%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU167+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n006.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 08:47:14 EDT 2022 % Result : Theorem 13.26s 3.81s % Output : Proof 17.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU167+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n006.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jun 18 19:54:55 EDT 2022 % 0.12/0.33 % CPUTime : % 0.54/0.57 ____ _ % 0.54/0.57 ___ / __ \_____(_)___ ________ __________ % 0.54/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.57 % 0.54/0.57 A Theorem Prover for First-Order Logic % 0.54/0.57 (ePrincess v.1.0) % 0.54/0.57 % 0.54/0.57 (c) Philipp Rümmer, 2009-2015 % 0.54/0.57 (c) Peter Backeman, 2014-2015 % 0.54/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.54/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.54/0.57 Bug reports to peter@backeman.se % 0.54/0.57 % 0.54/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.54/0.57 % 0.54/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.59/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.33/0.85 Prover 0: Preprocessing ... % 1.59/0.98 Prover 0: Warning: ignoring some quantifiers % 1.59/0.99 Prover 0: Constructing countermodel ... % 3.84/1.56 Prover 0: gave up % 3.84/1.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.84/1.58 Prover 1: Preprocessing ... % 3.84/1.60 Prover 1: Constructing countermodel ... % 4.30/1.64 Prover 1: gave up % 4.30/1.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.30/1.65 Prover 2: Preprocessing ... % 4.30/1.68 Prover 2: Warning: ignoring some quantifiers % 4.30/1.68 Prover 2: Constructing countermodel ... % 5.03/1.80 Prover 2: gave up % 5.03/1.80 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 5.03/1.81 Prover 3: Preprocessing ... % 5.13/1.82 Prover 3: Warning: ignoring some quantifiers % 5.13/1.82 Prover 3: Constructing countermodel ... % 6.40/2.20 Prover 3: gave up % 6.40/2.20 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 6.40/2.21 Prover 4: Preprocessing ... % 6.90/2.24 Prover 4: Warning: ignoring some quantifiers % 6.90/2.24 Prover 4: Constructing countermodel ... % 11.61/3.38 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 11.69/3.38 Prover 5: Preprocessing ... % 11.69/3.41 Prover 5: Constructing countermodel ... % 13.26/3.81 Prover 5: proved (431ms) % 13.26/3.81 Prover 4: stopped % 13.26/3.81 % 13.26/3.81 No countermodel exists, formula is valid % 13.26/3.81 % SZS status Theorem for theBenchmark % 13.26/3.81 % 13.26/3.81 Generating proof ... found it (size 34) % 17.10/4.67 % 17.10/4.67 % SZS output start Proof for theBenchmark % 17.10/4.67 Assumed formulas after preprocessing and simplification: % 17.10/4.67 | (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] : ( ~ (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) % 17.10/4.70 | Applying alpha-rule on (0) yields: % 17.10/4.70 | (1) ! [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)) % 17.10/4.70 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 17.10/4.70 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) % 17.10/4.70 | (4) ! [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)) % 17.10/4.70 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 17.10/4.70 | (6) ! [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)) % 