%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE003+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n004.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 01:50:47 EDT 2022 % Result : Theorem 2.36s 1.21s % Output : Proof 3.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : KLE003+1 : TPTP v8.1.0. Released v4.0.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n004.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 12:33:53 EDT 2022 % 0.12/0.34 % CPUTime : % 0.54/0.59 ____ _ % 0.54/0.59 ___ / __ \_____(_)___ ________ __________ % 0.54/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.59 % 0.54/0.59 A Theorem Prover for First-Order Logic % 0.61/0.59 (ePrincess v.1.0) % 0.61/0.59 % 0.61/0.59 (c) Philipp Rümmer, 2009-2015 % 0.61/0.59 (c) Peter Backeman, 2014-2015 % 0.61/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.61/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.61/0.59 Bug reports to peter@backeman.se % 0.61/0.59 % 0.61/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.61/0.59 % 0.61/0.59 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 % 1.47/0.93 Prover 0: Preprocessing ... % 1.94/1.12 Prover 0: Warning: ignoring some quantifiers % 1.94/1.14 Prover 0: Constructing countermodel ... % 2.36/1.21 Prover 0: proved (568ms) % 2.36/1.21 % 2.36/1.21 No countermodel exists, formula is valid % 2.36/1.21 % SZS status Theorem for theBenchmark % 2.36/1.21 % 2.36/1.21 Generating proof ... Warning: ignoring some quantifiers % 3.01/1.40 found it (size 11) % 3.01/1.40 % 3.01/1.40 % SZS output start Proof for theBenchmark % 3.01/1.40 Assumed formulas after preprocessing and simplification: % 3.01/1.40 | (0) ? [v0] : ? [v1] : ? [v2] : (addition(one, one) = v0 & ! [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] : ( ~ (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 | ~ (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) | ~ leq(v3, v4)) & ! [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] : ( ~ (addition(v3, v4) = v4) | leq(v3, v4)) & ((v0 = one & ~ (v2 = v1) & addition(v1, v1) = v2) | ( ~ (v0 = one) & ? [v3] : addition(v3, v3) = v3))) % 3.01/1.45 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 3.01/1.45 | (1) addition(one, one) = all_0_2_2 & ! [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(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 | ~ (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) | ~ leq(v0, v1)) & ! [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] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) & ((all_0_2_2 = one & ~ (all_0_0_0 = all_0_1_1) & addition(all_0_1_1, all_0_1_1) = all_0_0_0) | ( ~ (all_0_2_2 = one) & ? [v0] : addition(v0, v0) = v0)) % 3.01/1.46 | % 3.01/1.46 | Applying alpha-rule on (1) yields: % 3.01/1.46 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 3.01/1.46 | (3) ! [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)) % 3.24/1.46 | (4) addition(one, one) = all_0_2_2 % 3.24/1.46 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 3.24/1.46 | (6) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 3.24/1.46 | (7) ! [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)) % 3.24/1.46 | (8) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) % 3.24/1.46 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 3.24/1.46 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 3.24/1.46 | (11) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 3.24/1.46 | (12) (all_0_2_2 = one & ~ (all_0_0_0 = all_0_1_1) & addition(all_0_1_1, all_0_1_1) = all_0_0_0) | ( ~ (all_0_2_2 = one) & ? [v0] : addition(v0, v0) = v0) % 3.24/1.46 | (13) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 3.24/1.46 | (14) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) % 3.24/1.46 | (15) ! [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)) % 3.24/1.46 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 3.24/1.47 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 3.24/1.47 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 3.24/1.47 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 3.24/1.47 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 3.24/1.47 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 3.24/1.47 | (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)) % 3.24/1.47 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 3.24/1.47 | % 3.24/1.47 | Instantiating formula (13) with all_0_2_2, one and discharging atoms addition(one, one) = all_0_2_2, yields: % 3.24/1.47 | (24) all_0_2_2 = one % 3.24/1.47 | % 3.24/1.47 +-Applying beta-rule and splitting (12), into two cases. % 3.24/1.47 |-Branch one: % 3.24/1.47 | (25) all_0_2_2 = one & ~ (all_0_0_0 = all_0_1_1) & addition(all_0_1_1, all_0_1_1) = all_0_0_0 % 3.24/1.47 | % 3.24/1.47 | Applying alpha-rule on (25) yields: % 3.24/1.47 | (24) all_0_2_2 = one % 3.24/1.47 | (27) ~ (all_0_0_0 = all_0_1_1) % 3.24/1.47 | (28) addition(all_0_1_1, all_0_1_1) = all_0_0_0 % 3.24/1.47 | % 3.24/1.47 | Instantiating formula (13) with all_0_0_0, all_0_1_1 and discharging atoms addition(all_0_1_1, all_0_1_1) = all_0_0_0, yields: % 3.24/1.47 | (29) all_0_0_0 = all_0_1_1 % 3.24/1.47 | % 3.24/1.47 | Equations (29) can reduce 27 to: % 3.24/1.47 | (30) $false % 3.24/1.47 | % 3.24/1.47 |-The branch is then unsatisfiable % 3.24/1.47 |-Branch two: % 3.24/1.47 | (31) ~ (all_0_2_2 = one) & ? [v0] : addition(v0, v0) = v0 % 3.24/1.47 | % 3.24/1.47 | Applying alpha-rule on (31) yields: % 3.24/1.47 | (32) ~ (all_0_2_2 = one) % 3.24/1.47 | (33) ? [v0] : addition(v0, v0) = v0 % 3.24/1.47 | % 3.24/1.47 | Equations (24) can reduce 32 to: % 3.24/1.47 | (30) $false % 3.24/1.47 | % 3.24/1.47 |-The branch is then unsatisfiable % 3.24/1.47 % SZS output end Proof for theBenchmark % 3.24/1.47 % 3.24/1.47 869ms %------------------------------------------------------------------------------