%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : NUM924+1 : TPTP v8.1.0. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n025.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 : Mon Jul 18 08:49:40 EDT 2022 % Result : Theorem 6.11s 1.95s % Output : Proof 9.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM924+1 : TPTP v8.1.0. Released v5.3.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n025.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Wed Jul 6 00:32:12 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.58 ____ _ % 0.19/0.58 ___ / __ \_____(_)___ ________ __________ % 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.58 % 0.19/0.58 A Theorem Prover for First-Order Logic % 0.61/0.58 (ePrincess v.1.0) % 0.61/0.58 % 0.61/0.58 (c) Philipp Rümmer, 2009-2015 % 0.61/0.58 (c) Peter Backeman, 2014-2015 % 0.61/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.61/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.61/0.58 Bug reports to peter@backeman.se % 0.61/0.58 % 0.61/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.61/0.58 % 0.61/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.75/1.02 Prover 0: Preprocessing ... % 4.39/1.58 Prover 0: Warning: ignoring some quantifiers % 4.73/1.61 Prover 0: Constructing countermodel ... % 6.11/1.95 Prover 0: proved (1321ms) % 6.11/1.95 % 6.11/1.95 No countermodel exists, formula is valid % 6.11/1.95 % SZS status Theorem for theBenchmark % 6.11/1.95 % 6.11/1.95 Generating proof ... Warning: ignoring some quantifiers % 9.12/2.62 found it (size 13) % 9.12/2.62 % 9.12/2.62 % SZS output start Proof for theBenchmark % 9.12/2.62 Assumed formulas after preprocessing and simplification: % 9.12/2.62 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (power_power_nat(zero_zero_nat, v8) = zero_zero_nat & power_power_nat(one_one_nat, v8) = one_one_nat & number_number_of_nat(v1) = v8 & number_number_of_nat(v0) = one_one_nat & number_number_of_nat(pls) = zero_zero_nat & bit0(v1) = v2 & bit0(v0) = v1 & bit1(pls) = v0 & plus_plus_nat(one_one_nat, one_one_nat) = v8 & times_times_int(v5, v10) = v6 & times_times_int(v5, zero_zero_int) = v7 & times_times_int(v5, t) = v6 & times_times_int(v3, m) = v4 & number_number_of_int(v2) = v3 & number_number_of_int(pls) = zero_zero_int & power_power_int(s, v8) = v9 & power_power_int(one_one_int, v8) = one_one_int & power_power_int(zero_zero_int, v8) = zero_zero_int & plus_plus_int(v9, one_one_int) = v6 & plus_plus_int(v4, one_one_int) = v5 & twoSqu526106917sum2sq(v6) & zprime(v5) & ord_less_eq_int(pls, pls) & ord_less_int(v6, v7) & ord_less_int(zero_zero_int, v5) & ord_less_int(t, v5) & ord_less_int(t, one_one_int) & ord_less_int(t, zero_zero_int) & ~ ord_less_eq_int(one_one_int, t) & ~ ord_less_int(v6, zero_zero_int) & ~ ord_less_int(zero_zero_int, zero_zero_int) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (times_times_nat(v14, v13) = v16) | ~ (times_times_nat(v14, v12) = v15) | ~ (number_number_of_nat(v11) = v14) | ~ (plus_plus_nat(v15, v16) = v17) | ? [v18] : (times_times_nat(v14, v18) = v17 & plus_plus_nat(v12, v13) = v18)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (times_times_nat(v12, v14) = v16) | ~ (times_times_nat(v11, v14) = v15) | ~ (number_number_of_nat(v13) = v14) | ~ (plus_plus_nat(v15, v16) = v17) | ? [v18] : (times_times_nat(v18, v14) = v17 & plus_plus_nat(v11, v12) = v18)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (times_times_int(v15, v13) = v16) | ~ (times_times_int(v14, v16) = v17) | ~ (number_number_of_int(v12) = v15) | ~ (number_number_of_int(v11) = v14) | ? [v18] : ? [v19] : (times_times_int(v19, v13) = v17 & times_times_int(v11, v12) = v18 & number_number_of_int(v18) = v19)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (times_times_int(v14, v13) = v16) | ~ (times_times_int(v14, v12) = v15) | ~ (number_number_of_int(v11) = v14) | ~ (plus_plus_int(v15, v16) = v17) | ? [v18] : (times_times_int(v14, v18) = v17 & plus_plus_int(v12, v13) = v18)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (times_times_int(v12, v14) = v16) | ~ (times_times_int(v11, v14) = v15) | ~ (number_number_of_int(v13) = v14) | ~ (plus_plus_int(v15, v16) = v17) | ? [v18] : (times_times_int(v18, v14) = v17 & plus_plus_int(v11, v12) = v18)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (times_times_nat(v14, v15) = v16) | ~ (number_number_of_nat(v13) = v15) | ~ (plus_plus_nat(v11, v12) = v14) | ? [v17] : ? [v18] : (times_times_nat(v12, v15) = v18 & times_times_nat(v11, v15) = v17 & plus_plus_nat(v17, v18) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (times_times_nat(v14, v15) = v16) | ~ (number_number_of_nat(v11) = v14) | ~ (plus_plus_nat(v12, v13) = v15) | ? [v17] : ? [v18] : (times_times_nat(v14, v13) = v18 & times_times_nat(v14, v12) = v17 & plus_plus_nat(v17, v18) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (times_times_int(v15, v13) = v16) | ~ (times_times_int(v11, v12) = v14) | ~ (number_number_of_int(v14) = v15) | ? [v17] : ? [v18] : ? [v19] : (times_times_int(v18, v13) = v19 & times_times_int(v17, v19) = v16 & number_number_of_int(v12) = v18 & number_number_of_int(v11) = v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (times_times_int(v14, v15) = v16) | ~ (number_number_of_int(v13) = v15) | ~ (plus_plus_int(v11, v12) = v14) | ? [v17] : ? [v18] : (times_times_int(v12, v15) = v18 & times_times_int(v11, v15) = v17 & plus_plus_int(v17, v18) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (times_times_int(v14, v15) = v16) | ~ (number_number_of_int(v11) = v14) | ~ (plus_plus_int(v12, v13) = v15) | ? [v17] : ? [v18] : (times_times_int(v14, v13) = v18 & times_times_int(v14, v12) = v17 & plus_plus_int(v17, v18) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (times_times_int(v14, v15) = v16) | ~ (power_power_int(v11, v13) = v15) | ~ (power_power_int(v11, v12) = v14) | ? [v17] : (plus_plus_nat(v12, v13) = v17 & power_power_int(v11, v17) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (times_times_int(v12, v13) = v15) | ~ (times_times_int(v11, v13) = v14) | ~ (plus_plus_int(v14, v15) = v16) | ? [v17] : (times_times_int(v17, v13) = v16 & plus_plus_int(v11, v12) = v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (times_times_int(v11, v13) = v15) | ~ (times_times_int(v11, v12) = v14) | ~ (plus_plus_int(v14, v15) = v16) | ? [v17] : (times_times_int(v11, v17) = v16 & plus_plus_int(v12, v13) = v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (plus_plus_int(v14, v12) = v16) | ~ (plus_plus_int(v13, v11) = v15) | ~ ord_less_eq_int(v11, v12) | ~ ord_less_int(v13, v14) | ord_less_int(v15, v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (number_number_of_nat(v12) = v13) | ~ (number_number_of_nat(v11) = v14) | ~ (plus_plus_nat(v13, v14) = v15) | ~ ord_less_int(v12, pls)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (number_number_of_nat(v12) = v13) | ~ (number_number_of_nat(v11) = v14) | ~ (plus_plus_nat(v13, v14) = v15) | ~ ord_less_int(v11, pls) | ord_less_int(v12, pls)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = zero_zero_int | ~ (times_times_int(v12, v12) = v14) | ~ (times_times_int(v11, v11) = v13) | ~ (plus_plus_int(v13, v14) = v15) | ~ ord_less_eq_int(v15, zero_zero_int)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = zero_zero_int | ~ (power_power_int(v12, v8) = v14) | ~ (power_power_int(v11, v8) = v13) | ~ (plus_plus_int(v13, v14) = v15) | ord_less_int(zero_zero_int, v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v11 = zero_zero_int | ~ (times_times_int(v12, v12) = v14) | ~ (times_times_int(v11, v11) = v13) | ~ (plus_plus_int(v13, v14) = v15) | ~ ord_less_eq_int(v15, zero_zero_int)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v11 = zero_zero_int | ~ (power_power_int(v12, v8) = v14) | ~ (power_power_int(v11, v8) = v13) | ~ (plus_plus_int(v13, v14) = v15) | ord_less_int(zero_zero_int, v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (times_times_nat(v13, v14) = v15) | ~ (number_number_of_nat(v12) = v13) | ~ (number_number_of_nat(v11) = v14) | ~ ord_less_eq_int(pls, v12) | ~ ord_less_eq_int(pls, v11) | ? [v16] : (number_number_of_nat(v16) = v15 & times_times_int(v12, v11) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (number_number_of_nat(v12) = v13) | ~ (number_number_of_nat(v11) = v14) | ~ (plus_plus_nat(v13, v14) = v15) | ~ ord_less_eq_int(pls, v12) | ~ ord_less_eq_int(pls, v11) | ? [v16] : (number_number_of_nat(v16) = v15 & plus_plus_int(v12, v11) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (number_number_of_nat(v12) = v13) | ~ (number_number_of_nat(v11) = v14) | ~ (plus_plus_nat(v13, v14) = v15) | ord_less_int(v12, pls) | ord_less_int(v11, pls) | ? [v16] : (number_number_of_nat(v16) = v15 & plus_plus_int(v12, v11) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (plus_plus_nat(v12, v13) = v14) | ~ (power_power_int(v11, v14) = v15) | ? [v16] : ? [v17] : (times_times_int(v16, v17) = v15 & power_power_int(v11, v13) = v17 & power_power_int(v11, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (times_times_int(v14, v13) = v15) | ~ (times_times_int(v11, v12) = v14) | ? [v16] : (times_times_int(v12, v13) = v16 & times_times_int(v11, v16) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (times_times_int(v14, v13) = v15) | ~ (plus_plus_int(v11, v12) = v14) | ? [v16] : ? [v17] : (times_times_int(v12, v13) = v17 & times_times_int(v11, v13) = v16 & plus_plus_int(v16, v17) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (times_times_int(v13, v14) = v15) | ~ (number_number_of_int(v12) = v14) | ~ (number_number_of_int(v11) = v13) | ? [v16] : (times_times_int(v11, v12) = v16 & number_number_of_int(v16) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (times_times_int(v13, v14) = v15) | ~ (number_number_of_int(v12) = v13) | ~ (number_number_of_int(v11) = v14) | ~ ord_less_eq_int(pls, v12) | ~ ord_less_eq_int(pls, v11) | ? [v16] : (times_times_int(v12, v11) = v16 & number_number_of_int(v16) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (times_times_int(v12, v13) = v14) | ~ (times_times_int(v11, v14) = v15) | ? [v16] : (times_times_int(v16, v13) = v15 & times_times_int(v11, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (times_times_int(v12, v12) = v14) | ~ (times_times_int(v11, v11) = v13) | ~ (plus_plus_int(v13, v14) = v15) | ord_less_eq_int(zero_zero_int, v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (times_times_int(v11, v14) = v15) | ~ (plus_plus_int(v12, v13) = v14) | ? [v16] : ? [v17] : (times_times_int(v11, v13) = v17 & times_times_int(v11, v12) = v16 & plus_plus_int(v16, v17) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (number_number_of_int(v12) = v14) | ~ (number_number_of_int(v11) = v13) | ~ (plus_plus_int(v13, v14) = v15) | ? [v16] : (number_number_of_int(v16) = v15 & plus_plus_int(v11, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (number_number_of_int(v12) = v13) | ~ (number_number_of_int(v11) = v14) | ~ (plus_plus_int(v13, v14) = v15) | ~ ord_less_eq_int(pls, v12) | ~ ord_less_eq_int(pls, v11) | ? [v16] : (number_number_of_int(v16) = v15 & plus_plus_int(v12, v11) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (power_power_int(v12, v8) = v14) | ~ (power_power_int(v11, v8) = v13) | ~ (plus_plus_int(v13, v14) = v15) | ~ ord_less_int(v15, zero_zero_int)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (plus_plus_int(v14, v13) = v15) | ~ (plus_plus_int(v11, v12) = v14) | ? [v16] : (plus_plus_int(v12, v13) = v16 & plus_plus_int(v11, v16) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (plus_plus_int(v12, v14) = v15) | ~ (plus_plus_int(v11, v13) = v14) | ? [v16] : (plus_plus_int(v12, v13) = v16 & plus_plus_int(v11, v16) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (plus_plus_int(v12, v13) = v14) | ~ (plus_plus_int(v11, v14) = v15) | ? [v16] : (plus_plus_int(v16, v13) = v15 & plus_plus_int(v11, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (plus_plus_int(v12, v13) = v14) | ~ (plus_plus_int(v11, v14) = v15) | ? [v16] : (plus_plus_int(v12, v16) = v15 & plus_plus_int(v11, v13) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (plus_plus_int(v11, v13) = v15) | ~ (plus_plus_int(v11, v12) = v14) | ~ ord_less_eq_int(v12, v13) | ord_less_eq_int(v14, v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (power_power_nat(v14, v13) = v12) | ~ (power_power_nat(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (times_times_nat(v14, v13) = v12) | ~ (times_times_nat(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (plus_plus_nat(v14, v13) = v12) | ~ (plus_plus_nat(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (times_times_int(v14, v13) = v12) | ~ (times_times_int(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (power_power_int(v14, v13) = v12) | ~ (power_power_int(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (plus_plus_int(v14, v13) = v12) | ~ (plus_plus_int(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = zero_zero_int | ~ (times_times_int(v12, v12) = v14) | ~ (times_times_int(v11, v11) = v13) | ~ (plus_plus_int(v13, v14) = zero_zero_int)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = zero_zero_int | ~ (power_power_int(v12, v8) = v14) | ~ (power_power_int(v11, v8) = v13) | ~ (plus_plus_int(v13, v14) = zero_zero_int)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = zero_zero_int | ~ (times_times_int(v12, v12) = v14) | ~ (times_times_int(v11, v11) = v13) | ~ (plus_plus_int(v13, v14) = zero_zero_int)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = zero_zero_int | ~ (power_power_int(v12, v8) = v14) | ~ (power_power_int(v11, v8) = v13) | ~ (plus_plus_int(v13, v14) = zero_zero_int)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (number_number_of_nat(v12) = v14) | ~ (number_number_of_nat(v11) = v13) | ~ ord_less_eq_nat(v13, v14) | ~ ord_less_nat(v14, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (number_number_of_nat(v12) = v14) | ~ (number_number_of_nat(v11) = v13) | ~ ord_less_nat(v13, v14) | ~ ord_less_int(v11, v12) | ord_less_int(pls, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (number_number_of_nat(v12) = v14) | ~ (number_number_of_nat(v11) = v13) | ~ ord_less_nat(v13, v14) | ord_less_int(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (number_number_of_nat(v12) = v14) | ~ (number_number_of_nat(v11) = v13) | ~ ord_less_int(v11, v12) | ~ ord_less_int(pls, v12) | ord_less_nat(v13, v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (number_number_of_nat(v12) = v13) | ~ (number_number_of_nat(v11) = v14) | ord_less_eq_nat(v14, v13) | ord_less_nat(v13, v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (bit0(v12) = v14) | ~ (bit0(v11) = v13) | ~ ord_less_eq_int(v13, v14) | ord_less_eq_int(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (bit0(v12) = v14) | ~ (bit0(v11) = v13) | ~ ord_less_eq_int(v11, v12) | ord_less_eq_int(v13, v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (bit0(v12) = v14) | ~ (bit1(v11) = v13) | ~ ord_less_eq_int(v13, v14) | ord_less_int(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (bit0(v12) = v14) | ~ (bit1(v11) = v13) | ~ ord_less_int(v11, v12) | ord_less_eq_int(v13, v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (bit0(v11) = v13) | ~ (bit1(v12) = v14) | ~ ord_less_eq_int(v13, v14) | ord_less_eq_int(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (bit0(v11) = v13) | ~ (bit1(v12) = v14) | ~ ord_less_eq_int(v11, v12) | ord_less_eq_int(v13, v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (bit0(v11) = v13) | ~ (bit1(v12) = v14) | ~ ord_less_eq_int(v11, v12) | ord_less_int(v13, v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (bit0(v11) = v13) | ~ (bit1(v12) = v14) | ~ ord_less_int(v13, v14) | ord_less_eq_int(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (bit0(v11) = v13) | ~ (times_times_int(v13, v12) = v14) | ? [v15] : (bit0(v15) = v14 & times_times_int(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (bit1(v12) = v14) | ~ (bit1(v11) = v13) | ~ ord_less_eq_int(v13, v14) | ord_less_eq_int(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (bit1(v12) = v14) | ~ (bit1(v11) = v13) | ~ ord_less_eq_int(v11, v12) | ord_less_eq_int(v13, v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (number_number_of_int(v12) = v14) | ~ (number_number_of_int(v11) = v13) | ~ ord_less_eq_int(v13, v14) | ~ ord_less_int(v14, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (number_number_of_int(v12) = v14) | ~ (number_number_of_int(v11) = v13) | ~ ord_less_eq_int(v13, v14) | ord_less_eq_int(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (number_number_of_int(v12) = v14) | ~ (number_number_of_int(v11) = v13) | ~ ord_less_eq_int(v11, v12) | ord_less_eq_int(v13, v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (number_number_of_int(v12) = v14) | ~ (number_number_of_int(v11) = v13) | ~ ord_less_int(v13, v14) | ord_less_int(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (number_number_of_int(v12) = v14) | ~ (number_number_of_int(v11) = v13) | ~ ord_less_int(v11, v12) | ord_less_int(v13, v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (number_number_of_int(v12) = v13) | ~ (number_number_of_int(v11) = v14) | ord_less_eq_int(v14, v13) | ord_less_int(v13, v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (bit0(v11) = v13) | ~ (bit0(v11) = v12)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (bit1(v11) = v13) | ~ (bit1(v11) = v12)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (number_number_of_int(v11) = v13) | ~ (number_number_of_int(v11) = v12)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (number_number_of_nat(v13) = v12) | ~ (number_number_of_nat(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (bit0(v13) = v12) | ~ (bit0(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (bit0(v12) = v13) | ~ (bit0(v11) = v13)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (bit1(v13) = v12) | ~ (bit1(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (bit1(v12) = v13) | ~ (bit1(v11) = v13)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (number_number_of_int(v13) = v12) | ~ (number_number_of_int(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (number_number_of_int(v12) = v13) | ~ (number_number_of_int(v11) = v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (times_times_int(v12, v11) = v13) | ~ ord_less_eq_int(pls, v12) | ~ ord_less_eq_int(pls, v11) | ? [v14] : ? [v15] : ? [v16] : (times_times_nat(v14, v15) = v16 & number_number_of_nat(v13) = v16 & number_number_of_nat(v12) = v14 & number_number_of_nat(v11) = v15)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (times_times_int(v12, v11) = v13) | ~ ord_less_eq_int(pls, v12) | ~ ord_less_eq_int(pls, v11) | ? [v14] : ? [v15] : ? [v16] : (times_times_int(v14, v15) = v16 & number_number_of_int(v13) = v16 & number_number_of_int(v12) = v14 & number_number_of_int(v11) = v15)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (times_times_int(v12, v11) = v13) | times_times_int(v11, v12) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (times_times_int(v11, v12) = v13) | times_times_int(v12, v11) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (times_times_int(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (times_times_int(v15, v16) = v14 & number_number_of_int(v13) = v14 & number_number_of_int(v12) = v16 & number_number_of_int(v11) = v15)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (times_times_int(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (times_times_int(v14, v15) = v16 & number_number_of_int(v13) = v16 & number_number_of_int(v12) = v15 & number_number_of_int(v11) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (times_times_int(v11, v12) = v13) | ? [v14] : ? [v15] : (bit0(v13) = v15 & bit0(v11) = v14 & times_times_int(v14, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (plus_plus_int(v12, v11) = v13) | ~ ord_less_eq_int(pls, v12) | ~ ord_less_eq_int(pls, v11) | ? [v14] : ? [v15] : ? [v16] : (number_number_of_nat(v13) = v16 & number_number_of_nat(v12) = v14 & number_number_of_nat(v11) = v15 & plus_plus_nat(v14, v15) = v16)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (plus_plus_int(v12, v11) = v13) | ~ ord_less_eq_int(pls, v12) | ~ ord_less_eq_int(pls, v11) | ? [v14] : ? [v15] : ? [v16] : (number_number_of_int(v13) = v16 & number_number_of_int(v12) = v14 & number_number_of_int(v11) = v15 & plus_plus_int(v14, v15) = v16)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (plus_plus_int(v12, v11) = v13) | plus_plus_int(v11, v12) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (plus_plus_int(v12, v11) = v13) | ord_less_int(v12, pls) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (number_number_of_nat(v13) = v17 & number_number_of_nat(v12) = v14 & number_number_of_nat(v11) = v15 & plus_plus_nat(v14, v15) = v16 & (v17 = v16 | ord_less_int(v11, pls)) & (v16 = v14 | ~ ord_less_int(v11, pls)))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (plus_plus_int(v12, one_one_int) = v13) | ~ ord_less_eq_int(v11, v12) | ord_less_int(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (plus_plus_int(v12, one_one_int) = v13) | ~ ord_less_int(v11, v13) | ord_less_eq_int(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (plus_plus_int(v11, v12) = v13) | plus_plus_int(v12, v11) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (plus_plus_int(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (number_number_of_int(v13) = v16 & number_number_of_int(v12) = v15 & number_number_of_int(v11) = v14 & plus_plus_int(v14, v15) = v16)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (plus_plus_int(v11, one_one_int) = v13) | ~ ord_less_eq_int(v13, v12) | ord_less_int(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (plus_plus_int(v11, one_one_int) = v13) | ~ ord_less_int(v11, v12) | ord_less_eq_int(v13, v12)) & ! [v11] : ! [v12] : ! [v13] : ( ~ ord_less_eq_int(v13, v11) | ~ ord_less_eq_int(v12, v13) | ord_less_eq_int(v12, v11)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (times_times_int(v11, one_one_int) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (times_times_int(one_one_int, v11) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (number_number_of_int(v11) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ ord_less_eq_int(v12, v11) | ~ ord_less_eq_int(v11, v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ ord_less_eq_int(v11, v12) | ord_less_int(v11, v12)) & ! [v11] : ! [v12] : (v12 = zero_zero_nat | ~ (number_number_of_nat(v11) = v12) | ~ ord_less_eq_int(v11, pls)) & ! [v11] : ! [v12] : (v12 = pls | ~ (times_times_int(pls, v11) = v12)) & ! [v11] : ! [v12] : (v12 = zero_zero_int | ~ (times_times_int(zero_zero_int, zero_zero_int) = v11) | ~ (plus_plus_int(v11, v11) = v12)) & ! [v11] : ! [v12] : (v11 = zero_zero_int | ~ (power_power_int(v11, v8) = v12) | ord_less_int(zero_zero_int, v12)) & ! [v11] : ! [v12] : ( ~ (number_number_of_nat(v11) = v12) | ~ ord_less_nat(zero_zero_nat, v12) | ord_less_int(pls, v11)) & ! [v11] : ! [v12] : ( ~ (number_number_of_nat(v11) = v12) | ~ ord_less_int(pls, v11) | ord_less_nat(zero_zero_nat, v12)) & ! [v11] : ! [v12] : ( ~ (bit0(v11) = v12) | ~ ord_less_eq_int(v12, pls) | ord_less_eq_int(v11, pls)) & ! [v11] : ! [v12] : ( ~ (bit0(v11) = v12) | ~ ord_less_eq_int(v11, pls) | ord_less_eq_int(v12, pls)) & ! [v11] : ! [v12] : ( ~ (bit0(v11) = v12) | ~ ord_less_eq_int(pls, v12) | ord_less_eq_int(pls, v11)) & ! [v11] : ! [v12] : ( ~ (bit0(v11) = v12) | ~ ord_less_eq_int(pls, v11) | ord_less_eq_int(pls, v12)) & ! [v11] : ! [v12] : ( ~ (bit1(v11) = v12) | ~ ord_less_eq_int(v12, pls) | ord_less_int(v11, pls)) & ! [v11] : ! [v12] : ( ~ (bit1(v11) = v12) | ~ ord_less_eq_int(pls, v12) | ord_less_eq_int(pls, v11)) & ! [v11] : ! [v12] : ( ~ (bit1(v11) = v12) | ~ ord_less_eq_int(pls, v11) | ord_less_eq_int(pls, v12)) & ! [v11] : ! [v12] : ( ~ (bit1(v11) = v12) | ~ ord_less_eq_int(pls, v11) | ord_less_int(pls, v12)) & ! [v11] : ! [v12] : ( ~ (bit1(v11) = v12) | ~ ord_less_int(v11, pls) | ord_less_eq_int(v12, pls)) & ! [v11] : ! [v12] : ( ~ (bit1(v11) = v12) | ~ ord_less_int(pls, v12) | ord_less_eq_int(pls, v11)) & ! [v11] : ! [v12] : ( ~ (times_times_int(zero_zero_int, zero_zero_int) = v11) | ~ (plus_plus_int(v11, v11) = v12) | ord_less_eq_int(v12, zero_zero_int)) & ! [v11] : ! [v12] : ( ~ (number_number_of_int(v11) = v12) | ~ ord_less_eq_int(v12, one_one_int) | ord_less_eq_int(v11, v0)) & ! [v11] : ! [v12] : ( ~ (number_number_of_int(v11) = v12) | ~ ord_less_eq_int(v12, zero_zero_int) | ord_less_eq_int(v11, pls)) & ! [v11] : ! [v12] : ( ~ (number_number_of_int(v11) = v12) | ~ ord_less_eq_int(v11, v0) | ord_less_eq_int(v12, one_one_int)) & ! [v11] : ! [v12] : ( ~ (number_number_of_int(v11) = v12) | ~ ord_less_eq_int(v11, pls) | ord_less_eq_int(v12, zero_zero_int)) & ! [v11] : ! [v12] : ( ~ (number_number_of_int(v11) = v12) | ~ ord_less_eq_int(v0, v11) | ord_less_eq_int(one_one_int, v12)) & ! [v11] : ! [v12] : ( ~ (number_number_of_int(v11) = v12) | ~ ord_less_eq_int(pls, v11) | ord_less_eq_int(zero_zero_int, v12)) & ! [v11] : ! [v12] : ( ~ (number_number_of_int(v11) = v12) | ~ ord_less_eq_int(one_one_int, v12) | ord_less_eq_int(v0, v11)) & ! [v11] : ! [v12] : ( ~ (number_number_of_int(v11) = v12) | ~ ord_less_eq_int(zero_zero_int, v12) | ord_less_eq_int(pls, v11)) & ! [v11] : ! [v12] : ( ~ (number_number_of_int(v11) = v12) | ? [v13] : ? [v14] : (number_number_of_int(v14) = v13 & plus_plus_int(v12, one_one_int) = v13 & plus_plus_int(v11, v0) = v14)) & ! [v11] : ! [v12] : ( ~ (number_number_of_int(v11) = v12) | ? [v13] : ? [v14] : (number_number_of_int(v14) = v13 & plus_plus_int(v0, v11) = v14 & plus_plus_int(one_one_int, v12) = v13)) & ! [v11] : ! [v12] : ( ~ (power_power_int(v11, v8) = v12) | ~ ord_less_int(v12, zero_zero_int)) & ! [v11] : ! [v12] : ( ~ (plus_plus_int(v11, v0) = v12) | ? [v13] : ? [v14] : (number_number_of_int(v12) = v14 & number_number_of_int(v11) = v13 & plus_plus_int(v13, one_one_int) = v14)) & ! [v11] : ! [v12] : ( ~ (plus_plus_int(v0, v11) = v12) | ? [v13] : ? [v14] : (number_number_of_int(v12) = v14 & number_number_of_int(v11) = v13 & plus_plus_int(one_one_int, v13) = v14)) & ! [v11] : ! [v12] : ( ~ (plus_plus_int(one_one_int, v11) = v12) | ~ ord_less_eq_int(zero_zero_int, v11) | ord_less_int(zero_zero_int, v12)) & ! [v11] : ! [v12] : ( ~ ord_less_int(v11, v12) | ord_less_eq_int(v11, v12)) & ! [v11] : (v11 = zero_zero_int | ~ (power_power_int(v11, v8) = zero_zero_int)) & ! [v11] : (v11 = zero_zero_int | ~ (plus_plus_int(zero_zero_int, zero_zero_int) = v11)) & ! [v11] : ( ~ (number_number_of_nat(v11) = zero_zero_nat) | ord_less_eq_int(v11, pls)) & ! [v11] : ( ~ (plus_plus_int(zero_zero_int, zero_zero_int) = v11) | ~ ord_less_int(zero_zero_int, v11)) & ! [v11] : ( ~ ord_less_eq_int(one_one_int, v11) | ord_less_int(zero_zero_int, v11)) & ! [v11] : ~ ord_less_int(v11, v11) & ! [v11] : ( ~ ord_less_int(zero_zero_int, v11) | ord_less_eq_int(one_one_int, v11)) & ? [v11] : ? [v12] : (v12 = v11 | ord_less_int(v12, v11) | ord_less_int(v11, v12)) & ? [v11] : ? [v12] : (ord_less_eq_int(v12, v11) | ord_less_eq_int(v11, v12)) & ? [v11] : ord_less_eq_int(v11, v11) & ( ~ (zero_zero_int = t) | v6 = t)) % 9.12/2.68 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10 yields: % 9.12/2.68 | (1) power_power_nat(zero_zero_nat, all_0_2_2) = zero_zero_nat & power_power_nat(one_one_nat, all_0_2_2) = one_one_nat & number_number_of_nat(all_0_9_9) = all_0_2_2 & number_number_of_nat(all_0_10_10) = one_one_nat & number_number_of_nat(pls) = zero_zero_nat & bit0(all_0_9_9) = all_0_8_8 & bit0(all_0_10_10) = all_0_9_9 & bit1(pls) = all_0_10_10 & plus_plus_nat(one_one_nat, one_one_nat) = all_0_2_2 & times_times_int(all_0_5_5, all_0_0_0) = all_0_4_4 & times_times_int(all_0_5_5, zero_zero_int) = all_0_3_3 & times_times_int(all_0_5_5, t) = all_0_4_4 & times_times_int(all_0_7_7, m) = all_0_6_6 & number_number_of_int(all_0_8_8) = all_0_7_7 & number_number_of_int(pls) = zero_zero_int & power_power_int(s, all_0_2_2) = all_0_1_1 & power_power_int(one_one_int, all_0_2_2) = one_one_int & power_power_int(zero_zero_int, all_0_2_2) = zero_zero_int & plus_plus_int(all_0_1_1, one_one_int) = all_0_4_4 & plus_plus_int(all_0_6_6, one_one_int) = all_0_5_5 & twoSqu526106917sum2sq(all_0_4_4) & zprime(all_0_5_5) & ord_less_eq_int(pls, pls) & ord_less_int(all_0_4_4, all_0_3_3) & ord_less_int(zero_zero_int, all_0_5_5) & ord_less_int(t, all_0_5_5) & ord_less_int(t, one_one_int) & ord_less_int(t, zero_zero_int) & ~ ord_less_eq_int(one_one_int, t) & ~ ord_less_int(all_0_4_4, zero_zero_int) & ~ ord_less_int(zero_zero_int, zero_zero_int) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (times_times_nat(v3, v2) = v5) | ~ (times_times_nat(v3, v1) = v4) | ~ (number_number_of_nat(v0) = v3) | ~ (plus_plus_nat(v4, v5) = v6) | ? [v7] : (times_times_nat(v3, v7) = v6 & plus_plus_nat(v1, v2) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (times_times_nat(v1, v3) = v5) | ~ (times_times_nat(v0, v3) = v4) | ~ (number_number_of_nat(v2) = v3) | ~ (plus_plus_nat(v4, v5) = v6) | ? [v7] : (times_times_nat(v7, v3) = v6 & plus_plus_nat(v0, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (times_times_int(v4, v2) = v5) | ~ (times_times_int(v3, v5) = v6) | ~ (number_number_of_int(v1) = v4) | ~ (number_number_of_int(v0) = v3) | ? [v7] : ? [v8] : (times_times_int(v8, v2) = v6 & times_times_int(v0, v1) = v7 & number_number_of_int(v7) = v8)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (times_times_int(v3, v2) = v5) | ~ (times_times_int(v3, v1) = v4) | ~ (number_number_of_int(v0) = v3) | ~ (plus_plus_int(v4, v5) = v6) | ? [v7] : (times_times_int(v3, v7) = v6 & plus_plus_int(v1, v2) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (times_times_int(v1, v3) = v5) | ~ (times_times_int(v0, v3) = v4) | ~ (number_number_of_int(v2) = v3) | ~ (plus_plus_int(v4, v5) = v6) | ? [v7] : (times_times_int(v7, v3) = v6 & plus_plus_int(v0, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (times_times_nat(v3, v4) = v5) | ~ (number_number_of_nat(v2) = v4) | ~ (plus_plus_nat(v0, v1) = v3) | ? [v6] : ? [v7] : (times_times_nat(v1, v4) = v7 & times_times_nat(v0, v4) = v6 & plus_plus_nat(v6, v7) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (times_times_nat(v3, v4) = v5) | ~ (number_number_of_nat(v0) = v3) | ~ (plus_plus_nat(v1, v2) = v4) | ? [v6] : ? [v7] : (times_times_nat(v3, v2) = v7 & times_times_nat(v3, v1) = v6 & plus_plus_nat(v6, v7) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (times_times_int(v4, v2) = v5) | ~ (times_times_int(v0, v1) = v3) | ~ (number_number_of_int(v3) = v4) | ? [v6] : ? [v7] : ? [v8] : (times_times_int(v7, v2) = v8 & times_times_int(v6, v8) = v5 & number_number_of_int(v1) = v7 & number_number_of_int(v0) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (times_times_int(v3, v4) = v5) | ~ (number_number_of_int(v2) = v4) | ~ (plus_plus_int(v0, v1) = v3) | ? [v6] : ? [v7] : (times_times_int(v1, v4) = v7 & times_times_int(v0, v4) = v6 & plus_plus_int(v6, v7) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (times_times_int(v3, v4) = v5) | ~ (number_number_of_int(v0) = v3) | ~ (plus_plus_int(v1, v2) = v4) | ? [v6] : ? [v7] : (times_times_int(v3, v2) = v7 & times_times_int(v3, v1) = v6 & plus_plus_int(v6, v7) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (times_times_int(v3, v4) = v5) | ~ (power_power_int(v0, v2) = v4) | ~ (power_power_int(v0, v1) = v3) | ? [v6] : (plus_plus_nat(v1, v2) = v6 & power_power_int(v0, v6) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (times_times_int(v1, v2) = v4) | ~ (times_times_int(v0, v2) = v3) | ~ (plus_plus_int(v3, v4) = v5) | ? [v6] : (times_times_int(v6, v2) = v5 & plus_plus_int(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (times_times_int(v0, v2) = v4) | ~ (times_times_int(v0, v1) = v3) | ~ (plus_plus_int(v3, v4) = v5) | ? [v6] : (times_times_int(v0, v6) = v5 & plus_plus_int(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (plus_plus_int(v3, v1) = v5) | ~ (plus_plus_int(v2, v0) = v4) | ~ ord_less_eq_int(v0, v1) | ~ ord_less_int(v2, v3) | ord_less_int(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (number_number_of_nat(v1) = v2) | ~ (number_number_of_nat(v0) = v3) | ~ (plus_plus_nat(v2, v3) = v4) | ~ ord_less_int(v1, pls)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (number_number_of_nat(v1) = v2) | ~ (number_number_of_nat(v0) = v3) | ~ (plus_plus_nat(v2, v3) = v4) | ~ ord_less_int(v0, pls) | ord_less_int(v1, pls)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = zero_zero_int | ~ (times_times_int(v1, v1) = v3) | ~ (times_times_int(v0, v0) = v2) | ~ (plus_plus_int(v2, v3) = v4) | ~ ord_less_eq_int(v4, zero_zero_int)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = zero_zero_int | ~ (power_power_int(v1, all_0_2_2) = v3) | ~ (power_power_int(v0, all_0_2_2) = v2) | ~ (plus_plus_int(v2, v3) = v4) | ord_less_int(zero_zero_int, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = zero_zero_int | ~ (times_times_int(v1, v1) = v3) | ~ (times_times_int(v0, v0) = v2) | ~ (plus_plus_int(v2, v3) = v4) | ~ ord_less_eq_int(v4, zero_zero_int)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = zero_zero_int | ~ (power_power_int(v1, all_0_2_2) = v3) | ~ (power_power_int(v0, all_0_2_2) = v2) | ~ (plus_plus_int(v2, v3) = v4) | ord_less_int(zero_zero_int, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (times_times_nat(v2, v3) = v4) | ~ (number_number_of_nat(v1) = v2) | ~ (number_number_of_nat(v0) = v3) | ~ ord_less_eq_int(pls, v1) | ~ ord_less_eq_int(pls, v0) | ? [v5] : (number_number_of_nat(v5) = v4 & times_times_int(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (number_number_of_nat(v1) = v2) | ~ (number_number_of_nat(v0) = v3) | ~ (plus_plus_nat(v2, v3) = v4) | ~ ord_less_eq_int(pls, v1) | ~ ord_less_eq_int(pls, v0) | ? [v5] : (number_number_of_nat(v5) = v4 & plus_plus_int(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (number_number_of_nat(v1) = v2) | ~ (number_number_of_nat(v0) = v3) | ~ (plus_plus_nat(v2, v3) = v4) | ord_less_int(v1, pls) | ord_less_int(v0, pls) | ? [v5] : (number_number_of_nat(v5) = v4 & plus_plus_int(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (plus_plus_nat(v1, v2) = v3) | ~ (power_power_int(v0, v3) = v4) | ? [v5] : ? [v6] : (times_times_int(v5, v6) = v4 & power_power_int(v0, v2) = v6 & power_power_int(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (times_times_int(v3, v2) = v4) | ~ (times_times_int(v0, v1) = v3) | ? [v5] : (times_times_int(v1, v2) = v5 & times_times_int(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (times_times_int(v3, v2) = v4) | ~ (plus_plus_int(v0, v1) = v3) | ? [v5] : ? [v6] : (times_times_int(v1, v2) = v6 & times_times_int(v0, v2) = v5 & plus_plus_int(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (times_times_int(v2, v3) = v4) | ~ (number_number_of_int(v1) = v3) | ~ (number_number_of_int(v0) = v2) | ? [v5] : (times_times_int(v0, v1) = v5 & number_number_of_int(v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (times_times_int(v2, v3) = v4) | ~ (number_number_of_int(v1) = v2) | ~ (number_number_of_int(v0) = v3) | ~ ord_less_eq_int(pls, v1) | ~ ord_less_eq_int(pls, v0) | ? [v5] : (times_times_int(v1, v0) = v5 & number_number_of_int(v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (times_times_int(v1, v2) = v3) | ~ (times_times_int(v0, v3) = v4) | ? [v5] : (times_times_int(v5, v2) = v4 & times_times_int(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (times_times_int(v1, v1) = v3) | ~ (times_times_int(v0, v0) = v2) | ~ (plus_plus_int(v2, v3) = v4) | ord_less_eq_int(zero_zero_int, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (times_times_int(v0, v3) = v4) | ~ (plus_plus_int(v1, v2) = v3) | ? [v5] : ? [v6] : (times_times_int(v0, v2) = v6 & times_times_int(v0, v1) = v5 & plus_plus_int(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (number_number_of_int(v1) = v3) | ~ (number_number_of_int(v0) = v2) | ~ (plus_plus_int(v2, v3) = v4) | ? [v5] : (number_number_of_int(v5) = v4 & plus_plus_int(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (number_number_of_int(v1) = v2) | ~ (number_number_of_int(v0) = v3) | ~ (plus_plus_int(v2, v3) = v4) | ~ ord_less_eq_int(pls, v1) | ~ ord_less_eq_int(pls, v0) | ? [v5] : (number_number_of_int(v5) = v4 & plus_plus_int(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (power_power_int(v1, all_0_2_2) = v3) | ~ (power_power_int(v0, all_0_2_2) = v2) | ~ (plus_plus_int(v2, v3) = v4) | ~ ord_less_int(v4, zero_zero_int)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (plus_plus_int(v3, v2) = v4) | ~ (plus_plus_int(v0, v1) = v3) | ? [v5] : (plus_plus_int(v1, v2) = v5 & plus_plus_int(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (plus_plus_int(v1, v3) = v4) | ~ (plus_plus_int(v0, v2) = v3) | ? [v5] : (plus_plus_int(v1, v2) = v5 & plus_plus_int(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (plus_plus_int(v1, v2) = v3) | ~ (plus_plus_int(v0, v3) = v4) | ? [v5] : (plus_plus_int(v5, v2) = v4 & plus_plus_int(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (plus_plus_int(v1, v2) = v3) | ~ (plus_plus_int(v0, v3) = v4) | ? [v5] : (plus_plus_int(v1, v5) = v4 & plus_plus_int(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (plus_plus_int(v0, v2) = v4) | ~ (plus_plus_int(v0, v1) = v3) | ~ ord_less_eq_int(v1, v2) | ord_less_eq_int(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (power_power_nat(v3, v2) = v1) | ~ (power_power_nat(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (times_times_nat(v3, v2) = v1) | ~ (times_times_nat(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (plus_plus_nat(v3, v2) = v1) | ~ (plus_plus_nat(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (times_times_int(v3, v2) = v1) | ~ (times_times_int(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (power_power_int(v3, v2) = v1) | ~ (power_power_int(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (plus_plus_int(v3, v2) = v1) | ~ (plus_plus_int(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = zero_zero_int | ~ (times_times_int(v1, v1) = v3) | ~ (times_times_int(v0, v0) = v2) | ~ (plus_plus_int(v2, v3) = zero_zero_int)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = zero_zero_int | ~ (power_power_int(v1, all_0_2_2) = v3) | ~ (power_power_int(v0, all_0_2_2) = v2) | ~ (plus_plus_int(v2, v3) = zero_zero_int)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = zero_zero_int | ~ (times_times_int(v1, v1) = v3) | ~ (times_times_int(v0, v0) = v2) | ~ (plus_plus_int(v2, v3) = zero_zero_int)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = zero_zero_int | ~ (power_power_int(v1, all_0_2_2) = v3) | ~ (power_power_int(v0, all_0_2_2) = v2) | ~ (plus_plus_int(v2, v3) = zero_zero_int)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_nat(v1) = v3) | ~ (number_number_of_nat(v0) = v2) | ~ ord_less_eq_nat(v2, v3) | ~ ord_less_nat(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_nat(v1) = v3) | ~ (number_number_of_nat(v0) = v2) | ~ ord_less_nat(v2, v3) | ~ ord_less_int(v0, v1) | ord_less_int(pls, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_nat(v1) = v3) | ~ (number_number_of_nat(v0) = v2) | ~ ord_less_nat(v2, v3) | ord_less_int(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_nat(v1) = v3) | ~ (number_number_of_nat(v0) = v2) | ~ ord_less_int(v0, v1) | ~ ord_less_int(pls, v1) | ord_less_nat(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_nat(v1) = v2) | ~ (number_number_of_nat(v0) = v3) | ord_less_eq_nat(v3, v2) | ord_less_nat(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v1) = v3) | ~ (bit0(v0) = v2) | ~ ord_less_eq_int(v2, v3) | ord_less_eq_int(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v1) = v3) | ~ (bit0(v0) = v2) | ~ ord_less_eq_int(v0, v1) | ord_less_eq_int(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v1) = v3) | ~ (bit1(v0) = v2) | ~ ord_less_eq_int(v2, v3) | ord_less_int(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v1) = v3) | ~ (bit1(v0) = v2) | ~ ord_less_int(v0, v1) | ord_less_eq_int(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v0) = v2) | ~ (bit1(v1) = v3) | ~ ord_less_eq_int(v2, v3) | ord_less_eq_int(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v0) = v2) | ~ (bit1(v1) = v3) | ~ ord_less_eq_int(v0, v1) | ord_less_eq_int(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v0) = v2) | ~ (bit1(v1) = v3) | ~ ord_less_eq_int(v0, v1) | ord_less_int(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v0) = v2) | ~ (bit1(v1) = v3) | ~ ord_less_int(v2, v3) | ord_less_eq_int(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v0) = v2) | ~ (times_times_int(v2, v1) = v3) | ? [v4] : (bit0(v4) = v3 & times_times_int(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit1(v1) = v3) | ~ (bit1(v0) = v2) | ~ ord_less_eq_int(v2, v3) | ord_less_eq_int(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit1(v1) = v3) | ~ (bit1(v0) = v2) | ~ ord_less_eq_int(v0, v1) | ord_less_eq_int(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_int(v1) = v3) | ~ (number_number_of_int(v0) = v2) | ~ ord_less_eq_int(v2, v3) | ~ ord_less_int(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_int(v1) = v3) | ~ (number_number_of_int(v0) = v2) | ~ ord_less_eq_int(v2, v3) | ord_less_eq_int(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_int(v1) = v3) | ~ (number_number_of_int(v0) = v2) | ~ ord_less_eq_int(v0, v1) | ord_less_eq_int(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_int(v1) = v3) | ~ (number_number_of_int(v0) = v2) | ~ ord_less_int(v2, v3) | ord_less_int(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_int(v1) = v3) | ~ (number_number_of_int(v0) = v2) | ~ ord_less_int(v0, v1) | ord_less_int(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_int(v1) = v2) | ~ (number_number_of_int(v0) = v3) | ord_less_eq_int(v3, v2) | ord_less_int(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (bit0(v0) = v2) | ~ (bit0(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (bit1(v0) = v2) | ~ (bit1(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (number_number_of_int(v0) = v2) | ~ (number_number_of_int(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (number_number_of_nat(v2) = v1) | ~ (number_number_of_nat(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (bit0(v2) = v1) | ~ (bit0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (bit0(v1) = v2) | ~ (bit0(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (bit1(v2) = v1) | ~ (bit1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (bit1(v1) = v2) | ~ (bit1(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (number_number_of_int(v2) = v1) | ~ (number_number_of_int(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (number_number_of_int(v1) = v2) | ~ (number_number_of_int(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (times_times_int(v1, v0) = v2) | ~ ord_less_eq_int(pls, v1) | ~ ord_less_eq_int(pls, v0) | ? [v3] : ? [v4] : ? [v5] : (times_times_nat(v3, v4) = v5 & number_number_of_nat(v2) = v5 & number_number_of_nat(v1) = v3 & number_number_of_nat(v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (times_times_int(v1, v0) = v2) | ~ ord_less_eq_int(pls, v1) | ~ ord_less_eq_int(pls, v0) | ? [v3] : ? [v4] : ? [v5] : (times_times_int(v3, v4) = v5 & number_number_of_int(v2) = v5 & number_number_of_int(v1) = v3 & number_number_of_int(v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (times_times_int(v1, v0) = v2) | times_times_int(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (times_times_int(v0, v1) = v2) | times_times_int(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (times_times_int(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (times_times_int(v4, v5) = v3 & number_number_of_int(v2) = v3 & number_number_of_int(v1) = v5 & number_number_of_int(v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (times_times_int(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (times_times_int(v3, v4) = v5 & number_number_of_int(v2) = v5 & number_number_of_int(v1) = v4 & number_number_of_int(v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (times_times_int(v0, v1) = v2) | ? [v3] : ? [v4] : (bit0(v2) = v4 & bit0(v0) = v3 & times_times_int(v3, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v1, v0) = v2) | ~ ord_less_eq_int(pls, v1) | ~ ord_less_eq_int(pls, v0) | ? [v3] : ? [v4] : ? [v5] : (number_number_of_nat(v2) = v5 & number_number_of_nat(v1) = v3 & number_number_of_nat(v0) = v4 & plus_plus_nat(v3, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v1, v0) = v2) | ~ ord_less_eq_int(pls, v1) | ~ ord_less_eq_int(pls, v0) | ? [v3] : ? [v4] : ? [v5] : (number_number_of_int(v2) = v5 & number_number_of_int(v1) = v3 & number_number_of_int(v0) = v4 & plus_plus_int(v3, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v1, v0) = v2) | plus_plus_int(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v1, v0) = v2) | ord_less_int(v1, pls) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (number_number_of_nat(v2) = v6 & number_number_of_nat(v1) = v3 & number_number_of_nat(v0) = v4 & plus_plus_nat(v3, v4) = v5 & (v6 = v5 | ord_less_int(v0, pls)) & (v5 = v3 | ~ ord_less_int(v0, pls)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v1, one_one_int) = v2) | ~ ord_less_eq_int(v0, v1) | ord_less_int(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v1, one_one_int) = v2) | ~ ord_less_int(v0, v2) | ord_less_eq_int(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v0, v1) = v2) | plus_plus_int(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (number_number_of_int(v2) = v5 & number_number_of_int(v1) = v4 & number_number_of_int(v0) = v3 & plus_plus_int(v3, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v0, one_one_int) = v2) | ~ ord_less_eq_int(v2, v1) | ord_less_int(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v0, one_one_int) = v2) | ~ ord_less_int(v0, v1) | ord_less_eq_int(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ ord_less_eq_int(v2, v0) | ~ ord_less_eq_int(v1, v2) | ord_less_eq_int(v1, v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (times_times_int(v0, one_one_int) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (times_times_int(one_one_int, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (number_number_of_int(v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ ord_less_eq_int(v1, v0) | ~ ord_less_eq_int(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ ord_less_eq_int(v0, v1) | ord_less_int(v0, v1)) & ! [v0] : ! [v1] : (v1 = zero_zero_nat | ~ (number_number_of_nat(v0) = v1) | ~ ord_less_eq_int(v0, pls)) & ! [v0] : ! [v1] : (v1 = pls | ~ (times_times_int(pls, v0) = v1)) & ! [v0] : ! [v1] : (v1 = zero_zero_int | ~ (times_times_int(zero_zero_int, zero_zero_int) = v0) | ~ (plus_plus_int(v0, v0) = v1)) & ! [v0] : ! [v1] : (v0 = zero_zero_int | ~ (power_power_int(v0, all_0_2_2) = v1) | ord_less_int(zero_zero_int, v1)) & ! [v0] : ! [v1] : ( ~ (number_number_of_nat(v0) = v1) | ~ ord_less_nat(zero_zero_nat, v1) | ord_less_int(pls, v0)) & ! [v0] : ! [v1] : ( ~ (number_number_of_nat(v0) = v1) | ~ ord_less_int(pls, v0) | ord_less_nat(zero_zero_nat, v1)) & ! [v0] : ! [v1] : ( ~ (bit0(v0) = v1) | ~ ord_less_eq_int(v1, pls) | ord_less_eq_int(v0, pls)) & ! [v0] : ! [v1] : ( ~ (bit0(v0) = v1) | ~ ord_less_eq_int(v0, pls) | ord_less_eq_int(v1, pls)) & ! [v0] : ! [v1] : ( ~ (bit0(v0) = v1) | ~ ord_less_eq_int(pls, v1) | ord_less_eq_int(pls, v0)) & ! [v0] : ! [v1] : ( ~ (bit0(v0) = v1) | ~ ord_less_eq_int(pls, v0) | ord_less_eq_int(pls, v1)) & ! [v0] : ! [v1] : ( ~ (bit1(v0) = v1) | ~ ord_less_eq_int(v1, pls) | ord_less_int(v0, pls)) & ! [v0] : ! [v1] : ( ~ (bit1(v0) = v1) | ~ ord_less_eq_int(pls, v1) | ord_less_eq_int(pls, v0)) & ! [v0] : ! [v1] : ( ~ (bit1(v0) = v1) | ~ ord_less_eq_int(pls, v0) | ord_less_eq_int(pls, v1)) & ! [v0] : ! [v1] : ( ~ (bit1(v0) = v1) | ~ ord_less_eq_int(pls, v0) | ord_less_int(pls, v1)) & ! [v0] : ! [v1] : ( ~ (bit1(v0) = v1) | ~ ord_less_int(v0, pls) | ord_less_eq_int(v1, pls)) & ! [v0] : ! [v1] : ( ~ (bit1(v0) = v1) | ~ ord_less_int(pls, v1) | ord_less_eq_int(pls, v0)) & ! [v0] : ! [v1] : ( ~ (times_times_int(zero_zero_int, zero_zero_int) = v0) | ~ (plus_plus_int(v0, v0) = v1) | ord_less_eq_int(v1, zero_zero_int)) & ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ~ ord_less_eq_int(v1, one_one_int) | ord_less_eq_int(v0, all_0_10_10)) & ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ~ ord_less_eq_int(v1, zero_zero_int) | ord_less_eq_int(v0, pls)) & ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ~ ord_less_eq_int(v0, all_0_10_10) | ord_less_eq_int(v1, one_one_int)) & ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ~ ord_less_eq_int(v0, pls) | ord_less_eq_int(v1, zero_zero_int)) & ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ~ ord_less_eq_int(all_0_10_10, v0) | ord_less_eq_int(one_one_int, v1)) & ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ~ ord_less_eq_int(pls, v0) | ord_less_eq_int(zero_zero_int, v1)) & ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ~ ord_less_eq_int(one_one_int, v1) | ord_less_eq_int(all_0_10_10, v0)) & ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ~ ord_less_eq_int(zero_zero_int, v1) | ord_less_eq_int(pls, v0)) & ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ? [v2] : ? [v3] : (number_number_of_int(v3) = v2 & plus_plus_int(v1, one_one_int) = v2 & plus_plus_int(v0, all_0_10_10) = v3)) & ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ? [v2] : ? [v3] : (number_number_of_int(v3) = v2 & plus_plus_int(all_0_10_10, v0) = v3 & plus_plus_int(one_one_int, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (power_power_int(v0, all_0_2_2) = v1) | ~ ord_less_int(v1, zero_zero_int)) & ! [v0] : ! [v1] : ( ~ (plus_plus_int(v0, all_0_10_10) = v1) | ? [v2] : ? [v3] : (number_number_of_int(v1) = v3 & number_number_of_int(v0) = v2 & plus_plus_int(v2, one_one_int) = v3)) & ! [v0] : ! [v1] : ( ~ (plus_plus_int(all_0_10_10, v0) = v1) | ? [v2] : ? [v3] : (number_number_of_int(v1) = v3 & number_number_of_int(v0) = v2 & plus_plus_int(one_one_int, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (plus_plus_int(one_one_int, v0) = v1) | ~ ord_less_eq_int(zero_zero_int, v0) | ord_less_int(zero_zero_int, v1)) & ! [v0] : ! [v1] : ( ~ ord_less_int(v0, v1) | ord_less_eq_int(v0, v1)) & ! [v0] : (v0 = zero_zero_int | ~ (power_power_int(v0, all_0_2_2) = zero_zero_int)) & ! [v0] : (v0 = zero_zero_int | ~ (plus_plus_int(zero_zero_int, zero_zero_int) = v0)) & ! [v0] : ( ~ (number_number_of_nat(v0) = zero_zero_nat) | ord_less_eq_int(v0, pls)) & ! [v0] : ( ~ (plus_plus_int(zero_zero_int, zero_zero_int) = v0) | ~ ord_less_int(zero_zero_int, v0)) & ! [v0] : ( ~ ord_less_eq_int(one_one_int, v0) | ord_less_int(zero_zero_int, v0)) & ! [v0] : ~ ord_less_int(v0, v0) & ! [v0] : ( ~ ord_less_int(zero_zero_int, v0) | ord_less_eq_int(one_one_int, v0)) & ? [v0] : ? [v1] : (v1 = v0 | ord_less_int(v1, v0) | ord_less_int(v0, v1)) & ? [v0] : ? [v1] : (ord_less_eq_int(v1, v0) | ord_less_eq_int(v0, v1)) & ? [v0] : ord_less_eq_int(v0, v0) & ( ~ (zero_zero_int = t) | all_0_4_4 = t) % 9.62/2.71 | % 9.62/2.71 | Applying alpha-rule on (1) yields: % 9.62/2.71 | (2) ord_less_int(t, zero_zero_int) % 9.62/2.71 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = zero_zero_int | ~ (times_times_int(v1, v1) = v3) | ~ (times_times_int(v0, v0) = v2) | ~ (plus_plus_int(v2, v3) = v4) | ~ ord_less_eq_int(v4, zero_zero_int)) % 9.62/2.71 | (4) ! [v0] : ! [v1] : (v1 = zero_zero_nat | ~ (number_number_of_nat(v0) = v1) | ~ ord_less_eq_int(v0, pls)) % 9.62/2.71 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (power_power_int(v3, v2) = v1) | ~ (power_power_int(v3, v2) = v0)) % 9.62/2.71 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (times_times_int(v3, v2) = v1) | ~ (times_times_int(v3, v2) = v0)) % 9.62/2.71 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = zero_zero_int | ~ (times_times_int(v1, v1) = v3) | ~ (times_times_int(v0, v0) = v2) | ~ (plus_plus_int(v2, v3) = zero_zero_int)) % 9.62/2.71 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (times_times_nat(v3, v2) = v1) | ~ (times_times_nat(v3, v2) = v0)) % 9.62/2.71 | (9) ! [v0] : ! [v1] : ( ~ (bit0(v0) = v1) | ~ ord_less_eq_int(v0, pls) | ord_less_eq_int(v1, pls)) % 9.62/2.71 | (10) ! [v0] : ! [v1] : ( ~ (bit0(v0) = v1) | ~ ord_less_eq_int(v1, pls) | ord_less_eq_int(v0, pls)) % 9.62/2.71 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (times_times_int(v0, v3) = v4) | ~ (plus_plus_int(v1, v2) = v3) | ? [v5] : ? [v6] : (times_times_int(v0, v2) = v6 & times_times_int(v0, v1) = v5 & plus_plus_int(v5, v6) = v4)) % 9.62/2.71 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (times_times_int(v0, v2) = v4) | ~ (times_times_int(v0, v1) = v3) | ~ (plus_plus_int(v3, v4) = v5) | ? [v6] : (times_times_int(v0, v6) = v5 & plus_plus_int(v1, v2) = v6)) % 9.62/2.71 | (13) ! [v0] : ! [v1] : ( ~ (plus_plus_int(one_one_int, v0) = v1) | ~ ord_less_eq_int(zero_zero_int, v0) | ord_less_int(zero_zero_int, v1)) % 9.62/2.71 | (14) power_power_nat(one_one_nat, all_0_2_2) = one_one_nat % 9.62/2.71 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (times_times_int(v1, v3) = v5) | ~ (times_times_int(v0, v3) = v4) | ~ (number_number_of_int(v2) = v3) | ~ (plus_plus_int(v4, v5) = v6) | ? [v7] : (times_times_int(v7, v3) = v6 & plus_plus_int(v0, v1) = v7)) % 9.62/2.71 | (16) power_power_int(s, all_0_2_2) = all_0_1_1 % 9.62/2.71 | (17) ? [v0] : ? [v1] : (v1 = v0 | ord_less_int(v1, v0) | ord_less_int(v0, v1)) % 9.62/2.71 | (18) times_times_int(all_0_5_5, t) = all_0_4_4 % 9.62/2.71 | (19) ~ ord_less_eq_int(one_one_int, t) % 9.62/2.71 | (20) ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ? [v2] : ? [v3] : (number_number_of_int(v3) = v2 & plus_plus_int(v1, one_one_int) = v2 & plus_plus_int(v0, all_0_10_10) = v3)) % 9.62/2.72 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_nat(v1) = v3) | ~ (number_number_of_nat(v0) = v2) | ~ ord_less_eq_nat(v2, v3) | ~ ord_less_nat(v3, v2)) % 9.62/2.72 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (plus_plus_int(v3, v2) = v1) | ~ (plus_plus_int(v3, v2) = v0)) % 9.62/2.72 | (23) ord_less_int(t, one_one_int) % 9.62/2.72 | (24) ! [v0] : ! [v1] : (v0 = zero_zero_int | ~ (power_power_int(v0, all_0_2_2) = v1) | ord_less_int(zero_zero_int, v1)) % 9.62/2.72 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (times_times_int(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (times_times_int(v3, v4) = v5 & number_number_of_int(v2) = v5 & number_number_of_int(v1) = v4 & number_number_of_int(v0) = v3)) % 9.62/2.72 | (26) ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ~ ord_less_eq_int(v0, pls) | ord_less_eq_int(v1, zero_zero_int)) % 9.62/2.72 | (27) ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ~ ord_less_eq_int(v1, zero_zero_int) | ord_less_eq_int(v0, pls)) % 9.62/2.72 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (bit0(v0) = v2) | ~ (bit0(v0) = v1)) % 9.62/2.72 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = zero_zero_int | ~ (power_power_int(v1, all_0_2_2) = v3) | ~ (power_power_int(v0, all_0_2_2) = v2) | ~ (plus_plus_int(v2, v3) = v4) | ord_less_int(zero_zero_int, v4)) % 9.62/2.72 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (plus_plus_int(v3, v1) = v5) | ~ (plus_plus_int(v2, v0) = v4) | ~ ord_less_eq_int(v0, v1) | ~ ord_less_int(v2, v3) | ord_less_int(v4, v5)) % 9.62/2.72 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v1, v0) = v2) | ~ ord_less_eq_int(pls, v1) | ~ ord_less_eq_int(pls, v0) | ? [v3] : ? [v4] : ? [v5] : (number_number_of_int(v2) = v5 & number_number_of_int(v1) = v3 & number_number_of_int(v0) = v4 & plus_plus_int(v3, v4) = v5)) % 9.62/2.72 | (32) ! [v0] : ! [v1] : (v1 = v0 | ~ (times_times_int(one_one_int, v0) = v1)) % 9.62/2.72 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (power_power_nat(v3, v2) = v1) | ~ (power_power_nat(v3, v2) = v0)) % 9.62/2.72 | (34) ! [v0] : ! [v1] : ( ~ (bit1(v0) = v1) | ~ ord_less_int(v0, pls) | ord_less_eq_int(v1, pls)) % 9.62/2.72 | (35) ! [v0] : ! [v1] : ( ~ (bit1(v0) = v1) | ~ ord_less_eq_int(v1, pls) | ord_less_int(v0, pls)) % 9.62/2.72 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (times_times_nat(v1, v3) = v5) | ~ (times_times_nat(v0, v3) = v4) | ~ (number_number_of_nat(v2) = v3) | ~ (plus_plus_nat(v4, v5) = v6) | ? [v7] : (times_times_nat(v7, v3) = v6 & plus_plus_nat(v0, v1) = v7)) % 9.62/2.72 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (times_times_int(v1, v1) = v3) | ~ (times_times_int(v0, v0) = v2) | ~ (plus_plus_int(v2, v3) = v4) | ord_less_eq_int(zero_zero_int, v4)) % 9.62/2.72 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (plus_plus_int(v1, v3) = v4) | ~ (plus_plus_int(v0, v2) = v3) | ? [v5] : (plus_plus_int(v1, v2) = v5 & plus_plus_int(v0, v5) = v4)) % 9.62/2.72 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (number_number_of_int(v1) = v3) | ~ (number_number_of_int(v0) = v2) | ~ (plus_plus_int(v2, v3) = v4) | ? [v5] : (number_number_of_int(v5) = v4 & plus_plus_int(v0, v1) = v5)) % 9.62/2.72 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (times_times_int(v3, v4) = v5) | ~ (number_number_of_int(v0) = v3) | ~ (plus_plus_int(v1, v2) = v4) | ? [v6] : ? [v7] : (times_times_int(v3, v2) = v7 & times_times_int(v3, v1) = v6 & plus_plus_int(v6, v7) = v5)) % 9.62/2.72 | (41) ! [v0] : ( ~ (number_number_of_nat(v0) = zero_zero_nat) | ord_less_eq_int(v0, pls)) % 9.62/2.72 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_nat(v1) = v2) | ~ (number_number_of_nat(v0) = v3) | ord_less_eq_nat(v3, v2) | ord_less_nat(v2, v3)) % 9.62/2.72 | (43) ? [v0] : ? [v1] : (ord_less_eq_int(v1, v0) | ord_less_eq_int(v0, v1)) % 9.62/2.72 | (44) ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ? [v2] : ? [v3] : (number_number_of_int(v3) = v2 & plus_plus_int(all_0_10_10, v0) = v3 & plus_plus_int(one_one_int, v1) = v2)) % 9.62/2.72 | (45) number_number_of_int(all_0_8_8) = all_0_7_7 % 9.62/2.72 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (bit0(v1) = v2) | ~ (bit0(v0) = v2)) % 9.62/2.72 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_int(v1) = v3) | ~ (number_number_of_int(v0) = v2) | ~ ord_less_eq_int(v0, v1) | ord_less_eq_int(v2, v3)) % 9.62/2.72 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_int(v1) = v3) | ~ (number_number_of_int(v0) = v2) | ~ ord_less_eq_int(v2, v3) | ord_less_eq_int(v0, v1)) % 9.62/2.72 | (49) ord_less_int(t, all_0_5_5) % 9.62/2.72 | (50) ! [v0] : ! [v1] : ( ~ (bit0(v0) = v1) | ~ ord_less_eq_int(pls, v0) | ord_less_eq_int(pls, v1)) % 9.62/2.72 | (51) ! [v0] : ! [v1] : ( ~ (bit0(v0) = v1) | ~ ord_less_eq_int(pls, v1) | ord_less_eq_int(pls, v0)) % 9.62/2.72 | (52) ! [v0] : ! [v1] : (v1 = v0 | ~ ord_less_eq_int(v0, v1) | ord_less_int(v0, v1)) % 9.62/2.72 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (bit0(v2) = v1) | ~ (bit0(v2) = v0)) % 9.62/2.72 | (54) ! [v0] : (v0 = zero_zero_int | ~ (plus_plus_int(zero_zero_int, zero_zero_int) = v0)) % 9.62/2.72 | (55) ! [v0] : (v0 = zero_zero_int | ~ (power_power_int(v0, all_0_2_2) = zero_zero_int)) % 9.62/2.72 | (56) power_power_nat(zero_zero_nat, all_0_2_2) = zero_zero_nat % 9.62/2.72 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (power_power_int(v1, all_0_2_2) = v3) | ~ (power_power_int(v0, all_0_2_2) = v2) | ~ (plus_plus_int(v2, v3) = v4) | ~ ord_less_int(v4, zero_zero_int)) % 9.62/2.72 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = zero_zero_int | ~ (times_times_int(v1, v1) = v3) | ~ (times_times_int(v0, v0) = v2) | ~ (plus_plus_int(v2, v3) = v4) | ~ ord_less_eq_int(v4, zero_zero_int)) % 9.62/2.72 | (59) power_power_int(zero_zero_int, all_0_2_2) = zero_zero_int % 9.62/2.72 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (times_times_int(v2, v3) = v4) | ~ (number_number_of_int(v1) = v3) | ~ (number_number_of_int(v0) = v2) | ? [v5] : (times_times_int(v0, v1) = v5 & number_number_of_int(v5) = v4)) % 9.62/2.72 | (61) ! [v0] : ~ ord_less_int(v0, v0) % 9.62/2.72 | (62) times_times_int(all_0_7_7, m) = all_0_6_6 % 9.62/2.72 | (63) number_number_of_nat(all_0_10_10) = one_one_nat % 9.62/2.72 | (64) ~ ord_less_int(all_0_4_4, zero_zero_int) % 9.62/2.72 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_nat(v1) = v3) | ~ (number_number_of_nat(v0) = v2) | ~ ord_less_int(v0, v1) | ~ ord_less_int(pls, v1) | ord_less_nat(v2, v3)) % 9.62/2.72 | (66) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (bit1(v2) = v1) | ~ (bit1(v2) = v0)) % 9.62/2.72 | (67) ! [v0] : ! [v1] : (v1 = v0 | ~ (number_number_of_int(v0) = v1)) % 9.62/2.72 | (68) ~ (zero_zero_int = t) | all_0_4_4 = t % 9.62/2.72 | (69) ! [v0] : ! [v1] : (v1 = v0 | ~ (times_times_int(v0, one_one_int) = v1)) % 9.62/2.72 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (number_number_of_nat(v1) = v2) | ~ (number_number_of_nat(v0) = v3) | ~ (plus_plus_nat(v2, v3) = v4) | ~ ord_less_int(v0, pls) | ord_less_int(v1, pls)) % 9.62/2.72 | (71) ord_less_int(zero_zero_int, all_0_5_5) % 9.62/2.72 | (72) ! [v0] : ! [v1] : (v1 = pls | ~ (times_times_int(pls, v0) = v1)) % 9.62/2.72 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v1, v0) = v2) | ord_less_int(v1, pls) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (number_number_of_nat(v2) = v6 & number_number_of_nat(v1) = v3 & number_number_of_nat(v0) = v4 & plus_plus_nat(v3, v4) = v5 & (v6 = v5 | ord_less_int(v0, pls)) & (v5 = v3 | ~ ord_less_int(v0, pls)))) % 9.62/2.72 | (74) ? [v0] : ord_less_eq_int(v0, v0) % 9.62/2.72 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = zero_zero_int | ~ (power_power_int(v1, all_0_2_2) = v3) | ~ (power_power_int(v0, all_0_2_2) = v2) | ~ (plus_plus_int(v2, v3) = zero_zero_int)) % 9.62/2.72 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_nat(v1) = v3) | ~ (number_number_of_nat(v0) = v2) | ~ ord_less_nat(v2, v3) | ~ ord_less_int(v0, v1) | ord_less_int(pls, v1)) % 9.62/2.73 | (77) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (number_number_of_int(v2) = v1) | ~ (number_number_of_int(v2) = v0)) % 9.62/2.73 | (78) twoSqu526106917sum2sq(all_0_4_4) % 9.62/2.73 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = zero_zero_int | ~ (power_power_int(v1, all_0_2_2) = v3) | ~ (power_power_int(v0, all_0_2_2) = v2) | ~ (plus_plus_int(v2, v3) = v4) | ord_less_int(zero_zero_int, v4)) % 9.62/2.73 | (80) number_number_of_nat(pls) = zero_zero_nat % 9.62/2.73 | (81) plus_plus_int(all_0_1_1, one_one_int) = all_0_4_4 % 9.62/2.73 | (82) ~ ord_less_int(zero_zero_int, zero_zero_int) % 9.62/2.73 | (83) number_number_of_int(pls) = zero_zero_int % 9.62/2.73 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ ord_less_eq_int(v2, v0) | ~ ord_less_eq_int(v1, v2) | ord_less_eq_int(v1, v0)) % 9.62/2.73 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v0) = v2) | ~ (bit1(v1) = v3) | ~ ord_less_int(v2, v3) | ord_less_eq_int(v0, v1)) % 9.62/2.73 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v0) = v2) | ~ (bit1(v1) = v3) | ~ ord_less_eq_int(v0, v1) | ord_less_int(v2, v3)) % 9.62/2.73 | (87) ! [v0] : ! [v1] : ( ~ (bit1(v0) = v1) | ~ ord_less_eq_int(pls, v0) | ord_less_eq_int(pls, v1)) % 9.62/2.73 | (88) ! [v0] : ! [v1] : ( ~ (bit1(v0) = v1) | ~ ord_less_eq_int(pls, v1) | ord_less_eq_int(pls, v0)) % 9.62/2.73 | (89) bit0(all_0_9_9) = all_0_8_8 % 9.62/2.73 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (times_times_int(v3, v4) = v5) | ~ (number_number_of_int(v2) = v4) | ~ (plus_plus_int(v0, v1) = v3) | ? [v6] : ? [v7] : (times_times_int(v1, v4) = v7 & times_times_int(v0, v4) = v6 & plus_plus_int(v6, v7) = v5)) % 9.62/2.73 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = zero_zero_int | ~ (power_power_int(v1, all_0_2_2) = v3) | ~ (power_power_int(v0, all_0_2_2) = v2) | ~ (plus_plus_int(v2, v3) = zero_zero_int)) % 9.62/2.73 | (92) times_times_int(all_0_5_5, zero_zero_int) = all_0_3_3 % 9.62/2.73 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_int(v1) = v3) | ~ (number_number_of_int(v0) = v2) | ~ ord_less_int(v0, v1) | ord_less_int(v2, v3)) % 9.62/2.73 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_int(v1) = v3) | ~ (number_number_of_int(v0) = v2) | ~ ord_less_int(v2, v3) | ord_less_int(v0, v1)) % 9.62/2.73 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (plus_plus_int(v0, v2) = v4) | ~ (plus_plus_int(v0, v1) = v3) | ~ ord_less_eq_int(v1, v2) | ord_less_eq_int(v3, v4)) % 9.62/2.73 | (96) ! [v0] : ! [v1] : ( ~ (plus_plus_int(v0, all_0_10_10) = v1) | ? [v2] : ? [v3] : (number_number_of_int(v1) = v3 & number_number_of_int(v0) = v2 & plus_plus_int(v2, one_one_int) = v3)) % 9.62/2.73 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ (times_times_int(v0, v1) = v2) | times_times_int(v1, v0) = v2) % 9.62/2.73 | (98) ! [v0] : ! [v1] : ! [v2] : ( ~ (times_times_int(v1, v0) = v2) | times_times_int(v0, v1) = v2) % 9.62/2.73 | (99) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v0, v1) = v2) | plus_plus_int(v1, v0) = v2) % 9.62/2.73 | (100) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v1, v0) = v2) | plus_plus_int(v0, v1) = v2) % 9.62/2.73 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (times_times_int(v3, v2) = v4) | ~ (plus_plus_int(v0, v1) = v3) | ? [v5] : ? [v6] : (times_times_int(v1, v2) = v6 & times_times_int(v0, v2) = v5 & plus_plus_int(v5, v6) = v4)) % 9.62/2.73 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (times_times_int(v4, v2) = v5) | ~ (times_times_int(v3, v5) = v6) | ~ (number_number_of_int(v1) = v4) | ~ (number_number_of_int(v0) = v3) | ? [v7] : ? [v8] : (times_times_int(v8, v2) = v6 & times_times_int(v0, v1) = v7 & number_number_of_int(v7) = v8)) % 9.62/2.73 | (103) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v1, v0) = v2) | ~ ord_less_eq_int(pls, v1) | ~ ord_less_eq_int(pls, v0) | ? [v3] : ? [v4] : ? [v5] : (number_number_of_nat(v2) = v5 & number_number_of_nat(v1) = v3 & number_number_of_nat(v0) = v4 & plus_plus_nat(v3, v4) = v5)) % 9.62/2.73 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (number_number_of_nat(v1) = v2) | ~ (number_number_of_nat(v0) = v3) | ~ (plus_plus_nat(v2, v3) = v4) | ord_less_int(v1, pls) | ord_less_int(v0, pls) | ? [v5] : (number_number_of_nat(v5) = v4 & plus_plus_int(v1, v0) = v5)) % 9.62/2.73 | (105) ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ~ ord_less_eq_int(zero_zero_int, v1) | ord_less_eq_int(pls, v0)) % 9.62/2.73 | (106) ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ~ ord_less_eq_int(pls, v0) | ord_less_eq_int(zero_zero_int, v1)) % 9.62/2.73 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_nat(v1) = v3) | ~ (number_number_of_nat(v0) = v2) | ~ ord_less_nat(v2, v3) | ord_less_int(v0, v1)) % 9.62/2.73 | (108) ! [v0] : ! [v1] : ( ~ (times_times_int(zero_zero_int, zero_zero_int) = v0) | ~ (plus_plus_int(v0, v0) = v1) | ord_less_eq_int(v1, zero_zero_int)) % 9.62/2.73 | (109) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (bit1(v1) = v2) | ~ (bit1(v0) = v2)) % 9.62/2.73 | (110) plus_plus_int(all_0_6_6, one_one_int) = all_0_5_5 % 9.62/2.73 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (times_times_int(v3, v2) = v5) | ~ (times_times_int(v3, v1) = v4) | ~ (number_number_of_int(v0) = v3) | ~ (plus_plus_int(v4, v5) = v6) | ? [v7] : (times_times_int(v3, v7) = v6 & plus_plus_int(v1, v2) = v7)) % 9.62/2.73 | (112) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (number_number_of_int(v1) = v2) | ~ (number_number_of_int(v0) = v2)) % 9.62/2.73 | (113) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v1, one_one_int) = v2) | ~ ord_less_int(v0, v2) | ord_less_eq_int(v0, v1)) % 9.62/2.73 | (114) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v1, one_one_int) = v2) | ~ ord_less_eq_int(v0, v1) | ord_less_int(v0, v2)) % 9.62/2.73 | (115) ! [v0] : ! [v1] : (v1 = v0 | ~ ord_less_eq_int(v1, v0) | ~ ord_less_eq_int(v0, v1)) % 9.62/2.73 | (116) ! [v0] : ! [v1] : ( ~ ord_less_int(v0, v1) | ord_less_eq_int(v0, v1)) % 9.62/2.73 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_int(v1) = v3) | ~ (number_number_of_int(v0) = v2) | ~ ord_less_eq_int(v2, v3) | ~ ord_less_int(v3, v2)) % 9.62/2.73 | (118) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (number_number_of_int(v0) = v2) | ~ (number_number_of_int(v0) = v1)) % 9.62/2.73 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (number_number_of_int(v1) = v2) | ~ (number_number_of_int(v0) = v3) | ~ (plus_plus_int(v2, v3) = v4) | ~ ord_less_eq_int(pls, v1) | ~ ord_less_eq_int(pls, v0) | ? [v5] : (number_number_of_int(v5) = v4 & plus_plus_int(v1, v0) = v5)) % 9.62/2.73 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (times_times_int(v4, v2) = v5) | ~ (times_times_int(v0, v1) = v3) | ~ (number_number_of_int(v3) = v4) | ? [v6] : ? [v7] : ? [v8] : (times_times_int(v7, v2) = v8 & times_times_int(v6, v8) = v5 & number_number_of_int(v1) = v7 & number_number_of_int(v0) = v6)) % 9.62/2.73 | (121) ! [v0] : ! [v1] : ! [v2] : ( ~ (times_times_int(v1, v0) = v2) | ~ ord_less_eq_int(pls, v1) | ~ ord_less_eq_int(pls, v0) | ? [v3] : ? [v4] : ? [v5] : (times_times_nat(v3, v4) = v5 & number_number_of_nat(v2) = v5 & number_number_of_nat(v1) = v3 & number_number_of_nat(v0) = v4)) % 9.62/2.73 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (plus_plus_int(v1, v2) = v3) | ~ (plus_plus_int(v0, v3) = v4) | ? [v5] : (plus_plus_int(v5, v2) = v4 & plus_plus_int(v0, v1) = v5)) % 9.62/2.73 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v0) = v2) | ~ (times_times_int(v2, v1) = v3) | ? [v4] : (bit0(v4) = v3 & times_times_int(v0, v1) = v4)) % 9.62/2.73 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (times_times_int(v3, v2) = v4) | ~ (times_times_int(v0, v1) = v3) | ? [v5] : (times_times_int(v1, v2) = v5 & times_times_int(v0, v5) = v4)) % 9.62/2.73 | (125) zprime(all_0_5_5) % 9.62/2.73 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (times_times_nat(v3, v4) = v5) | ~ (number_number_of_nat(v2) = v4) | ~ (plus_plus_nat(v0, v1) = v3) | ? [v6] : ? [v7] : (times_times_nat(v1, v4) = v7 & times_times_nat(v0, v4) = v6 & plus_plus_nat(v6, v7) = v5)) % 9.62/2.73 | (127) bit1(pls) = all_0_10_10 % 9.62/2.74 | (128) ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ~ ord_less_eq_int(v0, all_0_10_10) | ord_less_eq_int(v1, one_one_int)) % 9.62/2.74 | (129) ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ~ ord_less_eq_int(v1, one_one_int) | ord_less_eq_int(v0, all_0_10_10)) % 9.62/2.74 | (130) times_times_int(all_0_5_5, all_0_0_0) = all_0_4_4 % 9.62/2.74 | (131) ord_less_int(all_0_4_4, all_0_3_3) % 9.62/2.74 | (132) ! [v0] : ! [v1] : ! [v2] : ( ~ (times_times_int(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (times_times_int(v4, v5) = v3 & number_number_of_int(v2) = v3 & number_number_of_int(v1) = v5 & number_number_of_int(v0) = v4)) % 9.62/2.74 | (133) ! [v0] : ! [v1] : ! [v2] : ( ~ (times_times_int(v1, v0) = v2) | ~ ord_less_eq_int(pls, v1) | ~ ord_less_eq_int(pls, v0) | ? [v3] : ? [v4] : ? [v5] : (times_times_int(v3, v4) = v5 & number_number_of_int(v2) = v5 & number_number_of_int(v1) = v3 & number_number_of_int(v0) = v4)) % 9.62/2.74 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (times_times_int(v2, v3) = v4) | ~ (number_number_of_int(v1) = v2) | ~ (number_number_of_int(v0) = v3) | ~ ord_less_eq_int(pls, v1) | ~ ord_less_eq_int(pls, v0) | ? [v5] : (times_times_int(v1, v0) = v5 & number_number_of_int(v5) = v4)) % 9.62/2.74 | (135) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (number_number_of_int(v2) = v5 & number_number_of_int(v1) = v4 & number_number_of_int(v0) = v3 & plus_plus_int(v3, v4) = v5)) % 9.62/2.74 | (136) ! [v0] : ! [v1] : ( ~ (plus_plus_int(all_0_10_10, v0) = v1) | ? [v2] : ? [v3] : (number_number_of_int(v1) = v3 & number_number_of_int(v0) = v2 & plus_plus_int(one_one_int, v2) = v3)) % 9.62/2.74 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (number_number_of_nat(v1) = v2) | ~ (number_number_of_nat(v0) = v3) | ~ (plus_plus_nat(v2, v3) = v4) | ~ ord_less_eq_int(pls, v1) | ~ ord_less_eq_int(pls, v0) | ? [v5] : (number_number_of_nat(v5) = v4 & plus_plus_int(v1, v0) = v5)) % 9.62/2.74 | (138) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (times_times_int(v1, v2) = v4) | ~ (times_times_int(v0, v2) = v3) | ~ (plus_plus_int(v3, v4) = v5) | ? [v6] : (times_times_int(v6, v2) = v5 & plus_plus_int(v0, v1) = v6)) % 9.62/2.74 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (number_number_of_nat(v1) = v2) | ~ (number_number_of_nat(v0) = v3) | ~ (plus_plus_nat(v2, v3) = v4) | ~ ord_less_int(v1, pls)) % 9.62/2.74 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = zero_zero_int | ~ (times_times_int(v1, v1) = v3) | ~ (times_times_int(v0, v0) = v2) | ~ (plus_plus_int(v2, v3) = zero_zero_int)) % 9.62/2.74 | (141) bit0(all_0_10_10) = all_0_9_9 % 9.62/2.74 | (142) ord_less_eq_int(pls, pls) % 9.62/2.74 | (143) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (times_times_nat(v2, v3) = v4) | ~ (number_number_of_nat(v1) = v2) | ~ (number_number_of_nat(v0) = v3) | ~ ord_less_eq_int(pls, v1) | ~ ord_less_eq_int(pls, v0) | ? [v5] : (number_number_of_nat(v5) = v4 & times_times_int(v1, v0) = v5)) % 9.62/2.74 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (number_number_of_int(v1) = v2) | ~ (number_number_of_int(v0) = v3) | ord_less_eq_int(v3, v2) | ord_less_int(v2, v3)) % 9.62/2.74 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit1(v1) = v3) | ~ (bit1(v0) = v2) | ~ ord_less_eq_int(v0, v1) | ord_less_eq_int(v2, v3)) % 9.62/2.74 | (146) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit1(v1) = v3) | ~ (bit1(v0) = v2) | ~ ord_less_eq_int(v2, v3) | ord_less_eq_int(v0, v1)) % 9.62/2.74 | (147) number_number_of_nat(all_0_9_9) = all_0_2_2 % 9.62/2.74 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v1) = v3) | ~ (bit0(v0) = v2) | ~ ord_less_eq_int(v0, v1) | ord_less_eq_int(v2, v3)) % 9.62/2.74 | (149) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v1) = v3) | ~ (bit0(v0) = v2) | ~ ord_less_eq_int(v2, v3) | ord_less_eq_int(v0, v1)) % 9.62/2.74 | (150) ! [v0] : ! [v1] : ! [v2] : ( ~ (times_times_int(v0, v1) = v2) | ? [v3] : ? [v4] : (bit0(v2) = v4 & bit0(v0) = v3 & times_times_int(v3, v1) = v4)) % 9.62/2.74 | (151) ! [v0] : ( ~ ord_less_int(zero_zero_int, v0) | ord_less_eq_int(one_one_int, v0)) % 9.62/2.74 | (152) ! [v0] : ( ~ ord_less_eq_int(one_one_int, v0) | ord_less_int(zero_zero_int, v0)) % 9.62/2.74 | (153) ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ~ ord_less_eq_int(one_one_int, v1) | ord_less_eq_int(all_0_10_10, v0)) % 9.62/2.74 | (154) ! [v0] : ! [v1] : ( ~ (number_number_of_int(v0) = v1) | ~ ord_less_eq_int(all_0_10_10, v0) | ord_less_eq_int(one_one_int, v1)) % 9.62/2.74 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (plus_plus_nat(v3, v2) = v1) | ~ (plus_plus_nat(v3, v2) = v0)) % 9.62/2.74 | (156) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v0) = v2) | ~ (bit1(v1) = v3) | ~ ord_less_eq_int(v0, v1) | ord_less_eq_int(v2, v3)) % 9.62/2.74 | (157) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v0) = v2) | ~ (bit1(v1) = v3) | ~ ord_less_eq_int(v2, v3) | ord_less_eq_int(v0, v1)) % 9.62/2.74 | (158) ! [v0] : ( ~ (plus_plus_int(zero_zero_int, zero_zero_int) = v0) | ~ ord_less_int(zero_zero_int, v0)) % 9.62/2.74 | (159) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (number_number_of_nat(v2) = v1) | ~ (number_number_of_nat(v2) = v0)) % 9.62/2.74 | (160) ! [v0] : ! [v1] : ( ~ (number_number_of_nat(v0) = v1) | ~ ord_less_int(pls, v0) | ord_less_nat(zero_zero_nat, v1)) % 9.62/2.74 | (161) ! [v0] : ! [v1] : ( ~ (number_number_of_nat(v0) = v1) | ~ ord_less_nat(zero_zero_nat, v1) | ord_less_int(pls, v0)) % 9.62/2.74 | (162) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (bit1(v0) = v2) | ~ (bit1(v0) = v1)) % 9.62/2.74 | (163) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (times_times_nat(v3, v2) = v5) | ~ (times_times_nat(v3, v1) = v4) | ~ (number_number_of_nat(v0) = v3) | ~ (plus_plus_nat(v4, v5) = v6) | ? [v7] : (times_times_nat(v3, v7) = v6 & plus_plus_nat(v1, v2) = v7)) % 9.62/2.74 | (164) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (times_times_int(v3, v4) = v5) | ~ (power_power_int(v0, v2) = v4) | ~ (power_power_int(v0, v1) = v3) | ? [v6] : (plus_plus_nat(v1, v2) = v6 & power_power_int(v0, v6) = v5)) % 9.62/2.74 | (165) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (times_times_nat(v3, v4) = v5) | ~ (number_number_of_nat(v0) = v3) | ~ (plus_plus_nat(v1, v2) = v4) | ? [v6] : ? [v7] : (times_times_nat(v3, v2) = v7 & times_times_nat(v3, v1) = v6 & plus_plus_nat(v6, v7) = v5)) % 9.62/2.74 | (166) plus_plus_nat(one_one_nat, one_one_nat) = all_0_2_2 % 9.62/2.74 | (167) ! [v0] : ! [v1] : ( ~ (power_power_int(v0, all_0_2_2) = v1) | ~ ord_less_int(v1, zero_zero_int)) % 9.62/2.74 | (168) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (times_times_int(v1, v2) = v3) | ~ (times_times_int(v0, v3) = v4) | ? [v5] : (times_times_int(v5, v2) = v4 & times_times_int(v0, v1) = v5)) % 9.62/2.74 | (169) ! [v0] : ! [v1] : ( ~ (bit1(v0) = v1) | ~ ord_less_int(pls, v1) | ord_less_eq_int(pls, v0)) % 9.62/2.74 | (170) ! [v0] : ! [v1] : ( ~ (bit1(v0) = v1) | ~ ord_less_eq_int(pls, v0) | ord_less_int(pls, v1)) % 9.62/2.74 | (171) power_power_int(one_one_int, all_0_2_2) = one_one_int % 9.62/2.74 | (172) ! [v0] : ! [v1] : (v1 = zero_zero_int | ~ (times_times_int(zero_zero_int, zero_zero_int) = v0) | ~ (plus_plus_int(v0, v0) = v1)) % 9.62/2.74 | (173) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (plus_plus_int(v1, v2) = v3) | ~ (plus_plus_int(v0, v3) = v4) | ? [v5] : (plus_plus_int(v1, v5) = v4 & plus_plus_int(v0, v2) = v5)) % 9.62/2.74 | (174) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (plus_plus_nat(v1, v2) = v3) | ~ (power_power_int(v0, v3) = v4) | ? [v5] : ? [v6] : (times_times_int(v5, v6) = v4 & power_power_int(v0, v2) = v6 & power_power_int(v0, v1) = v5)) % 9.62/2.74 | (175) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v1) = v3) | ~ (bit1(v0) = v2) | ~ ord_less_int(v0, v1) | ord_less_eq_int(v2, v3)) % 9.62/2.74 | (176) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (bit0(v1) = v3) | ~ (bit1(v0) = v2) | ~ ord_less_eq_int(v2, v3) | ord_less_int(v0, v1)) % 9.62/2.74 | (177) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (plus_plus_int(v3, v2) = v4) | ~ (plus_plus_int(v0, v1) = v3) | ? [v5] : (plus_plus_int(v1, v2) = v5 & plus_plus_int(v0, v5) = v4)) % 9.62/2.74 | (178) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v0, one_one_int) = v2) | ~ ord_less_int(v0, v1) | ord_less_eq_int(v2, v1)) % 9.62/2.74 | (179) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus_plus_int(v0, one_one_int) = v2) | ~ ord_less_eq_int(v2, v1) | ord_less_int(v0, v1)) % 9.62/2.74 | % 9.62/2.74 | Instantiating formula (67) with zero_zero_int, pls and discharging atoms number_number_of_int(pls) = zero_zero_int, yields: % 9.62/2.75 | (180) pls = zero_zero_int % 9.62/2.75 | % 9.62/2.75 | Instantiating formula (98) with all_0_3_3, all_0_5_5, zero_zero_int and discharging atoms times_times_int(all_0_5_5, zero_zero_int) = all_0_3_3, yields: % 9.62/2.75 | (181) times_times_int(zero_zero_int, all_0_5_5) = all_0_3_3 % 9.62/2.75 | % 9.62/2.75 | Instantiating formula (72) with all_0_3_3, all_0_5_5 yields: % 9.62/2.75 | (182) all_0_3_3 = pls | ~ (times_times_int(pls, all_0_5_5) = all_0_3_3) % 9.62/2.75 | % 9.62/2.75 +-Applying beta-rule and splitting (182), into two cases. % 9.62/2.75 |-Branch one: % 9.62/2.75 | (183) ~ (times_times_int(pls, all_0_5_5) = all_0_3_3) % 9.62/2.75 | % 9.62/2.75 | From (180) and (183) follows: % 9.62/2.75 | (184) ~ (times_times_int(zero_zero_int, all_0_5_5) = all_0_3_3) % 9.62/2.75 | % 9.62/2.75 | Using (181) and (184) yields: % 9.62/2.75 | (185) $false % 9.62/2.75 | % 9.62/2.75 |-The branch is then unsatisfiable % 9.62/2.75 |-Branch two: % 9.62/2.75 | (186) times_times_int(pls, all_0_5_5) = all_0_3_3 % 9.62/2.75 | (187) all_0_3_3 = pls % 9.62/2.75 | % 9.62/2.75 | Combining equations (180,187) yields a new equation: % 9.62/2.75 | (188) all_0_3_3 = zero_zero_int % 9.62/2.75 | % 9.62/2.75 | From (188) and (131) follows: % 9.62/2.75 | (189) ord_less_int(all_0_4_4, zero_zero_int) % 9.62/2.75 | % 9.62/2.75 | Using (189) and (64) yields: % 9.62/2.75 | (185) $false % 9.62/2.75 | % 9.62/2.75 |-The branch is then unsatisfiable % 9.62/2.75 % SZS output end Proof for theBenchmark % 9.62/2.75 % 9.62/2.75 2156ms %------------------------------------------------------------------------------