TSTP Solution File: SET960+1 by nanoCoP---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SET960+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n025.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 : 300s
% DateTime : Fri May 19 11:56:44 EDT 2023
% Result : Theorem 8.85s 9.64s
% Output : Proof 8.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET960+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.12 % Command : nanocop.sh %s %d
% 0.12/0.33 % Computer : n025.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 : 300
% 0.12/0.33 % DateTime : Thu May 18 19:11:03 EDT 2023
% 0.12/0.33 % CPUTime :
% 8.85/9.64
% 8.85/9.64 /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 8.85/9.64 Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.85/9.64 %-----------------------------------------------------
% 8.85/9.64 ncf(matrix, plain, [(174 ^ _36070) ^ [] : [175 ^ _36070 : [(176 ^ _36070) ^ [] : [-(cartesian_product2(171 ^ [], 172 ^ []) = empty_set)], (178 ^ _36070) ^ [] : [171 ^ [] = empty_set], (180 ^ _36070) ^ [] : [172 ^ [] = empty_set]], 181 ^ _36070 : [(188 ^ _36070) ^ [] : [cartesian_product2(171 ^ [], 172 ^ []) = empty_set], (182 ^ _36070) ^ [] : [-(171 ^ [] = empty_set), -(172 ^ [] = empty_set)]]], (80 ^ _36070) ^ [_38854, _38856] : [in(_38856, _38854), in(_38854, _38856)], (86 ^ _36070) ^ [_39050, _39052] : [-(unordered_pair(_39052, _39050) = unordered_pair(_39050, _39052))], (88 ^ _36070) ^ [_39180] : [_39180 = empty_set, 91 ^ _36070 : [(92 ^ _36070) ^ [_39293] : [in(_39293, _39180)]]], (94 ^ _36070) ^ [_39359] : [-(in(95 ^ [_39359], _39359)), -(_39359 = empty_set)], (160 ^ _36070) ^ [_42154, _42156] : [-(ordered_pair(_42156, _42154) = unordered_pair(unordered_pair(_42156, _42154), singleton(_42156)))], (162 ^ _36070) ^ [] : [-(empty(empty_set))], (164 ^ _36070) ^ [_42311, _42313] : [empty(ordered_pair(_42313, _42311))], (167 ^ _36070) ^ [] : [-(empty(165 ^ []))], (170 ^ _36070) ^ [] : [empty(168 ^ [])], (131 ^ _36070) ^ [_40921, _40923, _40925] : [-(_40921 = cartesian_product2(_40925, _40923)), 149 ^ _36070 : [(150 ^ _36070) ^ [] : [-(in(147 ^ [_40921, _40923, _40925], _40925))], (152 ^ _36070) ^ [] : [-(in(148 ^ [_40921, _40923, _40925], _40923))], (154 ^ _36070) ^ [] : [-(132 ^ [_40921, _40923, _40925] = ordered_pair(147 ^ [_40921, _40923, _40925], 148 ^ [_40921, _40923, _40925]))], (156 ^ _36070) ^ [] : [in(132 ^ [_40921, _40923, _40925], _40921)]], 135 ^ _36070 : [(136 ^ _36070) ^ [] : [-(in(132 ^ [_40921, _40923, _40925], _40921))], (138 ^ _36070) ^ [_41259, _41261] : [in(_41261, _40925), in(_41259, _40923), 132 ^ [_40921, _40923, _40925] = ordered_pair(_41261, _41259)]]], (101 ^ _36070) ^ [_39664, _39666, _39668] : [_39664 = cartesian_product2(_39668, _39666), 104 ^ _36070 : [(105 ^ _36070) ^ [_39865] : [in(_39865, _39664), 110 ^ _36070 : [(111 ^ _36070) ^ [] : [-(in(108 ^ [_39664, _39666, _39668, _39865], _39668))], (113 ^ _36070) ^ [] : [-(in(109 ^ [_39664, _39666, _39668, _39865], _39666))], (115 ^ _36070) ^ [] : [-(_39865 = ordered_pair(108 ^ [_39664, _39666, _39668, _39865], 109 ^ [_39664, _39666, _39668, _39865]))]]], (117 ^ _36070) ^ [_40425] : [-(in(_40425, _39664)), 118 ^ _36070 : [(119 ^ _36070) ^ [_40555, _40557] : [in(_40557, _39668), in(_40555, _39666), _40425 = ordered_pair(_40557, _40555)]]]]], (44 ^ _36070) ^ [_37593, _37595, _37597, _37599] : [-(unordered_pair(_37599, _37595) = unordered_pair(_37597, _37593)), _37599 = _37597, _37595 = _37593], (54 ^ _36070) ^ [_37924, _37926] : [_37926 = _37924, -(singleton(_37926) = singleton(_37924))], (60 ^ _36070) ^ [_38170, _38172, _38174, _38176] : [-(ordered_pair(_38176, _38172) = ordered_pair(_38174, _38170)), _38176 = _38174, _38172 = _38170], (70 ^ _36070) ^ [_38509, _38511, _38513, _38515] : [-(cartesian_product2(_38515, _38511) = cartesian_product2(_38513, _38509)), _38515 = _38513, _38511 = _38509], (2 ^ _36070) ^ [_36214] : [-(_36214 = _36214)], (4 ^ _36070) ^ [_36321, _36323] : [_36323 = _36321, -(_36321 = _36323)], (10 ^ _36070) ^ [_36525, _36527, _36529] : [-(_36529 = _36525), _36529 = _36527, _36527 = _36525], (34 ^ _36070) ^ [_37262, _37264] : [-(empty(_37262)), _37264 = _37262, empty(_37264)], (20 ^ _36070) ^ [_36866, _36868, _36870, _36872] : [-(in(_36870, _36866)), in(_36872, _36868), _36872 = _36870, _36868 = _36866]], input).
% 8.85/9.64 ncf('1',plain,[cartesian_product2(171 ^ [], 172 ^ []) = empty_set, 92 : in(95 ^ [cartesian_product2(171 ^ [], 172 ^ [])], cartesian_product2(171 ^ [], 172 ^ []))],start(88 ^ 0,bind([[_39180, _39293], [cartesian_product2(171 ^ [], 172 ^ []), 95 ^ [cartesian_product2(171 ^ [], 172 ^ [])]]]))).
% 8.85/9.64 ncf('1.1',plain,[-(cartesian_product2(171 ^ [], 172 ^ []) = empty_set), 182 : -(171 ^ [] = empty_set), 182 : -(172 ^ [] = empty_set)],extension(174 ^ 1)).
% 8.85/9.64 ncf('1.1.1',plain,[171 ^ [] = empty_set, 92 : in(147 ^ [cartesian_product2(171 ^ [], 172 ^ []), _19700, 171 ^ []], 171 ^ [])],extension(88 ^ 4,bind([[_39180, _39293], [171 ^ [], 147 ^ [cartesian_product2(171 ^ [], 172 ^ []), _19700, 171 ^ []]]]))).
% 8.85/9.64 ncf('1.1.1.1',plain,[-(in(147 ^ [cartesian_product2(171 ^ [], 172 ^ []), _19700, 171 ^ []], 171 ^ [])), -(cartesian_product2(171 ^ [], 172 ^ []) = cartesian_product2(171 ^ [], _19700)), 136 : -(in(132 ^ [cartesian_product2(171 ^ [], 172 ^ []), _19700, 171 ^ []], cartesian_product2(171 ^ [], 172 ^ [])))],extension(131 ^ 7,bind([[_40921, _40923, _40925], [cartesian_product2(171 ^ [], 172 ^ []), _19700, 171 ^ []]]))).
% 8.85/9.64 ncf('1.1.1.1.1',plain,[cartesian_product2(171 ^ [], 172 ^ []) = cartesian_product2(171 ^ [], _19700), 105 : in(95 ^ [cartesian_product2(171 ^ [], 172 ^ [])], cartesian_product2(171 ^ [], 172 ^ [])), 111 : -(in(108 ^ [cartesian_product2(171 ^ [], 172 ^ []), _19700, 171 ^ [], 95 ^ [cartesian_product2(171 ^ [], 172 ^ [])]], 171 ^ []))],extension(101 ^ 8,bind([[_39664, _39666, _39668, _39865], [cartesian_product2(171 ^ [], 172 ^ []), _19700, 171 ^ [], 95 ^ [cartesian_product2(171 ^ [], 172 ^ [])]]]))).
