%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : KLE065+1 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n028.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 01:51:13 EDT 2022 % Result : Theorem 27.36s 8.71s % Output : Proof 28.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : KLE065+1 : TPTP v8.1.0. Released v4.0.0. % 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n028.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 07:46:11 EDT 2022 % 0.13/0.34 % CPUTime : % 0.55/0.60 ____ _ % 0.55/0.60 ___ / __ \_____(_)___ ________ __________ % 0.55/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.60 % 0.55/0.60 A Theorem Prover for First-Order Logic % 0.62/0.60 (ePrincess v.1.0) % 0.62/0.60 % 0.62/0.60 (c) Philipp Rümmer, 2009-2015 % 0.62/0.60 (c) Peter Backeman, 2014-2015 % 0.62/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.62/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.62/0.60 Bug reports to peter@backeman.se % 0.62/0.60 % 0.62/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.62/0.60 % 0.62/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.73/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.39/0.94 Prover 0: Preprocessing ... % 2.22/1.21 Prover 0: Constructing countermodel ... % 18.25/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 18.25/5.97 Prover 1: Preprocessing ... % 18.68/6.06 Prover 1: Constructing countermodel ... % 26.69/8.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 26.71/8.56 Prover 2: Preprocessing ... % 27.02/8.63 Prover 2: Warning: ignoring some quantifiers % 27.02/8.64 Prover 2: Constructing countermodel ... % 27.36/8.70 Prover 2: proved (165ms) % 27.36/8.71 Prover 1: stopped % 27.36/8.71 Prover 0: stopped % 27.36/8.71 % 27.36/8.71 No countermodel exists, formula is valid % 27.36/8.71 % SZS status Theorem for theBenchmark % 27.36/8.71 % 27.36/8.71 Generating proof ... Warning: ignoring some quantifiers % 28.07/8.86 found it (size 37) % 28.07/8.86 % 28.07/8.86 % SZS output start Proof for theBenchmark % 28.07/8.86 Assumed formulas after preprocessing and simplification: % 28.07/8.87 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = zero) & domain(v1) = v2 & domain(zero) = zero & multiplication(v0, v2) = v3 & multiplication(v0, v1) = zero & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v5, v6) = v8) | ~ (multiplication(v4, v6) = v7) | ~ (addition(v7, v8) = v9) | ? [v10] : (multiplication(v10, v6) = v9 & addition(v4, v5) = v10)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (multiplication(v4, v6) = v8) | ~ (multiplication(v4, v5) = v7) | ~ (addition(v7, v8) = v9) | ? [v10] : (multiplication(v4, v10) = v9 & addition(v5, v6) = v10)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (domain(v5) = v7) | ~ (domain(v4) = v6) | ~ (addition(v6, v7) = v8) | ? [v9] : (domain(v9) = v8 & addition(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v7, v6) = v8) | ~ (multiplication(v4, v5) = v7) | ? [v9] : (multiplication(v5, v6) = v9 & multiplication(v4, v9) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v7, v6) = v8) | ~ (addition(v4, v5) = v7) | ? [v9] : ? [v10] : (multiplication(v5, v6) = v10 & multiplication(v4, v6) = v9 & addition(v9, v10) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v5, v6) = v7) | ~ (multiplication(v4, v7) = v8) | ? [v9] : (multiplication(v9, v6) = v8 & multiplication(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (multiplication(v4, v7) = v8) | ~ (addition(v5, v6) = v7) | ? [v9] : ? [v10] : (multiplication(v4, v6) = v10 & multiplication(v4, v5) = v9 & addition(v9, v10) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v7, v4) = v8) | ~ (addition(v6, v5) = v7) | ? [v9] : (addition(v6, v9) = v8 & addition(v5, v4) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (addition(v6, v7) = v8) | ~ (addition(v5, v4) = v7) | ? [v9] : (addition(v9, v4) = v8 & addition(v6, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (leq(v7, v6) = v5) | ~ (leq(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (multiplication(v7, v6) = v5) | ~ (multiplication(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (addition(v7, v6) = v5) | ~ (addition(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (domain(v5) = v6) | ~ (multiplication(v4, v6) = v7) | ? [v8] : ? [v9] : (domain(v8) = v9 & domain(v7) = v9 & multiplication(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (addition(v4, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & leq(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (leq(v4, v5) = v6) | ? [v7] : ( ~ (v7 = v5) & addition(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (domain(v6) = v5) | ~ (domain(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (multiplication(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : (domain(v9) = v7 & domain(v6) = v7 & domain(v5) = v8 & multiplication(v4, v8) = v9)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (addition(v5, v4) = v6) | addition(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (addition(v4, v5) = v6) | addition(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (addition(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : (domain(v6) = v7 & domain(v5) = v9 & domain(v4) = v8 & addition(v8, v9) = v7)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (multiplication(v4, one) = v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (multiplication(one, v4) = v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (addition(v4, v4) = v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (addition(v4, zero) = v5)) & ! [v4] : ! [v5] : (v5 = zero | ~ (multiplication(v4, zero) = v5)) & ! [v4] : ! [v5] : (v5 = zero | ~ (multiplication(zero, v4) = v5)) & ! [v4] : ! [v5] : ( ~ (domain(v4) = v5) | addition(v5, one) = one) & ! [v4] : ! [v5] : ( ~ (domain(v4) = v5) | ? [v6] : (multiplication(v5, v4) = v6 & addition(v4, v6) = v6)) & ! [v4] : ! [v5] : ( ~ (leq(v4, v5) = 0) | addition(v4, v5) = v5) & ! [v4] : ! [v5] : ( ~ (addition(v4, v5) = v5) | leq(v4, v5) = 0) & ? [v4] : ? [v5] : ? [v6] : leq(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : multiplication(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : addition(v5, v4) = v6 & ? [v4] : ? [v5] : domain(v4) = v5) % 28.07/8.90 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 28.07/8.90 | (1) ~ (all_0_0_0 = zero) & domain(all_0_2_2) = all_0_1_1 & domain(zero) = zero & multiplication(all_0_3_3, all_0_1_1) = all_0_0_0 & multiplication(all_0_3_3, all_0_2_2) = zero & ! [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] : (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] : ! [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) | ? [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 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) & ! [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] : ( ~ (domain(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(v0, v2) = v2)) & ! [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] : domain(v0) = v1 % 28.07/8.91 | % 28.07/8.91 | Applying alpha-rule on (1) yields: % 28.07/8.91 | (2) domain(all_0_2_2) = all_0_1_1 % 28.07/8.91 | (3) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(v0, zero) = v1)) % 28.07/8.91 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0)) % 28.07/8.91 