%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE076+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n023.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 01:51:15 EDT 2022 % Result : Theorem 2.32s 1.31s % Output : Proof 3.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : KLE076+1 : TPTP v8.1.0. Released v4.0.0. % 0.08/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.15/0.36 % Computer : n023.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 600 % 0.15/0.36 % DateTime : Thu Jun 16 11:10:20 EDT 2022 % 0.15/0.36 % CPUTime : % 0.44/0.62 ____ _ % 0.44/0.62 ___ / __ \_____(_)___ ________ __________ % 0.44/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.44/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.44/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.44/0.62 % 0.44/0.62 A Theorem Prover for First-Order Logic % 0.44/0.62 (ePrincess v.1.0) % 0.44/0.62 % 0.44/0.62 (c) Philipp Rümmer, 2009-2015 % 0.44/0.62 (c) Peter Backeman, 2014-2015 % 0.44/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.44/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.44/0.62 Bug reports to peter@backeman.se % 0.44/0.62 % 0.44/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.44/0.62 % 0.44/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.52/0.97 Prover 0: Preprocessing ... % 2.05/1.23 Prover 0: Constructing countermodel ... % 2.32/1.30 Prover 0: proved (633ms) % 2.32/1.31 % 2.32/1.31 No countermodel exists, formula is valid % 2.32/1.31 % SZS status Theorem for theBenchmark % 2.32/1.31 % 2.32/1.31 Generating proof ... found it (size 7) % 3.10/1.53 % 3.10/1.53 % SZS output start Proof for theBenchmark % 3.10/1.53 Assumed formulas after preprocessing and simplification: % 3.10/1.53 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = zero) & domain(v1) = v2 & domain(zero) = zero & multiplication(v0, zero) = v1 & ! [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] : ( ~ (domain(v4) = v6) | ~ (domain(v3) = v5) | ~ (addition(v5, v6) = v7) | ? [v8] : (domain(v8) = v7 & addition(v3, v4) = v8)) & ! [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] : (v6 = v5 | ~ (domain(v3) = v4) | ~ (multiplication(v4, v3) = v5) | ~ (addition(v3, v5) = v6)) & ! [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] : ! [v6] : ( ~ (domain(v4) = v5) | ~ (multiplication(v3, v5) = v6) | ? [v7] : ? [v8] : (domain(v7) = v8 & domain(v6) = v8 & multiplication(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (addition(v3, v4) = v5) | ~ leq(v3, v4)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (domain(v5) = v4) | ~ (domain(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (domain(v3) = v4) | ~ (multiplication(v4, v3) = v5) | addition(v3, v5) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (multiplication(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : (domain(v8) = v6 & domain(v5) = v6 & domain(v4) = v7 & multiplication(v3, v7) = v8)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (addition(v4, v3) = v5) | addition(v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (addition(v3, v4) = v5) | addition(v4, v3) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (addition(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : (domain(v5) = v6 & domain(v4) = v8 & domain(v3) = v7 & addition(v7, v8) = v6)) & ! [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] : ( ~ (domain(v3) = v4) | addition(v4, one) = one) & ! [v3] : ! [v4] : ( ~ (addition(v3, v4) = v4) | leq(v3, v4))) % 3.50/1.58 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 3.50/1.58 | (1) ~ (all_0_0_0 = zero) & domain(all_0_1_1) = all_0_0_0 & domain(zero) = zero & multiplication(all_0_2_2, zero) = 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] : ( ~ (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5)) & ! [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] : (v3 = v2 | ~ (domain(v0) = v1) | ~ (multiplication(v1, v0) = v2) | ~ (addition(v0, v2) = v3)) & ! [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] : ! [v3] : ( ~ (domain(v1) = v2) | ~ (multiplication(v0, v2) = v3) | ? [v4] : ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (domain(v0) = v1) | ~ (multiplication(v1, v0) = v2) | addition(v0, v2) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3)) & ! [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] : ( ~ (domain(v0) = v1) | addition(v1, one) = one) & ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 3.50/1.59 | % 3.50/1.59 | Applying alpha-rule on (1) yields: % 3.50/1.59 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 3.50/1.59 | (3) ! [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)) % 3.50/1.59 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 3.50/1.59 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5)) % 3.50/1.59 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 3.50/1.59 | (7) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 3.50/1.59 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (domain(v1) = v2) | ~ (multiplication(v0, v2) = v3) | ? [v4] : ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4)) % 3.50/1.59 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) % 3.50/1.59 | (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)) % 3.50/1.59 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ~ leq(v0, v1)) % 3.50/1.59 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 3.50/1.59 | (13) ! [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)) % 3.50/1.59 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 3.50/1.59 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (domain(v0) = v1) | ~ (multiplication(v1, v0) = v2) | ~ (addition(v0, v2) = v3)) % 3.50/1.59 | (16) domain(all_0_1_1) = all_0_0_0 % 3.50/1.59 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3)) % 3.50/1.59 | (18) ! [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)) % 3.50/1.59 | (19) ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one) % 3.50/1.60 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 3.50/1.60 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 3.50/1.60 | (22) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1)) % 3.50/1.60 | (23) domain(zero) = zero % 3.50/1.60 | (24) multiplication(all_0_2_2, zero) = all_0_1_1 % 3.50/1.60 | (25) ~ (all_0_0_0 = zero) % 3.50/1.60 | (26) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) % 3.50/1.60 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5)) % 3.50/1.60 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 3.50/1.60 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 3.50/1.60 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (domain(v0) = v1) | ~ (multiplication(v1, v0) = v2) | addition(v0, v2) = v2) % 3.50/1.60 | (31) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 3.50/1.60 | (32) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 3.50/1.60 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 3.50/1.60 | % 3.50/1.60 | Instantiating formula (26) with all_0_1_1, all_0_2_2 and discharging atoms multiplication(all_0_2_2, zero) = all_0_1_1, yields: % 3.50/1.60 | (34) all_0_1_1 = zero % 3.50/1.60 | % 3.50/1.60 | From (34) and (16) follows: % 3.50/1.60 | (35) domain(zero) = all_0_0_0 % 3.50/1.60 | % 3.50/1.60 | Instantiating formula (9) with zero, all_0_0_0, zero and discharging atoms domain(zero) = all_0_0_0, domain(zero) = zero, yields: % 3.50/1.60 | (36) all_0_0_0 = zero % 3.50/1.60 | % 3.50/1.60 | Equations (36) can reduce 25 to: % 3.50/1.60 | (37) $false % 3.50/1.60 | % 3.50/1.60 |-The branch is then unsatisfiable % 3.50/1.60 % SZS output end Proof for theBenchmark % 3.50/1.60 % 3.50/1.60 974ms %------------------------------------------------------------------------------