4) = 0 & leq(v11, v4) = 0 & leq(n0, v12) = 0 & leq(n0, v11) = 0) | (v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & ~ (v18 = v17) & a_select3(v5, v12, v11) = v18 & a_select3(v5, v11, v12) = v17 & leq(v12, v4) = 0 & leq(v11, v4) = 0 & leq(n0, v12) = 0 & leq(n0, v11) = 0) | (a_select3(v7, v9, v8) = v15 & leq(v9, v4) = v14 & leq(v8, v4) = v12 & leq(n0, v9) = v13 & leq(n0, v8) = v11 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | v15 = v10)))) & ? [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (tptp_madd(v5, v6) = v7) | ~ (a_select3(v7, v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & ~ (v18 = v17) & a_select3(v6, v12, v11) = v18 & a_select3(v6, v11, v12) = v17 & leq(v12, v4) = 0 & leq(v11, v4) = 0 & leq(n0, v12) = 0 & leq(n0, v11) = 0) | (v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & ~ (v18 = v17) & a_select3(v5, v12, v11) = v18 & a_select3(v5, v11, v12) = v17 & leq(v12, v4) = 0 & leq(v11, v4) = 0 & leq(n0, v12) = 0 & leq(n0, v11) = 0) | (a_select3(v7, v9, v8) = v15 & leq(v9, v4) = v14 & leq(v8, v4) = v12 & leq(n0, v9) = v13 & leq(n0, v8) = v11 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | v15 = v10)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (tptp_update2(v6, v5, v7) = v8) | ~ (a_select2(v8, v4) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v12 = 0 & v11 = 0 & ~ (v13 = v7) & a_select2(v6, v10) = v13 & leq(v10, v5) = 0 & leq(n0, v10) = 0) | (leq(v4, v5) = v11 & leq(n0, v4) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (tptp_update3(v4, v5, v6, v7) = v8) | ~ (a_select3(v8, v5, v6) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v5 = v4 | ~ (tptp_update3(v9, v8, v7, v6) = v5) | ~ (tptp_update3(v9, v8, v7, v6) = v4)) & ? [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (inv(v5) = v6) | ~ (a_select3(v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & ~ (v17 = v16) & a_select3(v5, v11, v10) = v17 & a_select3(v5, v10, v11) = v16 & leq(v11, v4) = 0 & leq(v10, v4) = 0 & leq(n0, v11) = 0 & leq(n0, v10) = 0) | (a_select3(v6, v8, v7) = v14 & leq(v8, v4) = v13 & leq(v7, v4) = v11 & leq(n0, v8) = v12 & leq(n0, v7) = v10 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v14 = v9)))) & ? [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (trans(v5) = v6) | ~ (a_select3(v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & ~ (v17 = v16) & a_select3(v5, v11, v10) = v17 & a_select3(v5, v10, v11) = v16 & leq(v11, v4) = 0 & leq(v10, v4) = 0 & leq(n0, v11) = 0 & leq(n0, v10) = 0) | (a_select3(v6, v8, v7) = v14 & leq(v8, v4) = v13 & leq(v7, v4) = v11 & leq(n0, v8) = v12 & leq(n0, v7) = v10 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v14 = v9)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v6 | ~ (tptp_update2(v4, v5, v6) = v7) | ~ (a_select2(v7, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (succ(v5) = v7) | ~ (succ(v4) = v6) | ~ (leq(v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & leq(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (tptp_update2(v8, v7, v6) = v5) | ~ (tptp_update2(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (sum(v8, v7, v6) = v5) | ~ (sum(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (tptp_const_array2(v8, v7, v6) = v5) | ~ (tptp_const_array2(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (a_select3(v8, v7, v6) = v5) | ~ (a_select3(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (uniform_int_rnd(v5, v4) = v6) | ~ (leq(v6, v4) = v7) | ? [v8] : ( ~ (v8 = 0) & leq(n0, v4) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (succ(v5) = v6) | ~ (leq(v4, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & leq(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (succ(v5) = v6) | ~ (gt(v6, v4) = v7) | ? [v8] : ( ~ (v8 = 0) & leq(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (pred(v5) = v6) | ~ (leq(v4, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & gt(v5, v4) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (leq(v4, v6) = v7) | ~ (leq(v4, v5) = 0) | ? [v8] : ( ~ (v8 = 0) & leq(v5, v6) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (gt(v4, v6) = v7) | ~ (gt(v4, v5) = 0) | ? [v8] : ( ~ (v8 = 0) & gt(v5, v6) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (minus(v7, v6) = v5) | ~ (minus(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (plus(v7, v6) = v5) | ~ (plus(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (tptp_mmul(v7, v6) = v5) | ~ (tptp_mmul(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (tptp_msub(v7, v6) = v5) | ~ (tptp_msub(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (tptp_madd(v7, v6) = v5) | ~ (tptp_madd(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (dim(v7, v6) = v5) | ~ (dim(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (tptp_const_array1(v7, v6) = v5) | ~ (tptp_const_array1(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (a_select2(v7, v6) = v5) | ~ (a_select2(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (uniform_int_rnd(v7, v6) = v5) | ~ (uniform_int_rnd(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (geq(v7, v6) = v5) | ~ (geq(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (lt(v7, v6) = v5) | ~ (lt(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (leq(v7, v6) = v5) | ~ (leq(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (gt(v7, v6) = v5) | ~ (gt(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (succ(v5) = v7) | ~ (succ(v4) = v6) | ~ (leq(v6, v7) = 0) | leq(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = init | ~ (a_select3(q_init, v4, v5) = v6) | ~ (leq(v4, n135299) = 0) | ? [v7] : ? [v8] : (( ~ (v7 = 0) & leq(n0, v4) = v7) | (leq(v5, n4) = v8 & leq(n0, v5) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = v4 | ~ (gt(v5, v4) = v6) | ? [v7] : ( ~ (v7 = 0) & leq(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = v4 | ~ (gt(v4, v5) = v6) | gt(v5, v4) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (succ(v4) = v5) | ~ (gt(v5, v4) = v6)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (geq(v4, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & leq(v5, v4) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (lt(v4, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & gt(v5, v4) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (inv(v6) = v5) | ~ (inv(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (trans(v6) = v5) | ~ (trans(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (succ(v6) = v5) | ~ (succ(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (pred(v6) = v5) | ~ (pred(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (minus(v4, v5) = v6) | ~ (leq(v6, v4) = 0) | leq(n0, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (uniform_int_rnd(v5, v4) = v6) | ? [v7] : ? [v8] : (leq(n0, v6) = v8 & leq(n0, v4) = v7 & ( ~ (v7 = 0) | v8 = 0))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (succ(v5) = v6) | ~ (gt(v6, v4) = 0) | leq(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (succ(v4) = v6) | ~ (leq(v6, v5) = 0) | gt(v5, v4) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (pred(v5) = v6) | ~ (leq(v4, v6) = 0) | gt(v5, v4) = 0) & ! [v4] : ! [v5] : (v5 = init | ~ (a_select3(center_init, v4, n0) = v5) | ? [v6] : ? [v7] : (leq(v4, n4) = v7 & leq(n0, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v4] : ! [v5] : (v5 = init | ~ (a_select2(rho_init, v4) = v5) | ? [v6] : ? [v7] : (leq(v4, n4) = v7 & leq(n0, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v4] : ! [v5] : (v5 = tptp_float_0_0 | ~ (sum(n0, tptp_minus_1, v4) = v5)) & ! [v4] : ! [v5] : (v5 = n0 | ~ (sum(n0, tptp_minus_1, v4) = v5)) & ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v4, v4) = v5)) & ! [v4] : ! [v5] : ( ~ (minus(v4, n1) = v5) | pred(v4) = v5) & ! [v4] : ! [v5] : ( ~ (plus(v4, n5) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (succ(v9) = v5 & succ(v8) = v9 & succ(v7) = v8 & succ(v6) = v7 & succ(v4) = v6)) & ! [v4] : ! [v5] : ( ~ (plus(v4, n4) = v5) | ? [v6] : ? [v7] : ? [v8] : (succ(v8) = v5 & succ(v7) = v8 & succ(v6) = v7 & succ(v4) = v6)) & ! [v4] : ! [v5] : ( ~ (plus(v4, n3) = v5) | ? [v6] : ? [v7] : (succ(v7) = v5 & succ(v6) = v7 & succ(v4) = v6)) & ! [v4] : ! [v5] : ( ~ (plus(v4, n2) = v5) | ? [v6] : (succ(v6) = v5 & succ(v4) = v6)) & ! [v4] : ! [v5] : ( ~ (plus(v4, n1) = v5) | succ(v4) = v5) & ! [v4] : ! [v5] : ( ~ (plus(n5, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (succ(v9) = v5 & succ(v8) = v9 & succ(v7) = v8 & succ(v6) = v7 & succ(v4) = v6)) & ! [v4] : ! [v5] : ( ~ (plus(n4, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : (succ(v8) = v5 & succ(v7) = v8 & succ(v6) = v7 & succ(v4) = v6)) & ! [v4] : ! [v5] : ( ~ (plus(n3, v4) = v5) | ? [v6] : ? [v7] : (succ(v7) = v5 & succ(v6) = v7 & succ(v4) = v6)) & ! [v4] : ! [v5] : ( ~ (plus(n2, v4) = v5) | ? [v6] : (succ(v6) = v5 & succ(v4) = v6)) & ! [v4] : ! [v5] : ( ~ (plus(n1, v4) = v5) | succ(v4) = v5) & ! [v4] : ! [v5] : ( ~ (succ(v4) = v5) | pred(v5) = v4) & ! [v4] : ! [v5] : ( ~ (pred(v4) = v5) | succ(v5) = v4) & ! [v4] : ! [v5] : ( ~ (geq(v4, v5) = 0) | leq(v5, v4) = 0) & ! [v4] : ! [v5] : ( ~ (lt(v4, v5) = 0) | gt(v5, v4) = 0) & ! [v4] : ! [v5] : ( ~ (gt(v5, v4) = 0) | leq(v4, v5) = 0) & ! [v4] : (v4 = n5 | v4 = n4 | v4 = n3 | v4 = n2 | v4 = n1 | v4 = n0 | ~ (leq(v4, n5) = 0) | ? [v5] : ( ~ (v5 = 0) & leq(n0, v4) = v5)) & ! [v4] : (v4 = n4 | v4 = n3 | v4 = n2 | v4 = n1 | v4 = n0 | ~ (leq(v4, n4) = 0) | ? [v5] : ( ~ (v5 = 0) & leq(n0, v4) = v5)) & ! [v4] : (v4 = n3 | v4 = n2 | v4 = n1 | v4 = n0 | ~ (leq(v4, n3) = 0) | ? [v5] : ( ~ (v5 = 0) & leq(n0, v4) = v5)) & ! [v4] : (v4 = n2 | v4 = n1 | v4 = n0 | ~ (leq(v4, n2) = 0) | ? [v5] : ( ~ (v5 = 0) & leq(n0, v4) = v5)) & ! [v4] : (v4 = n1 | v4 = n0 | ~ (leq(v4, n1) = 0) | ? [v5] : ( ~ (v5 = 0) & leq(n0, v4) = v5)) & ! [v4] : (v4 = n0 | ~ (leq(n0, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & leq(v4, n0) = v5)) & ! [v4] : ( ~ (leq(v4, v0) = 0) | ? [v5] : ? [v6] : (a_select2(sigma_init, v4) = v6 & leq(n0, v4) = v5 & ( ~ (v5 = 0) | v6 = init))) & ! [v4] : ( ~ (leq(v4, v0) = 0) | ? [v5] : ? [v6] : (a_select2(mu_init, v4) = v6 & leq(n0, v4) = v5 & ( ~ (v5 = 0) | v6 = init))) & ! [v4] : ~ (gt(v4, v4) = 0) & ( ~ (v1 = 0) | ! [v4] : ! [v5] : (v5 = init | ~ (a_select2(sigmaold_init, v4) = v5) | ? [v6] : ? [v7] : (leq(v4, n4) = v7 & leq(n0, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ( ~ (v1 = 0) | ! [v4] : ! [v5] : (v5 = init | ~ (a_select2(rhoold_init, v4) = v5) | ? [v6] : ? [v7] : (leq(v4, n4) = v7 & leq(n0, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ( ~ (v1 = 0) | ! [v4] : ! [v5] : (v5 = init | ~ (a_select2(muold_init, v4) = v5) | ? [v6] : ? [v7] : (leq(v4, n4) = v7 & leq(n0, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))))
% 37.35/10.15 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 37.35/10.15 | (1) ~ (all_0_0_0 = init) & ~ (def = use) & a_select2(sigma_init, pv40) = init & a_select2(mu_init, all_0_1_1) = all_0_0_0 & a_select2(mu_init, pv40) = init & succ(n4) = n5 & succ(n3) = n4 & succ(n2) = n3 & succ(n1) = n2 & succ(tptp_minus_1) = n0 & succ(n0) = n1 & pred(pv40) = all_0_3_3 & leq(all_0_1_1, pv40) = 0 & leq(pv40, n4) = 0 & leq(n0, all_0_1_1) = 0 & leq(n0, pv40) = 0 & gt(loopcounter, n1) = all_0_2_2 & gt(n135299, n5) = 0 & gt(n135299, n4) = 0 & gt(n135299, n3) = 0 & gt(n135299, n2) = 0 & gt(n135299, n1) = 0 & gt(n135299, tptp_minus_1) = 0 & gt(n135299, n0) = 0 & gt(n5, n4) = 0 & gt(n5, n3) = 0 & gt(n5, n2) = 0 & gt(n5, n1) = 0 & gt(n5, tptp_minus_1) = 0 & gt(n5, n0) = 0 & gt(n4, n3) = 0 & gt(n4, n2) = 0 & gt(n4, n1) = 0 & gt(n4, tptp_minus_1) = 0 & gt(n4, n0) = 0 & gt(n3, n2) = 0 & gt(n3, n1) = 0 & gt(n3, tptp_minus_1) = 0 & gt(n3, n0) = 0 & gt(n2, n1) = 0 & gt(n2, tptp_minus_1) = 0 & gt(n2, n0) = 0 & gt(n1, tptp_minus_1) = 0 & gt(n1, n0) = 0 & gt(n0, tptp_minus_1) = 0 & true & ? [v0] : ? [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (tptp_mmul(v14, v15) = v16) | ~ (tptp_mmul(v7, v11) = v12) | ~ (tptp_mmul(v6, v12) = v13) | ~ (tptp_mmul(v5, v8) = v9) | ~ (tptp_mmul(v4, v9) = v10) | ~ (tptp_mmul(v3, v16) = v17) | ~ (tptp_madd(v10, v13) = v14) | ~ (tptp_madd(v2, v17) = v18) | ~ (trans(v6) = v11) | ~ (trans(v4) = v8) | ~ (trans(v3) = v15) | ~ (a_select3(v18, v19, v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ((v27 = 0 & v26 = 0 & v25 = 0 & v24 = 0 & ~ (v29 = v28) & a_select3(v7, v23, v22) = v29 & a_select3(v7, v22, v23) = v28 & leq(v23, v0) = 0 & leq(v22, v0) = 0 & leq(n0, v23) = 0 & leq(n0, v22) = 0) | (v27 = 0 & v26 = 0 & v25 = 0 & v24 = 0 & ~ (v29 = v28) & a_select3(v5, v23, v22) = v29 & a_select3(v5, v22, v23) = v28 & leq(v23, v1) = 0 & leq(v22, v1) = 0 & leq(n0, v23) = 0 & leq(n0, v22) = 0) | (v27 = 0 & v26 = 0 & v25 = 0 & v24 = 0 & ~ (v29 = v28) & a_select3(v2, v23, v22) = v29 & a_select3(v2, v22, v23) = v28 & leq(v23, v0) = 0 & leq(v22, v0) = 0 & leq(n0, v23) = 0 & leq(n0, v22) = 0) | (a_select3(v18, v20, v19) = v26 & leq(v20, v0) = v25 & leq(v19, v0) = v23 & leq(n0, v20) = v24 & leq(n0, v19) = v22 & ( ~ (v25 = 0) | ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0) | v26 = v21)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v6 | ~ (tptp_const_array2(v7, v8, v6) = v9) | ~ (a_select3(v9, v0, v3) = v10) | ~ (dim(v4, v5) = v8) | ~ (dim(v1, v2) = v7) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (leq(v4, v3) = v13 & leq(v3, v5) = v14 & leq(v1, v0) = v11 & leq(v0, v2) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ? [v0] : ? [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (tptp_mmul(v3, v4) = v5) | ~ (tptp_mmul(v2, v5) = v6) | ~ (trans(v2) = v4) | ~ (a_select3(v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & ~ (v17 = v16) & a_select3(v3, v11, v10) = v17 & a_select3(v3, v10, v11) = v16 & leq(v11, v1) = 0 & leq(v10, v1) = 0 & leq(n0, v11) = 0 & leq(n0, v10) = 0) | (a_select3(v6, v8, v7) = v14 & leq(v8, v0) = v13 & leq(v7, v0) = v11 & leq(n0, v8) = v12 & leq(n0, v7) = v10 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v14 = v9)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (tptp_mmul(v2, v3) = v4) | ~ (tptp_mmul(v1, v4) = v5) | ~ (trans(v1) = v3) | ~ (a_select3(v5, v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & ~ (v16 = v15) & a_select3(v2, v10, v9) = v16 & a_select3(v2, v9, v10) = v15 & leq(v10, v0) = 0 & leq(v9, v0) = 0 & leq(n0, v10) = 0 & leq(n0, v9) = 0) | (a_select3(v5, v7, v6) = v13 & leq(v7, v0) = v12 & leq(v6, v0) = v10 & leq(n0, v7) = v11 & leq(n0, v6) = v9 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | v13 = v8)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (tptp_update3(v4, v2, v3, v5) = v6) | ~ (a_select3(v6, v0, v1) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & ~ (v14 = v5) & a_select3(v4, v8, v9) = v14 & leq(v9, v3) = 0 & leq(v8, v2) = 0 & leq(n0, v9) = 0 & leq(n0, v8) = 0) | (leq(v1, v3) = v11 & leq(v0, v2) = v9 & leq(n0, v1) = v10 & leq(n0, v0) = v8 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v0 | v3 = v1 | ~ (tptp_update3(v4, v1, v2, v5) = v6) | ~ (a_select3(v6, v3, v2) = v7) | ? [v8] : ( ~ (v8 = v0) & a_select3(v4, v3, v2) = v8)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (tptp_update3(v1, v4, v4, v5) = v6) | ~ (a_select3(v6, v2, v3) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & ~ (v15 = v14) & a_select3(v1, v9, v8) = v15 & a_select3(v1, v8, v9) = v14 & leq(v9, v0) = 0 & leq(v8, v0) = 0 & leq(n0, v9) = 0 & leq(n0, v8) = 0) | (a_select3(v6, v3, v2) = v14 & leq(v4, v0) = v13 & leq(v3, v0) = v11 & leq(v2, v0) = v9 & leq(n0, v4) = v12 & leq(n0, v3) = v10 & leq(n0, v2) = v8 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | v14 = v7)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v3 | ~ (dim(v1, v2) = v4) | ~ (tptp_const_array1(v4, v3) = v5) | ~ (a_select2(v5, v0) = v6) | ? [v7] : ? [v8] : (leq(v1, v0) = v7 & leq(v0, v2) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v0 | v2 = v1 | ~ (tptp_update2(v3, v1, v4) = v5) | ~ (a_select2(v5, v2) = v6) | ? [v7] : ( ~ (v7 = v0) & a_select2(v3, v2) = v7)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (tptp_msub(v1, v2) = v3) | ~ (a_select3(v3, v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & ~ (v14 = v13) & a_select3(v2, v8, v7) = v14 & a_select3(v2, v7, v8) = v13 & leq(v8, v0) = 0 & leq(v7, v0) = 0 & leq(n0, v8) = 0 & leq(n0, v7) = 0) | (v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & ~ (v14 = v13) & a_select3(v1, v8, v7) = v14 & a_select3(v1, v7, v8) = v13 & leq(v8, v0) = 0 & leq(v7, v0) = 0 & leq(n0, v8) = 0 & leq(n0, v7) = 0) | (a_select3(v3, v5, v4) = v11 & leq(v5, v0) = v10 & leq(v4, v0) = v8 & leq(n0, v5) = v9 & leq(n0, v4) = v7 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v11 = v6)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (tptp_madd(v1, v2) = v3) | ~ (a_select3(v3, v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & ~ (v14 = v13) & a_select3(v2, v8, v7) = v14 & a_select3(v2, v7, v8) = v13 & leq(v8, v0) = 0 & leq(v7, v0) = 0 & leq(n0, v8) = 0 & leq(n0, v7) = 0) | (v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & ~ (v14 = v13) & a_select3(v1, v8, v7) = v14 & a_select3(v1, v7, v8) = v13 & leq(v8, v0) = 0 & leq(v7, v0) = 0 & leq(n0, v8) = 0 & leq(n0, v7) = 0) | (a_select3(v3, v5, v4) = v11 & leq(v5, v0) = v10 & leq(v4, v0) = v8 & leq(n0, v5) = v9 & leq(n0, v4) = v7 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v11 = v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (tptp_update2(v2, v1, v3) = v4) | ~ (a_select2(v4, v0) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v8 = 0 & v7 = 0 & ~ (v9 = v3) & a_select2(v2, v6) = v9 & leq(v6, v1) = 0 & leq(n0, v6) = 0) | (leq(v0, v1) = v7 & leq(n0, v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (tptp_update3(v0, v1, v2, v3) = v4) | ~ (a_select3(v4, v1, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ (tptp_update3(v5, v4, v3, v2) = v0)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (inv(v1) = v2) | ~ (a_select3(v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & ~ (v13 = v12) & a_select3(v1, v7, v6) = v13 & a_select3(v1, v6, v7) = v12 & leq(v7, v0) = 0 & leq(v6, v0) = 0 & leq(n0, v7) = 0 & leq(n0, v6) = 0) | (a_select3(v2, v4, v3) = v10 & leq(v4, v0) = v9 & leq(v3, v0) = v7 & leq(n0, v4) = v8 & leq(n0, v3) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | v10 = v5)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (trans(v1) = v2) | ~ (a_select3(v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & ~ (v13 = v12) & a_select3(v1, v7, v6) = v13 & a_select3(v1, v6, v7) = v12 & leq(v7, v0) = 0 & leq(v6, v0) = 0 & leq(n0, v7) = 0 & leq(n0, v6) = 0) | (a_select3(v2, v4, v3) = v10 & leq(v4, v0) = v9 & leq(v3, v0) = v7 & leq(n0, v4) = v8 & leq(n0, v3) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | v10 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (tptp_update2(v0, v1, v2) = v3) | ~ (a_select2(v3, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (succ(v1) = v3) | ~ (succ(v0) = v2) | ~ (leq(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & leq(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | ~ (sum(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (uniform_int_rnd(v1, v0) = v2) | ~ (leq(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & leq(n0, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (succ(v1) = v2) | ~ (leq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & leq(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (succ(v1) = v2) | ~ (gt(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & leq(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (gt(v0, v2) = v3) | ~ (gt(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & gt(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ (dim(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (succ(v1) = v3) | ~ (succ(v0) = v2) | ~ (leq(v2, v3) = 0) | leq(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = init | ~ (a_select3(q_init, v0, v1) = v2) | ~ (leq(v0, n135299) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & leq(n0, v0) = v3) | (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (gt(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (gt(v0, v1) = v2) | gt(v1, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (succ(v0) = v1) | ~ (gt(v1, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (geq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (lt(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & gt(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (minus(v0, v1) = v2) | ~ (leq(v2, v0) = 0) | leq(n0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (uniform_int_rnd(v1, v0) = v2) | ? [v3] : ? [v4] : (leq(n0, v2) = v4 & leq(n0, v0) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ (gt(v2, v0) = 0) | leq(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v0) = v2) | ~ (leq(v2, v1) = 0) | gt(v1, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | gt(v1, v0) = 0) & ! [v0] : ! [v1] : (v1 = init | ~ (a_select3(center_init, v0, n0) = v1) | ? [v2] : ? [v3] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = init | ~ (a_select2(rho_init, v0) = v1) | ? [v2] : ? [v3] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = tptp_float_0_0 | ~ (sum(n0, tptp_minus_1, v0) = v1)) & ! [v0] : ! [v1] : (v1 = n0 | ~ (sum(n0, tptp_minus_1, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (minus(v0, n1) = v1) | pred(v0) = v1) & ! [v0] : ! [v1] : ( ~ (plus(v0, n5) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (succ(v5) = v1 & succ(v4) = v5 & succ(v3) = v4 & succ(v2) = v3 & succ(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (plus(v0, n4) = v1) | ? [v2] : ? [v3] : ? [v4] : (succ(v4) = v1 & succ(v3) = v4 & succ(v2) = v3 & succ(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (plus(v0, n3) = v1) | ? [v2] : ? [v3] : (succ(v3) = v1 & succ(v2) = v3 & succ(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (plus(v0, n2) = v1) | ? [v2] : (succ(v2) = v1 & succ(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (plus(v0, n1) = v1) | succ(v0) = v1) & ! [v0] : ! [v1] : ( ~ (plus(n5, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (succ(v5) = v1 & succ(v4) = v5 & succ(v3) = v4 & succ(v2) = v3 & succ(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (plus(n4, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (succ(v4) = v1 & succ(v3) = v4 & succ(v2) = v3 & succ(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (plus(n3, v0) = v1) | ? [v2] : ? [v3] : (succ(v3) = v1 & succ(v2) = v3 & succ(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (plus(n2, v0) = v1) | ? [v2] : (succ(v2) = v1 & succ(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (plus(n1, v0) = v1) | succ(v0) = v1) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | pred(v1) = v0) & ! [v0] : ! [v1] : ( ~ (pred(v0) = v1) | succ(v1) = v0) & ! [v0] : ! [v1] : ( ~ (geq(v0, v1) = 0) | leq(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (lt(v0, v1) = 0) | gt(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (gt(v1, v0) = 0) | leq(v0, v1) = 0) & ! [v0] : (v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n5) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(n0, v0) = v1)) & ! [v0] : (v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n4) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(n0, v0) = v1)) & ! [v0] : (v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n3) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(n0, v0) = v1)) & ! [v0] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n2) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(n0, v0) = v1)) & ! [v0] : (v0 = n1 | v0 = n0 | ~ (leq(v0, n1) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(n0, v0) = v1)) & ! [v0] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) & ! [v0] : ( ~ (leq(v0, all_0_3_3) = 0) | ? [v1] : ? [v2] : (a_select2(sigma_init, v0) = v2 & leq(n0, v0) = v1 & ( ~ (v1 = 0) | v2 = init))) & ! [v0] : ( ~ (leq(v0, all_0_3_3) = 0) | ? [v1] : ? [v2] : (a_select2(mu_init, v0) = v2 & leq(n0, v0) = v1 & ( ~ (v1 = 0) | v2 = init))) & ! [v0] : ~ (gt(v0, v0) = 0) & ( ~ (all_0_2_2 = 0) | ! [v0] : ! [v1] : (v1 = init | ~ (a_select2(sigmaold_init, v0) = v1) | ? [v2] : ? [v3] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ( ~ (all_0_2_2 = 0) | ! [v0] : ! [v1] : (v1 = init | ~ (a_select2(rhoold_init, v0) = v1) | ? [v2] : ? [v3] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ( ~ (all_0_2_2 = 0) | ! [v0] : ! [v1] : (v1 = init | ~ (a_select2(muold_init, v0) = v1) | ? [v2] : ? [v3] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 37.35/10.18 |
% 37.35/10.18 | Applying alpha-rule on (1) yields:
% 37.35/10.18 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, v2) = v0))
% 37.35/10.18 | (3) leq(pv40, n4) = 0
% 37.35/10.18 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (tptp_update3(v0, v1, v2, v3) = v4) | ~ (a_select3(v4, v1, v2) = v5))
% 37.35/10.18 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (succ(v1) = v2) | ~ (gt(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & leq(v0, v1) = v4))
% 37.35/10.18 | (6) gt(n4, n2) = 0
% 37.35/10.18 | (7) ! [v0] : ! [v1] : (v1 = init | ~ (a_select2(rho_init, v0) = v1) | ? [v2] : ? [v3] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 37.35/10.18 | (8) ! [v0] : ! [v1] : ( ~ (plus(v0, n1) = v1) | succ(v0) = v1)
% 37.35/10.18 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ (gt(v2, v0) = 0) | leq(v0, v1) = 0)
% 37.35/10.18 | (10) succ(n2) = n3
% 37.35/10.18 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v0) = v2) | ~ (leq(v2, v1) = 0) | gt(v1, v0) = 0)
% 37.35/10.18 | (12) ~ (all_0_2_2 = 0) | ! [v0] : ! [v1] : (v1 = init | ~ (a_select2(rhoold_init, v0) = v1) | ? [v2] : ? [v3] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 37.35/10.18 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | gt(v1, v0) = 0)
% 37.35/10.18 | (14) leq(n0, pv40) = 0
% 37.35/10.18 | (15) ! [v0] : ! [v1] : ( ~ (plus(n3, v0) = v1) | ? [v2] : ? [v3] : (succ(v3) = v1 & succ(v2) = v3 & succ(v0) = v2))
% 37.35/10.18 | (16) gt(loopcounter, n1) = all_0_2_2
% 37.35/10.18 | (17) gt(n135299, tptp_minus_1) = 0
% 37.35/10.18 | (18) leq(n0, all_0_1_1) = 0
% 37.35/10.18 | (19) ~ (all_0_2_2 = 0) | ! [v0] : ! [v1] : (v1 = init | ~ (a_select2(muold_init, v0) = v1) | ? [v2] : ? [v3] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 37.35/10.18 | (20) ! [v0] : ! [v1] : ( ~ (plus(v0, n3) = v1) | ? [v2] : ? [v3] : (succ(v3) = v1 & succ(v2) = v3 & succ(v0) = v2))
% 37.35/10.18 | (21) gt(n3, tptp_minus_1) = 0
% 37.35/10.18 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 37.35/10.18 | (23) ! [v0] : ! [v1] : (v1 = tptp_float_0_0 | ~ (sum(n0, tptp_minus_1, v0) = v1))
% 37.35/10.18 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v3 | ~ (dim(v1, v2) = v4) | ~ (tptp_const_array1(v4, v3) = v5) | ~ (a_select2(v5, v0) = v6) | ? [v7] : ? [v8] : (leq(v1, v0) = v7 & leq(v0, v2) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 37.78/10.18 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0))
% 37.78/10.18 | (26) gt(n2, n1) = 0
% 37.78/10.18 | (27) a_select2(mu_init, pv40) = init
% 37.78/10.18 | (28) ! [v0] : ! [v1] : ( ~ (plus(n5, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (succ(v5) = v1 & succ(v4) = v5 & succ(v3) = v4 & succ(v2) = v3 & succ(v0) = v2))
% 37.78/10.18 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (uniform_int_rnd(v1, v0) = v2) | ~ (leq(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & leq(n0, v0) = v4))
% 37.78/10.18 | (30) gt(n4, n0) = 0
% 37.78/10.18 | (31) ! [v0] : ! [v1] : ( ~ (plus(v0, n5) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (succ(v5) = v1 & succ(v4) = v5 & succ(v3) = v4 & succ(v2) = v3 & succ(v0) = v2))
% 37.78/10.18 | (32) ~ (all_0_0_0 = init)
% 37.78/10.18 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (minus(v0, v1) = v2) | ~ (leq(v2, v0) = 0) | leq(n0, v1) = 0)
% 37.78/10.18 | (34) ! [v0] : ! [v1] : ( ~ (geq(v0, v1) = 0) | leq(v1, v0) = 0)
% 37.78/10.18 | (35) ? [v0] : ? [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (tptp_mmul(v3, v4) = v5) | ~ (tptp_mmul(v2, v5) = v6) | ~ (trans(v2) = v4) | ~ (a_select3(v6, v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v15 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & ~ (v17 = v16) & a_select3(v3, v11, v10) = v17 & a_select3(v3, v10, v11) = v16 & leq(v11, v1) = 0 & leq(v10, v1) = 0 & leq(n0, v11) = 0 & leq(n0, v10) = 0) | (a_select3(v6, v8, v7) = v14 & leq(v8, v0) = v13 & leq(v7, v0) = v11 & leq(n0, v8) = v12 & leq(n0, v7) = v10 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v14 = v9))))
