The CADE ATP System Competition

Design and Organization

This document contains information about the:

Divisions
- Competition Divisions
- Demonstration Division
Infrastructure
System Evaluation
System Entry
- System Description
- Sample Solutions
System Requirements

The rules, specifications, and deadlines given here are absolute. Only the competition panel has the right to make exceptions.

Disclaimer

Every effort has been made to organize the competition in a fair and constructive manner. No responsibility is taken if, for one reason or the other, your system does not win.

The design and procedures of this CASC evolved from those of previous CASCs. Important changes for this CASC are:

For systems running on entrant supplied hardware in the demonstration division, entrants must deliver a source code package to the competition organizers by the start of the competition. The entrant specifies whether or not the source code is placed on the CASC WWW site after the competition.

Divisions

CASC is run in divisions according to problem and system characteristics. There are competition divisions in which systems are explicitly ranked, and a demonstration division in which systems demonstrate their abilities without being formally ranked.

Competition Divisions

Each competition division uses problems that have certain logical, language, and syntactic characteristics, so that the ATP systems that compete in the division are, in principle, able to attempt all the problems in the division. Some divisions are further divided into problem categories, which make it possible to analyze, at a more fine grained level, which systems work well for what types of problems. The problem categories have no effect on the competition rankings, which are made at only the division level.

The MIX division: Mixed CNF really non-propositional theorems (unsatisfiable clause sets).
Mixed means Horn and non-Horn problems, with or without equality, but not unit equality problems (see the UEQ division below). Really non-propositional means with an infinite Herbrand universe. The MIX division has five problem categories:
- The HNE category: Horn with No Equality
- The HEQ category: Horn with some (but not pure) Equality
- The NNE category: Non-Horn with No Equality
- The NEQ category: Non-Horn with some (but not pure) Equality
- The PEQ category: Pure Equality
The FOF division: First-order form non-propositional theorems (axioms with a provable conjecture).
The FOF division has two problem categories:
- The FNE category: FOF with no Equality
- The FEQ category: FOF with Equality
The SAT division: CNF really non-propositional non-theorems (satisfiable clause sets).
The SAT division has two problem categories:
- The SNE category: SAT with No Equality
- The SEQ category: SAT with Equality
The EPR division: Effectively propositional CNF theorems and non-theorems (clause sets).
Effectively propositional means non-propositional with a finite Herbrand Universe. The EPR division has two problem categories:
- The EPT category: Effectively Propositional Theorems (unsatisfiable clause sets)
- The EPS category: Effectively Propositional non-theorems (Satisfiable clause sets)
The UEQ division: Unit equality CNF really non-propositional theorems (unsatisfiable clause sets).

The Problems section explains what problems are eligible for use in each division and category. The System Evaluation section explains how the systems are ranked in each division.

Demonstration Division

ATP systems that cannot run on the competition computers, or cannot be entered into the competition divisions for any other reason, can be entered into the demonstration division. Demonstration division systems can run on the competition computers, or the hardware can be supplied by the entrant. Hardware supplied by the entrant may be brought to CASC, or may be accessed via the internet.

The entry specifies which competition divisions' problems are to be used. The results are presented along with the competition divisions' results, but may not be comparable with those results.

Infrastructure

Computers

The competition computers is Dell Precision 330 computers, each having:

AMD Athlon XP 2200+, 1797MHz CPU
512MB memory
Linux 2.6.9-1.11_FC2 operating system

Problems

Problem Selection
The problems are from the TPTP Problem Library. The TPTP version used for the competition is not released until after the system installation deadline, so that new problems have not been seen by the entrants.

The problems have to meet certain criteria to be eligible for selection:

The TPTP uses system performance data to compute problem difficulty ratings, and from the ratings classifies problems as one of:
- Easy: Solvable by all state-of-the-art ATP systems
- Difficult: Solvable by some state-of-the-art ATP systems
- Unsolved: Not yet solved by any ATP system
- Open: Theorem-hood unknown
Difficult problems with a rating in the range 0.21 to 0.99 are eligible. Performance data from systems submitted by the system submission deadline is used for computing the problem ratings for the TPTP version used for the competition.
The TPTP distinguishes versions of problems as one of standard, incomplete, augmented, especial, or biased. All except biased problems are eligible.

