TSTP Solution File: SET894+1 by nanoCoP---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SET894+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.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 : 300s
% DateTime : Fri May 19 11:56:37 EDT 2023
% Result : Theorem 231.96s 224.05s
% Output : Proof 231.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET894+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.07/0.13 % Command : nanocop.sh %s %d
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu May 18 19:06:27 EDT 2023
% 0.14/0.35 % CPUTime :
% 231.96/224.05
% 231.96/224.05 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 231.96/224.05 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 231.96/224.05 %-----------------------------------------------------
% 231.96/224.05 ncf(matrix, plain, [(223 ^ _55864) ^ [] : [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])) = singleton(ordered_pair(220 ^ [], 221 ^ []))], !, (204 ^ _47549) ^ [] : [empty(202 ^ [])], (182 ^ _47549) ^ [_54515, _54517, _54519, _54521] : [in(ordered_pair(_54521, _54519), cartesian_product2(_54517, _54515)), 185 ^ _47549 : [(188 ^ _47549) ^ [] : [-(in(_54519, _54515))], (186 ^ _47549) ^ [] : [-(in(_54521, _54517))]]], (206 ^ _47549) ^ [_55272, _55274] : [-(_55274 = _55272), 210 ^ _47549 : [(213 ^ _47549) ^ [] : [in(207 ^ [_55272, _55274], _55272)], (211 ^ _47549) ^ [] : [-(in(207 ^ [_55272, _55274], _55274))]], 214 ^ _47549 : [(217 ^ _47549) ^ [] : [in(207 ^ [_55272, _55274], _55274)], (215 ^ _47549) ^ [] : [-(in(207 ^ [_55272, _55274], _55272))]]], (10 ^ _47549) ^ [_47984, _47986, _47988] : [-(_47988 = _47984), _47988 = _47986, _47986 = _47984], (119 ^ _47549) ^ [_51753, _51755, _51757] : [_51753 = cartesian_product2(_51757, _51755), 122 ^ _47549 : [(135 ^ _47549) ^ [_52514] : [-(in(_52514, _51753)), 136 ^ _47549 : [(137 ^ _47549) ^ [_52644, _52646] : [in(_52646, _51757), in(_52644, _51755), _52514 = ordered_pair(_52646, _52644)]]], (123 ^ _47549) ^ [_51954] : [in(_51954, _51753), 128 ^ _47549 : [(131 ^ _47549) ^ [] : [-(in(127 ^ [_51753, _51755, _51757, _51954], _51755))], (133 ^ _47549) ^ [] : [-(_51954 = ordered_pair(126 ^ [_51753, _51755, _51757, _51954], 127 ^ [_51753, _51755, _51757, _51954]))], (129 ^ _47549) ^ [] : [-(in(126 ^ [_51753, _51755, _51757, _51954], _51757))]]]]], (70 ^ _47549) ^ [_49968, _49970, _49972, _49974] : [-(ordered_pair(_49974, _49970) = ordered_pair(_49972, _49968)), _49974 = _49972, _49970 = _49968], (178 ^ _47549) ^ [_54243, _54245] : [-(ordered_pair(_54245, _54243) = unordered_pair(unordered_pair(_54245, _54243), singleton(_54245)))], (86 ^ _47549) ^ [_50509, _50511] : [-(unordered_pair(_50511, _50509) = unordered_pair(_50509, _50511))], (88 ^ _47549) ^ [_50653, _50655] : [_50653 = singleton(_50655), 91 ^ _47549 : [(98 ^ _47549) ^ [_50995] : [_50995 = _50655, -(in(_50995, _50653))], (92 ^ _47549) ^ [_50823] : [in(_50823, _50653), -(_50823 = _50655)]]], (180 ^ _47549) ^ [_54347, _54349] : [empty(ordered_pair(_54349, _54347))], (30 ^ _47549) ^ [_48600, _48602, _48604, _48606] : [-(in(_48604, _48600)), in(_48606, _48602), _48606 = _48604, _48602 = _48600], (201 ^ _47549) ^ [] : [-(empty(199 ^ []))], (2 ^ _47549) ^ [_47673] : [-(_47673 = _47673)], (104 ^ _47549) ^ [_51174, _51176] : [-(_51174 = singleton(_51176)), 108 ^ _47549 : [(111 ^ _47549) ^ [] : [105 ^ [_51174, _51176] = _51176], (109 ^ _47549) ^ [] : [-(in(105 ^ [_51174, _51176], _51174))]], 112 ^ _47549 : [(115 ^ _47549) ^ [] : [in(105 ^ [_51174, _51176], _51174)], (113 ^ _47549) ^ [] : [-(105 ^ [_51174, _51176] = _51176)]]], (149 ^ _47549) ^ [_53010, _53012, _53014] : [-(_53010 = cartesian_product2(_53014, _53012)), 167 ^ _47549 : [(168 ^ _47549) ^ [] : [-(in(165 ^ [_53010, _53012, _53014], _53014))], (170 ^ _47549) ^ [] : [-(in(166 ^ [_53010, _53012, _53014], _53012))], (174 ^ _47549) ^ [] : [in(150 ^ [_53010, _53012, _53014], _53010)], (172 ^ _47549) ^ [] : [-(150 ^ [_53010, _53012, _53014] = ordered_pair(165 ^ [_53010, _53012, _53014], 166 ^ [_53010, _53012, _53014]))]], 153 ^ _47549 : [(156 ^ _47549) ^ [_53348, _53350] : [in(_53350, _53014), in(_53348, _53012), 150 ^ [_53010, _53012, _53014] = ordered_pair(_53350, _53348)], (154 ^ _47549) ^ [] : [-(in(150 ^ [_53010, _53012, _53014], _53010))]]], (20 ^ _47549) ^ [_48297, _48299] : [-(empty(_48297)), _48299 = _48297, empty(_48299)], (44 ^ _47549) ^ [_49052, _49054, _49056, _49058] : [-(unordered_pair(_49058, _49054) = unordered_pair(_49056, _49052)), _49058 = _49056, _49054 = _49052], (54 ^ _47549) ^ [_49411, _49413, _49415, _49417] : [-(cartesian_product2(_49417, _49413) = cartesian_product2(_49415, _49411)), _49417 = _49415, _49413 = _49411], (64 ^ _47549) ^ [_49742, _49744] : [_49744 = _49742, -(singleton(_49744) = singleton(_49742))], (4 ^ _47549) ^ [_47780, _47782] : [_47782 = _47780, -(_47780 = _47782)], (80 ^ _47549) ^ [_50313, _50315] : [in(_50315, _50313), in(_50313, _50315)], (190 ^ _47549) ^ [_54780, _54782, _54784, _54786] : [-(in(ordered_pair(_54786, _54784), cartesian_product2(_54782, _54780))), in(_54786, _54782), in(_54784, _54780)]], input).
% 231.96/224.05 ncf('1',plain,[cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])) = singleton(ordered_pair(220 ^ [], 221 ^ []))],start(223 ^ 0)).
% 231.96/224.05 ncf('1.1',plain,[-(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])) = singleton(ordered_pair(220 ^ [], 221 ^ []))), 109 : -(in(105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])], cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])))), 115 : in(105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])], cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])))],extension(104 ^ 1,bind([[_51174, _51176], [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]]))).
% 231.96/224.05 ncf('1.1.1',plain,[in(105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])], cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))), 131 : -(in(127 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]], singleton(221 ^ []))), 123 : cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])) = cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))],extension(119 ^ 4,bind([[_51753, _51755, _51757, _51954], [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]]]))).
% 231.96/224.05 ncf('1.1.1.1',plain,[in(127 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]], singleton(221 ^ [])), 92 : -(127 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]] = 221 ^ []), 92 : singleton(221 ^ []) = singleton(221 ^ [])],extension(88 ^ 9,bind([[_50653, _50655, _50823], [singleton(221 ^ []), 221 ^ [], 127 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]]]]))).
% 231.96/224.05 ncf('1.1.1.1.1',plain,[127 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]] = 221 ^ [], -(ordered_pair(126 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]], 127 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]]) = ordered_pair(220 ^ [], 221 ^ [])), 126 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]] = 220 ^ []],extension(70 ^ 12,bind([[_49968, _49970, _49972, _49974], [221 ^ [], 127 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]], 220 ^ [], 126 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]]]]))).