% 37.78/10.19 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0))
% 37.78/10.19 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ (dim(v3, v2) = v0))
% 37.78/10.19 | (38) ! [v0] : ! [v1] : ( ~ (plus(n2, v0) = v1) | ? [v2] : (succ(v2) = v1 & succ(v0) = v2))
% 37.78/10.19 | (39) ! [v0] : ! [v1] : ( ~ (plus(v0, n4) = v1) | ? [v2] : ? [v3] : ? [v4] : (succ(v4) = v1 & succ(v3) = v4 & succ(v2) = v3 & succ(v0) = v2))
% 37.78/10.19 | (40) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (inv(v1) = v2) | ~ (a_select3(v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & ~ (v13 = v12) & a_select3(v1, v7, v6) = v13 & a_select3(v1, v6, v7) = v12 & leq(v7, v0) = 0 & leq(v6, v0) = 0 & leq(n0, v7) = 0 & leq(n0, v6) = 0) | (a_select3(v2, v4, v3) = v10 & leq(v4, v0) = v9 & leq(v3, v0) = v7 & leq(n0, v4) = v8 & leq(n0, v3) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | v10 = v5))))
% 37.78/10.19 | (41) succ(n0) = n1
% 37.78/10.19 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0))
% 37.78/10.19 | (43) gt(n5, n2) = 0
% 37.78/10.19 | (44) ! [v0] : ! [v1] : ( ~ (lt(v0, v1) = 0) | gt(v1, v0) = 0)
% 37.78/10.19 | (45) ! [v0] : ! [v1] : ( ~ (plus(v0, n2) = v1) | ? [v2] : (succ(v2) = v1 & succ(v0) = v2))
% 37.78/10.19 | (46) gt(n5, n4) = 0
% 37.78/10.19 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ (tptp_update3(v5, v4, v3, v2) = v0))
% 37.78/10.19 | (48) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (tptp_update3(v1, v4, v4, v5) = v6) | ~ (a_select3(v6, v2, v3) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & ~ (v15 = v14) & a_select3(v1, v9, v8) = v15 & a_select3(v1, v8, v9) = v14 & leq(v9, v0) = 0 & leq(v8, v0) = 0 & leq(n0, v9) = 0 & leq(n0, v8) = 0) | (a_select3(v6, v3, v2) = v14 & leq(v4, v0) = v13 & leq(v3, v0) = v11 & leq(v2, v0) = v9 & leq(n0, v4) = v12 & leq(n0, v3) = v10 & leq(n0, v2) = v8 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | v14 = v7))))
% 37.78/10.19 | (49) ! [v0] : ! [v1] : ( ~ (gt(v1, v0) = 0) | leq(v0, v1) = 0)
% 37.78/10.19 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, v2) = v0))
% 37.78/10.19 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (tptp_update3(v4, v2, v3, v5) = v6) | ~ (a_select3(v6, v0, v1) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & ~ (v14 = v5) & a_select3(v4, v8, v9) = v14 & leq(v9, v3) = 0 & leq(v8, v2) = 0 & leq(n0, v9) = 0 & leq(n0, v8) = 0) | (leq(v1, v3) = v11 & leq(v0, v2) = v9 & leq(n0, v1) = v10 & leq(n0, v0) = v8 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0)))))
% 37.78/10.19 | (52) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (gt(v0, v1) = v2) | gt(v1, v0) = 0)
% 37.78/10.19 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (succ(v1) = v3) | ~ (succ(v0) = v2) | ~ (leq(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & leq(v0, v1) = v5))
% 37.78/10.19 | (54) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (lt(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & gt(v1, v0) = v3))
% 37.78/10.19 | (55) gt(n1, n0) = 0
% 37.78/10.19 | (56) gt(n5, tptp_minus_1) = 0
% 37.78/10.19 | (57) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (tptp_madd(v1, v2) = v3) | ~ (a_select3(v3, v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & ~ (v14 = v13) & a_select3(v2, v8, v7) = v14 & a_select3(v2, v7, v8) = v13 & leq(v8, v0) = 0 & leq(v7, v0) = 0 & leq(n0, v8) = 0 & leq(n0, v7) = 0) | (v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & ~ (v14 = v13) & a_select3(v1, v8, v7) = v14 & a_select3(v1, v7, v8) = v13 & leq(v8, v0) = 0 & leq(v7, v0) = 0 & leq(n0, v8) = 0 & leq(n0, v7) = 0) | (a_select3(v3, v5, v4) = v11 & leq(v5, v0) = v10 & leq(v4, v0) = v8 & leq(n0, v5) = v9 & leq(n0, v4) = v7 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v11 = v6))))
% 37.78/10.20 | (58) gt(n2, n0) = 0
% 37.78/10.20 | (59) ? [v0] : ? [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (tptp_mmul(v14, v15) = v16) | ~ (tptp_mmul(v7, v11) = v12) | ~ (tptp_mmul(v6, v12) = v13) | ~ (tptp_mmul(v5, v8) = v9) | ~ (tptp_mmul(v4, v9) = v10) | ~ (tptp_mmul(v3, v16) = v17) | ~ (tptp_madd(v10, v13) = v14) | ~ (tptp_madd(v2, v17) = v18) | ~ (trans(v6) = v11) | ~ (trans(v4) = v8) | ~ (trans(v3) = v15) | ~ (a_select3(v18, v19, v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ((v27 = 0 & v26 = 0 & v25 = 0 & v24 = 0 & ~ (v29 = v28) & a_select3(v7, v23, v22) = v29 & a_select3(v7, v22, v23) = v28 & leq(v23, v0) = 0 & leq(v22, v0) = 0 & leq(n0, v23) = 0 & leq(n0, v22) = 0) | (v27 = 0 & v26 = 0 & v25 = 0 & v24 = 0 & ~ (v29 = v28) & a_select3(v5, v23, v22) = v29 & a_select3(v5, v22, v23) = v28 & leq(v23, v1) = 0 & leq(v22, v1) = 0 & leq(n0, v23) = 0 & leq(n0, v22) = 0) | (v27 = 0 & v26 = 0 & v25 = 0 & v24 = 0 & ~ (v29 = v28) & a_select3(v2, v23, v22) = v29 & a_select3(v2, v22, v23) = v28 & leq(v23, v0) = 0 & leq(v22, v0) = 0 & leq(n0, v23) = 0 & leq(n0, v22) = 0) | (a_select3(v18, v20, v19) = v26 & leq(v20, v0) = v25 & leq(v19, v0) = v23 & leq(n0, v20) = v24 & leq(n0, v19) = v22 & ( ~ (v25 = 0) | ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0) | v26 = v21))))
% 37.78/10.20 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = v0))
% 37.78/10.20 | (61) ! [v0] : (v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n3) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(n0, v0) = v1))
% 37.78/10.20 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | ~ (tptp_const_array2(v4, v3, v2) = v0))
% 37.78/10.20 | (63) leq(all_0_1_1, pv40) = 0
% 37.78/10.20 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0))
% 37.78/10.20 | (65) ! [v0] : ! [v1] : (v1 = init | ~ (a_select3(center_init, v0, n0) = v1) | ? [v2] : ? [v3] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 37.78/10.20 | (66) gt(n5, n3) = 0
% 37.78/10.20 | (67) ! [v0] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n2) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(n0, v0) = v1))
% 37.78/10.20 | (68) ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1))
% 37.78/10.20 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = v0))
% 37.78/10.20 | (70) ! [v0] : ( ~ (leq(v0, all_0_3_3) = 0) | ? [v1] : ? [v2] : (a_select2(mu_init, v0) = v2 & leq(n0, v0) = v1 & ( ~ (v1 = 0) | v2 = init)))
% 37.78/10.20 | (71) true
% 37.78/10.20 | (72) succ(tptp_minus_1) = n0
% 37.78/10.20 | (73) gt(n5, n1) = 0
% 37.78/10.20 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = v1) | ~ (tptp_update2(v4, v3, v2) = v0))
% 37.78/10.20 | (75) ! [v0] : ! [v1] : ! [v2] : (v2 = init | ~ (a_select3(q_init, v0, v1) = v2) | ~ (leq(v0, n135299) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & leq(n0, v0) = v3) | (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))))
% 37.78/10.20 | (76) gt(n135299, n4) = 0
% 37.78/10.20 | (77) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (succ(v0) = v1) | ~ (gt(v1, v0) = v2))
% 37.78/10.20 | (78) ! [v0] : ! [v1] : ( ~ (minus(v0, n1) = v1) | pred(v0) = v1)
% 37.78/10.20 | (79) ! [v0] : ! [v1] : ( ~ (pred(v0) = v1) | succ(v1) = v0)
% 37.78/10.20 | (80) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | pred(v1) = v0)
% 37.78/10.20 | (81) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v0 | v3 = v1 | ~ (tptp_update3(v4, v1, v2, v5) = v6) | ~ (a_select3(v6, v3, v2) = v7) | ? [v8] : ( ~ (v8 = v0) & a_select3(v4, v3, v2) = v8))
% 37.78/10.20 | (82) ! [v0] : ~ (gt(v0, v0) = 0)
% 37.78/10.20 | (83) gt(n4, n1) = 0
% 37.78/10.20 | (84) ! [v0] : (v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n4) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(n0, v0) = v1))
% 37.78/10.20 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (tptp_update2(v2, v1, v3) = v4) | ~ (a_select2(v4, v0) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v8 = 0 & v7 = 0 & ~ (v9 = v3) & a_select2(v2, v6) = v9 & leq(v6, v1) = 0 & leq(n0, v6) = 0) | (leq(v0, v1) = v7 & leq(n0, v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))))
% 37.78/10.20 | (86) ! [v0] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 37.78/10.21 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (gt(v0, v2) = v3) | ~ (gt(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & gt(v1, v2) = v4))
% 37.78/10.21 | (88) gt(n2, tptp_minus_1) = 0
% 37.78/10.21 | (89) ! [v0] : (v0 = n1 | v0 = n0 | ~ (leq(v0, n1) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(n0, v0) = v1))
% 37.78/10.21 | (90) gt(n1, tptp_minus_1) = 0
% 37.78/10.21 | (91) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0))
% 37.78/10.21 | (92) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (tptp_mmul(v2, v3) = v4) | ~ (tptp_mmul(v1, v4) = v5) | ~ (trans(v1) = v3) | ~ (a_select3(v5, v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & ~ (v16 = v15) & a_select3(v2, v10, v9) = v16 & a_select3(v2, v9, v10) = v15 & leq(v10, v0) = 0 & leq(v9, v0) = 0 & leq(n0, v10) = 0 & leq(n0, v9) = 0) | (a_select3(v5, v7, v6) = v13 & leq(v7, v0) = v12 & leq(v6, v0) = v10 & leq(n0, v7) = v11 & leq(n0, v6) = v9 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | v13 = v8))))
% 37.78/10.21 | (93) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (trans(v2) = v1) | ~ (trans(v2) = v0))
% 37.78/10.21 | (94) gt(n4, n3) = 0
% 37.78/10.21 | (95) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (gt(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3))
% 37.78/10.21 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0))
% 37.78/10.21 | (97) ! [v0] : ! [v1] : ( ~ (plus(n1, v0) = v1) | succ(v0) = v1)
% 37.78/10.21 | (98) gt(n3, n0) = 0
% 37.78/10.21 | (99) gt(n5, n0) = 0
% 37.78/10.21 | (100) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0))
% 37.78/10.21 | (101) gt(n4, tptp_minus_1) = 0
% 37.78/10.21 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (succ(v1) = v2) | ~ (leq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & leq(v0, v1) = v4))
% 37.78/10.21 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4))
% 37.78/10.21 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0))
% 37.78/10.21 | (105) succ(n3) = n4
% 37.78/10.21 | (106) gt(n135299, n1) = 0
% 37.78/10.21 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & gt(v1, v0) = v4))
% 37.78/10.21 | (108) a_select2(mu_init, all_0_1_1) = all_0_0_0
% 37.78/10.21 | (109) gt(n0, tptp_minus_1) = 0
% 37.78/10.21 | (110) ! [v0] : ( ~ (leq(v0, all_0_3_3) = 0) | ? [v1] : ? [v2] : (a_select2(sigma_init, v0) = v2 & leq(n0, v0) = v1 & ( ~ (v1 = 0) | v2 = init)))
% 37.78/10.21 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (tptp_update2(v0, v1, v2) = v3) | ~ (a_select2(v3, v1) = v4))
% 37.78/10.21 | (112) a_select2(sigma_init, pv40) = init
% 37.78/10.21 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) | ~ (tptp_mmul(v3, v2) = v0))
% 37.78/10.21 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 37.78/10.21 | (115) succ(n1) = n2
% 37.78/10.21 | (116) ! [v0] : (v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n5) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(n0, v0) = v1))
% 37.78/10.21 | (117) gt(n3, n1) = 0
% 37.78/10.21 | (118) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (trans(v1) = v2) | ~ (a_select3(v2, v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & ~ (v13 = v12) & a_select3(v1, v7, v6) = v13 & a_select3(v1, v6, v7) = v12 & leq(v7, v0) = 0 & leq(v6, v0) = 0 & leq(n0, v7) = 0 & leq(n0, v6) = 0) | (a_select3(v2, v4, v3) = v10 & leq(v4, v0) = v9 & leq(v3, v0) = v7 & leq(n0, v4) = v8 & leq(n0, v3) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | v10 = v5))))
% 37.78/10.21 | (119) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (tptp_msub(v1, v2) = v3) | ~ (a_select3(v3, v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & ~ (v14 = v13) & a_select3(v2, v8, v7) = v14 & a_select3(v2, v7, v8) = v13 & leq(v8, v0) = 0 & leq(v7, v0) = 0 & leq(n0, v8) = 0 & leq(n0, v7) = 0) | (v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & ~ (v14 = v13) & a_select3(v1, v8, v7) = v14 & a_select3(v1, v7, v8) = v13 & leq(v8, v0) = 0 & leq(v7, v0) = 0 & leq(n0, v8) = 0 & leq(n0, v7) = 0) | (a_select3(v3, v5, v4) = v11 & leq(v5, v0) = v10 & leq(v4, v0) = v8 & leq(n0, v5) = v9 & leq(n0, v4) = v7 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v11 = v6))))
% 37.78/10.21 | (120) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v0 | v2 = v1 | ~ (tptp_update2(v3, v1, v4) = v5) | ~ (a_select2(v5, v2) = v6) | ? [v7] : ( ~ (v7 = v0) & a_select2(v3, v2) = v7))
% 37.78/10.21 | (121) ! [v0] : ! [v1] : (v1 = n0 | ~ (sum(n0, tptp_minus_1, v0) = v1))
% 37.78/10.21 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | ~ (sum(v4, v3, v2) = v0))
% 37.78/10.21 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v6 | ~ (tptp_const_array2(v7, v8, v6) = v9) | ~ (a_select3(v9, v0, v3) = v10) | ~ (dim(v4, v5) = v8) | ~ (dim(v1, v2) = v7) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (leq(v4, v3) = v13 & leq(v3, v5) = v14 & leq(v1, v0) = v11 & leq(v0, v2) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0))))
% 37.78/10.21 | (124) ~ (def = use)
% 37.78/10.21 | (125) succ(n4) = n5
% 37.78/10.21 | (126) gt(n135299, n0) = 0
% 37.78/10.21 | (127) gt(n135299, n5) = 0
% 37.78/10.21 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (succ(v1) = v3) | ~ (succ(v0) = v2) | ~ (leq(v2, v3) = 0) | leq(v0, v1) = 0)
% 37.78/10.21 | (129) ! [v0] : ! [v1] : ! [v2] : ( ~ (uniform_int_rnd(v1, v0) = v2) | ? [v3] : ? [v4] : (leq(n0, v2) = v4 & leq(n0, v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 37.78/10.21 | (130) gt(n135299, n2) = 0
% 37.78/10.22 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0))
% 37.78/10.22 | (132) gt(n135299, n3) = 0
% 37.78/10.22 | (133) gt(n3, n2) = 0
% 37.78/10.22 | (134) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (geq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v1, v0) = v3))
% 37.78/10.22 | (135) pred(pv40) = all_0_3_3
% 37.78/10.22 | (136) ~ (all_0_2_2 = 0) | ! [v0] : ! [v1] : (v1 = init | ~ (a_select2(sigmaold_init, v0) = v1) | ? [v2] : ? [v3] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 37.78/10.22 | (137) ! [v0] : ! [v1] : ( ~ (plus(n4, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (succ(v4) = v1 & succ(v3) = v4 & succ(v2) = v3 & succ(v0) = v2))