The problems used are randomly selected from the eligible problems at the start of the competition, based on a seed supplied by the competition panel.

The selection is constrained so that no division or category contains an excessive number of very similar problems.
The selection mechanism is biased to select problems that are new in the TPTP version used, until 50% of the problems in each category have been selected, after which random selection (from old and new problems) continues. The actual percentage of new problems used depends on how many new problems are eligible and the limitation on very similar problems.

Number of Problems
The minimal numbers of problems that have to be used in each division and category, to ensure sufficient confidence in the competition results, are determined from the numbers of eligible problems in each division and category (the competition organizers have to ensure that there is sufficient CPU time available to run the ATP systems on this minimal number of problems). The minimal numbers of problems are used in determining the CPU time limit imposed on each solution attempt.

A lower bound on the total number of problems to be used is determined from the number of computers available, the time allocated to the competition, the number of ATP systems to be run on the competition computers over all the divisions, and the CPU time limit, according to the following relationship:

                   NumberOfComputers * TimeAllocated
NumberOfProblems = ---------------------------------
                   NumberOfATPSystems * CPUTimeLimit

It is a lower bound on the total number of problems because it assumes that every system uses all of the CPU time limit for each problem. Since some solution attempts succeed before the CPU time limit is reached, more problems can be used.

The numbers of problems used in the categories in the various divisions is (roughly) proportional to the numbers of eligible problems than can be used in the categories, after taking into account the limitation on very similar problems.

The numbers of problems used in each division and category are determined according to the judgement of the competition organizers.

Problem Preparation
In order to ensure that no system receives an advantage or disadvantage due to the specific presentation of the problems in the TPTP, the tptp2X utility (distributed with the TPTP) is used to:

rename all predicate and function symbols to meaningless symbols

randomly reorder the clauses and literals in CNF problems

randomly reorder the formulae in FOF problems

randomly reverse the equalities in the UEQ problems

remove equality axioms that are not needed by the ATP systems

add equality axioms that are needed by the ATP systems

output the problems in the formats required by the ATP systems (The clause type information, one of axiom, hypothesis, or conjecture, may be included in the final output of each formula.)

Further, to prevent systems from recognizing problems from their file names, symbolic links are made to the selected problems, using names of the form CCCNNN-1.p for the symbolic links, with NNN running from 001 to the number of problems in the respective division or category. The problems are specified to the ATP systems using the symbolic link names.

In the demonstration division the same problems are used as for the competition divisions, with the same tptp2X transformations applied. However, the original file names can be retained.

Resource Limits

In the competition divisions, CPU and wall clock time limits are imposed on each solution attempt. A minimal CPU time limit of 240 seconds is used. The maximal CPU time limit is determined using the relationship used for determining the number of problems, with the minimal number of problems as the NumberOfProblems. The CPU time limit is chosen as a reasonable value within the range allowed, and is announced at the competition. The wall clock time limit is imposed in addition to the CPU time limit, to limit very high memory usage that causes swapping. The wall clock time limit is double the CPU time limit.

In the demonstration division, each entrant can choose to use either a CPU or a wall clock time limit, whose value is the CPU time limit of the competition divisions.

System Evaluation

All the divisions have an assurance ranking class, ranked according to the number of problems solved (a "yes" output, giving an assurance of the existence of a proof/model). The MIX, FOF, and SAT divisions additionally have and a proof/model ranking class, ranked according to the number of problems solved with an acceptable proof/model output on stdout. Ties are broken according to the average CPU times over problems solved. All systems are automatically ranked in the assurance classes, and are ranked in the proof/model classes if they output acceptable proofs/models.

For each ATP system, for each problem, three items of data are recorded: whether or not a solution was found, the CPU time taken, and whether or not a solution (proof or model) was output on stdout. The systems are ranked from this performance data. Division and class winners are announced and prizes are awarded.

The competition panel decides whether or not the systems' proofs and models are acceptable. The criteria include:

Derivations must be complete, starting at formulae from the problem, and ending at the conjecture (for axiomatic proofs) or a false formula (for proofs by contradiction, including CNF refutations).
- For proofs of FOF problems by CNF refutation, the conversion from FOF to CNF must be adequately documented.
Derivations must show only relevant inference steps.
Inference steps must document the parent formulae, the inference rule used, and the inferred formula.
Inference steps must be reasonably fine-grained.
An unsatisfiable set of ground instances of clauses is acceptable for establishing the unsatisfiability of a set of clauses.
Models must be complete, documenting the domain, function maps, and predicate maps. The domain, function maps, and predicate maps may be specified by explicit ground lists (of mappings), or by any clear, terminating algorithm.