% 8.85/9.64 ncf('1.1.1.1.1.1',plain,[-(in(95 ^ [cartesian_product2(171 ^ [], 172 ^ [])], cartesian_product2(171 ^ [], 172 ^ []))), -(cartesian_product2(171 ^ [], 172 ^ []) = empty_set)],extension(94 ^ 11,bind([[_39359], [cartesian_product2(171 ^ [], 172 ^ [])]]))).
% 8.85/9.64 ncf('1.1.1.1.1.1.1',plain,[cartesian_product2(171 ^ [], 172 ^ []) = empty_set],reduction('1')).
% 8.85/9.64 ncf('1.1.1.1.1.2',plain,[in(108 ^ [cartesian_product2(171 ^ [], 172 ^ []), _19700, 171 ^ [], 95 ^ [cartesian_product2(171 ^ [], 172 ^ [])]], 171 ^ [])],extension(92 ^ 13,bind([[_39293], [108 ^ [cartesian_product2(171 ^ [], 172 ^ []), _19700, 171 ^ [], 95 ^ [cartesian_product2(171 ^ [], 172 ^ [])]]]]))).
% 8.85/9.64 ncf('1.1.1.1.2',plain,[in(132 ^ [cartesian_product2(171 ^ [], 172 ^ []), _19700, 171 ^ []], cartesian_product2(171 ^ [], 172 ^ [])), 111 : -(in(108 ^ [cartesian_product2(171 ^ [], 172 ^ []), 172 ^ [], 171 ^ [], 132 ^ [cartesian_product2(171 ^ [], 172 ^ []), _19700, 171 ^ []]], 171 ^ [])), 105 : cartesian_product2(171 ^ [], 172 ^ []) = cartesian_product2(171 ^ [], 172 ^ [])],extension(101 ^ 10,bind([[_39664, _39666, _39668, _39865], [cartesian_product2(171 ^ [], 172 ^ []), 172 ^ [], 171 ^ [], 132 ^ [cartesian_product2(171 ^ [], 172 ^ []), _19700, 171 ^ []]]]))).
% 8.85/9.64 ncf('1.1.1.1.2.1',plain,[in(108 ^ [cartesian_product2(171 ^ [], 172 ^ []), 172 ^ [], 171 ^ [], 132 ^ [cartesian_product2(171 ^ [], 172 ^ []), _19700, 171 ^ []]], 171 ^ [])],extension(92 ^ 15,bind([[_39293], [108 ^ [cartesian_product2(171 ^ [], 172 ^ []), 172 ^ [], 171 ^ [], 132 ^ [cartesian_product2(171 ^ [], 172 ^ []), _19700, 171 ^ []]]]]))).
% 8.85/9.64 ncf('1.1.1.1.2.2',plain,[-(cartesian_product2(171 ^ [], 172 ^ []) = cartesian_product2(171 ^ [], 172 ^ [])), 171 ^ [] = 171 ^ [], 172 ^ [] = 172 ^ []],extension(70 ^ 11,bind([[_38509, _38511, _38513, _38515], [172 ^ [], 172 ^ [], 171 ^ [], 171 ^ []]]))).
% 8.85/9.64 ncf('1.1.1.1.2.2.1',plain,[-(171 ^ [] = 171 ^ [])],extension(2 ^ 12,bind([[_36214], [171 ^ []]]))).
% 8.85/9.64 ncf('1.1.1.1.2.2.2',plain,[-(172 ^ [] = 172 ^ [])],extension(2 ^ 12,bind([[_36214], [172 ^ []]]))).
