TSTP Solution File: SEU026+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU026+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 04:12:01 EST 2010
% Result : Theorem 0.56s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 9 unt; 0 def)
% Number of atoms : 212 ( 53 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 279 ( 122 ~; 121 |; 23 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 50 ( 2 sgn 30 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(10,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_dom(relation_composition(function_inverse(X1),X1)) = relation_rng(X1)
& relation_rng(relation_composition(function_inverse(X1),X1)) = relation_rng(X1) ) ) ),
file('/tmp/tmpqcW46y/sel_SEU026+1.p_1',t59_funct_1) ).
fof(11,axiom,
! [X1,X2] : subset(X1,X1),
file('/tmp/tmpqcW46y/sel_SEU026+1.p_1',reflexivity_r1_tarski) ).
fof(15,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/tmp/tmpqcW46y/sel_SEU026+1.p_1',dt_k2_funct_1) ).
fof(17,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_rng(X1),relation_dom(X2))
=> relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ) ),
file('/tmp/tmpqcW46y/sel_SEU026+1.p_1',t46_relat_1) ).
fof(20,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(relation_dom(X1),relation_rng(X2))
=> relation_rng(relation_composition(X2,X1)) = relation_rng(X1) ) ) ),
file('/tmp/tmpqcW46y/sel_SEU026+1.p_1',t47_relat_1) ).
fof(38,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/tmpqcW46y/sel_SEU026+1.p_1',t55_funct_1) ).
fof(42,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_dom(relation_composition(function_inverse(X1),X1)) = relation_rng(X1)
& relation_rng(relation_composition(function_inverse(X1),X1)) = relation_rng(X1) ) ) ),
inference(assume_negation,[status(cth)],[10]) ).
fof(85,negated_conjecture,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& ( relation_dom(relation_composition(function_inverse(X1),X1)) != relation_rng(X1)
| relation_rng(relation_composition(function_inverse(X1),X1)) != relation_rng(X1) ) ),
inference(fof_nnf,[status(thm)],[42]) ).
fof(86,negated_conjecture,
? [X2] :
( relation(X2)
& function(X2)
& one_to_one(X2)
& ( relation_dom(relation_composition(function_inverse(X2),X2)) != relation_rng(X2)
| relation_rng(relation_composition(function_inverse(X2),X2)) != relation_rng(X2) ) ),
inference(variable_rename,[status(thm)],[85]) ).
fof(87,negated_conjecture,
( relation(esk5_0)
& function(esk5_0)
& one_to_one(esk5_0)
& ( relation_dom(relation_composition(function_inverse(esk5_0),esk5_0)) != relation_rng(esk5_0)
| relation_rng(relation_composition(function_inverse(esk5_0),esk5_0)) != relation_rng(esk5_0) ) ),
inference(skolemize,[status(esa)],[86]) ).
cnf(88,negated_conjecture,
( relation_rng(relation_composition(function_inverse(esk5_0),esk5_0)) != relation_rng(esk5_0)
| relation_dom(relation_composition(function_inverse(esk5_0),esk5_0)) != relation_rng(esk5_0) ),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(89,negated_conjecture,
one_to_one(esk5_0),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(90,negated_conjecture,
function(esk5_0),
inference(split_conjunct,[status(thm)],[87]) ).
cnf(91,negated_conjecture,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[87]) ).
fof(92,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[11]) ).
cnf(93,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[92]) ).
fof(103,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(104,plain,
! [X2] :
( ~ relation(X2)
| ~ function(X2)
| ( relation(function_inverse(X2))
& function(function_inverse(X2)) ) ),
inference(variable_rename,[status(thm)],[103]) ).
fof(105,plain,
! [X2] :
( ( relation(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) )
& ( function(function_inverse(X2))
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[104]) ).
cnf(107,plain,
( relation(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[105]) ).
fof(111,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ~ subset(relation_rng(X1),relation_dom(X2))
| relation_dom(relation_composition(X1,X2)) = relation_dom(X1) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(112,plain,
! [X3] :
( ~ relation(X3)
| ! [X4] :
( ~ relation(X4)
| ~ subset(relation_rng(X3),relation_dom(X4))
| relation_dom(relation_composition(X3,X4)) = relation_dom(X3) ) ),
inference(variable_rename,[status(thm)],[111]) ).
fof(113,plain,
! [X3,X4] :
( ~ relation(X4)
| ~ subset(relation_rng(X3),relation_dom(X4))
| relation_dom(relation_composition(X3,X4)) = relation_dom(X3)
| ~ relation(X3) ),
inference(shift_quantors,[status(thm)],[112]) ).
cnf(114,plain,
( relation_dom(relation_composition(X1,X2)) = relation_dom(X1)
| ~ relation(X1)
| ~ subset(relation_rng(X1),relation_dom(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[113]) ).
fof(120,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ~ subset(relation_dom(X1),relation_rng(X2))
| relation_rng(relation_composition(X2,X1)) = relation_rng(X1) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(121,plain,
! [X3] :
( ~ relation(X3)
| ! [X4] :
( ~ relation(X4)
| ~ subset(relation_dom(X3),relation_rng(X4))
| relation_rng(relation_composition(X4,X3)) = relation_rng(X3) ) ),
inference(variable_rename,[status(thm)],[120]) ).
fof(122,plain,
! [X3,X4] :
( ~ relation(X4)
| ~ subset(relation_dom(X3),relation_rng(X4))
| relation_rng(relation_composition(X4,X3)) = relation_rng(X3)
| ~ relation(X3) ),
inference(shift_quantors,[status(thm)],[121]) ).
