%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE085+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n024.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 01:51:18 EDT 2022 % Result : Theorem 13.26s 6.30s % Output : Proof 15.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : KLE085+1 : TPTP v8.1.0. Released v4.0.0. % 0.06/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n024.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Thu Jun 16 15:56:03 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.59 ____ _ % 0.20/0.59 ___ / __ \_____(_)___ ________ __________ % 0.20/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic % 0.20/0.59 (ePrincess v.1.0) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2015 % 0.20/0.59 (c) Peter Backeman, 2014-2015 % 0.20/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.59 Bug reports to peter@backeman.se % 0.20/0.59 % 0.20/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.51/0.94 Prover 0: Preprocessing ... % 2.28/1.22 Prover 0: Constructing countermodel ... % 12.01/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 12.01/5.96 Prover 1: Preprocessing ... % 12.38/6.06 Prover 1: Constructing countermodel ... % 12.78/6.15 Prover 1: gave up % 12.78/6.15 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 12.78/6.17 Prover 2: Preprocessing ... % 13.26/6.22 Prover 2: Warning: ignoring some quantifiers % 13.26/6.23 Prover 2: Constructing countermodel ... % 13.26/6.30 Prover 2: proved (147ms) % 13.26/6.30 Prover 0: stopped % 13.26/6.30 % 13.26/6.30 No countermodel exists, formula is valid % 13.26/6.30 % SZS status Theorem for theBenchmark % 13.26/6.30 % 13.26/6.30 Generating proof ... Warning: ignoring some quantifiers % 14.55/6.55 found it (size 31) % 14.55/6.55 % 14.55/6.55 % SZS output start Proof for theBenchmark % 14.55/6.55 Assumed formulas after preprocessing and simplification: % 14.55/6.55 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = one) & domain(v0) = v1 & addition(v1, one) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v4, v5) = v7) | ~ (multiplication(v3, v5) = v6) | ~ (addition(v6, v7) = v8) | ? [v9] : (multiplication(v9, v5) = v8 & addition(v3, v4) = v9)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v3, v5) = v7) | ~ (multiplication(v3, v4) = v6) | ~ (addition(v6, v7) = v8) | ? [v9] : (multiplication(v3, v9) = v8 & addition(v4, v5) = v9)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (coantidomain(v5) = v6) | ~ (coantidomain(v3) = v5) | ~ (multiplication(v6, v4) = v7) | ? [v8] : ? [v9] : ? [v10] : (coantidomain(v8) = v9 & coantidomain(v7) = v10 & multiplication(v3, v4) = v8 & addition(v9, v10) = v10)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (antidomain(v5) = v6) | ~ (antidomain(v4) = v5) | ~ (multiplication(v3, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : (antidomain(v8) = v9 & antidomain(v7) = v10 & multiplication(v3, v4) = v8 & addition(v9, v10) = v10)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (multiplication(v6, v5) = v7) | ~ (multiplication(v3, v4) = v6) | ? [v8] : (multiplication(v4, v5) = v8 & multiplication(v3, v8) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (multiplication(v6, v5) = v7) | ~ (addition(v3, v4) = v6) | ? [v8] : ? [v9] : (multiplication(v4, v5) = v9 & multiplication(v3, v5) = v8 & addition(v8, v9) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (multiplication(v4, v5) = v6) | ~ (multiplication(v3, v6) = v7) | ? [v8] : (multiplication(v8, v5) = v7 & multiplication(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (multiplication(v3, v6) = v7) | ~ (addition(v4, v5) = v6) | ? [v8] : ? [v9] : (multiplication(v3, v5) = v9 & multiplication(v3, v4) = v8 & addition(v8, v9) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (addition(v6, v3) = v7) | ~ (addition(v5, v4) = v6) | ? [v8] : (addition(v5, v8) = v7 & addition(v4, v3) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (addition(v5, v6) = v7) | ~ (addition(v4, v3) = v6) | ? [v8] : (addition(v8, v3) = v7 & addition(v5, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (leq(v6, v5) = v4) | ~ (leq(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (multiplication(v6, v5) = v4) | ~ (multiplication(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (addition(v6, v5) = v4) | ~ (addition(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (addition(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & leq(v3, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (leq(v3, v4) = v5) | ? [v6] : ( ~ (v6 = v4) & addition(v3, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (codomain(v5) = v4) | ~ (codomain(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (coantidomain(v5) = v4) | ~ (coantidomain(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (domain(v5) = v4) | ~ (domain(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (antidomain(v5) = v4) | ~ (antidomain(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (coantidomain(v9) = v10 & coantidomain(v7) = v8 & coantidomain(v5) = v6 & coantidomain(v3) = v7 & multiplication(v8, v4) = v9 & addition(v6, v10) = v10)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (antidomain(v9) = v10 & antidomain(v7) = v8 & antidomain(v5) = v6 & antidomain(v4) = v7 & multiplication(v3, v8) = v9 & addition(v6, v10) = v10)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (addition(v4, v3) = v5) | addition(v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (addition(v3, v4) = v5) | addition(v4, v3) = v5) & ! [v3] : ! [v4] : (v4 = v3 | ~ (multiplication(v3, one) = v4)) & ! [v3] : ! [v4] : (v4 = v3 | ~ (multiplication(one, v3) = v4)) & ! [v3] : ! [v4] : (v4 = v3 | ~ (addition(v3, v3) = v4)) & ! [v3] : ! [v4] : (v4 = v3 | ~ (addition(v3, zero) = v4)) & ! [v3] : ! [v4] : (v4 = zero | ~ (multiplication(v3, zero) = v4)) & ! [v3] : ! [v4] : (v4 = zero | ~ (multiplication(zero, v3) = v4)) & ! [v3] : ! [v4] : ( ~ (codomain(v3) = v4) | ? [v5] : (coantidomain(v5) = v4 & coantidomain(v3) = v5)) & ! [v3] : ! [v4] : ( ~ (coantidomain(v3) = v4) | multiplication(v3, v4) = zero) & ! [v3] : ! [v4] : ( ~ (coantidomain(v3) = v4) | ? [v5] : (codomain(v3) = v5 & coantidomain(v4) = v5)) & ! [v3] : ! [v4] : ( ~ (coantidomain(v3) = v4) | ? [v5] : (coantidomain(v4) = v5 & addition(v5, v4) = one)) & ! [v3] : ! [v4] : ( ~ (domain(v3) = v4) | ? [v5] : (antidomain(v5) = v4 & antidomain(v3) = v5)) & ! [v3] : ! [v4] : ( ~ (antidomain(v3) = v4) | multiplication(v4, v3) = zero) & ! [v3] : ! [v4] : ( ~ (antidomain(v3) = v4) | ? [v5] : (domain(v3) = v5 & antidomain(v4) = v5)) & ! [v3] : ! [v4] : ( ~ (antidomain(v3) = v4) | ? [v5] : (antidomain(v4) = v5 & addition(v5, v4) = one)) & ! [v3] : ! [v4] : ( ~ (leq(v3, v4) = 0) | addition(v3, v4) = v4) & ! [v3] : ! [v4] : ( ~ (addition(v3, v4) = v4) | leq(v3, v4) = 0) & ? [v3] : ? [v4] : ? [v5] : leq(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : multiplication(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : addition(v4, v3) = v5 & ? [v3] : ? [v4] : codomain(v3) = v4 & ? [v3] : ? [v4] : coantidomain(v3) = v4 & ? [v3] : ? [v4] : domain(v3) = v4 & ? [v3] : ? [v4] : antidomain(v3) = v4) % 15.07/6.60 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 15.07/6.60 | (1) ~ (all_0_0_0 = one) & domain(all_0_2_2) = all_0_1_1 & addition(all_0_1_1, one) = all_0_0_0 & ! [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] : ( ~ (coantidomain(v2) = v3) | ~ (coantidomain(v0) = v2) | ~ (multiplication(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : (coantidomain(v5) = v6 & coantidomain(v4) = v7 & multiplication(v0, v1) = v5 & addition(v6, v7) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (antidomain(v2) = v3) | ~ (antidomain(v1) = v2) | ~ (multiplication(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (antidomain(v5) = v6 & antidomain(v4) = v7 & multiplication(v0, v1) = v5 & addition(v6, v7) = v7)) & ! [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(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] : ( ~ (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 | ~ (codomain(v2) = v1) | ~ (codomain(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (coantidomain(v2) = v1) | ~ (coantidomain(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (antidomain(v2) = v1) | ~ (antidomain(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (coantidomain(v6) = v7 & coantidomain(v4) = v5 & coantidomain(v2) = v3 & coantidomain(v0) = v4 & multiplication(v5, v1) = v6 & addition(v3, v7) = v7)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (antidomain(v6) = v7 & antidomain(v4) = v5 & antidomain(v2) = v3 & antidomain(v1) = v4 & multiplication(v0, v5) = v6 & addition(v3, v7) = v7)) & ! [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(v0, zero) = v1)) & ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (codomain(v0) = v1) | ? [v2] : (coantidomain(v2) = v1 & coantidomain(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (coantidomain(v0) = v1) | multiplication(v0, v1) = zero) & ! [v0] : ! [v1] : ( ~ (coantidomain(v0) = v1) | ? [v2] : (codomain(v0) = v2 & coantidomain(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (coantidomain(v0) = v1) | ? [v2] : (coantidomain(v1) = v2 & addition(v2, v1) = one)) & ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | ? [v2] : (antidomain(v2) = v1 & antidomain(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (antidomain(v0) = v1) | multiplication(v1, v0) = zero) & ! [v0] : ! [v1] : ( ~ (antidomain(v0) = v1) | ? [v2] : (domain(v0) = v2 & antidomain(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (antidomain(v0) = v1) | ? [v2] : (antidomain(v1) = v2 & addition(v2, v1) = one)) & ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = 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] : codomain(v0) = v1 & ? [v0] : ? [v1] : coantidomain(v0) = v1 & ? [v0] : ? [v1] : domain(v0) = v1 & ? [v0] : ? [v1] : antidomain(v0) = v1 % 15.07/6.61 | % 15.07/6.61 | Applying alpha-rule on (1) yields: % 15.07/6.61 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (codomain(v2) = v1) | ~ (codomain(v2) = v0)) % 15.14/6.61 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 15.15/6.61 | (4) ? [v0] : ? [v1] : antidomain(v0) = v1 % 15.15/6.61 | (5) ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2 % 15.15/6.61 | (6) ! [v0] : ! [v1] : ( ~ (coantidomain(v0) = v1) | multiplication(v0, v1) = zero) % 15.15/6.61 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 15.15/6.61 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 15.15/6.61 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) % 15.15/6.61 | (10) ! [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)) % 15.15/6.61 | (11) ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2 % 15.15/6.61 | (12) ! [v0] : ! [v1] : ( ~ (antidomain(v0) = v1) | ? [v2] : (domain(v0) = v2 & antidomain(v1) = v2)) % 15.15/6.61 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 15.15/6.61 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (coantidomain(v6) = v7 & coantidomain(v4) = v5 & coantidomain(v2) = v3 & coantidomain(v0) = v4 & multiplication(v5, v1) = v6 & addition(v3, v7) = v7)) % 15.15/6.61 | (15) ! [v0] : ! [v1] : ( ~ (coantidomain(v0) = v1) | ? [v2] : (coantidomain(v1) = v2 & addition(v2, v1) = one)) % 15.15/6.61 | (16) ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2 % 15.15/6.61 | (17) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 15.15/6.61 | (18) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 15.15/6.62 | (19) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) % 15.15/6.62 | (20) ! [v0] : ! [v1] : ( ~ (antidomain(v0) = v1) | multiplication(v1, v0) = zero) % 15.15/6.62 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 15.15/6.62 | (22) ! [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)) % 15.15/6.62 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (coantidomain(v2) = v1) | ~ (coantidomain(v2) = v0)) % 15.15/6.62 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (antidomain(v6) = v7 & antidomain(v4) = v5 & antidomain(v2) = v3 & antidomain(v1) = v4 & multiplication(v0, v5) = v6 & addition(v3, v7) = v7)) % 15.15/6.62 | (25) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 15.15/6.62 