In the assurance classes, and the SAT and EPR divisions, the ATP systems are not required to output solutions (proofs or models). However, systems that do output solutions on stdout are highlighted in the presentation of results.

If a system is found to be unsound during or after the competition, but before the competition report is published, and it cannot be shown that the unsoundness did not manifest itself in the competition, then the system is retrospectively disqualified. At some time after the competition, all high ranking systems in the competition divisions are tested over the entire TPTP. This provides a final check for soundness (see the section on System Properties regarding soundness checking before the competition). At some time after the competition, the proofs from the winners of the MIX and FOF division proof classes, and the models from the winner of the SAT division model class, are checked by the panel. If any of the proofs or models are unacceptable, i.e., they are significantly worse than the samples provided, then that system is retrospectively disqualified. All disqualifications are explained in the competition report.

System Entry

To be entered into CASC, systems have to be registered using the CASC system registration form. No registrations are accepted after the registration deadline. For each system entered, an entrant has to be nominated to handle all issues (including execution difficulties) arising before and during the competition. The nominated entrant must formally register for CASC. However, it is not necessary for entrants to physically attend the competition.

Systems can be entered at only the division level, and can be entered into more than one division (a system that is not entered into a competition division is assumed to perform worse than the entered systems, for that type of problem - wimping out is not an option). Entering many similar versions of the same system is deprecated, and entrants may be required to limit the number of system versions that they enter. The division winners from the previous CASC are automatically entered into their divisions, to provide benchmarks against which progress can be judged.

It is assumed that each entrant has read the WWW pages related to the competition, and has complied with the competition rules. Non-compliance with the rules could lead to disqualification. A "catch-all" rule is used to deal with any unforseen circumstances: No cheating is allowed. The panel is allowed to disqualify entrants due to unfairness, and to adjust the competition rules in case of misuse.

System Description

A system description has to be provided for each ATP system entered, using this HTML schema. The system description must fit onto two pages, using 12pt times font. The schema has the following sections:

Architecture. This section introduces the ATP system, and describes the calculus and inference rules used.
Implementation. This section describes the implementation of the ATP system, including the programming language used, important internal data structures, and any special code libraries used.
Strategies. This section describes the search strategies used, why they are effective, and how they are selected for given problems. Any strategy tuning that is based on specific problems' characteristics must be clearly described (and justified in light of the tuning restrictions).
Expected competition performance. This section makes some predictions about the performance of the ATP system in each of the divisions and categories in which the system is competing.
References.

The system description has to be emailed to the competition organizers before the system description deadline. The system descriptions, along with information regarding the competition design and procedures, form the proceedings for the competition.

Sample Solutions

For systems in the proof and model classes representative sample solutions must be emailed to the competition organizers before the sample solutions deadline. Proof samples for the MIX proof class must include a proof for SYN075-1. Proof samples for the FOF proof class must include a proof for SYN075+1. Model samples for the the SAT model class must include a model for MGT031-1. The sample solutions must illustrate the use of all inference rules. A key must be provided if any non-obvious abbreviations for inference rules or other information are used.

System Requirements

System Properties

Systems are required to have the following properties:

The ATP systems have to run on a single locally provided standard UNIX computer (the competition computers). ATP systems that cannot run on the competition computers can be entered into the demonstration division.
Systems have to be fully automatic, i.e., any command line switches have to be the same for all problems.
Systems have to be sound. At some time before the competition all the systems in the competition divisions are tested for soundness. Non-theorems are submitted to the systems in the MIX, FOF, EPR, and UEQ divisions, and theorems are submitted to the systems in the SAT and EPR divisions. Finding a proof of a non-theorem or a disproof of a theorem indicates unsoundness. If an ATP system fails the soundness testing it must be repaired by the unsoundness repair deadline or be withdrawn. The soundness testing eliminates the possibility of an ATP system simply delaying for some amount of time and then claiming to have found a solution. For systems running on entrant supplied hardware in the demonstration division, the entrant must perform the soundness testing and report the results to the competition organizers.
Systems do not have to be complete in any sense, including calculus, search control, implementation, or resource requirements.
The ATP systems have to be executable by a single command line, using an absolute path name for the executable, which might not be in the current directory. The command line arguments are the absolute path name of a symbolic link as the problem file name, the time limit (if required by the entrant), and entrant specified system switches (the same for all problems). No shell features, such as input or output redirection, may be used in the command line. No assumptions may be made about the format of the problem file name.
The ATP systems that run on the competition computers have to be interruptable by a SIGXCPU signal, so that the CPU time limit can be imposed on each solution attempt, and interruptable by a SIGALRM signal, so that the wall clock time limit can be imposed on each solution attempt. For systems that create multiple processes, the signal is sent first to the process at the top of the hierarchy, then one second later to all processes in the hierarchy. Any orphan processes are killed after that, using SIGKILL. The default action on receiving these signals is to exit (thus complying with the time limit, as required), but systems may catch the signals and exit of their own accord. If a system runs past a time limit this is noticed in the timing data, and the system is considered to have not solved that problem.
When terminating of their own accord, the ATP systems have to output a distinguished string (specified by the entrant) on stdout indicating the result, one of:
- A proof exists (for CNF problems, the clause set is unsatisfiable, for FOF problems, the conjecture is a theorem).
- No prooof exists (for CNF problems, the clause set is satisfiable, for FOF problems, the conjecture is a non-theorem).
- No conclusion reached.
Only the first such string is recognized, and accepted as the system's claimed result.
When outputing proofs/models for the proof/model ranking classes, the start and end of the proof/model must be identified by distinguished strings (specified by the entrant). These pairs of strings must be different for proofs and models. The string specifying the result must be output before the start of a proof or model.
If an ATP system terminates of its own accord, it may not leave any temporary or other output files. If an ATP system is terminated by a SIGXCPU or SIGALRM, it may not leave any temporary or other output files anywhere other than in /tmp. Multiple copies of the ATP systems have to be executable concurrently on different machines but in the same (NFS cross mounted) directory. It is therefore necessary to avoid producing temporary files that do not have unique names, with respect to the machines and other processes. An adequate solution is a file name including the host machine name and the process id.
For practical reasons excessive output from the ATP systems is not allowed. A limit, dependent on the disk space available, is imposed on the amount of stdout and stderr output that can be produced. The limit is at least 10KB per problem (averaged over all problems so that it is possible to produce some long proofs).
The precomputation and storage of any information specifically about TPTP problems is not allowed. Strategies and strategy selection based on the characteristics of a few specific TPTP problems are not allowed, i.e., strategies and strategy selection must be general purpose and expected to extend usefully to new unseen problems. If automatic strategy learning procedures are used, the learning must ensure that sufficient generalization is obtained, and that no learning at the individual problem level is performed.
For every problem solved, the system's solution process must be reproducible by running the system again.

Access to the competition computers (or equivalent) is available from the competition computers access deadline. Entrants must install their systems on the competition computers, and ensure that their systems execute in the competition environment, according to the system checks. Entrants are advised to perform these checks well in advance of the system installation deadline. This gives the competition organizers time to help resolve any difficulties encountered.

System Delivery

For systems running on the competition computers, entrants must deliver an installation package to the competition organizers by the installation deadline. The installation package must be a .tar.gz file containing the system source code, any other files required for installation, and a ReadMe file. The ReadMe file must contain:

Instructions for installation
Instructions for executing the system
- Format of problem files, in the form of tptp2X format and transformation parameters.
- Command line, using %s and %d to indicate where the problem file name and CPU time limit must appear.
The distinguished strings output.

The installation procedure may require changing path variables, invoking make or something similar, etc, but nothing unreasonably complicated. All system binaries must be created in the installation process; they cannot be delivered as part of the installation package. The system is reinstalled onto the competition computers by the competition organizers, following the instructions in the ReadMe file. Installation failures before the installation deadline are passed back to the entrant. After the installation deadline access to the competition computers is denied, and no further changes or late systems are accepted (i.e., deliver your installation package before the installation deadline so if the installation fails you have a chance to fix it!). If you are in doubt about your installation package or procedure, please email the competition organizers.

