%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU167+3 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n019.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 : Tue Jul 19 08:47:15 EDT 2022 % Result : Theorem 13.92s 4.02s % Output : Proof 19.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEU167+3 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n019.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 : Sun Jun 19 07:13:39 EDT 2022 % 0.13/0.35 % CPUTime : % 0.61/0.61 ____ _ % 0.61/0.61 ___ / __ \_____(_)___ ________ __________ % 0.61/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.61/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.61/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.61/0.61 % 0.61/0.61 A Theorem Prover for First-Order Logic % 0.61/0.61 (ePrincess v.1.0) % 0.61/0.61 % 0.61/0.61 (c) Philipp Rümmer, 2009-2015 % 0.61/0.61 (c) Peter Backeman, 2014-2015 % 0.61/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.61/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.61/0.61 Bug reports to peter@backeman.se % 0.61/0.61 % 0.61/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.61/0.61 % 0.61/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.67/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.36/0.94 Prover 0: Preprocessing ... % 1.60/1.07 Prover 0: Warning: ignoring some quantifiers % 1.60/1.09 Prover 0: Constructing countermodel ... % 3.89/1.63 Prover 0: gave up % 3.89/1.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.89/1.64 Prover 1: Preprocessing ... % 3.89/1.67 Prover 1: Constructing countermodel ... % 4.26/1.71 Prover 1: gave up % 4.26/1.71 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.26/1.72 Prover 2: Preprocessing ... % 4.26/1.75 Prover 2: Warning: ignoring some quantifiers % 4.26/1.75 Prover 2: Constructing countermodel ... % 4.66/1.88 Prover 2: gave up % 4.66/1.88 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 5.05/1.89 Prover 3: Preprocessing ... % 5.05/1.90 Prover 3: Warning: ignoring some quantifiers % 5.14/1.90 Prover 3: Constructing countermodel ... % 6.85/2.32 Prover 3: gave up % 6.85/2.32 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 6.85/2.33 Prover 4: Preprocessing ... % 6.85/2.35 Prover 4: Warning: ignoring some quantifiers % 6.85/2.36 Prover 4: Constructing countermodel ... % 11.52/3.49 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 11.52/3.50 Prover 5: Preprocessing ... % 11.95/3.54 Prover 5: Constructing countermodel ... % 13.92/4.02 Prover 5: proved (528ms) % 13.92/4.02 Prover 4: stopped % 13.92/4.02 % 13.92/4.02 No countermodel exists, formula is valid % 13.92/4.02 % SZS status Theorem for theBenchmark % 13.92/4.02 % 13.92/4.02 Generating proof ... found it (size 63) % 19.10/5.30 % 19.10/5.30 % SZS output start Proof for theBenchmark % 19.10/5.30 Assumed formulas after preprocessing and simplification: % 19.10/5.30 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v1, v2) = v7 & cartesian_product2(v0, v2) = v6 & subset(v6, v7) = v8 & subset(v3, v4) = v9 & subset(v0, v1) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v8 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v2, v0) = v8 & cartesian_product2(v1, v2) = v6 & subset(v8, v4) = v9 & subset(v3, v6) = v7 & subset(v0, v1) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v0) = v4) | ~ (cartesian_product2(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v2, v1) = v8 & cartesian_product2(v0, v2) = v6 & subset(v6, v3) = v7 & subset(v4, v8) = v9 & subset(v0, v1) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v2, v1) = v8 & cartesian_product2(v2, v0) = v7 & subset(v7, v8) = v9 & subset(v3, v4) = v6 & subset(v0, v1) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v2, v1) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (cartesian_product2(v2, v0) = v6 & cartesian_product2(v1, v2) = v5 & cartesian_product2(v0, v2) = v4 & subset(v6, v3) = 0 & subset(v4, v5) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v2, v0) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v1, v2) = v5 & cartesian_product2(v0, v2) = v4 & subset(v4, v5) = 0 & subset(v3, v6) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v1, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & cartesian_product2(v0, v2) = v4 & subset(v5, v6) = 0 & subset(v4, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & cartesian_product2(v1, v2) = v4 & subset(v5, v6) = 0 & subset(v3, v4) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & cartesian_product2(v1, v3) = v5 & cartesian_product2(v0, v2) = v4 & subset(v4, v5) = v6 & subset(v2, v3) = 0 & subset(v0, v1) = 0) & ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1) & ? [v0] : empty(v0) = 0 % 19.50/5.33 | Applying alpha-rule on (0) yields: % 19.50/5.33 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) % 19.50/5.33 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v0) = v4) | ~ (cartesian_product2(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v2, v1) = v8 & cartesian_product2(v0, v2) = v6 & subset(v6, v3) = v7 & subset(v4, v8) = v9 & subset(v0, v1) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))) % 19.50/5.33 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) % 19.50/5.33 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 19.50/5.34 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v2, v0) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v1, v2) = v5 & cartesian_product2(v0, v2) = v4 & subset(v4, v5) = 0 & subset(v3, v6) = 0)) % 19.50/5.34 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & cartesian_product2(v1, v2) = v4 & subset(v5, v6) = 0 & subset(v3, v4) = 0)) % 19.50/5.34 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v2, v1) = v8 & cartesian_product2(v2, v0) = v7 & subset(v7, v8) = v9 & subset(v3, v4) = v6 & subset(v0, v1) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v6 = 0)))) % 19.50/5.34 