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 15.15/6.62 | (27) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) % 15.15/6.62 | (28) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) % 15.15/6.62 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (antidomain(v2) = v1) | ~ (antidomain(v2) = v0)) % 15.15/6.62 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 15.15/6.62 | (31) ? [v0] : ? [v1] : codomain(v0) = v1 % 15.15/6.62 | (32) ! [v0] : ! [v1] : ( ~ (antidomain(v0) = v1) | ? [v2] : (antidomain(v1) = v2 & addition(v2, v1) = one)) % 15.15/6.62 | (33) ? [v0] : ? [v1] : domain(v0) = v1 % 15.15/6.62 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (coantidomain(v2) = v3) | ~ (coantidomain(v0) = v2) | ~ (multiplication(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : (coantidomain(v5) = v6 & coantidomain(v4) = v7 & multiplication(v0, v1) = v5 & addition(v6, v7) = v7)) % 15.15/6.62 | (35) ! [v0] : ! [v1] : ( ~ (coantidomain(v0) = v1) | ? [v2] : (codomain(v0) = v2 & coantidomain(v1) = v2)) % 15.15/6.62 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (antidomain(v2) = v3) | ~ (antidomain(v1) = v2) | ~ (multiplication(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (antidomain(v5) = v6 & antidomain(v4) = v7 & multiplication(v0, v1) = v5 & addition(v6, v7) = v7)) % 15.15/6.62 | (37) ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | ? [v2] : (antidomain(v2) = v1 & antidomain(v0) = v2)) % 15.15/6.62 | (38) ~ (all_0_0_0 = one) % 15.15/6.62 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 15.15/6.62 | (40) ! [v0] : ! [v1] : ( ~ (codomain(v0) = v1) | ? [v2] : (coantidomain(v2) = v1 & coantidomain(v0) = v2)) % 15.15/6.62 | (41) ! [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)) % 15.15/6.62 | (42) ! [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)) % 15.15/6.62 | (43) addition(all_0_1_1, one) = all_0_0_0 % 15.15/6.62 | (44) domain(all_0_2_2) = all_0_1_1 % 15.15/6.62 | (45) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) % 15.15/6.62 | (46) ? [v0] : ? [v1] : coantidomain(v0) = v1 % 15.15/6.62 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 15.15/6.62 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 15.15/6.62 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 15.15/6.62 | (50) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) % 15.15/6.62 | % 15.15/6.63 | Instantiating formula (37) with all_0_1_1, all_0_2_2 and discharging atoms domain(all_0_2_2) = all_0_1_1, yields: % 15.15/6.63 | (51) ? [v0] : (antidomain(v0) = all_0_1_1 & antidomain(all_0_2_2) = v0) % 15.15/6.63 | % 15.15/6.63 | Instantiating formula (9) with all_0_0_0, one, all_0_1_1 and discharging atoms addition(all_0_1_1, one) = all_0_0_0, yields: % 15.15/6.63 | (52) all_0_0_0 = one | ? [v0] : ( ~ (v0 = 0) & leq(all_0_1_1, one) = v0) % 15.15/6.63 | % 15.15/6.63 | Instantiating formula (49) with all_0_0_0, all_0_1_1, one and discharging atoms addition(all_0_1_1, one) = all_0_0_0, yields: % 15.15/6.63 | (53) addition(one, all_0_1_1) = all_0_0_0 % 15.15/6.63 | % 15.15/6.63 | Instantiating (51) with all_23_0_20 yields: % 15.15/6.63 | (54) antidomain(all_23_0_20) = all_0_1_1 & antidomain(all_0_2_2) = all_23_0_20 % 15.15/6.63 | % 15.15/6.63 | Applying alpha-rule on (54) yields: % 15.15/6.63 | (55) antidomain(all_23_0_20) = all_0_1_1 % 15.15/6.63 | (56) antidomain(all_0_2_2) = all_23_0_20 % 15.15/6.63 | % 15.15/6.63 +-Applying beta-rule and splitting (52), into two cases. % 15.15/6.63 |-Branch one: % 15.15/6.63 | (57) all_0_0_0 = one % 15.15/6.63 | % 15.15/6.63 | Equations (57) can reduce 38 to: % 15.15/6.63 | (58) $false % 15.15/6.63 | % 15.15/6.63 |-The branch is then unsatisfiable % 15.15/6.63 |-Branch two: % 15.15/6.63 | (38) ~ (all_0_0_0 = one) % 15.15/6.63 | (60) ? [v0] : ( ~ (v0 = 0) & leq(all_0_1_1, one) = v0) % 15.15/6.63 | % 15.15/6.63 | Instantiating formula (32) with all_0_1_1, all_23_0_20 and discharging atoms antidomain(all_23_0_20) = all_0_1_1, yields: % 15.15/6.63 | (61) ? [v0] : (antidomain(all_0_1_1) = v0 & addition(v0, all_0_1_1) = one) % 