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (96) with mu_init, pv40, init, all_0_0_0 and discharging atoms a_select2(mu_init, pv40) = init, yields:
% 37.78/10.22 | (138) all_0_0_0 = init | ~ (a_select2(mu_init, pv40) = all_0_0_0)
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (82) with n3 yields:
% 37.78/10.22 | (139) ~ (gt(n3, n3) = 0)
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (82) with n2 yields:
% 37.78/10.22 | (140) ~ (gt(n2, n2) = 0)
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (82) with n1 yields:
% 37.78/10.22 | (141) ~ (gt(n1, n1) = 0)
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (82) with n0 yields:
% 37.78/10.22 | (142) ~ (gt(n0, n0) = 0)
% 37.78/10.22 |
% 37.78/10.22 | Using (98) and (139) yields:
% 37.78/10.22 | (143) ~ (n3 = n0)
% 37.78/10.22 |
% 37.78/10.22 | Using (58) and (140) yields:
% 37.78/10.22 | (144) ~ (n2 = n0)
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (80) with n2, n1 and discharging atoms succ(n1) = n2, yields:
% 37.78/10.22 | (145) pred(n2) = n1
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (80) with n1, n0 and discharging atoms succ(n0) = n1, yields:
% 37.78/10.22 | (146) pred(n1) = n0
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (79) with all_0_3_3, pv40 and discharging atoms pred(pv40) = all_0_3_3, yields:
% 37.78/10.22 | (147) succ(all_0_3_3) = pv40
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (11) with n4, pv40, n3 and discharging atoms succ(n3) = n4, yields:
% 37.78/10.22 | (148) ~ (leq(n4, pv40) = 0) | gt(pv40, n3) = 0
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (11) with n3, pv40, n2 and discharging atoms succ(n2) = n3, yields:
% 37.78/10.22 | (149) ~ (leq(n3, pv40) = 0) | gt(pv40, n2) = 0
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (11) with n2, pv40, n1 and discharging atoms succ(n1) = n2, yields:
% 37.78/10.22 | (150) ~ (leq(n2, pv40) = 0) | gt(pv40, n1) = 0
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (110) with all_0_1_1 yields:
% 37.78/10.22 | (151) ~ (leq(all_0_1_1, all_0_3_3) = 0) | ? [v0] : ? [v1] : (a_select2(sigma_init, all_0_1_1) = v1 & leq(n0, all_0_1_1) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (70) with all_0_1_1 yields:
% 37.78/10.22 | (152) ~ (leq(all_0_1_1, all_0_3_3) = 0) | ? [v0] : ? [v1] : (a_select2(mu_init, all_0_1_1) = v1 & leq(n0, all_0_1_1) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (84) with all_0_1_1 yields:
% 37.78/10.22 | (153) all_0_1_1 = n4 | all_0_1_1 = n3 | all_0_1_1 = n2 | all_0_1_1 = n1 | all_0_1_1 = n0 | ~ (leq(all_0_1_1, n4) = 0) | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (61) with all_0_1_1 yields:
% 37.78/10.22 | (154) all_0_1_1 = n3 | all_0_1_1 = n2 | all_0_1_1 = n1 | all_0_1_1 = n0 | ~ (leq(all_0_1_1, n3) = 0) | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (67) with all_0_1_1 yields:
% 37.78/10.22 | (155) all_0_1_1 = n2 | all_0_1_1 = n1 | all_0_1_1 = n0 | ~ (leq(all_0_1_1, n2) = 0) | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (89) with all_0_1_1 yields:
% 37.78/10.22 | (156) all_0_1_1 = n1 | all_0_1_1 = n0 | ~ (leq(all_0_1_1, n1) = 0) | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (86) with pv40 and discharging atoms leq(n0, pv40) = 0, yields:
% 37.78/10.22 | (157) pv40 = n0 | ? [v0] : ( ~ (v0 = 0) & leq(pv40, n0) = v0)
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (84) with pv40 and discharging atoms leq(pv40, n4) = 0, yields:
% 37.78/10.22 | (158) pv40 = n4 | pv40 = n3 | pv40 = n2 | pv40 = n1 | pv40 = n0 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (13) with all_0_3_3, pv40, n0 and discharging atoms pred(pv40) = all_0_3_3, yields:
% 37.78/10.22 | (159) ~ (leq(n0, all_0_3_3) = 0) | gt(pv40, n0) = 0
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (110) with n0 yields:
% 37.78/10.22 | (160) ~ (leq(n0, all_0_3_3) = 0) | ? [v0] : ? [v1] : (a_select2(sigma_init, n0) = v1 & leq(n0, n0) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (70) with n0 yields:
% 37.78/10.22 | (161) ~ (leq(n0, all_0_3_3) = 0) | ? [v0] : ? [v1] : (a_select2(mu_init, n0) = v1 & leq(n0, n0) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (86) with all_0_1_1 and discharging atoms leq(n0, all_0_1_1) = 0, yields:
% 37.78/10.22 | (162) all_0_1_1 = n0 | ? [v0] : ( ~ (v0 = 0) & leq(all_0_1_1, n0) = v0)
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (9) with n5, n4, n4 and discharging atoms succ(n4) = n5, gt(n5, n4) = 0, yields:
% 37.78/10.22 | (163) leq(n4, n4) = 0
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (9) with n4, n3, n3 and discharging atoms succ(n3) = n4, gt(n4, n3) = 0, yields:
% 37.78/10.22 | (164) leq(n3, n3) = 0
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (49) with n4, n3 and discharging atoms gt(n4, n3) = 0, yields:
% 37.78/10.22 | (165) leq(n3, n4) = 0
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (49) with n4, n2 and discharging atoms gt(n4, n2) = 0, yields:
% 37.78/10.22 | (166) leq(n2, n4) = 0
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (49) with n4, n1 and discharging atoms gt(n4, n1) = 0, yields:
% 37.78/10.22 | (167) leq(n1, n4) = 0
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (9) with n3, n2, n2 and discharging atoms succ(n2) = n3, gt(n3, n2) = 0, yields:
% 37.78/10.22 | (168) leq(n2, n2) = 0
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (49) with n3, n2 and discharging atoms gt(n3, n2) = 0, yields:
% 37.78/10.22 | (169) leq(n2, n3) = 0
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (49) with n3, n1 and discharging atoms gt(n3, n1) = 0, yields:
% 37.78/10.22 | (170) leq(n1, n3) = 0
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (49) with n3, n0 and discharging atoms gt(n3, n0) = 0, yields:
% 37.78/10.22 | (171) leq(n0, n3) = 0
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (9) with n2, n1, n1 and discharging atoms succ(n1) = n2, gt(n2, n1) = 0, yields:
% 37.78/10.22 | (172) leq(n1, n1) = 0
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (49) with n2, n1 and discharging atoms gt(n2, n1) = 0, yields:
% 37.78/10.22 | (173) leq(n1, n2) = 0
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (49) with n2, n0 and discharging atoms gt(n2, n0) = 0, yields:
% 37.78/10.22 | (174) leq(n0, n2) = 0
% 37.78/10.22 |
% 37.78/10.22 | Instantiating formula (9) with n1, n0, n0 and discharging atoms succ(n0) = n1, gt(n1, n0) = 0, yields:
% 37.78/10.22 | (175) leq(n0, n0) = 0
% 37.78/10.22 |
% 37.78/10.22 +-Applying beta-rule and splitting (152), into two cases.
% 37.78/10.22 |-Branch one:
% 37.78/10.22 | (176) ~ (leq(all_0_1_1, all_0_3_3) = 0)
% 37.78/10.22 |
% 37.78/10.23 | Instantiating formula (128) with pv40, n4, all_0_3_3, n3 and discharging atoms succ(all_0_3_3) = pv40, succ(n3) = n4, yields:
% 37.78/10.23 | (177) ~ (leq(n4, pv40) = 0) | leq(n3, all_0_3_3) = 0
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (128) with pv40, n3, all_0_3_3, n2 and discharging atoms succ(all_0_3_3) = pv40, succ(n2) = n3, yields:
% 37.78/10.23 | (178) ~ (leq(n3, pv40) = 0) | leq(n2, all_0_3_3) = 0
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (128) with pv40, n2, all_0_3_3, n1 and discharging atoms succ(all_0_3_3) = pv40, succ(n1) = n2, yields:
% 37.78/10.23 | (179) ~ (leq(n2, pv40) = 0) | leq(n1, all_0_3_3) = 0
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (9) with pv40, all_0_3_3, n1 and discharging atoms succ(all_0_3_3) = pv40, yields:
% 37.78/10.23 | (180) ~ (gt(pv40, n1) = 0) | leq(n1, all_0_3_3) = 0
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (13) with n1, n2, all_0_1_1 and discharging atoms pred(n2) = n1, yields:
% 37.78/10.23 | (181) ~ (leq(all_0_1_1, n1) = 0) | gt(n2, all_0_1_1) = 0
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (13) with n0, n1, all_0_1_1 and discharging atoms pred(n1) = n0, yields:
% 37.78/10.23 | (182) ~ (leq(all_0_1_1, n0) = 0) | gt(n1, all_0_1_1) = 0
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (110) with n3 yields:
% 37.78/10.23 | (183) ~ (leq(n3, all_0_3_3) = 0) | ? [v0] : ? [v1] : (a_select2(sigma_init, n3) = v1 & leq(n0, n3) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (70) with n3 yields:
% 37.78/10.23 | (184) ~ (leq(n3, all_0_3_3) = 0) | ? [v0] : ? [v1] : (a_select2(mu_init, n3) = v1 & leq(n0, n3) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (110) with n2 yields:
% 37.78/10.23 | (185) ~ (leq(n2, all_0_3_3) = 0) | ? [v0] : ? [v1] : (a_select2(sigma_init, n2) = v1 & leq(n0, n2) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (70) with n2 yields:
% 37.78/10.23 | (186) ~ (leq(n2, all_0_3_3) = 0) | ? [v0] : ? [v1] : (a_select2(mu_init, n2) = v1 & leq(n0, n2) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (110) with n1 yields:
% 37.78/10.23 | (187) ~ (leq(n1, all_0_3_3) = 0) | ? [v0] : ? [v1] : (a_select2(sigma_init, n1) = v1 & leq(n0, n1) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (70) with n1 yields:
% 37.78/10.23 | (188) ~ (leq(n1, all_0_3_3) = 0) | ? [v0] : ? [v1] : (a_select2(mu_init, n1) = v1 & leq(n0, n1) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (128) with n4, n1, all_0_3_3, n0 and discharging atoms succ(n0) = n1, leq(n1, n4) = 0, yields:
% 37.78/10.23 | (189) ~ (succ(all_0_3_3) = n4) | leq(n0, all_0_3_3) = 0
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (128) with n3, n1, all_0_3_3, n0 and discharging atoms succ(n0) = n1, leq(n1, n3) = 0, yields:
% 37.78/10.23 | (190) ~ (succ(all_0_3_3) = n3) | leq(n0, all_0_3_3) = 0
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (128) with n2, n1, all_0_3_3, n0 and discharging atoms succ(n0) = n1, leq(n1, n2) = 0, yields:
% 37.78/10.23 | (191) ~ (succ(all_0_3_3) = n2) | leq(n0, all_0_3_3) = 0
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (128) with n1, n1, all_0_3_3, n0 and discharging atoms succ(n0) = n1, leq(n1, n1) = 0, yields:
% 37.78/10.23 | (192) ~ (succ(all_0_3_3) = n1) | leq(n0, all_0_3_3) = 0
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (86) with n3 and discharging atoms leq(n0, n3) = 0, yields:
% 37.78/10.23 | (193) n3 = n0 | ? [v0] : ( ~ (v0 = 0) & leq(n3, n0) = v0)
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (86) with n2 and discharging atoms leq(n0, n2) = 0, yields:
% 37.78/10.23 | (194) n2 = n0 | ? [v0] : ( ~ (v0 = 0) & leq(n2, n0) = v0)
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (128) with n0, n0, tptp_minus_1, all_0_3_3 and discharging atoms succ(tptp_minus_1) = n0, leq(n0, n0) = 0, yields:
% 37.78/10.23 | (195) ~ (succ(all_0_3_3) = n0) | leq(all_0_3_3, tptp_minus_1) = 0
% 37.78/10.23 |
% 37.78/10.23 +-Applying beta-rule and splitting (193), into two cases.
% 37.78/10.23 |-Branch one:
% 37.78/10.23 | (196) n3 = n0
% 37.78/10.23 |
% 37.78/10.23 | Equations (196) can reduce 143 to:
% 37.78/10.23 | (197) $false
% 37.78/10.23 |
% 37.78/10.23 |-The branch is then unsatisfiable
% 37.78/10.23 |-Branch two:
% 37.78/10.23 | (143) ~ (n3 = n0)
% 37.78/10.23 | (199) ? [v0] : ( ~ (v0 = 0) & leq(n3, n0) = v0)
% 37.78/10.23 |
% 37.78/10.23 | Instantiating (199) with all_109_0_28 yields:
% 37.78/10.23 | (200) ~ (all_109_0_28 = 0) & leq(n3, n0) = all_109_0_28
% 37.78/10.23 |
% 37.78/10.23 | Applying alpha-rule on (200) yields:
% 37.78/10.23 | (201) ~ (all_109_0_28 = 0)
% 37.78/10.23 | (202) leq(n3, n0) = all_109_0_28
% 37.78/10.23 |
% 37.78/10.23 +-Applying beta-rule and splitting (194), into two cases.
% 37.78/10.23 |-Branch one:
% 37.78/10.23 | (203) n2 = n0
% 37.78/10.23 |
% 37.78/10.23 | Equations (203) can reduce 144 to:
% 37.78/10.23 | (197) $false
% 37.78/10.23 |
% 37.78/10.23 |-The branch is then unsatisfiable
% 37.78/10.23 |-Branch two:
% 37.78/10.23 | (144) ~ (n2 = n0)
% 37.78/10.23 | (206) ? [v0] : ( ~ (v0 = 0) & leq(n2, n0) = v0)
% 37.78/10.23 |
% 37.78/10.23 | Instantiating (206) with all_114_0_29 yields:
% 37.78/10.23 | (207) ~ (all_114_0_29 = 0) & leq(n2, n0) = all_114_0_29
% 37.78/10.23 |
% 37.78/10.23 | Applying alpha-rule on (207) yields:
% 37.78/10.23 | (208) ~ (all_114_0_29 = 0)
% 37.78/10.23 | (209) leq(n2, n0) = all_114_0_29
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (53) with all_109_0_28, n0, n3, all_0_3_3, n2 and discharging atoms succ(n2) = n3, leq(n3, n0) = all_109_0_28, yields:
% 37.78/10.23 | (210) all_109_0_28 = 0 | ~ (succ(all_0_3_3) = n0) | ? [v0] : ( ~ (v0 = 0) & leq(n2, all_0_3_3) = v0)
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (102) with all_114_0_29, n0, all_0_3_3, n2 and discharging atoms leq(n2, n0) = all_114_0_29, yields:
% 37.78/10.23 | (211) all_114_0_29 = 0 | ~ (succ(all_0_3_3) = n0) | ? [v0] : ( ~ (v0 = 0) & leq(n2, all_0_3_3) = v0)
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (53) with all_114_0_29, n0, n2, tptp_minus_1, n1 and discharging atoms succ(n1) = n2, succ(tptp_minus_1) = n0, leq(n2, n0) = all_114_0_29, yields:
% 37.78/10.23 | (212) all_114_0_29 = 0 | ? [v0] : ( ~ (v0 = 0) & leq(n1, tptp_minus_1) = v0)
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (102) with all_114_0_29, n0, tptp_minus_1, n2 and discharging atoms succ(tptp_minus_1) = n0, leq(n2, n0) = all_114_0_29, yields:
% 37.78/10.23 | (213) all_114_0_29 = 0 | ? [v0] : ( ~ (v0 = 0) & leq(n2, tptp_minus_1) = v0)
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (107) with all_114_0_29, n0, pv40, n2 and discharging atoms leq(n2, n0) = all_114_0_29, yields:
% 37.78/10.23 | (214) all_114_0_29 = 0 | ~ (pred(pv40) = n0) | ? [v0] : ( ~ (v0 = 0) & gt(pv40, n2) = v0)
% 37.78/10.23 |
% 37.78/10.23 | Instantiating formula (107) with all_114_0_29, n0, n1, n2 and discharging atoms pred(n1) = n0, leq(n2, n0) = all_114_0_29, yields:
% 37.78/10.23 | (215) all_114_0_29 = 0 | ? [v0] : ( ~ (v0 = 0) & gt(n1, n2) = v0)
% 37.78/10.23 |
% 37.78/10.23 +-Applying beta-rule and splitting (212), into two cases.
% 37.78/10.23 |-Branch one:
% 37.78/10.23 | (216) all_114_0_29 = 0
% 37.78/10.23 |
% 37.78/10.23 | Equations (216) can reduce 208 to:
% 37.78/10.23 | (197) $false
% 37.78/10.23 |
% 37.78/10.23 |-The branch is then unsatisfiable
% 37.78/10.23 |-Branch two:
% 37.78/10.23 | (208) ~ (all_114_0_29 = 0)
% 37.78/10.23 | (219) ? [v0] : ( ~ (v0 = 0) & leq(n1, tptp_minus_1) = v0)
% 37.78/10.23 |
% 37.78/10.23 +-Applying beta-rule and splitting (213), into two cases.
