TSTP Solution File: SET169+3 by leanCoP---2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : leanCoP---2.2
% Problem : SET169+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leancop_casc.sh %s %d
% Computer : n007.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 02:52:01 EDT 2022
% Result : Theorem 0.81s 1.40s
% Output : Proof 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET169+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : leancop_casc.sh %s %d
% 0.12/0.33 % Computer : n007.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 Jul 10 02:11:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.81/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.81/1.41 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.81/1.41
% 0.81/1.41 %-----------------------------------------------------
% 0.81/1.41 fof(prove_intersection_distributes_over_union, conjecture, ! [_33975, _33978, _33981] : intersection(_33975, union(_33978, _33981)) = union(intersection(_33975, _33978), intersection(_33975, _33981)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prove_intersection_distributes_over_union)).
% 0.81/1.41 fof(union_defn, axiom, ! [_34220, _34223, _34226] : (member(_34226, union(_34220, _34223)) <=> member(_34226, _34220) | member(_34226, _34223)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', union_defn)).
% 0.81/1.41 fof(intersection_defn, axiom, ! [_34445, _34448, _34451] : (member(_34451, intersection(_34445, _34448)) <=> member(_34451, _34445) & member(_34451, _34448)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', intersection_defn)).
% 0.81/1.41 fof(commutativity_of_union, axiom, ! [_34673, _34676] : union(_34673, _34676) = union(_34676, _34673), file('/export/starexec/sandbox/benchmark/theBenchmark.p', commutativity_of_union)).
% 0.81/1.41 fof(equal_member_defn, axiom, ! [_34826, _34829] : (_34826 = _34829 <=> ! [_34843] : (member(_34843, _34826) <=> member(_34843, _34829))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', equal_member_defn)).
% 0.81/1.41
% 0.81/1.41 cnf(1, plain, [intersection(3 ^ [], union(4 ^ [], 5 ^ [])) = union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))], clausify(prove_intersection_distributes_over_union)).
% 0.81/1.41 cnf(2, plain, [-(_5971 = _5971)], theory(equality)).
% 0.81/1.41 cnf(3, plain, [_6124 = _6169, -(_6169 = _6124)], theory(equality)).
% 0.81/1.41 cnf(4, plain, [-(member(_6946, _7077)), member(_6879, _7012), _6879 = _6946, _7012 = _7077], theory(equality)).
% 0.81/1.41 cnf(5, plain, [-(member(_9553, union(_9436, _9495))), member(_9553, _9436)], clausify(union_defn)).
% 0.81/1.41 cnf(6, plain, [-(member(_9553, union(_9436, _9495))), member(_9553, _9495)], clausify(union_defn)).
% 0.81/1.41 cnf(7, plain, [member(_9553, union(_9436, _9495)), -(member(_9553, _9436)), -(member(_9553, _9495))], clausify(union_defn)).
% 0.81/1.41 cnf(8, plain, [member(_10066, intersection(_9949, _10008)), -(member(_10066, _9949))], clausify(intersection_defn)).
% 0.81/1.41 cnf(9, plain, [member(_10066, intersection(_9949, _10008)), -(member(_10066, _10008))], clausify(intersection_defn)).
% 0.81/1.41 cnf(10, plain, [-(member(_10066, intersection(_9949, _10008))), member(_10066, _9949), member(_10066, _10008)], clausify(intersection_defn)).
% 0.81/1.41 cnf(11, plain, [-(union(_10858, _10903) = union(_10903, _10858))], clausify(commutativity_of_union)).
% 0.81/1.41 cnf(12, plain, [-(_12103 = _12159), member(2 ^ [_12159, _12103], _12103), member(2 ^ [_12159, _12103], _12159)], clausify(equal_member_defn)).
% 0.81/1.41 cnf(13, plain, [-(_12103 = _12159), -(member(2 ^ [_12159, _12103], _12103)), -(member(2 ^ [_12159, _12103], _12159))], clausify(equal_member_defn)).