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 19.50/5.34 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 19.50/5.34 | (10) ? [v0] : empty(v0) = 0 % 19.50/5.34 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v1, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & cartesian_product2(v0, v2) = v4 & subset(v5, v6) = 0 & subset(v4, v3) = 0)) % 19.50/5.34 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v1, v2) = v7 & cartesian_product2(v0, v2) = v6 & subset(v6, v7) = v8 & subset(v3, v4) = v9 & subset(v0, v1) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v8 = 0)))) % 19.50/5.34 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 19.50/5.34 | (14) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & cartesian_product2(v1, v3) = v5 & cartesian_product2(v0, v2) = v4 & subset(v4, v5) = v6 & subset(v2, v3) = 0 & subset(v0, v1) = 0) % 19.50/5.34 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v2, v0) = v8 & cartesian_product2(v1, v2) = v6 & subset(v8, v4) = v9 & subset(v3, v6) = v7 & subset(v0, v1) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))) % 19.50/5.34 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v2, v1) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (cartesian_product2(v2, v0) = v6 & cartesian_product2(v1, v2) = v5 & cartesian_product2(v0, v2) = v4 & subset(v6, v3) = 0 & subset(v4, v5) = 0)) % 19.50/5.34 | (17) ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1) % 19.50/5.34 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 19.50/5.34 | % 19.50/5.34 | Instantiating (14) with all_5_0_3, all_5_1_4, all_5_2_5, all_5_3_6, all_5_4_7, all_5_5_8, all_5_6_9 yields: % 19.50/5.34 | (19) ~ (all_5_0_3 = 0) & cartesian_product2(all_5_5_8, all_5_3_6) = all_5_1_4 & cartesian_product2(all_5_6_9, all_5_4_7) = all_5_2_5 & subset(all_5_2_5, all_5_1_4) = all_5_0_3 & subset(all_5_4_7, all_5_3_6) = 0 & subset(all_5_6_9, all_5_5_8) = 0 % 19.50/5.34 | % 19.50/5.34 | Applying alpha-rule on (19) yields: % 19.50/5.34 | (20) subset(all_5_4_7, all_5_3_6) = 0 % 19.50/5.35 | (21) cartesian_product2(all_5_5_8, all_5_3_6) = all_5_1_4 % 19.50/5.35 | (22) subset(all_5_6_9, all_5_5_8) = 0 % 19.50/5.35 | (23) subset(all_5_2_5, all_5_1_4) = all_5_0_3 % 19.50/5.35 | (24) ~ (all_5_0_3 = 0) % 19.50/5.35 | (25) cartesian_product2(all_5_6_9, all_5_4_7) = all_5_2_5 % 19.50/5.35 | % 19.50/5.35 | Instantiating formula (13) with all_5_0_3, all_5_2_5 yields: % 19.50/5.35 | (26) all_5_0_3 = 0 | ~ (subset(all_5_2_5, all_5_2_5) = all_5_0_3) % 19.50/5.35 | % 19.50/5.35 | Instantiating formula (12) with all_5_2_5, all_5_2_5, all_5_6_9, all_5_4_7, all_5_4_7 and discharging atoms cartesian_product2(all_5_6_9, all_5_4_7) = all_5_2_5, yields: % 19.50/5.35 | (27) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (cartesian_product2(all_5_4_7, all_5_6_9) = v2 & cartesian_product2(all_5_4_7, all_5_6_9) = v1 & subset(v1, v2) = v3 & subset(all_5_2_5, all_5_2_5) = v4 & subset(all_5_4_7, all_5_4_7) = v0 & ( ~ (v0 = 0) | (v4 = 0 & v3 = 0))) % 19.50/5.35 | % 19.50/5.35 | Instantiating formula (7) with all_5_2_5, all_5_2_5, all_5_4_7, all_5_6_9, all_5_6_9 and discharging atoms cartesian_product2(all_5_6_9, all_5_4_7) = all_5_2_5, yields: % 19.50/5.35 | (28) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (cartesian_product2(all_5_4_7, all_5_6_9) = v3 & cartesian_product2(all_5_4_7, all_5_6_9) = v2 & subset(v2, v3) = v4 & subset(all_5_2_5, all_5_2_5) = v1 & subset(all_5_6_9, all_5_6_9) = v0 & ( ~ (v0 = 0) | (v4 = 0 & v1 = 0))) % 19.50/5.35 | % 19.50/5.35 | Instantiating formula (16) with all_5_1_4, all_5_5_8, all_5_3_6, all_5_4_7 and discharging atoms cartesian_product2(all_5_5_8, all_5_3_6) = all_5_1_4, subset(all_5_4_7, all_5_3_6) = 0, yields: % 19.50/5.35 | (29) ? [v0] : ? [v1] : ? [v2] : (cartesian_product2(all_5_3_6, all_5_5_8) = v1 & cartesian_product2(all_5_4_7, all_5_5_8) = v0 & cartesian_product2(all_5_5_8, all_5_4_7) = v2 & subset(v2, all_5_1_4) = 0 & subset(v0, v1) = 0) % 19.50/5.35 | % 19.50/5.35 | Instantiating formula (5) with all_5_2_5, all_5_6_9, all_5_3_6, all_5_4_7 and discharging atoms cartesian_product2(all_5_6_9, all_5_4_7) = all_5_2_5, subset(all_5_4_7, all_5_3_6) = 0, yields: % 19.50/5.35 | (30) ? [v0] : ? [v1] : ? [v2] : (cartesian_product2(all_5_3_6, all_5_6_9) = v1 & cartesian_product2(all_5_4_7, all_5_6_9) = v0 & cartesian_product2(all_5_6_9, all_5_3_6) = v2 & subset(v0, v1) = 0 & subset(all_5_2_5, v2) = 0) % 19.50/5.35 | % 19.50/5.35 | Instantiating formula (11) with all_5_1_4, all_5_3_6, all_5_5_8, all_5_6_9 and discharging atoms cartesian_product2(all_5_5_8, all_5_3_6) = all_5_1_4, subset(all_5_6_9, all_5_5_8) = 0, yields: % 19.50/5.35 | (31) ? [v0] : ? [v1] : ? [v2] : (cartesian_product2(all_5_3_6, all_5_5_8) = v2 & cartesian_product2(all_5_3_6, all_5_6_9) = v1 & cartesian_product2(all_5_6_9, all_5_3_6) = v0 & subset(v1, v2) = 0 & subset(v0, all_5_1_4) = 0) % 19.50/5.35 | % 19.50/5.35 | Instantiating formula (6) with all_5_2_5, all_5_4_7, all_5_5_8, all_5_6_9 and discharging atoms cartesian_product2(all_5_6_9, all_5_4_7) = all_5_2_5, subset(all_5_6_9, all_5_5_8) = 0, yields: % 19.50/5.35 | (32) ? [v0] : ? [v1] : ? [v2] : (cartesian_product2(all_5_4_7, all_5_5_8) = v2 & cartesian_product2(all_5_4_7, all_5_6_9) = v1 & cartesian_product2(all_5_5_8, all_5_4_7) = v0 & subset(v1, v2) = 0 & subset(all_5_2_5, v0) = 0) % 19.50/5.35 | % 19.50/5.35 | Instantiating (32) with all_12_0_10, all_12_1_11, all_12_2_12 yields: % 19.50/5.35 | (33) cartesian_product2(all_5_4_7, all_5_5_8) = all_12_0_10 & cartesian_product2(all_5_4_7, all_5_6_9) = all_12_1_11 & cartesian_product2(all_5_5_8, all_5_4_7) = all_12_2_12 & subset(all_12_1_11, all_12_0_10) = 0 & subset(all_5_2_5, all_12_2_12) = 0 % 19.50/5.35 | % 19.50/5.35 | Applying alpha-rule on (33) yields: % 19.50/5.35 | (34) cartesian_product2(all_5_4_7, all_5_6_9) = all_12_1_11 % 19.50/5.35 | (35) cartesian_product2(all_5_5_8, all_5_4_7) = all_12_2_12 % 19.50/5.35 | (36) cartesian_product2(all_5_4_7, all_5_5_8) = all_12_0_10 % 19.50/5.35 | (37) subset(all_12_1_11, all_12_0_10) = 0 % 19.50/5.35 | (38) subset(all_5_2_5, all_12_2_12) = 0 % 19.50/5.35 | % 19.50/5.35 | Instantiating (30) with all_14_0_13, all_14_1_14, all_14_2_15 yields: % 19.50/5.35 | (39) cartesian_product2(all_5_3_6, all_5_6_9) = all_14_1_14 & cartesian_product2(all_5_4_7, all_5_6_9) = all_14_2_15 & cartesian_product2(all_5_6_9, all_5_3_6) = all_14_0_13 & subset(all_14_2_15, all_14_1_14) = 0 & subset(all_5_2_5, all_14_0_13) = 0 % 19.50/5.35 | % 19.50/5.35 | Applying alpha-rule on (39) yields: % 19.50/5.35 | (40) subset(all_5_2_5, all_14_0_13) = 0 % 19.50/5.35 | (41) subset(all_14_2_15, all_14_1_14) = 0 % 19.50/5.35 | (42) cartesian_product2(all_5_3_6, all_5_6_9) = all_14_1_14 % 19.50/5.35 | (43) cartesian_product2(all_5_6_9, all_5_3_6) = all_14_0_13 % 19.50/5.35 | (44) cartesian_product2(all_5_4_7, all_5_6_9) = all_14_2_15 % 19.50/5.35 | % 19.50/5.35 | Instantiating (27) with all_16_0_16, all_16_1_17, all_16_2_18, all_16_3_19, all_16_4_20 yields: % 19.50/5.35 | (45) cartesian_product2(all_5_4_7, all_5_6_9) = all_16_2_18 & cartesian_product2(all_5_4_7, all_5_6_9) = all_16_3_19 & subset(all_16_3_19, all_16_2_18) = all_16_1_17 & subset(all_5_2_5, all_5_2_5) = all_16_0_16 & subset(all_5_4_7, all_5_4_7) = all_16_4_20 & ( ~ (all_16_4_20 = 0) | (all_16_0_16 = 0 & all_16_1_17 = 0)) % 19.50/5.35 | % 19.50/5.35 | Applying alpha-rule on (45) yields: % 19.50/5.35 | (46) cartesian_product2(all_5_4_7, all_5_6_9) = all_16_3_19 % 19.50/5.35 | (47) cartesian_product2(all_5_4_7, all_5_6_9) = all_16_2_18 % 19.50/5.35 | (48) subset(all_16_3_19, all_16_2_18) = all_16_1_17 % 19.50/5.35 | (49) ~ (all_16_4_20 = 0) | (all_16_0_16 = 0 & all_16_1_17 = 0) % 19.50/5.35 | (50) subset(all_5_2_5, all_5_2_5) = all_16_0_16 % 19.50/5.35 | (51) subset(all_5_4_7, all_5_4_7) = all_16_4_20 % 19.50/5.35 | % 19.50/5.35 | Instantiating (31) with all_18_0_21, all_18_1_22, all_18_2_23 yields: % 19.50/5.35 | (52) cartesian_product2(all_5_3_6, all_5_5_8) = all_18_0_21 & cartesian_product2(all_5_3_6, all_5_6_9) = all_18_1_22 & cartesian_product2(all_5_6_9, all_5_3_6) = all_18_2_23 & subset(all_18_1_22, all_18_0_21) = 0 & subset(all_18_2_23, all_5_1_4) = 0 % 19.50/5.35 | % 19.50/5.35 | Applying alpha-rule on (52) yields: % 19.50/5.35 | (53) subset(all_18_1_22, all_18_0_21) = 0 % 19.50/5.35 | (54) cartesian_product2(all_5_3_6, all_5_6_9) = all_18_1_22 % 19.50/5.35 | (55) cartesian_product2(all_5_3_6, all_5_5_8) = all_18_0_21 % 19.50/5.35 | (56) cartesian_product2(all_5_6_9, all_5_3_6) = all_18_2_23 % 19.50/5.35 | (57) subset(all_18_2_23, all_5_1_4) = 0 % 19.50/5.35 | % 19.50/5.35 | Instantiating (29) with all_20_0_24, all_20_1_25, all_20_2_26 yields: % 19.50/5.35 | (58) cartesian_product2(all_5_3_6, all_5_5_8) = all_20_1_25 & cartesian_product2(all_5_4_7, all_5_5_8) = all_20_2_26 & cartesian_product2(all_5_5_8, all_5_4_7) = all_20_0_24 & subset(all_20_0_24, all_5_1_4) = 0 & subset(all_20_2_26, all_20_1_25) = 0 % 19.50/5.36 | % 19.50/5.36 | Applying alpha-rule on (58) yields: % 19.50/5.36 | (59) subset(all_20_2_26, all_20_1_25) = 0 % 19.50/5.36 | (60) cartesian_product2(all_5_3_6, all_5_5_8) = all_20_1_25 % 19.50/5.36 | (61) subset(all_20_0_24, all_5_1_4) = 0 % 19.50/5.36 | (62) cartesian_product2(all_5_5_8, all_5_4_7) = all_20_0_24 % 19.50/5.36 | (63) cartesian_product2(all_5_4_7, all_5_5_8) = all_20_2_26 % 19.50/5.36 | % 19.50/5.36 | Instantiating (28) with all_26_0_37, all_26_1_38, all_26_2_39, all_26_3_40, all_26_4_41 yields: % 19.50/5.36 | (64) cartesian_product2(all_5_4_7, all_5_6_9) = all_26_1_38 & cartesian_product2(all_5_4_7, all_5_6_9) = all_26_2_39 & subset(all_26_2_39, all_26_1_38) = all_26_0_37 & subset(all_5_2_5, all_5_2_5) = all_26_3_40 & subset(all_5_6_9, all_5_6_9) = all_26_4_41 & ( ~ (all_26_4_41 = 0) | (all_26_0_37 = 0 & all_26_3_40 = 0)) % 19.50/5.36 | % 19.50/5.36 | Applying alpha-rule on (64) yields: % 19.50/5.36 | (65) cartesian_product2(all_5_4_7, all_5_6_9) = all_26_1_38 % 19.50/5.36 | (66) subset(all_5_2_5, all_5_2_5) = all_26_3_40 % 19.50/5.36 | (67) ~ (all_26_4_41 = 0) | (all_26_0_37 = 0 & all_26_3_40 = 0) % 19.50/5.36 | (68) subset(all_5_6_9, all_5_6_9) = all_26_4_41 % 19.50/5.36 | (69) cartesian_product2(all_5_4_7, all_5_6_9) = all_26_2_39 % 19.50/5.36 | (70) subset(all_26_2_39, all_26_1_38) = all_26_0_37 % 19.50/5.36 | % 19.50/5.36 +-Applying beta-rule and splitting (26), into two cases. % 19.50/5.36 |-Branch one: % 19.50/5.36 | (71) ~ (subset(all_5_2_5, all_5_2_5) = all_5_0_3) % 19.50/5.36 | % 19.50/5.36 | Instantiating formula (9) with all_5_5_8, all_5_4_7, all_12_2_12, all_20_0_24 and discharging atoms cartesian_product2(all_5_5_8, all_5_4_7) = all_20_0_24, cartesian_product2(all_5_5_8, all_5_4_7) = all_12_2_12, yields: % 19.50/5.36 | (72) all_20_0_24 = all_12_2_12 % 19.50/5.36 | % 19.50/5.36 | Instantiating formula (9) with all_5_6_9, all_5_3_6, all_14_0_13, all_18_2_23 and discharging atoms cartesian_product2(all_5_6_9, all_5_3_6) = all_18_2_23, cartesian_product2(all_5_6_9, all_5_3_6) = all_14_0_13, yields: % 19.50/5.36 | (73) all_18_2_23 = all_14_0_13 % 19.50/5.36 | % 19.50/5.36 | Instantiating formula (18) with all_5_2_5, all_5_1_4, 0, all_5_0_3 and discharging atoms subset(all_5_2_5, all_5_1_4) = all_5_0_3, yields: % 19.50/5.36 | (74) all_5_0_3 = 0 | ~ (subset(all_5_2_5, all_5_1_4) = 0) % 19.50/5.36 | % 19.50/5.36 | Instantiating formula (13) with all_26_3_40, all_5_2_5 and discharging atoms subset(all_5_2_5, all_5_2_5) = all_26_3_40, yields: % 19.50/5.36 | (75) all_26_3_40 = 0 % 19.50/5.36 | % 19.50/5.36 | Instantiating formula (18) with all_5_2_5, all_5_2_5, all_16_0_16, all_26_3_40 and discharging atoms subset(all_5_2_5, all_5_2_5) = all_26_3_40, subset(all_5_2_5, all_5_2_5) = all_16_0_16, yields: % 19.50/5.36 | (76) all_26_3_40 = all_16_0_16 % 19.50/5.36 | % 19.50/5.36 | Using (50) and (71) yields: % 19.50/5.36 | (77) ~ (all_16_0_16 = all_5_0_3) % 19.50/5.36 | % 19.50/5.36 | Combining equations (76,75) yields a new equation: % 19.50/5.36 | (78) all_16_0_16 = 0 % 19.50/5.36 | % 19.50/5.36 | Simplifying 78 yields: % 19.50/5.36 | (79) all_16_0_16 = 0 % 19.50/5.36 | % 19.50/5.36 | Equations (79) can reduce 77 to: % 19.50/5.36 | (80) ~ (all_5_0_3 = 0) % 19.50/5.36 | % 19.50/5.36 | Simplifying 80 yields: % 19.50/5.36 | (24) ~ (all_5_0_3 = 0) % 19.50/5.36 | % 19.50/5.36 | From (72) and (61) follows: % 19.50/5.36 | (82) subset(all_12_2_12, all_5_1_4) = 0 % 19.50/5.36 | % 19.50/5.36 | From (73) and (57) follows: % 19.50/5.36 | (83) subset(all_14_0_13, all_5_1_4) = 0 % 19.50/5.36 | % 19.50/5.36 | Instantiating formula (8) with all_5_0_3, all_5_1_4, all_14_0_13, all_5_2_5 and discharging atoms subset(all_14_0_13, all_5_1_4) = 0, subset(all_5_2_5, all_5_1_4) = all_5_0_3, yields: % 19.50/5.36 | (84) all_5_0_3 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_5_2_5, all_14_0_13) = v0) % 19.50/5.36 | % 19.50/5.36 | Instantiating formula (1) with all_5_0_3, all_5_1_4, all_5_1_4, all_5_2_5 and discharging atoms subset(all_5_2_5, all_5_1_4) = all_5_0_3, yields: % 19.50/5.36 | (85) all_5_0_3 = 0 | ~ (subset(all_5_2_5, all_5_1_4) = 0) | ? [v0] : ( ~ (v0 = 0) & subset(all_5_1_4, all_5_1_4) = v0) % 19.50/5.36 | % 19.50/5.36 | Instantiating formula (8) with all_5_0_3, all_5_1_4, all_12_2_12, all_5_2_5 and discharging atoms subset(all_12_2_12, all_5_1_4) = 0, subset(all_5_2_5, all_5_1_4) = all_5_0_3, yields: % 19.50/5.36 | (86) all_5_0_3 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_5_2_5, all_12_2_12) = v0) % 19.50/5.36 | % 19.50/5.36 | Instantiating formula (1) with all_5_0_3, all_5_1_4, all_14_0_13, all_5_2_5 and discharging atoms subset(all_5_2_5, all_14_0_13) = 0, subset(all_5_2_5, all_5_1_4) = all_5_0_3, yields: % 19.50/5.36 | (87) all_5_0_3 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_14_0_13, all_5_1_4) = v0) % 19.50/5.36 | % 19.50/5.36 | Instantiating formula (3) with all_5_1_4, all_12_2_12, all_5_2_5 and discharging atoms subset(all_12_2_12, all_5_1_4) = 0, subset(all_5_2_5, all_12_2_12) = 0, yields: % 19.50/5.36 | (88) subset(all_5_2_5, all_5_1_4) = 0 % 19.50/5.36 | % 19.50/5.36 | Instantiating formula (1) with all_5_0_3, all_5_1_4, all_12_2_12, all_5_2_5 and discharging atoms subset(all_5_2_5, all_12_2_12) = 0, subset(all_5_2_5, all_5_1_4) = all_5_0_3, yields: % 19.50/5.36 | (89) all_5_0_3 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_12_2_12, all_5_1_4) = v0) % 19.50/5.36 | % 19.50/5.36 +-Applying beta-rule and splitting (89), into two cases. % 19.50/5.36 |-Branch one: % 19.50/5.36 | (90) all_5_0_3 = 0 % 19.50/5.36 | % 19.50/5.36 | Equations (90) can reduce 24 to: % 19.50/5.36 | (91) $false % 19.50/5.36 | % 19.50/5.36 |-The branch is then unsatisfiable % 19.50/5.36 |-Branch two: % 19.50/5.36 | (24) ~ (all_5_0_3 = 0) % 19.50/5.36 | (93) ? [v0] : ( ~ (v0 = 0) & subset(all_12_2_12, all_5_1_4) = v0) % 19.50/5.36 | % 19.50/5.36 +-Applying beta-rule and splitting (86), into two cases. % 19.50/5.36 |-Branch one: % 19.50/5.36 | (90) all_5_0_3 = 0 % 19.50/5.37 | % 19.50/5.37 | Equations (90) can reduce 24 to: % 19.50/5.37 | (91) $false % 19.50/5.37 | % 19.50/5.37 |-The branch is then unsatisfiable % 19.50/5.37 |-Branch two: % 19.50/5.37 | (24) ~ (all_5_0_3 = 0) % 19.50/5.37 | (97) ? [v0] : ( ~ (v0 = 0) & subset(all_5_2_5, all_12_2_12) = v0) % 19.50/5.37 | % 19.50/5.37 +-Applying beta-rule and splitting (87), into two cases. % 19.50/5.37 |-Branch one: % 19.50/5.37 | (90) all_5_0_3 = 0 % 19.50/5.37 | % 19.50/5.37 | Equations (90) can reduce 24 to: % 19.50/5.37 | (91) $false % 19.50/5.37 | % 19.50/5.37 |-The branch is then unsatisfiable % 19.50/5.37 |-Branch two: % 19.50/5.37 | (24) ~ (all_5_0_3 = 0) % 19.50/5.37 | (101) ? [v0] : ( ~ (v0 = 0) & subset(all_14_0_13, all_5_1_4) = v0) % 19.50/5.37 | % 19.50/5.37 +-Applying beta-rule and splitting (84), into two cases. % 19.50/5.37 |-Branch one: % 19.50/5.37 | (90) all_5_0_3 = 0 % 19.50/5.37 | % 19.50/5.37 | Equations (90) can reduce 24 to: % 19.50/5.37 | (91) $false % 19.50/5.37 | % 19.50/5.37 |-The branch is then unsatisfiable % 19.50/5.37 |-Branch two: % 19.50/5.37 | (24) ~ (all_5_0_3 = 0) % 19.50/5.37 | (105) ? [v0] : ( ~ (v0 = 0) & subset(all_5_2_5, all_14_0_13) = v0) % 19.50/5.37 | % 19.50/5.37 +-Applying beta-rule and splitting (85), into two cases. % 19.50/5.37 |-Branch one: % 19.50/5.37 | (106) ~ (subset(all_5_2_5, all_5_1_4) = 0) % 19.50/5.37 | % 19.50/5.37 | Using (88) and (106) yields: % 19.50/5.37 | (107) $false % 19.50/5.37 | % 19.50/5.37 |-The branch is then unsatisfiable % 19.50/5.37 |-Branch two: % 19.50/5.37 | (88) subset(all_5_2_5, all_5_1_4) = 0 % 19.50/5.37 | (109) all_5_0_3 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_5_1_4, all_5_1_4) = v0) % 19.50/5.37 | % 19.50/5.37 +-Applying beta-rule and splitting (74), into two cases. % 19.50/5.37 |-Branch one: % 19.50/5.37 | (106) ~ (subset(all_5_2_5, all_5_1_4) = 0) % 19.50/5.37 | % 19.50/5.37 | Using (88) and (106) yields: % 19.50/5.37 | (107) $false % 19.50/5.37 | % 19.50/5.37 |-The branch is then unsatisfiable % 19.50/5.37 |-Branch two: % 19.50/5.37 | (88) subset(all_5_2_5, all_5_1_4) = 0 % 19.50/5.37 | (90) all_5_0_3 = 0 % 19.50/5.37 | % 19.50/5.37 | Equations (90) can reduce 24 to: % 19.50/5.37 | (91) $false % 19.50/5.37 | % 19.50/5.37 |-The branch is then unsatisfiable % 19.50/5.37 |-Branch two: % 19.50/5.37 | (115) subset(all_5_2_5, all_5_2_5) = all_5_0_3 % 19.50/5.37 | (90) all_5_0_3 = 0 % 19.50/5.37 | % 19.50/5.37 | Equations (90) can reduce 24 to: % 19.50/5.37 | (91) $false % 19.50/5.37 | % 19.50/5.37 |-The branch is then unsatisfiable % 19.50/5.37 % SZS output end Proof for theBenchmark % 19.50/5.37 % 19.50/5.37 4742ms %------------------------------------------------------------------------------