cnf(123,plain,
( relation_rng(relation_composition(X2,X1)) = relation_rng(X1)
| ~ relation(X1)
| ~ subset(relation_dom(X1),relation_rng(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[122]) ).
fof(186,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)],[38]) ).
fof(187,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)],[186]) ).
fof(188,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)],[187]) ).
cnf(189,plain,
( relation_dom(X1) = relation_rng(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[188]) ).
cnf(190,plain,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[188]) ).
cnf(244,plain,
( relation_dom(relation_composition(function_inverse(X1),X2)) = relation_dom(function_inverse(X1))
| ~ subset(relation_dom(X1),relation_dom(X2))
| ~ relation(X2)
| ~ relation(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[114,189,theory(equality)]) ).
cnf(254,plain,
( relation_rng(relation_composition(function_inverse(X1),X2)) = relation_rng(X2)
| ~ subset(relation_dom(X2),relation_dom(X1))
| ~ relation(function_inverse(X1))
| ~ relation(X2)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[123,189,theory(equality)]) ).
cnf(704,plain,
( relation_dom(relation_composition(function_inverse(X1),X2)) = relation_dom(function_inverse(X1))
| ~ subset(relation_dom(X1),relation_dom(X2))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(csr,[status(thm)],[244,107]) ).
cnf(705,plain,
( relation_dom(relation_composition(function_inverse(X1),X1)) = relation_dom(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[704,93,theory(equality)]) ).
cnf(1016,plain,
( relation_rng(relation_composition(function_inverse(X1),X2)) = relation_rng(X2)
| ~ subset(relation_dom(X2),relation_dom(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(csr,[status(thm)],[254,107]) ).
cnf(1017,plain,
( relation_rng(relation_composition(function_inverse(X1),X1)) = relation_rng(X1)
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[1016,93,theory(equality)]) ).
cnf(8299,negated_conjecture,
( relation_dom(function_inverse(esk5_0)) != relation_rng(esk5_0)
| relation_rng(relation_composition(function_inverse(esk5_0),esk5_0)) != relation_rng(esk5_0)
| ~ one_to_one(esk5_0)
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(spm,[status(thm)],[88,705,theory(equality)]) ).
cnf(8355,negated_conjecture,
( relation_dom(function_inverse(esk5_0)) != relation_rng(esk5_0)
| relation_rng(relation_composition(function_inverse(esk5_0),esk5_0)) != relation_rng(esk5_0)
| $false
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[8299,89,theory(equality)]) ).
cnf(8356,negated_conjecture,
( relation_dom(function_inverse(esk5_0)) != relation_rng(esk5_0)
| relation_rng(relation_composition(function_inverse(esk5_0),esk5_0)) != relation_rng(esk5_0)
| $false
| $false
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[8355,90,theory(equality)]) ).
cnf(8357,negated_conjecture,
( relation_dom(function_inverse(esk5_0)) != relation_rng(esk5_0)
| relation_rng(relation_composition(function_inverse(esk5_0),esk5_0)) != relation_rng(esk5_0)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[8356,91,theory(equality)]) ).
cnf(8358,negated_conjecture,
( relation_dom(function_inverse(esk5_0)) != relation_rng(esk5_0)
| relation_rng(relation_composition(function_inverse(esk5_0),esk5_0)) != relation_rng(esk5_0) ),
inference(cn,[status(thm)],[8357,theory(equality)]) ).
cnf(8748,negated_conjecture,
( relation_dom(function_inverse(esk5_0)) != relation_rng(esk5_0)
| ~ one_to_one(esk5_0)
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(spm,[status(thm)],[8358,1017,theory(equality)]) ).
cnf(8771,negated_conjecture,
( relation_dom(function_inverse(esk5_0)) != relation_rng(esk5_0)
| $false
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[8748,89,theory(equality)]) ).
cnf(8772,negated_conjecture,
( relation_dom(function_inverse(esk5_0)) != relation_rng(esk5_0)
| $false
| $false
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[8771,90,theory(equality)]) ).
cnf(8773,negated_conjecture,
( relation_dom(function_inverse(esk5_0)) != relation_rng(esk5_0)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[8772,91,theory(equality)]) ).
cnf(8774,negated_conjecture,
relation_dom(function_inverse(esk5_0)) != relation_rng(esk5_0),
inference(cn,[status(thm)],[8773,theory(equality)]) ).
cnf(8775,negated_conjecture,
( ~ one_to_one(esk5_0)
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(spm,[status(thm)],[8774,190,theory(equality)]) ).
cnf(8786,negated_conjecture,
( $false
| ~ function(esk5_0)
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[8775,89,theory(equality)]) ).
cnf(8787,negated_conjecture,
( $false
| $false
| ~ relation(esk5_0) ),
inference(rw,[status(thm)],[8786,90,theory(equality)]) ).
cnf(8788,negated_conjecture,
( $false
| $false
| $false ),
inference(rw,[status(thm)],[8787,91,theory(equality)]) ).
cnf(8789,negated_conjecture,
$false,
inference(cn,[status(thm)],[8788,theory(equality)]) ).
cnf(8790,negated_conjecture,
$false,
8789,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU026+1.p
% --creating new selector for []
% -running prover on /tmp/tmpqcW46y/sel_SEU026+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU026+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU026+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU026+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
%
%------------------------------------------------------------------------------