%------------------------------------------------------------------------------
% File     : leanCoP---2.2
% Problem  : SWV487+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : leancop_casc.sh %s %d

% Computer : n014.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 : Wed Jul 20 19:51:14 EDT 2022

% Result   : Theorem 39.86s 38.81s
% Output   : Proof 39.87s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : SWV487+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : leancop_casc.sh %s %d
% 0.14/0.35  % Computer : n014.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Wed Jun 15 07:10:36 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 39.86/38.81  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.87/38.82  % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.87/38.82  
% 39.87/38.82  %-----------------------------------------------------
% 39.87/38.82  fof(qiu, hypothesis, ! [_42064, _42067] : (int_leq(int_one, _42064) & int_leq(_42064, n) & int_leq(int_one, _42067) & int_leq(_42067, n) => ! [_42115] : (int_less(int_zero, _42115) & _42064 = plus(_42067, _42115) => ! [_42146] : (int_leq(int_one, _42146) & int_leq(_42146, _42067) => a(plus(_42146, _42115), _42146) = real_zero)) & ! [_42115] : (int_leq(int_zero, _42115) & _42067 = plus(_42064, _42115) => ! [_42146] : (int_leq(int_one, _42146) & int_leq(_42146, _42064) => a(_42146, plus(_42146, _42115)) = lu(_42146, plus(_42146, _42115))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', qiu)).
% 39.87/38.82  fof(plus_and_inverse, axiom, ! [_42776, _42779] : (int_less(_42776, _42779) <=> ? [_42797] : (plus(_42776, _42797) = _42779 & int_less(int_zero, _42797))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', plus_and_inverse)).
% 39.87/38.82  fof(int_leq, axiom, ! [_43004, _43007] : (int_leq(_43004, _43007) <=> int_less(_43004, _43007) | _43004 = _43007), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', int_leq)).
% 39.87/38.82  fof(ut, conjecture, ! [_43186, _43189] : (int_leq(int_one, _43189) & int_less(_43189, _43186) & int_leq(_43186, n) => a(_43186, _43189) = real_zero), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ut)).
% 39.87/38.82  fof(int_less_transitive, axiom, ! [_43523, _43526, _43529] : (int_less(_43523, _43526) & int_less(_43526, _43529) => int_less(_43523, _43529)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', int_less_transitive)).
% 39.87/38.82  fof(int_less_irreflexive, axiom, ! [_43708, _43711] : (int_less(_43708, _43711) => (! _43708) = _43711), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', int_less_irreflexive)).
% 39.87/38.82  fof(int_less_total, axiom, ! [_43857, _43860] : (int_less(_43857, _43860) | int_leq(_43860, _43857)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', int_less_total)).
% 39.87/38.82  fof(one_successor_of_zero, axiom, ! [_44031] : (int_less(int_zero, _44031) <=> int_leq(int_one, _44031)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', one_successor_of_zero)).
% 39.87/38.82  
% 39.87/38.82  cnf(1, plain, [-(4 ^ [_16319, _16158]), _16158 = plus(_16319, _16770), int_less(int_zero, _16770), -(a(plus(_17020, _16770), _17020) = real_zero), int_leq(int_one, _17020), int_leq(_17020, _16319)], clausify(qiu)).
% 39.87/38.82  cnf(2, plain, [-(3 ^ [_15316, _15257]), -(int_less(int_zero, 2 ^ [_15316, _15257]))], clausify(plus_and_inverse)).
% 39.87/38.82  cnf(3, plain, [-(3 ^ [_15316, _15257]), -(plus(_15257, 2 ^ [_15316, _15257]) = _15316)], clausify(plus_and_inverse)).
% 39.87/38.82  cnf(4, plain, [-(1 ^ [_12503, _12452]), _12452 = _12503], clausify(int_leq)).
% 39.87/38.82  cnf(5, plain, [-(1 ^ [_12503, _12452]), int_less(_12452, _12503)], clausify(int_leq)).
% 39.87/38.82  cnf(6, plain, [-(int_leq(int_one, 6 ^ []))], clausify(ut)).