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (multiplication(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v5) = v3 & domain(v2) = v3 & domain(v1) = v4 & multiplication(v0, v4) = v5)) % 28.07/8.91 | (6) ! [v0] : ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1) = 0) % 28.07/8.91 | (7) ! [v0] : ! [v1] : ( ~ (leq(v0, v1) = 0) | addition(v0, v1) = v1) % 28.07/8.91 | (8) ! [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)) % 28.07/8.91 | (9) ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | ? [v2] : (multiplication(v1, v0) = v2 & addition(v0, v2) = v2)) % 28.07/8.91 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (domain(v2) = v3 & domain(v1) = v5 & domain(v0) = v4 & addition(v4, v5) = v3)) % 28.07/8.91 | (11) ! [v0] : ! [v1] : (v1 = zero | ~ (multiplication(zero, v0) = v1)) % 28.07/8.91 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(one, v0) = v1)) % 28.07/8.91 | (13) ? [v0] : ? [v1] : ? [v2] : leq(v1, v0) = v2 % 28.07/8.91 | (14) ! [v0] : ! [v1] : ( ~ (domain(v0) = v1) | addition(v1, one) = one) % 28.07/8.91 | (15) ! [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)) % 28.07/8.91 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) % 28.07/8.91 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) % 28.07/8.91 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (domain(v1) = v3) | ~ (domain(v0) = v2) | ~ (addition(v2, v3) = v4) | ? [v5] : (domain(v5) = v4 & addition(v0, v1) = v5)) % 28.07/8.91 | (19) ? [v0] : ? [v1] : ? [v2] : addition(v1, v0) = v2 % 28.07/8.92 | (20) multiplication(all_0_3_3, all_0_2_2) = zero % 28.07/8.92 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, v0) = v1)) % 28.07/8.92 | (22) ? [v0] : ? [v1] : ? [v2] : multiplication(v1, v0) = v2 % 28.07/8.92 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (domain(v1) = v2) | ~ (multiplication(v0, v2) = v3) | ? [v4] : ? [v5] : (domain(v4) = v5 & domain(v3) = v5 & multiplication(v0, v1) = v4)) % 28.07/8.92 | (24) ! [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)) % 28.07/8.92 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) % 28.07/8.92 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v3, v2) = v4) | ~ (multiplication(v0, v1) = v3) | ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) % 28.07/8.92 | (27) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (addition(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & leq(v0, v1) = v3)) % 28.07/8.92 | (28) multiplication(all_0_3_3, all_0_1_1) = all_0_0_0 % 28.07/8.92 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (multiplication(v1, v2) = v3) | ~ (multiplication(v0, v3) = v4) | ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) % 28.07/8.92 | (30) ! [v0] : ! [v1] : (v1 = v0 | ~ (multiplication(v0, one) = v1)) % 28.07/8.92 | (31) ~ (all_0_0_0 = zero) % 28.07/8.92 | (32) ? [v0] : ? [v1] : domain(v0) = v1 % 28.07/8.92 | (33) ! [v0] : ! [v1] : (v1 = v0 | ~ (addition(v0, zero) = v1)) % 28.07/8.92 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain(v2) = v1) | ~ (domain(v2) = v0)) % 28.07/8.92 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (multiplication(v3, v2) = v1) | ~ (multiplication(v3, v2) = v0)) % 28.07/8.92 | (36) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (leq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v1) & addition(v0, v1) = v3)) % 28.07/8.92 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) % 28.07/8.92 | (38) domain(zero) = zero % 28.07/8.92 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) % 28.07/8.92 | (40) ! [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)) % 28.07/8.92 | % 28.07/8.92 | Instantiating formula (9) with zero, zero and