%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE089+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n003.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 01:51:19 EDT 2022 % Result : Theorem 12.46s 6.36s % Output : Proof 14.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KLE089+1 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n003.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 10:01:41 EDT 2022 % 0.12/0.34 % CPUTime : % 0.60/0.59 ____ _ % 0.60/0.59 ___ / __ \_____(_)___ ________ __________ % 0.60/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.60/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.60/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.60/0.59 % 0.60/0.59 A Theorem Prover for First-Order Logic % 0.60/0.59 (ePrincess v.1.0) % 0.60/0.59 % 0.60/0.59 (c) Philipp Rümmer, 2009-2015 % 0.60/0.59 (c) Peter Backeman, 2014-2015 % 0.60/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.60/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.60/0.59 Bug reports to peter@backeman.se % 0.60/0.59 % 0.60/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.60/0.59 % 0.60/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.55/0.93 Prover 0: Preprocessing ... % 2.49/1.21 Prover 0: Constructing countermodel ... % 10.69/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 10.69/5.96 Prover 1: Preprocessing ... % 11.07/6.05 Prover 1: Constructing countermodel ... % 11.47/6.18 Prover 1: gave up % 11.86/6.18 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 11.86/6.20 Prover 2: Preprocessing ... % 11.86/6.26 Prover 2: Warning: ignoring some quantifiers % 11.86/6.26 Prover 2: Constructing countermodel ... % 12.46/6.36 Prover 2: proved (176ms) % 12.46/6.36 Prover 0: stopped % 12.46/6.36 % 12.46/6.36 No countermodel exists, formula is valid % 12.46/6.36 % SZS status Theorem for theBenchmark % 12.46/6.36 % 12.46/6.36 Generating proof ... Warning: ignoring some quantifiers % 13.80/6.63 found it (size 37) % 13.80/6.63 % 13.80/6.63 % SZS output start Proof for theBenchmark % 13.80/6.63 Assumed formulas after preprocessing and simplification: % 13.80/6.64 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = zero) & domain(v0) = v2 & antidomain(v1) = v3 & multiplication(v2, v1) = v4 & addition(v2, v3) = v3 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v6, v7) = v9) | ~ (multiplication(v5, v7) = v8) | ~ (addition(v8, v9) = v10) | ? [v11] : (multiplication(v11, v7) = v10 & addition(v5, v6) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (multiplication(v5, v7) = v9) | ~ (multiplication(v5, v6) = v8) | ~ (addition(v8, v9) = v10) | ? [v11] : (multiplication(v5, v11) = v10 & addition(v6, v7) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (coantidomain(v7) = v8) | ~ (coantidomain(v5) = v7) | ~ (multiplication(v8, v6) = v9) | ? [v10] : ? [v11] : ? [v12] : (coantidomain(v10) = v11 & coantidomain(v9) = v12 & multiplication(v5, v6) = v10 & addition(v11, v12) = v12)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (antidomain(v7) = v8) | ~ (antidomain(v6) = v7) | ~ (multiplication(v5, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (antidomain(v10) = v11 & antidomain(v9) = v12 & multiplication(v5, v6) = v10 & addition(v11, v12) = v12)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v8, v7) = v9) | ~ (multiplication(v5, v6) = v8) | ? [v10] : (multiplication(v6, v7) = v10 & multiplication(v5, v10) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v8, v7) = v9) | ~ (addition(v5, v6) = v8) | ? [v10] : ? [v11] : (multiplication(v6, v7) = v11 & multiplication(v5, v7) = v10 & addition(v10, v11) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v6, v7) = v8) | ~ (multiplication(v5, v8) = v9) | ? [v10] : (multiplication(v10, v7) = v9 & multiplication(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v5, v8) = v9) | ~ (addition(v6, v7) = v8) | ? [v10] : ? [v11] : (multiplication(v5, v7) = v11 & multiplication(v5, v6) = v10 & addition(v10, v11) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (addition(v8, v5) = v9) | ~ (addition(v7, v6) = v8) | ? [v10] : (addition(v7, v10) = v9 & addition(v6, v5) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (addition(v7, v8) = v9) | ~ (addition(v6, v5) = v8) | ? [v10] : (addition(v10, v5) = v9 & addition(v7, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (leq(v8, v7) = v6) | ~ (leq(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (multiplication(v8, v7) = v6) | ~ (multiplication(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (addition(v8, v7) = v6) | ~ (addition(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (addition(v5, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & leq(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (leq(v5, v6) = v7) | ? [v8] : ( ~ (v8 = v6) & addition(v5, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (codomain(v7) = v6) | ~ (codomain(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (coantidomain(v7) = v6) | ~ (coantidomain(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (domain(v7) = v6) | ~ (domain(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (antidomain(v7) = v6) | ~ (antidomain(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (multiplication(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (coantidomain(v11) = v12 & coantidomain(v9) = v10 & coantidomain(v7) = v8 & coantidomain(v5) = v9 & multiplication(v10, v6) = v11 & addition(v8, v12) = v12)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (multiplication(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (antidomain(v11) = v12 & antidomain(v9) = v10 & antidomain(v7) = v8 & antidomain(v6) = v9 & multiplication(v5, v10) = v11 & addition(v8, v12) = v12)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (addition(v6, v5) = v7) | addition(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (addition(v5, v6) = v7) | addition(v6, v5) = v7) & ! [v5] : ! [v6] : (v6 = v5 | ~ (multiplication(v5, one) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (multiplication(one, v5) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (addition(v5, v5) = v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (addition(v5, zero) = v6)) & ! [v5] : ! [v6] : (v6 = zero | ~ (multiplication(v5, zero) = v6)) & ! [v5] : ! [v6] : (v6 = zero | ~ (multiplication(zero, v5) = v6)) & ! [v5] : ! [v6] : ( ~ (codomain(v5) = v6) | ? [v7] : (coantidomain(v7) = v6 & coantidomain(v5) = v7)) & ! [v5] : ! [v6] : ( ~ (coantidomain(v5) = v6) | multiplication(v5, v6) = zero) & ! [v5] : ! [v6] : ( ~ (coantidomain(v5) = v6) | ? [v7] : (codomain(v5) = v7 & coantidomain(v6) = v7)) & ! [v5] : ! [v6] : ( ~ (coantidomain(v5) = v6) | ? [v7] : (coantidomain(v6) = v7 & addition(v7, v6) = one)) & ! [v5] : ! [v6] : ( ~ (domain(v5) = v6) | ? [v7] : (antidomain(v7) = v6 & antidomain(v5) = v7)) & ! [v5] : ! [v6] : ( ~ (antidomain(v5) = v6) | multiplication(v6, v5) = zero) & ! [v5] : ! [v6] : ( ~ (antidomain(v5) = v6) | ? [v7] : (domain(v5) = v7 & antidomain(v6) = v7)) & ! [v5] : ! [v6] : ( ~ (antidomain(v5) = v6) | ? [v7] : (antidomain(v6) = v7 & addition(v7, v6) = one)) & ! [v5] : ! [v6] : ( ~ (leq(v5, v6) = 0) | addition(v5, v6) = v6) & ! [v5] : ! [v6] : ( ~ (addition(v5, v6) = v6) | leq(v5, v6) = 0) & ? [v5] : ? [v6] : ? [v7] : leq(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : multiplication(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : addition(v6, v5) = v7 & ? [v5] : ? [v6] : codomain(v5) = v6 & ? [v5] : ? [v6] : coantidomain(v5) = v6 & ? [v5] : ? [v6] : domain(v5) = v6 & ? [v5] : ? [v6] : antidomain(v5) = v6) % 13.80/6.67 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 13.80/6.67 | (1) ~ (all_0_0_0 = zero) & domain(all_0_4_4) = all_0_2_2 & antidomain(all_0_3_3) = all_0_1_1 & multiplication(all_0_2_2, all_0_3_3) = all_0_0_0 & addition(all_0_2_2, all_0_1_1) = all_0_1_1 & ! [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 % 13.80/6.68 | % 13.80/6.68 | Applying alpha-rule on (1) yields: % 13.80/6.68 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (codomain(v2) = v1) | ~ (codomain(v2) = v0)) % 13.80/6.68 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 13.80/6.68 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) % 13.80/6.68 | (5) ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2 % 13.80/6.68 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 13.80/6.68 | (7) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 13.80/6.68 | (8) ? [v0] : ? [v1] : antidomain(v0) = v1 % 13.80/6.68 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 13.80/6.68 | (10) ~ (all_0_0_0 = zero) % 13.80/6.68 | (11) ! [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)) % 13.80/6.68 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 13.80/6.68 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 13.80/6.68 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 13.80/6.68 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 13.80/6.68 | (16) ! [v0] : ! [v1] : ( ~ (coantidomain(v0) = v1) | ? [v2] : (codomain(v0) = v2 & coantidomain(v1) = v2)) % 13.80/6.68 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) % 13.80/6.68 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 13.80/6.68 | (19) ! [v0] : ! [v1] : ( ~ (antidomain(v0) = v1) | multiplication(v1, v0) = zero) % 13.80/6.68 | (20) addition(all_0_2_2, all_0_1_1) = all_0_1_1 % 13.80/6.68 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) % 13.80/6.68 | (22) ! [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)) % 13.80/6.68 | (23) ? [v0] : ? [v1] : domain(v0) = v1 % 13.80/6.68 | (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)) % 13.80/6.68 | (25) ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | ? [v2] : (antidomain(v2) = v1 & antidomain(v0) = v2)) % 13.80/6.68 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (coantidomain(v2) = v1) | ~ (coantidomain(v2) = v0)) % 13.80/6.68 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (antidomain(v2) = v1) | ~ (antidomain(v2) = v0)) % 13.80/6.68 | (28) ? [v0] : ? [v1] : codomain(v0) = v1 % 13.80/6.68 | (29) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) % 13.80/6.68 | (30) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) % 13.80/6.68 | (31) ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2 % 13.80/6.68 | (32) ! [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)) % 13.80/6.68 | (33) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 13.80/6.68 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 13.80/6.68 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 13.80/6.68 | (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)) % 13.80/6.68 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 13.80/6.68 | (38) ? [v0] : ? [v1] : coantidomain(v0) = v1 % 13.80/6.68 | (39) ! [v0] : ! [v1] : ( ~ (codomain(v0) = v1) | ? [v2] : (coantidomain(v2) = v1 & coantidomain(v0) = v2)) % 13.80/6.68 | (40) ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2 % 13.80/6.68 | (41) ! [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)) % 13.80/6.69 | (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)) % 13.80/6.69 | (43) ! [v0] : ! [v1] : ( ~ (antidomain(v0) = v1) | ? [v2] : (domain(v0) = v2 & antidomain(v1) = v2)) % 13.80/6.69 | (44) ! [v0] : ! [v1] : ( ~ (antidomain(v0) = v1) | ? [v2] : (antidomain(v1) = v2 & addition(v2, v1) = one)) % 13.80/6.69 | (45) antidomain(all_0_3_3) = all_0_1_1 % 13.80/6.69 | (46) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) % 13.80/6.69 | (47) ! [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)) % 13.80/6.69 | (48) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 13.80/6.69 | (49) ! [v0] : ! [v1] : ( ~ (coantidomain(v0) = v1) | multiplication(v0, v1) = zero) % 13.80/6.69 | (50) multiplication(all_0_2_2, all_0_3_3) = all_0_0_0 % 13.80/6.69 | (51) domain(all_0_4_4) = all_0_2_2 % 13.80/6.69 | (52) ! [v0] : ! [v1] : ( ~ (coantidomain(v0) = v1) | ? [v2] : (coantidomain(v1) = v2 & addition(v2, v1) = one)) % 13.80/6.69 | % 13.80/6.69 | Instantiating formula (19) with all_0_1_1, all_0_3_3 and discharging atoms antidomain(all_0_3_3) = all_0_1_1, yields: % 13.80/6.69 | (53) multiplication(all_0_1_1, all_0_3_3) = zero % 13.80/6.69 | % 13.80/6.69 | Instantiating formula (15) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_2_2, all_0_1_1 and discharging atoms addition(all_0_2_2, all_0_1_1) = all_0_1_1, yields: % 13.80/6.69 | (54) ? [v0] : (addition(v0, all_0_1_1) = all_0_1_1 & addition(all_0_2_2, all_0_2_2) = v0) % 13.80/6.69 | % 13.80/6.69 | Instantiating formula (14) with all_0_1_1, all_0_2_2, all_0_1_1 and discharging atoms addition(all_0_2_2, all_0_1_1) = all_0_1_1, yields: % 13.80/6.69 | (55) addition(all_0_1_1, all_0_2_2) = all_0_1_1 % 13.80/6.69 | % 13.80/6.69 | Instantiating (54) with all_31_0_34 yields: % 13.80/6.69 | (56) addition(all_31_0_34, all_0_1_1) = all_0_1_1 & addition(all_0_2_2, all_0_2_2) = all_31_0_34 % 13.80/6.69 | % 13.80/6.69 | Applying alpha-rule on (56) yields: % 13.80/6.69 | (57) addition(all_31_0_34, all_0_1_1) = all_0_1_1 % 13.80/6.69 | (58) addition(all_0_2_2, all_0_2_2) = all_31_0_34 % 13.80/6.69 | % 13.80/6.69 | Instantiating formula (48) with all_31_0_34, all_0_2_2 and discharging atoms addition(all_0_2_2, all_0_2_2) = all_31_0_34, yields: % 13.80/6.69 | (59) all_31_0_34 = all_0_2_2 % 13.80/6.69 | % 13.80/6.69 | From (59) and (57) follows: % 13.80/6.69 | (20) addition(all_0_2_2, all_0_1_1) = all_0_1_1 % 13.80/6.69 | % 13.80/6.69 | From (59) and (58) follows: % 13.80/6.69 | (61) addition(all_0_2_2, all_0_2_2) = all_0_2_2 % 13.80/6.69 | % 13.80/6.69 | Instantiating formula (11) with zero, all_0_1_1, all_0_3_3, all_0_1_1, all_0_2_2 and discharging atoms multiplication(all_0_1_1, all_0_3_3) = zero, addition(all_0_2_2, all_0_1_1) = all_0_1_1, yields: % 13.80/6.69 | (62) ? [v0] : ? [v1] : (multiplication(all_0_1_1, all_0_3_3) = v1 & multiplication(all_0_2_2, all_0_3_3) = v0 & addition(v0, v1) = zero) % 13.80/6.69 | % 13.80/6.69 | Instantiating formula (11) with zero, all_0_1_1, all_0_3_3, all_0_2_2, all_0_1_1 and discharging atoms multiplication(all_0_1_1, all_0_3_3) = zero, addition(all_0_1_1, all_0_2_2) = all_0_1_1, yields: % 13.80/6.69 | (63) ? [v0] : ? [v1] : (multiplication(all_0_1_1, all_0_3_3) = v0 & multiplication(all_0_2_2, all_0_3_3) = v1 & addition(v0, v1) = zero) % 13.80/6.69 | % 13.80/6.69 | Instantiating formula (11) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_2_2, all_0_2_2 and discharging atoms multiplication(all_0_2_2, all_0_3_3) = all_0_0_0, addition(all_0_2_2, all_0_2_2) = all_0_2_2, yields: % 13.80/6.69 | (64) ? [v0] : ? [v1] : (multiplication(all_0_2_2, all_0_3_3) = v1 & multiplication(all_0_2_2, all_0_3_3) = v0 & addition(v0, v1) = all_0_0_0) % 13.80/6.69 | % 13.80/6.69 | Instantiating (64) with all_53_0_39, all_53_1_40 yields: % 13.80/6.69 | (65) multiplication(all_0_2_2, all_0_3_3) = all_53_0_39 & multiplication(all_0_2_2, all_0_3_3) = all_53_1_40 & addition(all_53_1_40, all_53_0_39) = all_0_0_0 % 13.80/6.69 | % 13.80/6.69 | Applying alpha-rule on (65) yields: % 13.80/6.69 | (66) multiplication(all_0_2_2, all_0_3_3) = all_53_0_39 % 13.80/6.69 | (67) multiplication(all_0_2_2, all_0_3_3) = all_53_1_40 % 13.80/6.69 | (68) addition(all_53_1_40, all_53_0_39) = all_0_0_0 % 13.80/6.69 | % 13.80/6.69 | Instantiating (62) with all_67_0_59, all_67_1_60 yields: % 13.80/6.69 | (69) multiplication(all_0_1_1, all_0_3_3) = all_67_0_59 & multiplication(all_0_2_2, all_0_3_3) = all_67_1_60 & addition(all_67_1_60, all_67_0_59) = zero % 13.80/6.69 | % 13.80/6.69 | Applying alpha-rule on (69) yields: % 13.80/6.69 | (70) multiplication(all_0_1_1, all_0_3_3) = all_67_0_59 % 13.80/6.69 | (71) multiplication(all_0_2_2, all_0_3_3) = all_67_1_60 % 13.80/6.69 | (72) addition(all_67_1_60, all_67_0_59) = zero % 13.80/6.69 | % 13.80/6.69 | Instantiating (63) with all_83_0_72, all_83_1_73 yields: % 13.80/6.69 | (73) multiplication(all_0_1_1, all_0_3_3) = all_83_1_73 & multiplication(all_0_2_2, all_0_3_3) = all_83_0_72 & addition(all_83_1_73, all_83_0_72) = zero % 13.80/6.69 | % 13.80/6.69 | Applying alpha-rule on (73) yields: % 13.80/6.69 | (74) multiplication(all_0_1_1, all_0_3_3) = all_83_1_73 % 13.80/6.69 | (75) multiplication(all_0_2_2, all_0_3_3) = all_83_0_72 % 13.80/6.69 | (76) addition(all_83_1_73, all_83_0_72) = zero % 13.80/6.69 | % 13.80/6.69 | Instantiating formula (12) with all_0_1_1, all_0_3_3, all_83_1_73, zero and discharging atoms multiplication(all_0_1_1, all_0_3_3) = all_83_1_73, multiplication(all_0_1_1, all_0_3_3) = zero, yields: % 13.80/6.69 | (77) all_83_1_73 = zero % 13.80/6.69 | % 13.80/6.69 | Instantiating formula (12) with all_0_1_1, all_0_3_3, all_67_0_59, all_83_1_73 and discharging atoms multiplication(all_0_1_1, all_0_3_3) = all_83_1_73, multiplication(all_0_1_1, all_0_3_3) = all_67_0_59, yields: % 13.80/6.69 | (78) all_83_1_73 = all_67_0_59 % 13.80/6.69 | % 13.80/6.70 | Instantiating formula (12) with all_0_2_2, all_0_3_3, all_67_1_60, all_0_0_0 and discharging atoms multiplication(all_0_2_2, all_0_3_3) = all_67_1_60, multiplication(all_0_2_2, all_0_3_3) = all_0_0_0, yields: % 13.80/6.70 | (79) all_67_1_60 = all_0_0_0 % 13.80/6.70 | % 13.80/6.70 | Instantiating formula (12) with all_0_2_2, all_0_3_3, all_67_1_60, all_83_0_72 and discharging atoms multiplication(all_0_2_2, all_0_3_3) = all_83_0_72, multiplication(all_0_2_2, all_0_3_3) = all_67_1_60, yields: % 13.80/6.70 | (80) all_83_0_72 = all_67_1_60 % 13.80/6.70 | % 13.80/6.70 | Instantiating formula (12) with all_0_2_2, all_0_3_3, all_53_0_39, all_67_1_60 and discharging atoms multiplication(all_0_2_2, all_0_3_3) = all_67_1_60, multiplication(all_0_2_2, all_0_3_3) = all_53_0_39, yields: % 13.80/6.70 | (81) all_67_1_60 = all_53_0_39 % 13.80/6.70 | % 13.80/6.70 | Instantiating formula (12) with all_0_2_2, all_0_3_3, all_53_1_40, all_83_0_72 and discharging atoms multiplication(all_0_2_2, all_0_3_3) = all_83_0_72, multiplication(all_0_2_2, all_0_3_3) = all_53_1_40, yields: % 13.80/6.70 | (82) all_83_0_72 = all_53_1_40 % 13.80/6.70 | % 13.80/6.70 | Combining equations (80,82) yields a new equation: % 13.80/6.70 | (83) all_67_1_60 = all_53_1_40 % 13.80/6.70 | % 14.27/6.70 | Simplifying 83 yields: % 14.27/6.70 | (84) all_67_1_60 = all_53_1_40 % 14.27/6.70 | % 14.27/6.70 | Combining equations (77,78) yields a new equation: % 14.27/6.70 | (85) all_67_0_59 = zero % 14.27/6.70 | % 14.27/6.70 | Combining equations (79,81) yields a new equation: % 14.27/6.70 | (86) all_53_0_39 = all_0_0_0 % 14.27/6.70 | % 14.27/6.70 | Combining equations (84,81) yields a new equation: % 14.27/6.70 | (87) all_53_0_39 = all_53_1_40 % 14.27/6.70 | % 14.27/6.70 | Combining equations (86,87) yields a new equation: % 14.27/6.70 | (88) all_53_1_40 = all_0_0_0 % 14.27/6.70 | % 14.27/6.70 | Combining equations (88,87) yields a new equation: % 14.27/6.70 | (86) all_53_0_39 = all_0_0_0 % 14.27/6.70 | % 14.27/6.70 | Combining equations (86,81) yields a new equation: % 14.27/6.70 | (79) all_67_1_60 = all_0_0_0 % 14.27/6.70 | % 14.27/6.70 | From (79)(85) and (72) follows: % 14.27/6.70 | (91) addition(all_0_0_0, zero) = zero % 14.27/6.70 | % 14.27/6.70 | Instantiating formula (33) with zero, all_0_0_0 and discharging atoms addition(all_0_0_0, zero) = zero, yields: % 14.27/6.70 | (92) all_0_0_0 = zero % 14.27/6.70 | % 14.27/6.70 | Equations (92) can reduce 10 to: % 14.27/6.70 | (93) $false % 14.27/6.70 | % 14.27/6.70 |-The branch is then unsatisfiable % 14.27/6.70 % SZS output end Proof for theBenchmark % 14.27/6.70 % 14.27/6.70 6100ms %------------------------------------------------------------------------------