% 39.87/38.82  cnf(7, plain, [-(int_less(6 ^ [], 5 ^ []))], clausify(ut)).
% 39.87/38.82  cnf(8, plain, [-(int_leq(5 ^ [], n))], clausify(ut)).
% 39.87/38.82  cnf(9, plain, [a(5 ^ [], 6 ^ []) = real_zero], clausify(ut)).
% 39.87/38.82  cnf(10, plain, [-(a(_10524, _10657) = a(_10591, _10722)), _10524 = _10591, _10657 = _10722], theory(equality)).
% 39.87/38.82  cnf(11, plain, [-(_8348 = _8348)], theory(equality)).
% 39.87/38.82  cnf(12, plain, [_8501 = _8546, -(_8546 = _8501)], theory(equality)).
% 39.87/38.82  cnf(13, plain, [-(_8780 = _8891), _8780 = _8836, _8836 = _8891], theory(equality)).
% 39.87/38.82  cnf(14, plain, [-(int_leq(_9323, _9454)), int_leq(_9256, _9389), _9256 = _9323, _9389 = _9454], theory(equality)).
% 39.87/38.82  cnf(15, plain, [-(int_leq(_12452, _12503)), 1 ^ [_12503, _12452]], clausify(int_leq)).
% 39.87/38.82  cnf(16, plain, [int_leq(_12452, _12503), -(int_less(_12452, _12503)), -(_12452 = _12503)], clausify(int_leq)).
% 39.87/38.82  cnf(17, plain, [-(int_less(_12848, _12959)), int_less(_12848, _12904), int_less(_12904, _12959)], clausify(int_less_transitive)).
% 39.87/38.82  cnf(18, plain, [int_less(_13315, _13362), _13315 = _13362], clausify(int_less_irreflexive)).
% 39.87/38.82  cnf(19, plain, [-(int_less(_13645, _13690)), -(int_leq(_13690, _13645))], clausify(int_less_total)).
% 39.87/38.82  cnf(20, plain, [int_less(_15257, _15316), 3 ^ [_15316, _15257]], clausify(plus_and_inverse)).
% 39.87/38.82  cnf(21, plain, [-(int_less(_15257, _15316)), plus(_15257, _15434) = _15316, int_less(int_zero, _15434)], clausify(plus_and_inverse)).
% 39.87/38.82  cnf(22, plain, [int_less(int_zero, _15765), -(int_leq(int_one, _15765))], clausify(one_successor_of_zero)).
% 39.87/38.82  cnf(23, plain, [-(int_less(int_zero, _15765)), int_leq(int_one, _15765)], clausify(one_successor_of_zero)).
% 39.87/38.82  cnf(24, plain, [int_leq(_16319, n), int_leq(int_one, _16319), int_leq(_16158, n), int_leq(int_one, _16158), 4 ^ [_16319, _16158]], clausify(qiu)).
% 39.87/38.82  
% 39.87/38.82  cnf('1',plain,[-(int_leq(int_one, 6 ^ []))],start(6)).
% 39.87/38.82  cnf('1.1',plain,[int_leq(int_one, 6 ^ []), int_leq(6 ^ [], n), int_leq(5 ^ [], n), int_leq(int_one, 5 ^ []), 4 ^ [6 ^ [], 5 ^ []]],extension(24,bind([[_16319, _16158], [6 ^ [], 5 ^ []]]))).
% 39.87/38.82  cnf('1.1.1',plain,[-(int_leq(6 ^ [], n)), 1 ^ [n, 6 ^ []]],extension(15,bind([[_12503, _12452], [n, 6 ^ []]]))).
% 39.87/38.82  cnf('1.1.1.1',plain,[-(1 ^ [n, 6 ^ []]), int_less(6 ^ [], n)],extension(5,bind([[_12452, _12503], [6 ^ [], n]]))).
% 39.87/38.82  cnf('1.1.1.1.1',plain,[-(int_less(6 ^ [], n)), plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]) = n, int_less(int_zero, 2 ^ [5 ^ [], 6 ^ []])],extension(21,bind([[_15257, _15316, _15434], [6 ^ [], n, 2 ^ [5 ^ [], 6 ^ []]]]))).
