TSTP Solution File: SEU324+1 by leanCoP---2.2
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- Process Solution
%------------------------------------------------------------------------------
% File : leanCoP---2.2
% Problem : SEU324+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leancop_casc.sh %s %d
% Computer : n021.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 12:02:00 EDT 2022
% Result : Theorem 0.92s 1.40s
% Output : Proof 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU324+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : leancop_casc.sh %s %d
% 0.12/0.33 % Computer : n021.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 06:23:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.92/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.92/1.40 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.92/1.41
% 0.92/1.41 %-----------------------------------------------------
% 0.92/1.41 fof(t55_tops_1, conjecture, ! [_54920] : (topological_space(_54920) & top_str(_54920) => ! [_54942] : (top_str(_54942) => ! [_54957] : (element(_54957, powerset(the_carrier(_54920))) => ! [_54983] : (element(_54983, powerset(the_carrier(_54942))) => (open_subset(_54983, _54942) => interior(_54942, _54983) = _54983) & (interior(_54920, _54957) = _54957 => open_subset(_54957, _54920)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', t55_tops_1)).
% 0.92/1.41 fof(d1_tops_1, axiom, ! [_55571] : (top_str(_55571) => ! [_55586] : (element(_55586, powerset(the_carrier(_55571))) => interior(_55571, _55586) = subset_complement(the_carrier(_55571), topstr_closure(_55571, subset_complement(the_carrier(_55571), _55586))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', d1_tops_1)).
% 0.92/1.41 fof(dt_k3_subset_1, axiom, ! [_55854, _55857] : (element(_55857, powerset(_55854)) => element(subset_complement(_55854, _55857), powerset(_55854))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dt_k3_subset_1)).
% 0.92/1.41 fof(fc6_tops_1, axiom, ! [_56042, _56045] : (topological_space(_56042) & top_str(_56042) & element(_56045, powerset(the_carrier(_56042))) => open_subset(interior(_56042, _56045), _56042)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fc6_tops_1)).
% 0.92/1.41 fof(involutiveness_k3_subset_1, axiom, ! [_56264, _56267] : (element(_56267, powerset(_56264)) => subset_complement(_56264, subset_complement(_56264, _56267)) = _56267), file('/export/starexec/sandbox/benchmark/theBenchmark.p', involutiveness_k3_subset_1)).
% 0.92/1.41 fof(t30_tops_1, axiom, ! [_56455] : (top_str(_56455) => ! [_56470] : (element(_56470, powerset(the_carrier(_56455))) => (open_subset(_56470, _56455) <=> closed_subset(subset_complement(the_carrier(_56455), _56470), _56455)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', t30_tops_1)).
% 0.92/1.41 fof(t52_pre_topc, axiom, ! [_56715] : (top_str(_56715) => ! [_56730] : (element(_56730, powerset(the_carrier(_56715))) => (closed_subset(_56730, _56715) => topstr_closure(_56715, _56730) = _56730) & (topological_space(_56715) & topstr_closure(_56715, _56730) = _56730 => closed_subset(_56730, _56715)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', t52_pre_topc)).
% 0.92/1.41
% 0.92/1.41 cnf(1, plain, [-(12 ^ []), open_subset(9 ^ [], 7 ^ [])], clausify(t55_tops_1)).
% 0.92/1.41 cnf(2, plain, [-(12 ^ []), -(interior(7 ^ [], 9 ^ []) = 9 ^ [])], clausify(t55_tops_1)).
% 0.92/1.41 cnf(3, plain, [-(11 ^ []), interior(8 ^ [], 10 ^ []) = 10 ^ []], clausify(t55_tops_1)).
% 0.92/1.41 cnf(4, plain, [-(11 ^ []), -(open_subset(10 ^ [], 8 ^ []))], clausify(t55_tops_1)).
% 0.92/1.41 cnf(5, plain, [-(topological_space(7 ^ []))], clausify(t55_tops_1)).
% 0.92/1.41 cnf(6, plain, [-(top_str(7 ^ []))], clausify(t55_tops_1)).
% 0.92/1.41 cnf(7, plain, [-(top_str(8 ^ []))], clausify(t55_tops_1)).
% 0.92/1.41 cnf(8, plain, [-(element(9 ^ [], powerset(the_carrier(7 ^ []))))], clausify(t55_tops_1)).