15.15/6.63 | % 15.15/6.63 | Instantiating formula (32) with all_23_0_20, all_0_2_2 and discharging atoms antidomain(all_0_2_2) = all_23_0_20, yields: % 15.15/6.63 | (62) ? [v0] : (antidomain(all_23_0_20) = v0 & addition(v0, all_23_0_20) = one) % 15.15/6.63 | % 15.15/6.63 | Instantiating (62) with all_37_0_22 yields: % 15.15/6.63 | (63) antidomain(all_23_0_20) = all_37_0_22 & addition(all_37_0_22, all_23_0_20) = one % 15.15/6.63 | % 15.15/6.63 | Applying alpha-rule on (63) yields: % 15.15/6.63 | (64) antidomain(all_23_0_20) = all_37_0_22 % 15.15/6.63 | (65) addition(all_37_0_22, all_23_0_20) = one % 15.15/6.63 | % 15.15/6.63 | Instantiating (61) with all_39_0_23 yields: % 15.15/6.63 | (66) antidomain(all_0_1_1) = all_39_0_23 & addition(all_39_0_23, all_0_1_1) = one % 15.15/6.63 | % 15.15/6.63 | Applying alpha-rule on (66) yields: % 15.15/6.63 | (67) antidomain(all_0_1_1) = all_39_0_23 % 15.15/6.63 | (68) addition(all_39_0_23, all_0_1_1) = one % 15.15/6.63 | % 15.15/6.63 | Instantiating formula (29) with all_23_0_20, all_37_0_22, all_0_1_1 and discharging atoms antidomain(all_23_0_20) = all_37_0_22, antidomain(all_23_0_20) = all_0_1_1, yields: % 15.15/6.63 | (69) all_37_0_22 = all_0_1_1 % 15.15/6.63 | % 15.15/6.63 | From (69) and (65) follows: % 15.15/6.63 | (70) addition(all_0_1_1, all_23_0_20) = one % 15.15/6.63 | % 15.15/6.63 | Instantiating formula (8) with all_0_0_0, one, all_39_0_23, all_0_1_1, all_0_1_1 and discharging atoms addition(all_39_0_23, all_0_1_1) = one, addition(one, all_0_1_1) = all_0_0_0, yields: % 15.15/6.63 | (71) ? [v0] : (addition(all_39_0_23, v0) = all_0_0_0 & addition(all_0_1_1, all_0_1_1) = v0) % 15.15/6.63 | % 15.15/6.63 | Instantiating formula (7) with all_0_0_0, one, all_0_1_1, all_0_1_1, all_23_0_20 and discharging atoms addition(all_0_1_1, all_23_0_20) = one, addition(all_0_1_1, one) = all_0_0_0, yields: % 15.15/6.63 | (72) ? [v0] : (addition(v0, all_23_0_20) = all_0_0_0 & addition(all_0_1_1, all_0_1_1) = v0) % 15.15/6.63 | % 15.15/6.63 | Instantiating (72) with all_55_0_26 yields: % 15.15/6.63 | (73) addition(all_55_0_26, all_23_0_20) = all_0_0_0 & addition(all_0_1_1, all_0_1_1) = all_55_0_26 % 15.15/6.63 | % 15.15/6.63 | Applying alpha-rule on (73) yields: % 15.15/6.63 | (74) addition(all_55_0_26, all_23_0_20) = all_0_0_0 % 15.15/6.63 | (75) addition(all_0_1_1, all_0_1_1) = all_55_0_26 % 15.15/6.63 | % 15.15/6.63 | Instantiating (71) with all_65_0_39 yields: % 15.15/6.63 | (76) addition(all_39_0_23, all_65_0_39) = all_0_0_0 & addition(all_0_1_1, all_0_1_1) = all_65_0_39 % 15.15/6.63 | % 15.15/6.63 | Applying alpha-rule on (76) yields: % 15.15/6.63 | (77) addition(all_39_0_23, all_65_0_39) = all_0_0_0 % 15.15/6.63 | (78) addition(all_0_1_1, all_0_1_1) = all_65_0_39 % 15.15/6.64 | % 15.15/6.64 | Instantiating formula (17) with all_65_0_39, all_0_1_1 and discharging atoms addition(all_0_1_1, all_0_1_1) = all_65_0_39, yields: % 15.15/6.64 | (79) all_65_0_39 = all_0_1_1 % 15.15/6.64 | % 15.15/6.64 | Instantiating formula (39) with all_0_1_1, all_0_1_1, all_55_0_26, all_65_0_39 and discharging atoms addition(all_0_1_1, all_0_1_1) = all_65_0_39, addition(all_0_1_1, all_0_1_1) = all_55_0_26, yields: % 15.15/6.64 | (80) all_65_0_39 = all_55_0_26 % 15.15/6.64 | % 15.15/6.64 | Combining equations (79,80) yields a new equation: % 15.15/6.64 | (81) all_55_0_26 = all_0_1_1 % 15.15/6.64 | % 15.15/6.64 | From (81) and (74) follows: % 15.15/6.64 | (82) addition(all_0_1_1, all_23_0_20) = all_0_0_0 % 15.15/6.64 | % 15.15/6.64 | Instantiating formula (39) with all_0_1_1, all_23_0_20, all_0_0_0, one and discharging atoms addition(all_0_1_1, all_23_0_20) = all_0_0_0, addition(all_0_1_1, all_23_0_20) = one, yields: % 15.15/6.64 | (57) all_0_0_0 = one % 15.15/6.64 | % 15.15/6.64 | Equations (57) can reduce 38 to: % 15.15/6.64 | (58) $false % 15.15/6.64 | % 15.15/6.64 |-The branch is then unsatisfiable % 15.15/6.64 % SZS output end Proof for theBenchmark % 15.15/6.64 % 15.15/6.64 6038ms %------------------------------------------------------------------------------