For systems running on entrant supplied hardware in the demonstration division, entrants must deliver a source code package to the competition organizers by the start of the competition. The source code package must be a .tar.gz file containing the system source code.

After the competition all competition division systems' source code, is made publically available on the CASC WWW site. In the demonstration division, the entrant specifies whether or not the source code is placed on the CASC WWW site.

System Execution

Execution of the ATP systems on the competition computers is controlled by a perl script, provided by the competition organizers. The jobs are queued onto the computers so that each computer is running one job at a time. All attempts at the Nth problems in all the divisions and categories are started before any attempts at the (N+1)th problems.

During the competition a perl script parses the systems' outputs. If any of an ATP system's distinguished strings are found then the CPU time used to that point is noted. A system has solved a problem iff it outputs its "success" string within the CPU time limit, and a system has produced a proof iff it outputs its "end of solution" string within the CPU time limit. The result and timing data is used to generate an HTML file, and a WWW browser is used to display the results.

The execution of the demonstration division systems is supervised by their entrants.

System Checks

Check: The ATP system can be run by an absolute path name for the executable. For example:

prompt> pwd
/home/tptp
prompt> which MyATPSystem
/home/tptp/bin/MyATPSystem
prompt> /home/tptp/bin/MyATPSystem /home/tptp/TPTP/Problems/GRP/GRP001-1.p
Proof found in 147 seconds.

Check: The ATP system accepts an absolute path name of a symbolic link as the problem file name. For example:

prompt> cd /home/tptp/tmp
prompt> ln -s /home/tptp/TPTP/Problems/GRP/GRP001-1.p CCC001-1.p
prompt> cd /home/tptp
prompt> /home/tptp/bin/MyATPSystem /home/tptp/tmp/CCC001-1.p
Proof found in 147 seconds.

Check: The ATP system makes no assumptions about the format of the problem file name. For example:

prompt> ln -s /home/tptp/TPTP/Problems/GRP/GRP001-1.p _foo-Blah
prompt> /home/tptp/bin/MyATPSystem _foo-Blah
Proof found in 147 seconds.

Check: The ATP system can run under the TreeLimitedRun program. For example:

prompt> which TreeLimitedRun
/home/tptp/bin/TreeLimitedRun
prompt> /home/tptp/bin/TreeLimitedRun -q0 200 400 /home/tptp/bin/MyATPSystem /home/tptp/tmp/CCC001-1.p
TreeLimitedRun: ----------------------------------------------------------
TreeLimitedRun: /home/tptp/bin/MyATPSystem
TreeLimitedRun: CPU time limit is 200s
TreeLimitedRun: WC  time limit is 400s
TreeLimitedRun: PID is 4867
TreeLimitedRun: ----------------------------------------------------------
Proof found in 147 seconds.
FINAL WATCH: 147.8 CPU 150.0 WC

Check: The ATP system's CPU time can be limited using the TreeLimitedRun program. For example:

prompt> /home/tptp/bin/TreeLimitedRun -q0 10 20 /home/tptp/bin/MyATPSystem /home/tptp/tmp/CCC001-1.p
TreeLimitedRun: ----------------------------------------------------------
TreeLimitedRun: /home/tptp/bin/MyATPSystem
TreeLimitedRun: CPU time limit is 10s
TreeLimitedRun: WC  time limit is 20s
TreeLimitedRun: PID is 5827
TreeLimitedRun: ----------------------------------------------------------
CPU time limit exceeded 
FINAL WATCH: 10.7 CPU 13.1 WC

Check: The ATP system's wall clock time can be limited using the TreeLimitedRun program. For example:

prompt> /home/tptp/bin/TreeLimitedRun -q0 20 10 /home/tptp/bin/MyATPSystem /home/tptp/tmp/CCC001-1.p
TreeLimitedRun: ----------------------------------------------------------
TreeLimitedRun: /home/tptp/bin/MyATPSystem
TreeLimitedRun: CPU time limit is 20s
TreeLimitedRun: WC  time limit is 10s
TreeLimitedRun: PID is 5827
TreeLimitedRun: ----------------------------------------------------------
Alarm clock
FINAL WATCH: 9.7 CPU 10.1 WC