% 0.92/1.41 cnf(9, plain, [-(element(10 ^ [], powerset(the_carrier(8 ^ []))))], clausify(t55_tops_1)).
% 0.92/1.41 cnf(10, plain, [11 ^ [], 12 ^ []], clausify(t55_tops_1)).
% 0.92/1.41 cnf(11, plain, [-(interior(_18408, _18541) = interior(_18475, _18606)), _18408 = _18475, _18541 = _18606], theory(equality)).
% 0.92/1.41 cnf(12, plain, [-(subset_complement(_19361, _19494) = subset_complement(_19428, _19559)), _19361 = _19428, _19494 = _19559], theory(equality)).
% 0.92/1.41 cnf(13, plain, [_19985 = _20034, -(the_carrier(_19985) = the_carrier(_20034))], theory(equality)).
% 0.92/1.41 cnf(14, plain, [-(_13922 = _13922)], theory(equality)).
% 0.92/1.41 cnf(15, plain, [_14075 = _14120, -(_14120 = _14075)], theory(equality)).
% 0.92/1.41 cnf(16, plain, [-(_14354 = _14465), _14354 = _14410, _14410 = _14465], theory(equality)).
% 0.92/1.41 cnf(17, plain, [-(open_subset(_16474, _16605)), open_subset(_16407, _16540), _16407 = _16474, _16540 = _16605], theory(equality)).
% 0.92/1.41 cnf(18, plain, [top_str(_21024), element(_21132, powerset(the_carrier(_21024))), -(interior(_21024, _21132) = subset_complement(the_carrier(_21024), topstr_closure(_21024, subset_complement(the_carrier(_21024), _21132))))], clausify(d1_tops_1)).
% 0.92/1.41 cnf(19, plain, [element(_22325, powerset(_22273)), -(element(subset_complement(_22273, _22325), powerset(_22273)))], clausify(dt_k3_subset_1)).
% 0.92/1.41 cnf(20, plain, [-(open_subset(interior(_26071, _26133), _26071)), topological_space(_26071), top_str(_26071), element(_26133, powerset(the_carrier(_26071)))], clausify(fc6_tops_1)).
% 0.92/1.41 cnf(21, plain, [element(_26643, powerset(_26590)), -(subset_complement(_26590, subset_complement(_26590, _26643)) = _26643)], clausify(involutiveness_k3_subset_1)).
% 0.92/1.41 cnf(22, plain, [top_str(_28717), element(_28820, powerset(the_carrier(_28717))), open_subset(_28820, _28717), -(closed_subset(subset_complement(the_carrier(_28717), _28820), _28717))], clausify(t30_tops_1)).
% 0.92/1.41 cnf(23, plain, [top_str(_29594), element(_29715, powerset(the_carrier(_29594))), closed_subset(_29715, _29594), -(topstr_closure(_29594, _29715) = _29715)], clausify(t52_pre_topc)).
% 0.92/1.41
% 0.92/1.41 cnf('1',plain,[11 ^ [], 12 ^ []],start(10)).
% 0.92/1.41 cnf('1.1',plain,[-(11 ^ []), interior(8 ^ [], 10 ^ []) = 10 ^ []],extension(3)).
% 0.92/1.41 cnf('1.1.1',plain,[-(interior(8 ^ [], 10 ^ []) = 10 ^ []), interior(8 ^ [], 10 ^ []) = subset_complement(the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ []))), subset_complement(the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ []))) = 10 ^ []],extension(16,bind([[_14354, _14410, _14465], [interior(8 ^ [], 10 ^ []), subset_complement(the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ []))), 10 ^ []]]))).
% 0.92/1.41 cnf('1.1.1.1',plain,[-(interior(8 ^ [], 10 ^ []) = subset_complement(the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ [])))), subset_complement(the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ []))) = interior(8 ^ [], 10 ^ [])],extension(15,bind([[_14075, _14120], [subset_complement(the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ []))), interior(8 ^ [], 10 ^ [])]]))).
% 0.92/1.41 cnf('1.1.1.1.1',plain,[-(subset_complement(the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ []))) = interior(8 ^ [], 10 ^ [])), subset_complement(the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ []))) = interior(8 ^ [], 10 ^ []), interior(8 ^ [], 10 ^ []) = interior(8 ^ [], 10 ^ [])],extension(16,bind([[_14354, _14410, _14465], [subset_complement(the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ []))), interior(8 ^ [], 10 ^ []), interior(8 ^ [], 10 ^ [])]]))).