discharging atoms domain(zero) = zero, yields: % 28.07/8.92 | (41) ? [v0] : (multiplication(zero, zero) = v0 & addition(zero, v0) = v0) % 28.07/8.92 | % 28.07/8.92 | Instantiating formula (23) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms domain(all_0_2_2) = all_0_1_1, multiplication(all_0_3_3, all_0_1_1) = all_0_0_0, yields: % 28.07/8.92 | (42) ? [v0] : ? [v1] : (domain(v0) = v1 & domain(all_0_0_0) = v1 & multiplication(all_0_3_3, all_0_2_2) = v0) % 28.07/8.92 | % 28.07/8.92 | Instantiating formula (5) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms multiplication(all_0_3_3, all_0_1_1) = all_0_0_0, yields: % 28.07/8.92 | (43) ? [v0] : ? [v1] : ? [v2] : (domain(v2) = v0 & domain(all_0_0_0) = v0 & domain(all_0_1_1) = v1 & multiplication(all_0_3_3, v1) = v2) % 28.07/8.92 | % 28.07/8.92 | Instantiating formula (5) with zero, all_0_2_2, all_0_3_3 and discharging atoms multiplication(all_0_3_3, all_0_2_2) = zero, yields: % 28.07/8.92 | (44) ? [v0] : ? [v1] : ? [v2] : (domain(v2) = v0 & domain(all_0_2_2) = v1 & domain(zero) = v0 & multiplication(all_0_3_3, v1) = v2) % 28.07/8.92 | % 28.07/8.92 | Instantiating (44) with all_17_0_15, all_17_1_16, all_17_2_17 yields: % 28.07/8.92 | (45) domain(all_17_0_15) = all_17_2_17 & domain(all_0_2_2) = all_17_1_16 & domain(zero) = all_17_2_17 & multiplication(all_0_3_3, all_17_1_16) = all_17_0_15 % 28.50/8.92 | % 28.50/8.92 | Applying alpha-rule on (45) yields: % 28.50/8.92 | (46) domain(all_17_0_15) = all_17_2_17 % 28.50/8.92 | (47) domain(all_0_2_2) = all_17_1_16 % 28.50/8.92 | (48) domain(zero) = all_17_2_17 % 28.50/8.92 | (49) multiplication(all_0_3_3, all_17_1_16) = all_17_0_15 % 28.50/8.92 | % 28.50/8.92 | Instantiating (43) with all_19_0_18, all_19_1_19, all_19_2_20 yields: % 28.50/8.92 | (50) domain(all_19_0_18) = all_19_2_20 & domain(all_0_0_0) = all_19_2_20 & domain(all_0_1_1) = all_19_1_19 & multiplication(all_0_3_3, all_19_1_19) = all_19_0_18 % 28.50/8.93 | % 28.50/8.93 | Applying alpha-rule on (50) yields: % 28.50/8.93 | (51) domain(all_19_0_18) = all_19_2_20 % 28.50/8.93 | (52) domain(all_0_0_0) = all_19_2_20 % 28.50/8.93 | (53) domain(all_0_1_1) = all_19_1_19 % 28.50/8.93 | (54) multiplication(all_0_3_3, all_19_1_19) = all_19_0_18 % 28.50/8.93 | % 28.50/8.93 | Instantiating (42) with all_21_0_21, all_21_1_22 yields: % 28.50/8.93 | (55) domain(all_21_1_22) = all_21_0_21 & domain(all_0_0_0) = all_21_0_21 & multiplication(all_0_3_3, all_0_2_2) = all_21_1_22 % 28.50/8.93 | % 28.50/8.93 | Applying alpha-rule on (55) yields: % 28.50/8.93 | (56) domain(all_21_1_22) = all_21_0_21 % 28.50/8.93 | (57) domain(all_0_0_0) = all_21_0_21 % 28.50/8.93 | (58) multiplication(all_0_3_3, all_0_2_2) = all_21_1_22 % 28.50/8.93 | % 28.50/8.93 | Instantiating (41) with all_25_0_24 yields: % 28.50/8.93 | (59) multiplication(zero, zero) = all_25_0_24 & addition(zero, all_25_0_24) = all_25_0_24 % 28.50/8.93 | % 28.50/8.93 | Applying alpha-rule on (59) yields: % 28.50/8.93 | (60) multiplication(zero, zero) = all_25_0_24 % 28.50/8.93 | (61) addition(zero, all_25_0_24) = all_25_0_24 % 28.50/8.93 | % 28.50/8.93 | Instantiating formula (34) with all_0_0_0, all_19_2_20, all_21_0_21 and discharging atoms domain(all_0_0_0) = all_21_0_21, domain(all_0_0_0) = all_19_2_20, yields: % 28.50/8.93 | (62) all_21_0_21 = all_19_2_20 % 28.50/8.93 | % 28.50/8.93 | Instantiating formula (34) with zero, all_17_2_17, zero and discharging atoms domain(zero) = all_17_2_17, domain(zero) = zero, yields: % 28.50/8.93 | (63) all_17_2_17 = zero % 28.50/8.93 | % 28.50/8.93 | Instantiating formula (35) with all_0_3_3, all_0_2_2, all_21_1_22, zero and discharging atoms