============================== Prover9 ===============================
Prover9 (32) version August-2006A, August 2006.
Process 10668 was started by mccune on cleo.thornwood,
Sat Aug 12 20:57:46 2006
The command was "/home/mccune/bin/prover9 -f idempotent.in".
============================== end of head ===========================

============================== INPUT =================================

% Reading from file idempotent.in


formulas(sos).
(x * e) * x = x.
x * (x * y) = y.
(x * y) * (z * u) = (x * z) * (y * u).
((x * x) * x) * x = e.
end_of_list.

formulas(goals).
e * e = e.
end_of_list.

============================== end of input ==========================

============================== PROCESS NON-CLAUSAL FORMULAS ==========

% Formulas that are not ordinary clauses:
1 e * e = e.  [goal].

============================== end of process non-clausal formulas ===

============================== PROCESS INITIAL CLAUSES ===============

% Clauses before input processing:

formulas(usable).
end_of_list.

formulas(sos).
(x * e) * x = x.  [assumption].
x * (x * y) = y.  [assumption].
(x * y) * (z * u) = (x * z) * (y * u).  [assumption].
((x * x) * x) * x = e.  [assumption].
e * e != e.  [deny(1)].
end_of_list.

formulas(demodulators).
end_of_list.

============================== PREDICATE ELIMINATION =================

No predicates eliminated.

============================== end predicate elimination =============

Auto_denials:  (no changes).

Term ordering decisions:
Relation symbol precedence:  lex([ = ]).
Function symbol precedence:  lex([ e, * ]).
After inverse_order:  (no changes).
Unfolding symbols: (none).

Auto_inference settings:
  % set(paramodulation).  % (positive equality literals)
    % set(paramodulation) -> set(back_demod).

Auto_process settings:  (no changes).

============================== end of process initial clauses ========

============================== CLAUSES FOR SEARCH ====================

% Clauses after input processing:

formulas(usable).
end_of_list.

formulas(sos).
2 (x * e) * x = x.  [assumption].
3 x * (x * y) = y.  [assumption].
4 (x * y) * (z * u) = (x * z) * (y * u).  [assumption].
5 ((x * x) * x) * x = e.  [assumption].
6 e * e != e.  [deny(1)].
end_of_list.

formulas(demodulators).
2 (x * e) * x = x.  [assumption].
3 x * (x * y) = y.  [assumption].
5 ((x * x) * x) * x = e.  [assumption].
end_of_list.

============================== end of clauses for search =============

============================== SEARCH ================================

% Starting search at 0.00 seconds.

given #1 (I,wt=7): 2 (x * e) * x = x.  [assumption].

============================== PROOF =================================

% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 6.
% Level of proof is 2.
% Maximum clause weight is 7.
% Given clauses 1.

1 e * e = e.  [goal].
2 (x * e) * x = x.  [assumption].
3 x * (x * y) = y.  [assumption].
6 e * e != e.  [deny(1)].
7 e * e = e.  [para(2(a,1),2(a,1,1)),rewrite(3(5)),flip(a)].
8 $F.  [resolve(7,a,6,a)].

============================== end of proof ==========================

============================== STATISTICS ============================

Given=1. Generated=6. Kept=6. proofs=1.
Usable=1. Sos=4. Demods=3. Limbo=0, Disabled=5. Hints=0.
Weight_deleted=0. Literals_deleted=0.
Forward_subsumed=0. Back_subsumed=0.
Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
New_demodulators=3 (0 lex), Back_demodulated=0. Back_unit_deleted=0.
Demod_attempts=49. Demod_rewrites=1.
Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0.
Megabytes=0.02.
User_CPU=0.00, System_CPU=0.00, Wall_clock=0.

============================== end of statistics =====================

============================== end of search =========================

THEOREM PROVED

Exiting with 1 proof.

Process 10668 exit (max_proofs) Sat Aug 12 20:57:46 2006