% 8.85/9.64 ncf('1.1.2',plain,[172 ^ [] = empty_set, 92 : in(147 ^ [cartesian_product2(171 ^ [], 172 ^ []), _22428, 172 ^ []], 172 ^ [])],extension(88 ^ 4,bind([[_39180, _39293], [172 ^ [], 147 ^ [cartesian_product2(171 ^ [], 172 ^ []), _22428, 172 ^ []]]]))).
% 8.85/9.64 ncf('1.1.2.1',plain,[-(in(147 ^ [cartesian_product2(171 ^ [], 172 ^ []), _22428, 172 ^ []], 172 ^ [])), -(cartesian_product2(171 ^ [], 172 ^ []) = cartesian_product2(172 ^ [], _22428)), 136 : -(in(132 ^ [cartesian_product2(171 ^ [], 172 ^ []), _22428, 172 ^ []], cartesian_product2(171 ^ [], 172 ^ [])))],extension(131 ^ 7,bind([[_40921, _40923, _40925], [cartesian_product2(171 ^ [], 172 ^ []), _22428, 172 ^ []]]))).
% 8.85/9.64 ncf('1.1.2.1.1',plain,[cartesian_product2(171 ^ [], 172 ^ []) = cartesian_product2(172 ^ [], _22428), 105 : in(95 ^ [cartesian_product2(171 ^ [], 172 ^ [])], cartesian_product2(171 ^ [], 172 ^ [])), 111 : -(in(108 ^ [cartesian_product2(171 ^ [], 172 ^ []), _22428, 172 ^ [], 95 ^ [cartesian_product2(171 ^ [], 172 ^ [])]], 172 ^ []))],extension(101 ^ 8,bind([[_39664, _39666, _39668, _39865], [cartesian_product2(171 ^ [], 172 ^ []), _22428, 172 ^ [], 95 ^ [cartesian_product2(171 ^ [], 172 ^ [])]]]))).
% 8.85/9.64 ncf('1.1.2.1.1.1',plain,[-(in(95 ^ [cartesian_product2(171 ^ [], 172 ^ [])], cartesian_product2(171 ^ [], 172 ^ []))), -(cartesian_product2(171 ^ [], 172 ^ []) = empty_set)],extension(94 ^ 11,bind([[_39359], [cartesian_product2(171 ^ [], 172 ^ [])]]))).
% 8.85/9.64 ncf('1.1.2.1.1.1.1',plain,[cartesian_product2(171 ^ [], 172 ^ []) = empty_set],reduction('1')).
% 8.85/9.64 ncf('1.1.2.1.1.2',plain,[in(108 ^ [cartesian_product2(171 ^ [], 172 ^ []), _22428, 172 ^ [], 95 ^ [cartesian_product2(171 ^ [], 172 ^ [])]], 172 ^ [])],extension(92 ^ 13,bind([[_39293], [108 ^ [cartesian_product2(171 ^ [], 172 ^ []), _22428, 172 ^ [], 95 ^ [cartesian_product2(171 ^ [], 172 ^ [])]]]]))).
% 8.85/9.64 ncf('1.1.2.1.2',plain,[in(132 ^ [cartesian_product2(171 ^ [], 172 ^ []), _22428, 172 ^ []], cartesian_product2(171 ^ [], 172 ^ [])), 113 : -(in(109 ^ [cartesian_product2(171 ^ [], 172 ^ []), 172 ^ [], 171 ^ [], 132 ^ [cartesian_product2(171 ^ [], 172 ^ []), _22428, 172 ^ []]], 172 ^ [])), 105 : cartesian_product2(171 ^ [], 172 ^ []) = cartesian_product2(171 ^ [], 172 ^ [])],extension(101 ^ 10,bind([[_39664, _39666, _39668, _39865], [cartesian_product2(171 ^ [], 172 ^ []), 172 ^ [], 171 ^ [], 132 ^ [cartesian_product2(171 ^ [], 172 ^ []), _22428, 172 ^ []]]]))).
