TSTP Solution File: SET894+1 by leanCoP---2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : leanCoP---2.2
% Problem : SET894+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leancop_casc.sh %s %d
% Computer : n028.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 02:56:52 EDT 2022
% Result : Theorem 9.24s 9.69s
% Output : Proof 9.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET894+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.11/0.13 % Command : leancop_casc.sh %s %d
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 16:55:12 EDT 2022
% 0.19/0.34 % CPUTime :
% 9.24/9.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.24/9.70 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.24/9.70
% 9.24/9.70 %-----------------------------------------------------
% 9.24/9.70 fof(t35_zfmisc_1, conjecture, ! [_37352, _37355] : cartesian_product2(singleton(_37352), singleton(_37355)) = singleton(ordered_pair(_37352, _37355)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', t35_zfmisc_1)).
% 9.24/9.70 fof(d1_tarski, axiom, ! [_37591, _37594] : (_37594 = singleton(_37591) <=> ! [_37612] : (in(_37612, _37594) <=> _37612 = _37591)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', d1_tarski)).
% 9.24/9.70 fof(d2_zfmisc_1, axiom, ! [_37841, _37844, _37847] : (_37847 = cartesian_product2(_37841, _37844) <=> ! [_37868] : (in(_37868, _37847) <=> ? [_37886, _37889] : (in(_37886, _37841) & in(_37889, _37844) & _37868 = ordered_pair(_37886, _37889)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', d2_zfmisc_1)).
% 9.24/9.70
% 9.24/9.70 cnf(1, plain, [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])) = singleton(ordered_pair(10 ^ [], 11 ^ []))], clausify(t35_zfmisc_1)).
% 9.24/9.70 cnf(2, plain, [-(cartesian_product2(_8757, _8890) = cartesian_product2(_8824, _8955)), _8757 = _8824, _8890 = _8955], theory(equality)).
% 9.24/9.70 cnf(3, plain, [-(ordered_pair(_9381, _9514) = ordered_pair(_9448, _9579)), _9381 = _9448, _9514 = _9579], theory(equality)).
% 9.24/9.70 cnf(4, plain, [_10005 = _10054, -(singleton(_10005) = singleton(_10054))], theory(equality)).
% 9.24/9.70 cnf(5, plain, [-(_6876 = _6876)], theory(equality)).
% 9.24/9.70 cnf(6, plain, [-(_7308 = _7419), _7308 = _7364, _7364 = _7419], theory(equality)).
% 9.24/9.70 cnf(7, plain, [_11727 = singleton(_11669), in(_11859, _11727), -(_11859 = _11669)], clausify(d1_tarski)).
% 9.24/9.70 cnf(8, plain, [_11727 = singleton(_11669), -(in(_11859, _11727)), _11859 = _11669], clausify(d1_tarski)).
% 9.24/9.70 cnf(9, plain, [-(_11727 = singleton(_11669)), in(1 ^ [_11727, _11669], _11727), 1 ^ [_11727, _11669] = _11669], clausify(d1_tarski)).
% 9.24/9.70 cnf(10, plain, [-(_11727 = singleton(_11669)), -(in(1 ^ [_11727, _11669], _11727)), -(1 ^ [_11727, _11669] = _11669)], clausify(d1_tarski)).
% 9.24/9.70 cnf(11, plain, [_12327 = cartesian_product2(_12150, _12239), in(_12510, _12327), -(in(2 ^ [_12510, _12327, _12239, _12150], _12150))], clausify(d2_zfmisc_1)).
% 9.24/9.70 cnf(12, plain, [_12327 = cartesian_product2(_12150, _12239), in(_12510, _12327), -(in(3 ^ [_12510, _12327, _12239, _12150], _12239))], clausify(d2_zfmisc_1)).
% 9.24/9.70 cnf(13, plain, [_12327 = cartesian_product2(_12150, _12239), in(_12510, _12327), -(_12510 = ordered_pair(2 ^ [_12510, _12327, _12239, _12150], 3 ^ [_12510, _12327, _12239, _12150]))], clausify(d2_zfmisc_1)).