% 0.92/1.41 cnf('1.1.1.1.1.1',plain,[-(subset_complement(the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ []))) = interior(8 ^ [], 10 ^ [])), interior(8 ^ [], 10 ^ []) = subset_complement(the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ [])))],extension(15,bind([[_14075, _14120], [interior(8 ^ [], 10 ^ []), subset_complement(the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ [])))]]))).
% 0.92/1.41 cnf('1.1.1.1.1.1.1',plain,[-(interior(8 ^ [], 10 ^ []) = subset_complement(the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ [])))), top_str(8 ^ []), element(10 ^ [], powerset(the_carrier(8 ^ [])))],extension(18,bind([[_21132, _21024], [10 ^ [], 8 ^ []]]))).
% 0.92/1.41 cnf('1.1.1.1.1.1.1.1',plain,[-(top_str(8 ^ []))],extension(7)).
% 0.92/1.41 cnf('1.1.1.1.1.1.1.2',plain,[-(element(10 ^ [], powerset(the_carrier(8 ^ []))))],extension(9)).
% 0.92/1.41 cnf('1.1.1.1.1.2',plain,[-(interior(8 ^ [], 10 ^ []) = interior(8 ^ [], 10 ^ [])), 8 ^ [] = 8 ^ [], 10 ^ [] = 10 ^ []],extension(11,bind([[_18408, _18475, _18541, _18606], [8 ^ [], 8 ^ [], 10 ^ [], 10 ^ []]]))).
% 0.92/1.41 cnf('1.1.1.1.1.2.1',plain,[-(8 ^ [] = 8 ^ [])],extension(14,bind([[_13922], [8 ^ []]]))).
% 0.92/1.41 cnf('1.1.1.1.1.2.2',plain,[-(10 ^ [] = 10 ^ [])],extension(14,bind([[_13922], [10 ^ []]]))).
% 0.92/1.41 cnf('1.1.1.2',plain,[-(subset_complement(the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ []))) = 10 ^ []), subset_complement(the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ []))) = subset_complement(the_carrier(8 ^ []), subset_complement(the_carrier(8 ^ []), 10 ^ [])), subset_complement(the_carrier(8 ^ []), subset_complement(the_carrier(8 ^ []), 10 ^ [])) = 10 ^ []],extension(16,bind([[_14354, _14410, _14465], [subset_complement(the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ []))), subset_complement(the_carrier(8 ^ []), subset_complement(the_carrier(8 ^ []), 10 ^ [])), 10 ^ []]]))).
% 0.92/1.41 cnf('1.1.1.2.1',plain,[-(subset_complement(the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ []))) = subset_complement(the_carrier(8 ^ []), subset_complement(the_carrier(8 ^ []), 10 ^ []))), the_carrier(8 ^ []) = the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ [])) = subset_complement(the_carrier(8 ^ []), 10 ^ [])],extension(12,bind([[_19361, _19428, _19494, _19559], [the_carrier(8 ^ []), the_carrier(8 ^ []), topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ [])), subset_complement(the_carrier(8 ^ []), 10 ^ [])]]))).
% 0.92/1.41 cnf('1.1.1.2.1.1',plain,[-(the_carrier(8 ^ []) = the_carrier(8 ^ [])), 8 ^ [] = 8 ^ []],extension(13,bind([[_19985, _20034], [8 ^ [], 8 ^ []]]))).
% 0.92/1.41 cnf('1.1.1.2.1.1.1',plain,[-(8 ^ [] = 8 ^ [])],extension(14,bind([[_13922], [8 ^ []]]))).
% 0.92/1.41 cnf('1.1.1.2.1.2',plain,[-(topstr_closure(8 ^ [], subset_complement(the_carrier(8 ^ []), 10 ^ [])) = subset_complement(the_carrier(8 ^ []), 10 ^ [])), top_str(8 ^ []), element(subset_complement(the_carrier(8 ^ []), 10 ^ []), powerset(the_carrier(8 ^ []))), closed_subset(subset_complement(the_carrier(8 ^ []), 10 ^ []), 8 ^ [])],extension(23,bind([[_29715, _29594], [subset_complement(the_carrier(8 ^ []), 10 ^ []), 8 ^ []]]))).