% 37.78/10.23 |-Branch one:
% 37.78/10.23 | (216) all_114_0_29 = 0
% 37.78/10.23 |
% 37.78/10.23 | Equations (216) can reduce 208 to:
% 37.78/10.23 | (197) $false
% 37.78/10.23 |
% 37.78/10.23 |-The branch is then unsatisfiable
% 37.78/10.23 |-Branch two:
% 37.78/10.23 | (208) ~ (all_114_0_29 = 0)
% 37.78/10.23 | (223) ? [v0] : ( ~ (v0 = 0) & leq(n2, tptp_minus_1) = v0)
% 37.78/10.23 |
% 37.78/10.23 +-Applying beta-rule and splitting (215), into two cases.
% 37.78/10.23 |-Branch one:
% 37.78/10.23 | (216) all_114_0_29 = 0
% 37.78/10.23 |
% 37.78/10.23 | Equations (216) can reduce 208 to:
% 37.78/10.23 | (197) $false
% 37.78/10.23 |
% 37.78/10.23 |-The branch is then unsatisfiable
% 37.78/10.23 |-Branch two:
% 37.78/10.23 | (208) ~ (all_114_0_29 = 0)
% 37.78/10.23 | (227) ? [v0] : ( ~ (v0 = 0) & gt(n1, n2) = v0)
% 37.78/10.23 |
% 37.78/10.23 +-Applying beta-rule and splitting (138), into two cases.
% 37.78/10.23 |-Branch one:
% 37.78/10.23 | (228) ~ (a_select2(mu_init, pv40) = all_0_0_0)
% 37.78/10.23 |
% 37.78/10.23 | Using (108) and (228) yields:
% 37.78/10.23 | (229) ~ (all_0_1_1 = pv40)
% 37.78/10.23 |
% 37.78/10.23 +-Applying beta-rule and splitting (149), into two cases.
% 37.78/10.23 |-Branch one:
% 37.78/10.23 | (230) ~ (leq(n3, pv40) = 0)
% 37.78/10.23 |
% 37.78/10.23 | Using (165) and (230) yields:
% 37.78/10.23 | (231) ~ (pv40 = n4)
% 37.78/10.23 |
% 37.78/10.23 | Using (164) and (230) yields:
% 37.78/10.23 | (232) ~ (pv40 = n3)
% 37.78/10.23 |
% 37.78/10.23 +-Applying beta-rule and splitting (159), into two cases.
% 37.78/10.23 |-Branch one:
% 37.78/10.23 | (233) ~ (leq(n0, all_0_3_3) = 0)
% 37.78/10.23 |
% 37.78/10.23 +-Applying beta-rule and splitting (191), into two cases.
% 37.78/10.23 |-Branch one:
% 37.78/10.23 | (234) leq(n0, all_0_3_3) = 0
% 37.78/10.23 |
% 37.78/10.23 | Using (234) and (233) yields:
% 37.78/10.23 | (235) $false
% 37.78/10.23 |
% 37.78/10.23 |-The branch is then unsatisfiable
% 37.78/10.23 |-Branch two:
% 37.78/10.23 | (233) ~ (leq(n0, all_0_3_3) = 0)
% 37.78/10.23 | (237) ~ (succ(all_0_3_3) = n2)
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (192), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (234) leq(n0, all_0_3_3) = 0
% 37.78/10.24 |
% 37.78/10.24 | Using (234) and (233) yields:
% 37.78/10.24 | (235) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (233) ~ (leq(n0, all_0_3_3) = 0)
% 37.78/10.24 | (241) ~ (succ(all_0_3_3) = n1)
% 37.78/10.24 |
% 37.78/10.24 | Using (147) and (237) yields:
% 37.78/10.24 | (242) ~ (pv40 = n2)
% 37.78/10.24 |
% 37.78/10.24 | Using (147) and (241) yields:
% 37.78/10.24 | (243) ~ (pv40 = n1)
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (158), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (244) pv40 = n0
% 37.78/10.24 |
% 37.78/10.24 | Equations (244) can reduce 229 to:
% 37.78/10.24 | (245) ~ (all_0_1_1 = n0)
% 37.78/10.24 |
% 37.78/10.24 | From (244) and (63) follows:
% 37.78/10.24 | (246) leq(all_0_1_1, n0) = 0
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (162), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (247) all_0_1_1 = n0
% 37.78/10.24 |
% 37.78/10.24 | Equations (247) can reduce 245 to:
% 37.78/10.24 | (197) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (245) ~ (all_0_1_1 = n0)
% 37.78/10.24 | (250) ? [v0] : ( ~ (v0 = 0) & leq(all_0_1_1, n0) = v0)
% 37.78/10.24 |
% 37.78/10.24 | Instantiating (250) with all_519_0_86 yields:
% 37.78/10.24 | (251) ~ (all_519_0_86 = 0) & leq(all_0_1_1, n0) = all_519_0_86
% 37.78/10.24 |
% 37.78/10.24 | Applying alpha-rule on (251) yields:
% 37.78/10.24 | (252) ~ (all_519_0_86 = 0)
% 37.78/10.24 | (253) leq(all_0_1_1, n0) = all_519_0_86
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (182), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (254) ~ (leq(all_0_1_1, n0) = 0)
% 37.78/10.24 |
% 37.78/10.24 | Using (246) and (254) yields:
% 37.78/10.24 | (235) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (246) leq(all_0_1_1, n0) = 0
% 37.78/10.24 | (257) gt(n1, all_0_1_1) = 0
% 37.78/10.24 |
% 37.78/10.24 | Instantiating formula (114) with all_0_1_1, n0, 0, all_519_0_86 and discharging atoms leq(all_0_1_1, n0) = all_519_0_86, leq(all_0_1_1, n0) = 0, yields:
% 37.78/10.24 | (258) all_519_0_86 = 0
% 37.78/10.24 |
% 37.78/10.24 | Equations (258) can reduce 252 to:
% 37.78/10.24 | (197) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (260) ~ (pv40 = n0)
% 37.78/10.24 | (261) pv40 = n4 | pv40 = n3 | pv40 = n2 | pv40 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (261), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (262) pv40 = n4
% 37.78/10.24 |
% 37.78/10.24 | Equations (262) can reduce 231 to:
% 37.78/10.24 | (197) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (231) ~ (pv40 = n4)
% 37.78/10.24 | (265) pv40 = n3 | pv40 = n2 | pv40 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (265), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (266) pv40 = n1
% 37.78/10.24 |
% 37.78/10.24 | Equations (266) can reduce 243 to:
% 37.78/10.24 | (197) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (243) ~ (pv40 = n1)
% 37.78/10.24 | (269) pv40 = n3 | pv40 = n2 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (269), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (270) pv40 = n2
% 37.78/10.24 |
% 37.78/10.24 | Equations (270) can reduce 242 to:
% 37.78/10.24 | (197) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (242) ~ (pv40 = n2)
% 37.78/10.24 | (273) pv40 = n3 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (273), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (274) pv40 = n3
% 37.78/10.24 |
% 37.78/10.24 | Equations (274) can reduce 232 to:
% 37.78/10.24 | (197) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (232) ~ (pv40 = n3)
% 37.78/10.24 | (277) ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.24 |
% 37.78/10.24 | Instantiating (277) with all_515_0_88 yields:
% 37.78/10.24 | (278) ~ (all_515_0_88 = 0) & leq(n0, pv40) = all_515_0_88
% 37.78/10.24 |
% 37.78/10.24 | Applying alpha-rule on (278) yields:
% 37.78/10.24 | (279) ~ (all_515_0_88 = 0)
% 37.78/10.24 | (280) leq(n0, pv40) = all_515_0_88
% 37.78/10.24 |
% 37.78/10.24 | Instantiating formula (114) with n0, pv40, all_515_0_88, 0 and discharging atoms leq(n0, pv40) = all_515_0_88, leq(n0, pv40) = 0, yields:
% 37.78/10.24 | (281) all_515_0_88 = 0
% 37.78/10.24 |
% 37.78/10.24 | Equations (281) can reduce 279 to:
% 37.78/10.24 | (197) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (234) leq(n0, all_0_3_3) = 0
% 37.78/10.24 | (284) gt(pv40, n0) = 0
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (160), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (233) ~ (leq(n0, all_0_3_3) = 0)
% 37.78/10.24 |
% 37.78/10.24 | Using (234) and (233) yields:
% 37.78/10.24 | (235) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (234) leq(n0, all_0_3_3) = 0
% 37.78/10.24 | (288) ? [v0] : ? [v1] : (a_select2(sigma_init, n0) = v1 & leq(n0, n0) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (161), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (233) ~ (leq(n0, all_0_3_3) = 0)
% 37.78/10.24 |
% 37.78/10.24 | Using (234) and (233) yields:
% 37.78/10.24 | (235) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (234) leq(n0, all_0_3_3) = 0
% 37.78/10.24 | (292) ? [v0] : ? [v1] : (a_select2(mu_init, n0) = v1 & leq(n0, n0) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.24 |
% 37.78/10.24 | Using (234) and (176) yields:
% 37.78/10.24 | (245) ~ (all_0_1_1 = n0)
% 37.78/10.24 |
% 37.78/10.24 | Using (284) and (142) yields:
% 37.78/10.24 | (260) ~ (pv40 = n0)
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (157), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (244) pv40 = n0
% 37.78/10.24 |
% 37.78/10.24 | Equations (244) can reduce 260 to:
% 37.78/10.24 | (197) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (260) ~ (pv40 = n0)
% 37.78/10.24 | (298) ? [v0] : ( ~ (v0 = 0) & leq(pv40, n0) = v0)
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (162), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (247) all_0_1_1 = n0
% 37.78/10.24 |
% 37.78/10.24 | Equations (247) can reduce 245 to:
% 37.78/10.24 | (197) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (245) ~ (all_0_1_1 = n0)
% 37.78/10.24 | (250) ? [v0] : ( ~ (v0 = 0) & leq(all_0_1_1, n0) = v0)
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (150), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (303) ~ (leq(n2, pv40) = 0)
% 37.78/10.24 |
% 37.78/10.24 | Using (168) and (303) yields:
% 37.78/10.24 | (242) ~ (pv40 = n2)
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (158), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (244) pv40 = n0
% 37.78/10.24 |
% 37.78/10.24 | Equations (244) can reduce 260 to:
% 37.78/10.24 | (197) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (260) ~ (pv40 = n0)
% 37.78/10.24 | (261) pv40 = n4 | pv40 = n3 | pv40 = n2 | pv40 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (261), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (262) pv40 = n4
% 37.78/10.24 |
% 37.78/10.24 | Equations (262) can reduce 231 to:
% 37.78/10.24 | (197) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (231) ~ (pv40 = n4)
% 37.78/10.24 | (265) pv40 = n3 | pv40 = n2 | pv40 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (265), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (266) pv40 = n1
% 37.78/10.24 |
% 37.78/10.24 | Equations (266) can reduce 229 to:
% 37.78/10.24 | (314) ~ (all_0_1_1 = n1)
% 37.78/10.24 |
% 37.78/10.24 | From (266) and (63) follows:
% 37.78/10.24 | (315) leq(all_0_1_1, n1) = 0
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (181), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (316) ~ (leq(all_0_1_1, n1) = 0)
% 37.78/10.24 |
% 37.78/10.24 | Using (315) and (316) yields:
% 37.78/10.24 | (235) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (315) leq(all_0_1_1, n1) = 0
% 37.78/10.24 | (319) gt(n2, all_0_1_1) = 0
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (156), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (316) ~ (leq(all_0_1_1, n1) = 0)
% 37.78/10.24 |
% 37.78/10.24 | Using (315) and (316) yields:
% 37.78/10.24 | (235) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (315) leq(all_0_1_1, n1) = 0
% 37.78/10.24 | (323) all_0_1_1 = n1 | all_0_1_1 = n0 | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.24 |
% 37.78/10.24 +-Applying beta-rule and splitting (323), into two cases.
% 37.78/10.24 |-Branch one:
% 37.78/10.24 | (247) all_0_1_1 = n0
% 37.78/10.24 |
% 37.78/10.24 | Equations (247) can reduce 245 to:
% 37.78/10.24 | (197) $false
% 37.78/10.24 |
% 37.78/10.24 |-The branch is then unsatisfiable
% 37.78/10.24 |-Branch two:
% 37.78/10.24 | (245) ~ (all_0_1_1 = n0)
% 37.78/10.24 | (327) all_0_1_1 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.24 |
% 37.78/10.25 +-Applying beta-rule and splitting (327), into two cases.
% 37.78/10.25 |-Branch one:
% 37.78/10.25 | (328) all_0_1_1 = n1
% 37.78/10.25 |
% 37.78/10.25 | Equations (328) can reduce 314 to:
% 37.78/10.25 | (197) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.25 |-Branch two:
% 37.78/10.25 | (314) ~ (all_0_1_1 = n1)
% 37.78/10.25 | (331) ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.25 |
% 37.78/10.25 | Instantiating (331) with all_560_0_96 yields:
% 37.78/10.25 | (332) ~ (all_560_0_96 = 0) & leq(n0, all_0_1_1) = all_560_0_96
% 37.78/10.25 |
% 37.78/10.25 | Applying alpha-rule on (332) yields:
% 37.78/10.25 | (333) ~ (all_560_0_96 = 0)
% 37.78/10.25 | (334) leq(n0, all_0_1_1) = all_560_0_96
% 37.78/10.25 |
% 37.78/10.25 | Instantiating formula (114) with n0, all_0_1_1, all_560_0_96, 0 and discharging atoms leq(n0, all_0_1_1) = all_560_0_96, leq(n0, all_0_1_1) = 0, yields:
% 37.78/10.25 | (335) all_560_0_96 = 0
% 37.78/10.25 |
% 37.78/10.25 | Equations (335) can reduce 333 to:
% 37.78/10.25 | (197) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.25 |-Branch two:
% 37.78/10.25 | (243) ~ (pv40 = n1)
% 37.78/10.25 | (269) pv40 = n3 | pv40 = n2 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.25 |
% 37.78/10.25 +-Applying beta-rule and splitting (269), into two cases.
% 37.78/10.25 |-Branch one:
% 37.78/10.25 | (270) pv40 = n2
% 37.78/10.25 |
% 37.78/10.25 | Equations (270) can reduce 242 to:
% 37.78/10.25 | (197) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.25 |-Branch two:
% 37.78/10.25 | (242) ~ (pv40 = n2)
% 37.78/10.25 | (273) pv40 = n3 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.25 |
% 37.78/10.25 +-Applying beta-rule and splitting (273), into two cases.
% 37.78/10.25 |-Branch one:
% 37.78/10.25 | (274) pv40 = n3
% 37.78/10.25 |
% 37.78/10.25 | Equations (274) can reduce 232 to:
% 37.78/10.25 | (197) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.25 |-Branch two:
% 37.78/10.25 | (232) ~ (pv40 = n3)
% 37.78/10.25 | (277) ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.25 |
% 37.78/10.25 | Instantiating (277) with all_536_0_98 yields:
% 37.78/10.25 | (347) ~ (all_536_0_98 = 0) & leq(n0, pv40) = all_536_0_98
% 37.78/10.25 |
% 37.78/10.25 | Applying alpha-rule on (347) yields:
% 37.78/10.25 | (348) ~ (all_536_0_98 = 0)
% 37.78/10.25 | (349) leq(n0, pv40) = all_536_0_98
% 37.78/10.25 |
% 37.78/10.25 | Instantiating formula (114) with n0, pv40, all_536_0_98, 0 and discharging atoms leq(n0, pv40) = all_536_0_98, leq(n0, pv40) = 0, yields:
% 37.78/10.25 | (350) all_536_0_98 = 0
% 37.78/10.25 |
% 37.78/10.25 | Equations (350) can reduce 348 to:
% 37.78/10.25 | (197) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.25 |-Branch two:
% 37.78/10.25 | (352) leq(n2, pv40) = 0
% 37.78/10.25 | (353) gt(pv40, n1) = 0
% 37.78/10.25 |
% 37.78/10.25 +-Applying beta-rule and splitting (180), into two cases.
% 37.78/10.25 |-Branch one:
% 37.78/10.25 | (354) leq(n1, all_0_3_3) = 0
% 37.78/10.25 |
% 37.78/10.25 +-Applying beta-rule and splitting (188), into two cases.
% 37.78/10.25 |-Branch one:
% 37.78/10.25 | (355) ~ (leq(n1, all_0_3_3) = 0)
% 37.78/10.25 |
% 37.78/10.25 | Using (354) and (355) yields:
% 37.78/10.25 | (235) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.25 |-Branch two:
% 37.78/10.25 | (354) leq(n1, all_0_3_3) = 0
% 37.78/10.25 | (358) ? [v0] : ? [v1] : (a_select2(mu_init, n1) = v1 & leq(n0, n1) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.25 |
% 37.78/10.25 +-Applying beta-rule and splitting (187), into two cases.