17.10/4.70 | (7) ! [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)))) % 17.10/4.70 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) % 17.10/4.70 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 17.10/4.71 | (10) ! [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)) % 17.10/4.71 | (11) ! [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)))) % 17.10/4.71 | (12) ? [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) % 17.10/4.71 | (13) ! [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)))) % 17.10/4.71 | (14) ! [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)))) % 17.10/4.71 | (15) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 17.10/4.71 | % 17.10/4.71 | Instantiating (12) with all_1_0_0, all_1_1_1, all_1_2_2, all_1_3_3, all_1_4_4, all_1_5_5, all_1_6_6 yields: % 17.10/4.71 | (16) ~ (all_1_0_0 = 0) & cartesian_product2(all_1_5_5, all_1_3_3) = all_1_1_1 & cartesian_product2(all_1_6_6, all_1_4_4) = all_1_2_2 & subset(all_1_2_2, all_1_1_1) = all_1_0_0 & subset(all_1_4_4, all_1_3_3) = 0 & subset(all_1_6_6, all_1_5_5) = 0 % 17.10/4.71 | % 17.10/4.71 | Applying alpha-rule on (16) yields: % 17.10/4.71 | (17) ~ (all_1_0_0 = 0) % 17.10/4.71 | (18) subset(all_1_4_4, all_1_3_3) = 0 % 17.10/4.71 | (19) subset(all_1_6_6, all_1_5_5) = 0 % 17.10/4.71 | (20) cartesian_product2(all_1_6_6, all_1_4_4) = all_1_2_2 % 17.10/4.71 | (21) subset(all_1_2_2, all_1_1_1) = all_1_0_0 % 17.10/4.71 | (22) cartesian_product2(all_1_5_5, all_1_3_3) = all_1_1_1 % 17.10/4.71 | % 17.10/4.71 | Instantiating formula (15) with all_1_0_0, all_1_2_2 yields: % 17.10/4.71 | (23) all_1_0_0 = 0 | ~ (subset(all_1_2_2, all_1_2_2) = all_1_0_0) % 17.10/4.71 | % 17.10/4.71 | Instantiating formula (11) with all_1_2_2, all_1_2_2, all_1_6_6, all_1_4_4, all_1_4_4 and discharging atoms cartesian_product2(all_1_6_6, all_1_4_4) = all_1_2_2, yields: % 17.10/4.71 | (24) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (cartesian_product2(all_1_4_4, all_1_6_6) = v2 & cartesian_product2(all_1_4_4, all_1_6_6) = v1 & subset(v1, v2) = v3 & subset(all_1_2_2, all_1_2_2) = v4 & subset(all_1_4_4, all_1_4_4) = v0 & ( ~ (v0 = 0) | (v4 = 0 & v3 = 0))) % 17.10/4.71 | % 17.10/4.71 | Instantiating formula (14) with all_1_2_2, all_1_2_2, all_1_4_4, all_1_6_6, all_1_6_6 and discharging atoms cartesian_product2(all_1_6_6, all_1_4_4) = all_1_2_2, yields: % 17.10/4.71 | (25) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (cartesian_product2(all_1_4_4, all_1_6_6) = v3 & cartesian_product2(all_1_4_4, all_1_6_6) = v2 & subset(v2, v3) = v4 & subset(all_1_2_2, all_1_2_2) = v1 & subset(all_1_6_6, all_1_6_6) = v0 & ( ~ (v0 = 0) | (v4 = 0 & v1 = 0))) % 17.10/4.71 | % 17.10/4.71 | Instantiating formula (6) with all_1_1_1, all_1_5_5, all_1_3_3, all_1_4_4 and discharging atoms cartesian_product2(all_1_5_5, all_1_3_3) = all_1_1_1, subset(all_1_4_4, all_1_3_3) = 0, yields: % 17.10/4.71 | (26) ? [v0] : ? [v1] : ? [v2] : (cartesian_product2(all_1_3_3, all_1_5_5) = v1 & cartesian_product2(all_1_4_4, all_1_5_5) = v0 & cartesian_product2(all_1_5_5, all_1_4_4) = v2 & subset(v2, all_1_1_1) = 0 & subset(v0, v1) = 0) % 17.10/4.71 | % 17.10/4.71 | Instantiating formula (4) with all_1_2_2, all_1_4_4, all_1_5_5, all_1_6_6 and discharging atoms cartesian_product2(all_1_6_6, all_1_4_4) = all_1_2_2, subset(all_1_6_6, all_1_5_5) = 