TSTP Solution File: SEU049+1 by leanCoP---2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : leanCoP---2.2
% Problem : SEU049+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 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 11:59:56 EDT 2022
% Result : Theorem 13.06s 12.84s
% Output : Proof 13.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU049+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.07/0.13 % Command : leancop_casc.sh %s %d
% 0.14/0.34 % Computer : n007.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 : 600
% 0.14/0.34 % DateTime : Sun Jun 19 15:42:29 EDT 2022
% 0.14/0.34 % CPUTime :
% 13.06/12.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.06/12.85 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.06/12.86
% 13.06/12.86 %-----------------------------------------------------
% 13.06/12.86 fof(t117_funct_1, conjecture, ! [_58305, _58308] : (relation(_58308) & function(_58308) => in(_58305, relation_dom(_58308)) => relation_image(_58308, singleton(_58305)) = singleton(apply(_58308, _58305))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', t117_funct_1)).
% 13.06/12.86 fof(d12_funct_1, axiom, ! [_58657] : (relation(_58657) & function(_58657) => ! [_58679, _58682] : (_58682 = relation_image(_58657, _58679) <=> ! [_58703] : (in(_58703, _58682) <=> ? [_58721] : (in(_58721, relation_dom(_58657)) & in(_58721, _58679) & _58703 = apply(_58657, _58721))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', d12_funct_1)).
% 13.06/12.86 fof(d1_tarski, axiom, ! [_59080, _59083] : (_59083 = singleton(_59080) <=> ! [_59101] : (in(_59101, _59083) <=> _59101 = _59080)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', d1_tarski)).
% 13.06/12.86
% 13.06/12.86 cnf(1, plain, [-(relation(18 ^ []))], clausify(t117_funct_1)).
% 13.06/12.86 cnf(2, plain, [-(function(18 ^ []))], clausify(t117_funct_1)).
% 13.06/12.86 cnf(3, plain, [-(in(17 ^ [], relation_dom(18 ^ [])))], clausify(t117_funct_1)).
% 13.06/12.86 cnf(4, plain, [relation_image(18 ^ [], singleton(17 ^ [])) = singleton(apply(18 ^ [], 17 ^ []))], clausify(t117_funct_1)).
% 13.06/12.86 cnf(5, plain, [-(apply(_18933, _19066) = apply(_19000, _19131)), _18933 = _19000, _19066 = _19131], theory(equality)).
% 13.06/12.86 cnf(6, plain, [_20829 = _20878, -(singleton(_20829) = singleton(_20878))], theory(equality)).
% 13.06/12.86 cnf(7, plain, [-(relation_image(_20215, _20348) = relation_image(_20282, _20413)), _20215 = _20282, _20348 = _20413], theory(equality)).
% 13.06/12.86 cnf(8, plain, [-(_14398 = _14398)], theory(equality)).
% 13.06/12.86 cnf(9, plain, [-(_14830 = _14941), _14830 = _14886, _14886 = _14941], theory(equality)).
% 13.06/12.86 cnf(10, plain, [function(_22446), relation(_22446), _22718 = relation_image(_22446, _22633), in(_22898, _22718), -(in(1 ^ [_22898, _22718, _22633, _22446], _22633))], clausify(d12_funct_1)).
% 13.06/12.86 cnf(11, plain, [function(_22446), relation(_22446), _22718 = relation_image(_22446, _22633), in(_22898, _22718), -(_22898 = apply(_22446, 1 ^ [_22898, _22718, _22633, _22446]))], clausify(d12_funct_1)).
% 13.06/12.86 cnf(12, plain, [function(_22446), relation(_22446), _22718 = relation_image(_22446, _22633), -(in(_22898, _22718)), in(_23032, relation_dom(_22446)), in(_23032, _22633), _22898 = apply(_22446, _23032)], clausify(d12_funct_1)).
% 13.06/12.86 cnf(13, plain, [_23571 = singleton(_23513), in(_23703, _23571), -(_23703 = _23513)], clausify(d1_tarski)).
