%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE151+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n028.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Sun Jul 17 01:51:38 EDT 2022 % Result : Theorem 28.73s 8.70s % Output : Proof 30.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : KLE151+1 : TPTP v8.1.0. Released v4.0.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n028.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Thu Jun 16 07:23:11 EDT 2022 % 0.12/0.34 % 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 % 0.19/0.58 (ePrincess v.1.0) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2015 % 0.19/0.58 (c) Peter Backeman, 2014-2015 % 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.58 Bug reports to peter@backeman.se % 0.19/0.58 % 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.69/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.55/0.96 Prover 0: Preprocessing ... % 2.24/1.21 Prover 0: Constructing countermodel ... % 17.68/5.96 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 17.75/5.99 Prover 1: Preprocessing ... % 18.05/6.09 Prover 1: Constructing countermodel ... % 28.01/8.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 28.06/8.57 Prover 2: Preprocessing ... % 28.06/8.61 Prover 2: Warning: ignoring some quantifiers % 28.06/8.61 Prover 2: Constructing countermodel ... % 28.73/8.70 Prover 2: proved (143ms) % 28.73/8.70 Prover 1: stopped % 28.73/8.70 Prover 0: stopped % 28.73/8.70 % 28.73/8.70 No countermodel exists, formula is valid % 28.73/8.70 % SZS status Theorem for theBenchmark % 28.73/8.70 % 28.73/8.70 Generating proof ... Warning: ignoring some quantifiers % 29.55/8.93 found it (size 40) % 29.55/8.93 % 29.55/8.93 % SZS output start Proof for theBenchmark % 29.55/8.93 Assumed formulas after preprocessing and simplification: % 29.55/8.93 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & strong_iteration(v5) = v6 & strong_iteration(v2) = v3 & leq(v4, v7) = v8 & multiplication(v6, v0) = v7 & multiplication(v1, v0) = v2 & multiplication(v0, v3) = v4 & multiplication(v0, v1) = v5 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (strong_iteration(v9) = v12) | ~ (leq(v11, v13) = v14) | ~ (multiplication(v12, v10) = v13) | ? [v15] : ? [v16] : ? [v17] : ( ~ (v17 = 0) & leq(v11, v16) = v17 & multiplication(v9, v11) = v15 & addition(v15, v10) = v16)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (leq(v13, v11) = v14) | ~ (star(v9) = v12) | ~ (multiplication(v12, v10) = v13) | ? [v15] : ? [v16] : ? [v17] : ( ~ (v17 = 0) & leq(v16, v11) = v17 & multiplication(v9, v11) = v15 & addition(v15, v10) = v16)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (leq(v13, v11) = v14) | ~ (star(v9) = v12) | ~ (multiplication(v10, v12) = v13) | ? [v15] : ? [v16] : ? [v17] : ( ~ (v17 = 0) & leq(v16, v11) = v17 & multiplication(v11, v9) = v15 & addition(v15, v10) = v16)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (multiplication(v10, v11) = v13) | ~ (multiplication(v9, v11) = v12) | ~ (addition(v12, v13) = v14) | ? [v15] : (multiplication(v15, v11) = v14 & addition(v9, v10) = v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (multiplication(v9, v11) = v13) | ~ (multiplication(v9, v10) = v12) | ~ (addition(v12, v13) = v14) | ? [v15] : (multiplication(v9, v15) = v14 & addition(v10, v11) = v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (multiplication(v12, v11) = v13) | ~ (multiplication(v9, v10) = v12) | ? [v14] : (multiplication(v10, v11) = v14 & multiplication(v9, v14) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (multiplication(v12, v11) = v13) | ~ (addition(v9, v10) = v12) | ? [v14] : ? [v15] : (multiplication(v10, v11) = v15 & multiplication(v9, v11) = v14 & addition(v14, v15) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (multiplication(v11, v9) = v12) | ~ (addition(v12, v10) = v13) | ? [v14] : ? [v15] : ? [v16] : ((v16 = 0 & leq(v15, v11) = 0 & star(v9) = v14 & multiplication(v10, v14) = v15) | ( ~ (v14 = 0) & leq(v13, v11) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (multiplication(v10, v11) = v12) | ~ (multiplication(v9, v12) = v13) | ? [v14] : (multiplication(v14, v11) = v13 & multiplication(v9, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (multiplication(v9, v12) = v13) | ~ (addition(v10, v11) = v12) | ? [v14] : ? [v15] : (multiplication(v9, v11) = v15 & multiplication(v9, v10) = v14 & addition(v14, v15) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (multiplication(v9, v11) = v12) | ~ (addition(v12, v10) = v13) | ? [v14] : ? [v15] : ? [v16] : ((v16 = 0 & strong_iteration(v9) = v14 & leq(v11, v15) = 0 & multiplication(v14, v10) = v15) | ( ~ (v14 = 0) & leq(v11, v13) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (multiplication(v9, v11) = v12) | ~ (addition(v12, v10) = v13) | ? [v14] : ? [v15] : ? [v16] : ((v16 = 0 & leq(v15, v11) = 0 & star(v9) = v14 & multiplication(v14, v10) = v15) | ( ~ (v14 = 0) & leq(v13, v11) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (addition(v12, v9) = v13) | ~ (addition(v11, v10) = v12) | ? [v14] : (addition(v11, v14) = v13 & addition(v10, v9) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (addition(v11, v12) = v13) | ~ (addition(v10, v9) = v12) | ? [v14] : (addition(v14, v9) = v13 & addition(v11, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (leq(v12, v11) = v10) | ~ (leq(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (multiplication(v12, v11) = v10) | ~ (multiplication(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (addition(v12, v11) = v10) | ~ (addition(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (addition(v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & leq(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (leq(v9, v10) = v11) | ? [v12] : ( ~ (v12 = v10) & addition(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (strong_iteration(v11) = v10) | ~ (strong_iteration(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (star(v11) = v10) | ~ (star(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (addition(v10, v9) = v11) | addition(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (addition(v9, v10) = v11) | addition(v10, v9) = v11) & ! [v9] : ! [v10] : (v10 = v9 | ~ (multiplication(v9, one) = v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (multiplication(one, v9) = v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (addition(v9, v9) = v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (addition(v9, zero) = v10)) & ! [v9] : ! [v10] : (v10 = zero | ~ (multiplication(zero, v9) = v10)) & ! [v9] : ! [v10] : ( ~ (strong_iteration(v9) = v10) | ? [v11] : ? [v12] : (star(v9) = v11 & multiplication(v10, zero) = v12 & addition(v11, v12) = v10)) & ! [v9] : ! [v10] : ( ~ (strong_iteration(v9) = v10) | ? [v11] : (multiplication(v9, v10) = v11 & addition(v11, one) = v10)) & ! [v9] : ! [v10] : ( ~ (leq(v9, v10) = 0) | addition(v9, v10) = v10) & ! [v9] : ! [v10] : ( ~ (star(v9) = v10) | ? [v11] : ? [v12] : (strong_iteration(v9) = v11 & multiplication(v11, zero) = v12 & addition(v10, v12) = v11)) & ! [v9] : ! [v10] : ( ~ (star(v9) = v10) | ? [v11] : (multiplication(v10, v9) = v11 & addition(one, v11) = v10)) & ! [v9] : ! [v10] : ( ~ (star(v9) = v10) | ? [v11] : (multiplication(v9, v10) = v11 & addition(one, v11) = v10)) & ! [v9] : ! [v10] : ( ~ (addition(v9, v10) = v10) | leq(v9, v10) = 0) & ? [v9] : ? [v10] : ? [v11] : leq(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : multiplication(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : addition(v10, v9) = v11 & ? [v9] : ? [v10] : strong_iteration(v9) = v10 & ? [v9] : ? [v10] : star(v9) = v10) % 29.92/8.97 | 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 yields: % 29.92/8.97 | (1) ~ (all_0_0_0 = 