% 9.24/9.70 cnf(14, plain, [_12327 = cartesian_product2(_12150, _12239), -(in(_12510, _12327)), in(_12647, _12150), in(_12718, _12239), _12510 = ordered_pair(_12647, _12718)], clausify(d2_zfmisc_1)).
% 9.24/9.70
% 9.24/9.70 cnf('1',plain,[cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])) = singleton(ordered_pair(10 ^ [], 11 ^ []))],start(1)).
% 9.24/9.70 cnf('1.1',plain,[-(cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])) = singleton(ordered_pair(10 ^ [], 11 ^ []))), -(in(1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])))), -(1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])] = ordered_pair(10 ^ [], 11 ^ []))],extension(10,bind([[_11727, _11669], [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])]]))).
% 9.24/9.70 cnf('1.1.1',plain,[in(1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ []))), cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])) = cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), -(in(2 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])], singleton(10 ^ [])))],extension(11,bind([[_12510, _12327, _12239, _12150], [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])]]))).
% 9.24/9.70 cnf('1.1.1.1',plain,[-(cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])) = cartesian_product2(singleton(10 ^ []), singleton(11 ^ []))), singleton(10 ^ []) = singleton(10 ^ []), singleton(11 ^ []) = singleton(11 ^ [])],extension(2,bind([[_8757, _8824, _8890, _8955], [singleton(10 ^ []), singleton(10 ^ []), singleton(11 ^ []), singleton(11 ^ [])]]))).
% 9.24/9.70 cnf('1.1.1.1.1',plain,[-(singleton(10 ^ []) = singleton(10 ^ [])), 10 ^ [] = 10 ^ []],extension(4,bind([[_10005, _10054], [10 ^ [], 10 ^ []]]))).
% 9.24/9.70 cnf('1.1.1.1.1.1',plain,[-(10 ^ [] = 10 ^ [])],extension(5,bind([[_6876], [10 ^ []]]))).
% 9.24/9.70 cnf('1.1.1.1.2',plain,[-(singleton(11 ^ []) = singleton(11 ^ [])), 11 ^ [] = 11 ^ []],extension(4,bind([[_10005, _10054], [11 ^ [], 11 ^ []]]))).
% 9.24/9.70 cnf('1.1.1.1.2.1',plain,[-(11 ^ [] = 11 ^ [])],extension(5,bind([[_6876], [11 ^ []]]))).
% 9.24/9.70 cnf('1.1.1.2',plain,[in(2 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])], singleton(10 ^ [])), singleton(10 ^ []) = singleton(10 ^ []), -(2 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])] = 10 ^ [])],extension(7,bind([[_11727, _11859, _11669], [singleton(10 ^ []), 2 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])], 10 ^ []]]))).
% 9.24/9.70 cnf('1.1.1.2.1',plain,[-(singleton(10 ^ []) = singleton(10 ^ [])), 10 ^ [] = 10 ^ []],extension(4,bind([[_10005, _10054], [10 ^ [], 10 ^ []]]))).
% 9.24/9.70 cnf('1.1.1.2.1.1',plain,[-(10 ^ [] = 10 ^ [])],extension(5,bind([[_6876], [10 ^ []]]))).
% 9.24/9.70 cnf('1.1.1.2.2',plain,[2 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])] = 10 ^ [], -(ordered_pair(2 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])], 3 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])]) = ordered_pair(10 ^ [], 11 ^ [])), 3 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])] = 11 ^ []],extension(3,bind([[_9381, _9448, _9514, _9579], [2 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])], 10 ^ [], 3 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])], 11 ^ []]]))).
% 9.24/9.70 cnf('1.1.1.2.2.1',plain,[ordered_pair(2 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])], 3 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])]) = ordered_pair(10 ^ [], 11 ^ []), -(1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])] = ordered_pair(10 ^ [], 11 ^ [])), 1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])] = ordered_pair(2 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])], 3 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])])],extension(6,bind([[_7419, _7308, _7364], [ordered_pair(10 ^ [], 11 ^ []), 1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], ordered_pair(2 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])], 3 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])])]]))).
