%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWV161+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n006.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 17:50:13 EDT 2022 % Result : Theorem 22.41s 6.56s % Output : Proof 27.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : SWV161+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.32 % Computer : n006.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Thu Jun 16 05:39:26 EDT 2022 % 0.11/0.32 % CPUTime : % 0.53/0.57 ____ _ % 0.53/0.57 ___ / __ \_____(_)___ ________ __________ % 0.53/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.53/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.53/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.53/0.57 % 0.53/0.57 A Theorem Prover for First-Order Logic % 0.53/0.57 (ePrincess v.1.0) % 0.53/0.57 % 0.53/0.57 (c) Philipp Rümmer, 2009-2015 % 0.53/0.57 (c) Peter Backeman, 2014-2015 % 0.53/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.53/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.53/0.57 Bug reports to peter@backeman.se % 0.53/0.57 % 0.53/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.53/0.57 % 0.53/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.53/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.09/1.03 Prover 0: Preprocessing ... % 4.24/1.55 Prover 0: Warning: ignoring some quantifiers % 4.32/1.58 Prover 0: Constructing countermodel ... % 19.39/5.91 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 19.79/6.05 Prover 1: Preprocessing ... % 20.98/6.25 Prover 1: Warning: ignoring some quantifiers % 20.98/6.26 Prover 1: Constructing countermodel ... % 22.41/6.56 Prover 1: proved (645ms) % 22.41/6.56 Prover 0: stopped % 22.41/6.56 % 22.41/6.56 No countermodel exists, formula is valid % 22.41/6.56 % SZS status Theorem for theBenchmark % 22.41/6.56 % 22.41/6.56 Generating proof ... Warning: ignoring some quantifiers % 26.84/7.63 found it (size 53) % 26.84/7.63 % 26.84/7.63 % SZS output start Proof for theBenchmark % 26.84/7.63 Assumed formulas after preprocessing and simplification: % 26.84/7.63 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = n1) & ~ (def = use) & sum(n0, n4, v3) = v4 & sum(n0, n4, v0) = n1 & a_select3(q, v2, tptp_sum_index) = v3 & a_select3(q, pv10, tptp_sum_index) = v0 & succ(n4) = n5 & succ(n3) = n4 & succ(n2) = n3 & succ(n1) = n2 & succ(tptp_minus_1) = n0 & succ(n0) = n1 & pred(pv10) = v1 & leq(v2, pv10) = 0 & leq(pv10, n135299) = 0 & leq(n0, v2) = 0 & leq(n0, pv10) = 0 & 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 & ? [v5] : ? [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (tptp_mmul(v19, v20) = v21) | ~ (tptp_mmul(v12, v16) = v17) | ~ (tptp_mmul(v11, v17) = v18) | ~ (tptp_mmul(v10, v13) = v14) | ~ (tptp_mmul(v9, v14) = v15) | ~ (tptp_mmul(v8, v21) = v22) | ~ (tptp_madd(v15, v18) = v19) | ~ (tptp_madd(v7, v22) = v23) | ~ (trans(v11) = v16) | ~ (trans(v9) = v13) | ~ (trans(v8) = v20) | ~ (a_select3(v23, v24, v25) = v26) | ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : ? [v32] : ? [v33] : ? [v34] : ((v32 = 0 & v31 = 0 & v30 = 0 & v29 = 0 & ~ (v34 = v33) & a_select3(v12, v28, v27) = v34 & a_select3(v12, v27, v28) = v33 & leq(v28, v5) = 0 & leq(v27, v5) = 0 & leq(n0, v28) = 0 & leq(n0, v27) = 0) | (v32 = 0 & v31 = 0 & v30 = 0 & v29 = 0 & ~ (v34 = v33) & a_select3(v10, v28, v27) = v34 & a_select3(v10, v27, v28) = v33 & leq(v28, v6) = 0 & leq(v27, v6) = 0 & leq(n0, v28) = 0 & leq(n0, v27) = 0) | (v32 = 0 & v31 = 0 & v30 = 0 & v29 = 0 & ~ (v34 = v33) & a_select3(v7, v28, v27) = v34 & a_select3(v7, v27, v28) = v33 & leq(v28, v5) = 0 & leq(v27, v5) = 0 & leq(n0, v28) = 0 & leq(n0, v27) = 0) | (a_select3(v23, v25, v24) = v31 & leq(v25, v5) = v30 & leq(v24, v5) = v28 & leq(n0, v25) = v29 & leq(n0, v24) = v27 & ( ~ (v30 = 0) | ~ (v29 = 0) | ~ (v28 = 0) | ~ (v27 = 0) | v31 = v26)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v11 | ~ (tptp_const_array2(v12, v13, v11) = v14) | ~ (a_select3(v14, v5, v8) = v15) | ~ (dim(v9, v10) = v13) | ~ (dim(v6, v7) = v12) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (leq(v9, v8) = v18 & leq(v8, v10) = v19 & leq(v6, v5) = v16 & leq(v5, v7) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0)))) & ? [v5] : ? [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (tptp_mmul(v8, v9) = v10) | ~ (tptp_mmul(v7, v10) = v11) | ~ (trans(v7) = v9) | ~ (a_select3(v11, v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ((v20 = 0 & v19 = 0 & v18 = 0 & v17 = 0 & ~ (v22 = v21) & a_select3(v8, v16, v15) = v22 & a_select3(v8, v15, v16) = v21 & leq(v16, v6) = 0 & leq(v15, v6) = 0 & leq(n0, v16) = 0 & leq(n0, v15) = 