% 13.06/12.86 cnf(14, plain, [_23571 = singleton(_23513), -(in(_23703, _23571)), _23703 = _23513], clausify(d1_tarski)).
% 13.06/12.86 cnf(15, plain, [-(_23571 = singleton(_23513)), in(4 ^ [_23571, _23513], _23571), 4 ^ [_23571, _23513] = _23513], clausify(d1_tarski)).
% 13.06/12.86 cnf(16, plain, [-(_23571 = singleton(_23513)), -(in(4 ^ [_23571, _23513], _23571)), -(4 ^ [_23571, _23513] = _23513)], clausify(d1_tarski)).
% 13.06/12.86
% 13.06/12.86 cnf('1',plain,[relation_image(18 ^ [], singleton(17 ^ [])) = singleton(apply(18 ^ [], 17 ^ []))],start(4)).
% 13.06/12.86 cnf('1.1',plain,[-(relation_image(18 ^ [], singleton(17 ^ [])) = singleton(apply(18 ^ [], 17 ^ []))), -(in(4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ [])))), -(4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])] = apply(18 ^ [], 17 ^ []))],extension(16,bind([[_23571, _23513], [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])]]))).
% 13.06/12.86 cnf('1.1.1',plain,[in(4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ []))), function(18 ^ []), relation(18 ^ []), relation_image(18 ^ [], singleton(17 ^ [])) = relation_image(18 ^ [], singleton(17 ^ [])), -(in(1 ^ [4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ [])), singleton(17 ^ []), 18 ^ []], singleton(17 ^ [])))],extension(10,bind([[_22898, _22718, _22446, _22633], [4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ [])), 18 ^ [], singleton(17 ^ [])]]))).
% 13.06/12.86 cnf('1.1.1.1',plain,[-(function(18 ^ []))],extension(2)).
% 13.06/12.86 cnf('1.1.1.2',plain,[-(relation(18 ^ []))],extension(1)).
% 13.06/12.86 cnf('1.1.1.3',plain,[-(relation_image(18 ^ [], singleton(17 ^ [])) = relation_image(18 ^ [], singleton(17 ^ []))), 18 ^ [] = 18 ^ [], singleton(17 ^ []) = singleton(17 ^ [])],extension(7,bind([[_20215, _20282, _20348, _20413], [18 ^ [], 18 ^ [], singleton(17 ^ []), singleton(17 ^ [])]]))).
% 13.06/12.86 cnf('1.1.1.3.1',plain,[-(18 ^ [] = 18 ^ [])],extension(8,bind([[_14398], [18 ^ []]]))).
% 13.06/12.86 cnf('1.1.1.3.2',plain,[-(singleton(17 ^ []) = singleton(17 ^ [])), 17 ^ [] = 17 ^ []],extension(6,bind([[_20829, _20878], [17 ^ [], 17 ^ []]]))).
% 13.06/12.86 cnf('1.1.1.3.2.1',plain,[-(17 ^ [] = 17 ^ [])],extension(8,bind([[_14398], [17 ^ []]]))).
% 13.06/12.86 cnf('1.1.1.4',plain,[in(1 ^ [4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ [])), singleton(17 ^ []), 18 ^ []], singleton(17 ^ [])), singleton(17 ^ []) = singleton(17 ^ []), -(1 ^ [4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ [])), singleton(17 ^ []), 18 ^ []] = 17 ^ [])],extension(13,bind([[_23571, _23703, _23513], [singleton(17 ^ []), 1 ^ [4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ [])), singleton(17 ^ []), 18 ^ []], 17 ^ []]]))).
% 13.06/12.86 cnf('1.1.1.4.1',plain,[-(singleton(17 ^ []) = singleton(17 ^ [])), 17 ^ [] = 17 ^ []],extension(6,bind([[_20829, _20878], [17 ^ [], 17 ^ []]]))).