% 39.87/38.82  cnf('1.1.1.1.1.1',plain,[-(plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]) = n), plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]) = 5 ^ [], 5 ^ [] = n],extension(13,bind([[_8780, _8836, _8891], [plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]), 5 ^ [], n]]))).
% 39.87/38.82  cnf('1.1.1.1.1.1.1',plain,[-(plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]) = 5 ^ []), -(3 ^ [5 ^ [], 6 ^ []])],extension(3,bind([[_15316, _15257], [5 ^ [], 6 ^ []]]))).
% 39.87/38.82  cnf('1.1.1.1.1.1.1.1',plain,[3 ^ [5 ^ [], 6 ^ []], int_less(6 ^ [], 5 ^ [])],extension(20,bind([[_15257, _15316], [6 ^ [], 5 ^ []]]))).
% 39.87/38.82  cnf('1.1.1.1.1.1.1.1.1',plain,[-(int_less(6 ^ [], 5 ^ []))],extension(7)).
% 39.87/38.82  cnf('1.1.1.1.1.1.2',plain,[-(5 ^ [] = n), int_leq(5 ^ [], n), -(int_less(5 ^ [], n))],extension(16,bind([[_12452, _12503], [5 ^ [], n]]))).
% 39.87/38.82  cnf('1.1.1.1.1.1.2.1',plain,[-(int_leq(5 ^ [], n))],extension(8)).
% 39.87/38.82  cnf('1.1.1.1.1.1.2.2',plain,[int_less(5 ^ [], n), -(int_less(6 ^ [], n)), int_less(6 ^ [], 5 ^ [])],extension(17,bind([[_12959, _12848, _12904], [n, 6 ^ [], 5 ^ []]]))).
% 39.87/38.82  cnf('1.1.1.1.1.1.2.2.1',plain,[int_less(6 ^ [], n)],reduction('1.1.1.1')).
% 39.87/38.82  cnf('1.1.1.1.1.1.2.2.2',plain,[-(int_less(6 ^ [], 5 ^ []))],extension(7)).
% 39.87/38.82  cnf('1.1.1.1.1.2',plain,[-(int_less(int_zero, 2 ^ [5 ^ [], 6 ^ []])), -(3 ^ [5 ^ [], 6 ^ []])],extension(2,bind([[_15316, _15257], [5 ^ [], 6 ^ []]]))).
% 39.87/38.82  cnf('1.1.1.1.1.2.1',plain,[3 ^ [5 ^ [], 6 ^ []], int_less(6 ^ [], 5 ^ [])],extension(20,bind([[_15257, _15316], [6 ^ [], 5 ^ []]]))).
% 39.87/38.82  cnf('1.1.1.1.1.2.1.1',plain,[-(int_less(6 ^ [], 5 ^ []))],extension(7)).
% 39.87/38.82  cnf('1.1.2',plain,[-(int_leq(5 ^ [], n))],extension(8)).
% 39.87/38.82  cnf('1.1.3',plain,[-(int_leq(int_one, 5 ^ [])), int_leq(int_one, 6 ^ []), int_one = int_one, 6 ^ [] = 5 ^ []],extension(14,bind([[_9256, _9323, _9389, _9454], [int_one, int_one, 6 ^ [], 5 ^ []]]))).
% 39.87/38.82  cnf('1.1.3.1',plain,[-(int_leq(int_one, 6 ^ []))],extension(6)).
% 39.87/38.82  cnf('1.1.3.2',plain,[-(int_one = int_one)],extension(11,bind([[_8348], [int_one]]))).
% 39.87/38.82  cnf('1.1.3.3',plain,[-(6 ^ [] = 5 ^ []), 5 ^ [] = 6 ^ []],extension(12,bind([[_8501, _8546], [5 ^ [], 6 ^ []]]))).
% 39.87/38.82  cnf('1.1.3.3.1',plain,[-(5 ^ [] = 6 ^ []), int_leq(5 ^ [], 6 ^ []), -(int_less(5 ^ [], 6 ^ []))],extension(16,bind([[_12452, _12503], [5 ^ [], 6 ^ []]]))).
