%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU220+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 05:47:11 EST 2010
% Result : Theorem 6.79s
% Output : CNFRefutation 6.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 8 unt; 0 def)
% Number of atoms : 482 ( 148 equ)
% Maximal formula atoms : 130 ( 8 avg)
% Number of connectives : 725 ( 301 ~; 321 |; 87 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 91 ( 0 sgn 48 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(9,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/tmp/tmpvhk_eF/sel_SEU220+1.p_1',t23_funct_1) ).
fof(12,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/tmp/tmpvhk_eF/sel_SEU220+1.p_1',dt_k2_funct_1) ).
fof(19,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_rng(X1) = relation_dom(function_inverse(X1))
& relation_dom(X1) = relation_rng(function_inverse(X1)) ) ) ),
file('/tmp/tmpvhk_eF/sel_SEU220+1.p_1',t55_funct_1) ).
fof(26,conjecture,
! [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/tmpvhk_eF/sel_SEU220+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/tmpvhk_eF/sel_SEU220+1.p_1',t54_funct_1) ).
fof(40,negated_conjecture,
~ ! [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(assume_negation,[status(cth)],[26]) ).
fof(77,plain,
! [X1,X2] :
( ~ relation(X2)
| ~ function(X2)
| ! [X3] :
( ~ relation(X3)
| ~ function(X3)
| ~ in(X1,relation_dom(X2))
| apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(78,plain,
! [X4,X5] :
( ~ relation(X5)
| ~ function(X5)
| ! [X6] :
( ~ relation(X6)
| ~ function(X6)
| ~ in(X4,relation_dom(X5))
| apply(relation_composition(X5,X6),X4) = apply(X6,apply(X5,X4)) ) ),
inference(variable_rename,[status(thm)],[77]) ).
fof(79,plain,
! [X4,X5,X6] :
( ~ relation(X6)
| ~ function(X6)
| ~ in(X4,relation_dom(X5))
| apply(relation_composition(X5,X6),X4) = apply(X6,apply(X5,X4))
| ~ relation(X5)
| ~ function(X5) ),
inference(shift_quantors,[status(thm)],[78]) ).
cnf(80,plain,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X3,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[79]) ).
fof(87,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(88,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ( relation(function_inverse(X2))
& function(function_inverse(X2)) ) ),
inference(variable_rename,[status(thm)],[87]) ).
fof(89,plain,
! [X2] :
( ( relation(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) )
& ( function(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[88]) ).
cnf(90,plain,
( function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[89]) ).
cnf(91,plain,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[89]) ).
fof(110,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1)
| ( relation_rng(X1) = relation_dom(function_inverse(X1))
& relation_dom(X1) = relation_rng(function_inverse(X1)) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(111,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X2)
| ( relation_rng(X2) = relation_dom(function_inverse(X2))
& relation_dom(X2) = relation_rng(function_inverse(X2)) ) ),
inference(variable_rename,[status(thm)],[110]) ).
fof(112,plain,
! [X2] :
( ( relation_rng(X2) = relation_dom(function_inverse(X2))
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) )
& ( relation_dom(X2) = relation_rng(function_inverse(X2))
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[111]) ).
cnf(114,plain,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[112]) ).
fof(137,negated_conjecture,
? [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)],[40]) ).
fof(138,negated_conjecture,
? [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)],[137]) ).
fof(139,negated_conjecture,
( relation(esk6_0)
& function(esk6_0)
& one_to_one(esk6_0)
& in(esk5_0,relation_rng(esk6_0))
& ( esk5_0 != apply(esk6_0,apply(function_inverse(esk6_0),esk5_0))
| esk5_0 != apply(relation_composition(function_inverse(esk6_0),esk6_0),esk5_0) ) ),
inference(skolemize,[status(esa)],[138]) ).
cnf(140,negated_conjecture,
( esk5_0 != apply(relation_composition(function_inverse(esk6_0),esk6_0),esk5_0)
| esk5_0 != apply(esk6_0,apply(function_inverse(esk6_0),esk5_0)) ),
inference(split_conjunct,[status(thm)],[139]) ).
cnf(141,negated_conjecture,
in(esk5_0,relation_rng(esk6_0)),
inference(split_conjunct,[status(thm)],[139]) ).
cnf(142,negated_conjecture,
one_to_one(esk6_0),
inference(split_conjunct,[status(thm)],[139]) ).
cnf(143,negated_conjecture,
function(esk6_0),
inference(split_conjunct,[status(thm)],[139]) ).
cnf(144,negated_conjecture,
relation(esk6_0),
inference(split_conjunct,[status(thm)],[139]) ).
fof(160,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(161,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)],[160]) ).