% 13.06/12.86 cnf('1.1.1.4.1.1',plain,[-(17 ^ [] = 17 ^ [])],extension(8,bind([[_14398], [17 ^ []]]))).
% 13.06/12.86 cnf('1.1.1.4.2',plain,[1 ^ [4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ [])), singleton(17 ^ []), 18 ^ []] = 17 ^ [], -(apply(18 ^ [], 1 ^ [4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ [])), singleton(17 ^ []), 18 ^ []]) = apply(18 ^ [], 17 ^ [])), 18 ^ [] = 18 ^ []],extension(5,bind([[_19066, _19131, _18933, _19000], [1 ^ [4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ [])), singleton(17 ^ []), 18 ^ []], 17 ^ [], 18 ^ [], 18 ^ []]]))).
% 13.06/12.86 cnf('1.1.1.4.2.1',plain,[apply(18 ^ [], 1 ^ [4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ [])), singleton(17 ^ []), 18 ^ []]) = apply(18 ^ [], 17 ^ []), -(4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])] = apply(18 ^ [], 17 ^ [])), 4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])] = apply(18 ^ [], 1 ^ [4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ [])), singleton(17 ^ []), 18 ^ []])],extension(9,bind([[_14941, _14830, _14886], [apply(18 ^ [], 17 ^ []), 4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], apply(18 ^ [], 1 ^ [4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ [])), singleton(17 ^ []), 18 ^ []])]]))).
% 13.06/12.86 cnf('1.1.1.4.2.1.1',plain,[4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])] = apply(18 ^ [], 17 ^ []), -(relation_image(18 ^ [], singleton(17 ^ [])) = singleton(apply(18 ^ [], 17 ^ []))), in(4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ [])))],extension(15,bind([[_23513, _23571], [apply(18 ^ [], 17 ^ []), relation_image(18 ^ [], singleton(17 ^ []))]]))).
% 13.06/12.86 cnf('1.1.1.4.2.1.1.1',plain,[relation_image(18 ^ [], singleton(17 ^ [])) = singleton(apply(18 ^ [], 17 ^ []))],extension(4)).
% 13.06/12.86 cnf('1.1.1.4.2.1.1.2',plain,[-(in(4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ []))))],reduction('1.1')).
% 13.06/12.86 cnf('1.1.1.4.2.1.2',plain,[-(4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])] = apply(18 ^ [], 1 ^ [4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ [])), singleton(17 ^ []), 18 ^ []])), function(18 ^ []), relation(18 ^ []), relation_image(18 ^ [], singleton(17 ^ [])) = relation_image(18 ^ [], singleton(17 ^ [])), in(4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ [])))],extension(11,bind([[_22446, _22633, _22898, _22718], [18 ^ [], singleton(17 ^ []), 4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ []))]]))).
% 13.06/12.86 cnf('1.1.1.4.2.1.2.1',plain,[-(function(18 ^ []))],extension(2)).
% 13.06/12.86 cnf('1.1.1.4.2.1.2.2',plain,[-(relation(18 ^ []))],extension(1)).
% 13.06/12.86 cnf('1.1.1.4.2.1.2.3',plain,[-(relation_image(18 ^ [], singleton(17 ^ [])) = relation_image(18 ^ [], singleton(17 ^ [])))],extension(8,bind([[_14398], [relation_image(18 ^ [], singleton(17 ^ []))]]))).
% 13.06/12.86 cnf('1.1.1.4.2.1.2.4',plain,[-(in(4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ []))))],reduction('1.1')).
% 13.06/12.86 cnf('1.1.1.4.2.2',plain,[-(18 ^ [] = 18 ^ [])],extension(8,bind([[_14398], [18 ^ []]]))).
% 13.06/12.86 cnf('1.1.2',plain,[4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])] = apply(18 ^ [], 17 ^ []), -(relation_image(18 ^ [], singleton(17 ^ [])) = singleton(apply(18 ^ [], 17 ^ []))), in(4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ [])))],extension(15,bind([[_23513, _23571], [apply(18 ^ [], 17 ^ []), relation_image(18 ^ [], singleton(17 ^ []))]]))).
