Design and Organization

This document contains information about the:

• Changes
• Divisions
  • Competition Divisions
  • Demonstration Division
• Infrastructure
  • Computers
  • Problems
  • Resource Limits
• System Evaluation
• System Entry
  • System Description
  • Sample Solutions
• System Requirements
  • System Properties
  • System Delivery
  • System Execution
  • System Checks

Disclaimer

A Tense Note

• Proofs must be output in TPTP format. Their syntax and structure will be checked using TPTP4X and GDV.

• The EPR division has returned from hiatus.

Competition Divisions

• The THF division: Typed (monomorphic) Higher-order Form theorems (axioms with a provable conjecture). The THF division has two problem categories:
  • The TNE category: THF with No Equality
  • The TEQ category: THF with EQuality

• The TFA division: Typed (monomorphic) First-order theorems (axioms with a provable conjecture), with Arithmetic. The TFA division has two problem categories:
  • The TFI category: TFA with only Integer arithmetic
  • The TFE category: TFA with only rEal arithmetic

• The TFN division: Typed (monomorphic) First-order Non-theorems (axioms with a countersatisfiable conjecture, and satisfiable axiom sets), without arithmetic

• The FOF division: First-Order Form 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 EPR division: Effectively PRopositional clause normal form theorems and non-theorems (clause sets). Effectively propositional means that the problems are syntactically non-propositional but are known to be reducible to propositional problems, e.g., CNF problems that have no functions with arity greater than zero. The EPR division has two problem categories:
  • The EPU category: Effectively Propositional Unsatisfiable clause sets
  • The EPS category: Effectively Propositional Satisfiable clause sets

• The UEQ division: Unit EQuality clause normal form unsatisfiable clause sets.

• The SLH division: Typed (monomorphic) higher-order theorems without arithmetic (axioms with a provable conjecture), generated by Isabelle's Sledgehammer system.

• The ICU division: First-order theorems (axioms with a provable conjecture) provided by the entrants, by which they say to the other entrants: "I Challenge yoU".

Demonstration Division

Computers

• An octa-core Intel(R) Xeon(R) E5-2620 v4 @ 2.10GHz, without hyperthreading.
• 128GB memory
• The CentOS Linux release 7.4.1708 (Core) operating system, Linux kernel 3.10.0-693.el7.x86_64.

One ATP system runs on one CPU at a time. Systems can use all the cores on the CPU, which can be advantageous in divisions where a wall clock time limit is used.

Problems for the TPTP-based Divisions

• The TPTP tags problems that are designed specifically to be suited or ill-suited to some ATP system, calculus, or control strategy as biased. They are excluded from the competition.
• The problems must be syntactically non-propositional.
• The TPTP uses system performance data in the Thousands of Solutions from Theorem Provers (TSTP) solution library to compute problem difficulty ratings in the range 0.00 (easy) to 1.00 (unsolved). Difficult problems with a rating in the range 0.21 to 0.99 are eligible. Problems of lesser and greater ratings might also be eligible in some divisions if there are not enough problems with ratings in that range. Systems can be submitted before the competition so that their performance data is used in computing the problem ratings.

• stripping out all comment lines, including the problem header
• randomly reordering the formulae/clauses (include directives are left before formulae, type declarations and definitions are left before the symbols' uses)
• randomly swapping the arguments of associative connectives, and randomly reversing implications
• randomly reversing equalities

The problems used are randomly selected from the eligible problems based on a seed supplied by the competition panel:

• The selection is constrained so that no problem category contains an excessive number of very similar problems, according to the "very similar problems" (VSP) lists distributed with the TPTP: For each problem category in each division, if the category is going to use N problems and there are L VSP lists that have an intersection of at least N/(L + 1) with the eligible problems for the category, then maximally N/(L + 1) problems are taken from each of those VSP lists.
• In order to combat excessive tuning towards problems that are already in the preceding TPTP version, the selection is biased to select problems that are new in the TPTP version used, until 50% of the problems in each problem category have been selected or there are no more new problems to select, after which random selection from old and new problems continues.