% 39.87/38.82  cnf('1.1.3.3.1.1',plain,[-(int_leq(5 ^ [], 6 ^ [])), -(int_less(6 ^ [], 5 ^ []))],extension(19,bind([[_13645, _13690], [6 ^ [], 5 ^ []]]))).
% 39.87/38.82  cnf('1.1.3.3.1.1.1',plain,[int_less(6 ^ [], 5 ^ []), -(int_less(int_zero, 5 ^ [])), int_less(int_zero, 6 ^ [])],extension(17,bind([[_12959, _12848, _12904], [5 ^ [], int_zero, 6 ^ []]]))).
% 39.87/38.82  cnf('1.1.3.3.1.1.1.1',plain,[int_less(int_zero, 5 ^ []), -(int_leq(int_one, 5 ^ []))],extension(22,bind([[_15765], [5 ^ []]]))).
% 39.87/38.82  cnf('1.1.3.3.1.1.1.1.1',plain,[int_leq(int_one, 5 ^ [])],reduction('1.1')).
% 39.87/38.82  cnf('1.1.3.3.1.1.1.2',plain,[-(int_less(int_zero, 6 ^ [])), int_leq(int_one, 6 ^ [])],extension(23,bind([[_15765], [6 ^ []]]))).
% 39.87/38.82  cnf('1.1.3.3.1.1.1.2.1',plain,[-(int_leq(int_one, 6 ^ []))],extension(6)).
% 39.87/38.82  cnf('1.1.3.3.1.2',plain,[int_less(5 ^ [], 6 ^ []), -(int_less(5 ^ [], 5 ^ [])), int_less(6 ^ [], 5 ^ [])],extension(17,bind([[_12848, _12904, _12959], [5 ^ [], 6 ^ [], 5 ^ []]]))).
% 39.87/38.82  cnf('1.1.3.3.1.2.1',plain,[int_less(5 ^ [], 5 ^ []), 5 ^ [] = 5 ^ []],extension(18,bind([[_13315, _13362], [5 ^ [], 5 ^ []]]))).
% 39.87/38.82  cnf('1.1.3.3.1.2.1.1',plain,[-(5 ^ [] = 5 ^ [])],extension(11,bind([[_8348], [5 ^ []]]))).
% 39.87/38.82  cnf('1.1.3.3.1.2.2',plain,[-(int_less(6 ^ [], 5 ^ []))],extension(7)).
% 39.87/38.82  cnf('1.1.4',plain,[-(4 ^ [6 ^ [], 5 ^ []]), 5 ^ [] = plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]), int_less(int_zero, 2 ^ [5 ^ [], 6 ^ []]), -(a(plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]), 6 ^ []) = real_zero), int_leq(int_one, 6 ^ []), int_leq(6 ^ [], 6 ^ [])],extension(1,bind([[_16158, _16770, _17020, _16319], [5 ^ [], 2 ^ [5 ^ [], 6 ^ []], 6 ^ [], 6 ^ []]]))).
% 39.87/38.82  cnf('1.1.4.1',plain,[-(5 ^ [] = plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []])), plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]) = 5 ^ []],extension(12,bind([[_8501, _8546], [plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]), 5 ^ []]]))).
% 39.87/38.82  cnf('1.1.4.1.1',plain,[-(plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]) = 5 ^ []), -(3 ^ [5 ^ [], 6 ^ []])],extension(3,bind([[_15316, _15257], [5 ^ [], 6 ^ []]]))).
% 39.87/38.82  cnf('1.1.4.1.1.1',plain,[3 ^ [5 ^ [], 6 ^ []], int_less(6 ^ [], 5 ^ [])],extension(20,bind([[_15257, _15316], [6 ^ [], 5 ^ []]]))).
% 39.87/38.82  cnf('1.1.4.1.1.1.1',plain,[-(int_less(6 ^ [], 5 ^ []))],extension(7)).