fof(162,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(esk9_2(X5,X6),relation_rng(X5))
& esk10_2(X5,X6) = apply(X6,esk9_2(X5,X6))
& ( ~ in(esk10_2(X5,X6),relation_dom(X5))
| esk9_2(X5,X6) != apply(X5,esk10_2(X5,X6)) ) )
| ( in(esk10_2(X5,X6),relation_dom(X5))
& esk9_2(X5,X6) = apply(X5,esk10_2(X5,X6))
& ( ~ in(esk9_2(X5,X6),relation_rng(X5))
| esk10_2(X5,X6) != apply(X6,esk9_2(X5,X6)) ) )
| X6 = function_inverse(X5) ) ) ) ),
inference(skolemize,[status(esa)],[161]) ).
fof(163,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(esk9_2(X5,X6),relation_rng(X5))
& esk10_2(X5,X6) = apply(X6,esk9_2(X5,X6))
& ( ~ in(esk10_2(X5,X6),relation_dom(X5))
| esk9_2(X5,X6) != apply(X5,esk10_2(X5,X6)) ) )
| ( in(esk10_2(X5,X6),relation_dom(X5))
& esk9_2(X5,X6) = apply(X5,esk10_2(X5,X6))
& ( ~ in(esk9_2(X5,X6),relation_rng(X5))
| esk10_2(X5,X6) != apply(X6,esk9_2(X5,X6)) ) )
| X6 = function_inverse(X5) ) )
| ~ relation(X6)
| ~ function(X6)
| ~ one_to_one(X5)
| ~ relation(X5)
| ~ function(X5) ),
inference(shift_quantors,[status(thm)],[162]) ).
fof(164,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(esk10_2(X5,X6),relation_dom(X5))
| in(esk9_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) )
& ( esk9_2(X5,X6) = apply(X5,esk10_2(X5,X6))
| in(esk9_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(esk9_2(X5,X6),relation_rng(X5))
| esk10_2(X5,X6) != apply(X6,esk9_2(X5,X6))
| in(esk9_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_dom(X5))
| esk10_2(X5,X6) = apply(X6,esk9_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) )
& ( esk9_2(X5,X6) = apply(X5,esk10_2(X5,X6))
| esk10_2(X5,X6) = apply(X6,esk9_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(esk9_2(X5,X6),relation_rng(X5))
| esk10_2(X5,X6) != apply(X6,esk9_2(X5,X6))
| esk10_2(X5,X6) = apply(X6,esk9_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_dom(X5))
| ~ in(esk10_2(X5,X6),relation_dom(X5))
| esk9_2(X5,X6) != apply(X5,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) )
& ( esk9_2(X5,X6) = apply(X5,esk10_2(X5,X6))
| ~ in(esk10_2(X5,X6),relation_dom(X5))
| esk9_2(X5,X6) != apply(X5,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(esk9_2(X5,X6),relation_rng(X5))
| esk10_2(X5,X6) != apply(X6,esk9_2(X5,X6))
| ~ in(esk10_2(X5,X6),relation_dom(X5))
| esk9_2(X5,X6) != apply(X5,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) ) ),
inference(distribute,[status(thm)],[163]) ).
cnf(177,plain,
( X4 = apply(X1,X3)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1)
| ~ function(X2)
| ~ relation(X2)
| X2 != function_inverse(X1)
| X3 != apply(X2,X4)
| ~ in(X4,relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[164]) ).
cnf(308,plain,
( apply(relation_composition(function_inverse(X1),X2),X3) = apply(X2,apply(function_inverse(X1),X3))
| ~ in(X3,relation_rng(X1))
| ~ function(X2)
| ~ function(function_inverse(X1))
| ~ relation(X2)
| ~ relation(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[80,114,theory(equality)]) ).
cnf(309,plain,
( apply(X1,X2) = X3
| apply(function_inverse(X1),X3) != X2
| ~ one_to_one(X1)
| ~ in(X3,relation_rng(X1))
| ~ function(function_inverse(X1))
| ~ function(X1)
| ~ relation(function_inverse(X1))
| ~ relation(X1) ),
inference(er,[status(thm)],[177,theory(equality)]) ).
cnf(2337,plain,
( apply(relation_composition(function_inverse(X1),X2),X3) = apply(X2,apply(function_inverse(X1),X3))
| ~ one_to_one(X1)
| ~ in(X3,relation_rng(X1))
| ~ function(function_inverse(X1))
| ~ function(X1)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(csr,[status(thm)],[308,91]) ).
cnf(2338,plain,
( apply(relation_composition(function_inverse(X1),X2),X3) = apply(X2,apply(function_inverse(X1),X3))
| ~ one_to_one(X1)
| ~ in(X3,relation_rng(X1))
| ~ function(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(csr,[status(thm)],[2337,90]) ).
cnf(2339,negated_conjecture,
( apply(relation_composition(function_inverse(esk6_0),X1),esk5_0) = apply(X1,apply(function_inverse(esk6_0),esk5_0))
| ~ one_to_one(esk6_0)
| ~ function(X1)
| ~ function(esk6_0)
| ~ relation(X1)
| ~ relation(esk6_0) ),
inference(spm,[status(thm)],[2338,141,theory(equality)]) ).