% 231.96/224.05 ncf('1.1.1.1.1.1',plain,[ordered_pair(126 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]], 127 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]]) = ordered_pair(220 ^ [], 221 ^ []), -(105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])] = ordered_pair(220 ^ [], 221 ^ [])), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])] = ordered_pair(126 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]], 127 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]])],extension(10 ^ 13,bind([[_47984, _47986, _47988], [ordered_pair(220 ^ [], 221 ^ []), ordered_pair(126 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]], 127 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]]), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]]]))).
% 231.96/224.05 ncf('1.1.1.1.1.1.1',plain,[105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])] = ordered_pair(220 ^ [], 221 ^ [])],extension(111 ^ 14)).
% 231.96/224.05 ncf('1.1.1.1.1.1.2',plain,[-(105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])] = ordered_pair(126 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]], 127 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]]))],extension(133 ^ 14)).
% 231.96/224.05 ncf('1.1.1.1.1.2',plain,[-(126 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]] = 220 ^ []), 92 : in(126 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]], singleton(220 ^ [])), 92 : singleton(220 ^ []) = singleton(220 ^ [])],extension(88 ^ 13,bind([[_50653, _50655, _50823], [singleton(220 ^ []), 220 ^ [], 126 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]]]]))).
% 231.96/224.05 ncf('1.1.1.1.1.2.1',plain,[-(in(126 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])]], singleton(220 ^ [])))],extension(129 ^ 16)).
% 231.96/224.05 ncf('1.1.1.1.1.2.2',plain,[-(singleton(220 ^ []) = singleton(220 ^ []))],extension(2 ^ 14,bind([[_47673], [singleton(220 ^ [])]]))).
% 231.96/224.05 ncf('1.1.1.1.2',plain,[-(singleton(221 ^ []) = singleton(221 ^ [])), 213 : in(207 ^ [singleton(221 ^ []), singleton(221 ^ [])], singleton(221 ^ [])), 217 : in(207 ^ [singleton(221 ^ []), singleton(221 ^ [])], singleton(221 ^ []))],extension(206 ^ 10,bind([[_55272, _55274], [singleton(221 ^ []), singleton(221 ^ [])]]))).
% 231.96/224.05 ncf('1.1.1.1.2.1',plain,[-(in(207 ^ [singleton(221 ^ []), singleton(221 ^ [])], singleton(221 ^ [])))],extension(211 ^ 13)).
% 231.96/224.05 ncf('1.1.1.1.2.2',plain,[-(in(207 ^ [singleton(221 ^ []), singleton(221 ^ [])], singleton(221 ^ [])))],extension(215 ^ 13)).
% 231.96/224.05 ncf('1.1.1.2',plain,[-(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])) = cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))), 213 : in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))), 217 : in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])))],extension(206 ^ 5,bind([[_55272, _55274], [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]]))).
% 231.96/224.05 ncf('1.1.1.2.1',plain,[-(in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))))],extension(211 ^ 8)).
% 231.96/224.05 ncf('1.1.1.2.2',plain,[-(in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))))],extension(215 ^ 8)).
% 231.96/224.05 ncf('1.1.2',plain,[-(in(105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])], cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])))), 137 : in(220 ^ [], singleton(220 ^ [])), 137 : in(221 ^ [], singleton(221 ^ [])), 137 : 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])] = ordered_pair(220 ^ [], 221 ^ []), 135 : cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])) = cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))],extension(119 ^ 4,bind([[_51753, _51755, _51757, _52514, _52644, _52646], [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), singleton(221 ^ []), singleton(220 ^ []), 105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])], 221 ^ [], 220 ^ []]]))).
% 231.96/224.05 ncf('1.1.2.1',plain,[-(in(220 ^ [], singleton(220 ^ []))), 98 : 220 ^ [] = 220 ^ [], 98 : singleton(220 ^ []) = singleton(220 ^ [])],extension(88 ^ 9,bind([[_50653, _50655, _50995], [singleton(220 ^ []), 220 ^ [], 220 ^ []]]))).