Problems for the SLH Division

The number of problems is based on the CPU time limit, using a calculation similar to that used for the TPTP-based divisions. The problems are given in a roughly estimated increasing order of difficulty.

Problems for the ICU Division

It is expected that each system's problems will be easy enough for that system, but difficult for the other systems, i.e., each system is saying to the others: "I Challenge yoU!".

Time Limits

In the SLH division a CPU time limit is imposed for each problem. The minimal time limit is 15s, and the maximal time limit is 90s, which is the range of CPU time that can be usefully allocated for a proof attempt in the Sledgehammer context (according to Jasmin Blanchette, and he should know). The time limit is chosen as a reasonable value within the range allowed according to the judgement of the organizers, and is announced at the competition.

In the ICU division a wall clock time limit is imposed for each problem, and no CPU time limits are imposed (so that it can be advantageous to use all the cores on the CPU). The minimal time limit is 300s, and the maximal time limit is 600s. The time limit is chosen as a reasonable value within the range allowed according to the judgement of the organizers, and is announced at the competition.

The systems are ranked in the competition divisions according to the number of problems solved with an acceptable solution output, except in the EPR division that is ranked according to the number of problems solved, but not necessarily accompanied by a solution (but systems that do output solutions are highlighted in the presentation of results). Ties are broken according to the average time taken over problems solved. Trophies are awarded to the competition divisions' winners. In the demonstration division the systems are not ranked, and no trophies are awarded.

The competition panel decides whether or not the systems' solutions are "acceptable". The criteria include:

• Proofs must be in TPTP format. This will be checked using TPTP4X.
• Proofs must be structurally correct:
  • Proofs must have formulae from the problem as leaves, and end at the conjecture (for axiomatic proofs) or $false formula (for proofs by contradiction, e.g., CNF refutations).
  • For solutions that use translations from one form to another, e.g., translation of FOF problems to CNF, the translations must be adequately documented.
  • Proofs must show only relevant inference steps.
  Proof structure will be checked using GDV.
• Inference steps must be reasonably fine-grained, except in the SLH division where just a single inference step from the axioms used (no unused axioms) to the conjecture is acceptable.
• 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.

• The state-of-the-art contribution (SotAC) quantifies the unique abilities of each system (excluding the previous year's winners that are earlier versions of competing systems). For each problem solved by a system, its SotAC for the problem is the fraction of systems that do not solve the problem, and a system's overall SotAC is the average over the problems it solves but that are not solved by all the systems.
• The core usage measures the extent to which the systems take advantage of multiple cores. It is the average of the ratios of CPU time used to wall clock time used, over the problems solved.
• The efficiency measure balances the number of problems solved with the time taken. It is the average solution rate over the problems solved (the solution rate for one problem is the reciprocal of the time taken to solve it), multiplied by the fraction of problems solved. Efficiency is computed for both CPU time and wall clock time, to measure how efficiently the systems use one core and multiple cores respectively.

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). 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, the solutions from the winners are checked by the panel. If any of the solutions are unacceptable, i.e., they are sufficiently worse than the samples provided, then that system is retrospectively disqualified. All disqualifications are explained in the competition report.

Systems can be entered at only the division level, and can be entered into more than one division. All systems that are entered into a division are assumed to perform better than all systems not entered, 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. Systems that rely essentially on running other ATP systems without adding value are deprecated; the competition panel may disallow or move such systems to the demonstration division.

The division winners of the previous CASC are automatically entered into the corresponding demonstration divisions, to provide benchmarks against which progress can be judged. Prover9 1109a is automatically entered into the FOF demonstration division, to provide a fixed-point against which progress can be judged.

System Description

• Architecture. This section introduces the ATP system, and describes the calculus and inference rules 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).
• 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. The availability of the system is also given here.
• Expected competition performance. This section makes some predictions about the performance of the ATP system for each of the divisions and categories in which it is competing.
• References.

The system description must be emailed to the competition organizer by the system description deadline. The system descriptions form part of the competition proceedings.

