TSTP Solution File: SEU221+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU221+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 05:47:59 EST 2010
% Result : Theorem 0.66s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 61 ( 6 unt; 0 def)
% Number of atoms : 546 ( 140 equ)
% Maximal formula atoms : 130 ( 8 avg)
% Number of connectives : 825 ( 340 ~; 367 |; 102 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn 56 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(9,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
file('/tmp/tmpJAusTU/sel_SEU221+1.p_1',t62_funct_1) ).
fof(10,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3) )
=> X2 = X3 ) ) ),
file('/tmp/tmpJAusTU/sel_SEU221+1.p_1',d8_funct_1) ).
fof(13,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/tmp/tmpJAusTU/sel_SEU221+1.p_1',dt_k2_funct_1) ).
fof(26,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_rng(X2)) )
=> ( X1 = apply(X2,apply(function_inverse(X2),X1))
& X1 = apply(relation_composition(function_inverse(X2),X2),X1) ) ) ),
file('/tmp/tmpJAusTU/sel_SEU221+1.p_1',t57_funct_1) ).
fof(33,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = function_inverse(X1)
<=> ( relation_dom(X2) = relation_rng(X1)
& ! [X3,X4] :
( ( ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) )
=> ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) )
& ( ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) )
=> ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) ) ) ) ) ) ) ) ),
file('/tmp/tmpJAusTU/sel_SEU221+1.p_1',t54_funct_1) ).
fof(40,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
inference(assume_negation,[status(cth)],[9]) ).
fof(77,negated_conjecture,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& ~ one_to_one(function_inverse(X1)) ),
inference(fof_nnf,[status(thm)],[40]) ).
fof(78,negated_conjecture,
? [X2] :
( relation(X2)
& function(X2)
& one_to_one(X2)
& ~ one_to_one(function_inverse(X2)) ),
inference(variable_rename,[status(thm)],[77]) ).
fof(79,negated_conjecture,
( relation(esk5_0)
& function(esk5_0)
& one_to_one(esk5_0)
& ~ one_to_one(function_inverse(esk5_0)) ),
inference(skolemize,[status(esa)],[78]) ).
cnf(80,negated_conjecture,
~ one_to_one(function_inverse(esk5_0)),
inference(split_conjunct,[status(thm)],[79]) ).
cnf(81,negated_conjecture,
one_to_one(esk5_0),
inference(split_conjunct,[status(thm)],[79]) ).
cnf(82,negated_conjecture,
function(esk5_0),
inference(split_conjunct,[status(thm)],[79]) ).
cnf(83,negated_conjecture,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[79]) ).
fof(84,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ( ( ~ one_to_one(X1)
| ! [X2,X3] :
( ~ in(X2,relation_dom(X1))
| ~ in(X3,relation_dom(X1))
| apply(X1,X2) != apply(X1,X3)
| X2 = X3 ) )
& ( ? [X2,X3] :
( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3)
& X2 != X3 )
| one_to_one(X1) ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(85,plain,
! [X4] :
( ~ relation(X4)
| ~ function(X4)
| ( ( ~ one_to_one(X4)
| ! [X5,X6] :
( ~ in(X5,relation_dom(X4))
| ~ in(X6,relation_dom(X4))
| apply(X4,X5) != apply(X4,X6)
| X5 = X6 ) )
& ( ? [X7,X8] :
( in(X7,relation_dom(X4))
& in(X8,relation_dom(X4))
& apply(X4,X7) = apply(X4,X8)
& X7 != X8 )
| one_to_one(X4) ) ) ),
inference(variable_rename,[status(thm)],[84]) ).
fof(86,plain,
! [X4] :
( ~ relation(X4)
| ~ function(X4)
| ( ( ~ one_to_one(X4)
| ! [X5,X6] :
( ~ in(X5,relation_dom(X4))
| ~ in(X6,relation_dom(X4))
| apply(X4,X5) != apply(X4,X6)
| X5 = X6 ) )
& ( ( in(esk6_1(X4),relation_dom(X4))
& in(esk7_1(X4),relation_dom(X4))
& apply(X4,esk6_1(X4)) = apply(X4,esk7_1(X4))
& esk6_1(X4) != esk7_1(X4) )
| one_to_one(X4) ) ) ),
inference(skolemize,[status(esa)],[85]) ).
fof(87,plain,
! [X4,X5,X6] :
( ( ( ~ in(X5,relation_dom(X4))
| ~ in(X6,relation_dom(X4))
| apply(X4,X5) != apply(X4,X6)
| X5 = X6
| ~ one_to_one(X4) )
& ( ( in(esk6_1(X4),relation_dom(X4))
& in(esk7_1(X4),relation_dom(X4))
& apply(X4,esk6_1(X4)) = apply(X4,esk7_1(X4))
& esk6_1(X4) != esk7_1(X4) )
| one_to_one(X4) ) )
| ~ relation(X4)
| ~ function(X4) ),
inference(shift_quantors,[status(thm)],[86]) ).