% 9.24/9.70 cnf('1.1.1.2.2.1.1',plain,[1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])] = ordered_pair(10 ^ [], 11 ^ []), -(cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])) = singleton(ordered_pair(10 ^ [], 11 ^ []))), in(1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])))],extension(9,bind([[_11669, _11727], [ordered_pair(10 ^ [], 11 ^ []), cartesian_product2(singleton(10 ^ []), singleton(11 ^ []))]]))).
% 9.24/9.70 cnf('1.1.1.2.2.1.1.1',plain,[cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])) = singleton(ordered_pair(10 ^ [], 11 ^ []))],extension(1)).
% 9.24/9.70 cnf('1.1.1.2.2.1.1.2',plain,[-(in(1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ []))))],reduction('1.1')).
% 9.24/9.70 cnf('1.1.1.2.2.1.2',plain,[-(1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])] = ordered_pair(2 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])], 3 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])])), cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])) = cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), in(1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])))],extension(13,bind([[_12150, _12239, _12510, _12327], [singleton(10 ^ []), singleton(11 ^ []), 1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ []))]]))).
% 9.24/9.70 cnf('1.1.1.2.2.1.2.1',plain,[-(cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])) = cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])))],extension(5,bind([[_6876], [cartesian_product2(singleton(10 ^ []), singleton(11 ^ []))]]))).
% 9.24/9.70 cnf('1.1.1.2.2.1.2.2',plain,[-(in(1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ []))))],reduction('1.1')).
% 9.24/9.70 cnf('1.1.1.2.2.2',plain,[-(3 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])] = 11 ^ []), singleton(11 ^ []) = singleton(11 ^ []), in(3 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])], singleton(11 ^ []))],extension(7,bind([[_11669, _11859, _11727], [11 ^ [], 3 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])], singleton(11 ^ [])]]))).
% 9.24/9.70 cnf('1.1.1.2.2.2.1',plain,[-(singleton(11 ^ []) = singleton(11 ^ []))],extension(5,bind([[_6876], [singleton(11 ^ [])]]))).
% 9.24/9.70 cnf('1.1.1.2.2.2.2',plain,[-(in(3 ^ [1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(11 ^ []), singleton(10 ^ [])], singleton(11 ^ []))), cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])) = cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), in(1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])))],extension(12,bind([[_12150, _12239, _12510, _12327], [singleton(10 ^ []), singleton(11 ^ []), 1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ []))]]))).
% 9.24/9.70 cnf('1.1.1.2.2.2.2.1',plain,[-(cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])) = cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])))],extension(5,bind([[_6876], [cartesian_product2(singleton(10 ^ []), singleton(11 ^ []))]]))).
% 9.24/9.70 cnf('1.1.1.2.2.2.2.2',plain,[-(in(1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ []))))],reduction('1.1')).
% 9.24/9.70 cnf('1.1.2',plain,[1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])] = ordered_pair(10 ^ [], 11 ^ []), -(cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])) = singleton(ordered_pair(10 ^ [], 11 ^ []))), in(1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])))],extension(9,bind([[_11669, _11727], [ordered_pair(10 ^ [], 11 ^ []), cartesian_product2(singleton(10 ^ []), singleton(11 ^ []))]]))).
% 9.24/9.70 cnf('1.1.2.1',plain,[cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])) = singleton(ordered_pair(10 ^ [], 11 ^ []))],extension(1)).
% 9.24/9.70 cnf('1.1.2.2',plain,[-(in(1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])))), cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])) = cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), in(10 ^ [], singleton(10 ^ [])), in(11 ^ [], singleton(11 ^ [])), 1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])] = ordered_pair(10 ^ [], 11 ^ [])],extension(14,bind([[_12327, _12150, _12239, _12510, _12647, _12718], [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), singleton(10 ^ []), singleton(11 ^ []), 1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])], 10 ^ [], 11 ^ []]]))).