% 0.92/1.41 cnf('1.1.1.2.1.2.1',plain,[-(top_str(8 ^ []))],extension(7)).
% 0.92/1.41 cnf('1.1.1.2.1.2.2',plain,[-(element(subset_complement(the_carrier(8 ^ []), 10 ^ []), powerset(the_carrier(8 ^ [])))), element(10 ^ [], powerset(the_carrier(8 ^ [])))],extension(19,bind([[_22325, _22273], [10 ^ [], the_carrier(8 ^ [])]]))).
% 0.92/1.41 cnf('1.1.1.2.1.2.2.1',plain,[-(element(10 ^ [], powerset(the_carrier(8 ^ []))))],extension(9)).
% 0.92/1.41 cnf('1.1.1.2.1.2.3',plain,[-(closed_subset(subset_complement(the_carrier(8 ^ []), 10 ^ []), 8 ^ [])), top_str(8 ^ []), element(10 ^ [], powerset(the_carrier(8 ^ []))), open_subset(10 ^ [], 8 ^ [])],extension(22,bind([[_28820, _28717], [10 ^ [], 8 ^ []]]))).
% 0.92/1.41 cnf('1.1.1.2.1.2.3.1',plain,[-(top_str(8 ^ []))],extension(7)).
% 0.92/1.41 cnf('1.1.1.2.1.2.3.2',plain,[-(element(10 ^ [], powerset(the_carrier(8 ^ []))))],extension(9)).
% 0.92/1.41 cnf('1.1.1.2.1.2.3.3',plain,[-(open_subset(10 ^ [], 8 ^ [])), -(11 ^ [])],extension(4)).
% 0.92/1.41 cnf('1.1.1.2.1.2.3.3.1',plain,[11 ^ []],reduction('1')).
% 0.92/1.41 cnf('1.1.1.2.2',plain,[-(subset_complement(the_carrier(8 ^ []), subset_complement(the_carrier(8 ^ []), 10 ^ [])) = 10 ^ []), subset_complement(the_carrier(8 ^ []), subset_complement(the_carrier(8 ^ []), 10 ^ [])) = 10 ^ [], 10 ^ [] = 10 ^ []],extension(16,bind([[_14354, _14410, _14465], [subset_complement(the_carrier(8 ^ []), subset_complement(the_carrier(8 ^ []), 10 ^ [])), 10 ^ [], 10 ^ []]]))).
% 0.92/1.41 cnf('1.1.1.2.2.1',plain,[-(subset_complement(the_carrier(8 ^ []), subset_complement(the_carrier(8 ^ []), 10 ^ [])) = 10 ^ []), subset_complement(the_carrier(8 ^ []), subset_complement(the_carrier(8 ^ []), 10 ^ [])) = 10 ^ [], 10 ^ [] = 10 ^ []],extension(16,bind([[_14354, _14410, _14465], [subset_complement(the_carrier(8 ^ []), subset_complement(the_carrier(8 ^ []), 10 ^ [])), 10 ^ [], 10 ^ []]]))).
% 0.92/1.41 cnf('1.1.1.2.2.1.1',plain,[-(subset_complement(the_carrier(8 ^ []), subset_complement(the_carrier(8 ^ []), 10 ^ [])) = 10 ^ []), element(10 ^ [], powerset(the_carrier(8 ^ [])))],extension(21,bind([[_26643, _26590], [10 ^ [], the_carrier(8 ^ [])]]))).
% 0.92/1.41 cnf('1.1.1.2.2.1.1.1',plain,[-(element(10 ^ [], powerset(the_carrier(8 ^ []))))],extension(9)).
% 0.92/1.41 cnf('1.1.1.2.2.1.2',plain,[-(10 ^ [] = 10 ^ [])],extension(14,bind([[_13922], [10 ^ []]]))).
% 0.92/1.41 cnf('1.1.1.2.2.2',plain,[-(10 ^ [] = 10 ^ [])],extension(14,bind([[_13922], [10 ^ []]]))).
% 0.92/1.41 cnf('1.2',plain,[-(12 ^ []), open_subset(9 ^ [], 7 ^ [])],extension(1)).