fof(88,plain,
! [X4,X5,X6] :
( ( ~ in(X5,relation_dom(X4))
| ~ in(X6,relation_dom(X4))
| apply(X4,X5) != apply(X4,X6)
| X5 = X6
| ~ one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( in(esk6_1(X4),relation_dom(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( in(esk7_1(X4),relation_dom(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( apply(X4,esk6_1(X4)) = apply(X4,esk7_1(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( esk6_1(X4) != esk7_1(X4)
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[87]) ).
cnf(89,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| esk6_1(X1) != esk7_1(X1) ),
inference(split_conjunct,[status(thm)],[88]) ).
cnf(90,plain,
( one_to_one(X1)
| apply(X1,esk6_1(X1)) = apply(X1,esk7_1(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[88]) ).
cnf(91,plain,
( one_to_one(X1)
| in(esk7_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[88]) ).
cnf(92,plain,
( one_to_one(X1)
| in(esk6_1(X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[88]) ).
fof(100,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(101,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ( relation(function_inverse(X2))
& function(function_inverse(X2)) ) ),
inference(variable_rename,[status(thm)],[100]) ).
fof(102,plain,
! [X2] :
( ( relation(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) )
& ( function(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[101]) ).
cnf(103,plain,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[102]) ).
cnf(104,plain,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[102]) ).
fof(145,plain,
! [X1,X2] :
( ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X2)
| ~ in(X1,relation_rng(X2))
| ( X1 = apply(X2,apply(function_inverse(X2),X1))
& X1 = apply(relation_composition(function_inverse(X2),X2),X1) ) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(146,plain,
! [X3,X4] :
( ~ relation(X4)
| ~ function(X4)
| ~ one_to_one(X4)
| ~ in(X3,relation_rng(X4))
| ( X3 = apply(X4,apply(function_inverse(X4),X3))
& X3 = apply(relation_composition(function_inverse(X4),X4),X3) ) ),
inference(variable_rename,[status(thm)],[145]) ).
fof(147,plain,
! [X3,X4] :
( ( X3 = apply(X4,apply(function_inverse(X4),X3))
| ~ one_to_one(X4)
| ~ in(X3,relation_rng(X4))
| ~ relation(X4)
| ~ function(X4) )
& ( X3 = apply(relation_composition(function_inverse(X4),X4),X3)
| ~ one_to_one(X4)
| ~ in(X3,relation_rng(X4))
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[146]) ).
cnf(149,plain,
( X2 = apply(X1,apply(function_inverse(X1),X2))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[147]) ).
fof(165,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| ! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ( ( X2 != function_inverse(X1)
| ( relation_dom(X2) = relation_rng(X1)
& ! [X3,X4] :
( ( ~ in(X3,relation_rng(X1))
| X4 != apply(X2,X3)
| ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) )
& ( ~ in(X4,relation_dom(X1))
| X3 != apply(X1,X4)
| ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) ) ) ) ) )
& ( relation_dom(X2) != relation_rng(X1)
| ? [X3,X4] :
( ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3)
& ( ~ in(X4,relation_dom(X1))
| X3 != apply(X1,X4) ) )
| ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4)
& ( ~ in(X3,relation_rng(X1))
| X4 != apply(X2,X3) ) ) )
| X2 = function_inverse(X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(166,plain,
! [X5] :
( ~ relation(X5)
| ~ function(X5)
| ~ one_to_one(X5)
| ! [X6] :
( ~ relation(X6)
| ~ function(X6)
| ( ( X6 != function_inverse(X5)
| ( relation_dom(X6) = relation_rng(X5)
& ! [X7,X8] :
( ( ~ in(X7,relation_rng(X5))
| X8 != apply(X6,X7)
| ( in(X8,relation_dom(X5))
& X7 = apply(X5,X8) ) )
& ( ~ in(X8,relation_dom(X5))
| X7 != apply(X5,X8)
| ( in(X7,relation_rng(X5))
& X8 = apply(X6,X7) ) ) ) ) )
& ( relation_dom(X6) != relation_rng(X5)
| ? [X9,X10] :
( ( in(X9,relation_rng(X5))
& X10 = apply(X6,X9)
& ( ~ in(X10,relation_dom(X5))
| X9 != apply(X5,X10) ) )
| ( in(X10,relation_dom(X5))
& X9 = apply(X5,X10)
& ( ~ in(X9,relation_rng(X5))
| X10 != apply(X6,X9) ) ) )
| X6 = function_inverse(X5) ) ) ) ),
inference(variable_rename,[status(thm)],[165]) ).