% 37.78/10.25 |-Branch one:
% 37.78/10.25 | (355) ~ (leq(n1, all_0_3_3) = 0)
% 37.78/10.25 |
% 37.78/10.25 | Using (354) and (355) yields:
% 37.78/10.25 | (235) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.25 |-Branch two:
% 37.78/10.25 | (354) leq(n1, all_0_3_3) = 0
% 37.78/10.25 | (362) ? [v0] : ? [v1] : (a_select2(sigma_init, n1) = v1 & leq(n0, n1) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.25 |
% 37.78/10.25 | Using (354) and (176) yields:
% 37.78/10.25 | (314) ~ (all_0_1_1 = n1)
% 37.78/10.25 |
% 37.78/10.25 | Using (353) and (141) yields:
% 37.78/10.25 | (243) ~ (pv40 = n1)
% 37.78/10.25 |
% 37.78/10.25 +-Applying beta-rule and splitting (158), into two cases.
% 37.78/10.25 |-Branch one:
% 37.78/10.25 | (244) pv40 = n0
% 37.78/10.25 |
% 37.78/10.25 | Equations (244) can reduce 260 to:
% 37.78/10.25 | (197) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.25 |-Branch two:
% 37.78/10.25 | (260) ~ (pv40 = n0)
% 37.78/10.25 | (261) pv40 = n4 | pv40 = n3 | pv40 = n2 | pv40 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.25 |
% 37.78/10.25 +-Applying beta-rule and splitting (261), into two cases.
% 37.78/10.25 |-Branch one:
% 37.78/10.25 | (262) pv40 = n4
% 37.78/10.25 |
% 37.78/10.25 | Equations (262) can reduce 231 to:
% 37.78/10.25 | (197) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.25 |-Branch two:
% 37.78/10.25 | (231) ~ (pv40 = n4)
% 37.78/10.25 | (265) pv40 = n3 | pv40 = n2 | pv40 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.25 |
% 37.78/10.25 +-Applying beta-rule and splitting (265), into two cases.
% 37.78/10.25 |-Branch one:
% 37.78/10.25 | (266) pv40 = n1
% 37.78/10.25 |
% 37.78/10.25 | Equations (266) can reduce 243 to:
% 37.78/10.25 | (197) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.25 |-Branch two:
% 37.78/10.25 | (243) ~ (pv40 = n1)
% 37.78/10.25 | (269) pv40 = n3 | pv40 = n2 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.25 |
% 37.78/10.25 +-Applying beta-rule and splitting (269), into two cases.
% 37.78/10.25 |-Branch one:
% 37.78/10.25 | (270) pv40 = n2
% 37.78/10.25 |
% 37.78/10.25 | Equations (270) can reduce 229 to:
% 37.78/10.25 | (378) ~ (all_0_1_1 = n2)
% 37.78/10.25 |
% 37.78/10.25 | From (270) and (63) follows:
% 37.78/10.25 | (379) leq(all_0_1_1, n2) = 0
% 37.78/10.25 |
% 37.78/10.25 +-Applying beta-rule and splitting (155), into two cases.
% 37.78/10.25 |-Branch one:
% 37.78/10.25 | (380) ~ (leq(all_0_1_1, n2) = 0)
% 37.78/10.25 |
% 37.78/10.25 | Using (379) and (380) yields:
% 37.78/10.25 | (235) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.25 |-Branch two:
% 37.78/10.25 | (379) leq(all_0_1_1, n2) = 0
% 37.78/10.25 | (383) all_0_1_1 = n2 | all_0_1_1 = n1 | all_0_1_1 = n0 | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.25 |
% 37.78/10.25 +-Applying beta-rule and splitting (383), into two cases.
% 37.78/10.25 |-Branch one:
% 37.78/10.25 | (247) all_0_1_1 = n0
% 37.78/10.25 |
% 37.78/10.25 | Equations (247) can reduce 245 to:
% 37.78/10.25 | (197) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.25 |-Branch two:
% 37.78/10.25 | (245) ~ (all_0_1_1 = n0)
% 37.78/10.25 | (387) all_0_1_1 = n2 | all_0_1_1 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.25 |
% 37.78/10.25 +-Applying beta-rule and splitting (387), into two cases.
% 37.78/10.25 |-Branch one:
% 37.78/10.25 | (388) all_0_1_1 = n2
% 37.78/10.25 |
% 37.78/10.25 | Equations (388) can reduce 378 to:
% 37.78/10.25 | (197) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.25 |-Branch two:
% 37.78/10.25 | (378) ~ (all_0_1_1 = n2)
% 37.78/10.25 | (327) all_0_1_1 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.25 |
% 37.78/10.25 +-Applying beta-rule and splitting (327), into two cases.
% 37.78/10.25 |-Branch one:
% 37.78/10.25 | (328) all_0_1_1 = n1
% 37.78/10.25 |
% 37.78/10.25 | Equations (328) can reduce 314 to:
% 37.78/10.25 | (197) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.25 |-Branch two:
% 37.78/10.25 | (314) ~ (all_0_1_1 = n1)
% 37.78/10.25 | (331) ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.25 |
% 37.78/10.25 | Instantiating (331) with all_647_0_105 yields:
% 37.78/10.25 | (396) ~ (all_647_0_105 = 0) & leq(n0, all_0_1_1) = all_647_0_105
% 37.78/10.25 |
% 37.78/10.25 | Applying alpha-rule on (396) yields:
% 37.78/10.25 | (397) ~ (all_647_0_105 = 0)
% 37.78/10.25 | (398) leq(n0, all_0_1_1) = all_647_0_105
% 37.78/10.25 |
% 37.78/10.25 | Instantiating formula (114) with n0, all_0_1_1, all_647_0_105, 0 and discharging atoms leq(n0, all_0_1_1) = all_647_0_105, leq(n0, all_0_1_1) = 0, yields:
% 37.78/10.25 | (399) all_647_0_105 = 0
% 37.78/10.25 |
% 37.78/10.25 | Equations (399) can reduce 397 to:
% 37.78/10.25 | (197) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.25 |-Branch two:
% 37.78/10.25 | (242) ~ (pv40 = n2)
% 37.78/10.25 | (273) pv40 = n3 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.25 |
% 37.78/10.25 +-Applying beta-rule and splitting (273), into two cases.
% 37.78/10.25 |-Branch one:
% 37.78/10.25 | (274) pv40 = n3
% 37.78/10.25 |
% 37.78/10.25 | Equations (274) can reduce 232 to:
% 37.78/10.25 | (197) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.25 |-Branch two:
% 37.78/10.25 | (232) ~ (pv40 = n3)
% 37.78/10.25 | (277) ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.25 |
% 37.78/10.25 | Instantiating (277) with all_567_0_106 yields:
% 37.78/10.25 | (407) ~ (all_567_0_106 = 0) & leq(n0, pv40) = all_567_0_106
% 37.78/10.25 |
% 37.78/10.25 | Applying alpha-rule on (407) yields:
% 37.78/10.25 | (408) ~ (all_567_0_106 = 0)
% 37.78/10.25 | (409) leq(n0, pv40) = all_567_0_106
% 37.78/10.25 |
% 37.78/10.25 | Instantiating formula (114) with n0, pv40, all_567_0_106, 0 and discharging atoms leq(n0, pv40) = all_567_0_106, leq(n0, pv40) = 0, yields:
% 37.78/10.25 | (410) all_567_0_106 = 0
% 37.78/10.25 |
% 37.78/10.25 | Equations (410) can reduce 408 to:
% 37.78/10.25 | (197) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.25 |-Branch two:
% 37.78/10.25 | (355) ~ (leq(n1, all_0_3_3) = 0)
% 37.78/10.25 | (413) ~ (gt(pv40, n1) = 0)
% 37.78/10.25 |
% 37.78/10.25 | Using (353) and (413) yields:
% 37.78/10.25 | (235) $false
% 37.78/10.25 |
% 37.78/10.25 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (415) leq(n3, pv40) = 0
% 37.78/10.26 | (416) gt(pv40, n2) = 0
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (178), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (230) ~ (leq(n3, pv40) = 0)
% 37.78/10.26 |
% 37.78/10.26 | Using (415) and (230) yields:
% 37.78/10.26 | (235) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (415) leq(n3, pv40) = 0
% 37.78/10.26 | (420) leq(n2, all_0_3_3) = 0
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (185), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (421) ~ (leq(n2, all_0_3_3) = 0)
% 37.78/10.26 |
% 37.78/10.26 | Using (420) and (421) yields:
% 37.78/10.26 | (235) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (420) leq(n2, all_0_3_3) = 0
% 37.78/10.26 | (424) ? [v0] : ? [v1] : (a_select2(sigma_init, n2) = v1 & leq(n0, n2) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (210), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (425) ~ (succ(all_0_3_3) = n0)
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (214), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (426) ~ (pred(pv40) = n0)
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (186), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (421) ~ (leq(n2, all_0_3_3) = 0)
% 37.78/10.26 |
% 37.78/10.26 | Using (420) and (421) yields:
% 37.78/10.26 | (235) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (420) leq(n2, all_0_3_3) = 0
% 37.78/10.26 | (430) ? [v0] : ? [v1] : (a_select2(mu_init, n2) = v1 & leq(n0, n2) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.26 |
% 37.78/10.26 | Using (420) and (176) yields:
% 37.78/10.26 | (378) ~ (all_0_1_1 = n2)
% 37.78/10.26 |
% 37.78/10.26 | Using (416) and (140) yields:
% 37.78/10.26 | (242) ~ (pv40 = n2)
% 37.78/10.26 |
% 37.78/10.26 | Using (147) and (425) yields:
% 37.78/10.26 | (260) ~ (pv40 = n0)
% 37.78/10.26 |
% 37.78/10.26 | Using (146) and (426) yields:
% 37.78/10.26 | (243) ~ (pv40 = n1)
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (159), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (233) ~ (leq(n0, all_0_3_3) = 0)
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (189), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (234) leq(n0, all_0_3_3) = 0
% 37.78/10.26 |
% 37.78/10.26 | Using (234) and (233) yields:
% 37.78/10.26 | (235) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (233) ~ (leq(n0, all_0_3_3) = 0)
% 37.78/10.26 | (439) ~ (succ(all_0_3_3) = n4)
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (190), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (234) leq(n0, all_0_3_3) = 0
% 37.78/10.26 |
% 37.78/10.26 | Using (234) and (233) yields:
% 37.78/10.26 | (235) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (233) ~ (leq(n0, all_0_3_3) = 0)
% 37.78/10.26 | (443) ~ (succ(all_0_3_3) = n3)
% 37.78/10.26 |
% 37.78/10.26 | Using (147) and (439) yields:
% 37.78/10.26 | (231) ~ (pv40 = n4)
% 37.78/10.26 |
% 37.78/10.26 | Using (147) and (443) yields:
% 37.78/10.26 | (232) ~ (pv40 = n3)
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (158), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (244) pv40 = n0
% 37.78/10.26 |
% 37.78/10.26 | Equations (244) can reduce 260 to:
% 37.78/10.26 | (197) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (260) ~ (pv40 = n0)
% 37.78/10.26 | (261) pv40 = n4 | pv40 = n3 | pv40 = n2 | pv40 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (261), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (262) pv40 = n4
% 37.78/10.26 |
% 37.78/10.26 | Equations (262) can reduce 231 to:
% 37.78/10.26 | (197) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (231) ~ (pv40 = n4)
% 37.78/10.26 | (265) pv40 = n3 | pv40 = n2 | pv40 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (265), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (266) pv40 = n1
% 37.78/10.26 |
% 37.78/10.26 | Equations (266) can reduce 243 to:
% 37.78/10.26 | (197) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (243) ~ (pv40 = n1)
% 37.78/10.26 | (269) pv40 = n3 | pv40 = n2 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (269), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (270) pv40 = n2
% 37.78/10.26 |
% 37.78/10.26 | Equations (270) can reduce 242 to:
% 37.78/10.26 | (197) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (242) ~ (pv40 = n2)
% 37.78/10.26 | (273) pv40 = n3 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (273), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (274) pv40 = n3
% 37.78/10.26 |
% 37.78/10.26 | Equations (274) can reduce 232 to:
% 37.78/10.26 | (197) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (232) ~ (pv40 = n3)
% 37.78/10.26 | (277) ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.26 |
% 37.78/10.26 | Instantiating (277) with all_544_0_112 yields:
% 37.78/10.26 | (466) ~ (all_544_0_112 = 0) & leq(n0, pv40) = all_544_0_112
% 37.78/10.26 |
% 37.78/10.26 | Applying alpha-rule on (466) yields:
% 37.78/10.26 | (467) ~ (all_544_0_112 = 0)
% 37.78/10.26 | (468) leq(n0, pv40) = all_544_0_112
% 37.78/10.26 |
% 37.78/10.26 | Instantiating formula (114) with n0, pv40, all_544_0_112, 0 and discharging atoms leq(n0, pv40) = all_544_0_112, leq(n0, pv40) = 0, yields:
% 37.78/10.26 | (469) all_544_0_112 = 0
% 37.78/10.26 |
% 37.78/10.26 | Equations (469) can reduce 467 to:
% 37.78/10.26 | (197) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (234) leq(n0, all_0_3_3) = 0
% 37.78/10.26 | (284) gt(pv40, n0) = 0
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (161), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (233) ~ (leq(n0, all_0_3_3) = 0)
% 37.78/10.26 |
% 37.78/10.26 | Using (234) and (233) yields:
% 37.78/10.26 | (235) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (234) leq(n0, all_0_3_3) = 0
% 37.78/10.26 | (292) ? [v0] : ? [v1] : (a_select2(mu_init, n0) = v1 & leq(n0, n0) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (160), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (233) ~ (leq(n0, all_0_3_3) = 0)
% 37.78/10.26 |
% 37.78/10.26 | Using (234) and (233) yields:
% 37.78/10.26 | (235) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (234) leq(n0, all_0_3_3) = 0
% 37.78/10.26 | (288) ? [v0] : ? [v1] : (a_select2(sigma_init, n0) = v1 & leq(n0, n0) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.26 |
% 37.78/10.26 | Using (234) and (176) yields:
% 37.78/10.26 | (245) ~ (all_0_1_1 = n0)
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (162), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (247) all_0_1_1 = n0
% 37.78/10.26 |
% 37.78/10.26 | Equations (247) can reduce 245 to:
% 37.78/10.26 | (197) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (245) ~ (all_0_1_1 = n0)
% 37.78/10.26 | (250) ? [v0] : ( ~ (v0 = 0) & leq(all_0_1_1, n0) = v0)
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (150), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (303) ~ (leq(n2, pv40) = 0)
% 37.78/10.26 |
% 37.78/10.26 | Using (166) and (303) yields:
% 37.78/10.26 | (231) ~ (pv40 = n4)
% 37.78/10.26 |
% 37.78/10.26 | Using (169) and (303) yields:
% 37.78/10.26 | (232) ~ (pv40 = n3)
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (158), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (244) pv40 = n0
% 37.78/10.26 |
% 37.78/10.26 | Equations (244) can reduce 260 to:
% 37.78/10.26 | (197) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (260) ~ (pv40 = n0)
% 37.78/10.26 | (261) pv40 = n4 | pv40 = n3 | pv40 = n2 | pv40 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (261), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (262) pv40 = n4
% 37.78/10.26 |
% 37.78/10.26 | Equations (262) can reduce 231 to:
% 37.78/10.26 | (197) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (231) ~ (pv40 = n4)
% 37.78/10.26 | (265) pv40 = n3 | pv40 = n2 | pv40 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (265), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (266) pv40 = n1
% 37.78/10.26 |
% 37.78/10.26 | Equations (266) can reduce 243 to:
% 37.78/10.26 | (197) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (243) ~ (pv40 = n1)
% 37.78/10.26 | (269) pv40 = n3 | pv40 = n2 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (269), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (270) pv40 = n2
% 37.78/10.26 |
% 37.78/10.26 | Equations (270) can reduce 242 to:
% 37.78/10.26 | (197) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (242) ~ (pv40 = n2)
% 37.78/10.26 | (273) pv40 = n3 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.26 |
% 37.78/10.26 +-Applying beta-rule and splitting (273), into two cases.