% 8.85/9.64 ncf('1.1.2.1.2.1',plain,[in(109 ^ [cartesian_product2(171 ^ [], 172 ^ []), 172 ^ [], 171 ^ [], 132 ^ [cartesian_product2(171 ^ [], 172 ^ []), _22428, 172 ^ []]], 172 ^ [])],extension(92 ^ 15,bind([[_39293], [109 ^ [cartesian_product2(171 ^ [], 172 ^ []), 172 ^ [], 171 ^ [], 132 ^ [cartesian_product2(171 ^ [], 172 ^ []), _22428, 172 ^ []]]]]))).
% 8.85/9.64 ncf('1.1.2.1.2.2',plain,[-(cartesian_product2(171 ^ [], 172 ^ []) = cartesian_product2(171 ^ [], 172 ^ [])), 171 ^ [] = 171 ^ [], 172 ^ [] = 172 ^ []],extension(70 ^ 11,bind([[_38509, _38511, _38513, _38515], [172 ^ [], 172 ^ [], 171 ^ [], 171 ^ []]]))).
% 8.85/9.64 ncf('1.1.2.1.2.2.1',plain,[-(171 ^ [] = 171 ^ [])],extension(2 ^ 12,bind([[_36214], [171 ^ []]]))).
% 8.85/9.64 ncf('1.1.2.1.2.2.2',plain,[-(172 ^ [] = 172 ^ [])],extension(2 ^ 12,bind([[_36214], [172 ^ []]]))).
% 8.85/9.64 ncf('1.2',plain,[-(in(95 ^ [cartesian_product2(171 ^ [], 172 ^ [])], cartesian_product2(171 ^ [], 172 ^ []))), -(cartesian_product2(171 ^ [], 172 ^ []) = empty_set)],extension(94 ^ 3,bind([[_39359], [cartesian_product2(171 ^ [], 172 ^ [])]]))).
% 8.85/9.64 ncf('1.2.1',plain,[cartesian_product2(171 ^ [], 172 ^ []) = empty_set, -(empty_set = cartesian_product2(171 ^ [], 172 ^ []))],extension(4 ^ 4,bind([[_36321, _36323], [empty_set, cartesian_product2(171 ^ [], 172 ^ [])]]))).
% 8.85/9.64 ncf('1.2.1.1',plain,[empty_set = cartesian_product2(171 ^ [], 172 ^ []), 105 : in(ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []]), empty_set), 111 : -(in(108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])], 171 ^ []))],extension(101 ^ 5,bind([[_39664, _39666, _39668, _39865], [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])]]))).
% 8.85/9.64 ncf('1.2.1.1.1',plain,[-(in(ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []]), empty_set)), 119 : in(95 ^ [171 ^ []], 171 ^ []), 119 : in(95 ^ [172 ^ []], 172 ^ []), 119 : ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []]) = ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])],extension(117 ^ 8,bind([[_40425, _40555, _40557], [ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []]), 95 ^ [172 ^ []], 95 ^ [171 ^ []]]]))).
% 8.85/9.64 ncf('1.2.1.1.1.1',plain,[-(in(95 ^ [171 ^ []], 171 ^ [])), -(171 ^ [] = empty_set)],extension(94 ^ 11,bind([[_39359], [171 ^ []]]))).
% 8.85/9.64 ncf('1.2.1.1.1.1.1',plain,[171 ^ [] = empty_set, 188 : cartesian_product2(171 ^ [], 172 ^ []) = empty_set],extension(174 ^ 12)).
% 8.85/9.64 ncf('1.2.1.1.1.1.1.1',plain,[-(cartesian_product2(171 ^ [], 172 ^ []) = empty_set)],lemmata('x')).
% 8.85/9.64 ncf('1.2.1.1.1.2',plain,[-(in(95 ^ [172 ^ []], 172 ^ [])), -(172 ^ [] = empty_set)],extension(94 ^ 11,bind([[_39359], [172 ^ []]]))).
% 8.85/9.64 ncf('1.2.1.1.1.2.1',plain,[172 ^ [] = empty_set, 188 : cartesian_product2(171 ^ [], 172 ^ []) = empty_set],extension(174 ^ 12)).
% 8.85/9.64 ncf('1.2.1.1.1.2.1.1',plain,[-(cartesian_product2(171 ^ [], 172 ^ []) = empty_set)],lemmata('x')).
