%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU131+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n003.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 08:46:49 EDT 2022 % Result : Theorem 81.68s 47.64s % Output : Proof 91.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SEU131+2 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n003.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 : Sun Jun 19 01:06:13 EDT 2022 % 0.12/0.33 % CPUTime : % 0.53/0.59 ____ _ % 0.53/0.59 ___ / __ \_____(_)___ ________ __________ % 0.53/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.53/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.53/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.53/0.59 % 0.53/0.59 A Theorem Prover for First-Order Logic % 0.53/0.60 (ePrincess v.1.0) % 0.53/0.60 % 0.53/0.60 (c) Philipp Rümmer, 2009-2015 % 0.53/0.60 (c) Peter Backeman, 2014-2015 % 0.53/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.53/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.53/0.60 Bug reports to peter@backeman.se % 0.53/0.60 % 0.53/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.53/0.60 % 0.53/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.68/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.63/0.98 Prover 0: Preprocessing ... % 2.43/1.26 Prover 0: Warning: ignoring some quantifiers % 2.43/1.28 Prover 0: Constructing countermodel ... % 3.68/1.58 Prover 0: gave up % 3.68/1.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.68/1.62 Prover 1: Preprocessing ... % 4.31/1.75 Prover 1: Warning: ignoring some quantifiers % 4.31/1.76 Prover 1: Constructing countermodel ... % 4.87/1.83 Prover 1: gave up % 4.99/1.83 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.99/1.86 Prover 2: Preprocessing ... % 5.43/1.99 Prover 2: Warning: ignoring some quantifiers % 5.73/1.99 Prover 2: Constructing countermodel ... % 7.11/2.35 Prover 2: gave up % 7.11/2.35 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 7.36/2.37 Prover 3: Preprocessing ... % 7.36/2.41 Prover 3: Warning: ignoring some quantifiers % 7.36/2.41 Prover 3: Constructing countermodel ... % 7.92/2.52 Prover 3: gave up % 7.92/2.52 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 8.12/2.54 Prover 4: Preprocessing ... % 8.45/2.64 Prover 4: Warning: ignoring some quantifiers % 8.45/2.65 Prover 4: Constructing countermodel ... % 12.85/3.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 12.85/3.70 Prover 5: Preprocessing ... % 13.40/3.81 Prover 5: Warning: ignoring some quantifiers % 13.40/3.81 Prover 5: Constructing countermodel ... % 15.66/4.32 Prover 5: gave up % 15.66/4.32 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 15.66/4.34 Prover 6: Preprocessing ... % 15.89/4.41 Prover 6: Warning: ignoring some quantifiers % 15.89/4.41 Prover 6: Constructing countermodel ... % 16.73/4.61 Prover 6: gave up % 16.73/4.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 16.95/4.62 Prover 7: Preprocessing ... % 17.09/4.65 Prover 7: Proving ... % 39.07/14.25 Prover 8: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all % 39.28/14.29 Prover 8: Preprocessing ... % 39.28/14.34 Prover 8: Proving ... % 81.68/47.63 Prover 7: proved (14808ms) % 81.68/47.63 Prover 4: stopped % 81.68/47.64 Prover 8: stopped % 81.68/47.64 % 81.68/47.64 % SZS status Theorem for theBenchmark % 81.68/47.64 % 81.68/47.64 Generating proof ... found it (size 57) % 91.54/52.45 % 91.54/52.45 % SZS output start Proof for theBenchmark % 91.54/52.45 Assumed formulas after preprocessing and simplification: % 91.54/52.45 | (0) ? [v0] : (empty(v0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (set_intersection2(v2, v3) = v5) | ~ (set_intersection2(v1, v3) = v4) | ~ subset(v1, v2) | subset(v4, v5)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (set_difference(v4, v3) = v2) | ~ (set_difference(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (set_intersection2(v4, v3) = v2) | ~ (set_intersection2(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (set_union2(v4, v3) = v2) | ~ (set_union2(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v2, v3) = v4) | ~ subset(v1, v3) | ~ subset(v1, v2) | subset(v1, v4)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v1, v3) = v4) | ~ subset(v3, v2) | ~ subset(v1, v2) | subset(v4, v2)) & ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (set_union2(v1, v2) = v3) | ~ subset(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_intersection2(v1, v2) = v3) | ~ subset(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ disjoint(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ~ in(v5, v1) | in(v5, v2)) & (in(v5, v4) | (in(v5, v1) & ~ in(v5, v2)))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v2) = v3) | ( ! [v4] : ( ~ in(v4, v3) | (in(v4, v1) & ~ in(v4, v2))) & ! [v4] : ( ~ in(v4, v1) | in(v4, v3) | in(v4, v2)))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ disjoint(v1, v2) | ! [v4] : ~ in(v4, v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | set_intersection2(v2, v1) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | disjoint(v1, v2) | ? [v4] : in(v4, v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | subset(v3, v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ~ in(v5, v2) | ~ in(v5, v1)) & (in(v5, v4) | (in(v5, v2) & in(v5, v1)))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ( ! [v4] : ( ~ in(v4, v3) | (in(v4, v2) & in(v4, v1))) & ! [v4] : ( ~ in(v4, v2) | ~ in(v4, v1) | in(v4, v3)))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v2, v1) = v3) | ~ empty(v3) | empty(v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | ~ empty(v3) | empty(v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | set_union2(v2, v1) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | subset(v1, v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ( ~ in(v5, v2) & ~ in(v5, v1))) & (in(v5, v4) | in(v5, v2) | in(v5, v1))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | ( ! [v4] : ( ~ in(v4, v3) | in(v4, v2) | in(v4, v1)) & ! [v4] : (in(v4, v3) | ( ~ in(v4, v2) & ~ in(v4, v1))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ subset(v2, v3) | ~ subset(v1, v2) | subset(v1, v3)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_difference(v1, v0) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_intersection2(v1, v1) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v1, v1) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v1, v0) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ empty(v2) | ~ empty(v1)) & ! [v1] : ! [v2] : (v2 = v1 | ~ subset(v2, v1) | ~ subset(v1, v2)) & ! [v1] : ! [v2] : (v2 = v1 | ? [v3] : (( ~ in(v3, v2) | ~ in(v3, v1)) & (in(v3, v2) | in(v3, v1)))) & ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2)) & ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v1, v0) = v2)) & ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v2) = v0) | disjoint(v1, v2)) & ! [v1] : ! [v2] : ( ~ empty(v2) | ~ in(v1, v2)) & ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | disjoint(v2, v1)) & ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ! [v3] : ( ~ in(v3, v2) | ~ in(v3, v1))) & ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ! [v3] : ( ~ in(v3, v1) | in(v3, v2))) & ! [v1] : ! [v2] : ( ~ in(v2, v1) | ~ in(v1, v2)) & ! [v1] : ! [v2] : (disjoint(v1, v2) | ? [v3] : (in(v3, v2) & in(v3, v1))) & ! [v1] : ! [v2] : (subset(v1, v2) | ? [v3] : (in(v3, v1) & ~ in(v3, v2))) & ! [v1] : (v1 = v0 | ~ empty(v1)) & ! [v1] : (v1 = v0 | ~ subset(v1, v0)) & ! [v1] : (v1 = v0 | ? [v2] : in(v2, v1)) & ! [v1] : ~ in(v1, v0) & ! [v1] : subset(v1, v1) & ! [v1] : subset(v0, v1) & ? [v1] : ? [v2] : ? [v3] : (set_difference(v1, v2) = v3 & ((v3 = v0 & ~ subset(v1, v2)) | ( ~ (v3 = v0) & subset(v1, v2)))) & ? [v1] : ~ empty(v1) & ? [v1] : empty(v1)) % 91.54/52.48 | Instantiating (0) with all_0_0_0 yields: % 91.54/52.48 | (1) empty(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = all_0_0_0 | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v0) | in(v4, v1)) & (in(v4, v3) | (in(v4, v0) & ~ in(v4, v1)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v0) & ~ in(v3, v1))) & ! [v3] : ( ~ in(v3, v0) | in(v3, v2) | in(v3, v1)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ! [v3] : ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v3) | (in(v4, v1) & in(v4, v0)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v1) & in(v3, v0))) & ! [v3] : ( ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ( ~ in(v4, v1) & ~ in(v4, v0))) & (in(v4, v3) | in(v4, v1) | in(v4, v0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v3] : (in(v3, v2) | ( ~ in(v3, v1) & ~ in(v3, v0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, all_0_0_0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, all_0_0_0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) & ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_difference(all_0_0_0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_intersection2(v0, all_0_0_0) = v1)) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = all_0_0_0) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) & ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | ! [v2] : ( ~ in(v2, v1) | ~ in(v2, v0))) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ in(v2, v0) | in(v2, v1))) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) & ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ! [v0] : (v0 = all_0_0_0 | ~ empty(v0)) & ! [v0] : (v0 = all_0_0_0 | ~ subset(v0, all_0_0_0)) & ! [v0] : (v0 = all_0_0_0 | ? [v1] : in(v1, v0)) & ! [v0] : ~ in(v0, all_0_0_0) & ! [v0] : subset(v0, v0) & ! [v0] : subset(all_0_0_0, v0) & ? [v0] : ? [v1] : ? [v2] : (set_difference(v0, v1) = v2 & ((v2 = all_0_0_0 & ~ subset(v0, v1)) | ( ~ (v2 = all_0_0_0) & subset(v0, v1)))) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0) % 91.54/52.49 | % 91.54/52.49 | Applying alpha-rule on (1) yields: % 91.54/52.49 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v3) | (in(v4, v1) & in(v4, v0)))))) % 91.54/52.49 | (3) ! [v0] : (v0 = all_0_0_0 | ~ empty(v0)) % 91.54/52.49 | (4) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, all_0_0_0) = v1)) % 91.54/52.49 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 91.54/52.49 | (6) ? [v0] : empty(v0) % 91.54/52.49 | (7) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 91.54/52.49 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 91.54/52.49 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) % 91.54/52.49 | (10) ! [v0] : (v0 = all_0_0_0 | ~ subset(v0, all_0_0_0)) % 91.54/52.49 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ~ in(v4, v0) | in(v4, v1)) & (in(v4, v3) | (in(v4, v0) & ~ in(v4, v1)))))) % 91.54/52.49 | (12) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ in(v2, v0) | in(v2, v1))) % 91.54/52.49 | (13) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | ! [v2] : ( ~ in(v2, v1) | ~ in(v2, v0))) % 91.54/52.49 | (14) ! [v0] : subset(all_0_0_0, v0) % 91.54/52.49 | (15) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 91.54/52.49 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 91.54/52.49 | (17) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) % 91.54/52.49 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 91.54/52.49 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) % 