% 0.81/1.41
% 0.81/1.41 cnf('1',plain,[intersection(3 ^ [], union(4 ^ [], 5 ^ [])) = union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))],start(1)).
% 0.81/1.41 cnf('1.1',plain,[-(intersection(3 ^ [], union(4 ^ [], 5 ^ [])) = union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))), member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], union(4 ^ [], 5 ^ []))), member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])))],extension(12,bind([[_12103, _12159], [intersection(3 ^ [], union(4 ^ [], 5 ^ [])), union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))]]))).
% 0.81/1.41 cnf('1.1.1',plain,[-(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], union(4 ^ [], 5 ^ [])))), member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 3 ^ []), member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(4 ^ [], 5 ^ []))],extension(10,bind([[_9949, _10066, _10008], [3 ^ [], 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(4 ^ [], 5 ^ [])]]))).
% 0.81/1.41 cnf('1.1.1.1',plain,[-(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 3 ^ [])), member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(3 ^ [], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])))), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))))],extension(7,bind([[_9436, _9553, _9495], [3 ^ [], 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))]]))).
% 0.81/1.41 cnf('1.1.1.1.1',plain,[-(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(3 ^ [], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))))), member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), 3 ^ [])), 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))] = 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), 3 ^ []) = union(3 ^ [], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])))],extension(4,bind([[_6879, _6946, _7012, _7077], [2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), 3 ^ []), union(3 ^ [], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])))]]))).
% 0.81/1.41 cnf('1.1.1.1.1.1',plain,[-(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), 3 ^ []))), member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])))],extension(5,bind([[_9495, _9553, _9436], [3 ^ [], 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))]]))).
% 0.81/1.41 cnf('1.1.1.1.1.1.1',plain,[-(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])))), -(intersection(3 ^ [], union(4 ^ [], 5 ^ [])) = union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], union(4 ^ [], 5 ^ []))))],extension(13,bind([[_12159, _12103], [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))]]))).
% 0.81/1.41 cnf('1.1.1.1.1.1.1.1',plain,[intersection(3 ^ [], union(4 ^ [], 5 ^ [])) = union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))],extension(1)).
% 0.81/1.41 cnf('1.1.1.1.1.1.1.2',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], union(4 ^ [], 5 ^ [])))],reduction('1.1')).
% 0.81/1.41 cnf('1.1.1.1.1.2',plain,[-(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))] = 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))])],extension(2,bind([[_5971], [2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))]]]))).
% 0.81/1.41 cnf('1.1.1.1.1.3',plain,[-(union(union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), 3 ^ []) = union(3 ^ [], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])))), union(3 ^ [], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))) = union(union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), 3 ^ [])],extension(3,bind([[_6124, _6169], [union(3 ^ [], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))), union(union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), 3 ^ [])]]))).
% 0.81/1.41 cnf('1.1.1.1.1.3.1',plain,[-(union(3 ^ [], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))) = union(union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), 3 ^ []))],extension(11,bind([[_10903, _10858], [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), 3 ^ []]]))).
% 0.81/1.41 cnf('1.1.1.1.2',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], 4 ^ []))), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], 5 ^ [])))],extension(7,bind([[_9436, _9553, _9495], [intersection(3 ^ [], 4 ^ []), 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], 5 ^ [])]]))).
% 0.81/1.41 cnf('1.1.1.1.2.1',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], 4 ^ [])), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 3 ^ []))],extension(8,bind([[_10008, _10066, _9949], [4 ^ [], 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 3 ^ []]]))).
% 0.81/1.41 cnf('1.1.1.1.2.1.1',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 3 ^ [])],reduction('1.1.1')).
% 0.81/1.41 cnf('1.1.1.1.2.2',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], 5 ^ [])), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 3 ^ []))],extension(8,bind([[_10008, _10066, _9949], [5 ^ [], 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 3 ^ []]]))).