0) | (a_select3(v11, v13, v12) = v19 & leq(v13, v5) = v18 & leq(v12, v5) = v16 & leq(n0, v13) = v17 & leq(n0, v12) = v15 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | v19 = v14)))) & ? [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, v5) = v17 & leq(v11, v5) = v15 & leq(n0, v12) = v16 & leq(n0, v11) = v14 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | v18 = v13)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (tptp_update3(v9, v7, v8, v10) = v11) | ~ (a_select3(v11, v5, v6) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & ~ (v19 = v10) & a_select3(v9, v13, v14) = v19 & leq(v14, v8) = 0 & leq(v13, v7) = 0 & leq(n0, v14) = 0 & leq(n0, v13) = 0) | (leq(v6, v8) = v16 & leq(v5, v7) = v14 & leq(n0, v6) = v15 & leq(n0, v5) = v13 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0))))) & ? [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v5 | v8 = v6 | ~ (tptp_update3(v9, v6, v7, v10) = v11) | ~ (a_select3(v11, v8, v7) = v12) | ? [v13] : ( ~ (v13 = v5) & a_select3(v9, v8, v7) = v13)) & ? [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (tptp_update3(v6, v9, v9, v10) = v11) | ~ (a_select3(v11, v7, v8) = 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, v5) = 0 & leq(v13, v5) = 0 & leq(n0, v14) = 0 & leq(n0, v13) = 0) | (a_select3(v11, v8, v7) = v19 & leq(v9, v5) = v18 & leq(v8, v5) = v16 & leq(v7, v5) = v14 & leq(n0, v9) = v17 & leq(n0, v8) = v15 & leq(n0, v7) = v13 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | v19 = v12)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (dim(v6, v7) = v9) | ~ (tptp_const_array1(v9, v8) = v10) | ~ (a_select2(v10, v5) = v11) | ? [v12] : ? [v13] : (leq(v6, v5) = v12 & leq(v5, v7) = v13 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ? [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v5 | v7 = v6 | ~ (tptp_update2(v8, v6, v9) = v10) | ~ (a_select2(v10, v7) = v11) | ? [v12] : ( ~ (v12 = v5) & a_select2(v8, v7) = v12)) & ? [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (tptp_msub(v6, v7) = v8) | ~ (a_select3(v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & ~ (v19 = v18) & a_select3(v7, v13, v12) = v19 & a_select3(v7, v12, v13) = v18 & leq(v13, v5) = 0 & leq(v12, v5) = 0 & leq(n0, v13) = 0 & leq(n0, v12) = 0) | (v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & ~ (v19 = v18) & a_select3(v6, v13, v12) = v19 & a_select3(v6, v12, v13) = v18 & leq(v13, v5) = 0 & leq(v12, v5) = 0 & leq(n0, v13) = 0 & leq(n0, v12) = 0) | (a_select3(v8, v10, v9) = v16 & leq(v10, v5) = v15 & leq(v9, v5) = v13 & leq(n0, v10) = v14 & leq(n0, v9) = v12 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | v16 = v11)))) & ? [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (tptp_madd(v6, v7) = v8) | ~ (a_select3(v8, v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & ~ (v19 = v18) & a_select3(v7, v13, v12) = v19 & a_select3(v7, v12, v13) = v18 & leq(v13, v5) = 0 & leq(v12, v5) = 0 & leq(n0, v13) = 0 & leq(n0, v12) = 0) | (v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & ~ (v19 = v18) & a_select3(v6, v13, v12) = v19 & a_select3(v6, v12, v13) = v18 & leq(v13, v5) = 0 & leq(v12, v5) = 0 & leq(n0, v13) = 0 & leq(n0, v12) = 0) | (a_select3(v8, v10, v9) = v16 & leq(v10, v5) = v15 & leq(v9, v5) = v13 & leq(n0, v10) = v14 & leq(n0, v9) = v12 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | v16 = v11)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (tptp_update2(v7, v6, v8) = v9) | ~ (a_select2(v9, v5) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v13 = 0 & v12 = 0 & ~ (v14 = v8) & a_select2(v7, v11) = v14 & leq(v11, v6) = 0 & leq(n0, v11) = 0) | (leq(v5, v6) = v12 & leq(n0, v5) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (tptp_update3(v5, v6, v7, v8) = v9) | ~ (a_select3(v9, v6, v7) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v6 = v5 | ~ (tptp_update3(v10, v9, v8, v7) = v6) | ~ (tptp_update3(v10, v9, v8, v7) = v5)) & ? [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (inv(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, v5) = 0 & leq(v11, v5) = 0 & leq(n0, v12) = 0 & leq(n0, v11) = 0) | (a_select3(v7, v9, v8) = v15 & leq(v9, v5) = v14 & leq(v8, v5) = v12 & leq(n0, v9) = v13 & leq(n0, v8) = v11 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | v15 = v10)))) & ? [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (trans(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, v5) = 0 & leq(v11, v5) = 0 & leq(n0, v12) = 0 & leq(n0, v11) = 0) | (a_select3(v7, v9, v8) = v15 & leq(v9, v5) = v14 & leq(v8, v5) = v12 & leq(n0, v9) = v13 & leq(n0, v8) = v11 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | v15 = v10)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (tptp_update2(v5, v6, v7) = v8) | ~ (a_select2(v8, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (succ(v6) = v8) | ~ (succ(v5) = v7) | ~ (leq(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & leq(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (tptp_update2(v9, v8, v7) = v6) | ~ (tptp_update2(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (sum(v9, v8, v7) = v6) | ~ (sum(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (tptp_const_array2(v9, v8, v7) = v6) | ~ (tptp_const_array2(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (a_select3(v9, v8, v7) = v6) | ~ (a_select3(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (uniform_int_rnd(v6, v5) = v7) | ~ (leq(v7, v5) = v8) | ? [v9] : ( ~ (v9 = 0) & leq(n0, v5) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (succ(v6) = v7) | ~ (leq(v5, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & leq(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (succ(v6) = v7) | ~ (gt(v7, v5) = v8) | ? [v9] : ( ~ (v9 = 0) & leq(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (pred(v6) = v7) | ~ (leq(v5, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & gt(v6, v5) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (leq(v5, v7) = v8) | ~ (leq(v5, v6) = 0) | ? [v9] : ( ~ (v9 = 0) & leq(v6, v7) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (gt(v5, v7) = v8) | ~ (gt(v5, v6) = 0) | ? [v9] : ( ~ (v9 = 0) & gt(v6, v7) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (minus(v8, v7) = v6) | ~ (minus(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (plus(v8, v7) = v6) | ~ (plus(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (tptp_mmul(v8, v7) = v6) | ~ (tptp_mmul(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (tptp_msub(v8, v7) = v6) | ~ (tptp_msub(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (tptp_madd(v8, v7) = v6) | ~ (tptp_madd(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (dim(v8, v7) = v6) | ~ (dim(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (tptp_const_array1(v8, v7) = v6) | ~ (tptp_const_array1(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (a_select2(v8, v7) = v6) | ~ (a_select2(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (uniform_int_rnd(v8, v7) = v6) | ~ (uniform_int_rnd(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (geq(v8, v7) = v6) | ~ (geq(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (lt(v8, v7) = v6) | ~ (lt(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (leq(v8, v7) = v6) | ~ (leq(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (gt(v8, v7) = v6) | ~ (gt(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (succ(v6) = v8) | ~ (succ(v5) = v7) | ~ (leq(v7, v8) = 0) | leq(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = v5 | ~ (gt(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & leq(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = v5 | ~ (gt(v5, v6) = v7) | gt(v6, v5) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (succ(v5) = v6) | ~ (gt(v6, v5) = v7)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (geq(v5, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & leq(v6, v5) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (lt(v5, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & gt(v6, v5) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (inv(v7) = v6) | ~ (inv(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (trans(v7) = v6) | ~ (trans(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (succ(v7) = v6) | ~ (succ(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (pred(v7) = v6) | ~ (pred(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (minus(v5, v6) = v7) | ~ (leq(v7, v5) = 0) | leq(n0, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (uniform_int_rnd(v6, v5) = v7) | ? [v8] : ? [v9] : (leq(n0, v7) = v9 & leq(n0, v5) = v8 & ( ~ (v8 = 0) | v9 = 0))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (succ(v6) = v7) | ~ (gt(v7, v5) = 0) | leq(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (succ(v5) = v7) | ~ (leq(v7, v6) = 0) | gt(v6, v5) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (pred(v6) = v7) | ~ (leq(v5, v7) = 0) | gt(v6, v5) = 0) & ! [v5] : ! [v6] : (v6 = tptp_float_0_0 | ~ (sum(n0, tptp_minus_1, v5) = v6)) & ! [v5] : ! [v6] : (v6 = n0 | ~ (sum(n0, tptp_minus_1, v5) = v6)) & ! [v5] : ! [v6] : (v6 = 0 | ~ (leq(v5, v5) = v6)) & ! [v5] : ! [v6] : ( ~ (minus(v5, n1) = v6) | pred(v5) = v6) & ! [v5] : ! [v6] : ( ~ (plus(v5, n5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (succ(v10) = v6 & succ(v9) = v10 & succ(v8) = v9 & succ(v7) = v8 & succ(v5) = v7)) & ! [v5] : ! [v6] : ( ~ (plus(v5, n4) = v6) | ? [v7] : ? [v8] : ? [v9] : (succ(v9) = v6 & succ(v8) = v9 & succ(v7) = v8 & succ(v5) = v7)) & ! [v5] : ! [v6] : ( ~ (plus(v5, n3) = v6) | ? [v7] : ? [v8] : (succ(v8) = v6 & succ(v7) = v8 & succ(v5) = v7)) & ! [v5] : ! [v6] : ( ~ (plus(v5, n2) = v6) | ? [v7] : (succ(v7) = v6 & succ(v5) = v7)) & ! [v5] : ! [v6] : ( ~ (plus(v5, n1) = v6) | succ(v5) = v6) & ! [v5] : ! [v6] : ( ~ (plus(n5, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (succ(v10) = v6 & succ(v9) = v10 & succ(v8) = v9 & succ(v7) = v8 & succ(v5) = v7)) & ! [v5] : ! [v6] : ( ~ (plus(n4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : (succ(v9) = v6 & succ(v8) = v9 & succ(v7) = v8 & succ(v5) = v7)) & ! [v5] : ! [v6] : ( ~ (plus(n3, v5) = v6) | ? [v7] : ? [v8] : (succ(v8) = v6 & succ(v7) = v8 & succ(v5) = v7)) & ! [v5] : ! [v6] : ( ~ (plus(n2, v5) = v6) | ? [v7] : (succ(v7) = v6 & succ(v5) = v7)) & ! [v5] : ! [v6] : ( ~ (plus(n1, v5) = v6) | succ(v5) = v6) & ! [v5] : ! [v6] : ( ~ (a_select3(q, v5, tptp_sum_index) = v6) | ? [v7] : ? [v8] : ? [v9] : (sum(n0, n4, v6) = v9 & leq(v5, v1) = v8 & leq(n0, v5) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | v9 = n1))) & ! [v5] : ! [v6] : ( ~ (succ(v5) = v6) | pred(v6) = v5) & ! [v5] : ! [v6] : ( ~ (pred(v5) = v6) | succ(v6) = v5) & ! [v5] : ! [v6] : ( ~ (geq(v5, v6) = 0) | leq(v6, v5) = 0) & ! [v5] : ! [v6] : ( ~ (lt(v5, v6) = 0) | gt(v6, v5) = 0) & ! [v5] : ! [v6] : ( ~ (gt(v6, v5) = 0) | leq(v5, v6) = 0) & ! [v5] : (v5 = n5 | v5 = n4 | v5 = n3 | v5 = n2 | v5 = n1 | v5 = n0 | ~ (leq(v5, n5) = 0) | ? [v6] : ( ~ (v6 = 0) & leq(n0, v5) = v6)) & ! [v5] : (v5 = n4 | v5 = n3 | v5 = n2 | v5 = n1 | v5 = n0 | ~ (leq(v5, n4) = 0) | ? [v6] : ( ~ (v6 = 0) & leq(n0, v5) = v6)) & ! [v5] : (v5 = n3 | v5 = n2 | v5 = n1 | v5 = n0 | ~ (leq(v5, n3) = 0) | ? [v6] : ( ~ (v6 = 0) & leq(n0, v5) = v6)) & ! [v5] : (v5 = n2 | v5 = n1 | v5 = n0 | ~ (leq(v5, n2) = 0) | ? [v6] : ( ~ (v6 = 0) & leq(n0, v5) = v6)) & ! [v5] : (v5 = n1 | v5 = n0 | ~ (leq(v5, n1) = 0) | ? [v6] : ( ~ (v6 = 0) & leq(n0, v5) = v6)) & ! [v5] : (v5 = n0 | ~ (leq(n0, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & leq(v5, n0) = v6)) & ! [v5] : ~ (gt(v5, v5) = 0)) % 27.31/7.71 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 27.31/7.71 | (1) ~ (all_0_0_0 = n1) & ~ (def = use) & sum(n0, n4, all_0_1_1) = all_0_0_0 & sum(n0, n4, all_0_4_4) = n1 & a_select3(q, all_0_2_2, tptp_sum_index) = all_0_1_1 & a_select3(q, pv10, tptp_sum_index) = all_0_4_4 & succ(n4) = n5 & succ(n3) = n4 & succ(n2) = n3 & succ(n1) = n2 & succ(tptp_minus_1) = n0 & succ(n0) = n1 & pred(pv10) = all_0_3_3 & leq(all_0_2_2, pv10) = 0 & leq(pv10, n135299) = 0 & leq(n0, all_0_2_2) = 0 & leq(n0, pv10) = 0 & 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 = 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 = 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] : ( ~ (a_select3(q, v0, tptp_sum_index) = v1) | ? [v2] : ? [v3] : ? [v4] : (sum(n0, n4, v1) = v4 & leq(v0, all_0_3_3) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = n1))) & ! [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] : ~ (gt(v0, v0) = 0) % 27.62/7.74 | % 27.62/7.74 | Applying alpha-rule on (1) yields: % 27.62/7.74 | (2) ! [v0] : ! [v1] : ( ~ (pred(v0) = v1) | succ(v1) = v0) % 27.62/7.74 | (3) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | pred(v1) = v0) % 27.62/7.74 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) % 27.62/7.74 | (5) ! [v0] : ! [v1] : ( ~ (plus(v0, n2) = v1) | ? [v2] : (succ(v2) = v1 & succ(v0) = v2)) % 27.62/7.74 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (succ(v1) = v2) | ~ (leq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & leq(v0, v1) = v4)) % 27.62/7.74 | (7) gt(n2, n1) = 0 % 27.62/7.74 | (8) gt(n135299, n1) = 0 % 27.62/7.74 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (succ(v1) = v2) | ~ (gt(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & leq(v0, v1) = v4)) % 27.62/7.74 | (10) succ(n2) = n3 % 27.62/7.74 | (11) a_select3(q, pv10, tptp_sum_index) = all_0_4_4 % 27.62/7.74 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ (gt(v2, v0) = 0) | leq(v0, v1) = 0) % 27.62/7.74 | (13) gt(n5, n1) = 0 % 27.62/7.74 | (14) gt(n135299, n3) = 0 % 27.62/7.74 | (15) gt(n4, n0) = 0 % 27.62/7.74 | (16) ! [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))))) % 27.62/7.74 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (lt(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & gt(v1, v0) = v3)) % 27.62/7.74 | (18) ! [v0] : (v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n5) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(n0, v0) = v1)) % 