Check: The system outputs a distinguished string when terminating of its own accord. For example, here the entrant has specified that the distinguished string Proof found indicates that a solution exists. If appropriate, similar checks should be made for the cases where no solution exists and where no conclusion is reached.

prompt> /home/tptp/bin/TreeLimitedRun -q0 200 400 /home/tptp/bin/MyATPSystem /home/tptp/tmp/CCC001-1.p
TreeLimitedRun: ----------------------------------------------------------
TreeLimitedRun: /home/tptp/bin/MyATPSystem
TreeLimitedRun: CPU time limit is 200s
TreeLimitedRun: WC  time limit is 400s
TreeLimitedRun: PID is 5827
TreeLimitedRun: ----------------------------------------------------------
Proof found in 147 seconds.
FINAL WATCH: 147.8 CPU 150.0 WC

Check: The system outputs distinguished strings at the start and end of its solution. For example, here the entrant has specified that the distinguished strings START OF PROOF and END OF PROOF identify the start and end of the solution.

prompt> /home/tptp/bin/TreeLimitedRun -q0 200 400 /home/tptp/bin/MyATPSystem -output_proof /home/tptp/tmp/CCC001-1.p
TreeLimitedRun: ----------------------------------------------------------
TreeLimitedRun: /home/tptp/bin/MyATPSystem
TreeLimitedRun: CPU time limit is 200s
TreeLimitedRun: WC  time limit is 400s
TreeLimitedRun: PID is 5827
TreeLimitedRun: ----------------------------------------------------------
Proof found in 147 seconds.
START OF PROOF
    ... acceptable proof here ...
END OF PROOF
FINAL WATCH: 147.8 CPU 150.0 WC

Check: No temporary or other files are left if the system terminates of its own accord, and no temporary or other files are left anywhere other than in /tmp if the system is terminated by a SIGXCPU or SIGALRM. Check in the current directory, the ATP system's directory, the directory where the problem's symbolic link is located, and the directory where the actual problem file is located.

prompt> pwd
/home/tptp
prompt> /home/tptp/bin/TreeLimitedRun -q0 200 400 /home/tptp/bin/MyATPSystem /home/tptp/tmp/CCC001-1.p
TreeLimitedRun: ----------------------------------------------------------
TreeLimitedRun: /home/tptp/bin/MyATPSystem
TreeLimitedRun: CPU time limit is 200s
TreeLimitedRun: WC  time limit is 400s
TreeLimitedRun: PID is 13526
TreeLimitedRun: ----------------------------------------------------------
Proof found in 147 seconds.
FINAL WATCH: 147.8 CPU 150.0 WC
prompt> ls /home/tptp
    ... no temporary or other files left here ...
prompt> ls /home/tptp/bin
    ... no temporary or other files left here ...
prompt> ls /home/tptp/tmp
    ... no temporary or other files left here ...
prompt> ls /home/tptp/TPTP/Problems/GRP
    ... no temporary or other files left here ...
prompt> ls /tmp
    ... no temporary or other files left here by decent systems ...

Check: Multiple concurrent executions do not clash. For example:

prompt> (/home/tptp/bin/TreeLimitedRun -q0 200 400 /home/tptp/bin/MyATPSystem /home/tptp/tmp/CCC001-1.p) & (/home/tptp/bin/TreeLimitedRun -q0 200 400 /home/tptp/bin/MyATPSystem /home/tptp/tmp/CCC001-1.p)
TreeLimitedRun: ----------------------------------------------------------
TreeLimitedRun: /home/tptp/bin/MyATPSystem
TreeLimitedRun: CPU time limit is 200s
TreeLimitedRun: WC  time limit is 400s
TreeLimitedRun: PID is 5827
TreeLimitedRun: ----------------------------------------------------------
TreeLimitedRun: ----------------------------------------------------------
TreeLimitedRun: /home/tptp/bin/MyATPSystem
TreeLimitedRun: CPU time limit is 200s
TreeLimitedRun: WC  time limit is 400s
TreeLimitedRun: PID is 5829
TreeLimitedRun: ----------------------------------------------------------
Proof found in 147 seconds.
FINAL WATCH: 147.8 CPU 150.0 WC

Proof found in 147 seconds.
FINAL WATCH: 147.8 CPU 150.0 WC