% 0.81/1.41 cnf('1.1.1.1.2.2.1',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 3 ^ [])],reduction('1.1.1')).
% 0.81/1.41 cnf('1.1.1.2',plain,[-(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(4 ^ [], 5 ^ []))), member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(union(4 ^ [], 5 ^ []), union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])))), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))))],extension(7,bind([[_9436, _9553, _9495], [union(4 ^ [], 5 ^ []), 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))]]))).
% 0.81/1.41 cnf('1.1.1.2.1',plain,[-(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(union(4 ^ [], 5 ^ []), union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))))), member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), union(4 ^ [], 5 ^ []))), 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))] = 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), union(4 ^ [], 5 ^ [])) = union(union(4 ^ [], 5 ^ []), union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])))],extension(4,bind([[_6879, _6946, _7012, _7077], [2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), union(4 ^ [], 5 ^ [])), union(union(4 ^ [], 5 ^ []), union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])))]]))).
% 0.81/1.41 cnf('1.1.1.2.1.1',plain,[-(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), union(4 ^ [], 5 ^ [])))), member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])))],extension(5,bind([[_9495, _9553, _9436], [union(4 ^ [], 5 ^ []), 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))]]))).
% 0.81/1.41 cnf('1.1.1.2.1.1.1',plain,[-(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])))), -(intersection(3 ^ [], union(4 ^ [], 5 ^ [])) = union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], union(4 ^ [], 5 ^ []))))],extension(13,bind([[_12159, _12103], [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))]]))).
% 0.81/1.41 cnf('1.1.1.2.1.1.1.1',plain,[intersection(3 ^ [], union(4 ^ [], 5 ^ [])) = union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))],extension(1)).
% 0.81/1.41 cnf('1.1.1.2.1.1.1.2',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], union(4 ^ [], 5 ^ [])))],reduction('1.1')).
% 0.81/1.41 cnf('1.1.1.2.1.2',plain,[-(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))] = 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))])],extension(2,bind([[_5971], [2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))]]]))).
% 0.81/1.41 cnf('1.1.1.2.1.3',plain,[-(union(union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), union(4 ^ [], 5 ^ [])) = union(union(4 ^ [], 5 ^ []), union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])))), union(union(4 ^ [], 5 ^ []), union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))) = union(union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), union(4 ^ [], 5 ^ []))],extension(3,bind([[_6124, _6169], [union(union(4 ^ [], 5 ^ []), union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))), union(union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), union(4 ^ [], 5 ^ []))]]))).
% 0.81/1.41 cnf('1.1.1.2.1.3.1',plain,[-(union(union(4 ^ [], 5 ^ []), union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))) = union(union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), union(4 ^ [], 5 ^ [])))],extension(11,bind([[_10903, _10858], [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), union(4 ^ [], 5 ^ [])]]))).
% 0.81/1.41 cnf('1.1.1.2.2',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], 4 ^ []))), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], 5 ^ [])))],extension(7,bind([[_9436, _9553, _9495], [intersection(3 ^ [], 4 ^ []), 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], 5 ^ [])]]))).
% 0.81/1.41 cnf('1.1.1.2.2.1',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], 4 ^ [])), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 4 ^ []))],extension(9,bind([[_9949, _10066, _10008], [3 ^ [], 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 4 ^ []]]))).
% 0.81/1.41 cnf('1.1.1.2.2.1.1',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 4 ^ []), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(4 ^ [], 5 ^ [])))],extension(5,bind([[_9553, _9436, _9495], [2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 4 ^ [], 5 ^ []]]))).
% 0.81/1.41 cnf('1.1.1.2.2.1.1.1',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(4 ^ [], 5 ^ []))],reduction('1.1.1')).
% 0.81/1.41 cnf('1.1.1.2.2.2',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], 5 ^ [])), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 5 ^ []))],extension(9,bind([[_9949, _10066, _10008], [3 ^ [], 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 5 ^ []]]))).