% 37.78/10.26 |-Branch one:
% 37.78/10.26 | (274) pv40 = n3
% 37.78/10.26 |
% 37.78/10.26 | Equations (274) can reduce 232 to:
% 37.78/10.26 | (197) $false
% 37.78/10.26 |
% 37.78/10.26 |-The branch is then unsatisfiable
% 37.78/10.26 |-Branch two:
% 37.78/10.26 | (232) ~ (pv40 = n3)
% 37.78/10.26 | (277) ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.26 |
% 37.78/10.26 | Instantiating (277) with all_547_0_119 yields:
% 37.78/10.26 | (509) ~ (all_547_0_119 = 0) & leq(n0, pv40) = all_547_0_119
% 37.78/10.26 |
% 37.78/10.26 | Applying alpha-rule on (509) yields:
% 37.78/10.27 | (510) ~ (all_547_0_119 = 0)
% 37.78/10.27 | (511) leq(n0, pv40) = all_547_0_119
% 37.78/10.27 |
% 37.78/10.27 | Instantiating formula (114) with n0, pv40, all_547_0_119, 0 and discharging atoms leq(n0, pv40) = all_547_0_119, leq(n0, pv40) = 0, yields:
% 37.78/10.27 | (512) all_547_0_119 = 0
% 37.78/10.27 |
% 37.78/10.27 | Equations (512) can reduce 510 to:
% 37.78/10.27 | (197) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (352) leq(n2, pv40) = 0
% 37.78/10.27 | (353) gt(pv40, n1) = 0
% 37.78/10.27 |
% 37.78/10.27 +-Applying beta-rule and splitting (179), into two cases.
% 37.78/10.27 |-Branch one:
% 37.78/10.27 | (303) ~ (leq(n2, pv40) = 0)
% 37.78/10.27 |
% 37.78/10.27 | Using (352) and (303) yields:
% 37.78/10.27 | (235) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (352) leq(n2, pv40) = 0
% 37.78/10.27 | (354) leq(n1, all_0_3_3) = 0
% 37.78/10.27 |
% 37.78/10.27 +-Applying beta-rule and splitting (187), into two cases.
% 37.78/10.27 |-Branch one:
% 37.78/10.27 | (355) ~ (leq(n1, all_0_3_3) = 0)
% 37.78/10.27 |
% 37.78/10.27 | Using (354) and (355) yields:
% 37.78/10.27 | (235) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (354) leq(n1, all_0_3_3) = 0
% 37.78/10.27 | (362) ? [v0] : ? [v1] : (a_select2(sigma_init, n1) = v1 & leq(n0, n1) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.27 |
% 37.78/10.27 +-Applying beta-rule and splitting (188), into two cases.
% 37.78/10.27 |-Branch one:
% 37.78/10.27 | (355) ~ (leq(n1, all_0_3_3) = 0)
% 37.78/10.27 |
% 37.78/10.27 | Using (354) and (355) yields:
% 37.78/10.27 | (235) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (354) leq(n1, all_0_3_3) = 0
% 37.78/10.27 | (358) ? [v0] : ? [v1] : (a_select2(mu_init, n1) = v1 & leq(n0, n1) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.27 |
% 37.78/10.27 | Using (354) and (176) yields:
% 37.78/10.27 | (314) ~ (all_0_1_1 = n1)
% 37.78/10.27 |
% 37.78/10.27 +-Applying beta-rule and splitting (148), into two cases.
% 37.78/10.27 |-Branch one:
% 37.78/10.27 | (529) ~ (leq(n4, pv40) = 0)
% 37.78/10.27 |
% 37.78/10.27 | Using (163) and (529) yields:
% 37.78/10.27 | (231) ~ (pv40 = n4)
% 37.78/10.27 |
% 37.78/10.27 +-Applying beta-rule and splitting (158), into two cases.
% 37.78/10.27 |-Branch one:
% 37.78/10.27 | (244) pv40 = n0
% 37.78/10.27 |
% 37.78/10.27 | Equations (244) can reduce 260 to:
% 37.78/10.27 | (197) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (260) ~ (pv40 = n0)
% 37.78/10.27 | (261) pv40 = n4 | pv40 = n3 | pv40 = n2 | pv40 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.27 |
% 37.78/10.27 +-Applying beta-rule and splitting (261), into two cases.
% 37.78/10.27 |-Branch one:
% 37.78/10.27 | (262) pv40 = n4
% 37.78/10.27 |
% 37.78/10.27 | Equations (262) can reduce 231 to:
% 37.78/10.27 | (197) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (231) ~ (pv40 = n4)
% 37.78/10.27 | (265) pv40 = n3 | pv40 = n2 | pv40 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.27 |
% 37.78/10.27 +-Applying beta-rule and splitting (265), into two cases.
% 37.78/10.27 |-Branch one:
% 37.78/10.27 | (266) pv40 = n1
% 37.78/10.27 |
% 37.78/10.27 | Equations (266) can reduce 243 to:
% 37.78/10.27 | (197) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (243) ~ (pv40 = n1)
% 37.78/10.27 | (269) pv40 = n3 | pv40 = n2 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.27 |
% 37.78/10.27 +-Applying beta-rule and splitting (269), into two cases.
% 37.78/10.27 |-Branch one:
% 37.78/10.27 | (270) pv40 = n2
% 37.78/10.27 |
% 37.78/10.27 | Equations (270) can reduce 242 to:
% 37.78/10.27 | (197) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (242) ~ (pv40 = n2)
% 37.78/10.27 | (273) pv40 = n3 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.27 |
% 37.78/10.27 +-Applying beta-rule and splitting (273), into two cases.
% 37.78/10.27 |-Branch one:
% 37.78/10.27 | (274) pv40 = n3
% 37.78/10.27 |
% 37.78/10.27 | Equations (274) can reduce 229 to:
% 37.78/10.27 | (548) ~ (all_0_1_1 = n3)
% 37.78/10.27 |
% 37.78/10.27 | From (274) and (63) follows:
% 37.78/10.27 | (549) leq(all_0_1_1, n3) = 0
% 37.78/10.27 |
% 37.78/10.27 +-Applying beta-rule and splitting (154), into two cases.
% 37.78/10.27 |-Branch one:
% 37.78/10.27 | (550) ~ (leq(all_0_1_1, n3) = 0)
% 37.78/10.27 |
% 37.78/10.27 | Using (549) and (550) yields:
% 37.78/10.27 | (235) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (549) leq(all_0_1_1, n3) = 0
% 37.78/10.27 | (553) all_0_1_1 = n3 | all_0_1_1 = n2 | all_0_1_1 = n1 | all_0_1_1 = n0 | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.27 |
% 37.78/10.27 +-Applying beta-rule and splitting (553), into two cases.
% 37.78/10.27 |-Branch one:
% 37.78/10.27 | (247) all_0_1_1 = n0
% 37.78/10.27 |
% 37.78/10.27 | Equations (247) can reduce 245 to:
% 37.78/10.27 | (197) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (245) ~ (all_0_1_1 = n0)
% 37.78/10.27 | (557) all_0_1_1 = n3 | all_0_1_1 = n2 | all_0_1_1 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.27 |
% 37.78/10.27 +-Applying beta-rule and splitting (557), into two cases.
% 37.78/10.27 |-Branch one:
% 37.78/10.27 | (558) all_0_1_1 = n3
% 37.78/10.27 |
% 37.78/10.27 | Equations (558) can reduce 548 to:
% 37.78/10.27 | (197) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (548) ~ (all_0_1_1 = n3)
% 37.78/10.27 | (387) all_0_1_1 = n2 | all_0_1_1 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.27 |
% 37.78/10.27 +-Applying beta-rule and splitting (387), into two cases.
% 37.78/10.27 |-Branch one:
% 37.78/10.27 | (388) all_0_1_1 = n2
% 37.78/10.27 |
% 37.78/10.27 | Equations (388) can reduce 378 to:
% 37.78/10.27 | (197) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (378) ~ (all_0_1_1 = n2)
% 37.78/10.27 | (327) all_0_1_1 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.27 |
% 37.78/10.27 +-Applying beta-rule and splitting (327), into two cases.
% 37.78/10.27 |-Branch one:
% 37.78/10.27 | (328) all_0_1_1 = n1
% 37.78/10.27 |
% 37.78/10.27 | Equations (328) can reduce 314 to:
% 37.78/10.27 | (197) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (314) ~ (all_0_1_1 = n1)
% 37.78/10.27 | (331) ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.27 |
% 37.78/10.27 | Instantiating (331) with all_641_0_124 yields:
% 37.78/10.27 | (570) ~ (all_641_0_124 = 0) & leq(n0, all_0_1_1) = all_641_0_124
% 37.78/10.27 |
% 37.78/10.27 | Applying alpha-rule on (570) yields:
% 37.78/10.27 | (571) ~ (all_641_0_124 = 0)
% 37.78/10.27 | (572) leq(n0, all_0_1_1) = all_641_0_124
% 37.78/10.27 |
% 37.78/10.27 | Instantiating formula (114) with n0, all_0_1_1, all_641_0_124, 0 and discharging atoms leq(n0, all_0_1_1) = all_641_0_124, leq(n0, all_0_1_1) = 0, yields:
% 37.78/10.27 | (573) all_641_0_124 = 0
% 37.78/10.27 |
% 37.78/10.27 | Equations (573) can reduce 571 to:
% 37.78/10.27 | (197) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (232) ~ (pv40 = n3)
% 37.78/10.27 | (277) ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.27 |
% 37.78/10.27 | Instantiating (277) with all_589_0_125 yields:
% 37.78/10.27 | (577) ~ (all_589_0_125 = 0) & leq(n0, pv40) = all_589_0_125
% 37.78/10.27 |
% 37.78/10.27 | Applying alpha-rule on (577) yields:
% 37.78/10.27 | (578) ~ (all_589_0_125 = 0)
% 37.78/10.27 | (579) leq(n0, pv40) = all_589_0_125
% 37.78/10.27 |
% 37.78/10.27 | Instantiating formula (114) with n0, pv40, all_589_0_125, 0 and discharging atoms leq(n0, pv40) = all_589_0_125, leq(n0, pv40) = 0, yields:
% 37.78/10.27 | (580) all_589_0_125 = 0
% 37.78/10.27 |
% 37.78/10.27 | Equations (580) can reduce 578 to:
% 37.78/10.27 | (197) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (582) leq(n4, pv40) = 0
% 37.78/10.27 | (583) gt(pv40, n3) = 0
% 37.78/10.27 |
% 37.78/10.27 +-Applying beta-rule and splitting (177), into two cases.
% 37.78/10.27 |-Branch one:
% 37.78/10.27 | (529) ~ (leq(n4, pv40) = 0)
% 37.78/10.27 |
% 37.78/10.27 | Using (582) and (529) yields:
% 37.78/10.27 | (235) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (582) leq(n4, pv40) = 0
% 37.78/10.27 | (587) leq(n3, all_0_3_3) = 0
% 37.78/10.27 |
% 37.78/10.27 +-Applying beta-rule and splitting (184), into two cases.
% 37.78/10.27 |-Branch one:
% 37.78/10.27 | (588) ~ (leq(n3, all_0_3_3) = 0)
% 37.78/10.27 |
% 37.78/10.27 | Using (587) and (588) yields:
% 37.78/10.27 | (235) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (587) leq(n3, all_0_3_3) = 0
% 37.78/10.27 | (591) ? [v0] : ? [v1] : (a_select2(mu_init, n3) = v1 & leq(n0, n3) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.27 |
% 37.78/10.27 +-Applying beta-rule and splitting (183), into two cases.
% 37.78/10.27 |-Branch one:
% 37.78/10.27 | (588) ~ (leq(n3, all_0_3_3) = 0)
% 37.78/10.27 |
% 37.78/10.27 | Using (587) and (588) yields:
% 37.78/10.27 | (235) $false
% 37.78/10.27 |
% 37.78/10.27 |-The branch is then unsatisfiable
% 37.78/10.27 |-Branch two:
% 37.78/10.27 | (587) leq(n3, all_0_3_3) = 0
% 37.78/10.27 | (595) ? [v0] : ? [v1] : (a_select2(sigma_init, n3) = v1 & leq(n0, n3) = v0 & ( ~ (v0 = 0) | v1 = init))
% 37.78/10.28 |
% 37.78/10.28 | Using (587) and (176) yields:
% 37.78/10.28 | (548) ~ (all_0_1_1 = n3)
% 37.78/10.28 |
% 37.78/10.28 | Using (583) and (139) yields:
% 37.78/10.28 | (232) ~ (pv40 = n3)
% 37.78/10.28 |
% 37.78/10.28 +-Applying beta-rule and splitting (158), into two cases.
% 37.78/10.28 |-Branch one:
% 37.78/10.28 | (244) pv40 = n0
% 37.78/10.28 |
% 37.78/10.28 | Equations (244) can reduce 260 to:
% 37.78/10.28 | (197) $false
% 37.78/10.28 |
% 37.78/10.28 |-The branch is then unsatisfiable
% 37.78/10.28 |-Branch two:
% 37.78/10.28 | (260) ~ (pv40 = n0)
% 37.78/10.28 | (261) pv40 = n4 | pv40 = n3 | pv40 = n2 | pv40 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.28 |
% 37.78/10.28 +-Applying beta-rule and splitting (261), into two cases.
% 37.78/10.28 |-Branch one:
% 37.78/10.28 | (262) pv40 = n4
% 37.78/10.28 |
% 37.78/10.28 | Equations (262) can reduce 229 to:
% 37.78/10.28 | (603) ~ (all_0_1_1 = n4)
% 37.78/10.28 |
% 37.78/10.28 | From (262) and (63) follows:
% 37.78/10.28 | (604) leq(all_0_1_1, n4) = 0
% 37.78/10.28 |
% 37.78/10.28 +-Applying beta-rule and splitting (153), into two cases.
% 37.78/10.28 |-Branch one:
% 37.78/10.28 | (605) ~ (leq(all_0_1_1, n4) = 0)
% 37.78/10.28 |
% 37.78/10.28 | Using (604) and (605) yields:
% 37.78/10.28 | (235) $false
% 37.78/10.28 |
% 37.78/10.28 |-The branch is then unsatisfiable
% 37.78/10.28 |-Branch two:
% 37.78/10.28 | (604) leq(all_0_1_1, n4) = 0
% 37.78/10.28 | (608) all_0_1_1 = n4 | all_0_1_1 = n3 | all_0_1_1 = n2 | all_0_1_1 = n1 | all_0_1_1 = n0 | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.28 |
% 37.78/10.28 +-Applying beta-rule and splitting (608), into two cases.
% 37.78/10.28 |-Branch one:
% 37.78/10.28 | (247) all_0_1_1 = n0
% 37.78/10.28 |
% 37.78/10.28 | Equations (247) can reduce 245 to:
% 37.78/10.28 | (197) $false
% 37.78/10.28 |
% 37.78/10.28 |-The branch is then unsatisfiable
% 37.78/10.28 |-Branch two:
% 37.78/10.28 | (245) ~ (all_0_1_1 = n0)
% 37.78/10.28 | (612) all_0_1_1 = n4 | all_0_1_1 = n3 | all_0_1_1 = n2 | all_0_1_1 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.28 |
% 37.78/10.28 +-Applying beta-rule and splitting (612), into two cases.
% 37.78/10.28 |-Branch one:
% 37.78/10.28 | (613) all_0_1_1 = n4
% 37.78/10.28 |
% 37.78/10.28 | Equations (613) can reduce 603 to:
% 37.78/10.28 | (197) $false
% 37.78/10.28 |
% 37.78/10.28 |-The branch is then unsatisfiable
% 37.78/10.28 |-Branch two:
% 37.78/10.28 | (603) ~ (all_0_1_1 = n4)
% 37.78/10.28 | (557) all_0_1_1 = n3 | all_0_1_1 = n2 | all_0_1_1 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.28 |
% 37.78/10.28 +-Applying beta-rule and splitting (557), into two cases.
% 37.78/10.28 |-Branch one:
% 37.78/10.28 | (558) all_0_1_1 = n3
% 37.78/10.28 |
% 37.78/10.28 | Equations (558) can reduce 548 to:
% 37.78/10.28 | (197) $false
% 37.78/10.28 |
% 37.78/10.28 |-The branch is then unsatisfiable
% 37.78/10.28 |-Branch two:
% 37.78/10.28 | (548) ~ (all_0_1_1 = n3)
% 37.78/10.28 | (387) all_0_1_1 = n2 | all_0_1_1 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.28 |
% 37.78/10.28 +-Applying beta-rule and splitting (387), into two cases.
% 37.78/10.28 |-Branch one:
% 37.78/10.28 | (388) all_0_1_1 = n2
% 37.78/10.28 |
% 37.78/10.28 | Equations (388) can reduce 378 to:
% 37.78/10.28 | (197) $false
% 37.78/10.28 |
% 37.78/10.28 |-The branch is then unsatisfiable
% 37.78/10.28 |-Branch two:
% 37.78/10.28 | (378) ~ (all_0_1_1 = n2)
% 37.78/10.28 | (327) all_0_1_1 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.28 |
% 37.78/10.28 +-Applying beta-rule and splitting (327), into two cases.