fof(167,plain,
! [X5] :
( ~ relation(X5)
| ~ function(X5)
| ~ one_to_one(X5)
| ! [X6] :
( ~ relation(X6)
| ~ function(X6)
| ( ( X6 != function_inverse(X5)
| ( relation_dom(X6) = relation_rng(X5)
& ! [X7,X8] :
( ( ~ in(X7,relation_rng(X5))
| X8 != apply(X6,X7)
| ( in(X8,relation_dom(X5))
& X7 = apply(X5,X8) ) )
& ( ~ in(X8,relation_dom(X5))
| X7 != apply(X5,X8)
| ( in(X7,relation_rng(X5))
& X8 = apply(X6,X7) ) ) ) ) )
& ( relation_dom(X6) != relation_rng(X5)
| ( in(esk10_2(X5,X6),relation_rng(X5))
& esk11_2(X5,X6) = apply(X6,esk10_2(X5,X6))
& ( ~ in(esk11_2(X5,X6),relation_dom(X5))
| esk10_2(X5,X6) != apply(X5,esk11_2(X5,X6)) ) )
| ( in(esk11_2(X5,X6),relation_dom(X5))
& esk10_2(X5,X6) = apply(X5,esk11_2(X5,X6))
& ( ~ in(esk10_2(X5,X6),relation_rng(X5))
| esk11_2(X5,X6) != apply(X6,esk10_2(X5,X6)) ) )
| X6 = function_inverse(X5) ) ) ) ),
inference(skolemize,[status(esa)],[166]) ).
fof(168,plain,
! [X5,X6,X7,X8] :
( ( ( ( ( ~ in(X7,relation_rng(X5))
| X8 != apply(X6,X7)
| ( in(X8,relation_dom(X5))
& X7 = apply(X5,X8) ) )
& ( ~ in(X8,relation_dom(X5))
| X7 != apply(X5,X8)
| ( in(X7,relation_rng(X5))
& X8 = apply(X6,X7) ) )
& relation_dom(X6) = relation_rng(X5) )
| X6 != function_inverse(X5) )
& ( relation_dom(X6) != relation_rng(X5)
| ( in(esk10_2(X5,X6),relation_rng(X5))
& esk11_2(X5,X6) = apply(X6,esk10_2(X5,X6))
& ( ~ in(esk11_2(X5,X6),relation_dom(X5))
| esk10_2(X5,X6) != apply(X5,esk11_2(X5,X6)) ) )
| ( in(esk11_2(X5,X6),relation_dom(X5))
& esk10_2(X5,X6) = apply(X5,esk11_2(X5,X6))
& ( ~ in(esk10_2(X5,X6),relation_rng(X5))
| esk11_2(X5,X6) != apply(X6,esk10_2(X5,X6)) ) )
| X6 = function_inverse(X5) ) )
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) ),
inference(shift_quantors,[status(thm)],[167]) ).
fof(169,plain,
! [X5,X6,X7,X8] :
( ( in(X8,relation_dom(X5))
| ~ in(X7,relation_rng(X5))
| X8 != apply(X6,X7)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( X7 = apply(X5,X8)
| ~ in(X7,relation_rng(X5))
| X8 != apply(X6,X7)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(X7,relation_rng(X5))
| ~ in(X8,relation_dom(X5))
| X7 != apply(X5,X8)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( X8 = apply(X6,X7)
| ~ in(X8,relation_dom(X5))
| X7 != apply(X5,X8)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( relation_dom(X6) = relation_rng(X5)
| X6 != function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk11_2(X5,X6),relation_dom(X5))
| in(esk10_2(X5,X6),relation_rng(X5))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk10_2(X5,X6) = apply(X5,esk11_2(X5,X6))
| in(esk10_2(X5,X6),relation_rng(X5))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(esk10_2(X5,X6),relation_rng(X5))
| esk11_2(X5,X6) != apply(X6,esk10_2(X5,X6))
| in(esk10_2(X5,X6),relation_rng(X5))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk11_2(X5,X6),relation_dom(X5))
| esk11_2(X5,X6) = apply(X6,esk10_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk10_2(X5,X6) = apply(X5,esk11_2(X5,X6))
| esk11_2(X5,X6) = apply(X6,esk10_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(esk10_2(X5,X6),relation_rng(X5))
| esk11_2(X5,X6) != apply(X6,esk10_2(X5,X6))
| esk11_2(X5,X6) = apply(X6,esk10_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk11_2(X5,X6),relation_dom(X5))
| ~ in(esk11_2(X5,X6),relation_dom(X5))
| esk10_2(X5,X6) != apply(X5,esk11_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk10_2(X5,X6) = apply(X5,esk11_2(X5,X6))
| ~ in(esk11_2(X5,X6),relation_dom(X5))
| esk10_2(X5,X6) != apply(X5,esk11_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(esk10_2(X5,X6),relation_rng(X5))
| esk11_2(X5,X6) != apply(X6,esk10_2(X5,X6))
| ~ in(esk11_2(X5,X6),relation_dom(X5))
| esk10_2(X5,X6) != apply(X5,esk11_2(X5,X6))
| relation_dom(X6) != relation_rng(X5)
| X6 = function_inverse(X5)
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[168]) ).