0) & strong_iteration(all_0_3_3) = all_0_2_2 & strong_iteration(all_0_6_6) = all_0_5_5 & leq(all_0_4_4, all_0_1_1) = all_0_0_0 & multiplication(all_0_2_2, all_0_8_8) = all_0_1_1 & multiplication(all_0_7_7, all_0_8_8) = all_0_6_6 & multiplication(all_0_8_8, all_0_5_5) = all_0_4_4 & multiplication(all_0_8_8, all_0_7_7) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (strong_iteration(v0) = v3) | ~ (leq(v2, v4) = v5) | ~ (multiplication(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v2, v7) = v8 & multiplication(v0, v2) = v6 & addition(v6, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v4, v2) = v5) | ~ (star(v0) = v3) | ~ (multiplication(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v7, v2) = v8 & multiplication(v0, v2) = v6 & addition(v6, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v4, v2) = v5) | ~ (star(v0) = v3) | ~ (multiplication(v1, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v7, v2) = v8 & multiplication(v2, v0) = v6 & addition(v6, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ? [v5] : ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v2, v0) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & leq(v6, v2) = 0 & star(v0) = v5 & multiplication(v1, v5) = v6) | ( ~ (v5 = 0) & leq(v4, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ? [v5] : ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & strong_iteration(v0) = v5 & leq(v2, v6) = 0 & multiplication(v5, v1) = v6) | ( ~ (v5 = 0) & leq(v2, v4) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & leq(v6, v2) = 0 & star(v0) = v5 & multiplication(v5, v1) = v6) | ( ~ (v5 = 0) & leq(v4, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~ (strong_iteration(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1)) & ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1)) & ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) & ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : ? [v3] : (strong_iteration(v0) = v2 & multiplication(v2, zero) = v3 & addition(v1, v3) = v2)) & ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) & ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2 & ? [v0] : ? [v1] : strong_iteration(v0) = v1 & ? [v0] : ? [v1] : star(v0) = v1 % 30.11/8.98 | % 30.11/8.98 | Applying alpha-rule on (1) yields: % 30.11/8.98 | (2) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1)) % 30.11/8.98 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 30.11/8.98 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v4, v2) = v5) | ~ (star(v0) = v3) | ~ (multiplication(v1, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v7, v2) = v8 & multiplication(v2, v0) = v6 & addition(v6, v1) = v7)) % 30.11/8.99 | (5) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1)) % 30.11/8.99 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & leq(v6, v2) = 0 & star(v0) = v5 & multiplication(v5, v1) = v6) | ( ~ (v5 = 0) & leq(v4, v2) = v5))) % 30.11/8.99 | (7) multiplication(all_0_8_8, all_0_7_7) = all_0_3_3 % 30.11/8.99 | (8) ! [v0] : ! [v1] : ( ~ (star(v0) = v1) | ? [v2] : ? [v3] : (strong_iteration(v0) = v2 & multiplication(v2, zero) = v3 & addition(v1, v3) = v2)) % 30.11/8.99 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & strong_iteration(v0) = v5 & leq(v2, v6) = 0 & multiplication(v5, v1) = v6) | ( ~ (v5 = 0) & leq(v2, v4) = v5))) % 30.11/8.99 | (10) strong_iteration(all_0_3_3) = all_0_2_2 % 30.11/8.99 | (11) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 30.11/8.99 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v4, v2) = v5) | ~ (star(v0) = v3) | ~ (multiplication(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v7, v2) = v8 & multiplication(v0, v2) = v6 & addition(v6, v1) = v7)) % 30.11/8.99 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v0, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) % 30.11/8.99 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 30.11/8.99 | (15) leq(all_0_4_4, all_0_1_1) = all_0_0_0 % 30.11/8.99 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 30.11/8.99 | (17) multiplication(all_0_7_7, all_0_8_8) = all_0_6_6 % 30.11/8.99 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 30.11/8.99 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (strong_iteration(v0) = v3) | ~ (leq(v2, v4) = v5) | ~ (multiplication(v3, v1) = v4) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & leq(v2, v7) = v8 & multiplication(v0, v2) = v6 & addition(v6, v1) = v7)) % 30.11/8.99 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (addition(v0, v1) = v3) | ? [v5] : ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4)) % 30.11/8.99 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strong_iteration(v2) = v1) | ~ (strong_iteration(v2) = v0)) % 30.11/8.99 | (22) ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1)) % 30.11/8.99 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (star(v2) = v1) | ~ (star(v2) = v0)) % 30.11/8.99 | (24) ? [v0] : ? [v1] : star(v0) = v1 % 30.11/8.99 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v2, v0) = v3) | ~ (addition(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & leq(v6, v2) = 0 & star(v0) = v5 & multiplication(v1, v5) = v6) | ( ~ (v5 = 0) & leq(v4, v2) = v5))) % 30.11/8.99 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 30.11/8.99 | (27) ! [v0] : ! [v1] : ( ~ (strong_iteration(v0) = v1) | ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1)) % 30.11/8.99 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 30.11/8.99 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v1, v2) = v4) | ~ (multiplication(v0, v2) = v3) | ~ (addition(v3, v4) = v5) | ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) % 30.11/8.99 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 30.11/9.00 | (31) multiplication(all_0_8_8, all_0_5_5) = all_0_4_4 % 30.11/9.00 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 30.11/9.00 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 30.11/9.00 | (34) ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2 % 30.11/9.00 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v0, v3) = v4) | ~ (addition(v1, v2) = v3) | ? [v5] : ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4)) % 30.11/9.00 | (36) ? [v0] : ? [v1] : strong_iteration(v0) = v1 % 30.11/9.00 | (37) strong_iteration(all_0_6_6) = all_0_5_5 % 30.11/9.00 | (38) ~ (all_0_0_0 = 0) % 30.11/9.00 | (39) ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2 % 30.11/9.00 | (40) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 30.11/9.00 | (41) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) % 30.11/9.00 | (42) ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2 % 30.11/9.00 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) % 30.11/9.00 | (44) multiplication(all_0_2_2, all_0_8_8) = all_0_1_1 % 30.11/9.00 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 30.11/9.00 | (46) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) % 30.11/9.00 | (47) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) % 30.11/9.00 | (48) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 30.11/9.00 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 30.11/9.00 | % 30.11/9.00 | Instantiating formula (27) with all_0_5_5, all_0_6_6 and discharging atoms strong_iteration(all_0_6_6) = all_0_5_5, yields: % 30.11/9.00 | (50) ? [v0] : (multiplication(all_0_6_6, all_0_5_5) = v0 & addition(v0, one) = all_0_5_5) % 30.11/9.00 | % 30.11/9.00 | Instantiating formula (19) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_4_4, all_0_8_8, all_0_3_3 and discharging atoms strong_iteration(all_0_3_3) = all_0_2_2, leq(all_0_4_4, all_0_1_1) = all_0_0_0, multiplication(all_0_2_2, all_0_8_8) = all_0_1_1, yields: % 30.11/9.00 | (51) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & leq(all_0_4_4, v1) = v2 & multiplication(all_0_3_3, all_0_4_4) = v0 & addition(v0, all_0_8_8) = v1) % 30.11/9.00 | % 30.11/9.00 | Instantiating (50) with all_18_0_22 yields: % 30.11/9.00 | (52) multiplication(all_0_6_6, all_0_5_5) = all_18_0_22 & addition(all_18_0_22, one) = all_0_5_5 % 30.11/9.00 | % 30.11/9.00 | Applying alpha-rule on (52) yields: % 30.11/9.00 | (53) multiplication(all_0_6_6, all_0_5_5) = all_18_0_22 % 30.11/9.00 | (54) addition(all_18_0_22, one) = all_0_5_5 % 30.11/9.00 | % 30.11/9.00 +-Applying beta-rule and splitting (51), into two cases. % 30.11/9.00 |-Branch one: % 30.11/9.00 | (55) all_0_0_0 = 0 % 30.11/9.00 | % 30.11/9.00 | Equations (55) can reduce 38 to: % 30.11/9.00 | (56) $false % 30.11/9.00 | % 30.11/9.00 |-The branch is then unsatisfiable % 30.11/9.00 |-Branch two: % 30.11/9.00 | (38) ~ (all_0_0_0 = 0) % 30.11/9.00 | (58) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & leq(all_0_4_4, v1) = v2 & multiplication(all_0_3_3, all_0_4_4) = v0 & addition(v0, all_0_8_8) = v1) % 30.11/9.00 | % 30.11/9.00 | Instantiating (58) with all_30_0_28, all_30_1_29, all_30_2_30 yields: % 30.11/9.00 | (59) ~ (all_30_0_28 = 0) & leq(all_0_4_4, all_30_1_29) = all_30_0_28 & multiplication(all_0_3_3, all_0_4_4) = all_30_2_30 & addition(all_30_2_30, all_0_8_8) = all_30_1_29 % 30.11/9.00 | % 30.11/9.00 | Applying alpha-rule on (59) yields: % 30.11/9.00 | (60) ~ (all_30_0_28 = 0) % 30.11/9.00 | (61) leq(all_0_4_4, all_30_1_29) = all_30_0_28 % 30.11/9.00 | (62) multiplication(all_0_3_3, all_0_4_4) = all_30_2_30 % 30.11/9.00 | (63) addition(all_30_2_30, all_0_8_8) = all_30_1_29 % 30.11/9.00 | % 30.11/9.00 | Instantiating formula (43) with all_30_0_28, all_30_1_29, all_0_4_4 and discharging atoms leq(all_0_4_4, all_30_1_29) = all_30_0_28, yields: % 30.11/9.00 | (64) all_30_0_28 = 0 | ? [v0] : ( ~ (v0 = all_30_1_29) & addition(all_0_4_4, all_30_1_29) = v0) % 30.11/9.00 | % 30.11/9.00 | Instantiating formula (49) with all_30_2_30, all_0_3_3, all_0_4_4, all_0_7_7, all_0_8_8 and discharging atoms multiplication(all_0_3_3, all_0_4_4) = all_30_2_30, multiplication(all_0_8_8, all_0_7_7) = all_0_3_3, yields: % 30.11/9.01 | (65) ? [v0] : (multiplication(all_0_7_7, all_0_4_4) = v0 & multiplication(all_0_8_8, v0) = all_30_2_30) % 30.11/9.01 | % 30.11/9.01 | Instantiating formula (49) with all_18_0_22, all_0_6_6, all_0_5_5, all_0_8_8, all_0_7_7 and discharging atoms multiplication(all_0_6_6, all_0_5_5) = all_18_0_22, multiplication(all_0_7_7, all_0_8_8) = all_0_6_6, yields: % 30.11/9.01 | (66) ? [v0] : (multiplication(all_0_7_7, v0) = all_18_0_22 & multiplication(all_0_8_8, all_0_5_5) = v0) % 30.11/9.01 | % 30.11/9.01 | Instantiating formula (35) with all_0_4_4, all_0_5_5, one, all_18_0_22, all_0_8_8 and discharging atoms multiplication(all_0_8_8, all_0_5_5) = all_0_4_4, addition(all_18_0_22, one) = all_0_5_5, yields: % 30.11/9.01 | (67) ? [v0] : ? [v1] : (multiplication(all_0_8_8, all_18_0_22) = v0 & multiplication(all_0_8_8, one) = v1 & addition(v0, v1) = all_0_4_4) % 30.11/9.01 | % 30.11/9.01 | Instantiating (65) with all_50_0_45 yields: % 30.11/9.01 | (68) multiplication(all_0_7_7, all_0_4_4) = all_50_0_45 & multiplication(all_0_8_8, all_50_0_45) = all_30_2_30 % 30.11/9.01 | % 30.11/9.01 | Applying alpha-rule on (68) yields: % 30.11/9.01 | (69) multiplication(all_0_7_7, all_0_4_4) = all_50_0_45 % 30.11/9.01 | (70) multiplication(all_0_8_8, all_50_0_45) = all_30_2_30 % 30.11/9.01 | % 30.11/9.01 | Instantiating (67) with all_80_0_81, all_80_1_82 yields: % 30.11/9.01 | (71) multiplication(all_0_8_8, all_18_0_22) = all_80_1_82 & multiplication(all_0_8_8, one) = all_80_0_81 & addition(all_80_1_82, all_80_0_81) = all_0_4_4 % 30.11/9.01 | % 30.11/9.01 | Applying alpha-rule on (71) yields: % 30.11/9.01 | (72) multiplication(all_0_8_8, all_18_0_22) = all_80_1_82 % 30.11/9.01 | (73) multiplication(all_0_8_8, one) = all_80_0_81 % 30.11/9.01 | (74) addition(all_80_1_82, all_80_0_81) = all_0_4_4 % 30.11/9.01 | % 30.11/9.01 | Instantiating (66) with all_92_0_96 yields: % 30.11/9.01 | (75) multiplication(all_0_7_7, all_92_0_96) = all_18_0_22 & multiplication(all_0_8_8, all_0_5_5) = all_92_0_96 % 30.11/9.01 | % 30.11/9.01 | Applying alpha-rule on (75) yields: % 30.11/9.01 | (76) multiplication(all_0_7_7, all_92_0_96) = all_18_0_22 % 30.11/9.01 | (77) multiplication(all_0_8_8, all_0_5_5) = all_92_0_96 % 30.11/9.01 | % 30.11/9.01 +-Applying beta-rule and splitting (64), into two cases. % 30.11/9.01 |-Branch one: % 30.11/9.01 | (78) all_30_0_28 = 0 % 30.11/9.01 | % 30.11/9.01 | Equations (78) can reduce 60 to: % 30.11/9.01 | (56) $false % 30.11/9.01 | % 30.11/9.01 |-The branch is then unsatisfiable % 30.11/9.01 |-Branch two: % 30.11/9.01 | (60) ~ (all_30_0_28 = 0) % 30.11/9.01 | (81) ? [v0] : ( ~ (v0 = all_30_1_29) & addition(all_0_4_4, all_30_1_29) = v0) % 30.11/9.01 | % 30.11/9.01 | Instantiating (81) with all_98_0_97 yields: % 30.11/9.01 | (82) ~ (all_98_0_97 = all_30_1_29) & addition(all_0_4_4, all_30_1_29) = all_98_0_97 % 30.11/9.01 | % 30.11/9.01 | Applying alpha-rule on (82) yields: % 30.11/9.01 | (83) ~ (all_98_0_97 = all_30_1_29) % 30.11/9.01 | (84) addition(all_0_4_4, all_30_1_29) = all_98_0_97 % 30.11/9.01 | % 30.11/9.01 | Instantiating formula (3) with all_0_8_8, all_0_5_5, all_92_0_96, all_0_4_4 and discharging atoms multiplication(all_0_8_8, all_0_5_5) = all_92_0_96, multiplication(all_0_8_8, all_0_5_5) = all_0_4_4, yields: % 30.11/9.01 | (85) all_92_0_96 = all_0_4_4 % 30.11/9.01 | % 30.11/9.01 | Instantiating formula (48) with all_80_0_81, all_0_8_8 and discharging atoms multiplication(all_0_8_8, one) = all_80_0_81, yields: % 30.11/9.01 | (86) all_80_0_81 = all_0_8_8 % 30.11/9.01 | % 30.11/9.01 | From (85) and (76) follows: % 30.11/9.01 | (87) multiplication(all_0_7_7, all_0_4_4) = all_18_0_22 % 30.11/9.01 | % 30.11/9.01 | From (86) and (74) follows: % 30.11/9.01 | (88) addition(all_80_1_82, all_0_8_8) = all_0_4_4 % 30.11/9.01 | % 30.11/9.01 | Instantiating formula (3) with all_0_7_7, all_0_4_4, all_18_0_22, all_50_0_45 and discharging atoms multiplication(all_0_7_7, all_0_4_4) = all_50_0_45, multiplication(all_0_7_7, all_0_4_4) = all_18_0_22, yields: % 30.11/9.01 | (89) all_50_0_45 = all_18_0_22 % 30.11/9.01 | % 30.11/9.01 | From (89) and (70) follows: % 30.11/9.01 | (90) multiplication(all_0_8_8, all_18_0_22) = all_30_2_30 % 30.11/9.01 | % 30.11/9.01 | Instantiating formula (3) with all_0_8_8, all_18_0_22, all_30_2_30, all_80_1_82 and discharging atoms multiplication(all_0_8_8, all_18_0_22) = all_80_1_82, multiplication(all_0_8_8, all_18_0_22) = all_30_2_30, yields: % 30.11/9.01 | (91) all_80_1_82 = all_30_2_30 % 30.11/9.01 | % 30.11/9.01 | From (91) and (88) follows: % 30.11/9.01 | (92) addition(all_30_2_30, all_0_8_8) = all_0_4_4 % 30.11/9.01 | % 30.11/9.01 | Instantiating formula (14) with all_30_2_30, all_0_8_8, all_0_4_4, all_30_1_29 and discharging atoms addition(all_30_2_30, all_0_8_8) = all_30_1_29, addition(all_30_2_30, all_0_8_8) = all_0_4_4, yields: % 30.11/9.01 | (93) all_30_1_29 = all_0_4_4 % 30.11/9.01 | % 30.11/9.01 | Equations (93) can reduce 83 to: % 30.11/9.01 | (94) ~ (all_98_0_97 = all_0_4_4) % 30.11/9.01 | % 30.11/9.01 | From (93) and (84) follows: % 30.11/9.01 | (95) addition(all_0_4_4, all_0_4_4) = all_98_0_97 % 30.11/9.01 | % 30.11/9.01 | Instantiating formula (26) with all_98_0_97, all_0_4_4 and discharging atoms addition(all_0_4_4, all_0_4_4) = all_98_0_97, yields: % 30.11/9.01 | (96) all_98_0_97 = all_0_4_4 % 30.11/9.01 | % 30.11/9.01 | Equations (96) can reduce 94 to: % 30.11/9.01 | (56) $false % 30.11/9.01 | % 30.11/9.01 |-The branch is then unsatisfiable % 30.11/9.01 % SZS output end Proof for theBenchmark % 30.11/9.01 % 30.11/9.01 8417ms %------------------------------------------------------------------------------