91.54/52.49 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = all_0_0_0 | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) % 91.54/52.49 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 91.54/52.49 | (22) ! [v0] : ! [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) % 91.54/52.49 | (23) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 91.54/52.49 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 91.54/52.49 | (25) ! [v0] : ~ in(v0, all_0_0_0) % 91.54/52.49 | (26) ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_difference(all_0_0_0, v0) = v1)) % 91.54/52.49 | (27) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 91.54/52.49 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) % 91.54/52.49 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v0) & ~ in(v3, v1))) & ! [v3] : ( ~ in(v3, v0) | in(v3, v2) | in(v3, v1)))) % 91.54/52.49 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 91.54/52.49 | (31) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 91.54/52.49 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v1) & in(v3, v0))) & ! [v3] : ( ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)))) % 91.54/52.49 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) % 91.54/52.49 | (34) ! [v0] : ! [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) % 91.54/52.49 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 91.54/52.50 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) % 91.54/52.50 | (37) ! [v0] : subset(v0, v0) % 91.54/52.50 | (38) ? [v0] : ~ empty(v0) % 91.54/52.50 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ! [v3] : ~ in(v3, v2)) % 91.54/52.50 | (40) ? [v0] : ? [v1] : ? [v2] : (set_difference(v0, v1) = v2 & ((v2 = all_0_0_0 & ~ subset(v0, v1)) | ( ~ (v2 = all_0_0_0) & subset(v0, v1)))) % 91.54/52.50 | (41) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = all_0_0_0) | disjoint(v0, v1)) % 91.54/52.50 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v3] : (in(v3, v2) | ( ~ in(v3, v1) & ~ in(v3, v0))))) % 91.54/52.50 | (43) ! [v0] : (v0 = all_0_0_0 | ? [v1] : in(v1, v0)) % 91.54/52.50 | (44) ! [v0] : ! [v1] : (v1 = all_0_0_0 | ~ (set_intersection2(v0, all_0_0_0) = v1)) % 91.54/52.50 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 91.54/52.50 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ( ~ in(v4, v1) & ~ in(v4, v0))) & (in(v4, v3) | in(v4, v1) | in(v4, v0))))) % 91.54/52.50 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) % 91.54/52.50 | (48) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, all_0_0_0) = v1)) % 91.54/52.50 | (49) empty(all_0_0_0) % 91.54/52.50 | (50) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) % 91.54/52.50 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) % 91.54/52.50 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 91.54/52.50 | % 91.54/52.50 | Instantiating (40) with all_7_0_3, all_7_1_4, all_7_2_5 yields: % 91.54/52.50 | (53) set_difference(all_7_2_5, all_7_1_4) = all_7_0_3 & ((all_7_0_3 = all_0_0_0 & ~ subset(all_7_2_5, all_7_1_4)) | ( ~ (all_7_0_3 = all_0_0_0) & subset(all_7_2_5, all_7_1_4))) % 91.54/52.50 | % 91.54/52.50 | Applying alpha-rule on (53) yields: % 91.54/52.50 | (54) set_difference(all_7_2_5, all_7_1_4) = all_7_0_3 % 91.54/52.50 | (55) (all_7_0_3 = all_0_0_0 & ~ subset(all_7_2_5, all_7_1_4)) | ( ~ (all_7_0_3 = all_0_0_0) & subset(all_7_2_5, all_7_1_4)) % 91.54/52.50 | % 91.54/52.50 | Instantiating formula (29) with all_7_0_3, all_7_1_4, all_7_2_5 and discharging atoms set_difference(all_7_2_5, all_7_1_4) = all_7_0_3, yields: % 91.54/52.50 | (56) ! [v0] : ( ~ in(v0, all_7_0_3) | (in(v0, all_7_2_5) & ~ in(v0, all_7_1_4))) & ! [v0] : ( ~ in(v0, all_7_2_5) | in(v0, all_7_0_3) | in(v0, all_7_1_4)) % 91.54/52.50 | % 91.54/52.50 | Applying alpha-rule on (56) yields: % 91.54/52.50 | (57) ! [v0] : ( ~ in(v0, all_7_0_3) | (in(v0, all_7_2_5) & ~ in(v0, all_7_1_4))) % 91.54/52.50 | (58) ! [v0] : ( ~ in(v0, all_7_2_5) | in(v0, all_7_0_3) | in(v0, all_7_1_4)) % 91.54/52.50 | % 91.54/52.50 +-Applying beta-rule and splitting (55), into two cases. % 91.54/52.50 |-Branch one: % 91.54/52.50 | (59) all_7_0_3 = all_0_0_0 & ~ subset(all_7_2_5, all_7_1_4) % 91.54/52.50 | % 91.54/52.50 | Applying alpha-rule on (59) yields: % 91.54/52.50 | (60) all_7_0_3 = all_0_0_0 % 91.54/52.50 | (61) ~ subset(all_7_2_5, all_7_1_4) % 91.54/52.50 | % 91.54/52.50 | Introducing new symbol ex_75_1_22 defined by: % 91.54/52.50 | (62) ex_75_1_22 = all_7_2_5 % 91.54/52.50 | % 91.54/52.50 | Introducing new symbol ex_75_0_21 defined by: % 91.54/52.50 | (63) ex_75_0_21 = all_7_1_4 % 91.54/52.50 | % 91.54/52.50 | Instantiating formula (7) with ex_75_0_21, ex_75_1_22 yields: % 91.54/52.50 | (64) subset(ex_75_1_22, ex_75_0_21) | ? [v0] : (in(v0, ex_75_1_22) & ~ in(v0, ex_75_0_21)) % 91.54/52.50 | % 91.54/52.50 +-Applying beta-rule and splitting (64), into two cases. % 91.54/52.50 |-Branch one: % 91.54/52.50 | (65) subset(ex_75_1_22, ex_75_0_21) % 91.54/52.50 | % 91.54/52.50 | From (62)(63) and (65) follows: % 91.54/52.50 | (66) subset(all_7_2_5, all_7_1_4) % 91.54/52.50 | % 91.54/52.50 | Using (66) and (61) yields: % 91.54/52.50 | (67) $false % 91.54/52.50 | % 91.54/52.50 |-The branch is then unsatisfiable % 91.54/52.50 |-Branch two: % 91.54/52.50 | (68) ? [v0] : (in(v0, ex_75_1_22) & ~ in(v0, ex_75_0_21)) % 91.54/52.50 | % 91.54/52.50 | Instantiating (68) with all_77_0_23 yields: % 91.54/52.50 | (69) in(all_77_0_23, ex_75_1_22) & ~ in(all_77_0_23, ex_75_0_21) % 91.54/52.50 | % 91.54/52.50 | Applying alpha-rule on (69) yields: % 91.54/52.50 | (70) in(all_77_0_23, ex_75_1_22) % 91.54/52.50 | (71) ~ in(all_77_0_23, ex_75_0_21) % 91.54/52.50 | % 91.54/52.50 | Instantiating formula (25) with all_77_0_23 yields: % 91.54/52.50 | (72) ~ in(all_77_0_23, all_0_0_0) % 91.54/52.50 | % 91.54/52.50 | Instantiating formula (58) with all_77_0_23 yields: % 91.54/52.50 | (73) ~ in(all_77_0_23, all_7_2_5) | in(all_77_0_23, all_7_0_3) | in(all_77_0_23, all_7_1_4) % 91.54/52.50 | % 91.54/52.50 +-Applying beta-rule and splitting (73), into two cases. % 91.54/52.50 |-Branch one: % 91.54/52.50 | (74) ~ in(all_77_0_23, all_7_2_5) % 91.54/52.51 | % 91.54/52.51 | From (62) and (70) follows: % 91.54/52.51 | (75) in(all_77_0_23, all_7_2_5) % 91.54/52.51 | % 91.54/52.51 | Using (75) and (74) yields: % 91.54/52.51 | (67) $false % 91.54/52.51 | % 91.54/52.51 |-The branch is then unsatisfiable % 91.54/52.51 |-Branch two: % 91.54/52.51 | (77) in(all_77_0_23, all_7_0_3) | in(all_77_0_23, all_7_1_4) % 91.54/52.51 | % 91.54/52.51 +-Applying beta-rule and splitting (77), into two cases. % 91.54/52.51 |-Branch one: % 91.54/52.51 | (78) in(all_77_0_23, all_7_0_3) % 91.54/52.51 | % 91.54/52.51 | From (60) and (78) follows: % 91.54/52.51 | (79) in(all_77_0_23, all_0_0_0) % 91.54/52.51 | % 91.54/52.51 | Using (79) and (72) yields: % 91.54/52.51 | (67) $false % 91.54/52.51 | % 91.54/52.51 |-The branch is then unsatisfiable % 91.54/52.51 |-Branch two: % 91.54/52.51 | (81) in(all_77_0_23, all_7_1_4) % 91.54/52.51 | % 91.54/52.51 | From (63) and (71) follows: % 91.54/52.51 | (82) ~ in(all_77_0_23, all_7_1_4) % 91.54/52.51 | % 91.54/52.51 | Using (81) and (82) yields: % 91.54/52.51 | (67) $false % 91.54/52.51 | % 91.54/52.51 |-The branch is then unsatisfiable % 91.54/52.51 |-Branch two: % 91.54/52.51 | (84) ~ (all_7_0_3 = all_0_0_0) & subset(all_7_2_5, all_7_1_4) % 91.54/52.51 | % 91.54/52.51 | Applying alpha-rule on (84) yields: % 91.54/52.51 | (85) ~ (all_7_0_3 = all_0_0_0) % 91.54/52.51 | (66) subset(all_7_2_5, all_7_1_4) % 91.54/52.51 | % 91.54/52.51 | Instantiating formula (12) with all_7_1_4, all_7_2_5 and discharging atoms subset(all_7_2_5, all_7_1_4), yields: % 91.54/52.51 | (87) ! [v0] : ( ~ in(v0, all_7_2_5) | in(v0, all_7_1_4)) % 91.54/52.51 | % 91.54/52.51 | Introducing new symbol ex_47_0_45 defined by: % 91.54/52.51 | (88) ex_47_0_45 = all_7_0_3 % 91.54/52.51 | % 91.54/52.51 | Instantiating formula (43) with ex_47_0_45 yields: % 91.54/52.51 | (89) ex_47_0_45 = all_0_0_0 | ? [v0] : in(v0, ex_47_0_45) % 91.54/52.51 | % 91.54/52.51 +-Applying beta-rule and splitting (89), into two cases. % 91.54/52.51 |-Branch one: % 91.54/52.51 | (90) ex_47_0_45 = all_0_0_0 % 91.54/52.51 | % 91.54/52.51 | Combining equations (88,90) yields a new equation: % 91.54/52.51 | (91) all_7_0_3 = all_0_0_0 % 91.54/52.51 | % 91.54/52.51 | Simplifying 91 yields: % 91.54/52.51 | (60) all_7_0_3 = all_0_0_0 % 91.54/52.51 | % 91.54/52.51 | Equations (60) can reduce 85 to: % 91.54/52.51 | (93) $false % 91.54/52.51 | % 91.54/52.51 |-The branch is then unsatisfiable % 91.54/52.51 |-Branch two: % 91.54/52.51 | (94) ? [v0] : in(v0, ex_47_0_45) % 91.54/52.51 | % 91.54/52.51 | Instantiating (94) with all_50_0_46 yields: % 91.54/52.51 | (95) in(all_50_0_46, ex_47_0_45) % 91.54/52.51 | % 91.54/52.51 | Instantiating formula (87) with all_50_0_46 yields: % 91.54/52.51 | (96) ~ in(all_50_0_46, all_7_2_5) | in(all_50_0_46, all_7_1_4) % 91.54/52.51 | % 91.54/52.51 | Instantiating formula (57) with all_50_0_46 yields: % 91.54/52.51 | (97) ~ in(all_50_0_46, all_7_0_3) | (in(all_50_0_46, all_7_2_5) & ~ in(all_50_0_46, all_7_1_4)) % 91.54/52.51 | % 91.54/52.51 +-Applying beta-rule and splitting (96), into two cases. % 91.54/52.51 |-Branch one: % 91.54/52.51 | (98) ~ in(all_50_0_46, all_7_2_5) % 91.54/52.51 | % 91.54/52.51 +-Applying beta-rule and splitting (97), into two cases. % 91.54/52.51 |-Branch one: % 91.54/52.51 | (99) ~ in(all_50_0_46, all_7_0_3) % 91.54/52.51 | % 91.54/52.51 | From (88) and (95) follows: % 91.54/52.51 | (100) in(all_50_0_46, all_7_0_3) % 91.54/52.51 | % 91.54/52.51 | Using (100) and (99) yields: % 91.54/52.51 | (67) $false % 91.54/52.51 | % 91.54/52.51 |-The branch is then unsatisfiable % 91.54/52.51 |-Branch two: % 91.54/52.51 | (102) in(all_50_0_46, all_7_2_5) & ~ in(all_50_0_46, all_7_1_4) % 91.54/52.51 | % 91.54/52.51 | Applying alpha-rule on (102) yields: % 91.54/52.51 | (103) in(all_50_0_46, all_7_2_5) % 91.54/52.51 | (104) ~ in(all_50_0_46, all_7_1_4) % 91.54/52.51 | % 91.54/52.51 | Using (103) and (98) yields: % 91.54/52.51 | (67) $false % 91.54/52.51 | % 91.54/52.51 |-The branch is then unsatisfiable % 91.54/52.51 |-Branch two: % 91.54/52.51 | (106) in(all_50_0_46, all_7_1_4) % 91.54/52.51 | % 91.54/52.51 +-Applying beta-rule and splitting (97), into two cases. % 91.54/52.51 |-Branch one: % 91.54/52.51 | (99) ~ in(all_50_0_46, all_7_0_3) % 91.54/52.51 | % 91.54/52.51 | From (88) and (95) follows: % 91.54/52.51 | (100) in(all_50_0_46, all_7_0_3) % 91.54/52.51 | % 91.54/52.51 | Using (100) and (99) yields: % 91.54/52.51 | (67) $false % 91.54/52.51 | % 91.54/52.51 |-The branch is then unsatisfiable % 91.54/52.51 |-Branch two: % 91.54/52.51 | (102) in(all_50_0_46, all_7_2_5) & ~ in(all_50_0_46, all_7_1_4) % 91.54/52.51 | % 91.54/52.51 | Applying alpha-rule on (102) yields: % 91.54/52.51 | (103) in(all_50_0_46, all_7_2_5) % 91.54/52.51 | (104) ~ in(all_50_0_46, all_7_1_4) % 91.54/52.51 | % 91.54/52.51 | Using (106) and (104) yields: % 91.54/52.51 | (67) $false % 91.54/52.51 | % 91.54/52.51 |-The branch is then unsatisfiable % 91.54/52.51 % SZS output end Proof for theBenchmark % 91.54/52.51 % 91.54/52.51 51899ms %------------------------------------------------------------------------------