% 8.85/9.64 ncf('1.2.1.1.1.3',plain,[-(ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []]) = ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])), 95 ^ [171 ^ []] = 95 ^ [171 ^ []], 95 ^ [172 ^ []] = 95 ^ [172 ^ []]],extension(60 ^ 11,bind([[_38170, _38172, _38174, _38176], [95 ^ [172 ^ []], 95 ^ [172 ^ []], 95 ^ [171 ^ []], 95 ^ [171 ^ []]]]))).
% 8.85/9.64 ncf('1.2.1.1.1.3.1',plain,[-(95 ^ [171 ^ []] = 95 ^ [171 ^ []])],extension(2 ^ 12,bind([[_36214], [95 ^ [171 ^ []]]]))).
% 8.85/9.64 ncf('1.2.1.1.1.3.2',plain,[-(95 ^ [172 ^ []] = 95 ^ [172 ^ []])],extension(2 ^ 12,bind([[_36214], [95 ^ [172 ^ []]]]))).
% 8.85/9.64 ncf('1.2.1.1.2',plain,[in(108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])], 171 ^ []), 119 : in(95 ^ [172 ^ []], 172 ^ []), 119 : ordered_pair(108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])], 95 ^ [172 ^ []]) = ordered_pair(108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])], 95 ^ [172 ^ []]), 119 : -(in(ordered_pair(108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])], 95 ^ [172 ^ []]), empty_set))],extension(117 ^ 10,bind([[_40425, _40555, _40557], [ordered_pair(108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])], 95 ^ [172 ^ []]), 95 ^ [172 ^ []], 108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])]]]))).
% 8.85/9.64 ncf('1.2.1.1.2.1',plain,[-(in(95 ^ [172 ^ []], 172 ^ [])), -(172 ^ [] = empty_set)],extension(94 ^ 13,bind([[_39359], [172 ^ []]]))).
% 8.85/9.64 ncf('1.2.1.1.2.1.1',plain,[172 ^ [] = empty_set, 188 : cartesian_product2(171 ^ [], 172 ^ []) = empty_set],extension(174 ^ 14)).
% 8.85/9.64 ncf('1.2.1.1.2.1.1.1',plain,[-(cartesian_product2(171 ^ [], 172 ^ []) = empty_set)],lemmata('x')).
% 8.85/9.64 ncf('1.2.1.1.2.2',plain,[-(ordered_pair(108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])], 95 ^ [172 ^ []]) = ordered_pair(108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])], 95 ^ [172 ^ []])), 108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])] = 108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])], 95 ^ [172 ^ []] = 95 ^ [172 ^ []]],extension(60 ^ 13,bind([[_38170, _38172, _38174, _38176], [95 ^ [172 ^ []], 95 ^ [172 ^ []], 108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])], 108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])]]]))).
% 8.85/9.64 ncf('1.2.1.1.2.2.1',plain,[-(108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])] = 108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])])],extension(2 ^ 14,bind([[_36214], [108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])]]]))).
% 8.85/9.64 ncf('1.2.1.1.2.2.2',plain,[-(95 ^ [172 ^ []] = 95 ^ [172 ^ []])],extension(2 ^ 14,bind([[_36214], [95 ^ [172 ^ []]]]))).
% 8.85/9.64 ncf('1.2.1.1.2.3',plain,[in(ordered_pair(108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])], 95 ^ [172 ^ []]), empty_set), empty_set = empty_set],extension(88 ^ 11,bind([[_39180, _39293], [empty_set, ordered_pair(108 ^ [empty_set, 172 ^ [], 171 ^ [], ordered_pair(95 ^ [171 ^ []], 95 ^ [172 ^ []])], 95 ^ [172 ^ []])]]))).
% 8.85/9.64 ncf('1.2.1.1.2.3.1',plain,[-(empty_set = empty_set)],extension(2 ^ 12,bind([[_36214], [empty_set]]))).
% 8.85/9.64 %-----------------------------------------------------
% 8.85/9.64 End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------