27.62/7.75 | (19) ? [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)))) % 27.62/7.75 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1) | ~ (tptp_mmul(v3, v2) = v0)) % 27.62/7.75 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) % 27.62/7.75 | (22) ? [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)))) % 27.62/7.75 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (geq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v1, v0) = v3)) % 27.62/7.75 | (24) leq(n0, pv10) = 0 % 27.62/7.75 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) % 27.62/7.75 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (gt(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) % 27.62/7.75 | (27) gt(n1, tptp_minus_1) = 0 % 27.62/7.75 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (succ(v1) = v3) | ~ (succ(v0) = v2) | ~ (leq(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & leq(v0, v1) = v5)) % 27.62/7.75 | (29) gt(n5, n2) = 0 % 27.62/7.75 | (30) true % 27.62/7.75 | (31) ? [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)))) % 27.62/7.75 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) % 27.62/7.75 | (33) ! [v0] : ! [v1] : ( ~ (plus(n3, v0) = v1) | ? [v2] : ? [v3] : (succ(v3) = v1 & succ(v2) = v3 & succ(v0) = v2)) % 27.62/7.75 | (34) ! [v0] : ! [v1] : (v1 = tptp_float_0_0 | ~ (sum(n0, tptp_minus_1, v0) = v1)) % 27.62/7.75 | (35) gt(n2, n0) = 0 % 27.62/7.75 | (36) ! [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)))) % 27.62/7.75 | (37) ? [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)))) % 27.62/7.76 | (38) gt(n4, n3) = 0 % 27.62/7.76 | (39) pred(pv10) = all_0_3_3 % 27.62/7.76 | (40) ! [v0] : ~ (gt(v0, v0) = 0) % 27.62/7.76 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) | ~ (sum(v4, v3, v2) = v0)) % 27.62/7.76 | (42) gt(n1, n0) = 0 % 27.62/7.76 | (43) ! [v0] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(v0, n0) = v1)) % 27.62/7.76 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (trans(v2) = v1) | ~ (trans(v2) = v0)) % 27.62/7.76 | (45) gt(n0, tptp_minus_1) = 0 % 27.62/7.76 | (46) gt(n135299, n5) = 0 % 27.75/7.76 | (47) gt(n135299, n2) = 0 % 27.75/7.76 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) = v0)) % 27.75/7.76 | (49) succ(n1) = n2 % 27.75/7.76 | (50) gt(n3, n2) = 0 % 27.75/7.76 | (51) sum(n0, n4, all_0_4_4) = n1 % 27.75/7.76 | (52) ! [v0] : ! [v1] : ( ~ (gt(v1, v0) = 0) | leq(v0, v1) = 0) % 27.75/7.76 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~ (tptp_update3(v5, v4, v3, v2) = v0)) % 27.75/7.76 | (54) ! [v0] : (v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n3) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(n0, v0) = v1)) % 27.75/7.76 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (uniform_int_rnd(v1, v0) = v2) | ~ (leq(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & leq(n0, v0) = v4)) % 27.75/7.76 | (56) ? [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)))) % 27.75/7.76 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (minus(v0, v1) = v2) | ~ (leq(v2, v0) = 0) | leq(n0, v1) = 0) % 27.75/7.76 | (58) ! [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))))) % 27.75/7.76 | (59) gt(n3, tptp_minus_1) = 0 % 27.75/7.76 | (60) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) % 27.75/7.76 | (61) leq(pv10, n135299) = 0 % 27.75/7.76 | (62) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0)) % 27.75/7.76 | (63) succ(n0) = n1 % 27.75/7.76 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (pred(v1) = v2) | ~ (leq(v0, v2) = 0) | gt(v1, v0) = 0) % 27.75/7.76 | (65) succ(tptp_minus_1) = n0 % 27.75/7.76 | (66) ? [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)))) % 27.75/7.77 | (67) succ(n3) = n4 % 27.75/7.77 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) | ~ (tptp_const_array2(v4, v3, v2) = v0)) % 27.75/7.77 | (69) gt(n4, n2) = 0 % 27.75/7.77 | (70) ~ (all_0_0_0 = n1) % 27.75/7.77 | (71) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (succ(v0) = v1) | ~ (gt(v1, v0) = v2)) % 27.75/7.77 | (72) gt(n3, n0) = 0 % 27.75/7.77 | (73) leq(n0, all_0_2_2) = 0 % 27.75/7.77 | (74) ! [v0] : ! [v1] : ( ~ (plus(n2, v0) = v1) | ? [v2] : (succ(v2) = v1 & succ(v0) = v2)) % 27.75/7.77 | (75) gt(n135299, n0) = 0 % 27.75/7.77 | (76) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (gt(v0, v1) = v2) | gt(v1, v0) = 0) % 27.75/7.77 | (77) gt(n135299, n4) = 0 % 27.75/7.77 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (gt(v0, v2) = v3) | ~ (gt(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & gt(v1, v2) = v4)) % 27.75/7.77 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2) = v0)) % 