% 37.78/10.28 |-Branch one:
% 37.78/10.28 | (328) all_0_1_1 = n1
% 37.78/10.28 |
% 37.78/10.28 | Equations (328) can reduce 314 to:
% 37.78/10.28 | (197) $false
% 37.78/10.28 |
% 37.78/10.28 |-The branch is then unsatisfiable
% 37.78/10.28 |-Branch two:
% 37.78/10.28 | (314) ~ (all_0_1_1 = n1)
% 37.78/10.28 | (331) ? [v0] : ( ~ (v0 = 0) & leq(n0, all_0_1_1) = v0)
% 37.78/10.28 |
% 37.78/10.28 | Instantiating (331) with all_649_0_130 yields:
% 37.78/10.28 | (629) ~ (all_649_0_130 = 0) & leq(n0, all_0_1_1) = all_649_0_130
% 37.78/10.28 |
% 37.78/10.28 | Applying alpha-rule on (629) yields:
% 37.78/10.28 | (630) ~ (all_649_0_130 = 0)
% 37.78/10.28 | (631) leq(n0, all_0_1_1) = all_649_0_130
% 37.78/10.28 |
% 37.78/10.28 | Instantiating formula (114) with n0, all_0_1_1, all_649_0_130, 0 and discharging atoms leq(n0, all_0_1_1) = all_649_0_130, leq(n0, all_0_1_1) = 0, yields:
% 37.78/10.28 | (632) all_649_0_130 = 0
% 37.78/10.28 |
% 37.78/10.28 | Equations (632) can reduce 630 to:
% 37.78/10.28 | (197) $false
% 37.78/10.28 |
% 37.78/10.28 |-The branch is then unsatisfiable
% 37.78/10.28 |-Branch two:
% 37.78/10.28 | (231) ~ (pv40 = n4)
% 37.78/10.28 | (265) pv40 = n3 | pv40 = n2 | pv40 = n1 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.28 |
% 37.78/10.28 +-Applying beta-rule and splitting (265), into two cases.
% 37.78/10.28 |-Branch one:
% 37.78/10.28 | (266) pv40 = n1
% 37.78/10.28 |
% 37.78/10.28 | Equations (266) can reduce 243 to:
% 37.78/10.28 | (197) $false
% 37.78/10.28 |
% 37.78/10.28 |-The branch is then unsatisfiable
% 37.78/10.28 |-Branch two:
% 37.78/10.28 | (243) ~ (pv40 = n1)
% 37.78/10.28 | (269) pv40 = n3 | pv40 = n2 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.28 |
% 37.78/10.28 +-Applying beta-rule and splitting (269), into two cases.
% 37.78/10.28 |-Branch one:
% 37.78/10.28 | (270) pv40 = n2
% 37.78/10.28 |
% 37.78/10.28 | Equations (270) can reduce 242 to:
% 37.78/10.28 | (197) $false
% 37.78/10.28 |
% 37.78/10.28 |-The branch is then unsatisfiable
% 37.78/10.28 |-Branch two:
% 37.78/10.28 | (242) ~ (pv40 = n2)
% 37.78/10.28 | (273) pv40 = n3 | ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.28 |
% 37.78/10.28 +-Applying beta-rule and splitting (273), into two cases.
% 37.78/10.28 |-Branch one:
% 37.78/10.28 | (274) pv40 = n3
% 37.78/10.28 |
% 37.78/10.28 | Equations (274) can reduce 232 to:
% 37.78/10.28 | (197) $false
% 37.78/10.28 |
% 37.78/10.28 |-The branch is then unsatisfiable
% 37.78/10.28 |-Branch two:
% 37.78/10.28 | (232) ~ (pv40 = n3)
% 37.78/10.28 | (277) ? [v0] : ( ~ (v0 = 0) & leq(n0, pv40) = v0)
% 37.78/10.28 |
% 37.78/10.28 | Instantiating (277) with all_617_0_131 yields:
% 37.78/10.28 | (648) ~ (all_617_0_131 = 0) & leq(n0, pv40) = all_617_0_131
% 37.78/10.28 |
% 37.78/10.28 | Applying alpha-rule on (648) yields:
% 37.78/10.28 | (649) ~ (all_617_0_131 = 0)
% 37.78/10.28 | (650) leq(n0, pv40) = all_617_0_131
% 37.78/10.28 |
% 37.78/10.28 | Instantiating formula (114) with n0, pv40, all_617_0_131, 0 and discharging atoms leq(n0, pv40) = all_617_0_131, leq(n0, pv40) = 0, yields:
% 38.24/10.28 | (651) all_617_0_131 = 0
% 38.24/10.28 |
% 38.24/10.28 | Equations (651) can reduce 649 to:
% 38.24/10.28 | (197) $false
% 38.24/10.28 |
% 38.24/10.28 |-The branch is then unsatisfiable
% 38.24/10.28 |-Branch two:
% 38.24/10.28 | (653) pred(pv40) = n0
% 38.24/10.28 | (654) all_114_0_29 = 0 | ? [v0] : ( ~ (v0 = 0) & gt(pv40, n2) = v0)
% 38.24/10.28 |
% 38.24/10.28 +-Applying beta-rule and splitting (654), into two cases.
% 38.24/10.28 |-Branch one:
% 38.24/10.28 | (216) all_114_0_29 = 0
% 38.24/10.28 |
% 38.24/10.28 | Equations (216) can reduce 208 to:
% 38.24/10.28 | (197) $false
% 38.24/10.28 |
% 38.24/10.28 |-The branch is then unsatisfiable
% 38.24/10.28 |-Branch two:
% 38.24/10.28 | (208) ~ (all_114_0_29 = 0)
% 38.24/10.28 | (658) ? [v0] : ( ~ (v0 = 0) & gt(pv40, n2) = v0)
% 38.24/10.28 |
% 38.24/10.28 | Instantiating (658) with all_461_0_134 yields:
% 38.24/10.28 | (659) ~ (all_461_0_134 = 0) & gt(pv40, n2) = all_461_0_134
% 38.24/10.28 |
% 38.24/10.28 | Applying alpha-rule on (659) yields:
% 38.24/10.28 | (660) ~ (all_461_0_134 = 0)
% 38.24/10.28 | (661) gt(pv40, n2) = all_461_0_134
% 38.24/10.28 |
% 38.24/10.28 | Instantiating formula (64) with pv40, n2, all_461_0_134, 0 and discharging atoms gt(pv40, n2) = all_461_0_134, gt(pv40, n2) = 0, yields:
% 38.24/10.28 | (662) all_461_0_134 = 0
% 38.24/10.28 |
% 38.24/10.28 | Equations (662) can reduce 660 to:
% 38.24/10.28 | (197) $false
% 38.24/10.28 |
% 38.24/10.28 |-The branch is then unsatisfiable
% 38.24/10.28 |-Branch two:
% 38.24/10.28 | (664) succ(all_0_3_3) = n0
% 38.24/10.28 | (665) all_109_0_28 = 0 | ? [v0] : ( ~ (v0 = 0) & leq(n2, all_0_3_3) = v0)
% 38.24/10.28 |
% 38.24/10.28 +-Applying beta-rule and splitting (195), into two cases.
% 38.24/10.28 |-Branch one:
% 38.24/10.28 | (425) ~ (succ(all_0_3_3) = n0)
% 38.24/10.28 |
% 38.24/10.28 | Using (664) and (425) yields:
% 38.24/10.28 | (235) $false
% 38.24/10.28 |
% 38.24/10.28 |-The branch is then unsatisfiable
% 38.24/10.28 |-Branch two:
% 38.24/10.28 | (664) succ(all_0_3_3) = n0
% 38.24/10.28 | (669) leq(all_0_3_3, tptp_minus_1) = 0
% 38.24/10.28 |
% 38.24/10.28 +-Applying beta-rule and splitting (211), into two cases.
% 38.24/10.28 |-Branch one:
% 38.24/10.28 | (425) ~ (succ(all_0_3_3) = n0)
% 38.24/10.28 |
% 38.24/10.28 | Using (664) and (425) yields:
% 38.24/10.28 | (235) $false
% 38.24/10.28 |
% 38.24/10.28 |-The branch is then unsatisfiable
% 38.24/10.28 |-Branch two:
% 38.24/10.29 | (664) succ(all_0_3_3) = n0
% 38.24/10.29 | (673) all_114_0_29 = 0 | ? [v0] : ( ~ (v0 = 0) & leq(n2, all_0_3_3) = v0)
% 38.24/10.29 |
% 38.24/10.29 +-Applying beta-rule and splitting (673), into two cases.
% 38.24/10.29 |-Branch one:
% 38.24/10.29 | (216) all_114_0_29 = 0
% 38.24/10.29 |
% 38.24/10.29 | Equations (216) can reduce 208 to:
% 38.24/10.29 | (197) $false
% 38.24/10.29 |
% 38.24/10.29 |-The branch is then unsatisfiable
% 38.24/10.29 |-Branch two:
% 38.24/10.29 | (208) ~ (all_114_0_29 = 0)
% 38.24/10.29 | (677) ? [v0] : ( ~ (v0 = 0) & leq(n2, all_0_3_3) = v0)
% 38.24/10.29 |
% 38.24/10.29 | Instantiating (677) with all_530_0_151 yields:
% 38.24/10.29 | (678) ~ (all_530_0_151 = 0) & leq(n2, all_0_3_3) = all_530_0_151
% 38.24/10.29 |
% 38.24/10.29 | Applying alpha-rule on (678) yields:
% 38.24/10.29 | (679) ~ (all_530_0_151 = 0)
% 38.24/10.29 | (680) leq(n2, all_0_3_3) = all_530_0_151
% 38.24/10.29 |
% 38.24/10.29 +-Applying beta-rule and splitting (186), into two cases.
% 38.24/10.29 |-Branch one:
% 38.24/10.29 | (421) ~ (leq(n2, all_0_3_3) = 0)
% 38.24/10.29 |
% 38.24/10.29 | Using (420) and (421) yields:
% 38.24/10.29 | (235) $false
% 38.24/10.29 |
% 38.24/10.29 |-The branch is then unsatisfiable
% 38.24/10.29 |-Branch two:
% 38.24/10.29 | (420) leq(n2, all_0_3_3) = 0
% 38.24/10.29 | (430) ? [v0] : ? [v1] : (a_select2(mu_init, n2) = v1 & leq(n0, n2) = v0 & ( ~ (v0 = 0) | v1 = init))
% 38.24/10.29 |
% 38.24/10.29 | Instantiating formula (114) with n2, all_0_3_3, 0, all_530_0_151 and discharging atoms leq(n2, all_0_3_3) = all_530_0_151, leq(n2, all_0_3_3) = 0, yields:
% 38.24/10.29 | (685) all_530_0_151 = 0
% 38.24/10.29 |
% 38.24/10.29 | Equations (685) can reduce 679 to:
% 38.24/10.29 | (197) $false
% 38.24/10.29 |
% 38.24/10.29 |-The branch is then unsatisfiable
% 38.24/10.29 |-Branch two:
% 38.24/10.29 | (687) a_select2(mu_init, pv40) = all_0_0_0
% 38.24/10.29 | (688) all_0_0_0 = init
% 38.24/10.29 |
% 38.24/10.29 | Equations (688) can reduce 32 to:
% 38.24/10.29 | (197) $false
% 38.24/10.29 |
% 38.24/10.29 |-The branch is then unsatisfiable
% 38.24/10.29 |-Branch two:
% 38.24/10.29 | (690) leq(all_0_1_1, all_0_3_3) = 0
% 38.24/10.29 | (691) ? [v0] : ? [v1] : (a_select2(mu_init, all_0_1_1) = v1 & leq(n0, all_0_1_1) = v0 & ( ~ (v0 = 0) | v1 = init))
% 38.24/10.29 |
% 38.24/10.29 | Instantiating (691) with all_41_0_165, all_41_1_166 yields:
% 38.24/10.29 | (692) a_select2(mu_init, all_0_1_1) = all_41_0_165 & leq(n0, all_0_1_1) = all_41_1_166 & ( ~ (all_41_1_166 = 0) | all_41_0_165 = init)
% 38.24/10.29 |
% 38.24/10.29 | Applying alpha-rule on (692) yields:
% 38.24/10.29 | (693) a_select2(mu_init, all_0_1_1) = all_41_0_165
% 38.24/10.29 | (694) leq(n0, all_0_1_1) = all_41_1_166
% 38.24/10.29 | (695) ~ (all_41_1_166 = 0) | all_41_0_165 = init
% 38.24/10.29 |
% 38.24/10.29 +-Applying beta-rule and splitting (151), into two cases.
% 38.24/10.29 |-Branch one:
% 38.24/10.29 | (176) ~ (leq(all_0_1_1, all_0_3_3) = 0)
% 38.24/10.29 |
% 38.24/10.29 | Using (690) and (176) yields:
% 38.24/10.29 | (235) $false
% 38.24/10.29 |
% 38.24/10.29 |-The branch is then unsatisfiable
% 38.24/10.29 |-Branch two:
% 38.24/10.29 | (690) leq(all_0_1_1, all_0_3_3) = 0
% 38.24/10.29 | (699) ? [v0] : ? [v1] : (a_select2(sigma_init, all_0_1_1) = v1 & leq(n0, all_0_1_1) = v0 & ( ~ (v0 = 0) | v1 = init))
% 38.24/10.29 |
% 38.24/10.29 | Instantiating (699) with all_50_0_167, all_50_1_168 yields:
% 38.24/10.29 | (700) a_select2(sigma_init, all_0_1_1) = all_50_0_167 & leq(n0, all_0_1_1) = all_50_1_168 & ( ~ (all_50_1_168 = 0) | all_50_0_167 = init)
% 38.24/10.29 |
% 38.24/10.29 | Applying alpha-rule on (700) yields:
% 38.24/10.29 | (701) a_select2(sigma_init, all_0_1_1) = all_50_0_167
% 38.24/10.29 | (702) leq(n0, all_0_1_1) = all_50_1_168
% 38.24/10.29 | (703) ~ (all_50_1_168 = 0) | all_50_0_167 = init
% 38.24/10.29 |
% 38.24/10.29 | Instantiating formula (96) with mu_init, all_0_1_1, all_41_0_165, all_0_0_0 and discharging atoms a_select2(mu_init, all_0_1_1) = all_41_0_165, a_select2(mu_init, all_0_1_1) = all_0_0_0, yields:
% 38.24/10.29 | (704) all_41_0_165 = all_0_0_0
% 38.24/10.29 |
% 38.24/10.29 | Instantiating formula (114) with n0, all_0_1_1, all_50_1_168, 0 and discharging atoms leq(n0, all_0_1_1) = all_50_1_168, leq(n0, all_0_1_1) = 0, yields:
% 38.24/10.29 | (705) all_50_1_168 = 0
% 38.24/10.29 |
% 38.24/10.29 | Instantiating formula (114) with n0, all_0_1_1, all_41_1_166, all_50_1_168 and discharging atoms leq(n0, all_0_1_1) = all_50_1_168, leq(n0, all_0_1_1) = all_41_1_166, yields:
% 38.24/10.29 | (706) all_50_1_168 = all_41_1_166
% 38.24/10.29 |
% 38.24/10.29 | Combining equations (705,706) yields a new equation:
% 38.24/10.29 | (707) all_41_1_166 = 0
% 38.24/10.29 |
% 38.24/10.29 +-Applying beta-rule and splitting (695), into two cases.
% 38.24/10.29 |-Branch one:
% 38.24/10.29 | (708) ~ (all_41_1_166 = 0)
% 38.24/10.29 |
% 38.24/10.29 | Equations (707) can reduce 708 to:
% 38.24/10.29 | (197) $false
% 38.24/10.29 |
% 38.24/10.29 |-The branch is then unsatisfiable
% 38.24/10.29 |-Branch two:
% 38.24/10.29 | (707) all_41_1_166 = 0
% 38.24/10.29 | (711) all_41_0_165 = init
% 38.24/10.29 |
% 38.24/10.29 | Combining equations (704,711) yields a new equation:
% 38.24/10.29 | (712) all_0_0_0 = init
% 38.24/10.29 |
% 38.24/10.29 | Simplifying 712 yields:
% 38.24/10.29 | (688) all_0_0_0 = init
% 38.24/10.29 |
% 38.24/10.29 | Equations (688) can reduce 32 to:
% 38.24/10.29 | (197) $false
% 38.24/10.29 |
% 38.24/10.29 |-The branch is then unsatisfiable
% 38.24/10.29 % SZS output end Proof for theBenchmark
% 38.24/10.29
% 38.24/10.29 9817ms
%------------------------------------------------------------------------------