% 0.81/1.41 cnf('1.1.1.2.2.2.1',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 5 ^ []), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(4 ^ [], 5 ^ [])))],extension(6,bind([[_9553, _9436, _9495], [2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 4 ^ [], 5 ^ []]]))).
% 0.81/1.41 cnf('1.1.1.2.2.2.1.1',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(4 ^ [], 5 ^ []))],reduction('1.1.1')).
% 0.81/1.41 cnf('1.1.2',plain,[-(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])))), -(intersection(3 ^ [], union(4 ^ [], 5 ^ [])) = union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], union(4 ^ [], 5 ^ []))))],extension(13,bind([[_12159, _12103], [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))]]))).
% 0.81/1.41 cnf('1.1.2.1',plain,[intersection(3 ^ [], union(4 ^ [], 5 ^ [])) = union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))],extension(1)).
% 0.81/1.41 cnf('1.1.2.2',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], union(4 ^ [], 5 ^ []))), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(4 ^ [], 5 ^ [])))],extension(9,bind([[_9949, _10066, _10008], [3 ^ [], 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(4 ^ [], 5 ^ [])]]))).
% 0.81/1.41 cnf('1.1.2.2.1',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(4 ^ [], 5 ^ [])), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 4 ^ [])), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 5 ^ []))],extension(7,bind([[_9436, _9553, _9495], [4 ^ [], 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 5 ^ []]]))).
% 0.81/1.41 cnf('1.1.2.2.1.1',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 4 ^ []), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], 4 ^ []))), member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 3 ^ [])],extension(10,bind([[_10008, _10066, _9949], [4 ^ [], 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 3 ^ []]]))).
% 0.81/1.41 cnf('1.1.2.2.1.1.1',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], 4 ^ [])), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))))],extension(5,bind([[_9553, _9436, _9495], [2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])]]))).
% 0.81/1.41 cnf('1.1.2.2.1.1.1.1',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])))],reduction('1.1')).
% 0.81/1.41 cnf('1.1.2.2.1.1.2',plain,[-(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 3 ^ [])), member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], union(4 ^ [], 5 ^ [])))],extension(8,bind([[_10066, _9949, _10008], [2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 3 ^ [], union(4 ^ [], 5 ^ [])]]))).
% 0.81/1.41 cnf('1.1.2.2.1.1.2.1',plain,[-(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], union(4 ^ [], 5 ^ []))))],lemmata('1.1')).
% 0.81/1.41 cnf('1.1.2.2.1.2',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 5 ^ []), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], 5 ^ []))), member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 3 ^ [])],extension(10,bind([[_10008, _10066, _9949], [5 ^ [], 2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 3 ^ []]]))).
% 0.81/1.41 cnf('1.1.2.2.1.2.1',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], 5 ^ [])), -(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ []))))],extension(6,bind([[_9553, _9436, _9495], [2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])]]))).
% 0.81/1.41 cnf('1.1.2.2.1.2.1.1',plain,[member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])))],reduction('1.1')).
% 0.81/1.41 cnf('1.1.2.2.1.2.2',plain,[-(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 3 ^ [])), member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], union(4 ^ [], 5 ^ [])))],extension(8,bind([[_10066, _9949, _10008], [2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], 3 ^ [], union(4 ^ [], 5 ^ [])]]))).
% 0.81/1.41 cnf('1.1.2.2.1.2.2.1',plain,[-(member(2 ^ [union(intersection(3 ^ [], 4 ^ []), intersection(3 ^ [], 5 ^ [])), intersection(3 ^ [], union(4 ^ [], 5 ^ []))], intersection(3 ^ [], union(4 ^ [], 5 ^ []))))],lemmata('1.1')).
% 0.81/1.41 %-----------------------------------------------------
% 0.81/1.42
% 0.81/1.42 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------