% 231.96/224.05 ncf('1.1.2.1.1',plain,[-(220 ^ [] = 220 ^ []), 213 : in(207 ^ [220 ^ [], 220 ^ []], 220 ^ []), 217 : in(207 ^ [220 ^ [], 220 ^ []], 220 ^ [])],extension(206 ^ 12,bind([[_55272, _55274], [220 ^ [], 220 ^ []]]))).
% 231.96/224.05 ncf('1.1.2.1.1.1',plain,[-(in(207 ^ [220 ^ [], 220 ^ []], 220 ^ []))],extension(211 ^ 15)).
% 231.96/224.05 ncf('1.1.2.1.1.2',plain,[-(in(207 ^ [220 ^ [], 220 ^ []], 220 ^ []))],extension(215 ^ 15)).
% 231.96/224.05 ncf('1.1.2.1.2',plain,[-(singleton(220 ^ []) = singleton(220 ^ [])), 213 : in(207 ^ [singleton(220 ^ []), singleton(220 ^ [])], singleton(220 ^ [])), 217 : in(207 ^ [singleton(220 ^ []), singleton(220 ^ [])], singleton(220 ^ []))],extension(206 ^ 10,bind([[_55272, _55274], [singleton(220 ^ []), singleton(220 ^ [])]]))).
% 231.96/224.05 ncf('1.1.2.1.2.1',plain,[-(in(207 ^ [singleton(220 ^ []), singleton(220 ^ [])], singleton(220 ^ [])))],extension(211 ^ 13)).
% 231.96/224.05 ncf('1.1.2.1.2.2',plain,[-(in(207 ^ [singleton(220 ^ []), singleton(220 ^ [])], singleton(220 ^ [])))],extension(215 ^ 13)).
% 231.96/224.05 ncf('1.1.2.2',plain,[-(in(221 ^ [], singleton(221 ^ []))), 98 : 221 ^ [] = 221 ^ [], 98 : singleton(221 ^ []) = singleton(221 ^ [])],extension(88 ^ 9,bind([[_50653, _50655, _50995], [singleton(221 ^ []), 221 ^ [], 221 ^ []]]))).
% 231.96/224.05 ncf('1.1.2.2.1',plain,[-(221 ^ [] = 221 ^ []), 213 : in(207 ^ [221 ^ [], 221 ^ []], 221 ^ []), 217 : in(207 ^ [221 ^ [], 221 ^ []], 221 ^ [])],extension(206 ^ 12,bind([[_55272, _55274], [221 ^ [], 221 ^ []]]))).
% 231.96/224.05 ncf('1.1.2.2.1.1',plain,[-(in(207 ^ [221 ^ [], 221 ^ []], 221 ^ []))],extension(211 ^ 15)).
% 231.96/224.05 ncf('1.1.2.2.1.2',plain,[-(in(207 ^ [221 ^ [], 221 ^ []], 221 ^ []))],extension(215 ^ 15)).
% 231.96/224.05 ncf('1.1.2.2.2',plain,[-(singleton(221 ^ []) = singleton(221 ^ [])), 213 : in(207 ^ [singleton(221 ^ []), singleton(221 ^ [])], singleton(221 ^ [])), 217 : in(207 ^ [singleton(221 ^ []), singleton(221 ^ [])], singleton(221 ^ []))],extension(206 ^ 10,bind([[_55272, _55274], [singleton(221 ^ []), singleton(221 ^ [])]]))).
% 231.96/224.05 ncf('1.1.2.2.2.1',plain,[-(in(207 ^ [singleton(221 ^ []), singleton(221 ^ [])], singleton(221 ^ [])))],extension(211 ^ 13)).
% 231.96/224.05 ncf('1.1.2.2.2.2',plain,[-(in(207 ^ [singleton(221 ^ []), singleton(221 ^ [])], singleton(221 ^ [])))],extension(215 ^ 13)).
% 231.96/224.05 ncf('1.1.2.3',plain,[-(105 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(220 ^ [], 221 ^ [])] = ordered_pair(220 ^ [], 221 ^ []))],extension(113 ^ 9)).