27.75/7.77 | (80) ! [v0] : ! [v1] : ( ~ (plus(n4, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (succ(v4) = v1 & succ(v3) = v4 & succ(v2) = v3 & succ(v0) = v2)) % 27.75/7.77 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3, v2) = v0)) % 27.75/7.77 | (82) ? [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)) % 27.75/7.77 | (83) ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1)) % 27.75/7.77 | (84) ! [v0] : ! [v1] : ( ~ (lt(v0, v1) = 0) | gt(v1, v0) = 0) % 27.75/7.77 | (85) ! [v0] : ! [v1] : ( ~ (plus(v0, n1) = v1) | succ(v0) = v1) % 27.75/7.77 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3, v2) = v0)) % 27.75/7.77 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & leq(v1, v2) = v4)) % 27.75/7.77 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (tptp_update2(v0, v1, v2) = v3) | ~ (a_select2(v3, v1) = v4)) % 27.75/7.77 | (89) gt(n135299, tptp_minus_1) = 0 % 27.75/7.77 | (90) gt(n5, n3) = 0 % 27.75/7.77 | (91) gt(n5, tptp_minus_1) = 0 % 27.75/7.77 | (92) gt(n4, n1) = 0 % 27.75/7.77 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) % 27.75/7.77 | (94) ! [v0] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n2) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(n0, v0) = v1)) % 27.75/7.77 | (95) ! [v0] : (v0 = n1 | v0 = n0 | ~ (leq(v0, n1) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(n0, v0) = v1)) % 27.75/7.77 | (96) ? [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)))) % 27.75/7.77 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~ (dim(v3, v2) = v0)) % 27.75/7.77 | (98) ! [v0] : ! [v1] : (v1 = n0 | ~ (sum(n0, tptp_minus_1, v0) = v1)) % 27.75/7.77 | (99) ! [v0] : ! [v1] : ( ~ (plus(v0, n3) = v1) | ? [v2] : ? [v3] : (succ(v3) = v1 & succ(v2) = v3 & succ(v0) = v2)) % 27.75/7.77 | (100) ! [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)) % 27.75/7.77 | (101) gt(n5, n4) = 0 % 27.75/7.77 | (102) ! [v0] : ! [v1] : ( ~ (minus(v0, n1) = v1) | pred(v0) = v1) % 27.75/7.77 | (103) gt(n3, n1) = 0 % 27.75/7.77 | (104) sum(n0, n4, all_0_1_1) = all_0_0_0 % 27.75/7.77 | (105) ? [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)))) % 27.75/7.78 | (106) gt(n4, tptp_minus_1) = 0 % 27.75/7.78 | (107) a_select3(q, all_0_2_2, tptp_sum_index) = all_0_1_1 % 27.75/7.78 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) = v1) | ~ (tptp_update2(v4, v3, v2) = v0)) % 27.75/7.78 | (109) gt(n5, n0) = 0 % 27.75/7.78 | (110) ! [v0] : (v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n4) = 0) | ? [v1] : ( ~ (v1 = 0) & leq(n0, v0) = v1)) % 27.75/7.78 | (111) gt(n2, tptp_minus_1) = 0 % 27.75/7.78 | (112) ! [v0] : ! [v1] : ( ~ (a_select3(q, v0, tptp_sum_index) = v1) | ? [v2] : ? [v3] : ? [v4] : (sum(n0, n4, v1) = v4 & leq(v0, all_0_3_3) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = n1))) % 27.75/7.78 | (113) succ(n4) = n5 % 27.75/7.78 | (114) ! [v0] : ! [v1] : ( ~ (plus(v0, n4) = v1) | ? [v2] : ? [v3] : ? [v4] : (succ(v4) = v1 & succ(v3) = v4 & succ(v2) = v3 & succ(v0) = v2)) % 27.75/7.78 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) % 27.75/7.78 | (116) ~ (def = use) % 27.75/7.78 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 27.75/7.78 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) % 27.75/7.78 | (119) leq(all_0_2_2, pv10) = 0 % 27.75/7.78 | (120) ! [v0] : ! [v1] : ( ~ (plus(n1, v0) = v1) | succ(v0) = v1) % 27.75/7.78 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (pred(v1) = v2) | ~ (leq(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) % 27.75/7.78 | (122) ! [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)) % 27.75/7.78 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (succ(v1) = v3) | ~ (succ(v0) = v2) | ~ (leq(v2, v3) = 0) | leq(v0, v1) = 0) % 27.75/7.78 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) % 27.75/7.78 | (125) ! [v0] : ! [v1] : ( ~ (geq(v0, v1) = 0) | leq(v1, v0) = 0) % 27.75/7.78 | (126) ! [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)))) % 27.75/7.78 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (tptp_update3(v0, v1, v2, v3) = v4) | ~ (a_select3(v4, v1, v2) = v5)) % 27.75/7.78 | (128) ? [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)) % 27.75/7.78 | (129) ! [v0] : ! [v1] : ! [v2] : ( ~ (uniform_int_rnd(v1, v0) = v2) | ? [v3] : ? [v4] : (leq(n0, v2) = v4 & leq(n0, v0) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 27.75/7.78 | (130) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v0) = v2) | ~ (leq(v2, v1) = 0) | gt(v1, v0) = 0) % 27.75/7.78 | % 27.75/7.78 | Instantiating formula (41) with n0, n4, all_0_4_4, n1, all_0_0_0 and discharging atoms sum(n0, n4, all_0_4_4) = n1, yields: % 27.75/7.78 | (131) all_0_0_0 = n1 | ~ (sum(n0, n4, all_0_4_4) = all_0_0_0) % 27.75/7.78 | % 27.75/7.78 | Instantiating formula (79) with q, pv10, tptp_sum_index, all_0_4_4, all_0_1_1 and discharging atoms a_select3(q, pv10, tptp_sum_index) = all_0_4_4, yields: % 27.75/7.78 | (132) all_0_1_1 = all_0_4_4 | ~ (a_select3(q, pv10, tptp_sum_index) = all_0_1_1) % 27.75/7.78 | % 27.75/7.78 | Instantiating formula (112) with all_0_1_1, all_0_2_2 and discharging atoms a_select3(q, all_0_2_2, tptp_sum_index) = all_0_1_1, yields: % 27.75/7.78 | (133) ? [v0] : ? [v1] : ? [v2] : (sum(n0, n4, all_0_1_1) = v2 & leq(all_0_2_2, all_0_3_3) = v1 & leq(n0, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = n1)) % 27.75/7.78 | % 27.75/7.78 | Instantiating formula (112) with all_0_4_4, pv10 and discharging atoms a_select3(q, pv10, tptp_sum_index) = all_0_4_4, yields: % 27.75/7.78 | (134) ? [v0] : ? [v1] : ? [v2] : (sum(n0, n4, all_0_4_4) = v2 & leq(pv10, all_0_3_3) = v1 & leq(n0, pv10) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = n1)) % 27.75/7.78 | % 27.75/7.78 | Instantiating (134) with all_41_0_17, all_41_1_18, all_41_2_19 yields: % 27.75/7.78 | (135) sum(n0, n4, all_0_4_4) = all_41_0_17 & leq(pv10, all_0_3_3) = all_41_1_18 & leq(n0, pv10) = all_41_2_19 & ( ~ (all_41_1_18 = 0) | ~ (all_41_2_19 = 0) | all_41_0_17 = n1) % 27.75/7.79 | % 27.75/7.79 | Applying alpha-rule on (135) yields: % 27.75/7.79 | (136) sum(n0, n4, all_0_4_4) = all_41_0_17 % 27.75/7.79 | (137) leq(pv10, all_0_3_3) = all_41_1_18 % 27.75/7.79 | (138) leq(n0, pv10) = all_41_2_19 % 27.75/7.79 | (139) ~ (all_41_1_18 = 0) | ~ (all_41_2_19 = 0) | all_41_0_17 = n1 % 27.75/7.79 | % 27.75/7.79 | Instantiating (133) with all_43_0_20, all_43_1_21, all_43_2_22 yields: % 27.75/7.79 | (140) sum(n0, n4, all_0_1_1) = all_43_0_20 & leq(all_0_2_2, all_0_3_3) = all_43_1_21 & leq(n0, all_0_2_2) = all_43_2_22 & ( ~ (all_43_1_21 = 0) | ~ (all_43_2_22 = 0) | all_43_0_20 = n1) % 27.75/7.79 | % 27.75/7.79 | Applying alpha-rule on (140) yields: % 27.75/7.79 | (141) sum(n0, n4, all_0_1_1) = all_43_0_20 % 27.75/7.79 | (142) leq(all_0_2_2, all_0_3_3) = all_43_1_21 % 27.75/7.79 | (143) leq(n0, all_0_2_2) = all_43_2_22 % 27.75/7.79 | (144) ~ (all_43_1_21 = 0) | ~ (all_43_2_22 = 0) | all_43_0_20 = n1 % 27.75/7.79 | % 27.75/7.79 +-Applying beta-rule and splitting (131), into two cases. % 27.75/7.79 |-Branch one: % 27.75/7.79 | (145) ~ (sum(n0, n4, all_0_4_4) = all_0_0_0) % 27.75/7.79 | % 27.75/7.79 | Instantiating formula (41) with n0, n4, all_0_1_1, all_43_0_20, all_0_0_0 and discharging atoms sum(n0, n4, all_0_1_1) = all_43_0_20, sum(n0, n4, all_0_1_1) = all_0_0_0, yields: % 27.75/7.79 | (146) all_43_0_20 = all_0_0_0 % 27.75/7.79 | % 27.75/7.79 | Instantiating formula (41) with n0, n4, all_0_4_4, all_41_0_17, n1 and discharging atoms sum(n0, n4, all_0_4_4) = all_41_0_17, sum(n0, n4, all_0_4_4) = n1, yields: % 27.75/7.79 | (147) all_41_0_17 = n1 % 27.75/7.79 | % 27.75/7.79 | Instantiating formula (117) with n0, all_0_2_2, all_43_2_22, 0 and discharging atoms leq(n0, all_0_2_2) = all_43_2_22, leq(n0, all_0_2_2) = 0, yields: % 27.75/7.79 | (148) all_43_2_22 = 0 % 27.75/7.79 | % 27.75/7.79 | Using (104) and (145) yields: % 27.75/7.79 | (149) ~ (all_0_1_1 = all_0_4_4) % 27.75/7.79 | % 27.75/7.79 | Using (136) and (145) yields: % 27.75/7.79 | (150) ~ (all_41_0_17 = all_0_0_0) % 27.75/7.79 | % 27.75/7.79 | Equations (147) can reduce 150 to: % 27.75/7.79 | (151) ~ (all_0_0_0 = n1) % 27.75/7.79 | % 27.75/7.79 | Simplifying 151 yields: % 27.75/7.79 | (70) ~ (all_0_0_0 = n1) % 27.75/7.79 | % 27.75/7.79 +-Applying beta-rule and splitting (144), into two cases. % 27.75/7.79 |-Branch one: % 27.75/7.79 | (153) ~ (all_43_1_21 = 0) % 27.75/7.79 | % 27.75/7.79 | Instantiating formula (121) with all_43_1_21, all_0_3_3, pv10, all_0_2_2 and discharging atoms pred(pv10) = all_0_3_3, leq(all_0_2_2, all_0_3_3) = all_43_1_21, yields: % 27.75/7.79 | (154) all_43_1_21 = 0 | ? [v0] : ( ~ (v0 = 0) & gt(pv10, all_0_2_2) = v0) % 27.75/7.79 | % 27.75/7.79 | Instantiating formula (87) with all_43_1_21, all_0_3_3, pv10, all_0_2_2 and discharging atoms leq(all_0_2_2, all_0_3_3) = all_43_1_21, leq(all_0_2_2, pv10) = 0, yields: % 27.75/7.79 | (155) all_43_1_21 = 0 | ? [v0] : ( ~ (v0 = 0) & leq(pv10, all_0_3_3) = v0) % 27.75/7.79 | % 27.75/7.79 +-Applying beta-rule and splitting (155), into two cases. % 27.75/7.79 |-Branch one: % 27.75/7.79 | (156) all_43_1_21 = 0 % 27.75/7.79 | % 27.75/7.79 | Equations (156) can reduce 153 to: % 27.75/7.79 | (157) $false % 27.75/7.79 | % 27.75/7.79 |-The branch is then unsatisfiable % 27.75/7.79 |-Branch two: % 27.75/7.79 | (153) ~ (all_43_1_21 = 0) % 27.75/7.79 | (159) ? [v0] : ( ~ (v0 = 0) & leq(pv10, all_0_3_3) = v0) % 27.75/7.79 | % 27.75/7.79 +-Applying beta-rule and splitting (154), into two cases. % 27.75/7.79 |-Branch one: % 27.75/7.79 | (156) all_43_1_21 = 0 % 27.75/7.79 | % 27.75/7.79 | Equations (156) can reduce 153 to: % 27.75/7.79 | (157) $false % 27.75/7.79 | % 27.75/7.79 |-The branch is then unsatisfiable % 27.75/7.79 |-Branch two: % 27.75/7.79 | (153) ~ (all_43_1_21 = 0) % 27.75/7.79 | (163) ? [v0] : ( ~ (v0 = 0) & gt(pv10, all_0_2_2) = v0) % 27.75/7.79 | % 27.75/7.79 | Instantiating (163) with all_141_0_32 yields: % 27.75/7.79 | (164) ~ (all_141_0_32 = 0) & gt(pv10, all_0_2_2) = all_141_0_32 % 27.75/7.79 | % 27.75/7.79 | Applying alpha-rule on (164) yields: % 27.75/7.79 | (165) ~ (all_141_0_32 = 0) % 27.75/7.79 | (166) gt(pv10, all_0_2_2) = all_141_0_32 % 27.75/7.79 | % 27.75/7.79 | Instantiating formula (26) with all_141_0_32, pv10, all_0_2_2 and discharging atoms gt(pv10, all_0_2_2) = all_141_0_32, yields: % 27.75/7.79 | (167) all_141_0_32 = 0 | all_0_2_2 = pv10 | ? [v0] : ( ~ (v0 = 0) & leq(all_0_2_2, pv10) = v0) % 27.75/7.79 | % 27.75/7.79 +-Applying beta-rule and splitting (167), into two cases. % 27.75/7.79 |-Branch one: % 27.75/7.79 | (168) all_141_0_32 = 0 % 27.75/7.79 | % 27.75/7.79 | Equations (168) can reduce 165 to: % 27.75/7.79 | (157) $false % 27.75/7.79 | % 27.75/7.79 |-The branch is then unsatisfiable % 27.75/7.79 |-Branch two: % 27.75/7.79 | (165) ~ (all_141_0_32 = 0) % 27.75/7.79 | (171) all_0_2_2 = pv10 | ? [v0] : ( ~ (v0 = 0) & leq(all_0_2_2, pv10) = v0) % 27.75/7.79 | % 27.75/7.79 +-Applying beta-rule and splitting (171), into two cases. % 27.75/7.79 |-Branch one: % 27.75/7.79 | (172) all_0_2_2 = pv10 % 27.75/7.79 | % 27.75/7.79 | From (172) and (107) follows: % 27.75/7.79 | (173) a_select3(q, pv10, tptp_sum_index) = all_0_1_1 % 27.75/7.79 | % 27.75/7.79 +-Applying beta-rule and splitting (132), into two cases. % 27.75/7.79 |-Branch one: % 27.75/7.79 | (174) ~ (a_select3(q, pv10, tptp_sum_index) = all_0_1_1) % 27.75/7.79 | % 27.75/7.79 | Using (173) and (174) yields: % 27.75/7.79 | (175) $false % 27.75/7.79 | % 27.75/7.79 |-The branch is then unsatisfiable % 27.75/7.79 |-Branch two: % 27.75/7.79 | (173) a_select3(q, pv10, tptp_sum_index) = all_0_1_1 % 27.75/7.79 | (177) all_0_1_1 = all_0_4_4 % 27.75/7.79 | % 27.75/7.80 | Equations (177) can reduce 149 to: % 27.75/7.80 | (157) $false % 27.75/7.80 | % 27.75/7.80 |-The branch is then unsatisfiable % 27.75/7.80 |-Branch two: % 27.75/7.80 | (179) ~ (all_0_2_2 = pv10) % 27.75/7.80 | (180) ? [v0] : ( ~ (v0 = 0) & leq(all_0_2_2, pv10) = v0) % 27.75/7.80 | % 27.75/7.80 | Instantiating (180) with all_347_0_63 yields: % 27.75/7.80 | (181) ~ (all_347_0_63 = 0) & leq(all_0_2_2, pv10) = all_347_0_63 % 27.75/7.80 | % 27.75/7.80 | Applying alpha-rule on (181) yields: % 27.75/7.80 | (182) ~ (all_347_0_63 = 0) % 27.75/7.80 | (183) leq(all_0_2_2, pv10) = all_347_0_63 % 27.75/7.80 | % 27.75/7.80 | Instantiating formula (117) with all_0_2_2, pv10, all_347_0_63, 0 and discharging atoms leq(all_0_2_2, pv10) = all_347_0_63, leq(all_0_2_2, pv10) = 0, yields: % 27.75/7.80 | (184) all_347_0_63 = 0 % 27.75/7.80 | % 27.75/7.80 | Equations (184) can reduce 182 to: % 27.75/7.80 | (157) $false % 27.75/7.80 | % 27.75/7.80 |-The branch is then unsatisfiable % 27.75/7.80 |-Branch two: % 27.75/7.80 | (156) all_43_1_21 = 0 % 27.75/7.80 | (187) ~ (all_43_2_22 = 0) | all_43_0_20 = n1 % 27.75/7.80 | % 27.75/7.80 +-Applying beta-rule and splitting (187), into two cases. % 27.75/7.80 |-Branch one: % 27.75/7.80 | (188) ~ (all_43_2_22 = 0) % 27.75/7.80 | % 27.75/7.80 | Equations (148) can reduce 188 to: % 27.75/7.80 | (157) $false % 27.75/7.80 | % 27.75/7.80 |-The branch is then unsatisfiable % 27.75/7.80 |-Branch two: % 27.75/7.80 | (148) all_43_2_22 = 0 % 27.75/7.80 | (191) all_43_0_20 = n1 % 27.75/7.80 | % 27.75/7.80 | Combining equations (191,146) yields a new equation: % 27.75/7.80 | (192) all_0_0_0 = n1 % 27.75/7.80 | % 27.75/7.80 | Equations (192) can reduce 70 to: % 27.75/7.80 | (157) $false % 27.75/7.80 | % 27.75/7.80 |-The branch is then unsatisfiable % 27.75/7.80 |-Branch two: % 27.75/7.80 | (194) sum(n0, n4, all_0_4_4) = all_0_0_0 % 27.75/7.80 | (192) all_0_0_0 = n1 % 27.75/7.80 | % 27.75/7.80 | Equations (192) can reduce 70 to: % 27.75/7.80 | (157) $false % 27.75/7.80 | % 27.75/7.80 |-The branch is then unsatisfiable % 27.75/7.80 % SZS output end Proof for theBenchmark % 27.75/7.80 % 27.75/7.80 7214ms %------------------------------------------------------------------------------