cnf(179,plain,
( relation_dom(X2) = relation_rng(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1) ),
inference(split_conjunct,[status(thm)],[169]) ).
cnf(253,plain,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(function_inverse(X1))
| ~ function(X1)
| ~ relation(function_inverse(X1))
| ~ relation(X1) ),
inference(er,[status(thm)],[179,theory(equality)]) ).
cnf(254,plain,
( apply(X1,apply(function_inverse(X1),esk6_1(function_inverse(X1)))) = esk7_1(function_inverse(X1))
| one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ in(esk7_1(function_inverse(X1)),relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(function_inverse(X1))
| ~ relation(function_inverse(X1)) ),
inference(spm,[status(thm)],[149,90,theory(equality)]) ).
cnf(586,plain,
( relation_dom(function_inverse(X1)) = relation_rng(X1)
| ~ one_to_one(X1)
| ~ function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[253,104]) ).
cnf(587,plain,
( relation_dom(function_inverse(X1)) = relation_rng(X1)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[586,103]) ).
cnf(591,plain,
( one_to_one(function_inverse(X1))
| in(esk6_1(function_inverse(X1)),relation_rng(X1))
| ~ function(function_inverse(X1))
| ~ relation(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[92,587,theory(equality)]) ).
cnf(592,plain,
( one_to_one(function_inverse(X1))
| in(esk7_1(function_inverse(X1)),relation_rng(X1))
| ~ function(function_inverse(X1))
| ~ relation(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[91,587,theory(equality)]) ).
cnf(630,plain,
( apply(X1,apply(function_inverse(X1),esk6_1(function_inverse(X1)))) = esk7_1(function_inverse(X1))
| one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ in(esk7_1(function_inverse(X1)),relation_rng(X1))
| ~ function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[254,104]) ).
cnf(631,plain,
( apply(X1,apply(function_inverse(X1),esk6_1(function_inverse(X1)))) = esk7_1(function_inverse(X1))
| one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ in(esk7_1(function_inverse(X1)),relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[630,103]) ).
cnf(633,plain,
( esk7_1(function_inverse(X1)) = esk6_1(function_inverse(X1))
| one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ in(esk6_1(function_inverse(X1)),relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(esk7_1(function_inverse(X1)),relation_rng(X1)) ),
inference(spm,[status(thm)],[149,631,theory(equality)]) ).
cnf(6801,plain,
( one_to_one(function_inverse(X1))
| in(esk6_1(function_inverse(X1)),relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[591,104]) ).
cnf(6802,plain,
( one_to_one(function_inverse(X1))
| in(esk6_1(function_inverse(X1)),relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[6801,103]) ).
cnf(6886,plain,
( one_to_one(function_inverse(X1))
| in(esk7_1(function_inverse(X1)),relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[592,104]) ).
cnf(6887,plain,
( one_to_one(function_inverse(X1))
| in(esk7_1(function_inverse(X1)),relation_rng(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[6886,103]) ).
cnf(9210,plain,
( esk7_1(function_inverse(X1)) = esk6_1(function_inverse(X1))
| one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ in(esk6_1(function_inverse(X1)),relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[633,6887]) ).
cnf(9211,plain,
( esk7_1(function_inverse(X1)) = esk6_1(function_inverse(X1))
| one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[9210,6802]) ).
cnf(9213,plain,
( one_to_one(function_inverse(X1))
| ~ function(function_inverse(X1))
| ~ relation(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[89,9211,theory(equality)]) ).
cnf(9248,plain,
( one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[9213,104]) ).
cnf(9249,plain,
( one_to_one(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[9248,103]) ).
cnf(9251,negated_conjecture,
( ~ one_to_one(esk5_0)
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(spm,[status(thm)],[80,9249,theory(equality)]) ).
cnf(9274,negated_conjecture,
( $false
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[9251,81,theory(equality)]) ).
cnf(9275,negated_conjecture,
( $false
| $false
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[9274,82,theory(equality)]) ).
cnf(9276,negated_conjecture,
( $false
| $false
| $false ),
inference(rw,[status(thm)],[9275,83,theory(equality)]) ).
cnf(9277,negated_conjecture,
$false,
inference(cn,[status(thm)],[9276,theory(equality)]) ).
cnf(9278,negated_conjecture,
$false,
9277,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU221+1.p
% --creating new selector for []
% -running prover on /tmp/tmpJAusTU/sel_SEU221+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU221+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU221+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU221+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------