multiplication(all_0_3_3, all_0_2_2) = all_21_1_22, multiplication(all_0_3_3, all_0_2_2) = zero, yields: % 28.50/8.93 | (64) all_21_1_22 = zero % 28.50/8.93 | % 28.50/8.93 | Instantiating formula (3) with all_25_0_24, zero and discharging atoms multiplication(zero, zero) = all_25_0_24, yields: % 28.50/8.93 | (65) all_25_0_24 = zero % 28.50/8.93 | % 28.50/8.93 | From (64)(62) and (56) follows: % 28.50/8.93 | (66) domain(zero) = all_19_2_20 % 28.50/8.93 | % 28.50/8.93 | From (62) and (57) follows: % 28.50/8.93 | (52) domain(all_0_0_0) = all_19_2_20 % 28.50/8.93 | % 28.50/8.93 | From (63) and (48) follows: % 28.50/8.93 | (38) domain(zero) = zero % 28.50/8.93 | % 28.50/8.93 | From (65) and (60) follows: % 28.50/8.93 | (69) multiplication(zero, zero) = zero % 28.50/8.93 | % 28.50/8.93 | Instantiating formula (34) with zero, all_19_2_20, zero and discharging atoms domain(zero) = all_19_2_20, domain(zero) = zero, yields: % 28.50/8.93 | (70) all_19_2_20 = zero % 28.50/8.93 | % 28.50/8.93 | From (70) and (52) follows: % 28.50/8.93 | (71) domain(all_0_0_0) = zero % 28.50/8.93 | % 28.50/8.93 | Instantiating formula (9) with zero, all_0_0_0 and discharging atoms domain(all_0_0_0) = zero, yields: % 28.50/8.93 | (72) ? [v0] : (multiplication(zero, all_0_0_0) = v0 & addition(all_0_0_0, v0) = v0) % 28.50/8.93 | % 28.50/8.93 | Instantiating formula (23) with zero, zero, all_0_0_0, zero and discharging atoms domain(all_0_0_0) = zero, multiplication(zero, zero) = zero, yields: % 28.50/8.93 | (73) ? [v0] : ? [v1] : (domain(v0) = v1 & domain(zero) = v1 & multiplication(zero, all_0_0_0) = v0) % 28.50/8.93 | % 28.50/8.93 | Instantiating (72) with all_63_0_40 yields: % 28.50/8.93 | (74) multiplication(zero, all_0_0_0) = all_63_0_40 & addition(all_0_0_0, all_63_0_40) = all_63_0_40 % 28.50/8.93 | % 28.50/8.93 | Applying alpha-rule on (74) yields: % 28.50/8.93 | (75) multiplication(zero, all_0_0_0) = all_63_0_40 % 28.50/8.93 | (76) addition(all_0_0_0, all_63_0_40) = all_63_0_40 % 28.50/8.93 | % 28.50/8.93 | Instantiating (73) with all_75_0_50, all_75_1_51 yields: % 28.50/8.93 | (77) domain(all_75_1_51) = all_75_0_50 & domain(zero) = all_75_0_50 & multiplication(zero, all_0_0_0) = all_75_1_51 % 28.50/8.93 | % 28.50/8.93 | Applying alpha-rule on (77) yields: % 28.50/8.93 | (78) domain(all_75_1_51) = all_75_0_50 % 28.50/8.93 | (79) domain(zero) = all_75_0_50 % 28.50/8.93 | (80) multiplication(zero, all_0_0_0) = all_75_1_51 % 28.50/8.93 | % 28.50/8.93 | Instantiating formula (11) with all_75_1_51, all_0_0_0 and discharging atoms multiplication(zero, all_0_0_0) = all_75_1_51, yields: % 28.50/8.93 | (81) all_75_1_51 = zero % 28.50/8.93 | % 28.50/8.93 | Instantiating formula (35) with zero, all_0_0_0, all_63_0_40, all_75_1_51 and discharging atoms multiplication(zero, all_0_0_0) = all_75_1_51, multiplication(zero, all_0_0_0) = all_63_0_40, yields: % 28.50/8.93 | (82) all_75_1_51 = all_63_0_40 % 28.50/8.93 | % 28.50/8.93 | Combining equations (81,82) yields a new equation: % 28.50/8.93 | (83) all_63_0_40 = zero % 28.50/8.93 | % 28.50/8.93 | From (83)(83) and (76) follows: % 28.50/8.93 | (84) addition(all_0_0_0, zero) = zero % 28.50/8.93 | % 28.50/8.93 | Instantiating formula (33) with zero, all_0_0_0 and discharging atoms addition(all_0_0_0, zero) = zero, yields: % 28.50/8.93 | (85) all_0_0_0 = zero % 28.50/8.93 | % 28.50/8.93 | Equations (85) can reduce 31 to: % 28.50/8.93 | (86) $false % 28.50/8.93 | % 28.50/8.93 |-The branch is then unsatisfiable % 28.50/8.93 % SZS output end Proof for theBenchmark % 28.50/8.93 % 28.50/8.93 8326ms %------------------------------------------------------------------------------