% 39.87/38.82  cnf('1.1.4.2',plain,[-(int_less(int_zero, 2 ^ [5 ^ [], 6 ^ []])), -(3 ^ [5 ^ [], 6 ^ []])],extension(2,bind([[_15316, _15257], [5 ^ [], 6 ^ []]]))).
% 39.87/38.82  cnf('1.1.4.2.1',plain,[3 ^ [5 ^ [], 6 ^ []], int_less(6 ^ [], 5 ^ [])],extension(20,bind([[_15257, _15316], [6 ^ [], 5 ^ []]]))).
% 39.87/38.82  cnf('1.1.4.2.1.1',plain,[-(int_less(6 ^ [], 5 ^ []))],extension(7)).
% 39.87/38.82  cnf('1.1.4.3',plain,[a(plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]), 6 ^ []) = real_zero, -(real_zero = a(plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]), 6 ^ []))],extension(12,bind([[_8546, _8501], [real_zero, a(plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]), 6 ^ [])]]))).
% 39.87/38.82  cnf('1.1.4.3.1',plain,[real_zero = a(plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]), 6 ^ []), -(real_zero = a(5 ^ [], 6 ^ [])), a(plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]), 6 ^ []) = a(5 ^ [], 6 ^ [])],extension(13,bind([[_8780, _8836, _8891], [real_zero, a(plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]), 6 ^ []), a(5 ^ [], 6 ^ [])]]))).
% 39.87/38.82  cnf('1.1.4.3.1.1',plain,[real_zero = a(5 ^ [], 6 ^ []), -(a(5 ^ [], 6 ^ []) = real_zero)],extension(12,bind([[_8546, _8501], [a(5 ^ [], 6 ^ []), real_zero]]))).
% 39.87/38.82  cnf('1.1.4.3.1.1.1',plain,[a(5 ^ [], 6 ^ []) = real_zero],extension(9)).
% 39.87/38.82  cnf('1.1.4.3.1.2',plain,[-(a(plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]), 6 ^ []) = a(5 ^ [], 6 ^ [])), plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]) = 5 ^ [], 6 ^ [] = 6 ^ []],extension(10,bind([[_10524, _10591, _10657, _10722], [plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]), 5 ^ [], 6 ^ [], 6 ^ []]]))).
% 39.87/38.82  cnf('1.1.4.3.1.2.1',plain,[-(plus(6 ^ [], 2 ^ [5 ^ [], 6 ^ []]) = 5 ^ []), -(3 ^ [5 ^ [], 6 ^ []])],extension(3,bind([[_15316, _15257], [5 ^ [], 6 ^ []]]))).
% 39.87/38.82  cnf('1.1.4.3.1.2.1.1',plain,[3 ^ [5 ^ [], 6 ^ []], int_less(6 ^ [], 5 ^ [])],extension(20,bind([[_15257, _15316], [6 ^ [], 5 ^ []]]))).
% 39.87/38.82  cnf('1.1.4.3.1.2.1.1.1',plain,[-(int_less(6 ^ [], 5 ^ []))],extension(7)).
% 39.87/38.82  cnf('1.1.4.3.1.2.2',plain,[-(6 ^ [] = 6 ^ [])],extension(11,bind([[_8348], [6 ^ []]]))).
% 39.87/38.82  cnf('1.1.4.4',plain,[-(int_leq(int_one, 6 ^ []))],extension(6)).
% 39.87/38.82  cnf('1.1.4.5',plain,[-(int_leq(6 ^ [], 6 ^ [])), 1 ^ [6 ^ [], 6 ^ []]],extension(15,bind([[_12503, _12452], [6 ^ [], 6 ^ []]]))).
% 39.87/38.82  cnf('1.1.4.5.1',plain,[-(1 ^ [6 ^ [], 6 ^ []]), 6 ^ [] = 6 ^ []],extension(4,bind([[_12452, _12503], [6 ^ [], 6 ^ []]]))).
% 39.87/38.82  cnf('1.1.4.5.1.1',plain,[-(6 ^ [] = 6 ^ [])],extension(11,bind([[_8348], [6 ^ []]]))).
% 39.87/38.82  %-----------------------------------------------------
% 39.87/38.83  
% 39.87/38.83  % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------