% 9.24/9.70 cnf('1.1.2.2.1',plain,[-(cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])) = cartesian_product2(singleton(10 ^ []), singleton(11 ^ []))), singleton(10 ^ []) = singleton(10 ^ []), singleton(11 ^ []) = singleton(11 ^ [])],extension(2,bind([[_8757, _8824, _8890, _8955], [singleton(10 ^ []), singleton(10 ^ []), singleton(11 ^ []), singleton(11 ^ [])]]))).
% 9.24/9.70 cnf('1.1.2.2.1.1',plain,[-(singleton(10 ^ []) = singleton(10 ^ [])), 10 ^ [] = 10 ^ []],extension(4,bind([[_10005, _10054], [10 ^ [], 10 ^ []]]))).
% 9.24/9.70 cnf('1.1.2.2.1.1.1',plain,[-(10 ^ [] = 10 ^ [])],extension(5,bind([[_6876], [10 ^ []]]))).
% 9.24/9.70 cnf('1.1.2.2.1.2',plain,[-(singleton(11 ^ []) = singleton(11 ^ [])), 11 ^ [] = 11 ^ []],extension(4,bind([[_10005, _10054], [11 ^ [], 11 ^ []]]))).
% 9.24/9.70 cnf('1.1.2.2.1.2.1',plain,[-(11 ^ [] = 11 ^ [])],extension(5,bind([[_6876], [11 ^ []]]))).
% 9.24/9.70 cnf('1.1.2.2.2',plain,[-(in(10 ^ [], singleton(10 ^ []))), singleton(10 ^ []) = singleton(10 ^ []), 10 ^ [] = 10 ^ []],extension(8,bind([[_11727, _11859, _11669], [singleton(10 ^ []), 10 ^ [], 10 ^ []]]))).
% 9.24/9.70 cnf('1.1.2.2.2.1',plain,[-(singleton(10 ^ []) = singleton(10 ^ [])), 10 ^ [] = 10 ^ []],extension(4,bind([[_10005, _10054], [10 ^ [], 10 ^ []]]))).
% 9.24/9.70 cnf('1.1.2.2.2.1.1',plain,[-(10 ^ [] = 10 ^ [])],extension(5,bind([[_6876], [10 ^ []]]))).
% 9.24/9.70 cnf('1.1.2.2.2.2',plain,[-(10 ^ [] = 10 ^ [])],extension(5,bind([[_6876], [10 ^ []]]))).
% 9.24/9.70 cnf('1.1.2.2.3',plain,[-(in(11 ^ [], singleton(11 ^ []))), singleton(11 ^ []) = singleton(11 ^ []), 11 ^ [] = 11 ^ []],extension(8,bind([[_11727, _11859, _11669], [singleton(11 ^ []), 11 ^ [], 11 ^ []]]))).
% 9.24/9.70 cnf('1.1.2.2.3.1',plain,[-(singleton(11 ^ []) = singleton(11 ^ [])), 11 ^ [] = 11 ^ []],extension(4,bind([[_10005, _10054], [11 ^ [], 11 ^ []]]))).
% 9.24/9.70 cnf('1.1.2.2.3.1.1',plain,[-(11 ^ [] = 11 ^ [])],extension(5,bind([[_6876], [11 ^ []]]))).
% 9.24/9.70 cnf('1.1.2.2.3.2',plain,[-(11 ^ [] = 11 ^ [])],extension(5,bind([[_6876], [11 ^ []]]))).
% 9.24/9.70 cnf('1.1.2.2.4',plain,[-(1 ^ [cartesian_product2(singleton(10 ^ []), singleton(11 ^ [])), ordered_pair(10 ^ [], 11 ^ [])] = ordered_pair(10 ^ [], 11 ^ []))],reduction('1.1')).
% 9.24/9.70 %-----------------------------------------------------
% 9.24/9.71
% 9.27/9.71 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------