0, yields: % 17.10/4.71 | (27) ? [v0] : ? [v1] : ? [v2] : (cartesian_product2(all_1_4_4, all_1_5_5) = v2 & cartesian_product2(all_1_4_4, all_1_6_6) = v1 & cartesian_product2(all_1_5_5, all_1_4_4) = v0 & subset(v1, v2) = 0 & subset(all_1_2_2, v0) = 0) % 17.10/4.71 | % 17.10/4.71 | Instantiating (27) with all_8_0_7, all_8_1_8, all_8_2_9 yields: % 17.10/4.71 | (28) cartesian_product2(all_1_4_4, all_1_5_5) = all_8_0_7 & cartesian_product2(all_1_4_4, all_1_6_6) = all_8_1_8 & cartesian_product2(all_1_5_5, all_1_4_4) = all_8_2_9 & subset(all_8_1_8, all_8_0_7) = 0 & subset(all_1_2_2, all_8_2_9) = 0 % 17.10/4.71 | % 17.10/4.71 | Applying alpha-rule on (28) yields: % 17.10/4.71 | (29) cartesian_product2(all_1_5_5, all_1_4_4) = all_8_2_9 % 17.10/4.71 | (30) cartesian_product2(all_1_4_4, all_1_6_6) = all_8_1_8 % 17.10/4.71 | (31) subset(all_1_2_2, all_8_2_9) = 0 % 17.10/4.71 | (32) cartesian_product2(all_1_4_4, all_1_5_5) = all_8_0_7 % 17.10/4.71 | (33) subset(all_8_1_8, all_8_0_7) = 0 % 17.10/4.71 | % 17.10/4.71 | Instantiating (26) with all_12_0_13, all_12_1_14, all_12_2_15 yields: % 17.10/4.71 | (34) cartesian_product2(all_1_3_3, all_1_5_5) = all_12_1_14 & cartesian_product2(all_1_4_4, all_1_5_5) = all_12_2_15 & cartesian_product2(all_1_5_5, all_1_4_4) = all_12_0_13 & subset(all_12_0_13, all_1_1_1) = 0 & subset(all_12_2_15, all_12_1_14) = 0 % 17.10/4.71 | % 17.10/4.71 | Applying alpha-rule on (34) yields: % 17.10/4.71 | (35) cartesian_product2(all_1_5_5, all_1_4_4) = all_12_0_13 % 17.10/4.71 | (36) cartesian_product2(all_1_4_4, all_1_5_5) = all_12_2_15 % 17.10/4.72 | (37) cartesian_product2(all_1_3_3, all_1_5_5) = all_12_1_14 % 17.10/4.72 | (38) subset(all_12_2_15, all_12_1_14) = 0 % 17.10/4.72 | (39) subset(all_12_0_13, all_1_1_1) = 0 % 17.10/4.72 | % 17.10/4.72 | Instantiating (24) with all_14_0_16, all_14_1_17, all_14_2_18, all_14_3_19, all_14_4_20 yields: % 17.10/4.72 | (40) cartesian_product2(all_1_4_4, all_1_6_6) = all_14_2_18 & cartesian_product2(all_1_4_4, all_1_6_6) = all_14_3_19 & subset(all_14_3_19, all_14_2_18) = all_14_1_17 & subset(all_1_2_2, all_1_2_2) = all_14_0_16 & subset(all_1_4_4, all_1_4_4) = all_14_4_20 & ( ~ (all_14_4_20 = 0) | (all_14_0_16 = 0 & all_14_1_17 = 0)) % 17.10/4.72 | % 17.10/4.72 | Applying alpha-rule on (40) yields: % 17.10/4.72 | (41) subset(all_1_4_4, all_1_4_4) = all_14_4_20 % 17.10/4.72 | (42) ~ (all_14_4_20 = 0) | (all_14_0_16 = 0 & all_14_1_17 = 0) % 17.10/4.72 | (43) cartesian_product2(all_1_4_4, all_1_6_6) = all_14_3_19 % 17.10/4.72 | (44) cartesian_product2(all_1_4_4, all_1_6_6) = all_14_2_18 % 17.10/4.72 | (45) subset(all_14_3_19, all_14_2_18) = all_14_1_17 % 17.10/4.72 | (46) subset(all_1_2_2, all_1_2_2) = all_14_0_16 % 17.10/4.72 | % 17.10/4.72 | Instantiating (25) with all_20_0_31, all_20_1_32, all_20_2_33, all_20_3_34, all_20_4_35 yields: % 17.10/4.72 | (47) cartesian_product2(all_1_4_4, all_1_6_6) = all_20_1_32 & cartesian_product2(all_1_4_4, all_1_6_6) = all_20_2_33 & subset(all_20_2_33, all_20_1_32) = all_20_0_31 & subset(all_1_2_2, all_1_2_2) = all_20_3_34 & subset(all_1_6_6, all_1_6_6) = all_20_4_35 & ( ~ (all_20_4_35 = 0) | (all_20_0_31 = 0 & all_20_3_34 = 0)) % 17.10/4.72 | % 17.10/4.72 | Applying alpha-rule on (47) yields: % 17.10/4.72 | (48) cartesian_product2(all_1_4_4, all_1_6_6) = all_20_1_32 % 17.10/4.72 | (49) cartesian_product2(all_1_4_4, all_1_6_6) = all_20_2_33 % 17.10/4.72 | (50) subset(all_1_6_6, all_1_6_6) = all_20_4_35 % 17.10/4.72 | (51) subset(all_1_2_2, all_1_2_2) = all_20_3_34 % 17.10/4.72 | (52) subset(all_20_2_33, all_20_1_32) = all_20_0_31 % 17.10/4.72 | (53) ~ (all_20_4_35 = 0) | (all_20_0_31 = 0 & all_20_3_34 = 0) % 17.10/4.72 | % 17.10/4.72 +-Applying beta-rule and splitting (23), into two cases. % 17.10/4.72 |-Branch one: % 17.10/4.72 | (54) ~ (subset(all_1_2_2, all_1_2_2) = all_1_0_0) % 17.10/4.72 | % 17.10/4.72 | Instantiating formula (2) with all_1_5_5, all_1_4_4, all_8_2_9, all_12_0_13 and discharging atoms cartesian_product2(all_1_5_5, all_1_4_4) = all_12_0_13, cartesian_product2(all_1_5_5, all_1_4_4) = all_8_2_9, yields: % 17.10/4.72 | (55) all_12_0_13 = all_8_2_9 % 17.10/4.72 | % 17.10/4.72 | Instantiating formula (5) with all_1_2_2, all_1_1_1, 0, all_1_0_0 and discharging atoms subset(all_1_2_2, all_1_1_1) = all_1_0_0, yields: % 17.10/4.72 | (56) all_1_0_0 = 0 | ~ (subset(all_1_2_2, all_1_1_1) = 0) % 17.10/4.72 | % 17.10/4.72 | Instantiating formula (15) with all_20_3_34, all_1_2_2 and discharging atoms subset(all_1_2_2, all_1_2_2) = all_20_3_34, yields: % 17.10/4.72 | (57) all_20_3_34 = 0 % 17.10/4.72 | % 17.10/4.72 | Instantiating formula (5) with all_1_2_2, all_1_2_2, all_14_0_16, all_20_3_34 and discharging atoms subset(all_1_2_2, all_1_2_2) = all_20_3_34, subset(all_1_2_2, all_1_2_2) = all_14_0_16, yields: % 17.10/4.72 | (58) all_20_3_34 = all_14_0_16 % 17.10/4.72 | % 17.10/4.72 | Using (46) and (54) yields: % 17.10/4.72 | (59) ~ (all_14_0_16 = all_1_0_0) % 17.10/4.72 | % 17.10/4.72 | Combining equations (57,58) yields a new equation: % 17.10/4.72 | (60) all_14_0_16 = 0 % 17.10/4.72 | % 17.10/4.72 | Equations (60) can reduce 59 to: % 17.10/4.72 | (61) ~ (all_1_0_0 = 0) % 17.10/4.72 | % 17.10/4.72 | Simplifying 61 yields: % 17.10/4.72 | (17) ~ (all_1_0_0 = 0) % 17.10/4.72 | % 17.10/4.72 | From (55) and (39) follows: % 17.10/4.72 | (63) subset(all_8_2_9, all_1_1_1) = 0 % 17.10/4.72 | % 17.10/4.72 | Instantiating formula (8) with all_1_1_1, all_8_2_9, all_1_2_2 and discharging atoms subset(all_8_2_9, all_1_1_1) = 0, subset(all_1_2_2, all_8_2_9) = 0, yields: % 17.10/4.72 | (64) subset(all_1_2_2, all_1_1_1) = 0 % 17.10/4.72 | % 17.10/4.72 +-Applying beta-rule and splitting (56), into two cases. % 17.10/4.72 |-Branch one: % 17.10/4.72 | (65) ~ (subset(all_1_2_2, all_1_1_1) = 0) % 17.10/4.72 | % 17.10/4.72 | Using (64) and (65) yields: % 17.10/4.72 | (66) $false % 17.10/4.72 | % 17.10/4.72 |-The branch is then unsatisfiable % 17.10/4.72 |-Branch two: % 17.10/4.72 | (64) subset(all_1_2_2, all_1_1_1) = 0 % 17.10/4.72 | (68) all_1_0_0 = 0 % 17.10/4.72 | % 17.10/4.72 | Equations (68) can reduce 17 to: % 17.10/4.72 | (69) $false % 17.10/4.72 | % 17.10/4.72 |-The branch is then unsatisfiable % 17.10/4.72 |-Branch two: % 17.10/4.72 | (70) subset(all_1_2_2, all_1_2_2) = all_1_0_0 % 17.10/4.72 | (68) all_1_0_0 = 0 % 17.10/4.72 | % 17.10/4.72 | Equations (68) can reduce 17 to: % 17.10/4.72 | (69) $false % 17.10/4.72 | % 17.10/4.72 |-The branch is then unsatisfiable % 17.10/4.72 % SZS output end Proof for theBenchmark % 17.10/4.72 % 17.10/4.72 4141ms %------------------------------------------------------------------------------