% 231.96/224.05 ncf('1.1.2.4',plain,[-(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])) = cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))), 213 : in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))), 217 : in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])))],extension(206 ^ 5,bind([[_55272, _55274], [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]]))).
% 231.96/224.05 ncf('1.1.2.4.1',plain,[-(in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])))), in(ordered_pair(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]), cartesian_product2(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))))],extension(182 ^ 8,bind([[_54515, _54517, _54519, _54521], [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]]]))).
% 231.96/224.05 ncf('1.1.2.4.1.1',plain,[-(in(ordered_pair(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]), cartesian_product2(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))))), 137 : in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))), 137 : in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))), 137 : ordered_pair(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]) = ordered_pair(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]), 135 : cartesian_product2(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))) = cartesian_product2(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])))],extension(119 ^ 9,bind([[_51753, _51755, _51757, _52514, _52644, _52646], [cartesian_product2(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))), cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]), 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]]]))).
% 231.96/224.05 ncf('1.1.2.4.1.1.1',plain,[-(in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))))],extension(211 ^ 14)).
% 231.96/224.05 ncf('1.1.2.4.1.1.2',plain,[-(in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))))],extension(211 ^ 14)).
% 231.96/224.05 ncf('1.1.2.4.1.1.3',plain,[-(ordered_pair(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]) = ordered_pair(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]))],extension(2 ^ 14,bind([[_47673], [ordered_pair(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))])]]))).
% 231.96/224.05 ncf('1.1.2.4.1.1.4',plain,[-(cartesian_product2(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))) = cartesian_product2(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))))],extension(2 ^ 10,bind([[_47673], [cartesian_product2(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])))]]))).
% 231.96/224.05 ncf('1.1.2.4.2',plain,[-(in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])))), in(ordered_pair(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]), cartesian_product2(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))))],extension(182 ^ 8,bind([[_54515, _54517, _54519, _54521], [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]]]))).
% 231.96/224.05 ncf('1.1.2.4.2.1',plain,[-(in(ordered_pair(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]), cartesian_product2(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))))), 137 : in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))), 137 : in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))), 137 : ordered_pair(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]) = ordered_pair(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]), 135 : cartesian_product2(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))) = cartesian_product2(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])))],extension(119 ^ 9,bind([[_51753, _51755, _51757, _52514, _52644, _52646], [cartesian_product2(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))), cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), ordered_pair(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]), 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]]]))).
% 231.96/224.05 ncf('1.1.2.4.2.1.1',plain,[-(in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])))), -(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])) = cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))), 215 : -(in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))))],extension(206 ^ 14,bind([[_55272, _55274], [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]]))).
% 231.96/224.05 ncf('1.1.2.4.2.1.1.1',plain,[cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])) = cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))],reduction('1.1.2')).
% 231.96/224.05 ncf('1.1.2.4.2.1.1.2',plain,[in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])))],reduction('1.1.2.4.2.1')).
% 231.96/224.05 ncf('1.1.2.4.2.1.2',plain,[-(in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])))), -(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])) = cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))), 215 : -(in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))))],extension(206 ^ 14,bind([[_55272, _55274], [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]]))).
% 231.96/224.05 ncf('1.1.2.4.2.1.2.1',plain,[cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])) = cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))],reduction('1.1.2')).
% 231.96/224.05 ncf('1.1.2.4.2.1.2.2',plain,[in(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])))],reduction('1.1.2.4.2.1')).
% 231.96/224.05 ncf('1.1.2.4.2.1.3',plain,[-(ordered_pair(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]) = ordered_pair(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))]))],extension(2 ^ 14,bind([[_47673], [ordered_pair(207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))], 207 ^ [cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))])]]))).
% 231.96/224.05 ncf('1.1.2.4.2.1.4',plain,[-(cartesian_product2(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))) = cartesian_product2(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ []))))],extension(2 ^ 10,bind([[_47673], [cartesian_product2(cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])), cartesian_product2(singleton(220 ^ []), singleton(221 ^ [])))]]))).
% 231.96/224.05 %-----------------------------------------------------
% 231.96/224.05 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
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