%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE001+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 01:50:46 EDT 2022 % Result : Theorem 3.02s 1.38s % Output : Proof 3.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : KLE001+1 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.33 % Computer : n026.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 600 % 0.11/0.33 % DateTime : Thu Jun 16 14:57:23 EDT 2022 % 0.11/0.33 % CPUTime : % 0.55/0.58 ____ _ % 0.55/0.58 ___ / __ \_____(_)___ ________ __________ % 0.55/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.58 % 0.55/0.58 A Theorem Prover for First-Order Logic % 0.55/0.58 (ePrincess v.1.0) % 0.55/0.58 % 0.55/0.58 (c) Philipp Rümmer, 2009-2015 % 0.55/0.58 (c) Peter Backeman, 2014-2015 % 0.55/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.55/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.55/0.58 Bug reports to peter@backeman.se % 0.55/0.58 % 0.55/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.55/0.58 % 0.55/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.55/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.50/0.89 Prover 0: Preprocessing ... % 2.03/1.09 Prover 0: Constructing countermodel ... % 2.62/1.27 Prover 0: gave up % 2.62/1.27 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.62/1.29 Prover 1: Preprocessing ... % 2.86/1.34 Prover 1: Constructing countermodel ... % 3.02/1.38 Prover 1: proved (110ms) % 3.02/1.38 % 3.02/1.38 No countermodel exists, formula is valid % 3.02/1.38 % SZS status Theorem for theBenchmark % 3.02/1.38 % 3.02/1.38 Generating proof ... found it (size 11) % 3.71/1.56 % 3.71/1.56 % SZS output start Proof for theBenchmark % 3.71/1.56 Assumed formulas after preprocessing and simplification: % 3.71/1.56 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & leq(v3, v3) = v4 & leq(v0, v1) = 0 & addition(v0, v2) = 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] : ( ~ (multiplication(v8, v7) = v9) | ~ (multiplication(v5, v6) = v8) | ? [v10] : (multiplication(v6, v7) = v10 & multiplication(v5, v10) = 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] : (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 = 0 | ~ (leq(v5, v6) = v7) | ? [v8] : ( ~ (v8 = v6) & addition(v5, v6) = v8)) & ! [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] : ( ~ (leq(v5, v6) = 0) | addition(v5, v6) = v6)) % 3.71/1.59 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 3.71/1.59 | (1) ~ (all_0_0_0 = 0) & leq(all_0_1_1, all_0_1_1) = all_0_0_0 & leq(all_0_4_4, all_0_3_3) = 0 & addition(all_0_4_4, all_0_2_2) = 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] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = 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] : (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 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) & ! [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] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) % 3.71/1.60 | % 3.71/1.60 | Applying alpha-rule on (1) yields: % 3.71/1.60 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 3.71/1.60 | (3) leq(all_0_4_4, all_0_3_3) = 0 % 3.71/1.60 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 3.71/1.60 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 3.71/1.60 | (6) ! [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)) % 3.71/1.60 | (7) ! [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)) % 3.71/1.60 | (8) ~ (all_0_0_0 = 0) % 3.71/1.60 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 3.71/1.60 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 3.71/1.60 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 3.71/1.60 | (12) leq(all_0_1_1, all_0_1_1) = all_0_0_0 % 3.71/1.60 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 3.71/1.60 | (14) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) % 3.71/1.60 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 3.71/1.60 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) % 3.71/1.60 | (17) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) % 3.71/1.60 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 3.71/1.60 | (19) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 3.71/1.60 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 3.71/1.60 | (21) addition(all_0_4_4, all_0_2_2) = all_0_1_1 % 3.71/1.60 | % 3.71/1.60 | Instantiating formula (16) with all_0_0_0, all_0_1_1, all_0_1_1 and discharging atoms leq(all_0_1_1, all_0_1_1) = all_0_0_0, yields: % 3.71/1.60 | (22) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = all_0_1_1) & addition(all_0_1_1, all_0_1_1) = v0) % 3.71/1.60 | % 3.71/1.60 +-Applying beta-rule and splitting (22), into two cases. % 3.71/1.60 |-Branch one: % 3.71/1.60 | (23) all_0_0_0 = 0 % 3.71/1.60 | % 3.71/1.60 | Equations (23) can reduce 8 to: % 3.71/1.60 | (24) $false % 3.71/1.60 | % 3.71/1.61 |-The branch is then unsatisfiable % 3.71/1.61 |-Branch two: % 3.71/1.61 | (8) ~ (all_0_0_0 = 0) % 3.71/1.61 | (26) ? [v0] : ( ~ (v0 = all_0_1_1) & addition(all_0_1_1, all_0_1_1) = v0) % 3.71/1.61 | % 3.71/1.61 | Instantiating (26) with all_13_0_5 yields: % 3.71/1.61 | (27) ~ (all_13_0_5 = all_0_1_1) & addition(all_0_1_1, all_0_1_1) = all_13_0_5 % 3.71/1.61 | % 3.71/1.61 | Applying alpha-rule on (27) yields: % 3.71/1.61 | (28) ~ (all_13_0_5 = all_0_1_1) % 3.71/1.61 | (29) addition(all_0_1_1, all_0_1_1) = all_13_0_5 % 3.71/1.61 | % 3.71/1.61 | Instantiating formula (2) with all_13_0_5, all_0_1_1 and discharging atoms addition(all_0_1_1, all_0_1_1) = all_13_0_5, yields: % 3.71/1.61 | (30) all_13_0_5 = all_0_1_1 % 3.71/1.61 | % 3.71/1.61 | Equations (30) can reduce 28 to: % 3.71/1.61 | (24) $false % 3.71/1.61 | % 3.71/1.61 |-The branch is then unsatisfiable % 3.71/1.61 % SZS output end Proof for theBenchmark % 3.71/1.61 % 3.71/1.61 1018ms %------------------------------------------------------------------------------