% 0.92/1.41 cnf('1.2.1',plain,[-(open_subset(9 ^ [], 7 ^ [])), open_subset(9 ^ [], 7 ^ []), 9 ^ [] = 9 ^ [], 7 ^ [] = 7 ^ []],extension(17,bind([[_16407, _16474, _16540, _16605], [9 ^ [], 9 ^ [], 7 ^ [], 7 ^ []]]))).
% 0.92/1.41 cnf('1.2.1.1',plain,[-(open_subset(9 ^ [], 7 ^ [])), open_subset(9 ^ [], 7 ^ []), 9 ^ [] = 9 ^ [], 7 ^ [] = 7 ^ []],extension(17,bind([[_16407, _16474, _16540, _16605], [9 ^ [], 9 ^ [], 7 ^ [], 7 ^ []]]))).
% 0.92/1.41 cnf('1.2.1.1.1',plain,[-(open_subset(9 ^ [], 7 ^ [])), open_subset(9 ^ [], 7 ^ []), 9 ^ [] = 9 ^ [], 7 ^ [] = 7 ^ []],extension(17,bind([[_16407, _16474, _16540, _16605], [9 ^ [], 9 ^ [], 7 ^ [], 7 ^ []]]))).
% 0.92/1.41 cnf('1.2.1.1.1.1',plain,[-(open_subset(9 ^ [], 7 ^ [])), open_subset(interior(7 ^ [], 9 ^ []), 7 ^ []), interior(7 ^ [], 9 ^ []) = 9 ^ [], 7 ^ [] = 7 ^ []],extension(17,bind([[_16407, _16474, _16540, _16605], [interior(7 ^ [], 9 ^ []), 9 ^ [], 7 ^ [], 7 ^ []]]))).
% 0.92/1.41 cnf('1.2.1.1.1.1.1',plain,[-(open_subset(interior(7 ^ [], 9 ^ []), 7 ^ [])), topological_space(7 ^ []), top_str(7 ^ []), element(9 ^ [], powerset(the_carrier(7 ^ [])))],extension(20,bind([[_26133, _26071], [9 ^ [], 7 ^ []]]))).
% 0.92/1.41 cnf('1.2.1.1.1.1.1.1',plain,[-(topological_space(7 ^ []))],extension(5)).
% 0.92/1.41 cnf('1.2.1.1.1.1.1.2',plain,[-(top_str(7 ^ []))],extension(6)).
% 0.92/1.41 cnf('1.2.1.1.1.1.1.3',plain,[-(element(9 ^ [], powerset(the_carrier(7 ^ []))))],extension(8)).
% 0.92/1.41 cnf('1.2.1.1.1.1.2',plain,[-(interior(7 ^ [], 9 ^ []) = 9 ^ []), -(12 ^ [])],extension(2)).
% 0.92/1.41 cnf('1.2.1.1.1.1.2.1',plain,[12 ^ []],reduction('1')).
% 0.92/1.41 cnf('1.2.1.1.1.1.3',plain,[-(7 ^ [] = 7 ^ [])],extension(14,bind([[_13922], [7 ^ []]]))).
% 0.92/1.41 cnf('1.2.1.1.1.2',plain,[-(9 ^ [] = 9 ^ [])],extension(14,bind([[_13922], [9 ^ []]]))).
% 0.92/1.41 cnf('1.2.1.1.1.3',plain,[-(7 ^ [] = 7 ^ [])],extension(14,bind([[_13922], [7 ^ []]]))).
% 0.92/1.41 cnf('1.2.1.1.2',plain,[-(9 ^ [] = 9 ^ [])],extension(14,bind([[_13922], [9 ^ []]]))).
% 0.92/1.41 cnf('1.2.1.1.3',plain,[-(7 ^ [] = 7 ^ [])],extension(14,bind([[_13922], [7 ^ []]]))).
% 0.92/1.41 cnf('1.2.1.2',plain,[-(9 ^ [] = 9 ^ [])],extension(14,bind([[_13922], [9 ^ []]]))).
% 0.92/1.41 cnf('1.2.1.3',plain,[-(7 ^ [] = 7 ^ [])],extension(14,bind([[_13922], [7 ^ []]]))).
% 0.92/1.41 %-----------------------------------------------------
% 0.92/1.42
% 0.92/1.42 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------