Sample Solutions

Proof/model samples are required as follows:

• THF and SLH: SET014^4
• TFA: DAT013=1
• TFN: HWV042_1 and HWV042_3
• FOF: SEU140+2
• UEQ: BOO001-1

System Properties

Execution, Soundness, and Completeness

1. Systems must be fully automatic, i.e., all command line switches have to be the same for all problems in each division.
2. Systems' performances must be reproducible by running the system again.
3. Systems must 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 THF, TFA, FOF, EPR, and UEQ divisions, and theorems are submitted to the systems in the TFN and EPR divisions. Finding a proof of a non-theorem or a disproof of a theorem indicates unsoundness. If a system fails the soundness testing it must be repaired by the unsoundness repair deadline or be withdrawn.
4. Systems do not have to be complete in any sense, including calculus, search control, implementation, or resource requirements.
5. All techniques used must be general purpose, and expected to extend usefully to new unseen problems. The precomputation and storage of information about individual problems that might appear in the competition, or their solutions, is not allowed. Strategies and strategy selection based on individual problems or their solutions are not allowed. If machine learning procedures are used to tune a system, the learning must ensure that sufficient generalization is obtained so that there is no specialization to individual problems. The system description must explain any such tuning or training that has been done. The competition panel may disqualify any system that is deemed to be problem specific rather than general purpose. If you are in doubt, contact the competition organizer.

1. All output must be to stdout.
2. For each problem, the system must output a distinguished string indicating what solution has been found or that no conclusion has been reached. Systems must use the SZS ontology and standards for this. For example

   % SZS status Theorem for SYN075+1.p

   or

   % SZS status GaveUp for SYN075+1.p

3. When outputting a solution, the start and end of the solution must be delimited by distinguished strings. Systems must use the SZS ontology and standards for this. For example

   % SZS output start CNFRefutation for SYN075+1.p
     ...
   % SZS output end CNFRefutation for SYN075+1.p

   The string specifying the problem status must be output before the start of a solution. Use of the TPTP format for proofs is required, and use of the new TPTP format for interpretations is encouraged.
4. Solutions may not have irrelevant output (e.g., from other threads running in parallel) interleaved in the solution.

1. Systems that run on the competition computers must be interruptible by a SIGXCPU signal so that CPU time limits can be imposed, and interruptable by a SIGALRM signal so that wall clock time limits can be imposed. For systems that create multiple processes the signal is sent first to the process at the top of the process hierarchy, then one second later to all processes (even if they have disconnected from the process hierarchy). 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 the problem.
2. If a system terminates of its own accord it may not leave any temporary or intermediate output files. If a system is terminated by a SIGXCPU or SIGALRM it may not leave any temporary or intermediate output files anywhere other than in /tmp.
3. For practical reasons excessive output from an ATP system is not allowed. A limit, dependent on the disk space available, is imposed on the amount of output that can be produced.

System Delivery

For systems running on entrant supplied computers in the demonstration division, entrants must email a .tgz file containing the source code and any files required for building the executable system to the competition organizer by the system delivery deadline.

After the competition all competition division systems' source code is made publicly available on the CASC web site. In the demonstration division the entrant specifies whether or not the source code is placed on the site. An open source license is encouraged.

Entrants are encouraged to make a public release of their systems ASAP after the competition, so that users can enjoy the latest capabilities.

System Execution

A system has solved a problem iff it outputs its termination string within the time limit, and a system has produced a solution iff it outputs its end-of-solution string within the time limit. The result and timing data is used to generate an HTML file, and a web browser is used to display the results.

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

System Checks

• Check: You can login to StarExec Miami. If not, apply for an account in the TPTP community.

• Check: You can access the TPTP space. If not, email the competition organizer.

• Check: You can create and upload a StarExec installation package. The competition organizer has exemplar StarExec installation packages that you can use as a starting point - email the competition organizer to get one that is appropriate for your ATP system.

• Check: You can create a job and run it, and your ATP system gets the correct result. Use the SZS post processor.

• Check: Your ATP system can solve a problem that has include directives. Because of the way StarExec runs jobs, your ATP system must implement the TPTP requirement that "Include files with relative path names are expected to be found either under the directory of the current file, or if not found there then under the directory specified in the TPTP environment variable."

• Check: You can email your StarExec installation package to the competition organizer for testing.