% 13.06/12.86 cnf('1.1.2.1',plain,[relation_image(18 ^ [], singleton(17 ^ [])) = singleton(apply(18 ^ [], 17 ^ []))],extension(4)).
% 13.06/12.86 cnf('1.1.2.2',plain,[-(in(4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], relation_image(18 ^ [], singleton(17 ^ [])))), function(18 ^ []), relation(18 ^ []), relation_image(18 ^ [], singleton(17 ^ [])) = relation_image(18 ^ [], singleton(17 ^ [])), in(17 ^ [], relation_dom(18 ^ [])), in(17 ^ [], singleton(17 ^ [])), 4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])] = apply(18 ^ [], 17 ^ [])],extension(12,bind([[_22718, _22633, _22898, _22446, _23032], [relation_image(18 ^ [], singleton(17 ^ [])), singleton(17 ^ []), 4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])], 18 ^ [], 17 ^ []]]))).
% 13.06/12.86 cnf('1.1.2.2.1',plain,[-(function(18 ^ []))],extension(2)).
% 13.06/12.86 cnf('1.1.2.2.2',plain,[-(relation(18 ^ []))],extension(1)).
% 13.06/12.86 cnf('1.1.2.2.3',plain,[-(relation_image(18 ^ [], singleton(17 ^ [])) = relation_image(18 ^ [], singleton(17 ^ []))), 18 ^ [] = 18 ^ [], singleton(17 ^ []) = singleton(17 ^ [])],extension(7,bind([[_20215, _20282, _20348, _20413], [18 ^ [], 18 ^ [], singleton(17 ^ []), singleton(17 ^ [])]]))).
% 13.06/12.86 cnf('1.1.2.2.3.1',plain,[-(18 ^ [] = 18 ^ [])],extension(8,bind([[_14398], [18 ^ []]]))).
% 13.06/12.86 cnf('1.1.2.2.3.2',plain,[-(singleton(17 ^ []) = singleton(17 ^ [])), 17 ^ [] = 17 ^ []],extension(6,bind([[_20829, _20878], [17 ^ [], 17 ^ []]]))).
% 13.06/12.86 cnf('1.1.2.2.3.2.1',plain,[-(17 ^ [] = 17 ^ [])],extension(8,bind([[_14398], [17 ^ []]]))).
% 13.06/12.86 cnf('1.1.2.2.4',plain,[-(in(17 ^ [], relation_dom(18 ^ [])))],extension(3)).
% 13.06/12.86 cnf('1.1.2.2.5',plain,[-(in(17 ^ [], singleton(17 ^ []))), singleton(17 ^ []) = singleton(17 ^ []), 17 ^ [] = 17 ^ []],extension(14,bind([[_23571, _23703, _23513], [singleton(17 ^ []), 17 ^ [], 17 ^ []]]))).
% 13.06/12.86 cnf('1.1.2.2.5.1',plain,[-(singleton(17 ^ []) = singleton(17 ^ [])), 17 ^ [] = 17 ^ []],extension(6,bind([[_20829, _20878], [17 ^ [], 17 ^ []]]))).
% 13.06/12.86 cnf('1.1.2.2.5.1.1',plain,[-(17 ^ [] = 17 ^ [])],extension(8,bind([[_14398], [17 ^ []]]))).
% 13.06/12.86 cnf('1.1.2.2.5.2',plain,[-(17 ^ [] = 17 ^ [])],extension(8,bind([[_14398], [17 ^ []]]))).
% 13.06/12.86 cnf('1.1.2.2.6',plain,[-(4 ^ [relation_image(18 ^ [], singleton(17 ^ [])), apply(18 ^ [], 17 ^ [])] = apply(18 ^ [], 17 ^ []))],reduction('1.1')).
% 13.06/12.86 %-----------------------------------------------------
% 13.06/12.86
% 13.06/12.86 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
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