## TSTP Solution File: KLE089+1 by SInE---0.4

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KLE089+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art09.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 : Sat Dec 25 12:14:09 EST 2010

% Result   : Theorem 0.17s
% Output   : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   33 (  27 unt;   0 def)
%            Number of atoms       :   39 (  37 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   13 (   7   ~;   0   |;   3   &)
%                                         (   0 <=>;   1  =>;   2  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   40 (   0 sgn  22   !;   4   ?)

%------------------------------------------------------------------------------
fof(3,axiom,
! [X1] : addition(X1,zero) = X1,

fof(4,axiom,
file('/tmp/tmpo4CkMI/sel_KLE089+1.p_1',left_distributivity) ).

fof(5,axiom,

fof(16,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/tmp/tmpo4CkMI/sel_KLE089+1.p_1',domain1) ).

fof(18,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/tmp/tmpo4CkMI/sel_KLE089+1.p_1',domain4) ).

fof(19,conjecture,
! [X4,X5] :
( multiplication(domain(X4),X5) = zero
file('/tmp/tmpo4CkMI/sel_KLE089+1.p_1',goals) ).

fof(20,negated_conjecture,
~ ! [X4,X5] :
( multiplication(domain(X4),X5) = zero
inference(assume_negation,[status(cth)],[19]) ).

fof(21,negated_conjecture,
~ ! [X4,X5] :
=> multiplication(domain(X4),X5) = zero ),
inference(fof_simplification,[status(thm)],[20,theory(equality)]) ).

fof(26,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[3]) ).

cnf(27,plain,
inference(split_conjunct,[status(thm)],[26]) ).

fof(28,plain,
inference(variable_rename,[status(thm)],[4]) ).

cnf(29,plain,
inference(split_conjunct,[status(thm)],[28]) ).

fof(30,plain,
inference(variable_rename,[status(thm)],[5]) ).

cnf(31,plain,
inference(split_conjunct,[status(thm)],[30]) ).

fof(52,plain,
! [X5] : multiplication(antidomain(X5),X5) = zero,
inference(variable_rename,[status(thm)],[16]) ).

cnf(53,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[52]) ).

fof(56,plain,
! [X5] : domain(X5) = antidomain(antidomain(X5)),
inference(variable_rename,[status(thm)],[18]) ).

cnf(57,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[56]) ).

fof(58,negated_conjecture,
? [X4,X5] :
& multiplication(domain(X4),X5) != zero ),
inference(fof_nnf,[status(thm)],[21]) ).

fof(59,negated_conjecture,
? [X6,X7] :
& multiplication(domain(X6),X7) != zero ),
inference(variable_rename,[status(thm)],[58]) ).

fof(60,negated_conjecture,
& multiplication(domain(esk1_0),esk2_0) != zero ),
inference(skolemize,[status(esa)],[59]) ).

cnf(61,negated_conjecture,
multiplication(domain(esk1_0),esk2_0) != zero,
inference(split_conjunct,[status(thm)],[60]) ).

cnf(62,negated_conjecture,
inference(split_conjunct,[status(thm)],[60]) ).

cnf(63,negated_conjecture,
inference(rw,[status(thm)],[62,57,theory(equality)]),
[unfolding] ).

cnf(64,negated_conjecture,
multiplication(antidomain(antidomain(esk1_0)),esk2_0) != zero,
inference(rw,[status(thm)],[61,57,theory(equality)]),
[unfolding] ).

cnf(73,negated_conjecture,
inference(rw,[status(thm)],[63,31,theory(equality)]) ).

cnf(163,plain,
inference(spm,[status(thm)],[29,53,theory(equality)]) ).

cnf(184,plain,
inference(rw,[status(thm)],[163,27,theory(equality)]) ).

cnf(491,plain,
inference(spm,[status(thm)],[184,31,theory(equality)]) ).

cnf(532,negated_conjecture,
multiplication(antidomain(esk2_0),esk2_0) = multiplication(antidomain(antidomain(esk1_0)),esk2_0),
inference(spm,[status(thm)],[491,73,theory(equality)]) ).

cnf(553,negated_conjecture,
zero = multiplication(antidomain(antidomain(esk1_0)),esk2_0),
inference(rw,[status(thm)],[532,53,theory(equality)]) ).

cnf(554,negated_conjecture,
\$false,
inference(sr,[status(thm)],[553,64,theory(equality)]) ).

cnf(555,negated_conjecture,
\$false,
554,
[proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE089+1.p
% --creating new selector for [KLE001+0.ax, KLE001+4.ax]
% -running prover on /tmp/tmpo4CkMI/sel_KLE089+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE089+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE089+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE089+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
%
%------------------------------------------------------------------------------
```