cnf(2357,negated_conjecture,
( apply(relation_composition(function_inverse(esk6_0),X1),esk5_0) = apply(X1,apply(function_inverse(esk6_0),esk5_0))
| $false
| ~ function(X1)
| ~ function(esk6_0)
| ~ relation(X1)
| ~ relation(esk6_0) ),
inference(rw,[status(thm)],[2339,142,theory(equality)]) ).
cnf(2358,negated_conjecture,
( apply(relation_composition(function_inverse(esk6_0),X1),esk5_0) = apply(X1,apply(function_inverse(esk6_0),esk5_0))
| $false
| ~ function(X1)
| $false
| ~ relation(X1)
| ~ relation(esk6_0) ),
inference(rw,[status(thm)],[2357,143,theory(equality)]) ).
cnf(2359,negated_conjecture,
( apply(relation_composition(function_inverse(esk6_0),X1),esk5_0) = apply(X1,apply(function_inverse(esk6_0),esk5_0))
| $false
| ~ function(X1)
| $false
| ~ relation(X1)
| $false ),
inference(rw,[status(thm)],[2358,144,theory(equality)]) ).
cnf(2360,negated_conjecture,
( apply(relation_composition(function_inverse(esk6_0),X1),esk5_0) = apply(X1,apply(function_inverse(esk6_0),esk5_0))
| ~ function(X1)
| ~ relation(X1) ),
inference(cn,[status(thm)],[2359,theory(equality)]) ).
cnf(2363,plain,
( apply(X1,X2) = X3
| apply(function_inverse(X1),X3) != X2
| ~ one_to_one(X1)
| ~ in(X3,relation_rng(X1))
| ~ function(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[309,91]) ).
cnf(2364,plain,
( apply(X1,X2) = X3
| apply(function_inverse(X1),X3) != X2
| ~ one_to_one(X1)
| ~ in(X3,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[2363,90]) ).
cnf(2365,plain,
( apply(X1,apply(function_inverse(X1),X2)) = X2
| ~ one_to_one(X1)
| ~ in(X2,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(er,[status(thm)],[2364,theory(equality)]) ).
cnf(64667,negated_conjecture,
( apply(esk6_0,apply(function_inverse(esk6_0),esk5_0)) = esk5_0
| ~ one_to_one(esk6_0)
| ~ function(esk6_0)
| ~ relation(esk6_0) ),
inference(spm,[status(thm)],[2365,141,theory(equality)]) ).
cnf(64700,negated_conjecture,
( apply(esk6_0,apply(function_inverse(esk6_0),esk5_0)) = esk5_0
| $false
| ~ function(esk6_0)
| ~ relation(esk6_0) ),
inference(rw,[status(thm)],[64667,142,theory(equality)]) ).
cnf(64701,negated_conjecture,
( apply(esk6_0,apply(function_inverse(esk6_0),esk5_0)) = esk5_0
| $false
| $false
| ~ relation(esk6_0) ),
inference(rw,[status(thm)],[64700,143,theory(equality)]) ).
cnf(64702,negated_conjecture,
( apply(esk6_0,apply(function_inverse(esk6_0),esk5_0)) = esk5_0
| $false
| $false
| $false ),
inference(rw,[status(thm)],[64701,144,theory(equality)]) ).
cnf(64703,negated_conjecture,
apply(esk6_0,apply(function_inverse(esk6_0),esk5_0)) = esk5_0,
inference(cn,[status(thm)],[64702,theory(equality)]) ).
cnf(64851,negated_conjecture,
( $false
| apply(relation_composition(function_inverse(esk6_0),esk6_0),esk5_0) != esk5_0 ),
inference(rw,[status(thm)],[140,64703,theory(equality)]) ).
cnf(64852,negated_conjecture,
apply(relation_composition(function_inverse(esk6_0),esk6_0),esk5_0) != esk5_0,
inference(cn,[status(thm)],[64851,theory(equality)]) ).
cnf(64935,negated_conjecture,
( apply(esk6_0,apply(function_inverse(esk6_0),esk5_0)) != esk5_0
| ~ function(esk6_0)
| ~ relation(esk6_0) ),
inference(spm,[status(thm)],[64852,2360,theory(equality)]) ).
cnf(64955,negated_conjecture,
( $false
| ~ function(esk6_0)
| ~ relation(esk6_0) ),
inference(rw,[status(thm)],[64935,64703,theory(equality)]) ).
cnf(64956,negated_conjecture,
( $false
| $false
| ~ relation(esk6_0) ),
inference(rw,[status(thm)],[64955,143,theory(equality)]) ).
cnf(64957,negated_conjecture,
( $false
| $false
| $false ),
inference(rw,[status(thm)],[64956,144,theory(equality)]) ).
cnf(64958,negated_conjecture,
$false,
inference(cn,[status(thm)],[64957,theory(equality)]) ).
cnf(64959,negated_conjecture,
$false,
64958,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU220+1.p
% --creating new selector for []
% -running prover on /tmp/tmpvhk_eF/sel_SEU220+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU220+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU220+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU220+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
%
%------------------------------------------------------------------------------